Mathmatical Models Of Water Quality In The Great Lakes Part I Lake Huron and Saginow Bay July 1980

United States Environmental Protection Agency Environmental Research Laboratory Duluth MN 55804 EPA-600/3-80-056 July 1980 Research and Development Mathematical Models of Water Quality in Large Lakes Part 1 Lake Huron and Saginaw Bay ------- RESEARCH REPORTING SERIES Researcn repcfts of trie Office of Research arnj Dov'-jloorrent, U S Environmental Protect on Agency, nave been grouped into nine series These nine broad ca;e- gones were estabhsned to facilitate further development and application of en- vironmental technology Elimination of traditional grojpmg was consciously planned to foster technology trans'er and a maximum interface in related fields The nme series are 1 Environmental Health Effects Research ? Environmental Protection Technology 3 Ecological Research <- Environmental Monitoring (:• Socioeconomic Environmental Studies 6 Scientific and Technical Assessment Reports (STAR) /' Interagency Energy-Environment Research and Development 8 Special' Reports 9 Miscellaneous Reports This report has been assigned to the ECOLOGICAL RESEARCH series This series describes research on the effects of pollution on numans plant and animal spe- cies, and materials Problems are assessed for their long- and short-term influ- ences Investigations include forma'ion transport, ard pathway studies to deter- mine the fate cf pollutants and their ejects This work provides the technical basis for sett ng standards to minimize undesirable changes i •. living organisms in the aquatic terrestrial and atmospheric environments This document is available to the public through the National Technical Informa- tion Service, Springfield, Virginia 22161 ------- EPA-600/3-80-056 July 1980 MATHEMATICAL MODELS OF WATER QUALITY IN LARGE LAKES PART 1: LAKE HURON AND SAGINAW BAY Dominic M. DiToro Walter F. Matystik, Jr. Manhattan College Environmental Engineering and Science Program Bronx, New York 10171 Grant No. R803030 Project Officer William L. Richardson Large Lakes Research Station Grosse lie Laboratory - EPA Grosse lie, Michigan ENVIRONMENTAL RESEARCH LABORATORY OFFICE OF RESEARCH AND DEVELOPMENT U.S. ENVIRONMENTAL PROTECTION AGENCY DULUTH, MINNESOTA 5580^4 F;v:ronm,-iitc! Protection Agsncy '~"i V, Librar ?l'- • Sojtii Dearborn Street Chicle, Illinois 60604 ------- DISCLAIMER This report has "been reviewed by the Large Lakes Research Station, Grosse lie Laboratory, U.S. Environmental Protection Agency, and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the U.S. Environmental Protection Agency, nor does mention of trade names or commercial products constitute endorse- ment or recommendation for use. 11 ------- FOREWORD The Great Lakes comprise 80% of the surface freshwater in North America and provide 45 million people living in the basin with almost unlimited drinking water and industrial process water. Five thousand miles of shore- line provides access for much of the tourist and recreation activity in the surrounding basin. Lucrative sport and commercial fisheries rely on these waters as do the transport of tremendous quantities of raw and refined commercial products and the disposal of residual, industrial and municipal materials. This resource represents a complex system of competing water uses as well as a delicate, interacting ecosystem. Such a situation requires a balance between the economic well being of the region with the health related well being of the ecosystem. To arrive at this balance a rational and quantitative understanding of the interacting and competing components is required. In this way complex questions can be addressed and optimal decisions made. Research sponsored by the U.S. EPA, ERL-D, Large Lakes Research Station has in large part been directed toward this end. Primarily the modeling research has been conducted to synthesize surveillance and research data and to develop predictive capabilities of the transport and fate of pollutants in the Great Lakes. This report documents the results of a three year research project to develop a water quality model for Lake Huron and Saginaw Bay. The purpose of including the kinetic formulations, data analysis, and verification procedures is to provide sufficient detail that would not be available in journal publications so that much of this methodology could be applied to other water bodies throughout the world. Also, it is our intent to document the details for those Great Lakes' managers and researchers who have and will develop, recommend and judge pollution control strategies based on this research. Appreciation is extended to scientific reviewers at the University of Michigan and the NOAA, Great Lakes Environmental Research Laboratory. The report has also received extensive review by several Canadian and State agencies. William L. Richardson, P.E. Environmental Scientist ERL-D, Large Lakes Research Station Grosse He, Michigan 48138 iii ------- ABSTRACT This research was undertaken to develop and apply a mathematical model of the water quality in large lakes, particularly Lake Huron and Saginaw Bay (Part l) and Lake Erie (Part 2). A mathematical model of phytoplankton Momass was developed which incor- porates "both phytoplankton and zooplankton as well as phosphorus, nitrogen and silica nutrient forms. Extensive water quality data for Lake Huron and Saginaw Bay was analyzed and statistically reduced. The model was then cali- brated by comparison of computed results to these data. An exhaustive treatment of the kinetics employed for modeling the eutro- phication process is presented. The sensitivity of the model to some of its key parameters is examined. In addition, responses of water quality in Lake Huron and Saginaw Bay system to variations in total phosphorus inputs are projected. This report was submitted in fulfillment of Grant No. R803030 by Manhat- tan College under the sponsorship of the U.S. Environmental Protection Agency. This report covers the project period March 26, 197^ to March 25, 1977. IV ------- CONTENTS Foreword .............................. ill Abstract ............................... iv Figures ............................... vi Tables ............................... xii Acknowledgement ........................... xiv 1. Introduction ........................ 1 2. Summary and Conclusions ................... 2 3. Recommendations ....................... 7 k. Physical Features, Mass Loadings, and Segmentation ..... 8 5. Estimation of the Seasonal Transport Regime ......... l6 6. Kinetics .......................... 27 7. Data ............................ 57 8. Model Structure and Calibration ............... 85 9. Sensitivity Analysis .................... 125 10. Preliminary Applications .................. 135 References .............................. Appendix ............................... 150 ------- FIGURES Number Page 1 Segmentation of Lake Huron. Top Layer (Epilimnion) and Bottom Layer (Hypolimnion) of Northern and Southern Lake Huron. Segment 3 represents Saginaw Bay 2 2. Vertical Transport Calibration 3 3. Schematic Diagram of the Kinetic Interactions 3 k. Results of model calibration: Computed versus Observed Data in Southern Lake Huron and Saginaw Bay k 5. Final calibration computations for Southern Lake Huron, Lake Ontario, and Saginaw Bay phytoplankton chlorophyll. 5 6. Effect of Increases of Phosphorus Inputs to Southern Lake Huron. Percent change in yearly average epilimnion concentration versus percent change in total phosphorus input (a) Chlorophyll, P_; (b) Total phosphorus, p . . . 6 T. Lake Huron and Saginaw Bay Drainage Basin . „ 9 8. Annual distribution of Saginaw River flow and nutrient mass loading rates, 197^ ..... 12 9. Segmentation of Lake Huron. Top Layer (Epilinnion) and Bottom Layer (Hypolimnion) of Northern and Soxithern Lake Huron. Saginaw Bay is represented by one layer .... 1^4 10. Typical surface circulation pattern for Lake Huron (after Ayers et al. (1956) [l6] IT 11. Comparison of Saginaw River mass discharge rai;es for chlorides and total phosphorus as estimated from weekly and monthly sampling data 20 12. Vertical Transport Calibration 2k 13. Horizontal Transport Calibration 26 ik. Exponential Dependence of growth rate and respiration rate as a function of temperature. Data are from [27]. Straight lines correspond to the values of 8 as indicated 30 vi ------- FIGURES (continued) Number 15- Ratio of growth rate to maximum growth rate vs. external phosphorus concentration for external phosphorus concen- tration for Scenedesmus sp. (37). m'm = 1.33 day"1; qo = 1.6 f-mol/cell: V = k.8 f-mol/cell/hr : K = 18.6 u m m yg PO - P/£; K = 0.73 f-mol/cell. (f-mol = 10" J 5 mol 35 l6. Application of Algal growth and nutrient uptake equations (3k) to "batch kinetic data ........ , ....... 38 17. The relationship between filtering rate of Diaptomus ore- genensis and prey concentration ( chlamydamonus and chlor- ella). C'gm =2.0 m£/ animal/day"! Kmg = 40,000 cells/ m£. Curve is equation (kO) ............... k2 l8. Logarithm of normalized zooplankton respiration rate as a function of temperature. Exponential temperature depen- dence in the range 6 = 1.06 - 1.2 as indicated. For legend and references see [27] .............. ^5 19. Variation of the ratio of estimated unavailable to total phosphorus and of dissolved organic to total dissolved phosphorus ratio with chlorophyll. See Table 6 for legend .......................... 53 20. Comparison of observed and calculated ratio of unavail- able to total phosphorus for saturating (eq. 58b), first order (eq. 58a), and second order (eq. 58c) nutrient re- cycle kinetics ...................... 56 21. Sampling station locations for the major data sets used in this report. These correspond to the tabulations in Tables 8-10 ...................... 68 22. Comparison of data taken by CCIW, CIS, and GLRD at approximately the same location in Inner Saginaw Bay. . . 69 23. Comparison of data taken by CCIW, CIS, and GLRD at approximately the same' location in Northern Saginaw Bay . 70 2k. Comparison of data taken by CCIW, CIS, and GLRD at approximately the same location in Southern Saginaw Bay . 71 25- Model Calibration Data (Segment l) ............ 72 26. Model Calibration Data (Segment l) ............ 73 vii ------- FIGURES (continued) Number Page 27. Model Calibration Data (Segment 2) 76 28. Model Calibration Data (Segment 2) 77 29. Model Calibration Data (Segment 2) 78 30. Model Calibration Data (Segment 3) 79 31. Model Calibration Data (Segment 3) 80 32. Model Calibration Data (Segment k) 8l 33. Model Calibration Data (Segment k) 82 3k. Model Calibration Data (Segment 5) 83 35. Model Calibration Data (Segment 5) 84 36. Schematic diagram of the kinetic interactions incorpora- ted in the eutrophication model structure 86 37. Calibration calculation for a recycle rate characteristic of Southern Lake Huron (bottom figure). Saginaw Bay chlorophyll and nutrients comparison (top three figures) 88 38. Calibration calculation for a recycle rate characteristic of Saginaw Bay (bottom figure). Southern Lake Huron chlorophyll and nutrients comparison (top three figures) 90 39. Calibration calculation for a recycle rate characteristic of Southern Lake Huron. Saginaw Bay - Southern Lake Huron transport exchange rate set to zero 91 40. Northern Lake Huron epilimnion calibration calculation. Comparison of observations and computations for phyto- plankton chlorophyll, zooplankton carbon, ammonia nitro- gen and soluble reactive phosphorus, 197^. See figure for data symbol legend 9^ i»l. Northern Lake Huron epilimnion calibration calculation. Comparison of observations and computations for nitrate nitrogen, total phosphorus, and reactive silica nitrate nitrogen total 95 ii2. Northern Lake Huron epilimnion calibration calculation. Comparison of observations and computation for observed Secchi disk depth and gross primary production, (1971) • 97 viii ------- FIGURES (continued) Number k3. Computed versus Observed Data (So. Lake Huron epilimnion). . 98 kk. Computed versus Observed Data (So. Lake Huron epilimnion). . 99 45. Computed versus Observed Data (So. Lake Huron epilimnion). . 100 k6. Computed versus Observed Data (Saginaw Bay) ......... 102 17. Computed versus Observed Data ( Saginaw Bay) ......... 103 U8. Computed versus Observed Data (Saginaw Bay) ......... 10^ k9 . Computed versus Observed Data (No. Lake Huron hypolimnion) . 106 50. Computed versus Observed Data (No. Lake Huron hypolimnion) . 107 51. Computed versus Observed Data (So. Lake Huron hypolimnion) . 108 52. Computed versus Observed Data (So. Lake Huron hypolimnion) . 109 53. Phytoplankton growth and death rates in Southern Lake Huron epilimnion and hypolimnion ................. 110 5k. Nutrient limitation of growth rate. Inorganic nitrogen (N/N + KmN) and reactive phosphorus (P/p + Kmp) terms, and their product (total reduction) ............... 112 55. Comparison of kinetic fluxes of unavailable phosphorus in Southern Lake Huron and Saginaw Bay. Curves correspond to a _(l-f.)R for phytoplankton respiration; a (l-f ) p.r A Z pO A (R +R ) for zooplankton respiration; a (l-$)(l-f )R pn P o pJr A j for unassimilated phytoplankton, and a (l-e )(l-f )R, P w C /-i 4 for unassimilated zooplankton ................ 113 56. Cumulative plot of the components of total phosphorus in Southern Lake Huron and Saginaw Bay. The curves correspond to reactive phosphorus; reactive & unavailable phosphorus; and total phosphorus , which includes algal and zooplankton phosphorus ......................... 57. Seasonal distribution of phytoplankton growth and death rates showing light and nutrient limitation reductions . . . Il6 IX ------- FIGURES (continued) Number Page 58. Seasonal distribution of computed herbivorous zooplankton growth and death rates for Southern Lake Huron and Saginaw Bay growth rate, $a pFL; respiration rate, -R, ; carnivore grazing, -R^. . . ? 117 59- Lake Ontario calibration. Application of saturating recycle kinetics. Data from 196? - 1972 CCIW cruises 121 60. Lake Ontario calibration. Application of saturating recycle kinetics. Data from 1967 - 1972 CCIW cruises 122 6l. Final calibration computations for Southern Lake Huron, Lake Ontario, and Saginaw Bay phytoplankton chlorophyll. The phytoplankton and recycle kinetic constants are the same in each calculation. However Lake Ontario zooplankton kinetics are not those used for Lake Huron and Saginaw Bay 123 62. Sensitivity to phytoplankton kinetic constants. Saturated growth rate @ 20°C, K (middle). Growth rate temperature T—20 dependence, 6, with K 6 constant at T = 13°C (bottom). Labels in the figures correspond to computer program vari- able designations 127 63. Sensitivity to phosphorus system kinetic constants. Michaelis constant for phosphorus, K (top). Phosphorus to chlorophyll ratio, a (bottom) 128 6h. Sensitivity to recycle rate kinetic constant of phosphorus and nitrogen, phytoplankton chlorophyll, reactive phosphorus and nitrate nitrogen 130 65. Sensitivity to herbivore grazing rate. Kinetic constant and silica to chlorophyll stoichiometric constant a..p 132 t_) 1 ir 66. Sensitivity to phytoplankton settling velocity (top), satu- rating light intensity (middle) and stratifications (bottom), Southern Lake Huron epilimnion (left), Southern Lake Huron hypolimnion (center), Saginaw Bay (right) 13^ 67. Fifteen year distribution of and percent increase in yearly averaged phytoplankton chlorophyll a in Southern Lake Huron. Model is essentially at steady state in year 15 136 ------- FIGURES (continued) Number Page 68. Effect of increases of phosphorus inputs to Southern Lake Huron. Percent change in yearly average epilimnion concen- tration versus percent change in total phosphorus input (a) Chlorophyll, P_; ("b) Total phosphorus, p • (c) unavailable phosphorus, p ; (d) Ratio of algal phosphorus to total phosphorus, P'/p^ 139 "C 69. (Southern Lake Huron epilimnion) Yearly average chlorophyll concentration versus total phosphorus loading to Lake Huron. XI ------- TABLES NUMBER PAGE 1. Nutrient Loadings 11 2. Segment Parameters 15 3. Heat Flux Input for Transport Verification 23 k. Zooplankton Grazing Constants hi 5. Experimentally Determined Nutrient Recycle Rates 50 6. Data Used for Recycle Rate Analyses 52 T. Historical Data Summary 58 8. CCIW Lake Huron Surveys 63 9. GLRD Lake Huron Surveys 6h 10. CIS Saginaw Bay Surveys 65 11. Survey Stations and Model Segments 66 12. Inter-Survey Station Comparisons 7^ 13. Total Phosphorus Mass Balance 119 Ik. Effect of Various Nutrient Recycle Mechanisms 137 15. Results of Model Simulations lUl Al. Phytoplankton Growth 150 A2. Phytoplankton Respiration 152 A3. Herbivorous Zooplankton Growth 153 AH. Carnivorous Zooplankton Growth 15^ A5. Zooplankton Respiration 155 A6. Nitrification 156 xii ------- TABLES (continued) NUMBER PAGE AT. Mineralizations 157 A8. System Kinetic Derivitives 158 A9. Time Variable Saginaw Bay Waste Loadings 159 A10. Main Lake Huron Waste Loadings l6l All. Boundary Concentrations • l6l A12. Flows 162 A13. Exchanges 163 Al^. Segment Parameters l6k A15. Time Variable Functions 1.6k xiii ------- ACKNOWLEDGEMENTS This study could not "be undertaken without adequate data to serve as input and for calibration purposes. We therefore extend special thanks to the Cranbrook Institute of Science, the Casiada Centre for Inland Waters, and the Great Lakes Research Division of the University of Michigan for supplying and permitting us to use their water quality data. The cooperation of all members and committees of the Upper Lakes Reference Group of the International Joint Commission, particularly those who provided us with waste loading infor- mation, is also gratefully acknowledged. The participation, helpful criticism, and support of our colleagues at Manhattan College: Robert Thomann and Donald O'Connor, and at the EPA Grosse lie Laboratory: Nelson Thomas, William Richardson, Victor Bierman, and Tudor Davies (presently of EPA, Gulf Breeze, Florida) is greatly appreciated. Special thanks are also due to Mrs. Eileen Lutomski for her typing of the report manuscript. xiv ------- SECTION 1 INTRODUCTION The principle objective of this research project is to structure and apply a numerical model of phytoplankton Momass in lake Huron and Saginaw Bay in order to provide a framework for assessing, managing, and controlling eutrophication problems in these areas of the upper Great Lakes. This work is part of a larger study which also addressed water quality problems in Lake Erie, particularly the depletion of oxygen in the hypolimnetic waters of the Central Basin. Results of that study are reported separately in Part II of this report. The continuing eutrophication of the Great Lakes, the largest single freshwater system in the world, has been a widely recognized water quality problem. While the open lake waters of Lake Huron are classed as oligotro- phic, Saginaw Bay, a shallow, short residence time embayment which serves as a receiving body for a large percentage of the waste loadings entering Lake Huron, is a highly eutrophic area exhibiting, for example, phytoplankton chlorophyll concentrations which are an order of magnitude greater than those found in Huron's open lake waters. Recognizing the potential for large scale water quality deterioration, the International Joint Commission appointed a special committee in April, 1972, the Upper Lakes Reference Group, to deter- mine whether the waters of Lakes Superior or Huron were being polluted on either side of their respective international boundaries to an extent likely to cause a degradation of existing levels of water quality in the Great Lakes system. While this project did not form a part of the Upper lakes Reference Study, per se, it does provide a framework for responding to the reference questions raised therein. The computation comprises a kinetic structure which characterizes the interrelationship between phytoplankton, herbivorous and carnivorous zoo- plankton, ammonia, nitrate, and unavailable nitrogen, dissolved ortho and unavailable phosphorus, and silicate. These constituents form the nine de- pendent variables. This formulation is then coupled to the water transport in the Saginaw Bay/lake Huron system, the boundary concentrations and nutri- ent waste loadings. A new framework is developed which relates the rate of recycle of nutrients from unavailable to available inorganic forms to the phytoplankton biomass concentrations. The model is calibrated by comparing computed concentrations to observations. Sensitivity analyses are presented which indicate the extent to which the model's computations depend upon values chosen for key parameters which affect the kinetic interactions of the various model compartments. Finally, applications of the model are pre- sented which project water quality responses in southern Lake Huron and Saginaw Bay to various management strategies for reducing total phosphorus inputs to this system. ------- SECTION 2 SUMMARY AND CONCLUSIONS This research project develops a framework for an analysis of the causes and remedies of eutrophication of Lake Huron and Saginav Bay. The methodol- ogy employed is based on a mathematical model which expresses in quantitative terms the mass "balance relationships which interrelate the nutrient mass discharges to the lakes, the nutrient concentration in the lake, the phyto- plankton and zooplankton response to these nutrients, and their resulting seasonal distribution. The model calculations provide the method by which the fate and impact of present and projected levels of nutrient discharges can be evaluated in terms of their effect on the biomass of phytoplankton. It is for this specific purpose that they have been constructed: to provide a quantitative method by which nutrient management plans can be evaluated. It is concluded, based on this investigation, that the phytoplankton biomass, nitrogen and phosphorus concentrations in Lake Huron and Saginaw Bay can be adequately modeled using the formulation presented. This is suggested by the fact that the computations reproduce observed concentrations fairly well in both Saginaw Bay and the open waters of Lake Huron where concentra- tions of most variables span almost an .order of magnitude and conditions range from eutrophy to oligotrophy. Mass balance calculations are based on three components: estimates of the rate of nutrient mass discharges to the lake; estimates of the vertical and horizontal transport regime; and estimates of the nutrient, phytoplank- ton, an^zooplankton kinetics. This report is concerned with the latter two components; the mass discharge rates have been estimated "by the Upper Lakes Reference Study group. [98] The mass balance calculations; are made for each BOTTOM .LAYER Figure 1. kl 0-15m«t«rslmilnl>l»> 0-Mtom isigin* B>>> Segmentation of Lake Huron. Top, Layer (Epilimnion) and Bottom Layer (Hypolimnion) of Northern and Southern Lake Huron. Segment 3 represents Saginaw Bay. ------- of the five segments, illustrated in fig. 1, which represent the epilimnion and hypolimnion of Northern and Southern lake Huron, and Saginaw Bay. The transport regime between these segments is evaluated using convenient conser- vative tracers, primarily temperature. As shown in fig. 2 the vertical exchange coefficient is established from the seasonal distribution of temper- ature. The lines in the figure are the result of a temperature balance cal- culation employing the vertical exchange coefficient illustrated in the fig- ure. A similar calculation for Saginaw Bay using both temperature and chloride concentration establishes the horizontal exchange between Saginaw Bay and Southern Lake Huron. EPILIMNION NoftfHni tjlw Huron HYPOLIMNION 9.0 -6.0 J'F'M'A'M'J'J'A'S'O'N'O J'F'M'A'M'J'J'A'S'O'N'D SouttMm Lite Huron HYPOLIUNION * 9.0 « -5.0 J'F'M'A'M'J1J'A'S'O'N'D J'F'M'A'M'J'J'A'S'O'N'D The kinetics of the computation are illustrated j.n fig. 3. The phyto- plankton are represented by their chlorophyll concentration; the zoo- plankton are partitioned into herbiv- orous and carnivorous groups. The two major nutrient cycles considered are the phosphorus and nitrogen cycle. Both unavailable and available forms are considered and as shown subse- quently the rate of recycle of una- vailable to available phosphorus is a focal point of the analysis. These kinetics are expressed in mathematical terms and, together with the transport regime and the mass discharges , they comprise the mathematical model that is the basis of the calculation. Figure 2. Vertical Transport Calibration Figure 3 Schematic Diagram of the Kinetic Interactions ------- The critical step in the development of this or any model is calibra- tion; the comparison of computed concentrations for each of the nine vari- ables considered in each of the five segments of the lake. The ability of the model to reproduce present conditions is a necessary prerequisite in establishing its validity. An example of the calibration results for Saginaw Bay and the Southern Lake Huron epilimnion is shovn in fig. k. The concen- SAQINAW BAY SOUTHERN LAKE HURON J'F'M'A'M'J'J'A'S'O'N'D J'F'M'A'M1J'J'A'S'O'N'D M1J'J'A'S'O'N'D 25 t- 0 0.40 5g z 0.00 J'F'M'A'M'J'J'A'STQTN'D 8.0 4.0 0.0 0.016 0.008 0.000 0.004 0.002 0.000 0.40 0.20 0.00 I" -_-^"T\|?l J 'F 'M'A'M1 J r • ml FT] J 'F'M'A'M1 J NL-f-"^LM- ' J 'A'S'O'N'D [ i I i if 1 f f " p- ' J ' A ' S ' 0 1 N ' D n ^ ..* 0 T £ J 'F'M'A'M1 J 'J'A'S'O'N'D ii T! iiJL J T ,_J— J^_l_p j 'F'M'A'M' j rrf#!« ' J 'A'S'O'N'D Figure k. Results of model calibration: Computed versus Observed Data in Southern Lake Huron and Saginaw Bay. trations of nutrients and phytoplankton in these regions are quite different; Saginaw Bay is almost an order of magnitude more enriched in phosphorus and chlorophyll than the main lake and the computation responds accordingly. These and the other calibration results are used to assess the probable range of applicability of the model to projected conditions. In particular the calibration and other analyses described in section 6 indicate that the recycle rate in Southern Lake Huron is considerably slower than in Saginaw Bay. The effect has important implications in the projected response of Lake Huron to increased phosphorus discharges. In order to further verify this phenomenon a previous analysis of Lake Ontario was modified to include this new recycle rate formulation. The ------- SOUTHERN LAKE HURON 8 o> > X OL O GC O X (J z o * Q. O >- X a. JTFTMTA'MIJ'J'A'S'O'N'D LAKE ONTARIO 5> 00 J 'F'M'A'M1 J ' J 'A'S'O'N'D S4G//VXHV 40 20 J 'F'M'A'M1 J1 J Figure 5 result is that it is possible to reproduce the phytoplankton chloro- phyll and nutrient seasonal distri- butions for Southern Lake Huron and Lake Ontario epilimnia and Saginaw Bay using the same phytoplankton and nutrient kinetic structure and con- stants as shown in figure. 5. This simultaneous applicability suggests that the model employed in this cal- culation has a more general validity and its use in making projections is supported. A sensitivity analysis is pre- sented in order to assess the effects of varying kinetic constants on the computation. In particular it appears that although the shape of the seasonal distribution is strongly affected by the zooplankton kinetics the peak and yearly average concen- trations are rather insensitive. Therefore the projections for these measures of eutrophication are not invalidated by the uncertainties in the zoopla'nkton kinetic coefficients. Projection calculations for var- ious phosphorus mass discharge rates are presented in section 10, an ex- ample of which is shown in fig. 6. The importance of phosphorus recycle is shown in the projected yearly average chlorophyll change to be expected from changes in yearly aver- age phosphorus inputs. For satura- tion kinetics, which are suggested by the calibration results, a doubling of the phosphorus loading is pro- jected to increase the yearly average chlorophyll over 300$ whereas for first-order recycle a doubling would be projected. This implies that South- ern Lake Huron is quite senstive to changes in phosphorus loading and it would respond more dramatically than strictly linearly to increases in phos- phorus inputs. More detailed projection calculations including Saginaw Bay are included in section 10. The results indicate than an annual load of total phosphorus to Lake Huron of 3600 metric tonnes/yr. will maintain exist- ing chlorophyll levels in Southern Lake Huron achieving non-degradation. It is also projected that phosphorus reductions at municipal sewage treatment plants in the Saginaw Bay area to effluent concentrations of 1 mg/£ which will reduce the Saginaw Bay load by 600 tonnes/yr. will result in yearly Final calibration compu- tations for Southern Lake Huron, Lake Ontario, and Saginaw Bay phytoplankton chlorophyll. ------- SOUTHERN LAKE HURON EPILIMNION r= > K UJ f) 8 ZK < ui > 50 100 PERCENT CHANGE IN TOTAL PHOSPHORUS INPUT Figure 6. Effect of Increases of Phosphorus Inputs to Soiithern Lake Huron. Percent change in yearly average epilimnion concentration versus percent change in total phosphorus input (a) Chlorophyll, P_; (b) Total phosphorus, p . average chlorophyll concentrations of about 1.1 yg/Jl in Southern Lake Huron and 10.T Ug/& in Saginaw Bay. These results have been used by a United States-Canadian Task Group for purposes of developing total phosphorus load- ing objectives to the Great Lakes as part of the re-negotiation of the 1972 Water Quality Agreement [104], ------- SECTION 3 RECOMMENDATIONS Due to the significance of the role which nutrient recycle plays in the Lake Huron and Saginaw Bay ecosystem, experimental investigations should "be undertaken to provide additional insights into the factors affecting these mechanisms. Furthermore, since classical phytoplanktoij growth kinetics do not reproduce well what appears to be significant observed chlorophyll a_ concentrations in the cold and dark hypolimnion waters of Southern Lake Huron, further studies of this deep chlorophyll phenomenon are recommended to determine whether, for instance, low light adaptation, transport, migra- tion, or some combination thereof contributes to this observed effect. In addition, a verification of the model developed hereunder should be per- formed utilizing Saginaw Bay waste loadings which were lowered subsequent to this study as part of a remedial phosphorus reduction program. Some long term model simulations incorporating yearly variations in waste load- ing are also recommended to determine if present observations can be repro- duced. Such verification exercises would provide an additional degree of validity to the model as it presently stands. ------- SECTION h PHYSICAL FEATURES, MASS LOADINGS, AND SEGMENTATION A major legacy of Pleistocene glaciation is the formation of the Great Lakes [l], the largest freshwater system on earth. Lake Huron is the second largest of these Great Lakes and is the fifth largest lake in the world [2]. Saginaw Bay is an inland extension of the western shore of Lake Huron pro- jecting southwesterly midway into the southern peninsula of Michigan [3]. Lake Huron is connected to Lake Michigan by the Straits of Mackinac, to Lake Superior by the St. Mary's River, and to Lake St. CLair by the St. Clair River. Lake Huron with Saginaw Bay and the combined drainage basin is shown on fig. T. GEOMORPHOLOGY Lake Huron's water surface is 1?6 meters (579 feet) above sea level. The total water surface area, including Georgian and Saginaw Bay, is 59,570 km2 (23,000 mi2) [^,5]. The lake drains a total land and water area of 193,700 km2 (7^,800 mi2) [k], two-thirds of which is land drainage. Meas- ured from low water datum, Lake Huron has a maximum depth of 229 meters (750 feet) [U], Averaged over the lake, the mean depth is reported as 53-59 meters [^,5]. Total water volume of Lake Huron is 3535 km3 (8H8 mi3) [U,5]. The length of the lake is 330 km (205 miles) with its breadth being 292 km (l8l miles) [5]. Total shoreline including islands is 5,088 km (3162 miles) [51. Saginaw Bay is a shallow arm of Lake Huron h2 .km (26 miles) wide and approximately 82 km (51 miles) long. The bay's 2960 km2 (11^3 mi2) of surface area are equally divided between an inner and outer bay divided by a constriction where the bay narrows to 21 km (13 miles). The shallower inner zone has a mean depth of k.6 meters (15 feet) while the outer bay mean depth if lU.6 meters (H8 feet). The maximum depth is ^0.5 meters (133 feet) in the outer bay [3]. HYDROLOGY Lake Huron is in the central portion of the Great Lakes Basin, southeast of Lake Superior and east of Lake Michigan. It receives outflow from Lake Superior through the St. Mary's River, a channel 112 km (70 miles) long. Lake Huron also receives outflow from Lake Michigan via the Straits of Mackinac. The straits of Mackinac provide a broad and deep connection between Lake Michigan and Lake Huron, being more than three miles wide at ------- MINNESOTA WISCONSIN STRAITS OF MACKINAC INDIANA UNITED STATES SCALE IN MILES 0 10 20 30 40 50 Figure 7. Lake Huron and Saginaw Bay Drainage Basin ------- their narrowest point and ranging in depth to more than 6l meters (200 feet). Direction of currents in the Straits alternates from east to west depending upon meteorology. Net flow, however, is to Lake Huron [h]. It should be noted, however, that flow reversal with depth during the stratified season has been observed in the Straits of Mackinac [100]. This phenomena, in turn, has been determined to have a significant effect on the estimation of trans- port through the Straits [101]. Outflow from Lake Huron is via the St. Clair River at its southernmost tip. The average flow (1860-1970) to Lake Huron from the St. Mary's River draining Lake Superior is 2123 m3/sec (75000 cfs). The flow across the Straits of Mackinac from Lake Michigan is estimated to be 1^72 m3/sec (52,000 cfs); while that leaving via the St. Clair River is 5,303 m3/sec (187,300 cfs) [h]. The average annual precipitation (1900-1970) on Lake Huron's water surface is 79 cm (31 inches) [^,5], and the average annual evaporative loss has recently been estimated at 66 cm (26 inches)[l\|]. The Saginaw River is the major source of drainage flowing to Saginaw Bay. Formed by the convergence of the Shiawassee, Tittabawasee, Cass, and Flint Rivers, the Saginaw River is 35 km (22 miles) long and enters the bay at its southwestern end. The average annual water levels in Saginaw Bay are controlled by the Lake Huron water level. The bay itself, however, exhibits very short term, rapid and large fluctuations as a result of wave runup, wind driven tides, and seiches [3]. Some of these propagate down the Saginaw River and cause flow reversal. Flows typically range from ik to 227 m3/sec (500 to 8000 cfs) throughout a year with an average value estimated to be 109 m3/sec (3850 cfs) [3]. MASS INPUTS The earliest comprehensive mass loading data for Saginaw Bay is avail- able from the 1965 survey by the FWPCA of Michigan tributaries. They are based on Saginaw River and other bay tributary measurements of total and ortho phosphorus, and nitrate, ammonia and organic nitrogen. No Lake Huron estimates for the comparable period are available, however. Johnson [6] summarizes some typical Saginaw Bay loadings from its major tributaries based on the 1965 surveys. The Great Lakes Water Quality Board [7»8,9] has made estimates of the 1972 to 197^ overall lake loadings for total phosphorus and total nitrogen. Estimates of loadings under reduction policies are also included. The break- down of the total nutrient loading into various nitrogen a.nd phosphorus forms and their spatial distribution are not estimated. In view of the lack of comprehensive and detailed mass loading informa- tion for Lake Huron and Saginaw Bay, a major effort was instituted in order to rectify this situation. As part of the Upper Lakes References Study of the IJC, one of the aims of which is to document the present water quality status of Lake Huron, "data collection programs and studies were proposed for the purpose of determining the loading of materials to the lakes which could adversely affect their water quality" [10]. Sources studied included munici- 10 ------- pal, industrial and tributary point sources as well as other land and atmos- pheric inputs (nonpoint sources). These studies provide the necessary com- prehensive mass loading data without which it is impossible to perform mean- ingful mass balance calculations. In addition to total nutrient mass loading information it is necessary to know the forms of the nutrient, the important division being available or unavailable for phytoplankton growth. The division into the various nutri- ent forms: ammonia, nitrite plus nitrate, and organic for nitrogen; and soluble reactive and unavailable (total minus reactive) for phosphorus, were determined based on information which was available for Province of Ontario and State of Michigan tributary loadings. Atmospheric loads were evenly divided between ammonia and nitrate for nitrogen, while'all atmospheric phosphorus was considered to be in the soluble reactive form. For Lake Huron proper, average annual mass loadings suffice because of its large volume and long residence time for nutrients. However for Saginaw Bay more detailed information is necessary, since the bay is highly respon- sive. Based on the 197^- surveys of Saginaw Bay (Section VI), which had a few stations at the mouth of the Saginaw River, USGS flow data, and State of Michigan water quality stations, Richardson and Bierman [11] computed load- ings to Saginaw Bay from the Saginaw River, its major contaminant source. Figure 8 shows these loadings as a function of time together with the Sagi- naw River flow. As can be seen, all parameters are highly correlated to the flow, as would be expected, with spring runoff flows yielding the highest loading rates. Flow is relatively small in the latter half of the year as are the loadings. The mass loading estimates used in the subsequent calculations are a combination of the Lake Huron loadings computed by the Upper Lakes Reference Group and the time variable Saginaw Bay loadings. Both are computed using 197^ data. Table 1 summarizes the total nitrogen and phosphorus loadings which are used in the Lake Huron/Saginaw Bay computation. TABLE 1. NUTRIENT LOADINGS Location Total Phosphorus Total Nitrogen (tonnes/yr) (ibs/day) (tonnes/yr) (#/day) Northern Lake Huron Southern Lake Huron Saginaw Bay TOTALS 1,281 1,297 1,315 3,893 (7,739) (7,832) (7,9^5) (23,516) 58,186 35,773 17,678 111,637 (357,^1) (216,066) (106,773) (67^,280) SEGMENTATION Five segments are chosen to represent the significant regions of the .Lake Huron - Saginaw Bay system described in the preceding section. The 11 ------- 1974 SAGINAW RIVER LOADINGS TO SAGINAW BAY J F MAMJ J A SON D JFMAMJJASOND Figure 8. Annual distribution of Saginaw River flow and nutrient mass loading rates, 12 ------- choice is a compromise between a realistic characterization of the major fea- tures of the biological and chemical variations and the constraints of compu- tation and simplicity, with the emphasis on the latter requirements. Three surface segments are considered: Northern Lake Huron, a large open expanse of water which tends to be deeper and colder than other portions of the lake and receives the inputs from Lake Superior and Lake Michigan and from major Canadian tributaries feeding the North Channel and Georgian Bay; Southern Lake Huron bounded by the Canadian and Michigan shorelines which approach one another to form the St. Clair River outlet channel. It is influenced, to some degree, by the Saginaw Bay flow sweeping down its western shoreline. Concentrations of biological and chemical parameters tend to be slightly higher than in the open lake waters to the north. Saginaw Bay receives the loading from the Saginaw River. Its waters are significantly enriched as compared to the oligotrophic waters of the rest of Lake Huron. Figure 9 presents the segmentation. Segment 1 encompasses the northern Lake Huron epilimnion. Its depth ranges from the surface to 15 meters (^9-2 feet) which is the approximate thermocline depth as well as the eupho- tic zone depth (l$ surface light penetration depth). The lower boundary of segment 1 is the line of kh° 30' north latitude or roughly a line across the lake connecting a point 8 km (5 miles) north of Oscoda on the Michigan shoreline to a point just north of Southhampton on the Province of Ontario shoreline. Georgian Bay and the North Channel are not included as part of the segment. The epilimnion of southern Lake Huron comprises segment 2, also 15 meters deep. It is bounded to the north by segment 1 and it also interacts with the Saginaw Bay model segment to the west. Segment 2 is the outflow segment as its southern boundary is the St. Clair River outflow channel. Segments k and 5 comprise the northern and southern Lake Huron hypolim- nion, respectively. They are both 50 meters (l6k feet) deep and are situa- ted directly below their respective epilimnion segments with their outer ring boundary being the 15 meter depth contour of the lake. Together, they form the second vertical layer of the model. Inclusion of hypolimnetic seg- ments is required to characterize the thermocline formation, its effects on vertical transport, and the effect of phytoplankton sinking and net trans- port of biomass and associated nutrients to the sediment. Saginaw Bay is represented by segment 3. It encompasses all of the inner bay and part of the outer bay. The mean depth of this segment is 6 meters (19-7 feet) slightly deeper than the reported inner bay mean depth of k.6 meters, since some of the outer and deeper portions of the bay are also included. Saginaw Bay is characterized by only one vertical layer since only in the outer reaches of the bay does a well formed thermocline persist in the summer and fall. Table 2 lists the individual segment depths, surface areas, and vol- umes. These were obtained by using navigational charts [12,13], measuring the areas of concern with a planimeter, and converting using map scales. When the volumes for the North Channel and Georgian Bay are added to the 13 ------- TOP LAYER 0-15 meters (main lake) 0-bottom (Saginaw Bay) BOTTOM LAYER 15 meters-bottom Figure 9- Segmentation of Lake Huron. Top Layer (Epilimnion) and Bottom Layer (Hypolimnion) of Northern and Southern Lake Huron. Saginaw Bay is represented "by one layer. ------- total values for the five segments the result is within 3-5% of reported values [4,5] for total lake volume. TABLE 2. SEGMENT PARAMETERS Segment Depth meters (feet) 1 15 2 15 3 6 4 50 5 50 (49.2) (49.2) (19-7) (164.1) (164.1) Surface Area km2 (mi2) 24,882 14,780 1,815 41,477 (9,608) (5,707) (701) (16,016) Volume km3 373.4 221.7 10.8 1141.1 619.7 2366.7 (mi3) (89.6) (53.2) (2.6) (273.8) (148.7) (567-9) 15 ------- SECTION 5 ESTIMATION OF THE SEASONAL TRANSPORT REGIME The available estimates of the nutrient mass discharge rates to Lake Huron and Saginaw Bay are presented in the previous section as well as the relevant geomorphology and hydrology. These provide the volumes, flows, and material input rates to the surface segments. In order to calculate the resulting concentrations, it is necessary to know the transport rate between the segments. Three segment boundaries are considered: the Northern-Southern Lake segment boundary; the Saginaw Bay-Lake Huron boundary, and the thermo- cline. The estimates of the transport are based on observations of the mag- nitude and direction of the currents and the analysis of the distribution of conservative tracers. The former are used for the estimate of the Northern- Southern Lake exchange whereas suitable tracers are available for the Saginaw Bay exchange and thermocline transport. LAKE HURON CIRCULATION PATTERNS Many factors affect the currents in the Great Lakes. Although primarily wind driven, currents are also affected by temperature, which can form den- sity gradients in the lake; by basin geometry which modifies the currents; by the Coriolis force, an apparent force due to the rotation of the earth; by incoming flows; and by wave effects. A detailed discussion of the com- plexities involved and governing equations is available [L^]. Although current patterns in Lake Huron appear not to be well under- stood [15]> generalized patterns have been observed. Several investigators [6,l6,lT] have characterized a circulating flow from Lake Huron entering Saginaw Bay at its northwestern shore and exiting along the southeastern shore at least under some prevailing wind direction. Flow from the Saginaw River hugs the southern shore and then exits to Lake Huron [3]. The pre- vailing circulation seems to be counterclockwise. However, it should be noted that all of the investigators agree that the circulation is sensitive to changes in wind speed and direction which result in short term and rapid fluctuations. Another major feature of Lake Huron circulation which has been observed is a circulating flow between the northern and southern open lake waters which occurs towards the eastern shore near the center of the lake. Figure 10 illustrates the features of Lake Huron and Saginaw Bay transport described above. Recent intensive studies undertaken as part of IJC's Upper Lakes Refer- ence Study [102] have significantly enhanced knowledge of Lake Huron currents 16 ------- SCALE IN MILES 0 10 20 30 40 Figure 10. Typical surface circulation pattern for Lake Huron (after Ayers et al. (1956) [l6]). 17 ------- especially winter circulation patterns. These winter studies show patterns of flow similar to the circulation of epilimnion water during summer as well as a counterclockwise circulation of waters across the international boundary as shown on fig. 10. METHODOLOGY The estimation procedure for transport involves calculating the distri- bution of suitable tracers and comparing them to observations. This is only possible for the Saginaw Bay exchange with the southern Lake Huron segment since there exist sufficiently large gradients for chlorides, temperature, and total phosphorus. The northern-southern lake circulation is difficult to estimate since no strong gradients exist. The values used are consistent with observed surface velocities [16]. The magnitude of the vertical mixing is established by calibrating a temperature balance calciilation to the large gradients which exist between epilimnion and hypolimnion segments. The per- iod of intense stratification, during which no appreciable mixing appears to occur, commences in July and continues through October. Vertical exchanges that are consistent with the temperature observations are determined and used to parametize the seasonal vertical mixing pattern. The equation which governs the concentration of a conservative tracer in any segment is determined from a mass balance around that segment which takes into account flow into and out of the segment, dispersive exchange, and boundary inputs: dc. V. —- = £ Q..c. + I E!.(c.-c.) + W. (1) i dt . ij J ijx j i' i J J where: c. = concentration in the i segment (M/L3) V. = volume of the i segment (L3) Q.. = volumetric flow rate from segment j to segment i 1J (L3/T) E!. = volumetric exchange rate between segments i and j 1J (L3/T) W. = rate of mass input into the ±' segment (M/T) The flow rates, Q.., are thought of as the unidirectional flows due to the i J net advection through the segment boundaries. Thus the Saginaw River flow and the north to south Lake Huron flow described in Section ^, Hydrology, are represented by these terms. The exchange flows are the result of the horizontal circulating flows which are bi-directional, as illustrated in fig. 10, and whatever other mixing processes occur between adjacent segments. For the boundary at the location of the thermocline, the exchange coefficient is related to the vertical dispersion coefficient, E.., via the expression E!. = E..A..1%. . where A.. is the interfacial area and £.. is the length between ij ij ij 10 !J the segment midpoints [l8]. This relationship applies if the segment sizes 18 ------- are small enough so that finite difference approximations to derivatives are reasonable. For the large segments considered in this study, the relation- ship is only approximate. The estimation of the Saginaw Bay-Southern Lake Huron exchange coeffi- cient is based on the solution of equation (l) using chlorides as the conser- vative tracer. In addition, total phosphorus is considered although as shown subsequently some removal occurs due to particulate phosphorus settling. Finally, a temperature analysis is presented to further confirm the estimated exchange rate. The equation used for the chlorides and total phosphorus ana- lysis is: dc (2) where Q2s(t) is the observed Saginaw river flow and Ws(t) is the observed mass loading rate from the Saginaw River. These are obtained from the EPA and the IJC Upper Lakes Reference Group studies as outlined in Section k. Comparison to Saginaw Bay loadings calculated by the University of Michigan (Canale, personal communication) are shown on fig. 11. It is interesting to note that the weekly sampling data is necessary to resolve a number of sharp peaks which contribute to the total loading. The methodology for using temperature as a tracer is a simplification of a full thermal balance calculation. Heat storage in a lake is dependent on many factors including short and long wave solar radiation incident to the water surface; reflected solar radiation; long wave back radiation; sensible heat transfer to the atmosphere; and energy of condensation and evaporation. The net result of these is a net heat flux to the lake which can be thought of as a forcing function for temperature. Thus instead of developing rela- tionships for each of the terms which comprise total heat storage using observations for solar radiation, water reflectivity, air temperature, cloud cover, wind speed, vapor pressure and the like, which is a complex task requiring large amounts of data, heat storage is computed directly from observed temperature data. Mean temperatures for each segment (i) for each cruise (k),T., , are computed using the 197^ survey data. Because of the liC relatively uniform spacing of the observations volume-weighted means were a refinement that was judged to be unnecessary. Total heat content change in the lake, AH , between cruise k and & is then computed using: AHT =. AHi = * Vi (Tlk-Tl£) P °P where: AH. = change in heat content for the ith segment between cruise k and £ (calories) V. = volume of segment i (cm3) 19 ------- ro -D 10 c 8 LJJ Q cc 3 i 0 cc O Q- 00 O X a. D O .c 6 4 2 0 10 8 6 4 2 0 EPA UNIVERISTY OF MICHIGAN JIFIM'A'M[JIJTATSTO J ' F ' M ' A ' M ' J ' J'A'S'O Figure 11. Comparison of Saginaw River mass dischsirge rates for chlorides and total phosphorus as estimated from weekly and monthly sampling data. 20 ------- T. = volume average temperature in segment i on the ik kth cruise (°C) T. g = volume average temperature in segment i on the 1 Jlth cruise (°C) C = heat capacity of vater (cal/g-°C) p = density of water (g/cm3) The total lakewide daily average surface heat flux, J between the cruise dates , which represents the net amount of energy input over the surface area of the lake, can then "be determined using: where: A = total lake surface area (cm2) s At . = time between the kth and &th cruise (days) J = areal heat flux (cal/cm2-day ) In order to apportion the net heat flux to the surface segments of Lake Huron and Saginaw Bay a number of assumptions are possible. The simplest is- to assume that the flux is uniformly distributed over the entire lake. How- ever, certain of the mechanisms which cause this heat flux are dependent on the water surface temperature which is quite different for Saginaw Bay and Lake Huron. Thus a correction for this effect is necessary. The method is based on the assumption that the equilibrium temperature, E, is the same for Saginaw Bay and Lake Huron. This is reasonable since the equilibrium tem- perature does not depend on the water depth, but only on meteorological vari- ables, which can be presumed to be relatively uniform lakewide. In addition it is assumed that the net heat flux can be computed using a surface heat transfer coefficient coefficient. This approximation can be justified by linearizing the equations for long wave back radiation (Stephan-Boltzman equation) and the equations that depend on the saturated vapor pressure at the water surface temperature [19]. The result is that the net heat flux at location i, J. , is related to the local surface temperature by the equation: J. = K(E-Tp (5) where : K = surface heat transfer coefficient (cal/cm2-day-°C) E = equilibrium temperature (°C) T! = surface water temperature of segment i (°C) 21 ------- The prime denotes surface as opposed to volume average temperature. Con- sider this equation applied to the total lake surface: JT = rz JiAsiK(E-T1) s i where T" is the lakewide average surface temperature. If it is assumed that the heat transfer coefficient is also constant, for the same reasons that the equilibrium temperature is assumed constant, then a relationship is obtained between the segment specific and the lakewide average heat flux by subtracting eq. (6) from eq. (5): J. = JT - K(T^-T') (T) The correction depends on knowing the segment average and lakewide average surface temperatures, which are available from the cruise data, and the sur- face heat transfer coefficient. For Lake Huron it has been estimated to be K = 50-65 cal/cm2-day-°C [20], In units comparable to surface gas transfer coefficients this corresponds to K/pC = 0.5 - 0.65 m/day. The computed lakewide and segment specific heat fluxes resulting from application of this procedure are given in Table 3. The heat balance equation using the ad- justed net heat fluxes becomes: dT. V. T+ = Z Q. .T. + E E! .(T.-Tj + i i (8) i at j "U j . ^ 0 L> ^-g- where: Calibration H. is the average depth of segment i. (cm) The methodology outlined above is used to determine the degree of hor- izontal and vertical transport necessary to match observed concentration gradients in the lake. Figure 12 shows the results of this analysis for vertical transport. The temerature gradients between the northern and southern Lake Huron epilimnia and hypolimnia are matched fairly well using the computed segment specific heat fluxes (Table 3) and incorporating a vertical exchange coefficient of 10 m2/day (107-6 ft2/day) during periods of non-stratification. There is no vertical exchange in the model during periods of complete lake stratification. This seasonal trend is simulated with a temporally varying vertical exchange coefficient as shown on figure 12. Surface temperatures which are most sensitive to the vertical mixing are well reproduced using this vertical variation. Hypolimnion tempera- tures are overestimated in Northern Lake Huron segment but are well repro- duced for Southern Lake Huron with the exception of the rather erratic late August value. A circulating flow equivalent to 2.2 cm/sec across the northern and southern lake epilimnia is incorporated and is consistent with surface 22 ------- TABLE 3. Heat Flux Input for Transport Verification Time (days) 97-5 127.5 ll2.5 157.5 172.5 187.5 202.5 217.5 232.5 217.5 262.5 277.5 292.5 307.5 322.5 337-5 355.0 Lakewide Average Heat Flux 2 (gm-cal/cm -day) 120.37 336.77 510.81 553.65 1; 11. 03 298.92 211.36 86.38 39.21* 6.82 -7-71 -77.27 -99.71* -188.77 -23l. 09 -106.57 -815.50 Segment 139-32 371.02 515.06 612.35 502.73 327.22 239-66 136.93 89.79 55.32 10.79 -30.17 -52.6U -157.77 -203.09 _l0l.57 -813.75 Segment Specific Heat 2 (gm-cal/cm -day) 1 Segment 2 121* . 62 317.97 192.01 182.60 372.98 277 . 22 189.66 19.78 -27.36 -65.68 -80.21 -15^.87 -177.31* -238.27 -283.59 -121.07 -830.25 Flux Segment 3 -159.28 21.07 195.11 327.95 218.33 87.62 0.06 -61. 37 -111.51 -70.18 -81. 71 -91.52 -113.99 -211. 27 -259.59 -329.57 -738.75 K = 50 cal/cm2-day-°C 23 ------- TEMPERATURE VERIFICATION OF VERTICAL TRANSPORT EPILIMNION Northern Lake Huron o o cc D cc LU a. 23.0 9.0 -5.0 J 'F'M'A'M > TT N MD o o 111 CC. ? 8.0 < 4.0 cc LU a. uj 0.0 HYPOLIMNION l ' J 'A'S'O'N'D EPILIMNION Southern Lake Huron o o LU DC a. 23.0 9.0 -5.0 J 'F'M'A'M " o - 8-0 < 4.0 cc LU a. LU 0.0 HYPOLIMNION J 'F'M'A'M'.n J ] A'S'O'N'D1 _ji±i 5 <0 uj O j'F'M'A'M'j'J'A'S'O'N'D Figure 12. Vertical Transport Calibration 2k ------- current magnitudes given by Ayers, et al. [16]. The horizontal exchange between the respective epilimnia and hypolimnia Of northern and southern Lake Huron is set at 900 cm2/sec based on estimates of horizontal diffusivi- ties by Csanady [21]. Unfortunately there are no strong horizontal gra- dients here with which to calibrate these exchanges. Figure 13 shows the horizontal transport calibration for exchange between Saginaw Bay and southern Lake Huron. The marked gradients for chlor- ides, temperature, and total phosphorus can be used to obtain consistent mass transport coefficients which give a consistent agreement between observation and calculation. The temperature calculation which is begun after the ice has melted is quite sensitive to the magnitude and timing of the exchange coefficient since Saginaw Bay is shallow and the heat flux markedly affects the computed temperature profiles. This is balanced by the loss of heat via the exchange flow. Other estimates of the exchange flow are available, in addition to the Saginaw River advective flow which is inputted as a time-varying flow between 11,235 cfs (3l8 m3/sec) and l,56l cfs (kk m3/sec) in order to repro- duce the seasonal trend shown previously on fig. 2. The counterclockwise circulating flow from Lake Huron to Saginaw Bay is the major mechanism of this exchange. Danek and Saylor ]22] have estimated a typical exchange rate between the inner and outer bay of 3700 m3/sec (130,6^7 cfs) based on cur- rent meter and Lagrangian measurement during 197^• The Upper Lakes Refer- ence Group [23] approximates the annual average exchange from the inner to the outer bay at 800 m3/sec, and from the entire bay to Lake Huron at 5»000 m3/sec. Richardson [2U], using a sixteen segment model of Saginaw Bay, matched 197^ chloride profiles using an advective transport across inner and outer bay segment interfaces of 30^-686 m3/sec (10,737 - 21,229 cfs) during a thermal bar period and 1370 - 1750 m3/sec (W,388 - 6l,8lO cfs) for the remainder of the year. The magnitude of the counterclockwise cir- culation from Lake Huron to Saginaw Bay for this calibration ranges from an equivalent of U25 m3/sec (15,000 cfs) to 1,133 m3/sec (UO.OOO cfs) with this exchange flow increasing in the spring and continuing through the sum- mer as shown on fig. 13. Although there are differences in the magnitudes of the exchange rates estimated by various workers, the agreement shown on fig. 13 for three independent tracers indicates that the values used herein are consistent with observations. ------- SOUTHERN LAKE HURON SAG IN AW BAY u 23.0 9.00 LLJ Q. 5 ^ -5.00 I 8.0 CO LLJ 94.0 o o 0.0 ^,0.016 to D oc J 'F'M'A'M1J 'J IAT S CJ oc D oc LLJ O. J 'F 'M1 A1!^1 J ' J ' A'S'O1 N'D 20.0 0.0 -20.0 I 40.0 co" LLJ E 2°'° O _l o 0.00 'J'A'S'O'N'D J I I A 4 ll ILU J'F'M'A'M'J'J'A'S'O'N'D CL c/) O .0.008 0.000 J'F'M'A'M'J'J'A'S'O'N'D J'F'M'A'M'J1J'A'S'O'N'D < CO < 3 40,000 CD LL, z 20,000 J'F'M'A'M'j'J'A'S'O'N'D Figure 13. Horizontal Transport Calibration 26 ------- SECTION 6 KINETICS The interactions between the biological, chemical, and physical vari- ables of concern must be specified in a way consistent with the conservation of mass equations that are the basis of this analysis. The transport com- ponents of these equations have been estimated in the previous section. The method to be used in this section, which is derived from physical chem- istry, seeks to specify the rates of change of reacting species in terms of their concentrations. The application of these equations to essentially biological reactions has a long history [25] and is, in fact, currently a very active and fruitful guide for designing investigations and analyzing the resulting data. The principle concern in the analysis of eutrophication phenomena is the growth and death of photosynthetic microorganisms. The framework for their kinetic equations derives from the work of Monod and it is this formu- lation which forms the basis of the work to be discussed subsequently. GROWTH AND DEATH RATES The fundamental kinetic equation for microorganisms in terms of their biomass, X, expresses their rate of growth as a function of a growth rate, y, and a death rate, b: f=yx-bx (9) The growth rate is a function of nutrient concentration and, for photosyn- thetic organisms, light intensity, and both y and b are affected by temper- ature. In laboratory reactors the death rate is normally due only to endo- genous respiration, the maintenance energy reaction necessary to keep the cell functioning, while in the natural settings predation by higher order organisms can substantially increase it, as shown subsequently. Consider, first, the simplest situation with y and b constant, that is there are abundant nutrients and the temperature and light intensity are constants. The solution to the kinetic equation is X(t) = X(o) e(y~b)t (10) and exponential growth or decay of microorganism biomass is predicted. In fact, such behavior is commonly observed in both laboratory reactors and natural waters. Examples of sustained exponential growth for the Lake Ontario and Lake Erie phytoplankton populations have been documented and 27 ------- analyzed [26]. However, other modes of population behavior are possible since the growth and death rates are not always constants but can vary sub- stantially due to temperature, light, nutrient, and predation effects. Temperature Dependence ofJReactionJRate Constants The temperature at which a reaction occurs has a significant influence on the reaction rate. This is true whether the reaction is simple (ideal gas) or a complex chain of biological reactions. For the case of chemical reactions at equilibrium it is known from thermodynamics that the equilibrium constant, K , has an exponential temperature dependence. The usual formula is: e(1 d In K AH° ££ = _JL /-,-, \ dT 2 ^-"--L/ RT which upon integration and assuming that AH , the enthalpy change of the reaction, is constant, yields, AH° r_ K = K' e RT (12) where K' is the integration constant, R is the universal gas constant and T is the absolute temperature. For the rate constants, k, Arrhenius proposed the analogous relationship d In k E which leads to an exponential temperature variation. E is called the acti- vation energy of the reaction. Since the absolute temperature scale is somewhat inconvenient, the Arrhenius temperature variation equation can be recast in a more useful form. If k(T) = k' e-E/RT (HO and T = T + (T -20.) where T is temperature in centigrade and T = 293.l6°K then Eq. (ik) becomes: (T -20) k(T) = k2Q 0 C (15) with E/RT k2Q = k' e- 20 (16) 28 ------- + E/RT?n 6 = e+ 20 (IT) where the approximation (l + e)~ =l-e for e « 1 has been used. The normal range of 6 for chemical and biological reactions, over the range of interest (5 - 35°C) is 1.01 to 1.15, corresponding to an activation energy of 1.7 to 2k kcal/mole. The temperature dependence of biological reactions is often reported in terms of Qio, the ratio of the reaction rate at 20 C to that at 10 C. It is clear from the definition of 6 that Qio = 910. Thus a Qio = 2 implies that 6 = 1.072, a common value for biological reactions. The exponential temperature dependence of algal growth and respiration rates is clearly seen in fig. 1^, a plot of log \i and log b versus T. The sources of this data have been presented previously [27]. A detailed study of marine phytoplankton growth rate temperature dependence has been presented by Eppley [28] which indicates that the maximum growth rates vary with 9 = 1.065. It is well known, however, that a continually increasing growth rate with temperature is not realistic and, as higher temperatures are reached, the growth rate abruptly stops increasing and begins decreasing usually more sharply than it increased [29]. This effect can be important if species- specific calculations are being made. However for biomass as the dependent variable, the growth rate of an aggregration of species continues to rise until a maximum is reached at which no species can function. This is clearly shown in Eppley's fig. 7 [28] for which there exist species that can grow at maximal rates to beyond 25°C. Since the maximum temperatures reached in Saginaw Bay do not exceed this value, the decrease in growth rate due to high temperatures is not included in this calculation. Light Dependence For photosynthetic organisms, a relationship between growth rate and incident light energy is to be expected and this dependency has been studied quite intensively. However, until recently it is not growth rate that has been measured but primary production: the rate at which either Oa is evolved, or C02 is assimilated. If the carbon synthesis reaction of algae is taken as equivalent to growth, which is correct for carbon as the measure of biomass, then the primary production rate is a measure of the growth rate. This assumption can be inaccurate'for short term experiments, especially if environmental conditions are markedly varied during the measurement or for different measures of biomass. However, it provides a convenient starting point for the analysis. Let P(l) be the rate of primary production and P be the observed maxi- mum rate of primary production at high light intensity. Further assume that the biomass of the population is constant throughout the measurements as light intensity varies. For this situation a number of expressions have 29 ------- SnON330QN3 HlMOdE) 0) Si -p 05 JH 0) ft s • 0) Ti -p ri (L) O £1 •H -p -P n5 O Jn -P •H ------- "been proposed that relate P(l)/P to light intensity. The original sugges- tion by Tailing [30] is: m P(I) = P (l/Ik) (18) m where I is related to the slope of the photosynthesis-light relationship jfi low intensities: L- - 1 (dP) k m I=o This expression predicts a continuously increasing rate as intensity in- creases. However, it has been observed that at higher intensities the rate decreases. An expression with this property, proposed by Steele [31] is; =e (20) max s which reaches a maximum at I = I . As has been shown [27], this behavior is S observed and the shapes are comparable to eg.. (20). The relationship between I and I is easily found from eq. (l9)5 namely I = e I . Although these K S S K. expressions are somewhat different, it happens that for applications where depth-averaged primary production is required, they produce nearly equivalent expressions. The light intensity in a body of water usually changes with depth as an exponentially decreasing function of depth. Thus -K z I(z) = IQ e e (21) For a particular volume segment of depth, H, for which the biomass is uni- formly distributed in depth the average primary production and, by inference, the average growth rate is calculated from the expression: P H =r=/ P[l(z)]dz (22) m o where f is the fraction of daylight, the photoperiod, and r is the reduction factor due to the non-optimal light distribution. But from eq. (21): dz = - dl/K I (23) so that; 31 ------- P(DdI The evaluation of this integral is straightforward for both expressions of P(l). For eq. (l8), the average yields: f n X I where ^ = l(o)/I and ^ = l(H)/I . For eq. (20), the average yields: o K- o ^ n r = FIT e ~ e e where a = l(o)/I and OL. = l(H)/I . A direct comparison is possible since O S il S I = e I . For depths at which aR and ^ •• 0 the comparison is shown below where f/K H = 1 for convenience of presentation: I /I Tailing Eq. (25) Steele Eq. (26) O S 3.0 2.80 2.58 2.0 2.39 2.35 1.0 1.73 1.72 0.5 1.11 1.07 0.25 0.6U 0.60 The differences are quite small with the effect of decreasing primary pro- duction in Steele' s eq. (20) amounting to less than 10% for the highest incident intensity. It is also interesting to note that for either expression the difference between normalized surface intensities of 3.0 and 2.0 is small indicating that changes in I when the surface intensity is large have only a small s effect. However the converse is true for small I /I where the reduction is o s almost proportional. This is confirmed in section 9 which illustrates the sensitivity of the solution to I . In practice the measured incident solar S radiation is the total daily flux: I . Since this includes the dark period as well, the mean daily radiation intensity is l(o) = I /f. This is the cL v quantity used in evaluating the light reduction factor (see Table 32 ------- Nutrient Dependence The nature of the dependence of phytoplankton growth rate on nutrient concentration is a topic for which a large "body of experimental information exists. For this investigation the principle nutrients of concern for Lake Huron and Saginaw Bay are inorganic phosphorus and nitrogen. Recent inves- tigations of the growth kinetics of single species in chemostats have concen- trated on the dependence of growth rate, y, as a function of internal cellu- lar concentrations, q, of phosphorus [32] and nitrogen [33]. For investigations of single nutrient limitation of algal growth, the following expression has been found to apply to observed growth rate y fe — r where y' is the theoretical maximum growth rate at infinite cell quota, q is the internal cell quota in units of mass of nutrient per cell, and q is the minimum cell quota for that nutrient. Thus the growth rate is a saturating function of the internal "available" nutrient concentration q - q . The external concentration, S, together with the internal concentration, deter- mines the cellular uptake rate of the nutrient, v. For a specific internal concentration the relationship of uptake to external concentration is found to be: (28) a Michaelis-Menton function with half saturation constant K . m In order to examine the implications of these equations, consider the situation that occurs at steady state. For this situation an equilibrium is established between the internal cell quota and cell growth so that : v = yq (29) and nutrients are assimilated only insofar as they are required for cell growth. For this case, it is possible to express cell growth rate as a function of external nutrient concentration [3k]. Using eqs. (27), (28), and (29) to solve for q yields: m s (30) where "V " rhr (31) Ku V m 33 ------- y'q K mo m (32) Thus if these parameters are in fact constant, the Monod theory applies. However, it has been found that V varies inversely with q, i.e. more rapid nutrient assimilation occurs for small internal cell quota, and, therefore, the behavior is more complex than a purely Michaelis-Menton expression. For example, for phosphate limited Scenedesmus, the uptake velocity is found to be [371 V S K. V = m X K + S K. + i (33) where i is the internal nutrient concentration of total inorganic polyphos- phate and K. is a half saturation constant for this dependency. For this type of behavior the relationship of growth to external nutri- ent concentration is no longer exactly given by eq. (30). However, if K is S defined appropriately, the differences are of no practical importance [36] and eq. (30) applies as a very good approximation. This is illustrated in fig. 15 which compares eq. (30) to that which results from using the cellular nutrient expression for growth, eq. (27); the cellular and external nutrient equation for uptake, eq. (33) with i = q - q ; and assuming cellular equili- brium, eq. (29). The difference is of no practical importance. However, the Monod behavior occurs only if eq. (29) holds,which essen- tially specifies that there is no dynamic luxury uptake. Rather the uptake of nutrients is occurring in quantities sufficient to meet the cell quota at that growth rate. Thus depending on the conditions of the experiments or in the prototype, Monodfs theory may apply only approximately, and only for conditions approaching equilibrium for the internal cell quota. An estimate of the time scale for this condition to be reached, based on a dynamic per- turbation analysis [36], indicates that it is at least 1/U y where y is the non-nutrient limited growth rate of the population. Thus, except for short-term laboratory growth rate experiments, it is expected that cellular equilibrium is a reasonable approximation. The major difficulty with Monod1s theory of microorganism growth as applied to phytoplankton is that the variation of cell stoichiometry is not taken into account in the uptake expressions for nutrients. The problem is compounded by the lack of a clear choice of the proper biomass or aggregated population variable for a natural assembledge of plankton [36]. From a practical point of view the population variable for which a sufficient quantity of data exists for the Great Lakes is chlorophyll-a and the appro- priate stoichiometry is the nitrogen and phosphorus to chlorophyll-a ratios. It is well known that these ratios vary considerably with external nutrient concentration and past population history. Large ratios correspond to excess 31 ------- 1.0 0.8 0.6 I 0.4 0.2 0 0.1 MONOD THEORY CELLULAR EQUILIBRIUM THEORY 1.0 s, jug P04-p/i 10.0 Figure 15. Ratio of growth rate to maximum growth rate vs. external phosphorus concentration for external phosphorus concen- tration for Scenedesmus jsp. (37). rn'rn = 1.33 day"1; qo = 1.6 f-mol/cell; V^ ^4.8 f-mol/cell/hr; K = 18.6 m m yg PO^ - P/£; K± =-0.73 f-mol/cell. (f-mol = ICT1 5 mol PO^-P). 35 ------- nutrients and small ratios correspond to that nutrient limiting the growth rate. Thus the choice of the relevant ratio can be made with the situation of interest in mind. Since the population to be discussed subsequently is primarily phosphorus limited, the stoichiometry chosen can reflect these facts. The operational consequences of this choice is that the population stoichiometry under non-limiting conditions will be underestimated but the maximum chlorophyll concentrations under limiting conditions should be correctly estimated. Hence there is a tradeoff between a probable lack of realism during a portion of the year versus a correct estimate of population chlorophyll during the period of nutrient limitation. Since this is usually the critical period, and most questions to be answered are usually sensitive to the maximum population size, this choice is a practical expedient. A more detailed discussion of these issues, together with tabulations of the experimentally determined ratios is given elsewhere [37]. What is im- portant to realize is that the kinetics which finally emerge are essentially empirical since they are applied to natural populations vith chlorophyll as the aggregated population variable whereas their basis is derived from single species experiments. APPLICATION TO BATCH KINETICS Let P be the phytoplankton chlorophyll concentration and a , a p, etc. be the stoichiometric ratios of nitrogen, N, and phosphorus, p, to chloro- phyll. The rate of assimilation of inorganic nitrogen isi then a.^ GpP where G is the population growth rate and GpP is the rate of increase of popula- tion chlorophyll. The assimilation rate of phosphorus is a pGpP, and so on for all the constituents of the population. The kinetic equations which result from these considerations are : where D is the endogenous respiration rate, Si is the dissolved silica con- centration and a is the silica to chlorophyllstoichiometric ratio of the population. For this application to batch kinetics recycle has been neglected. As shown subsequently it is of prime importance for the actual situation in the Great Lakes. An application of these equations has been made for a series of batch phytoplankton growth experiments using a natural assemblage of phytoplankton from the estuary of San Francisco Bay [38]. This population is exclusively 36 ------- nitrogen limited. The calculation of the maximum growth rate for the popula- tion rate is based on the temperature and light intensity used for the exper- iments. As shown previously, the effect of temperature on algal growth and respiration is well represented by an exponential relationship below the optimum temperature. The effect of a non-optimal light intensity is to reduce this growth rate from its maximum. If it is assumed that these effects are multiplicative, it follows that: T-20 (35) and that : L - K6T-2° (36) Note that the depth-averaged form of the light reduction equation is not used since the reaction vessel is completely illuminated. A control and two different initial conditions for the nutrients, 0.2 mgN/£ and 0.5 mgN/£ were examined. The results for these experiments together with the calculations are presented in fig. 16. It is clear that the limiting nutrient is inorgan nitrogen since its concentration is calcu- lated to decrease to below the half saturation constant, K „, as the algae grow to their peak. The behavior of the phytoplankton biomass and nitrate nitrogen are well represented by the calculations. The uptake of dissolved silica is less well represented and the silica to chlorophyll ratio repre- sents a compromise for the observations. The uptake of phosphate is not in agreement with the observations. The phosphorus continues to decrease beyond that required for the growth, as indicated by the decrease of both algae and inorganic phosphorus during the later portion of the experiment. This luxury uptake cannot be explained in the terms of the Monod theory and constant stoichiometric coefficients, and, as pointed out previously, the variation of the stoichiometry of the microorganisms during short term experiments is perhaps the most frequently encountered effect which violates the assumptions of the Monod theory. Nevertheless the predicted behavior with respect to the limiting nutrient is reasonable and supports the use of these kinetics for calculation of changes in chlorophyll as a function of nutrient concentrations. ZOOPLANKTON KINETICS A major factor in the reduction of phytoplankton biomass after the spring bloom in the Great Lakes is the predation pressure exerted by the herbivorous zooplankton. In order to quantify this effect and relate it to the magnitude of the phytoplankton and zooplankton populations present it is necessary to develop an additional set of kinetic relationships. The basis for these equations are not the substrate-microorganism formulations appli- cable to dissolved nutrients and bacteria or algae but rather the relation- ships that have been developed to describe the behavior of larger predatory organisms such as fish. The principle difference is the mode of feeding. 37 ------- I^U I90 _J > 60 Q. O DC 0 i 30 o n 0.15 LU ^ 1— 0) lo ~> 0.10 O or 0 ^ T. CO fe g 0.05 O Q- n ' Hi. " A- /f O ° i i i i i i 012345 TIME, days DX»rx\ THEORY O CONTROL A +0.5 mg N/l T ^.n_ - - - 0_ , \| ? fi ', 1 0.6 Oi E z LU 0 0.4 DC h- LU < 02 DC 1- z o 0) . _ E 15 - (N 0 CO < 10 -i CO Q > 5 _J 5 0 - \ 1 \ \, \ kA \ * O jOSs».D^^O i i 01 2345 TIME, days _ ^TTI — \ y1 — — \ \ 9 \ i ^... iii i 11 012345 TIME, days 012345 TIME, days Figure l6. Application of algal growth and nutrient uptake equations (30 to batch kinetic data 38 ------- Phytoplankton are the prey and the predators are the herbivorous and omnivor- ous zooplankton. The classical equations of predator-prey interaction are those of Volterra [253 which, for phytoplankton-herbivorous zooplankton interactions, take the form: dZ = (G-Z (3T) with the growth rate G _ , given by: /i-L G = a e C P (38) where Z is the herbivorous zooplankton biomass, a is the zooplankton/ 1 ^-T phytoplankton stoichiometric ratio which, as in this case with zooplankton biomass in carbon units, corresponds to the carbon/chlorophyll ratio of the phytoplankton. The interaction coefficient £ C can be thought of as a O specific filtering rate C , with units &/mg C-day corresponding to the spe- & cific (i.e. per unit biomass) filtering rate of the zooplankton population, and e, the assimilation efficiency. For raptorial feeding these interpreta- tions do not apply and the coefficient must be regarded as empirical. The loss rate, D , is due to both respiration and higher order predation. ZiJL Growth Rate The filtering rate defined above varies as a function of the concentra- tion of the prey, the size of the grazing organism, and the temperature [39]. These effects are quite significant and are taken into account using the available data to suggest functional forms and the range of the parameters that are reasonable. To relate these terms to the more classical analysis of zooplankton feeding and growth, consider the ration, R, the weight of food consumed per animal per unit time. Investigations of the feeding of crustacean zooplank- ton indicate that the relationship of the ration to increasing food concen- tration is to increase in proportion to the increasing but small food concen- trations but then to level off and reach a maximum, R , as food concentra- tion continues to increase. This type of behavior, observed in the feeding behavior of fish by Ivlev, can be described by the equations [39»^0,4l]: R = Rm (1 - e-5P) (39) In terms of the growth equation (38), this suggests that the filtering rate is decreasing as the food concentration increases. If a hyperbolic function is used to represent this behavior as done previously [29], then the ration changes as 39 ------- C' P K mg where C' is the maximum filtering rate (A/animal-day) and K is the half gm mg saturation constant for filtering. By matching the maximums and the initial slopes of these two expressions the relationships: 1 V ' 5Em are derived. Table h, adopted from Sushchenya [39] illustrates some repre- sentative values. The value of the half saturation constant varies widely with lower values in the range of 1-10 yg Chl-a/& and appears to depend strongly on the species of both phytoplankton and zooplankton involved. The hyperbolic dependence of the specific filtering rate on phytoplank- ton concentration is illustrated in Fig. IT- The data from Richman [12] for Diaptomus oregonensis feeding on Chlamydomonas and Chlorella is well repre- sented by eq^i (10) with K = 10,000 cells/ml corresponding to an estimated K = 8 mg wet. wt./£ (11-32 yg Chl-a/£). mg The relationship of the ration to body weight of the animal follows an equation of the form: R = a W5 at constant food concentration and temperature. A review of the available values for 3 indicates that it varies from a low of $ - '3.6 to a high of 3-0.9 with the higher values predominating [11]. This suggests that the ration, defined per unit zooplankton biomass, R/W, is less dependent on the absolute body weights of the population since: f=aW3-1 (11) and 1-3 is in the range of 0.1 to 0.1. For a 10 fold increase in W, the pre- dicted change in R is a factor of 3 to 8 increase whereas the change in R/W is only a 21 to 60$ decrease. Thus for a formulation that aggregates the zooplankton population into a biomass concentration, the specific ration R/W is the useful parameter, since it is closer to being constant with changes in body weight. This useful fact gives some support to the validity of aggre- gating the zooplankton in terms of biomass rather than as individuals, a pro- cedure which is, as with the phytoplankton, a practical expedient Specific filtering rates have been summarized [27] arid vary in the range 0.1 - k.O &/mgC/day with the majority of the rates in the vicinity of 1-2 £/mgC/day. 10 ------- "ON 00 ( i CO EH 3 EH CO 3 o o H tSJ I • __^- JV1 3 9 EH cd bO ft =«= H 0 bO i bO -P S cu W U bO 6 - Sb 0? 0 a o? o? cd •d 1 •H s a JuJ^ o? • Jj) JJ -P 0) > ^p E B _O jj pi 4^ PH OJ ! bO 01 !>5 cd •d H cd .H TO a 0 -p £3 0(3 H Pi o CQ ft OO O "CO LA H _=r \c H i- . • o • • • j" H VO H 00 ON O OJ •f- 4- OJ LA i — 1 t°^ tjcn LA t1 — t— O LA 00 OJ O O LA r- -3- 0" . f ON -=f O O H 00 ) H O O 0 0 00 0 OHH OO 0 00 LA IT LA \ H t- OJOJHLA tm un 4- -f- OO IT \OO LAH VO OOOO O OOO HOJ OO H o dod ojo o OH 0) CQ 0) bO q bO H 0 H 0} o i •H CC cd 3 CQ i — I CD i — 1 i — 1 ft ft >PO) -HO) CU OO O ^t H ^ !H CQ CQ •HO Cd O O N N JH H § H H -P -P cd x\| 3 x! x\| -H -H > 0>0 QO 0 S3 ^ fx a •H cd CQ q CQ •3 03 -H -H CQ CQ cd a a H SH s C CQ CO CbO fl -P rClo S -HbO 03 -p3s,bO ft ft 3 fn ftcd jfHBH fto ft cd cdk -p CQO 0cu ^ >H o p cdH cd o -H^I ^ OH -Hl> ^ ft i) > (~°\ p is Is '&§. cd cd O H -H H H xl 0) O bO ?H CQ d O N •H H -P CQ ft -H ^ o a ------- I II I L I o o CN oo CD CN q csi q oq co «-' c> c> CN O E; O co O I r- O O T~ 00 x: § z o a.: h; 8 s z: C) r^ C) LLJ CO •H CO a (D a <", bO <1> C\J o § * •H n a >\| rH erf •H H a - cu . M •H 0 O •H -p cd 3 co •H j3 ca H H 0) O O O O f\ O (50 a erf a •H a erf Aep/\|Buume/\|iJU ' DNm3JL~lld ------- The temperature dependence of the filtering rate has been summarized [27] and the results indicate that, in contrast to all other biological rates included in the kinetics, the dependence is linear with temperature, with a zero filtering rate at 0°C a reasonable simplification. Thus the specific filtering rate is specified at 20°C and multiplied by T/20°C to account for its temperature dependence. The assimilation efficiency, e, has been reported in the range of hO-90% [4U], The efficiency is the fraction of the food ingested which is not excreted but is used for growth and metabolism. It has been observed to de- crease with increasing ration [39] and increasing food concentration [k3]- Since ration increases with food concentration it seems reasonable to incor- porate this effect as dependent on food concentration using a hyperbolic relationship of the form: e=eK /(K +P)by analogy to the grazing de- pendence with K as the half saturation constant. me The result of the above considerations is that the growth rate of the herbivorous zooplankton, G „, grazing on phytoplankton at concentration P is of the form: G = app e(P) C (P,T)P (15) L Lr g where me and mg The parameters to be specified are the maximum grazing rate at 20°C, C : gm the grazing half saturation concentration of phytoplankton, K ; the maximum assimilation efficiency, £ ; and its half saturation constant, K ; and the zooplankton to phytoplankton stoichiometric ratio, a . OJr Death Rate The components of the death rate included in this formulation of herbi- vorous zooplankton kinetics are the loss of biomass due to metabolism as measured by respiration, and that due to predation by carnivorous zooplank- ton. The respiration rate of zooplankton as measured by their 0 consumption has been found to be a strong function of both organism weight and tempera- ture [^5]. The dependency on organism weight is analogous to that found for 43 ------- grazing rates, eq. (^3), with the exponent in the same range. Thus the spe- cific respiration rate, the rate per unit biomass rather than per animal, can be expected to be more nearly constant with respect to organism weight although some variation has "been found [^l]. For organisms from temperate waters that rate varies from ^.6 to 2.3 y£0^,/mg dry wt./hr. for a 10 fold change (0.1-1.0 mg dry wt. /animal) in organism weight. The temperature variation of the respiration rate is an exponential function with 0 found to be in the range of 6 = 1.060 to 1.120 as shown in Fig. 18, a plot of the log of the ratio of specific respiration rate at T °C to that at 20°C. The legend, source, and references for these data have been given previously [27]. Thus respiration loss rate can be represented by the equation: RZ1 = K3 93T"2° (U8) where R the respiration rate in per day units, is available from the spe- /il cific oxygen consumption rate if the fraction of the dry weight that is car- bon and the respiratory quotient (RQ = ACOp produced/AOp consumed) are known. For reasonable values of these ratios (hO% C/dry wt. and RQ = l) the observed rates are in the range 0.06 to 0.2 day" [^l]. The observed values of the zooplankton respiration rate, K are somewhat less than the equivalent phy- toplankton respiration rates which is consistent with the observation that specific rates appear to decrease slightly with organism size or weight. Other experimentally observed effects which have not been explicitly included in the kinetics is the possible existence of a phytoplankton con- centration at which grazing ceases [^6] and the effect of nocturnal grazing as opposed to continuous or daily average grazing [17]. Perhaps the rather large range in observed parameters for the present paramerization reflects these effects as well as the specifics of the grazing experiments themselves, e.g. short versus long term experiments and starved versus normal zooplank- ton. The other major component of herbivorous zooplankton mortality is pre- dation by the carnivorous zooplankton population. The importance of carniv- orous grazing pressure in Lake Ontario is evident from the calculations of Thomann et al. [U8]. An interesting example of this effect has been ob- served and quantified [^9] for Daphnia grazing on phytoplankton, measured as chlorophyll, and being preyed upon by Leptodora. The relevant constants derived from the data are: a.™, e C = 0.025 £/ygC/day; zooplankton res- Cr m gm piration rate = 0.088 day" ; and Leptodora filtering rate of 9.5 m£/animal/ day, all of which are within reported ranges for these parameters. The for- mulation of the carnivorous grazing adopted in this analysis is entirely classical [25] and corresponds to the Volterra predator-prey formulation without saturating effects. That is the death rate by predation takes the form C 0(T)Z^ where the grazing rate is linear in temperature and Z is the carnivorous zooplankton biomass. ------- LO CN O CN o o cc Z) QC LLJ Q. LU h- q CN LO • o CN o 3 0Q3 IV 31VH NOIlVdidSBd § •H -P O c Q) IT— bQ OJ ?H (U 0) co' -P m 0) C O •H a -P 0) Oi O ?H fl 0) (1) •p ft oj 0 £H TJ •H ft C) -P 0) 03 H H !H O 0) ^ •P ft O 3 -P H ft H -d O Oi 0) O -H -P N -P 03 a o ro 0 H ------- The growth and death rates for the carnivors in turn determine their pop- ulation size: dZ d!T= (GZ2-DZ2)Z2 The growth rate follows from the filtering rate and an assimilation effi- ciency e: GZ2 = £Cg2(T)Zl The death rate is the sum of respiration losses and an empirical constant, K , which accounts for higher order predation so that: rp Of) DZ2 = VlT + K5 At this level of resolution Thomann et al. [hQ] have shown that, at least computationally, higher order dynamic predator-prey equations do not materi- ally influence the dynamics of the lower members of the food chain on an annual cycle. NUTRIENT RECYCLE The recycling of nutrients, that is, the transformation from unavail- able particulate and soluble organic forms to the available soluble inorganic forms, is the critical step in completing the cyclic nutrient pathways in aquatic systems. The purpose of this section is to present evidence that the rate of this recycle reaction for phosphorus in the lower Great Lakes is re- lated to the size of the phytoplankton population. It is also shown that under simplifying assumptions the rate of recycle, together with the growth rate of the algae determines the fraction of the total phosphorus concentra- tion which is present as either plankton, or in unavailable or available forms. The importance of phosphorus recycle is well known. If no significant recycle occurred, the plankton would rapidly deplete the available form, and the unavailable form being generated by the algal metabolic losses and zoo- plankton excretion processes would build up and eventually account for all the phosphorus present, thus terminating the cycle. However since recycle does in fact occur, the balance between the three forms of nutrients is maintained. The observational and experimental investigations of recycling have been described by a number of investigators [50,5l]- The two major processes which contribute to the recycle are the predation by zooplankton and the metabolic losses of the algae and zooplankton themselves. The role of bac- teria in the subsequent transformation has recently been documented [52]. 16 ------- Normally, healthy algal cells are not usually attacked by proteolytic "bacteria but if the cells are deprived of essential nutrients and/or suffi- cient light the cells become permeable and soluble nutrients leak out. The phenomena can be quite rapid with up to QQ% of the cell phosphorus and 20% of the cell nitrogen being released in 2-3 days [50]. The remainder of the cell nutrients are in the form of particulate cell fragments. The phenomena occurs as the population is stressed, possibly declining, and using its cellu- lar constituents in its metabolism. In this report, the process is termed respiration, since it is most pronounced in dark conditions which character- ize the oxygen consumption (e.g. the dark bottle of primary production studies) and nutrient release experiments that quantify the rates. A nutrient release process also occurs during zooplankton grazing of algal populations. For example, during active feeding, Calanus retained Yl% of the algal phosphorus for growth and excreted the remainder, 23% as fecal pellets and 60% as soluble phosphorus. For nitrogen 27% was retained while 3Q% was excreted as fecal pellets and 36% as soluble nitrogen [53]. A simi- lar result for natural marine zooplankton populations has been observed where 60% of the total excreted phosphorus is in the -form of phosphate [5^]- Thus the result of algal respiration, mortality, and zooplankton grazing is to release nutrients in both soluble and particulate forms. A portion of the soluble nutrients are in the available form with the remainder present as organic compounds. KINETIC FORMULATION The detailed characterization of the forms of nutrients in natural waters: inorganic or organic, particulate or dissolved, requires extensive data that, at the low concentrations in Great Lakes waters, are difficult to obtain. Perhaps the most difficult differentiation is between detrital and phytoplankton-bound nutrient since no simple separation is possible. In order to characterize the recycle process and at the same time not compli- cate the formulation to the point of impracticality, it appears that the division of the nutrient into three forms: plankton-bound, available, and unavailable is a reasonable first step. The available phosphorus form is directly measured as soluble reactive phosphorus. A portion of the unavail- able phosphorus is measured as dissolved organic phosphorus. The total phosphorus is also measured. The formulation of the kinetics of recycle requires an equation which specifies the rate at which the unavailable nutrient is transformed to the available form. To be specific, let p , p and p. be the concentrations of total, unavailable, and inorganic (= available) phosphorus respectively. The concentration of phosphorus associated with a concentration, P, of algal chlorophyll, is a P where a is the phosphorus to chlorophyll ratio of the population. Similarly, if Z is the zooplankton carbon concentration, then a Z is the zooplankton phosphorus. PZ> Consider a situation in which transport and external sources can be neglected, i.e. a purely kinetic setting. The kinetic equations which des- cribe phytoplankton and zooplankton growth and death, and phosphorus uptake ------- and recycle, with the modification that a fraction (l-p) of respired and excreted phosphorus is directly available, have the form [27,^8] P = (G - D - C Z)P (52a) r r g z = (GZ - DZ)Z (52b) pu = pDpP' + p(CgZP' - GZZ') + PDZZ' - Kpu (52c) p = (l-p)D P' + (l-p)(C ZP' - G Z') + (l-p)D Z' - G P' + Kp (52d) 1 i g A Zj.rU where G , D are the epilimnion averaged growth and respiration rates for phytoplankton; G , D are the growth and death rates for zooplankton; C L L g is the zooplankton grazing rate; p is the fraction of respired and excreted phosphorus that is in the unavailable form; P' = a P and Z' = a Z, the phosphorus equivalents of phytoplankton chlorophyll and 2;ooplankton carbon; and K is the recycle rate of unavailable to available phosphorus, which is assumed to be first order with respect to p . In this notation total phos- phorus is given by: p = p. + p + P1 + Z'. For steady state conditions the derivatives are all equal to zero and either eq. (52c) or eq. (52d) yields the following relationship: K pu pi 7' (l+-£-)-^+-i + f-=l (53) P P PT PT PT For the case that the fractions of the total phosphorus that are either in the available form, p./p^, or bound as zooplan] small relative to one, eq. (53) simplifies to: the available form, p./p^, or bound as zooplankton biomass, Z'/p , are both where: "£ the dimensionless ratio of recycle rate to the growth rate - fraction unavailable product. For rapid recycle relative to growth or for a small p, the unavailable fraction excreted or respired, 6 » 1, and only a small portion of total ------- phosphorus is in the unavailable form. Conversely for slow recycle relative to growth or a large unavailable excreted or respired fraction, 6 < 1, and most of the phosphorus is in the unavailable form. Thus the dimensionless parameter, S, is the important characteristic of the kinetics which deter- mines the distribution of total phosphorus for the case that the available and zooplankton fractions are small relative to the algal and unavailable fractions. The magnitude of the recycle rates from various laboratory experiments are listed in Table 5. The range is 0.01 to 0.06 day"1 corresponding to half lives of approximately 12 to TO days. The temperature coefficients are within the expected range for heterotrophic bacterial reactions. For G = 0.05 to 0.2 day"1 which is characteristic of the summer average epilimnion values and p = 0.5 as an estimate of the respired and excreted fraction that is unavailable, the range of 6 is 0.1 - 2.5 corresponding to a range in p /p of 30% to 90%. The large unavailable fraction corresponds to a low recycle rate and a high algal growth rate and therefore, at steady state, a high respiration plus grazing rate, whereas fast recycle and slow growth result in the low fraction unavailable. It is probable that under this condition the available and zooplankton fractions become significant, the approximations p./Pm <<: 1 an(i Z'/Pm <<: 1 are no longer reasonable, and eq. (3) is not appli- cable. This suggests that p /p may not decrease as low as 30%. For these kinetic equations and assumptions it is also possible to cal- culate the algal phosphorus fraction and the chlorophyll a/total phosphorus ratio, P/P-,. The latter follows from the approximation: a pP + p - p and eq. (50 '• r^rrfr (56) PT apP ± ° The importance of the stoichiometric coefficient a is clearly evident in this equation as is the effect of 6. RECYCLE RATE AND CHLOROPHYLL CONCENTRATION The relationship, eqs. (50 and (55)» between recycle rate, K, the fraction of respired and excreted phosphorus that is unavailable, p, and the ratio of unavailable to total phosphorus suggests that the observed variations in the latter be used to investigate variations in the former. As mentioned previously no direct measurement of unavailable phosphorus is available since the detrital and algal particulate phosphorus are not sep- arable. However if only soluble phosphorus is considered then unavailable phosphorus is equivalent to dissolved organic phosphorus which can be esti- mated as total dissolved minus soluble reactive phosphorus, and the ratio p /p for soluble phosphorus can be calculated. Alternately if a phosphorus to chlorophyll ratio is assumed then the algal bound phosphorus can be esti- mated and a direct calculation of p p is possible with the additional assumption that Z' is negligible. ------- CQ EH 2 H \|_^ 0 o QC K EH H 1 f=3 @ S H § W EH W « >H i-q i-q <; EH S ^ H P? W H LT\ 9 EH D O $3 g co •H pj CO bO £ CQ •d y ,3 o •iH K 08 H H •H fa O 1 VD , — \| o O p-i 1 -d O P^ TJ rt O CQ -P CO bO g E ^ 1 1 O\ [— H H O O • • o o •H & CQ t i- on • jxj S CQ PI O -p c3 H ft -P CO a -p CO o o s 08 H H 0) £j CO 1-3 1 -=)• oo 0 • o + 1 _^- o CD &" o -p o cd ^H Q (0 O ^ o 1 fl 0 CO H ,0 CO •H ^ cd J; =te o\ o • H 1 J. o H t— o • 0 1 LTN H o o ^ o -p o CO 08 o -p S3 •H p 1 (0 o 1 co c— o • 0 1 oo H o o (0 -p p-J H Q o O •rl O +3 cd p-t w •H H! bD 1 cd H H <0 J_l o H ,a 0 -=t o o I 00 o cu o PH O II •d o „ o o H II H O 0 "5 O II cd H O p-1 1 0 PH W) (3 •H CO " •d a) Id o •d o o o •rl EH O «H O OJ 1 EH CD O ------- Both of these methods can be used to estimate p /p . This has been done for the various data sets for which the appropriate measurements are avail- able. The procedure is to average the epilimnion observations during the period of stratification for the years indicated. The well mixed basins, Western Lake Erie and Saginaw Bay, are analyzed for the periods employed for the rest of that lake. The idea is to conform to the assumptions of the simple analysis of the previous section, namely steady state and constant parameters, by using long time averages. Admittedly, this is rather crude but the results are quite interesting. The data used for the calculations are given in Table 6. Plots of the ratio of soluble unavailable to total soluble phosphorus and the ratio of estimated total unavailable to total phosphorus versus chlorophyll a_ are shown in fig. 19. The results suggest an inverse relationship between the unavailable fraction of both the soluble and total phosphorus and chloro- phyll. The exceptionally large Saginaw Bay value for the soluble fraction is probably the result of the influence of inputs which have been neglected in the simple analysis of the previous section. For the computations that follow the relevant plot is that relating total unavailable phosphorus to total phosphorus, consistent with the phos- phorus species considered in the theoretical analysis. The decrease in the fraction unavailable: from p /p =0.8 for the low chlorophyll basins, to p /p = 0.7 for the intermediate basins (^ 5 yg Ch£-a£) to p /p = 0.65 for the basins with higher chlorophyll concentrations, suggest that the recycle rate is influenced by the chlorophyll &_ concentration. This 20 percent change in the ratio of p /p over an order of magnitude increase in chlorophyll a^ takes on added significance when one considers that there is only minor variability in the data given in Table 6. For Lake Ontario, for instance, the standard error is within 1.0 - 8.5% of the mean values listed for the component variables of the calculation, total, dis- solved, and available phosphorus and chlorophyll ji, with an average of some 1,000 data points from four lakewide cruises used as part of the computation. That such a relationship should exist can be seen from the following reasoning: If the agents of the recycle reaction are heterotrophic bacteria which convert unavailable phosphorus to available phosphorus as a byproduct of their metabolic activity, and if the major source of carbon for the energy and synthesis reactions of the bacteria is the detrital carbon pro- duced by the algal respiratory and excretion reactions, it is reasonable to expect that the bacterial biomass increases as the source of this detrital carbon, namely the standing stock of algae, increases. Evidence that bac- terial biomass increases as chlorophyll a_ increases has been reported for a series of Canadian Lakes [58] and for Lake Huron [59]- Although the rela- tionships are different for the different sets of data, the trend is clear in both cases. Evidence from other studies [60,61,62] indicates that the seasonal trends of chlorophyll and bacteria, although not in perfect phase, tend to follow the same pattern. 51 ------- to w to >H <1 p. «^ £ » W i-q 0 rH O w K K 0 P to H O "" f^^ H 1 PM !>» O o3 d "CM Q) EH _o Qj oi ^ •H ft -P W w EH H .ft H ft O to i — i -^J" ' — • i — i <^ 03 --. O^ ~1 r^H "* — "" 0 1 1 on i — i 0) -~~ PH <=* H -H 1 -^ ,£1 .p .J- t>0 ?! O O 3- H 03 PH ^ O CD to K "oj --^ L-. PH o? rH • 1 -^ 03 ra -3- bO -p CQ O 3. 0 -H PH — EH P , , i — I ^~^ ' — i PH =^ rH 1 ^ 0} -=f bD -p O 3- 0 PH ^ EH * § M O O • CM CM CO on rH • o _-,. vo vo o t- H LA 0 CO . LA H 0 • t- LPv • _^J- rH LT\ • -^ -d" ^ — «. pq 13 0) •H O V, LA J" W t- CM ON 1 QJ H 0 ,M CO i-3 H t- >> • ON 03 > H P ON • O CM VD on H • o CO H t— 0 on t— LA o LA • LA LA CM • on LA • t— on • H CM ,. N pq u ^ •H £_, pr"\| 0) 1 • o 0 LA _* t- CM O\ 1 H 0 CO " H H t- >» ON 03 H R LA • O CM CO CM H O O CO O on ON vo o o * on on • CM LA • t— CO • CO H X N pq w 0 •H O £H LA -J" W t— CM ON 1 0) H O X\ CO 03 •> H H3 H t— f>> • ON o3 W rH P ON , [^ — H t- ON LA O • O LA t- O V£) LA t — O _^- CM H CM MD * O _;j. LA • CM on LA • LA . — * \|T* to O !H O 3 -3" t- W t- CM ON 1 1) H O n3 "CM t — ^ • ON 03 to H P H ON H LA on H O 0 on 0 cxj co VD o H o CM H CM CM CM ON • vo CM • "3" on ^—^ pq -2- !>5 O oi -=t t— pq t- CM 0\ 1 > H 0 o3 rH fl 'CM •H H bO t- >5 c^ ON o3 to H P C^ OJ r-H LA CJ rH O VG ON cj C3 M.) Q CO -^t1 . ^J- 00 • on CO CD • C5N ^j- • 03 rH , — . ^ O ^O •H CM 'H VO 33 CM "a o o j- H aj CM r^l t" — ^S o3 ON cd J H P _1 ------- CL 0* CL LU _J CO _J ^f ^f \| CL \| 0 CL 0 — 1 cc. o Q LU _\| O CO CO Q 0.8 CL o" CL _i 0.7 h- o H 0.6 0.8 O_ i O Q_ Q LU 0.7 O 00 CO Q 0.6 _j H- O OF; • EB • SH • C5 o/v • • WB SB* — 1 III • SH EB* SB* • ON >— • CB WB I 1 11 1.0 2.0 5.0 10.0 CHLOROPHYLLa, /ig/l 20.0 Figure 19. Variation of the ratio of estimated unavailable to total phosphorus and of dissolved organic to total dissolved phosphorus ratio with chlorophyll. See Table 6 for legend. 53 ------- On the other hand, it is also known that certain species of algae can metabolize dissolved organic phosphorus directly [50] in which case the quan- tity of unavailable phosphorus would tend to decrease as chlorophyll in- creases. Hence if either or both these mechanisms are active the result is an increased recycle rate as chlorophyll increases. Alternately, the decrease in the ratio of unavailable to total phos- phorus as chlorophyll increases could be related to a decrease in, p, the unavailable fractions respired and excreted. The mechanism is related to the fraction of algal phosphorus that is labile and quickly available (l-p) and that which is structurally bound and unavailable, p. In oligotrophic situations it is probable that a smaller fraction is labile and p is larger than in eutrophic settings where p is smaller. This suggests that p would decrease as chlorophyll increases. Based on eqs. (5^) and (55), it is not possible to distinguish between K increasing and/or p decreasing as chloro- phyll increases since they occur as a ratio (eq. 55). All these mechanisms are known to occur and influence the relationship between unavailable to total phosphorus and chlorophyll. The question is: how to modify the equation structure to account for the observations. A number of approaches are possible. Bacterial biomass can be included direct- ly as a state variable with a governing differential equation [103]. The problem is that in most cases observations of bacterial biomass are not available and the kinetic constants obtained from a calibration with unob- served state variables are likely to be quite tentative and uncertain. The inclusion of state variables which partition the internal algal pools of phosphorus is also possible [99] but again these cellular concentra- tions are unobservable and add to the uncertainty of the calibration, while also increasing the realism of the formulation. An alternate approach, which has the attraction of simplicity, is to establish an empirical relationship between recycie rate and chlorophyll. As shown subsequently this adds only one more unknown kinetic coefficient to the formulation and no unobservable state variables. For this reason this latter approach seems appropriate. With the data in fig. 19 interpreted as suggesting that the recycle rate is chlorophyll dependent with p constant it is nece:ssary that the func- tional form of the dependence be established. The relationships which span the expected dependency for the recycle rate coefficient are: First order recycle: K = K'(T) (57a) Second order recycle: K = K"(T)P (57b) Saturating recycle: K = K'(T) -—^-^ (5Tc) mr with conventional 6 temperature dependence for the rate constants K'(T) and K"(T). First order kinetics, which are the conventional formulations for the transformation of organic to inorganic nutrient forms in estuaries [63] ------- and previous lake models [U8] assume a recycle rate constant that varies with temperature only. Second order recycle assumes that the rate of recycle is proportional to the phytoplankton biomass present as well as the amount of unavailable nutrient. In laboratory experiments, pure cultures with bacte- rial seeding appeared to follow a second order dependency [56]. Saturating recycle is a compromise between these two mechanisms : a second order depen- dency at low chlorophyll concentrations when P « K , where K is the half J J jjj.,,5 jjjp saturation constant for recycle, and first order recycle when the chlorophyll greatly exceeds the half saturation constant. Basically this parameteriza- tion slows the recycle rate if the algal population is small but does not allow the rate to increase continually as chlorophyll increases. The assump- tion is that at higher phytoplankton chlorophyll concentrations other factors are rate limiting the recycle kinetics so that it proce'eds at its maximum first order rate. Two tests of these forms for the recycle kinetics have been made. The first utilizes the expected relationship between p /p and & = K/pG given by eg.. (5^)« The growth rate G is calculated using the conventional expres- sions and the results of seasonal calculations, [37,^8] and p = 0.5 is used for all basins. In addition it is assumed that 0 = 1.08 for this reaction. Using the information in table 6, it is possible to calculate 6 for each hypothesized recycle mechanism: T_?n , Q-L-^U First Order: 6 = ^-^ - (58a) T-20 Saturating: 6 = £~ - P+ (58b) P mr T_?0 TT"fi Second Order: 6 = ^-^ - P (580) and to compare the observed ratio, p /p , for this basin with the expected ratio: l/(l+6). The results are shown invfig. 20 for K' = O.Oh day"1, K = 5 yg CM-a/Jl, and K" = 0.008^3 day-1/yg Ch£-a/£ which appears reason- able from the calculations to be discussed subsequently. Consistent results are obtained only if the saturating recycle formulation is used to calculate 6. Neither first nor second order kinetics are appropriate since the obser- vations are not consistent with the expected theoretical result, namely that P /Pm = 1/1+6. Thus in order to be consistent with observations in the var- ious basins it is necessary to adopt a saturating recycle rate as the func- tional dependency on chlorophyll. The second test of this formulation is a comparison of seasonal calcu- lations and observations in the various basins which is discussed below. 55 ------- SATURATING RECYCLE FIRST-ORDER RECYCLE 0.9 0.8 0.7 0.6 0.5 - ON WB 0.1 0.2 0.5 0.1 0.2 6 6 SECOND-ORDER RECYCLE 0.9 0.8 0.7 0.6 0.5 0.5 1.0 • EB • CB >s» 0.1 0.2 0.5 1.0 2.0 4.0 Figure 20. Comparison of observed and calculated ratio of unavailable to total phosphorus for saturating (eq. 5&"b), first order (eq. 58a), and second order (eq.. 58c) nutrient recycle kinetics. ------- SECTION 7 DATA The credibility of model calculations is determined, in large measure, by their agreement with observations. Besides the obvious constraints that the model should behave reasonably well and predict general patterns such as spring phytoplankton growth, this is perhaps the only external criteria which is available to determine the validity and hence the utility of a complex eutrophication model. A comparison to actual data indicate if the approxima- tions used in the model adequately represent the real situation. With this in mind, a detailed review of available data for Lake Huron and Saginaw Bay is presented and from these data a set of aggregated data were generated for use in calibration. HISTORICAL DATA Prior to 1971» not much comprehensive limnological data had been gath- ered for Lake Huron, and those data which were available fell short of pro- viding the substantial data base necessary for water quality modeling efforts. Data for Saginaw Bay were even more scarce. One observer, reviewing histori- cal data for the bay, noted that "presently, the necessary data for verifica- tion (of water quality models) does not exist."[3] The data summary presented in Table 7 encompasses all of the major Lake Huron surveys which were available for review. One of the earliest surveys of Lake Huron was that undertaken by Ayers, et al. [l6] in the summer of 195^- This survey consisting of three cruises during which a few chemical para- meters were measured (Ca, Mg, Si02), but of prime interest are the measure- ments of current magnitudes and directions made using drift bottles. To date, this is still one of the best sources of flow patterns for Lake Huron and its applicability to this modeling effort has been discussed in relation to transport regime estimation (section 5). Drift bottle current measurements were also made by the U.S. Fish and Wildlife Service in 1956 [6k]. Other analyses of Lake Huron circulation are also available [65,66,67]. Commencing in I960 and continuing through 1970, the Great Lakes Insti- tute (GLl) of the University of Toronto conducted several surveys of Lake Huron [68]. These consisted of temperature, geophysical, meteorological, internal wave and synoptic surveys. GLI data reports [69-73] include com- prehensive weather information and lakewide temperature data. In 1965, the FWPCA sampled Saginaw Bay and the Southern Lake Huron tri- butary area [7^K The stations in the bay were sampled twice a month during the summer and fall of 1965. These data are available through STORET. Data from similar surveys made by the FWPCA during the period 1967-1970 [75,76,77, 78] were also reviewed through STORET. In addition, tributary measurements, 57 ------- HURON 1 K 0 pH( ^J ^ ^ O o H O EH CO H ^ W l_3 pQ 5j E-* id oj ^j p w cd 0) S w -p 0) rf TO ^ PU w T— t {B^ 0 0 •H • -P O cd F^H -P CQ >, O s bC ^ 0) bfl cd ^_\| tu £ o r^ o •H £_j (D PH OJ ^ •H EH 1 -P o CJ Jj O tJ •H a CO O o ft M > ^^ cd O W ** I •> !>5 " fl O CD 0) G JH !H (U ^ M in -P 3 cd cd o O. C. CQ 0) * £3 Pi Sj cd S 4^ EH -P '> J- os 1 o CO § 3 o a; •3 H a •H * s- , • t — CM -^1" t1 — LT\ OS »' — - H CO LA CM CM •^^ "^^ so co — • — -p c cu ^ ^j J3 O CD w H -P -p a -P 0) O 0 ^i -P 3 CH m •H cd n a w E CO .5 ^s cd i~n H a -H •H bO >» acOPQ -N ^- H 'v-^l H VO H ITS os i H ^^. MD 1 — " 1 O 0) « " fl ft \|>5 W a) a -P -H Jn 0) -H O cd -p > G ft -H W " -P ^1 f3 W 0 ft CO ft pJ -P " G >i O O -P CQ " o o -H g O 4^ H O ^ O Cd cd O CO CO 1 LA rH H (_I\| O (U •3 H a •H cd a — * o "~* H CM -^ "^ CM 0 H ° H OS "CM H^O CM CM -^ •^ H VO H ~ ^o LA 1 vo H i_^ O co •H bO 0 i>> 0) cd & pq ^ — -. CM CM ^•^ H 0 H OS •> LTS H t— CM O H Hj-H £ co H i_^ O 0 •a H a •H cd a , * ITS H LTS CM ^ H H OS V.O " OS •> O H LA H CM • \ 0 U3 H £ LT\ H l_I} e> § •H bO ° &> cu cd O PQ x — x t — '— ~ CO LA «H H co ^ MD -^. O — os t— H ro H « " t- \\ CM t— Os H — ~ LA H 1 ~] 0 H 0 UA H CM ' „ ^ ^t CO ^ LTS rj- 1 VO H H 0 § -ti H •H a > ^i ro CD cd o fi & m & u ~H CM "^^ 00 MD VO CM -^ CM — CM VO Lf\ H OS •> « H OS CO H H J" OS — — 58 ------- -p a o o — t— EH rrt CD H CO o3 CD s CO 0) -P §0) CO PH CO TH C o o •H • -P 0 03 & -P CQ £>j O fl 3 bO o3 H ,3- OO -^. VO -•-. H H « » ON t— CM H -3- OO £ H O oi •H bO O r"a °™ Q CM CO •\ LPv - CM ON t— i — 1 •* ^~* j- o CM CM vo ON ^ — — o P 1 CQ o a * -P O m r5 "rl O .M -P S ft o3 d ** " p Woo g fl ft 0) " M C H a3 0 O ft -P CO rX -" o3 cd O ^ H PU -P ft O CM H ^J ^ & E 0) £_( •H CD "d Id H LTN ON H CO ^ « -H S H 0 P bO CQ O ^H * O O •* 0 " " PH CQ 1 « O CO [^ f^ W 1 O O VO fs CQ ^ _jj) n3 * 0) ft 1) -H -P & O « O O CU P CO c— <3^ u PH g Is 03 fl •H a? o? 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C CQ " •o -H (U m " c H a o ^ O o5 Tj O o a ,y JH W H H cd O " cci ft " O >5 Cd P « " S cd " -H O H •H Ti Pi O " H fi -H W H 0 43 "• " i>3 0 SH >3 -t "43 OJ 3 p. 0 bD ft CQ P -H CQ S O t— ON [^ M O O (U £_\| «H 0) -P iM O ON -x--. \£» OJ ON H H 1 00 "\ H H — £ ft [ •> N j>^ ,-{ ^ P nj 1 •H -H m Q ,0 M H ^! cd p " rM S cd >» bO p Sn • "•HO J- M !> O ft -H " O-l p H •> o O " ft -d "1 gf3 4- CM 000 EH O CQ S OJ dj P, 0 Q) ^ •H CU -g -^ W H ON O OJ t — ~^~^ ON t — H 1 c— OJ " — t— — 60 ------- f H t) -P a o o t— H EH CU H CO cd CU s CQ ^ CU -p i a PL, CQ <^j c] 0 0 •H • -P O a} s -p CO O c! 0 O o •H fn CU Pk cu 1 " 1 CO ft-H O " CM !H S -p P U O O -P 3 « bO B CO -H •d !>j JH 1 H •> £3 -p O <" •> O JH O -rl MHO O O C "SO H -rl H O •> H H " " CQ O !>j 03 >> -»• • fl .p ,kj ifO O O - -H H ft PU CQ -H •H fd CO O ,d "H £t " S H o P ** O ^ I o3 O k >j H O « 4^> CU 3 4J ^i O O CU CO -p -H O M B S O O H H O O s •H CU -P r^ SH CO H H CO 0 H ON LA H 1 H H LA • > •> 1 H ft -rl \|>J "> CIS g 40 +> O -P CU O -H B CU -p ?J a s >O -H •> CQ •> a H £3 " a ^ O «3 1 «M f-i O O Ai m O O H H M -H «H O « OJ B CO -H O !>» H •> -H W J" H O •H -d ft O 0 ^3 -H PH O ,Q •> •> CQ O )Li !>, •> -* S CU p -p O O O CO -P -H O CO -H H O H H O O £ •H CU -P M W I — 1 t— 0 \ t— 0 ON H H 1 ON CM ON 1 •H " " a * -p H co ^ " -^ b 2 1 M K fl CO m ft -H ft t^j rH O ""C^ B " td k ri !>s ^ O ro «> +J H H B T-I o3 ,£ d 1 !> 00 <" 'H •> -H O +3 t>3 « -P B o o •* n! P a o « » 'd CU CO -H N C M Vi O o ai « •H 0 ft H fl C CO CQ O O O " fl ,Q -H « •* aJ «> M -p O O M a3 a3 cd p a, .p u OH VO CM O -P CO nJ »S T3 & O CO Pi (H 0 fl 03 CU •H -p j CO ^j cd cd cu ccj CO A tS H 0 t- ON H 1 0 h ft !>> C f-i O & -P •H 03 in H ft-H ^ a ed CQ CQ H o3 H r"> " ft -P O -rl CO ^ t> O O -H -rl H -P -P ^! o o3 O S ^H ^o J- H o 0 0 £_l -H 0) 4^ rM fl TO Co o H •-- t- CM ON H H 1 ON H 5 « \| CM CU CQ O M 0 -rl P « fl CO -P £> P I CO -P « £n -H H m CU > 03 O ft -H -p B a -P o -P P « TJ " O Vi O -P O O -H •> H ^ a « O ^i rH § -p cd •H T! H ca o ,a M O ^ " O cu 3 o ,c! CO -P Q ft IS H O O 0) £_l •H ------- coupled with the lake surveys [79-85] and combined with USGS flow data, can provide mass loading information. In 1968, the Canada Centre for Inland Waters (CCIW) commenced synoptic surveys of Lake Huron. Their Limnological Data Reports [86,87] provide data from cruises in August of 1968 and September and November of 1969. Two cruises in 1970 were made during May and October. These surveys included data for several parameters and the spatial and depth coverage of the lake is extensive. Another 1970 cruise was conducted by the Great Lakes Research Division of the University of Michigan [2] concentrating mainly in Saginaw Bay and the Michigan shoreline region. In order to properly calibrate a eutrophication model, data sets which include phytoplankton chlorophyll and nutrient data measured over the entire lake, in depth, and with adequate temporal coverage are needed. The histor- ical surveys discussed above are not adequate for this purpose because they failed to meet one or several of 'these criteria. Calibration Data The data base used for calibration of the model is derived mainly from three sources: (l) Canada Centre for Inland Waters (CCIW) (2) Great Lake Research Division (GLRD), University of Michigan (3) Cranbrook Institute of Science (CIS) These sampling surveys together with a compilation of background mate- rial and an evaluation of sources and characteristics of material inputs form an integral part of the IJC Upper Lakes Reference Study [10], which should be consulted for a more detailed review of procedures and results. Data from the CCIW cruises are available for two survey years , 1971 and 197^. Table 8 lists the sampling dates and parameters measured on these cruises. The 1971 surveys [88] sampled at least 78 stations per cruise and the 197^ surveys [89] sampled ^5 stations, excluding the Morth Channel. Both surveys have only one sampling station in inner Saginaw Bay. Chlorophyll-a , primary production, and phytoplankton composition for the 1971 cruises have been analyzed [90,91,92] and zooplankton distribution for these same cruises have also been studied [93]. The 197^ GLRD Lake Huron surveys [9^] sampled a range of 36-UU stations for eight cruises. These stations are concentrated in southern Lake Huron and the outer reaches of Saginaw Bay. Sampling dates and parameters meas- ured on these cruises are listed in Table 9> Table 10 lists the cruise dates and measured parameters for the CIS surveys of Saginaw Bay [95]. These surveys form the most comprehensive study which has been undertaken for Saginaw Bay and fills many voids in the historical data base for the bay. A total of 59 bay stations were sampled, some of which are at the mouth of the Saginaw River , including 4 water intake stations. 62 ------- TABLE 8. CCIW LAKE HURON SURVEYS YEAR 1971 1971 1971 1971 1971 1971 1971 1971 1974 1974 1974 1974 1974 1974 1974 CRUISE 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 DATE 4/19-4/28 5/17-5/25 6/15-6/28 7/19-7/27 8/23-8/30 9/27-10/4 10/27-11/3 11/29-12/6 V23-4/28 5/14-5/18 6/22-6/28 7/22-7/28 8/26-9/2 9/30-10/6 12/4-12/10 PARAMETERS MEASURED ON ALL CRUISES Secchi, Temperature, Turbidity, pH, Specific Conductance, Chlorides, D.O. , Silica NH -N, N02+N0 -N, N02-N, * Inorganic Carbon Total Carbon , * Organic Carbon , Chlorophyll, Total P, Dissolved P, Reactive P. Secchi , Temperature , Specific Conductance, pH, Alkalinity, Particulate * Organic Carbon , D.O., Total P, Soluble P, Reactive P, total particulate * * Nitrogen , NO +NO -N, total N , SO, , Chlorides, Silica, Chlorophyll Not measured on all cruises. 63 ------- TABLE 9. 19T1* GLRD LAKE HURON SURVEYS CRUISE 1 2 3 U 5 6 7 8 DATE U/28-5/3 5/1U-5/17 6/OU-6/08 6/17-6/25 7/17-7/22 8/26-8/31 10/08-10/12 11/10-ll/lU PARAMETERS MEASURED ON ALL CRUISES Secchi, Temperature,, pH, Conductivity, SiO , NO -N, NH -N, Total P, Sol\ible P, SO^, Chlorides, Chlorophyll Phaeopnytin fraction, Alkalinity, carbon uptake, particle counts ------- TABLE 10. 1971* CIS SAGIMAW BAY SURVEYS CRUISE 3 U 5 6 7. 8 9 10 11 12 13 Ik 15 16 DATE 2/18-2/21 3/25 U/17-H/20 U/28-V30 5/13-5/17 6/02-6/05 6/18-6/22 7/08-7/10 7/25-7/27 8/25-8/27 9/18-9/20 10/06-10/08 ii/n-n/iU 12/16-12/18 PARAMETERS MEASURED ON ALL CRUISES Temperature, Secchi, Conductivity, DO, pH, Alkalinity, NH -N, Kjeldahl-N, N02+N0 -H, Total P, Dissolved P Dissolved Ortho-P, Ca, Mg, Na, K, Chlorides, SO. , Silics, Chlorophyll, Phaeophytin 65 ------- TABLE 11. SURVEY STATIONS AND MODEL SEGMENTS Model Segment No. 1 2 3 1* Depth Range (Meters) 0-15 0-15 0-6 (all depths measured used for bay sta- tions) 15-bottom (only val- 1971 CCIW* 37-^8 50-100 1-5, 7-30, 33-36, U9 31,32 Same as Seg. 1 197^ ** CCIW 108-13^ 157-167 101-105 107 166 106 Same as Seg. 1 19TU GLRD ND 1-7, 9-11, 13-15 , 20-26, 36-58, 60, 63-65 , ND ND 197^ CIS ND U2-53 57,58 2-1+0, 56 59 ND ues @ > 15 meter depth used) 15-"bottom (only val- ues @ > 15 meter depth used) Same as Seg. 2 Same as Seg. 2 Same as Seg,. 2 Same as Seg. 2 * CCIW Permanent Station Numbers ** Chlorophyll Values for 197^ are integrated samples (usually to 20m) these values are used for the top layer (0-15m) segments only ND No Data 66 ------- Figure 21 shows the lake coverage provided by the surveys cited. Sagi- naw Bay, northern, and southern Lake Huron are adequately covered by the sampling stations as a group. They are used collectively since the CCIW data gives adequate coverage of the northern and southern lake but not of Saginav Bay, CIS surveyed only in the bay, and GLRD concentrated the south- ern lake and outer bay. Taken together, the 197^ surveys provide the most comprehensive Lake Huron water quality to date and their utility for the calculations to be presented below cannot be overemphasized. Without such comprehensive data, calculations of this complexity could not be adequately calibrated. Data Reduction The data base resulting from an aggregation of the.surveys is quite large. Altogether there are a total of 35 cruises and approximately -225 individual sampling stations measured over a range of depths. The first step in processing these data is to match the sampling stations to the model segmentation. Using cruise maps from each of the four surveys, the individ- ual stations are assigned to the appropriate model segment as shown in Table 11. The cruise mean and standard deviation for each variable utilizing all stations within a segment are computed. These values for each survey are then overplotted and the result is a set of calibration data for each model segment for all parameters being considered. Aggregation and statistical reduction of data described above has been found to be appropriate and, in fact, quite necessary. As an illustration of the variation which may be encountered when dealing with data not only from different locations but different agencies as well, plots were made of surface values for several parameters measured by different groups at essen- tially the same location in the lake. Three separate comparisons are pre- sented. Table 12 lists the overlapping stations and figs. 22-2H show the results. Parameters near the limit of sensitivity of the test employed: reactive and total dissolved phosphorus, ammonia, and to a certain extent, chlorophyll show large variations whereas the nitrate measurements are in virtual agreement. Total phosphorus and reactive silica are in agreement for certain stations but not at others. The possible causes of these varia- tions are differences in sampling methods if a consistent difference is obtained; for example, soluble reactive phosphorus at the northern and southern Saginaw Bay comparison stations; and changes in actual concentra- tions over short time scales due to the transient nature of the circulation and mass loading for the locations chosen. The latter effect must be smoothed out of the data since the calcula- tions are not designed to reproduce short time scales but rather the longer monthly and seasonal changes. Thus aggregation of stations, comparison to several sources where they exist, and statistical reduction to means and standard deviations are necessary in order to smooth the variations encoun- tered. The results of the aggregation and statistical reduction of the 1971 and 197^ data sets are shown in figs. 25-35 for all the segments considered. The comparison is made between the two years and between the different 67 ------- 1971 CCIW 1974 CCIW 1974 GLRD 1974 CIS Figure 21. Sampling station locations for the major data sets used in this report. These correspond to the tabulations in Tables 8-10. 68 ------- 4 4 o o 4 0 D 4 O 4 t) £ \| \| Q Z O -< 3 ~"> _ 5 ^ 5 U- — i 4 4 LL — > 4 4 4 D «<> - 4 4 t) 0 ~ ~ , , g CO o CO o t CM § o CM s t-1 - o o o ifi o in '00 CN t— >— «— O unotnooo o o oo o CM 5 o O ^ C P o o a 4 , 'N3DOH1IN VINOIA11AIV VINOWWV 'N3DOU1IN qi 31 QNV Vinic VOI1IS 3AllOV3y 4 4 4 0 D - 4 oo 0 4 " 4 - 4 o rf 1 1 CO o o 00 0 ••fr CM o 00 o CM s o 4 4 4 o o 4 4 ° 4 _ 5 < u_ 4 4 4 °a - 4 Q 4 - 0 4 " 4 a 4 o o " 1 1 § o 0 00 o CM 8 <—i do'o'-d °. P P PPP"P I/BLU d °' d d d d d d I/6UJ I/ 6iu 'SndOHdSOHd 'SnUOHdSOHd 3AllDV3d 3iamos 1V101 a •H « o -p CtJ Q K ^\ o " o5 > fl O bD o nj a fl ------- 0 s a o 4 RD* 4 0 0 4 1 1 Q Z o CO — > _ * LL —) O a 0 0- 4 4 0 ° 4 ~ 40_ D < O 4~ O CD CO 0 ° O CM 0 oo 0 CM o CD o -t CM • o o g o s o °o °4 °4 0 40 40 < ~5 U. "^ 0 0° - 4" J8 o oo 40_ Q) Q 0 - 4 , , CO o 8 o CM 0 00 0 CM o co O co CN i/6iu'N3DOaiiN VINOIfllNV CO CM «- O vonis Q to to Cj 0 0 0 fj~ o~ 4 j: 0 4 - 03 D <>' - , , Nfc* CO 0 CO o CM 0 00 o CM s O O O 4 4 4 4 4 0 4 1 1 Q Z O CO < 7 - ^ S u. - 0 o _ Q ™ ^ 0 ° ~ 4 o6>~ 4O_ QJ Q 0 - - 1 I v CO 0 CO o CM o CO § o CD n I/6UJ 'snaoHdSOHd 1V101 CD^CM omo mo OOO O'— •" SO to co co co co co tO CD odd odd o'd l/6ui \|/ BLU 'snaoHdSOHd 'snaoHdSOHd 3Aiiov3a asAiossia H 0) -P ni X O ft Hi -P nJ § OD > H oj o a •H " bO \|S 03 H CQ O O « ^O c~j -p (1) O oi -p rt •H cd -P C ni O Tli "H -p o o O SH t~~{ o tfl ------- [_Q o o 2 — O CO o< -L. o» V -« o 0 0 6 o o 0 1 1 —3 5 < 5 u. —5 00 _ 00 fl~ OQ 0 O 0 °_ O ^1 o o — ™ 1 1 W CO Q Q CO o CM O oo 0 o CO ^•^ oo flO o On ° »J o 0 ^ of o o O O3 o 1 1 Q 2 _ O C/) _ OD — 00 0 o ~ o OOOOCO^-CN OLOOmococM«— o co CM ,— oooor^mcNO 7 l/6rf odd d d d d d I/ 0!S Buj 'e-l-IAHdObO-lHO l/6uj 'N^OdllN \|/Buj 'N39OU1IN VOIIIS VINOIAIWV 31VU1IN 3AI1DV3U dlW 31iailN LO ,3. 8 ° CM in o O co 8 O K §! to o o o 0 0 0 0_ 0 o- o °! oo ° o 0 0 D 1 1 O CM «— C 3 O O C 3 d d c o co CO o ° o CN o oo o CM o co o ! ! 0 0 0 ° o 0 0 o 0 o 0 Q 0 D 1 1 Q 2 0 CO —5 —5 P LL Q) ~ c 0 QO- o o_ C D - 3 iqqqqqqc •^ ^\ ^^\ /~N /"^ ^~N ^-" — o CO CO o 8 o CM o 00 o CM § 0 5 3 i /BUI '' \|/6uj 1V101 3AllOV3d l/Boi 'snaoHdsoHd a3A"iossia 0) -p ctf a •H X o -p ai Q K h^ o co > H cd o a •r-l « W) ts nJ H CQ o o a -P d ^ 0) O rM CQ cti •P fl •H 05 -P C nJ O o o o S H O W 01 ^H n5 ni w ft a cu 0) ^ faD 71 ------- 1971 DATA 1974 DATA z % £ 8.0 X -1 z -> PHYTOPLA CHLOROPHY 0 .• b o tO.04 , z z i S 0.02 s o " H z 0.00 ^ 0.40 UJ E H 2 £ g 0.20 d o z cc * 0.00 I 0.016 C = j 0 0.008 V) X 0.000 Occiw _ - _ T r ' "H:;HI J 'F'M'A'M1 J ' J 'A'S'O'N'D _ j IT T T {Ifi\|Iil J. X J 'F'M'A'M1 J ' J 'A'S'O'N'D m ~ ^\|l 5 f^? * - J 'F'M'A'M' J ' J 'A'S'O'N'D • j i ill i ?Ii I 1 1 P i M i A i M i .1 ------- 1971 DATA 1974 DATA LE REACTIVE HORUS, mg/l 0 0 § 8 NJ K §8 0 J 0.000 CO Q ^: > E 0.008 _i 5 0 0.004 < CO »- O £ J 0.000 § 2.0 10 "^ uj O > to 1.0 o E \| 0.0 E .j.- 12.0 O. UJ 0 6.0 X ill -. _. ri n n - Occiw !»?!.«» J 'F'M'A'M1 J ' J 'A'S'O'N'D - . - 1 l "• J 'F'M'A'M' J ' J 'A'S'O'N'D . : i{HnJ{ • J 'F'M'A'M' J ' J 'A'S'O'N'D . ; ji { } I H 1 - 0.004 0.002 0.000 0.008 0.004 0.000 2.0 1.0 0.0 12.0 6.0 00 QCCIW (1 5 e a o f J 'F 'M'A'M1 J ' J 'A'S'O'N'D T T 1 £ 8 $ ° 5 J 'F 'M'A'M1 J ' J 'A'S'O'N'D - : ** li { * " J 'F'M'A'M' J ' J 'A'S'O'N'D I 5 $ i ^ - Figure 26. Model Calibration Data (Segment 1) 73 ------- TABLE 12. INTER-SURVEY STATION COMPARISONS AGENCY '7^ CCIW CIS 'Ik CCIW CIS GLRD 'Ik CCIW CIS GLRD STATION NO. 006 028 007 Ok9 kk 005 052 in LATITUDE LONGITUDE ^3°51'30" 83°1\|0T12" 13051-35" 83°U0.25» 1\|1\|012'2V 83°23'00" lll\|o-L2t]4o" 83°22'liO" kk°ll'k2" 83°20'36" l+k°Qk'l6" 83°05'08" ^l^°0l+'10" 83°0l\|!50" W°03'18" 83°02'5U» LOCATION Inner Sagi- naw Bay Northern Saginaw Bay Southern Saginaw Bay agency sources if they overlap. The primary purpose of this comparison is to investigate the differences in the two years data as well as the differ- ences "between the segments. Figures 27 and 28 for the southern Lake Huron epilimnium show a seasonal pattern, especially in 197^ for which there is "both CCIW and GLRD data. At this level of aggregation the comparisons between the two different data sets are quite reasonable and they compliment each other nicely. The general trends are apparent and consistent with expected seasonal patterns: lower nutrient concentrations and secchi depths as the plankton population devel- ops, with the recovery of nutrient concentrations after the fall overturn. Zooplankton biomass data, however, is quite variable between the two years as is C11 primary production. Differing techniques are the probable cause, although the data does set the range for these variables. Figures 30-31 for Saginaw Bay show much more marked seasonal patterns but again no marked difference between the two years (the CCIW soluble reac- tive phosphorus for 1971 appears suspect). CCIW and CIS data are comparable for 197^ with the increased temporal and spatial coverage clearly delinea- ting the seasonal features: a bimodal chlorophyll distribution, sustained nitrate uptake, fairly constant total phosphorus concentrations, a marked silica uptake during the spring diatom bloom with a recovery during the sum- mer and fall and an essentially constant secchi depth during the ice-free period. Hypolimnion data for the northern and southern lake segment show prac- tically constant values for nearly all variables and no differences between the two years. A seasonal pattern for soluble reactive and total dissolved phosphorus is suggested by the data which, when combined with the chloro- phyll data for southern Lake Huron suggested seasonal algal activity in ------- these deep waters. This feature of the data will "be discussed subsequently in light of the model calculations for these segments. The similarity of the tvo years data in the large main lake segments is to some extent expected since the hydraulic detention times of the lake is in excess of twenty years and differences in mass loadings, if they existed, would not appreciably change the concentrations over the three year period "between the two sets of observations. For these comparisons it is clear that the 197^ data set is comprehensive and well suited for an analysis based on the kinetics and transport discussed in the previous sections. 75 ------- 1971 DATA 1974 DATA — 9 ^^ Z a_ £ •« 8.0 Z _l 5± £ 4.0 0 o > 0 ± 3- 0.0 o "5, 0.04 < £ z z" O LU 2 o 0.02 2 O < £ H z 0.00 ^> 0.40 E LU £ 1 0.20 t 0 z <£ K z 0.00 I 0.016 * i ^ 0 0.008 -> X - 0. CO o J 0.000 O cciw _ _ I ^ I 9 J 5^5 J 'F 'M' A'M1 J ' J ' A' S'O1 N'D - -r IT i T T V 1 i 1 I ? ^ I 5 J IF 'M1 A'M' J ' J ' A'S'O1 N'D . * * M i i * I ^ _ J 'F 'M' A'M' J ' J ' A'S'O1 N'D J T T <( i T T 1 J. 1 1 1 < ' I T T T ~" v J. 1 •• 11 Y i IP'M'A'M' i ' i ' A ' 9 ' o ' N ' n 8.0 4.0 0.0 0.04 0.02 0.00 0.40 0.20 0.00 0.016 0.008 0.000 a cciw y O GLRD (I I jl J) 1 I j I If, X 1 * J 'F 'M1 A'M J ' J 'A'S'O1 N'D _ () I Ir T J J L JT T J IiTrpiX f$ , -i i $ i J 'F 'M' A'M J ' J ' A1 S'O1 N'D T T A A Ti r Y 1(S " " ^ * \| c^ $ - J ' F 'M1 A'M1 J ' J 'A'S'O' N'D - T I ll I t\ j'p S T CD T t M (H U) mf Pi — L " ' 1 r- i T 1 I 1 1 ! I -L * J ' F 'M' A'M' J i j ' A' s in' IM' n Figure 27. Model Calibration Data (Segment 2) 76 ------- 1971 DATA 1974 DATA H E < w LU ^ tr oc m O « co O CO 0.004 0.002 0.000 O cciw ..... i. ?. j » $ J'F'M'A'M'J'J'A'S'O1N 0.004 0.002 0.000 O CCIW O GLRD ffi ffi J 'F 'M1 A'M1 J ' J 'A'S'O1 N'D 0.008 _i . o w co ^ 5 O 0.004 -j Q. < CO I- O O x 0.000 h- OL i j'F'M'A'M'J'J'A'S'O'N'D 0.008 0.004 0.000 j 'F 'M'A'MU^J 'A'S'O' N'D < y 2.0 _i _ CO "^g LU O > co 1.0 O 0.0 n J'F'M'A'M'J'J'A'S'O1N'D 2.0 1.0 0.0 a J'F'M'A'M'J'J'A'S'O'N'D E -£ 12.0 Q. LU Q 6.0 i o o co 0.0 i J 'F 'M'A'M1 Jijf A'S'O1 N'D 12.0 - 6.0 - 0.0 1 i if > 1 A J 'F 'M' A'M1 J ' J 'A'S'O'N'D Figure 28. Model Calibration Data (Segment 2) 77 ------- 1971 DATA 1974 DATA § - 0.16 ° F x E z z < 0 0.08 Si N 0.00 >- <5,8-° I h- S- oc o e M 0 " 4'° w O °> 0 oc E oc Q. <3 r\n 0.0 _ o cciw ~ i- .ll 1* . J "FjM'A'M1 J ' J 'A'S'O'NTD - I ? }I l l M .1 i F i M i A i M i .1 i.i i A i s i n i N i n 0.16 0.08 0.00 8.0 4.0 Ort - 0 GLRD 0 ~ - o 0 J 'F'M'A M1 J ' J "A'S'O'N'D l- < j 'F IM' A ) 'I ( [" ( ) M1 J ' J ' A k W ) IS'O1 N'D Figure 29. Model Calibration Data (Segment 2) ------- 1971 DATA 1974 DATA 2 S £ «f40.0 Zl •• i J 20.0 0 0 > 0 J i 0.0 CJ > 0.16 < E z z- O uj i 0 0.08 5 O < oc H z 0.00 > 0.80 UJ fc C UJ Hg 0.40 z oc Z 0.00 O) E 0.08 <1 £ 0 0.04 •- J c/j 0 J 0.00 . o cow ™ J 'F'M'A . . * , T ^ t * 1 . «, 'M' J ' J 'A'S $ « * < J'F'M'A'M'J' J'A'S ! ] i > $ f . . - J 'F'M'A'M' J ' J 'A'S - I I •L 1 < O1 T T > 1 o1 i N'D t N'D » a O7 I 1 N'D « A ' F ' M ' A 1 M 1 J Ij 1 A ' S 1 O 1 N 1 D 40.0 20.0 0.0 0.16 0.08 0.00 0.80 0.40 0.00 0.08 0.04 0.00 OCCIW - a cis -f 4 _ T J f ( 1 ] T 1 T 7 P f i T 1 4 j ' 1 ' } 5 _ T { I I I * -L ^ i ' x" J 'F 'M'A'M' _ ~ {_ 11^ Ji . J 'F'M'A'M « - 1 ! L I I •L ' J 'F'M'A'M' - - . .1 1 P 1 M d! , i l t } A 1 AlM> j ' i ^ J \| ' . ' J 'A'S1 r . . ' * 9. ' T n T T ' n % 1 J 'A'S1 b . j i i i • ^ j i \| ^ ? j 'A i c 1 T L X J ' A A 'S1 T , 'I 1 sl O'N'D T t A T O'N'D T 5 } O'N'D j ' * i 1 t 1 f O'N'D Figure 30. Model Calibration Data (Segment 3) 79 ------- 1971 DATA 1974 DATA UJ _ > "& g E 0.032 < LU 3 oc oc ug § 0.016 §8 gx 0.000 Q =c III n% > E 0.032 _j . O w tn U 00 QC 0 0 0.016 . i -J a. < M H O 0 X 0.000 1— Q- < y 4.0 i ^^ ^ ^** — CN cn o uj (7) > o. 2.0 I- E u < £ 0.0 £<•» t Q 2.0 X u u UJ «o 0.0 - O cciw * - • A A A A 4 J 'F'M'A'M' J ' J 'A . ™ . - * < k 1 > J 'F'M'A'M' J ' J 'A'S1 - 1 \ " I i t a O'N'D 5 # O'N'D 1 J'F'M'A'M'J'J'A'S1 - - — < - ^ 1 1 C 1 M 1 A 1 M 1 1 1 1 1 A ' - 1 c: 1 « O'N'D $ ni MI n 0.032 0.016 0.000 0.032 0.016 0.000 4.0 2.0 0.0 4.0 2.0 0.0 O cciw T a cis T } ll I X 1 Jft S X j? X ft^-X «• j 'F'M'A'M' j 'j 'A'S'O'N'D _ ™ - - • y T ' ' T T 1 B g J f T H 1 _ 1 J \| M 1 TTT«T^A7 m * A ^AJ T I X 2 1 i T n a,.( ^ i * i .f ,, J 'F'M'A'M1 J ' J 'A'S'O'N'D - • ~ _ > _ T T T * TT I ' ' "Ir IL^I I • 1 J'F'M'A'MU ' J 'A'S'O'N'D , t . i TO jAIllU i 11 J J FT TTITT^T i ° T l_-«-I-i- 11 1 •'• .1 ' P 1 M ' A 1 M ' J >J 1 A 1 S ' O ' N ' D Figure 31. Model Calibration Data (Segment 3) 80 ------- 1971 DATA 1974 DATA AMMONIA NITROGEN, mg/l 3 0 O § s 2 NITRATE NITROGEN, mg/l 300 § 3 S TOTAL HOSPHORUS, mg/l 3 p O ) 00 O) Q. U.UUV )LUBLE REACTIVE HOSPHORUS, mg/l D O O C/J ; h J 'F'M'A'M' J ' J 'A'S'O'N'D iiif\|f J 'F'M'A'M' J ' J 'A'S'O'N'D : ,(!„„, J 'F'M'A'M' J ' J 'A'S'O'N'D I I J I 1 1 J J J 'F'M'A^M' J ' J 'A'S'O'N'D 0.04 0.02 n nn u.uu 0.40 0.20 nnn 0.016 0.008 0000 0.004 0.002 n nnn - o cciw T " 55 ? J 'F'M'A'M1 J ' J 'A'S'O'N'D fa 0 a J ° J 'F'M'A'M' J ' J 'A'S'O'N'D • «,,„ . J 'F 'M'A'M' J ' J 'A'S'O'N'D [i if 0 8 J * J 'F 'M'A'M1 J ' J 'A'S'O'N'D Figure 32. Model Calibration Data (Segment U) 81 ------- 1971 DATA 1974 DATA Q - LJJ O) > E 0.008 <^ r/f TOTAL DISSC CA- PHOSPHORU p p w^ £ 9 1.0 ^ CO I- en < E o: 0-0 - o cciw : ,flinji J IF 'M'A'M' J ' J 'A'S'O' N'D ; Mi J } {} I - .1 1 P 1 M 1 A 1 M 1 1 I.I 1 A 1 R 1 n 1 N 1 n 0.008 0.004 0.000 2.0 1.0 0.0 - a caw I 1 t, i _ m -^ J 'F 'M' A'M1 J ' J 'A' S'O' N'D - *{}{ J - llFlMlAlMUUlA'SlOlN'D Figure 33- Model Calibration Data (Segment k) 82 ------- 1971 DATA 1974 DATA 0.40 UJ C «S020 z oc z 0.00 1 0.016 _i M" tOLUBLE REACTIVE TOTA »HOSPHORUS, mg/l PHOSPHOR p p p p p - o caw : .nnii, J 'F'M'A'M1 J ' J 'A'S'O'N'D m '- f M { i * * J 'F'M'A'M1 J ' J 'A'S'O'N'D _ - '• J^fUji J'F'M'A'M1 J ' J 'A'S'O'N'D - J ' F ' M ' A ' M ' J >J 1 A 1 S 1 n 1 N 1 n 0.04 0.02 0.00 0.40 0.20 0.00 0.016 0.008 0.000 0.004 0.002 0.000 - o caw O GLRD T IT\|! II m T C) J- -ff P r GJT I J 'F 'M'A'M1 J ' J 'A'S'O'N'D T S d T I ; Ni J 'F 'M'A'M' J ' J 'A'S'O'N'D . . : .ijJJm J 'F'M'A'M' J ' J 'A'S'O'N'D (i 0 , J 5 ffl m X I jlFlM'A'MljIjlAlSlO'NlD Figure 3k. Model Calibration Data (Segment 5) 83 ------- 1971 DATA 1974 DATA \| I 0.008 O to Q 0 0.004 _i i 1 — o £ J o.ooo y 2.0 So > w 1.0 — O) oc U-U O cciw T I T 1st I i i $ 1 J 'F'M'A'M1 J ' J 'A'S'O ' r ii i i J f} N'D i .1 i F i M i A i M 1. 1 i i iAi«;ir>iNin 0.008 0.004 0.000 2.0 1.0 On -U D CCIW O GLRD T J I Ii J ! J 'F 'M1 A'M1 J ' J 'A'S'O'N'D L I °*l I i "^ 5 1 I I 7 1 J- .1 ' F ' M' A' M > .1 ' .1 ' A R 'n' N' n Figure 35- Model Calibration Data (Segment 5) ------- SECTION 8 MODEL STRUCTURE AND CALIBRATION In the preceding sections the necessary components of the eutrophication model have been discussed: tha transport between the segments; the mass loadings to the segments; and the kinetics within the segments. It remains to combine these elements into a consistent set of equations and to estimate the values of certain kinetic coefficients by calibrating the model against the data set described in section J. MODEL STRUCTURE The variables included in the model calculations are dictated primarily by two f-'-'.cts: the available data, and their importance as either variables of concern, e.g. phyloplankton chlorophyll, or as a component of the kine- tics, e.g. unavailable phosphorus. The eight dependent variables of the calculations are shown in fig. 36. The phytoplankton biomass that develops in a body of water depends on the interactions of the transport to which they are subjected and the kinetics of growth, death, and recycling. Phyto- plankton biomass growth kinetics are a function of water temperature, inci- dent-available solar radiation, and nutrient concentrations, specifically inorganic nitrogen and phosphorus. Phytoplankton also endogenously respire and are predated by herbivorous zooplankton which grow as a consequence. They, in turn, are predated by carnivorous zooplankton whose biomass also increases. Zooplankton grazing and assimilation rates are functions of tem- perature and, for the herbivorous zooplankton, the phytoplankton biomass as well. Zooplankton respiration is temperature dependent. The nutrients, which result from phytoplankton and zooplankton respiration and excretion, recycle from unavailable particulate and soluble organic forms to inorganic forms, ammonia and orthophosphate for nitrogen and phosphorus respectively. The recycle kinetics are temperature dependent and the rate is also influ- enced by the algal biomass present as discussed previously. The spatial scale of the computation approaches a whole lake scale with the northern and southern regions of the lake, and the epilimnion and hypo- limnion, differentiated. Saginaw. Bay is also explicitly included. The time scale chosen for the calculation, which characterizes the main features of phytoplankton growth, is seasonal: the spring growing season'during which the plankton utilize and are eventually limited by available nutrients as well as zooplankton grazing; the summer minimum; the secondary period of growth due to the fall overturn and/or nutrient regeneration and finally the winter decline. Variations of the environmental parameters on a time scale of less than bi-weekly are not considered. Thus although it is known, for example, that phytoplankton exhibit diurnal variations, such variations are ------- O O to d o -P O 0) SH -P ^ •H -P O O ? •rl JH -P -P 0) W CH O O -H -p o -H W) cd •H •d •a o> -p cd (U a -c! 0) -P ,d o a CQ -rl CO 0) 86 ------- not characterized in this calculation. The numerical aspects are straightforward: it is time variable computa- tion and uses a finite difference scheme to solve the differential equations by explicit forward time differencing. A time step of 0.5 days is used. The model has eight dependent variables or systems and five segments, which com- prise 4 5 comprtments, a compartment being equivalent to one differential equation, which must be solved simultaneously. The computational burden is not excessive; it requires ^ 22 central processer unit (CPU) seconds of CDC 6600 computer execution time for a one year model simulation. Additional peripheral processing approximately doubles the above figure. These figures include rather complete graphical displays of the results. A complete presentation of the equations, the coefficients, and the forcing functions, boundary and initial conditions used in the subsequent calculations are presented in Appendix I. This is a complete specification of the model developed during this project. MODEL CALIBRATION The calibration is begun by assigning estimates of the coefficients which govern the kinetics based on field and/or laboratory information as well as prior studies. Successive adjustments of the coefficients are made until reasonable agreement is achieved between computed results and observed conditions. This process is critical to a modeling effort. It is not enough that governing equations are written and solved. The results must be com- pared with observed conditions for all variables in all model segments. Only then can any degree of confidence be assigned to the results. As shown in Section 7, Lake Huron and Saginaw Bay waters differ by more than an order of magnitude in some biological and chemical parameters. Thus the model must simultaneously reproduce the conditions in a locally eutrophic area as well as large oligotrophic areas. This section contains a discussion of the problems encountered in attempting this calibration over an order of magnitude in the variables, the basis for incorporation of kinetic effects outlined in section 6, and insights gained during calibration procedure. Recycle Rate Early in the process, it became clear that phosphorus availability was a focal point of the analysis. Figure 37 illustrates the problem. In fig. 37(a) a relatively low first order recycle rate for unavailable phosphorus (K1 = .0084 day"1) results in computed chlorophyll concentrations which match observed concentrations of phosphorus and chlorophyll fairly well in southern Lake Huron but not in Saginaw Bay. The observed peak concentrations in the bay are not reproduced, and the computed fall profile is substantially below the data. That this is due to low inorganic phosphorus availability is sug- gested by the fact that the effect is most apparent in the fall when recy- cling provides the major source of available nutrients due to low mass load- ings during this period (fig. 8). The available phosphorus pool, replenished by recycle in mid-June, is rapidly depleted as a fall peak forms, thereby limiting further growth. 87 ------- SAG IN AW BAY UJ __ > ^ E < LU oc O Q. 0.032 0.016 0000 0.16 O LLJ \| g C.08 J ' F ! M ' A J J ' A S . j' F' M ' A M ' j' PA'S SOUTHERN LAKE HURON Figure 37. Calibration calculation for a recycle rate characteristic of Southern lake Huron (bottom figure). Caginaw Bay chlor- ophyll and nutrients comparison (top three figures). ------- Figure 38 illustrates the opposite case. Using a relatively high first order recycle rate (K1 = .031 day"1), the computed chlorophyll concentrations match observed values in Saginaw Bay but are much too high in southern Lake Huron. Inorganic nutrient concentrations, especially soluble reactive phos- phorus during the beginning and towards the end of the year are also high in comparison to observed values, indicating too rapid recycling of phosphorus. Note that the late fall and winter observations of soluble reactive phos- phorus are critically important in determining the recycle rates. A number of alternate hypotheses were examined in order to account for this discrepancy. For example at the low recycle rate Saginaw Bay chloro- phyll is computed to be lower than observed. It might be possible that the transport across the Saginaw Bay-Lake Huron boundary is too large and the plankton are being flushed out too rapidly. Although the magnitude of the exchanging flow is set by the transport analysis based on conservative tracers (as described in section 5), it is possible that the phytoplankton calculation is more sensitive to this exchange rate than the conservative tracer calculation. The results, using the low first order recycle rate (K1 = . 0081\| day"1) which is suitable for southern Lake Huron, and with no exchanging flow between the bay and open lake, are that computed chlorophyll concentrations are comparable to observed magnitudes but computed total phos- phorus and Kjeldahl nitrogen concentrations are more than double observed values (fig. 39). The chlorides and temperature calculations would also exhibit the same lack of agreement with observations. Thus inaccurate basin- lake exchanges are not the source of the problem. Other possible hypotheses were investigated. For example, as shown in section 6, eq. (56), the phosphorus to chlorophyll ratio, a , is important in determining the quantity of total phosphorus that is assimilated and becomes algal chlorophyll. However if it is varying it would be expected that the ratio is larger in Saginaw Bay where the quantity of inorganic phosphorus is larger than in Lake Huron. But this just compounds the diffi- culty since, as shown by eq. (56), and the sensitivity calculations in section 9, this would lower the computed chlorophyll in Saginaw Bay which is contrary to the direction required if the low recycle rate that appears reasonable for Lake Huron is used. Thus the conclusion that the recylce rate is different in these two regions becomes inescapable. One possible solution to this dilemma would be to assign a different recycle rate to each segment. This, however, defeats the purpose of the calculations which are ultimately to be used to evaluate the effects of changes in mass loadings. For example if the loadings to Saginaw Bay were lowered substantially, with the high degree of mixing between the bay and the lake, Saginaw Bay would approach concentrations similar to those in the open lake waters. Then areas of similar properties .would have different re- cycle rates since the rate had been assigned by segment. Similarly, if the mass loadings to the open lake waters of Lake Huron were increased to such a degree as to approach concentrations existing in Saginaw Bay, the model would have an unrealistically low recycle rate in these segments. The fundamental problem with specifying site-specific kinetic constants 89 ------- SOUTHERN LAKE HURON J'F'M1A'M1J'J UJ _ H E 0.004 < co' LU 13 QC OC LU O 0.002 gi 3 ° o J o.ooo co °- 0.04 0.02 0.00 J'F'M'A'M'J'J'A'S'O'N'D J'F'M1A'M1J'J'A'S'O1N'D SAG IN AW BAY _ J'F'M'A'M1J'J'A1S'O1N'D Figure 38. Calibration calculation for a recycle rate characteristic of Saginaw Bay (bottom figure). Southern Lake Huron chlor- ophyll and nutrients comparison (top three figures) 90 ------- S 40 . . O O 20 > o £ i o O _ p f 0.032 o < w m ^ S O 0.016 J'F'M'A'M'J'J'A'S' O'N T D 3 o ? o.ooo CO "" J'F'M'A 'A'S'O'N'D J'F'M'A'M'J'J'A'S'O'N'D J'F'M'A'M1J'J'A'S'O'N'D Figure 39- Calibration calculation for a recycle rate characteristic of Southern Lake Huron. Saginaw Bay-Southern Lake Huron transport exchange rate set to zero. 91 ------- is that it defeats the purpose of the kinetic formulation, which is to prop- erly characterize processes, independent of the particular geographical location in which they are occurring. The more srce-specific the kinetic constants are, the less realistic is the modeling framework since the model is "being calibrated to one particular situation, rather than to the class of situations to which it is designed to apply. This theme is returned to sub- sequently in the discussion of the application of the modified recycle kine- tics to Lake Ontario. The varying recycle rates are accounted for in the present calculation by relating the recycle rate to the chlorophyll concentration. At higher chlorophyll concentrations the recycle rate increases up to a limit that is consistent with observed laboratory rates. As shown in section 6, the available data from various regions in the Great Lakes supports this hypoth- esis. Saginaw Bay with its higher chlorophyll concentrations would there- fore have a higher recycle rate and the inorganic phosphorus available for growth would be resupplied more quickly thus supporting a larger population. It should be noted that the same hypothesis is applied to the recycle of nitrogen and, since the recycle mechanisms are assumed to be the same as for phosphorus, the same rates are used. Initial calculations with the nutrient recycle rate directly proportional to phytoplankton concentrations (i.e. a second order recycle rate) indicated that this mechanism would provide the inorganic nutrient flux necessary to support observed growth in Saginaw Bay. Subsequent investigations described in the kinetics section (6) indicates that the recycle rate saturates with respect to chlorophyll concentration, and the calculations presented subsequently incorporate this formulation. Zooplankton Kinetics As discussed in section 6, the two mechanisms incorporated in zooplank- ton growth expression are a reduction in filtering rate and in assimilation efficiency as chlorophyll concentrations increase. Whereas the formulation for Lake Ontario included only assimilation efficiency decreases it was found that the same grazing rate did not apply to both Saginaw Bay and Lake Huron. A rate suitable for Lake Huron was invariably too large for Saginaw Bay. As soon as the spring bloom began in Saginaw Bay, herbivorous zooplank- ton growth would increase to such an extent that they would exert too much grazing pressure on the phytoplankton, reducing their concentrations to below observed peak values. Perhaps this effect appeared so dramatically in the Saginaw Bay-Lake Huron calculations because of the order of magnitude difference in chloro- phyll concentrations in the two regions. Zooplankton grazing at the high rates required to produce the observed population biomass in Lake Huron, would overgraze the Saginaw Bay population. The modification to the zoo- plankton feeding expression which reduces the grazing coefficient as chlor- ophyll increases is an attempt to parameterize this effect. Whether the effect is physiologically actually taking place, or whether this is just a method of computationally accounting for the different species of zooplank- ton in the very different regions awaits further investigation. 92 ------- Primary Production Primary production investigations of Lake Huron and Saginaw Bay are available [91] arid provide additional supporting data for the calibration. Both in situ and shipboard measurements can be used for comparisons to calcu- lations. The relevant expressions are directly available from the kinetic equations for biomass growth. Since these assume that growth, carbon and other nutrient assimilations are simultaneous and, on the weekly time scale of the calculation this is reasonable, the in situ gross carbon assimilation rate is a, G P where a is the carbon/chlorophyll-a ratio of the biomass. L-ir JT U.T For shipboard measurements the time and depth averaged light reduction factor is not appropriate so that the instantaneous rate reduction expression, eq. (26), evaluated at the light intensity of the incubator is used instead. The temperature and nutrient factors are assumed to be at their in situ values, which is consistent with the experimental procedure. The primary production data are, therefore, direct measurements of a rate, and a critical rate, in the kinetic equation of phytoplankton growth. And, unlike all the other data which measure the quantities at the time and location of sampling, and from which rates are inferred via the calibration, the primary production gives an estimate of the assimilation rate directly. Further the primary production exhibits a thirty fold variation between Southern Lake Huron and Saginaw Bay. This large difference is a stringent test of the calculations since if the kinetics can reproduce these variations one's confidence in their validity increases. Calibration Results Figures ^0 to ^2 show the comparison of computed profiles to observed data for the northern Lake Huron epilimnion segment. For these and all sub- sequent calibration plots the data are cruise averages +_ the standard devia- tion. Phytoplankton chlorophyll-a concentrations peak at approximately 2 yg/£ in early June, and are limited by the rate of phosphorus recycle. The decline to a mid-August minimum is due mainly to grazing pressure exerted by the herbivorous zooplankton. They in turn are grazed by the carnivors which develop a significant population commencing in early August leading to a decline in the herbivors and subsequent fall phytoplankton growth. Not quite enough fall phytoplankton growth is achieved, however, and it is apparently due to the combination of excess grazing, since the herbivors still maintain enough of a population to exert pressure throughout the fall, and perhaps to an underestimation of fall recycle rate. Ammonia concentrations are both computed and observed to be in the range of 5-10 ug N/£. The low concentra- tion is maintained by algal uptake and nitrification sinks. Available phos- phorus is computed to be reduced to below the half saturation constant of 0.5 yg POr-P/5- which then severely limits growth. The abnormally high obser- vations in April 197^ are unexplained and are not consistent with 1971 obser- vations. Nitrate nitrogen concentrations range between 0.2 and 0.3 yg N/£ as shown in fig. 35. The fall depression of nitrate is not reproduced by the calculation. It may represent a larger uptake of nitrate in the fall by a species with a larger nitrogen to chlorophyll ratio than the spring bloom 93 ------- H co 8.0 o- E 4.0 O o x ° °- x 0.0 o O ^,0.16 £ E 3 § 0.08 0.00 < EO-04 J'F'M'A'M1J'J"A'S'O'N'D HERBIVOROUS CARNIVOROUS J ' F MVIrATMTJTJ 'A'S rOTN ' D uu 0.02 o.oo E 0.004 LU D cr or O 0.002 o £ o.ooo CO J'F'M'A'M'J'J'A'S'O'NTD J"F'M'A'M1J'J'A'S'O'N'D Figure i0. Northern Lake Huron Epilimnion Calibration Calculation. Comparison of observations and computations for phyto- plankton chlorophyll, zooplankton carbon, ammonia nitro- gen and soluble reactive phosphorus, 197^. See figure for data symbol legend. ------- NITRATE NITROGEN, mg/ PPP O N) £ OOO J 'F 'M'A'M1 J ' J 'A'S'O1 N'D _l CO s gg Q. CO O X Q- o b -» O) o o O GO o b O O I J 'F'M'A'M1 J ' J 'A'S'O'N'D C ro • O 2 m mg -> • O o • O J'F'M'A'M'J'J'A'S'O'NTD Figure hi. Northern Lake Huron Epilimnion Calibration Calculation. Comparison of observations and computations for nitrate nitrogen, total phosphorus, and reactive silica nitrate nitrogen total. 95 ------- variety. Total phosphorus concentration is calculated to remain essentially con- stant at 5 Ug PO, -P/Si throughout the year. Some seasonal variation is ob- served in the data, together with the high April 197^ observation. Varia- tions in mass discharge rate cannot account for these fluctuations since the mass in the segment is much larger than the annual loading to the segment. Perhaps a transient settling of detrital particles into the hypolimnion dur- ing the latter part of the year is the cause, since an increase in unavail- able phosphorus is calculated to occur during this period. The reactive silica profile is computed by considering just silica up- take of the population. Since they are primarily dia,toms a reasonable com- parison is expected. The silica cycle is not included, however, and the computation is not meant to be representative of the actual recycle mech- anisms. The reasonable agreement is taken to mean that over a one year period, the recycle source of silica is not critical at these concentrations. Note, however, that the computed curve is decreasing below the observations by year's end so that the effects of recycle would be very important for adequate multi-year calculations of silica. Figure k2a compares computed and observed Secchi disk depth. The effect of increased chlorophyll during April through June in lowering the transpar- ency and the increase due to reduced populations during July and August are in reasonable agreement with observations. The comparison to observed primary production data is shown in fig. U2b. The data are for 1971 [91] in contrast to the other variables. However the comparison in section 7 of 197-1 and 197^ data support the comparability of both these years. The computation overestimates the spring and underesti- mates the fall primary production. A smaller carbon to chlorophyll-a ratio is suggested by the spring data. With the discrepancies in the later part of the year related to the discrepancy in computed and observed chlorophyll. The final carbon to chlorophyll ratio is a compromise for both seasons. The results for the southern Lake Huron epilimnion (segment 2), are shown in figures h3 to k5. Phytoplankton growth exhibits the same behavior as in northern Lake Huron epilimnion but both the computed and observed spring concentrations are slightly higher and in better agreement. Zooplank- ton growth is also similar and the fall peak is again limited by herbivore grazing and phosphorus limitation with nitrogen limitation not being a fac- tor. Calculated zooplankton biomass concentrations exceed that estimated to be present based on the 1971 data but is lower than the 197^ estimates (see fig. 18) which are not included in this figure. The general state of both biomass estimates and the calculation is unsatisfactory. The uncertainty in both the observations and the relevant kinetic constants is sufficiently large so that the level of credibility of this portion of the calculation is uncertain and probably low. Calculated ammonia nitrogen is within the range of the observations and is similar to the northern segment result. The available phosphorus calcula- 96 ------- tr • 12.0 - I LU Q X CJ (J UJ CO ^ ^ (— <«v o E co o ? O QC C CC Q. 8.0 4.0 0.0 j IF'M'A'M'J ' j 'A'S'O'N'D Figure k2. Northern Lake Huron Epilimnion Calibration Calculation. Comparison of observations and computation for observed Secchi disk depth and gross primary production, (1971)- 97 ------- 0 8.0 a- 4.0 g «•« IjTF^MWMTj IjlA'S'O'N'D 0.16 5 g 0.08 N QC < O 0.00- TOTAL I HERBIVOROUS CARNIVOROUS J'F'M'A'M1J'J"A'S'O'N'D . E S 0.02 O 0.00 UJ _ > "o. H E 0.004 I ao02 o £ o.ooo CO J'F'M'A'M'J'J'A S1 OnrN "D J'F'M'A'M'JU'A'S'O'N1^ Figiire 1+3. Computed versus Observed Data (So. Lake Huron epilimnion) 98 ------- LU O 0.40 DC 05 £ 0.20 QC £ 0.00 iii-J I f ffi Oj <<>- 1 J1- J ' F ' Mr A' M1 J Ij rA ' S ' 0 ' N ' D CO ID 0.016 - Q- C/3 O ^ x o) 0.008 a. E I- o.ooo 2.0 i i , i TTT T I TO 1 r -ii- f J "F'M'A'M" J ' J 'A'S'O'N'D 0.0 J ' J NTD Figure hk. Computed versus Observed Data (So. Lake Huron epilimnion) 99 ------- J'F'M'A'M'J'J'A'S'O'N'D Figure k$. Computed versus Observed Data (So. Lake Huron epilimnion). 100 ------- tion agrees with the observed 1971 data but not the substantially higher values observed in 197^. No ready explanation of this discrepancy is avail- able. Nitrate nitrogen data again shows a fall depression which is not reproduced by the calculation. Total phosphorus data are somewhat erratic if all the data are overplotted as in this figure. The individual year's data as shown in fig. 27 do not appear to have any strong seasonal trends although there is a suggestion of a fall decrease as in the northern lake epilimnion data. The silica profile follows observed patterns although it appears that more uptake is required. Transparency as measured by Secchi depth, agrees well and computed gross primary production falls within the range of observed data for both 1971 CCIW data and 197^ GLRD data as shown in fig. 15. The Saginaw Bay calculation is shown in figures k6 to 48. Notice the difference in plotting scales used for these computed profiles and observa- tions to those used for the open lake segments presented above. Phytoplank- ton and reactive phosphorus concentrations are approximately 15 times greater, zooplankton populations are approximately 5 times higher, while inorganic nitrogen, ammonia and nitrate values are approximately U times higher than in the main lake segments. Thus Saginaw Bay spans almost an order of magnitude change in the concentration of most variables. Both the data and the calculation show two peaks in Saginaw Bay phyto- plankton with the spring pulse declining during the beginning of July. A broad fall peak extending through November is indicated by the data. The calculated concentrations taper off progressively in the fall with a signi- ficant population decline starting at the end of October. Fall growth limi- tation is due to both zooplankton grazing and phosphorus limitation. It can be seen on figure k^c that the calculated total phosphorus also is low at the end of the year. This suggests that a significant phosphorus source at the end of the year may not have been accounted for. This may be due to resuspension of sediment phosphorus or a mass discharge which eluded measure ment. Zooplankton biomass is reproduced quite well as can be seen in fig. The magnitude of a pulse at the end of July which limits phytoplankton growth is reproduced although the calculated biomass is slightly in excess of that observed in the fall. Computed ammonia concentrations are slightly high during the spring as are the Kjeldahl nitrogen calculations. The problem may be due to an overestimation of the detrital nitrogen mass loading rate or increased settling of particulate nitrogen during the spring. Nitrate uptake as calculated and observed is shown in fig. ^7a. The agreement is quite remarkable. Soluble reactive phosphorus data are quite variable although the calculation appears to be below the observations for significant portions of the spring. Secchi disk observations are compared to calculations in fig. 48b. The small variations due to algal chlorophyll are not significant. The February measurement is through the ice cover and therefore is not representative of the total light available since the attenuation due to the ice is not meas- ured. The primary production data for the summer and fall are well repro- 101 ------- J ' F 'M'AMVll J ' J 'A'S'O1 N'D ^ 0.80 < 0.40 N < 0.00 TOTAL J'F'M'Anvl1 J'J'A'S'O1N'D 0.16 o oc 0.00 J 'F'M1A]M> J 'J 'A' > "^ H E 0.032 < co LU 12 cr a: LU 0.016 O 0.000 CO J'F'M'A H M ' J ' J • A ' S ' CM N'D Figure h6. Computed versus Observed Data (Saginaw Bay) 102 ------- x < LU O ~> QC 0.00 0.80 0.40 0.00 J'F'M'A'M1J"J'A'S'O'N'D J 'F I 0.08 = DC O 0.04 Q. CO O 0.00 J ' J 'A'S'O1 N'D 1 J'F'M'A' Figure ^7. Computed versus Observed Data (Saginaw Bay! 103 ------- o 4.0 at O > c/3 2.0 0.0 J'F'M'A'M'J1J'A'S'O'N'D x Q_ o o LU - 4.0 - n 0. J'F'M'A'M'JTJ 'A'S'O1N'D _ 160.0 — I— n oc o E E DC Q. 80.0 0.0 J'F'M'A'M'J1 Ji A 'S'O1 N1 D Figure U8. Computed versus Observed Data (.Saginaw Bay) 10 It ------- duced. The low values observed in the spring during the height of the diatom bloom are unexplained and appear suspect. The bottom layer segments representing the northern and southern lake hypolimnia are in reasonable agreement with observations. Figures ii9 and 50 show the computed profiles compared to observations for the northern Lake Huron hypolimnion. No chlorophyll data for comparison are available as the CCIW measurements are integrated samples only in 197^ and surface concentra- tions in 1971. Calculated concentrations average only 0.3 yg/& on a yearly basis due to light limitation as the hypolimnion is well below the euphotic zone. Computed profiles for the other variables agree reasonably well with observations. The comparison of the computation and observed data for the southern Lake Huron hypolimnion is shown in figs. 51 and 52. In fig. 51a, it can be seen that the model calculates phytoplankton chlorophyll-a concentrations substantially lower than the observations by GLRD in 197^. Nitrate and reac- tive phosphorus concentrations agree reasonably well, so there are no nutri- ent limitation problems. Total inorganic nitrogen and available phosphorus are both well above their respective half saturation constants. The reason for the lower computed profile can be seen in fig. 53, which presents the phytoplankton growth rate which results after light and nutrient limitations are imposed on the saturated temperature dependent rate. The comparison shown is between the epilimnion and hypolimnion segments in the southern lake. It can be seen that in the epilimnion, light limitation accounts for a 30 to 80 percent decrease in the saturating rate with nutrient limitation also being significant. In the hypolimnion, however, light limitation amounts to greater than a 99-9% reduction in the saturating rate. Nutrient limitation is unimportant as is zooplankton grazing in comparison to light effects. Based on the relationship developed by Beeton [17] from studies on Lake Huron, the extinction coefficient can be approximated as 1.9/Secchi depth. The epilimnion segment with an average Secchi depth of 6 meters has an extinction coefficient of .32 meter , yielding an equivalent euphotic zone depth of approximately 15 meters. Thus less than 1% of the surface irradia- tion is available at a depth of 15 meters, the upper bound of the hypolimnion segment. This lack of available radiation causes the large computed reduc- tion in the depth average growth rate in the hypolimnion. Since the computed respiration rate exceeds the computed growth rate as shown in fig. 53b, the phytoplankton kinetics are, on balance, causing a net loss of biomass. The slight increase calculated in the hypolimnion is due to vertical transport via mixing and settling from the epilimnion with the former predominating as shown subsequently. The phenomenon of a significant standing crop of phytoplankton in the meta- and hypolimnetic layers has come to be termed as "deep chlorophyll" and has been observed in recent lake studies [96]. The kinetics, as present- ly structured, are unable to characterize this effect since they are based on the hypothesis that severe light limitation will result in minimal phyto- plankton growth. If the deep chlorophyll phenomena are reasonably well verified by further observation, the kinetics may be adjusted to incorporate 105 ------- >- 0.0 J'F'M'A M'J'J'A'S'ON'D' - 0.04 en < E § uj 0.02 ^ £ ^ ° QQ co CO 0. [ < ] T , Y* a " i « ^ j5 ^ 5 < J 'F 'M1 A'M1 J ' J ' A 1 i 1 $ ? l i i S'O1 N'D UJ "\|> 0.40 < UJ oc o 0.20 I- O J.O J'F'M'A'M'JTJ1ATSTOTNTD Figxire ^9- Computed versus Observed Data (No. Lake Huron hypolimnion) 106 ------- E 0.016 O 0.008 CO 0.000 J rF 'MrATM'J 'J'A'S'O'N'D J ' F ' M'A'M'-J'J'A'S'O'N'D Figure 50. Computed versus Observed Data (No. Lake Huron) 107 ------- J "F'M'A'M1 J J "A S 0 N'D ^» 0.40 - uu ------- 3CA^r,wC c,, ,™ TOTAL DISSOLVED TOTAL REACTIVE SILICA, PHOSPHORUS, mg/l PHOSPHORUS, mg/l mg Si02/l ooo ooo 3-N88S882 D O O O 45* CO O 00 O) T T <( n $ y T lP XVllYTl J 'F 'M'A'M1 J ' J 'A'S'O'N'D ; j i i * 1 n j r J'F'M'A^M'J'J'A'S'O'N'D !______ T I T T T TT ' m-JIL T 1 T H. CT-HV-— X_ IT] 1 n) I Jtff t ^S— 4L -L J ± \| Y I Figure 52. Computed -vers-us Ohs-erved Data. ftypolimnion) (So. Lake Huron 109 ------- o 'E \| 1 § O oc D I uj ^_- QC UJ X I- D O Q Z O § Uj cc p < O T- T- r- ,- «- o q d o p d o ' Q 2: 0 «— t— o»— q d '31VH HIMOdO i-Aep '31VU H1V3Q N01>INVndOIAHd o •H a 0 •H a aJ o •H fl •H H •H a o OJ X ,3 a ^ a> ,d -p ^ o ca w 0) -p cd -p nJ (U ft £ o ho O -p rt 0} H o -p PL, oo LTN •H P-H 110 ------- the effect in some manner such as the inclusion of a light adaptive mechanism. The present kinetics do not deal with this phenomena. Analysis of the Computation Figures 5^ to 58 present a detailed analysis of the calculation des- cribed above. The analysis is presented as a comparison between the open lake waters, as characterized by southern Lake Huron, and Saginaw Bay. This yields further insight into the behavior of the model and the system under study. The effects of nutrient limitation of phytoplankton growth is shown on fig. 5^. Nitrogen is not an important factor in limiting growth in southern Lake Huron, since total inorganic nitrogen concentrations average more than 0.25 mg/£ and provide an abundant source for plankton growth. On the other hand, phosphorus limitation is significant yielding up to a 60 percent reduc- tion in the saturated growth rate. This is expected since available phos- phorus concentrations in southern Lake Huron are very close to the Michaelis half saturation constant of 0.5 yg P/&. Saginaw Bay is not nitrogen limited during spring growth but there is a limitation effect during fall growth with reductions up to 30 percent in the growth rate resulting. Phosphorus limitation dominates, however, especially during spring growth where 60 percent reductions result. The replenishment of the available phosphorus pool can be seen as a sharp increase in the limitation term from the beginning of June to mid-July coinciding with the decline in the phytoplankton standing crop and the recycling of unavailable phosphorus. The sources of unavailable phosphorus available for conversion to forms utilized for growth of phytoplankton is shown in fig. 55- In southern Lake Huron the principal source is from respiring phytoplankton. Phytoplankton grazed but not assimilated by the herbivorous zooplankton contribute signi- ficantly to the unavailable phosphorus pool in mid-July when the herbivore population is at a maximum. This is true in Saginaw Bay also where excreted phytoplankton phosphorus contributes significantly to phosphorus available for recycle at the peak of herbivorous phytoplankton growth. Zooplankton respiration and excreted zooplankton phosphorus also provide unavailable phosphorus and their relative importance can be seen. The unavailable phosphorus flux is higher in Saginaw Bay by nearly an order of magnitude. This is due to the higher concentrations of phytoplank- ton phosphorus which provides the main kinetic source. The rates are also slightly higher in Saginaw Bay due to the warmer temperatures, but the prin- cipal effect is the larger standing stock. The phosphorus concentrations which develop as a result of phytoplank- ton uptake and the recycle mechanisms are shown in fig. 56. The figure pre- sents the available phosphorus, then the available plus unavailable phos- phorus , and finally the total phosphorus which includes the algal phosphorus as well. Note the larger proportion of unavailable phosphorus in southern Lake Huron when compared to Saginaw Bay. This is primarily the result of 111 ------- SOUTHERN LAKE HURON z o 1.0 li 0.6 I- z LU E 0.2 D Z NO LIMITATION N/(N + KmN] TOTAL REDUCTION J'F'M'A'M1J'JT AISlQ'N'D SAG IN AW BAY jl 1.0 < H 1 0.6 I- z LU E 0.2 /VO LIMITATION TOTAL REDUCTION JTF'M'A'M1J'J'A'S"O'N'D Figure 5^. Nutrient limitation of growth rate. Inorganic nitrogen (N/N + KmN) and reactive phosphorus (P/p + Kmp) terms, and their product (total reduction) 112 ------- SOUTHERN LAKE HURON * DC O 10 0.1 0.001 I 0.00001 CL UJ > PHYTOPLANKTON RESPIRA TION ZOOPLANKTON RESPIRATION UNASSIMILA TED ZOOPLANKTON UNASSIMILA TED PHYTOPLANKTON O X J 'F 'M1 A'M1 J ' J 'A'S'O1 N'D SAG IN AW BAY 10 0.1 0.001 0.00001 J"F"M1A'M1J'J'A'S'O1N'D Figure 55. Comparison of kinetic fluxes of unavailable phosphorus in Southern Lake Huron and Saginaw Bay. Curves correspond to a (l-f )R for phytoplankton respiration: a _(l-f.) Pr "• L pC A (E +R ) for zooplankton respiration: a (1-8)(l-f )R ?n ?L pp A3 for unassimilated phytoplankton, and a „(!-£ )(l-f )R, pC c A 4 for unassimilated zooplankton. 113 ------- SOUTHERN LAKE HURON PHOSPHORUS, mg /I U.UUD 0.004 0.002 0.000 TOTAL PHOSPHORUS =___^- ^, 7 — UNA VA/LABLE PHOSPHORUS SOLUBLE REACTIVE PHOSPHORUS J 'F 'M'A'M1 J 1 J 'A'S'O N'D SAGINAW BAY - 0.06 O) oc O X 85 O Q. 0.04 0.02 0.00 TOTAL PHOSPHORUS UNAVAILABLE PHOSPHORUS SOLUBLE REACTIVE PHOSPHORUS J'F'M1A'MTJ'J'A'S'O1N'D Figure 56. Cumulative plot of the components of total phosphorus in Southern Lake Huron and Saginaw Bay. The curves corres- pond to reactive phosphorus; reactive & unavailable phos- phorus; and total phosphorus, which includes algal and zooplankton phosphorus. ------- the variable recycle rate which is small in southern Lake Huron and large in Saginaw Bay. An analysis of the phytoplankton growth and death rates is presented in fig. 57. It can he seen that light limitation is more of a factor in Sagi- naw Bay than it is in southern Lake Huron. This is expected since the Secchi depth averages 6 meters in the open lake but only 1 meter in Saginaw Bay. Nutrient limitation in Saginaw Bay can be seen to be minimal at the end of June when recycle has replenished the available nutrient pool. Respiration dominates the phytoplankton death term for most of the year in both areas until the herbivorous zooplankton build a significant population and grazing becomes the major factor. These terms peak in both areas at the time of maximum herbivorous zooplankton. In Saginaw Bay, it can be seen from the rapid rate of increase in zooplankton grazing as a major factor in phyto- plankton decline, that if no limitation were placed on zooplankton grazing rate as discussed earlier, they would develop large populations which is inconsistent with observations and also exert too much grazing pressure. In- stead of the herbivorous zooplankton growth rates leveling off in Saginaw Bay, as shown in fig. 58 "the rate would continue to increase. Zooplankton respiration rates are about equal in Saginaw Bay and southern Lake Huron with the slight difference due to warmer Saginaw Bay waters affecting the tempera- ture dependence. Carnivore grazing is seen to be much more significant in Saginaw Bay where more of a standing crop of herbivores are maintained which stimulates carnivore growth and causes the grazing pressure. The calculations presented above compare reasonably well with observed data for the variables of concern in the different areas of Lake Huron. An analysis of the results has also been presented highlighting some of the important mechanisms such as nutrient limitation, nutrient recycle, and phy- toplankton and zooplankton growth and death rates. These processes strongly affect the seasonal distribution of the phytoplankton and nutrients and the calibration is sufficiently sensitive to the values of the kinetic constants so that it is possible to make reasonable estimates of their magnitudes. There is an important process, however, for which the calibration of the seasonal model is insensitive because its time scale is longer than seasonal. It is the loss of particulate phosphorus to the sediments. The issue of whether Lake Huron is in equilibrium with its current mass inputs of phosphorus depends on the magnitude of the flux of phosphorus to the sedi- ment s. Phosphorus Sedimentation and Lake-wide Mass Balance The loss of total phosphorus from Lake Huron is primarily the result of sinking of particulate phosphorus into the sediments. The principle forms of phosphorus considered in this calculation are algal-bound phosphorus, un- available phosphorus and soluble reactive phosphorus, with zooplankton-bound phosphorus a small fraction of the total. Algal phosphorus and the particu- late portion of the unavailable phosphorus each have a sinking velocity which eventually leads to a fraction of this material being incorporated into the sediment. This mechanism is represented in the calculation by a sinking velocity across the epilimnion-hypolimnion interface and the same velocity 115 ------- SOUTHERN LAKE HURON O "J - 0.1 > 5 0.01 0.001 REDUCTION DUE TO LIGHT LIMITATION SATURATED GROWTH RATEl_ RESULTANT GROWTH RATE REDUCTION DUE TO NUTRIENT LIMITATION J'F'M'A'M1J'J'A'S'O'N'D O IU t$ Z OCr 1 0.1 —I i_ ro Q. C -O g § 0-01 > oc I C3 °- 0.001 SATURATED GROWTH RATE RESULTANT GROWTH RATE SAGINAW BAY REDUCTION DUE TO NUTRIENT LIMITA TION JIF'M'A'M'J'J'A'S'O'N'D 0.001 j'F'M'A'M1J'J'A'S'O'N'D Figure 57- Seasonal distribution of phytoplankton growth and death rates showing light and nutrient limitation reductions. 116 ------- SOUTHERN LAKE HURON LLJ Q Q Z 5 •§ 2 tf Z < O oc Q. o o N 1.0 0.1 0.01 0.001 1.0 0.1 0.01 0.001 GROWTH RA TE DEATH RATE DUE , TO CARNIVORE GRAZING J 'F 'M' A'M' J ' J 'A'S'O' N'D SAG IN AW BAY DEATH RATE DUE TO CARNIVORE GRAZING GROWTH RATE J'F'M'A'M'J'J'A1 S "0] N'D Figure 58. Seasonal distribution of computed herbivorous zooplankton grovth and death rates for Southern Lake Huron and Saginaw Bay growth rate, 3a R • respiration rate, - R, ; carnivore grazing, _R cr -5 4' 117 ------- across the sediment-water interface. For the coarse vertical segmentation used, i.e. two layers, the seasonal calculation of phytoplankton is not very sensitive to the absolute magnitude of the algal settling velocity as shown subsequently in section 9 so that it is not possible to infer this velocity from the calibration. Rather it is necessary to know the flux of phosphorus from independent estimates. The settling velocities are then suitably ad- justed to reflect these estimates. Robbins [97] has estimated the net phosphorus settling into the mud layer of fine grained sediments for Saginaw Bay to be 360 tonnes P/year. For southern Lake Huron, a loss to the sediments is estimated at 782 tonnes P/year. Utilizing loss rates corresponding to an algal settling velocity of 0.05 m/day and a settling velocity of unavailable phosphorus of 0.1 m/day in open lake waters, the model computes a yearly loss of 363 tonnes P/year for Saginaw Bay and 8^8 tonnes P/year for Southern Lake Huron. A comparison is also possible to an estimate of the lakewide sedimenta- tion loss based on the Upper Lakes Reference Study mass balance [98] for total phosphorus. Their reported difference between inputs and outputs for the whole lake is hhkO tonnes/yr and for the main lake is 26^0 tonnes/yr. Thus, there is a loss in Georgian Bay and the North Channel, areas not in- cluded in this model, of 1800 tonnes/yr. Adding this to the model's computed total sedimentation loss of 2626 tonnes/yr yields kh26 tonnes/yr. The lake- wide estimate of sediment loading including anthropogenic and natural sources is ^750 tonnes/yr [98], It is important to realize that these computed sedi- mentation fluxes are made using the same loss rates in1 both Saginaw Bay and Lake Huron. The difference is due to different concentrations of settleable phosphorus. Table 13 summarizes these results and includes a corr.parison to the IJC- ULRS mass balance of main Lake Huron. The most recent IJC-ULRS estimates of total phosphorus loading are very close to those used in this calculation. The major loss in the main lake segments is via the settling of unavailable phosphorus whereas in Saginaw Bay the principal mechanism is phytoplankton settling. The model computes total outflow that is lower than that measured, although it agrees with the concentrations in southern Lake Huron whose waters exit via the St. Glair River. This apparent discrepancy may be due to local inputs to the St. Glair River. With the settling velocities used in the calculation, Lake Huron is slightly out of equilibrium with respect to its present loading, amounting to a buildup of 36^ tonnes of phosphorus during 197^- or approximately a 10% change. Considering the uncertainties of the estimates it is reasonable to conclude that the lake is essentially in equilibrium. Application to Lake Ontario In order to further strengthen the calibration of the Saginaw Bay-Lake Huron model, and to investigate the generality of the proposed recycle kine- tic structure an application to Lake Ontario is presented. In terms of nutrient and chlorophyll concentrations, Lake Ontario is intermediate between Saginaw Bay and Lake Huron. It, therefore, is an ideal test case for the modified recycle kinetics, and in fact served as a guide for the ultimate choice of the half-saturation constant for recycle. 118 ------- H 0 s <( J dj pq CQ CO fr; O w CO o K PH i-^l j «H a -H ^~- •H 03 CQ CQ X !> Cl CQ C! Oj O O -H S -P l-^l CO tD O •H a -P O 0) s -p e O ^J 60 h fl & fin 03 -rH tl r^H U3 O\| fH ^ ^ CQ O -H O -P CQ PH CQ pf ^ H O TJ 03 -G ui -P ft O O W hi EH 0 r£3 PH CM O CO VD t-— oo .— , ft pi •H -0 LA CO OO VD i 1 + H -S- VO CM LTN -^- CO OO VD O CQ " " H CQ H CM — O rH CO ^—- K i-l O O P CM -3- 1 t— VO ON CO CTv VO O " " -3- H VO OO 1-71 00 CM OO CO CM H r. r. H CM H OO VD 0) ON CM VD O -=\|- O Tj CO VO VD oo ON ON O " « CM OO g OO CM CQ CQ o 1-H1 H t— LT\ OO CO OA H ON S CM CM OO CO O ^ . « « _p .H H H H OO pi -p ft 03 H -P H n (1) H S c! a 03 -H O O -P T^ f-< f-i O CU Pi pi !>> EH CQ W W cd 0) Q) >i ^H t5 cd cd cd hi hi & •H 60 O O cd S CQ CQ O CO O ^ H O O ON 0) £, •H K JH •H cd H O . -p co -p pi ft -p pi o J- vo OO ft pi •d rH •H pi PQ CQ pj JH O £l ft CQ O r] PH 119 ------- Two major modifications have been made to the recycle kinetics when compared to those used initially in Lake Ontario [U8]. The recycle rates for nitrogen and phosphorus are assumed to be the same, and the rate changes with changing chlorophyll concentration as described previously. Also a fraction of the nutrient fluxes due to respiration and excretion are assumed to be immediately available. The result of these kinetics when applied to Lake Ontario with all other parameters the same as in the previous calibration [kQ] is shown in fig. 59&. As can be seen the predicted fall peak is low when compared to observed values from 19&7 thru 1972 CCIW cruises of Lake Ontario. Computed reactive phosphorus concentrations are within the range of observed data but computed nitrate nitrogen values are larger than observed towards the end of the year. This is due to the low fall phytoplankton popu- lation that is calculated and consequently too little nitrate utilization. The second calculation, figure 59t>, illustrates the result of not only incorporating the changes outlined above but also the phosphorus to chloro- phyll ratio of the Lake Huron/Saginaw Bay model of 0.5 Pg P/Vg ChJl-a. Both the calculated spring and fall phytoplankton peaks are too large. Reactive phosphorus utilization is not as great as in the previous example and it can be seen that the low calculated nitrate concentrations indicate that nitro- gen has become limiting. The results of this exercise indicate that the carry-over of the kine- tic changes affecting the nutrient cycles from the Lake Huron/Saginaw Bay model to the Lake Ontario model do not have drastic effects on the computa- tion, although the chlorophyll verification is not as good as the original model. Figure 60 shows a final calibration^for Lake Ontario with the Lake Huron nutrient kinetics. It utilizes a phosphorus to chlorophyll ratio of 0.5 yg P/y Ch£-a and a slightly lower initial condition for reactive phos- phorus (10 ygPOij- P/& versus 1^ ugPOit- P/£) used previously. The results are quite reasonable although the spring peak is slightly larger than ob- served. It is reassuring that reactive phosphorus compares fairly well in the hypolimnion as well. This is due to the proportional recycle effect. Phytoplankton concentrations are not as high in the hypolimnion as in the epilimnion and therefore the recycle rate is lower. This low rate prevents a buildup in the lower layer. Figure 6l presents the final chlorophyll-a calculations for southern Lake Huron, Lake Ontario, and Saginaw Bay. These calculations embody the same phytoplankton growth and respiration kinetics, and the same recycle kinetics. The range over which these kine- tics apply is approximately an order of magnitude in chlorophyll-a concen- tration and almost two orders of magnitude in primary production. It is remarkable that not only the same equation structure applies but also that the same kinetic constants are applicable. This observation suggests that the kinetic constants and functional relationships have a fundamental basis. A set of constants that result from a single calibration of a single, rather homogeneous, setting are usually not regarded as certain until some verifications are performed using independent data. The kinetics employed in the calculation displayed in fig. 6l have not been verified in this sense. However they have been shown to have general applicability to three separate regions with widely varying characteristics. This display of con- 120 ------- eo "" SiS1!™™3 1/6 S KlUWdSOHd 3AI10V3« '/6UJ NOl^NVldOlAHd 'N390dllN 31VU1IN 6 O> a o> in 8 q o n .g to o « 1 \| g 0) H !>3 bO •H -P -P a § 'H O Z P CO CD 00 i/6rf'viAHdoao-iHO ,/BS 'snuoHdsoHd '/6uj N01>INVnd01AHd 3AI10V3U 'N390U1IN 31VU1IN o O) O) E 8 d n o > -§_ o 3 o "S o 0. o to •H 0) rH CQ ft-H ft ^i O a H o o O VD •H a\ f-i H ts 6 ------- Epilimnion z-J 5x8 Q. Q. 00 HOC x-" 0 Q. X U O O) E 0.2 >co ^c? ^ O 0.1 UJ J QC CO O ? 0.0 J'F'M'A'M'J'J'A7S'O1N'D J 'F "M" A'M'J'JTA'S OTNTD LU O 0.4 QC LU 0.2 = 0.0 J 'F 'M1 A'M" J ' J I A' S ' O' N ' D LU O) CO Si LU a. erg I a. Hypolymnion 0.2 0.1 0.0 i - j I ill Hi 1 * I: - \] [' • ^ • i 1 , i ( i i p m i ii i i t i 1 ; : * a ii T " "i If i N 3 1 • 1 j \| i i ^ ii X J 'F 'M'A'M1 J ' J 'A'S'O N'D Figure 60. Lake Ontario Calibration 122 ------- SOUTHERN LAKE HURON 8 o> I Q_ O QC O X O J 'F'M'A'M'JTJ ' AHS ' 0' N ' D LAKE ONTARIO 16 8 'A'S'O'N'D CL O \- SAG IN AW BAY 40 20 JrF'MTA1M'JrJ 6l. Final calibration computations for Southern Lake Huron, Lake Ontario, and Saginaw Bay phytoplankton chlorophyll. The phytoplankton and recycle kinetic constants are the same in each calculation. However Lake Ontario zooplankton kinetics are not those used for Lake Huron and Saginaw Bay. 123 ------- sistency argues rather strongly that the results are more than just a cali- brated calculation (or as it is sometimes put, a curve fit) but rather that they have a certain generality. This is somewhat surprising and gratifying if one considers that the processes have been idealized greatly in an attempt to make their quantitative description tractable. By the same token the zooplankton kinetic constants used are different for Lake Ontario than the Lake Huron/Saginaw Bay calculation and it is reasonable to conclude that this generality cannot be claimed for these kine- tics. As shown in the next section, the zooplankton responses are very sen- sitive to the magnitude of the coefficients employed which also suggests that the structure is not as robust as the phytoplankton kinetics. 12k ------- SECTION 9 SENSITIVITY ANALYSIS One of the means available for testing the quantitative framework em- ployed in this study is to perform a series of calculations in which the sensitivity of a model to its coefficients is determined. These coefficients are chosen within the range of reported values , and are the result of many calibration runs. However there is frequently a range of values which may be assigned and it is important to know what effect, if any, adjusting these coefficients has on the resulting computations. The coefficients chosen for investigation are those which affect primary variables and are related to important aspects of the calibration procedure. Since phytoplankton chlorophyll is a key variable, several coefficients directly related to its kinetics are investigated: l) phytoplankton growth rate: K 2} phytoplankton respiration rate: K_ 3) temperature dependence of phytoplankton growth rate: 6 U) zooplankton grazing rate: K~ 5) phytoplankton settling velocity: wp 6) saturating light intensity for phytoplankton growth: I0 o Coefficients affecting the inorganic nutrient systems, particularly phosphorus, are also investigated: l) Half saturation constant for available phosphorus: K ^ mp 2) Phosphorus to chlorophyll ratio: a 3) Rate of recycle of unavailable phosphorus and nitrogen to available forms : 1C and K Other effects investigated are: l) vertical transport (stratification) effects 2) silica to chlorophyll ratio: a . Dli The results of these sensitivity runs are presented as a series of plots showing the effect of parameter changes compared to the calibrated model results previously presented. Normally, sensitivity effects are investigated by +_ 50 percent changes in the value used for model calibration, thus brack- eting the results. 125 ------- Figure 62 shows the effect of varying the phytoplankton growth rate term, KI. Using a value of 2.08 day"1 reproduces the bimodal phytoplankton growth curve in Southern Lake Huron and Saginaw Bay fairly well. When the rate is increased to 3.12 day l, initial growth occurs earlier with the higher growth rate compensating for temperature limitation during these colder months causing a broader spring pulse in both areas. Lowering the rate to 1.0^ day"1 has dramatic effects on both areas. In Southern Lake Huron, the spring peak occurs late and the magnitude of both this and the fall peak is lower. The spring pulse in Saginaw Bay is ir.uch lower with the lower rate being unable to overcome the combination of temperature, light, nutrient limitation effects and transport losses. The effects of varying the phytoplankton endogenous respiration rate, K£, is also shown in fig. 62. Lowering the rate from .05 to .025 day"1 increases the concentration of phytoplankton chlorophyll both in Southern Lake Huron and Saginaw Bay as one might expect since a sink of phytoplankton is reduced. Increasing the rate causes more loss due to endogenous respira- tion to occur and lower phytoplankton concentrations result. It is interest- ing to note that the timings of the pulses and declines are virtually unaf- fected. Figure 62c illustrates the effect of varying the temperature dependence of phytoplankton growth. Since the effects of the saturated growth rate, KI , and the temperature dependence, 9i, are compounded in the growth rate term, and in order to isolate the effect of temperature dependence the saturated growth rates term for the three examples are set to be the same at 13 C. This corresponds to the approximate temperature during spring bloom. As can be seen, lowering 61 from 1.068 (KI = 2.08 day"1) to 1.03^ (KI = 1.65 day ) increases the growth rate during colder periods and spring growth starts earlier in both Southern Lake Huron arid Saginaw Bay. Increas- ing 61 to 1.102 (KI = 2.59 day :) results in the opposite effect, a delayed spring pulse which is less broad. The timing and magnitude during the fall period are virtually unaffected in both areas of the lake. Since phosphorus limitation has been shown to be an important mechanism during the calibration process, the next series of sensitivity runs addresses parameters affecting this process. Figure 63a shows the effect of varying K , the half saturation constant for inorganic phosphorus, and a , the phosphorus to chlorophyll ratio. Increasing the half saturation constant from 0.5 yg P/i to 1.0 and 2.0 yg P/£ has virtually no effect on Saginaw Bay, where concentrations of soluble reactive phosphorus average approximately 5 yg/&, well above the half saturation value. There is a sufficient inor- ganic phosphorus supply available for spring growth to commence as soon as temperature and light conditions warrant it. In Southern Lake Huron, how- ever, soluble reactive phosphorus concentrations average near 0.5 yg P/& which is right at the K value of the calibrated model. Any increase in mp this value results in a higher degree of nutrient limitation. At 1.0 yg P/& spring growth starts later since higher temperature and better light condi- tions are needed to overcome the added nutrient limitation. At 2.0 yg P/& this effect is even more pronounced. Soluble reactive phosphorus concentra- 126 ------- SOUTHERN LAKE HURON SAGINAWBAY 8.0 4.0 - 0.0 K1C 3.12day-' 2.08 •-•••1.04 j' j 'A'S'O'N'D 40.0 20.0 0.0 J'F'M'A'M'J'J EFFECT OF VARYING PHYTOPLANKTON RESPIRATION RATE 8.0 oc O K2C 0.075 day-' 0.050 •—• 0.025 g 4.0 £ 0.0 z Q. O 8.0 4.0 0.0 J'F'M'A'M'J'J'A'S'O'N'D 40.0 20.0 0.0 J'F'M'A'M'J'J'A'S'O'N'D EFFECT OF VARYING PHYTOPLANKTON GROWTH RATE TEMPERATURE DEPENDENCE KIT 1.112 1.069 ---1.034 J'F'M'A'M'J'J'A'S'O'N'D 40.0 20.0 0.0 j 'F 'M'AMVP J' Figure 62. Sensitivity to phytoplankton kinetic constants. Saturated growth rate % 20°C, K^ (top). Respiration rate @ 20°C, Kg (middle). Growth rate temperature dependence, 6, with m on KG constant at T = 13°C (bottom). Labels in the fig- ures correspond to computer program variable designations. 127 ------- EFFECT OF VARYING MICHAELIS CONSTANT FOR PHOSPHORUS SOUTHERN LAKE HURON SAG IN AW BAY 8.0 4.0 0.0 KMP 0.001 mgP/l 0.0005 ••-••0.002 J'F'M'A'M'J'J'A'S'O'N'D QJ — >£: ^J« !" 0.004 0.002 Deo CO Q. o.OOO J 'F'M'A'M1 J ' J 'A'S'O'N'D 40.0 20.0 0.0 0.032 0.016 0.000. J'F'M'A'M'J' ' "A'S'P'-N'D , , . ,-—, ". T J'F'M'A'M'J'J 'A'S'O' N'D EFFECT OF VARYING PHOSPHORUS-TO-CHLOROPHYLL RATIO 8.0 0.0 e 0.004 UJQ 0.002 Dt/5 OX 0.000 CO Q. PCHL - • - - 0.001 mg P/»g CHL a 0.0005 •••••0.002 J ' F ' M' A' M I J ' J ' A ' S ' 0 N ' D J ' F 'M'AiM' J ' N ' D 40.0 20.0 0.0 0.032 0.016 0.000 J ' F ' My A1 M ' J ' J 'A'S'O'N'D j A'S'O'N'D Figure 63. Sensitivity to phosphorus system kinetic constants, Michaelis constant for phosphorus, K (top). Phosphorus to chlorophyll ratio, a (bottom). 128 ------- tions follow the inverse pattern. Since limited growth implies less nutri- ent uptake, it follows that higher concentrations of inorganic phosphorus are computed, with increasing values of K The effects of varying the phosphorus to chlorophyll ratio, a = PCHL, are investigated in fig. 63t>. This coefficient effectively governs how much available phosphorus is utilized to produce a unit of chlorophyll a_. As a is increased the available supply of inorganic phosphorus will be depleted more rapidly. The calibrated model uses a value of 0.5 yg P/yg ChJl-a. It can be seen that doubling and redoubling this value to 1.0 and 2.0 yg P/yg ChJl-a has drastic effects on the calculation since two and four times the amount of phosphorus is being utilized by the phytoplankton for growth. In Southern Lake Huron a spring pulse of the magnitude observed is never gener- ated and the fall peak suffers as well. Soluble reactive phosphorus concen- trations are depleted to below the half saturation value and growth becomes severely limited. In Saginaw Bay the effect is equally dramatic. The spring peak is only about 15 yg/£ chlorophyll a_ using a = 1.0 yg Ch£-a/ yg POij-P and less than 10.0 yg/£ at a value of 2.0. These concentrations are well below observations. The increased rate of depletion of the soluble reactive phosphorus pool is also clearly seen. At a = 2.0 yg P/yg Ch£-a the available pool is essentially depleted by the end of March and phyto- plankton growth levels off. Some initial buildup of reactive phosphorus due to pulses of phosphorus from the Saginaw River (Section h) occurs at a = 1.0 yg P/yg Ch£-a but not enough to sustain a spring phytoplankton pulse of the magnitude observed. Thus, although a phosphorus to chlorophyll a_ rate of 0.5 yg P/yg Ch£-a is at the low end of the range of reported values, the concentrations of inorganic phosphorus in the open lake waters are small. Further the standing crop of phytoplankton which must be supported in Sagi- naw Bay is large. The computation is able to simultaneously reproduce ob- served conditions in both areas only for a value of a at this level. The importance of a correct phosphorus to chlorophyll a_ stoichiometric coefficient is clear from these sensitivity calculations. It is also sug- gested by eq. (56) of section 6 which indicates that the quantity of the total phosphorus that appears as chlorophyll is inversely proportional to the stoichiometric coefficient. The Lake Ontario results, see fig. 59 and 60, also support this inverse relationship. One of the principal drawbacks of Monod kinetics is that this ratio is assumed to be fixed. However it is well known that this ratio is quite variable and depends on the ambient phosphorus concentration. Thus it appears that an important refinement would be a kinetic structure which reflects this variability. Bierman's Saginaw Bay calculation [99] is one such structure, and a detailed analysis of this phenomena is available [37]• The choice of a minimum ratio is con- sistent with the discussion in section 6 and the observed data. The coefficient governing the rate of recycle of nutrients from the unavailable to an available inorganic form is assumed to apply to both the unavailable phosphorus and nitrogen. Figure 6k shows the results of sensi- tivity calculation with doubled and halved coefficients, K7 = KS, the 129 ------- 1 x o CO LL CM CO 00 0) bO • £H W -P p! -P S3 o •H cti 0) +3 » d H ^t i — 1 0) ,£ i — 1 ft o o o o V H o o -p a o ri -P -P .M •H fl •H H -P ft •H O W -P 0 ,d CO ft _^ VD (U ?H S 3AllOV3y 130 ------- recycle rates of organic nitrogen and unavailable phosphorus, respectively. Increases in the recycle rate result in higher calculated phytoplankton chlorophyll and soluble reactive phosphorus concentrations as expected from the theoretical analysis in section 6. As the calibrated rate 0.0k day"1 is increased to 0.08 day"1 more nutrient replenishment and utilization occurs vith larger populations resulting. As a lower rate (0.02 day M the con- verse is true and lower concentrations result. The nitrate profile in Southern Lake Huron is virtually unaffected by changes in the rate of re- cycle since the recycled nitrate is a small fraction of that already present, while in Saginaw Bay differences occur during the time of reduction in the spring phytoplankton pulse. These reflect a combination of the change in recycle flux and nitrification effects. The ammonia profile in both areas reflects the respective change in concentration due to increases or de- creases in the recycle rates. The effects of changes in herbivorous zooplankton grazing rates is shown on figure 65a. It can be seen that timing of phytoplankton growth and decline is greatly affected by changes in zooplankton grazing. This is true in both Southern Lake Huron and Saginaw Bay. Total zooplankton (herbivores plus carnivores) response also shows marked changes with a lower rate resulting in a delayed pulse in Southern Lake Huron and a delayed and smaller pulse in Saginaw Bay. The higher grazing rate results in earlier growth and more cropping of the spring phytoplankton crop in both areas of the lake. The model is very sensitive to changes in the herbivorous zooplankton grazing rate as well as the other zooplankton kinetic coefficients. With many factors affecting grazing it is difficult to specify what the actual grazing, efficiency, and limitation coefficients should be. However, the model is able to reproduce observed conditions fairly well. The coefficients governing the zooplankton systems in this model should not, therefore, be thought of as strictly unique. In fact there appears to be considerable uncertainty at the level of the kinetic structure itself. When a calculation is unduly sensitive to coefficients about which little is known, or which are known to vary over orders of magnitude, then considerable caution is required in interpreting the results of the calculation. This appears to be the case with the zooplankton formulation used in these calculations. However it is important to note that although the shape changes markedly the peak concentrations of phytoplankton chlorophyll are essentially the same over a four-fold change in filtering rate coefficient and the yearly average concentrations are not dramatically different. Therefore although the shape of the seasonal distribution is markedly affected, the characteristic concen- trations which are important in projected conditions are not as sensitive to this parameter of the zooplankton kinetics, and it is probable that for peak and average concentrations, the projected conditions are reasonably reliable. Figure 65b illustrates the effect of varying a the silica to chloro- oiP phyll ratio. Although the model is able to match open lake silicate concen- trations it fails to reproduce observed concentrations in Saginaw Bay. The reason is that without the inclusion of a diatom group the proper uptake rate 131 ------- 00 < Z o I I I ^ •J 1 Q Z b a z p en q 3 q d oq d q d I . r <=? o o o p < O (O q od q d to l/Bif «e m AHdOUOHHO 1/BuJ 'NOa«VO N01>INV-\|dOlAHd N01>INVndOOZ q d O i oc u. o u Q - o 03 o _ w ^ T-j I, § - -P -» d - -P ^ § < 8 q oi q d u .5 N O as o o ,o o z b c; oi q d •H tQ JH bO •H Hi bO 0) O •H fn 0) O -p •H -P •iH W -P Oj -P W P! o o o •H O SH O 0) CQ bO l/2O!S6uj S '31V:)niS3AllOV3U 132 ------- is not calculated. Also remineralization of silica is not taken into account. Varying a.,.^ does not help the situation in the bay, since rapid depletion is oljr calculated even at a lower stoichiometric coefficient. Since the calculation is not structured to represent the silica cycle in Lake Huron/Saginaw Bay, this exercise serves to demonstrate that a diatom species must be added to the calculation if observed conditions are to be reproduced. It also illus- trates that an incorrect kinetic structure cannot be tuned arbitratily to fit observations. Thus a calibrated model is an indication that the kinetic structure and constants are not inconsistent with the observations. For silica it is clear that both recycle and selective uptake by diatoms are required for calibration. The final sensitivity results, fig. 66, illustrate the effects of phyto- plankton settling velocity, saturating light intensity, and stratification. As shown earlier, the model is unable to reproduce observed chlorophyll con- centrations in the hypolimnion of Southern Lake Huron. Increasing the phyto- plankton settling velocity has no effect on the results in the hypolimnion with the increased downward flux of plankton adding little to concentrations in this large volume of water. The increased rate does affect the Saginaw Bay calibration, however, as can be seen. A lower settling rate results in expected higher concentrations. Increasing the vertical mixing during stratification and allowing more phytoplankton to exchange into the lower layer is another, although unlikely, mechanism by which higher concentrations in the hypolimnion might be calcu- lated. However, there is virtually no effect on the phytoplankton chloro- phyll distribution in the lower layer when stratification effects are re- moved. Thus, changes in transport in the form of phytoplankton settling velocity and vertical exchange as well as a lower saturating light intensity cannot account for high hypolimnetic chlorophyll concentrations. Once the mechanisms for survival at these deep, dark, and colder depths are known perhaps they can be incorporated into the model structure. The sensitivity calculations outlined above have shown what the effects of changes in kinetic coefficients have on the calculated results. For the phytoplankton and recycle kinetics, even large changes in coefficient values do not produce any computational difficulties and yields results which are plausible. Unfortunately the same is not true of the zooplankton kinetics. The coefficients finally chosen are based on the results of numerous cali- bration runs, application to Lake Ontario and the constraints provided in the available experimental information. By examining the effects of changes in these coefficients through a sensitivity analysis, one is able to respond to questions of effects of uncertainty in these values. 133 ------- >• I UJ O LU CO II p co q q q Q d d CM 0. (5 Z > u. o q 06 q d o Qc i Uj Z X O w Z oc > LL O \- LU U. U. UJ q 06 s 1 I I I oc o LL o I- CJ q od q o O co q 06 q o q od q d q co q d •H w a a ?H OJ 0) -p ^ c -P •H 3 o -P CO ^ fciO " •H ' ^ H -P CH bD 0) fl H •H • — ^ •P a O -P rf W ft 0) O -p a ^ o •H O (U O ,M H eg 0) h-i bO •H !H pq s d) •H ^1 H -P -P ^ -P O fl— 03 o a « -P O -H ^j -P bO fl -P 03 oi O CO iH t^ O, v ' ft O •—• fl O -P f^-ri a -P 0) o oi o -p o -^ •H -P -H O •H -P -H > «5 fl -P -P -H l/Brf 'e 11 AHdOdOHHO N01»NVHdOlAHd W fl 0) CO VD VD bO •H O 134 ------- SECTION 10 PRELIMINARY APPLICATIONS The calculation of the response of Lake Huron to increase in phosphorus mass inputs is one of the objectives of this study. In addition to their value for management decisions these calculations also provide considerable insight into the workings of the kinetics. Simulations are presented for a time span of 15 years. This is consid- erably shorter than the hydraulic detention time for the whole lake of 22.6 years. However the model does not incorporate the volumes associated with Georgian Bay and the North Channel which reduces the hydraulic detention time of the five segments to 1^.1 years. Phosphorus removal via settling consid- erably lowers the time to steady state. A fifteen year time span appears to be reasonable as shown in fig. 67 which shows the change in yearly average phytoplankton chlorophyll _a concentrations in Southern Lake Huron during a fifteen year time span. This projection, based on the final calibrated ver- sion of the model presented earlier and the present inputs of nutrients, shows yearly average phytoplankton chlorophyll &_ concentrations in Southern Lake Huron increasing from 1.33 yg/& at the end of the first year to 1.52 ug/£ at the end of the fifteenth year, a lh% increase. The concentration can be seen to level off, approaching dynamic equilibrium with the percent change approaching zero. All projections presented subsequently are fifteen year runs. Table 1^ summarizes the results for a series of such calculations. The values presented cover three phosphorus loading increases for the three different recycle mechanisms, with each simulation lasting fifteen years. There are differences in the base line for each case with respect to phos- phorus loading and equilibrium chlorophyll concentrations and direct com- parisons of absolute magnitudes are difficult. Therefore the results are converted to percentage changes for ease in comparison of the effects of the differing recycle mechanisms. As shown in fig. 68a, the first order recycle kinetics predict a strictly proportional increase in algal chlorophyll rela- tive to a change in total phosphorus input. However both saturating and second order recycle kinetics predict a more rapid change in algal chloro- phyll. This effect is due entirely to the changing quantity of unavailable phosphorus as the recycle rate increases. The total phosphorus concentra- tions are changing in almost direct proportion to the increasing mass input as shown in fig. 68b. However whereas the change in unavailable phosphorus is proportional for the first order kinetics, fig. 68c, the change is less for saturating kinetics and almost zero for second order kinetics. As a result the proportion of total phosphorus that is algal phosphorus changes dramatically for second order kinetics, almost as dramatically for saturating kinetics, but very little for first order recycle kinetics, fig. 68d. 135 ------- 1 11 13 15 YEAR Figure 67. Fifteen year distribution of and percent increase in yearly averaged phytoplankton chlorophyll a in Southern Lake Huron. Model is essentially at steady state in year 15. 136 ------- TABLE lit. EFFECT OF VARIOUS NUTRIENT RECYCLE MECHANISMS AND INCREASING PHOSPHORUS LOADING: LAKE HURON Percent Change in Total P Load + 100$ + 50$ BASE Total P Load (Ibs /day) Sedimentation Loss(lbs/day) Yrly Avg Chlorophyll (ug/&)# Unavailable P/Total P# Total P Load (its /day) Sedimentation Loss (ibs /day) Yrly Avg Chlorophyll (ug/£)# Unavailable P/Total# Total P Load (Ibs /day) Sedimentation Loss(lbs/day) u Yrly Avg Chlorophyll (yg/£) Unavailable P/Total P# Nutrient First Order Recycle Rate U8.27U 27,558 5.5U 0.80 36,205 20,7^9 it. 07 0.79 2it,137 13,950 2.66 0.78 Recycle Mechanism Saturating Recycle Rate itU,338 28JU5 it.9it 0.87 33,253 22,768 2.73 0.89 22,169 l6,13it 1.12 0.01 Second Order Recycle Rate it8,27it 23,210 10.38 0.56 36,205 19,928 6.27 0.7l' 2it,137 15,762 2.05 0.82 Southern Lake Huron Epilimnion Values 137 ------- As shown in section 6, the saturating kinetics appear to be the most realistic formulation for the Great Lakes. At chlorophyll concentrations that are large relative to the half saturation constant for the recycle reaction, K = 5 Ug Ch£-a/&, saturating kinetics behave as first order kinetics with roughly proportional changes in chlorophyll for changes in total phosphorus loading. However in the range of chlorophyll characteristic of Lake Huron, the behavior is more like the second order recycle kinetics with its accelerated response to small loading changes. This effect is quite important from a management point of view. The response of Lake Huron to small increases in total phosphorus loading is expected to be larger than strictly proportional. In fact the effect is more like a fourfold change in chlorophyll for a twofold change in phosphorus loading as shown in fig. 68a. The degree of reliability of these calcula- tions under projected conditions is unknown at present. "So verification of computational framework, in the sense of and independent computation of future widely different conditions and a check against field data, has been made. A two-fold difference in projected chlorophyll percent change exists between first order recycle kinetics and saturating kinetics (fig. 68a). Although saturating kinetics appear to be the probable mechanisms the sensi- tivity of the projections to this assumption is large and, therefore, this should be taken into account in utilizing these projections for management decisions. The results of a more extensive series of simulations for increasing phosphorus loadings are shown in fig. 69. These calculations represent the results from the final calibrated model using the saturating recycle kine- tics. An almost exponential increase is expected until 5 Pg Ch£-a/& is reached, after which the increases are more proportional to increasing load- ing. These results clearly indicate that a positive feedback mechanism exists at low chlorophyll concentrations. As phosphorus load increases not only does total phosphorus concentration increase but the fraction of un- available phosphorus decreases and the ratio of algal phosphorus to total phosphorus increases, compounding the increase in chlorophyll. For more eutrophic lakes this effect would not be observed since the recycle kinetics are saturated and behave as first order kinetics. However for Lake Huron, small increases in phosphorus loading produce significant changes in algal chlorophyll. The effect of loading reductions to Lake Huron are examined based on various waste management alternatives as outlined by the IJC. These plans consist of removing 60%, 83%, and a theoretical 100% of the controllable phosphorus input to Lake Huron. This results in actual removals of 3^.2%, ^7-3%, and 57% respectively, of the total load assuming ^3% of the input is from uncontrollable (non-point) sources. Effects of implementation of 80% phosphorus removal in the State of Michigan are also investigated as well as what type of waste load management is necessary to meet EPA's goal of non- degradation. The results of these simulations are presented in table 15. The assump- tions implicit in this analysis are: phosphorus load rediictions are instan- 138 ------- o in in CM mAHdOUOTHO snaoHdsoHd nvioi NOI1VU1N30NOO 3DVH3AV A1UV3A NI30NVH01N30y3d 0) ft O W s 05 ... fi ft S-t o w o O .f] -p & ft S ft CQ (!) O O H rd £H o5 ft W fl oi o3 (3 co ,cj jj . 4<4 O -P qj •' ^ ft i-l -p O -^ (^ v s - do; PL, ^H O • ^ 0 ^ EH * r] 0 fl^ 03 -P ft 2 O C .O W o f-{ -P O > W -p CQ O ?H ft o w ,d o O[ rd W ft o H O ft -H ft oj fl -P -P •H oj H O ^ cd -P W -P -P 2 fl O O ^ 0) EH -P O O ft O ,Q 3 CQ o ^-^ £n O O ^1 C! ••>,,£! ft O PL, ft •H W ttn S " O g H ^! H H ft O (U CO ft ft 0) fn O 0) O S-i H 0) O oi d ,c! CH fn O O 0) \|> ^^ O cd ci -H v _ ,, I I -P >s cri O H -P K O 0) 00 VD 0) !-, bO •H oj 0) 139 ------- SOUTHERN LAKE HURON "EQUILIBRIUM' CHLOROPHYLL a vs. TOTAL PHOSPHORUS LOADING 10.0 5.0 4.0 3.0 2.0 1.0 Q_ O cc O CJ 0.5 0.1 Figure 69. 0 5,000 10,000 TOTAL PHOSPHORUS LOAD TO LAKE HURON, metric tons/year (Southern Lake Huron epilimnion) Yearly average chlorophyll concentration versus total phosphorus loading to Lake Huron. ------- CO £5 0 M EH a ^j H CO 1-3 p-q p o s (in O CO EH CO w K . LT\ H ^ pQ 5\| EH >H PH 5j fVj >H >H «ai 0 pq S H E£ PH dj p4 S CO 1 — 1 O ^ CO >H I-H § H >H 1-3 P-i S ^« 0 W g W 0 SH EH 5^ \| — \| 1-3 PH PH IS! CO PH C£] prj EH f^ ] 1 \|_I] O PS CO «a! W ^H w p M EE W •CH h-H1 EE •aj M O EH M < 0 3. EH ^ O • u~\ oo cd 5J o^ p£J c~] PH O ' — ^ <=> bO 3. cd v- > fi < O Png • 1-3 PH O < > EH bfl < 0 3- EH -^ MD • OO t— t— H H 00 LP\ 0) ^ 0? p£] t~] PH O - — - c>? ^^, bO 03 --' > 3 < 0 oo oo • CM CM H P-t ^3 P -^ H EH ^~ to a PH C o J>^ C3 3j r^ •H ft cd >> O -p H in a ri C •H n3 H cd 0) ^ S >H O 1 as bO C 0) o P -H 1 -P rt cd O T( S oo • o CM \D • vo H H t~- O H ^ ON -^j" l/N O • CM O H H O t— CM C- OO o o t— CO ^ ^ 0 fi a ft-rl w C 0 H cd fcj o3 tiO PH > -H O r^H ^. S o o a; -H CO PH g ^^- o CO ON • oo CM t- • O CM L/\ CM OO H VD H • LTN t— CM • CM H CM H O OO ^•j- rt OO o MD CO a >> O cd •H pq H -P cd co o !s -P ^ S cd O J-i -d fl EH o Q) -H r^ pr\| tlD ^s. ft cd CM CO Tj CO • O cd J- ^ O 0 OO PH 1-3 -P O MD O 1-3 H rH • O CM .^j- • VD H VO Ln o H -J- ON • _jj- _j- o • CM ON O H O VO CM rt oo o ON vo G rS o cd •n pq rH -P cd w u > -P 2 3 cd O SH TJ S3 EH o eu -H ^! K bD '65. ft cd oo co fd co • O cd t— fi O O J- PL, 1-3 +3 OO CO 0 (-3 M _^- • £ — rH VO • OO H rH ITN CO ON t- • _^j- H ON • H O O H O OO H 0 oo o LTN (3 O •H •P CQ O H 3 0 cd £H 'd -POD 0 fi K EH ft CO T3 ^5. o cd t- ,a o LTN PH 1-3 O O H CJ (-3 H >3 cd pq js cd fl •H bO cd CO O -P ------- taneous; the transport regime is the same as that used in the base run including the time variable flow from the Saginaw River and the bay-lake exchange; and relative fractions of available and unavailable phosphorus for the loadings remain the same as that used in the calibrated model. Since Saginav Bay is sensitive to short term fluctuations because of its short hydraulic detention time these assumptions become importsjit and since the actual changes to be expected in these phenomena are unknown over the period of the simulation, results presented for Saginaw Bay should be viewed with this in mind. The effects on Southern Lake Huron are important since they directly address the first and fourth reference questions, of the Upper Lakes Reference Study: to what extent are the waters of Lake Huron being polluted on either side of the boundary to cause degradation of existing levels of water quality in the lake and what are the effects of preventative measures. These calculations enable one to gain some insight into these issues. The results of the simulations indicate that the allowable phosphorus loading which maintains present water quality is 3600 tonnes/year. This will maintain a level of 1.31 Ug/£ chlorophyll a_ in Southern Lake Huron epilimnion on a yearly average basis. Implementating an 80% phosphorus removal in Michigan yeilds levels of 1.1 yg Ch£-a/£ in the southern lake as well as a 15$ reduction in yearly averaged total phosphorus concentra- tions amounting to a decrease of 0.9 yg P/&. The lowest concentrations result from the IJC plan which postulates a reduction for the Saginaw Bay load to 569 tonnes/yr.. Here chlorophyll a_ levels in Southern Lake Huron are held to 1.0 yg/£ after 15 years. There is also an accompanying 39% decrease in the peak spring chlorophyll as well as an 18$ decrease in total phosphorus concentrations. Results in Saginaw Bay are mcst dramatic under this scheme showing an almost 50$ reduction in yearly averaged chlorophyll a_ values to 8.5 yg/£ and a spring peak reduction to 13.5 yg/£. Total phos- phorus concentrations show a 50$ reduction to 17 yg P/£. More detailed results of these calculations are given in table 15. It is important to emphasize that the absolute values of these pro- jected concentrations are not certain to the three and four digits reported in the tables. The absolute error associated with these projections is unknown at present. Rather it is the relative changes that have more validity and it is these results that should be used as a guide in formu- lating the phosphorus reduction plans for Lake Huron and Saginaw Bay. An important issue that should be addressed in future work is the relative errors that can be associated with projections, that is what is the probable range of projected concentrations based on the present uncertainty of the mass discharges, the observed data, and the transport and kinetic para- meters . ------- REFERENCES 1. Great Lakes Basin Commission. 1975- Great Lakes Basin Frameworks Study. Appendix 3 - Geology and Ground Water. 2. Schelske, Claire L. and James C. Roth. 1973. 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Lassiter, R.R. 1975- "Modeling Dynamics of Biological and Chemical Components of Aquatic Ecosystems". EPA Ecol. Res. Ser. EPA-660/3-75- 012, Corvallis, Oregon. 30. Vollenweider, R.A. 1965- "Calculation Models of Photosynthesis" in Primary Production in Aquatic Environments, ed. C.R. Goldman, Univ. Calif/Press, Berkeley, pp. 1+25-457. 31. Steele, J.H. 1965. "Note on Some Theoretical Problems in Production Ecology" in Primary Production in Aquatic Environments, ed. C.R. Gold- man, Univ. Calif. -Press, Berkeley, pp. 383-398. 32. Fuhs, G.W. 1968. Phosphorus content and rate of growth in the diatom Cyclotella nana and Thalassiosira fluviatilis J. Phycology, 5, pp. 312- 321. 33. Caperon, J. 1968. Population growth response of Isochaysis galbana to variable nitrate environment, Ecology, 49, pp. 866-872. 34. Droop, M.R. 1973. Some thoughts on nutrient limitation in algae. J. Phycology, 9, pp. 264-272. 35. Rhee, G-Y. 1973. A continuous culture study of phosphate uptake, growth rate, and polyphosphates in Scenedesmus sp. J. Phycology, 95 pp. 195-506. 36. DiToro, D.M. 1979- Applicability of A Cellular Equilibrium and Monod Theory (to appear in Ecological Modelling). 37- DiToro, D.M. and J. Connolly. Mathematical Models of Water Quality in Large Lakes. Part II - Lake Erie. To appear in EPA Ecological Research Series. 38. DiToro, D.M., D.J. O'Connor, J.L. Mancini, R.V. Thomann. 1974. "Pre- liminary Phytoplankton-Zooplankton Nutrient Model of Western Lake Erie" in Systems Analysis and Simulation in Ecology, Vol. 3, Academic Press. 39- Sushchenya, L.M. 1970. "Food Rations, metabolism, and growth of crustaceans" in Marine Food Chains, ed. J.H. Steele. Oliver and Boyd, Edinburgh, pp. 127-l4l. 40. Golterman, H. 1975. Physical Limnology. Elsevier Sci. Pub. Co., Amsterdam, Chapt. 15.2, pp. 280-324. 4l. Parsons, T.R., Takahashi, M. 1973. Biological Oceanographic Processes. Pergamon Press. Oxford, U.K., Chapt. 4, pp. 106-134. 42. Richman, S. 1966. "The effect of phytoplankton concentration on the feeding rate of Diaptomus oregonensis". Verh. Int. Ver. Theor. Angew. Limnol. 16, pp. 392-398. 145 ------- 13. Richman, S. 1958. "The transformation of energy by Daphnia pulex." Ecol. Monogr. 28, pp. 273-291. kh. Conover, R.J. 1966. "Assimilation of Organic Matter by Zooplankton. " Limnol. Oceanogr. 11, pp. 338-3^5- 1+5. Wetzel, E.G. 1975. Limnology. W.B. Saunders Co.,, Phila, Pa., p. 319- U6. Mullin, M.M. , E.F. Stewart, F.J. Fuglister. 1975. "Ingestion by Plankton grazers as a function of concentration of food." Limnol. Oceanogr. 20(2), pp. 259-262. ^7- McAllister, C.D. 1970. Zooplankton rations, phytoplankton mortality and the estimation of marine production, in Marine Food Chains , ed. J.H. Steele, Oliver & Boyd. Edinburgh, pp. U8. Thomann, R.V. , D.M. DiToro, R.W. Winfield. 197^. "Modeling of Phyto- plankton in Lake Ontario (IFYGL)." Proc. 17th Conf. Great Lakes Res., pp. 135-1^9. ^9. Wright, J.C. 1965. "The population dynamics and production of Daphnia in Canyon Ferry Reservoir, Montana." Limnol. Oceanogr. 10, pp. 583- 590. 50. Golterman, H.L. 1975. Physiological Limnology, Elsevier Scientific Publ. Co., Chapt. 8, pp. 13^-1^37 51. Verhoff, F.H. and J.V. DePinto. 1977. Modeling and Experimentation Related to Bacterial-Mediated Degradation of Algae and its effect on nutrient Regeneration in Lakes, Vol. 18, Develop, in Industrial Micro- biology. Soc. Indus. Microbiol., pp. 213-229. 52. DePinto, J.V. and F.H. Verhoff. 1977. Nutrient Regeneration from Aerobic Decomposition of Green Algae. Envir. Sci. Technol. ll(U), pp. 371-377. 53. Butler, E.I., E.D.S. Corner, S.M. Marshall. 1970. On the nutrition and metabolism of zooplankton VII. J. Mar. Biol. Assn. U.K., 50, pp. 525-560. 5^. Satomi , M. and L.R. Pomeroy. 1965. Respiration and Phosphorus Excretion in Some Marine Populations Ecology 46(6), pp. 877-881. 55. Grill, E.V. and F.A. Richards. 1964. "Nutrient Regeneration from Phytoplankton Decomposing in Sea Water." J. Mar. Research, 22, 51. 56. Jewell, W.J. and P.L. McCarty. 1971. "Aerobic Decomposition of Algae." Environ. Sci. Technol. 5(10), p. 1023. 57. Foree, E.G. and P.L. McCarty. 1970. "Anaerobic Decomposition of Algae." Environ. Sci. Technol. MlO), pp. 842-849. 146 ------- 58. Hendry, G.S. 1977- "Relationships Between Bacterial Levels and Other Characteristics of Recreational Lakes in the District of Muskoka." Interim Microbiology Report, Laboratory Services Branch, Ontario Ministry of the Environment. 59. Lowe, W.E. 1976. Canada Centre for Inland Waters, 867 Lakeshore Road, Burlington, Canada L7R 4A6. Personal communication. 60. Henrici, Arthur T. 1938. Seasonal fluctuation of lake bacteria in relation to plankton production. J. Bacteriol. , 35:129-139- 6l. Menon, A.S., W.A. Gloschenko and N.M. Burns. 1972. Bacteria-phyto- plankton relationships in Lake Erie. Proc. 15th Conf. Great Lakes Res. 1972:94-101. Inter. Assoc. Great Lakes Res. 62. Rao, S.S. 1976. Observations on Bacteriological Conditions in the Upper Great Lakes 1968-1974. Scientific Series, No. 64, Inland Waters Directorate' CCIW Branch, Burlington, Ontario. 63. O'Connor, D.J., R.V. Thomann and D.M. DiToro. 1973. Dynamic Water Quality Forecasting and Management. EPA Ecological Research Series EPA-660/3-73-009. 6k. Johnson, James H. 1958. Surface-current studies of Saginaw Bay and Lake Huron. 1956. U.S. Fish and Wildlife Service Spec. Sci. Rept. - Fisheries No. 267. 65. Csanady, G.T., P.J. Sullivan, M. Berretts, A. Berge and A.M. Hale. 1964. Hydrodynamic studies on Lake Huron at Baie du Dore, Summer 1964. Great Lakes Institute, Univ. Toronto Rept. No. PR 19. 66. Murty, T.S. and D.B. Rau. 1970. Wind Generated Circulations in Lakes Erie, Huron, Michigan, and Superior. Proc. 13th Conf. Great Lakes Res., Int. Assoc. Great Lakes Res. 67. Rodgers, G.K. 1964. Drift card studies - Lake Huron. Univ. Mich. Great Lakes Research Div. Pub. No. 11. 68. Rodgers, G.K. 1972. Great Lakes Institute data catalogue and methods for I960 to 1970. Univ. Toronto Great Lakes Institute Div. Pub. No. EG7. 69. Great Lakes Institute, Univ. of Toronto. 1965- Great Lakes Institute Data Record, 1963 surveys - Part 2: Lake Huron, Georgian Bay and Lake Superior, Report PR 2k. 70. Great Lakes Institute, Univ. of Toronto. 1964. Great Lakes Institute Data Record, 1962 surveys - Part 2: Lake Huron, Georgian Bay and Lake Superior, Report PR 17. 71. Great Lakes Institute, Univ. of Toronto. 1971. Great Lakes Institute Data Record, Surveys of 1964. Report PR 42. 147 ------- 72. Rodgers, G.K. 1962. Lake Huron Data Report, 1961. Univ. Toronto, Great Lakes Institute, Report PR 5. 73. Rodgers, G.K. 1963. Lake Superior, Lake Huron and Georgian Bay Data Report, I960. Univ. Toronto, Great Lakes Institute Report PR 12. 7^. U.S. Dept. of the Interior, FWPCA. 1969. Saginaw Bay and Southern Lake Huron tributaries - Michigan Water Quality Data 1965 Survey - LHBO-15-C. 75- U.S. Dept. of the Interior, FWPCA. 1969. Lake Huron Water Quality Control Plan. 76. U.S. Dept. of the Interior, FWPCA. 1970. Long term water quality surveillance - report of data collected - 1970. 51A. 77. U.S. Dept. of the Interior, FWPCA. 1970. Results of 1969 Water Quality Monitoring Program - Lake Huron Basin Office. LHBO 33-A. 78. U.S. Dept. of the Interior, FWPCA. 1968. Results of 1967 Sampling Program - Detroit Program Office. 79. U.S. Dept. of the Interior, FWPCA. 1969. Water Quality Data - 1965 Survey - An Sable River - Michigan. LHBO-18A. 80. U.S. Dept. of the Interior, FWPCA. 1968. Water Quality Data - 1965 Survey - Flint River - Michigan DPO-13C. 8l. U.S. Dept. of the Interior. FWPCA. 1969. Water Quality Data - 1965 Survey - Thunder River - Michigan. LHBO-19A. 82. U.S. Dept. of the Interior, FWPCA. 1969. Water Quality Data - 1965 Survey - Shiawassee River - Michigan. DPA-12C. 83. U.S. Dept. of the Interior, FWPCA. 1969. Water Quality Data - 1965 Survey - Cheboygan River - Michigan. LHBO-20A. Qh. U.S. Dept. of the Interior, FWPCA. 1969. Water Quality Data - 1965 Survey - An Sable River - Michigan. LHBO-18A. 85. U.S. Dept. of the Interior, FWPCA. 1968. Water Quality Data - 1965 Surveys - DPO-10C. 86. Canada Centre for Inland Waters. 1968. Limnological Data Report No. 1 - Lake Huron Cruise 68-301, Aug. 18-28. Canadian Oceanographic Data Centre, Burlington, Ontario. 87. Canada Centre for Inland Waters. 1969- Limnological Data Report No. 1 - Lake Huron Cruise 69-202, Sept. 22-29, Cruise 69-203, Nov. l8-Dec. 6. Canadian Oceanographic Data Centre, Burlington, Ontario. ------- 88. Canada Centre for Inland Waters. 197^. CCIW Water Quality Monitoring Program - Provisional Listing - 1971 Surveys. 89. Canada Centre for Inland Waters. 1975. CCIW Water Quality Monitoring Program - Provisional Listing - 197^ Surveys. 90. Glooschenko, W.A., J.E. Moore and R.A. Vollenweider. 1973. Chloro- phyll-a distribution in Lake Huron and interrelationship to primary productivity. Proc. l6th Conf. Great Lakes Res. Inter. Assoc. for Great Lakes Res. 91. Glooschenko, W.A. and J.E. Moore. 1973. Surface distribution of Chlorophyll and primary production in Lake Huron, 1971- Fisheries Research Board of Canada. Tech. Rept. No. Uo6. 92. Vollenweider, R.A., M. Munawar, and P. Stadelmann. 197^-• A compara- tive review of phytoplankton in the Laurential Great Lakes. J. Fish. Res. Board Can. 31: 739-762. 93. Watson, H.H.F. 197^. Zooplankton of the St. Lawrence Great Lakes - species composition, distribution, and abundance. J. Fish. Res. Bd. Can. 31: 783-79^. 9^. Schelske, Claire L., et al. 1976. Southern Lake Huron Surveys, Univ. Mich. Great Lakes Res. Div. Spec. Rept. & Data Listing. 95. Smith, V. Elliot. 1975- A survey of chemical and biological factors in Saginaw Bay (Lake Huron) - Annual Report II - Cranbrook Institute of Science. 96. Fee, Everett J. 1976. The vertical and seasonal distribution of chlorophyll in lakes of the Experimental Lakes Area, Northwestern Ontario: Implications for primary production estimates. Limnology and Oceanography, Vol. 21, No. 6, p. 767. 97- Bierman, V.J. Memo summarizing Robbins1 sedimentation estimates (personal communication). 98. International Joint Commission. 1976. The Waters of Lake Huron and Lake Superior - Volume I - Sunmary and Recommendations - Report to the IJC by the Upper Lake Reference Group. 99- Bierman, V.J., Jr. 1976. Mathematical model of selective enhancement of blue-green algae by nutrient enrichment, in Modeling Biochemical Processes in Aquatic Ecosystems, ed. R. Canale, Ann Arbor, Mich. 100. Saylor, J.H. and L.J. Danek. 1976. Water Volume Transport and Oscillatory Current Flow Through the Straits of Mackinac. Jour. Phys. Oceanogr. 6, pp. 229-237- 101. Quinn, F.H. 1977- Annual and Seasonal Flow Variation Through the Straits of Mackinac. Water Resources Research 13, pp. ------- 102. International Joint Commission. 1977. The Waters of Lake Huron and Superior, Volume II (Part B) - A Report to the IJC "by the Upper Lakes Reference Group, pp. 295-350. 103. Verhoff, F.H., C.F. Cordiero, W.F. Echelberger and M.W. Tenney. 1973. "Modeling of Nutrient Cycling in Microtiial Aquatic Environments" in The Aquatic Environment: Microbial Transformations and Management Implications. eds. L.G. Guarria and R.K. Ballantiie EPA U30/6-73-008, pp. 13-50. 10k. International Joint Commission. 1978. Fifth Year Review of Canada- United States Great Lakes Water Quality Agreement Report of Task Group III. 105. International Joint Commission. 1977. The Waters of Lake Huron and Superior, Volume II (Part A) - A Report to the IJC by the Upper Lakes Reference Group, p. 59 (Table 3.1-1), p. 64 (Table 3.1-6). 150 ------- o K O S O EH W § CM 0 EH ^-\| K CM si w CO 9 EH 1 1 03 1 H ft O H V i — i i •H fl 1 W H •— ' ,3 PM u •H i- w cd + '—• & & <—• on o a Is a i OH <— • • H ^ PL, -P 1 a) + -3- ^ o o* ' — ' CM 1 a _* •H W +3 1 ^ a -— H 0 •H CM h o o3 ^ •H (DO O + +3 CM -P 03 1 CO r— > K EH CM _J ^^ + h; ^ W CM 1 O~ c^ + p w "X H ' — H -^ -t H C! 1 S3 CD o -=1-0 •H O -H ^ -p CM -p o — o i cd CM o3 H ft ni OA H O MS •3 S3 0) B ^f S3 O O CM & W O ,3 O oo tn H II H o « i- CM H O CM CM O H 151 ------- X-— s -d ttJ d -P d o o s! 3 H to -p •H d r^ g O •H -P 03 •P O ^ [Q -P 03 O -P -H W -P d ft O -H O ?H O > 'd d ="? OO CO VD O 0 0 LT\ oj H on H H w W CD H o o 0 !>> CM -P •H Cg) -p tQ d d DO) a) -P -H -P o3 O d JH -i-t H XJ "Vn p Is O bO O O -H £H i—l C5 D JH bO -d 3 d ^ xT ft o !H O H C"j o 0 -p 03 O •H H •H CQ >> 03 •d S LT\ O o £s ^5 -p •H o 0 H (L) ^ bO d •H H P -p 0) CQ d 0 -p d CO H ft O -P r^M PH 152 ------- to -P •H s? (U fl O fl 0 a § H o5 LTN O LA -=!• O LT\ O bO «H I w fl O •H -P C OJ CD PL, 2! O P-i H •H 05 a -p o5 a< W o •H I •H O •H O -P CQ fl O •H -P a 0 PH 05 H ^3 O o CM EH CM CM CO -p cc! O -p -H CQ -p a ft O -H O JH O CD W -P CU 05 Q PH ft CM K t ""a? I 0 O •H -P O 0 0 o CM ca> 0) -p ct5 K a o •iH -P ^ •H ft CQ > C~J ft •d OJ •H ft CQ 0) ^ ^-t O a o •H -P O 05 ^ ^H 0) H f* o5 H •H o3 ^ ------- K EH g g (=5 0 £-\| a <\| PH 0 0 N CQ D 0 P3 O > H FP 1 . ro ^ 9 EH r^-> O 1 H •H 03 S3 £ ""< \ <-\ + ^ 0 ? ^ PH ft 03 + ,^ — i s bO £H Q t i , . < \ H + -3- S 7^ P-i S3 _fe O 03 •H w^ J3 CO. O^ 1 W H o •H + -P •— ' 0) \|i] •H P-i ^3 O O 03 •H O CO. JP CQ 00 f S3 K 0 r-i •H 03 -p 1 o H a3 A ? 3 H o3 I H £1 O bO 3- O O S3 O % on W EH f II PH S3 O •H -P O o3 0) K S3 O •H -p •H S3 O •H a •H CQ CJ W e CQ aJ I O bO O LT\ LJ .a o S3 O w CQ -P S3 S3 o3 O -P -H w -p S3 ft O -H 0 SH O (1) CQ -P 0) 03 Q K a 0 •H -P 03 -p •rH a •H l_^ CP -P P-J bO S3 •H f-, 0) -P H •H pt4 ?H O -P d CO -p CQ S3 O o S3 a) o +> -H Oi -P K 03 fn bD J3 S3 -P •H a3 5-t CQ tt) <-\ H •rH 03 O •H -P -P •rH £3 •H 0) -P o3 PH S3 O •H -p 03 H •H £3 •H CQ CQ 5 O S3 1) •H O •H ^-H CH pr"\| S3 O •H -P 03 H •H gd •H CQ CQ •c^ c3 ^ •H 03 S 151* ------- !§ u o E? o bO a o a o a O •H 1 •d 0\ o LTN • o H O _=)• O PL, CH a o •H o o	------- w -P •H a H 0) c o c w g 0) O CM O O o CM H O on o o LO -=f O ctf a o PM o •H -p o ir\ ir\ CD o «* O •H -P & O •H s o •H O -P CQ fl O •H -P O 03 ------- w -p •H g I 0) d o a o OJ co o § H I § •H -p o vo CD •H o •H O •H O -P CO g •H •P O 03 ------- bO !H O PL, H •H o3 £ a cu pi 3 W CO -p S3 S3 03 O -P -H CO +5 $3 P. O -H O f-t O CU M -P CU 03 Q P3 H 1 !>> oJ •ct on o o t— « o o 0 CM ca> 0) -p oi K S3 o •H -P 03 N •H ^ f-l , 0? Tj ro o o CO W o o O CM cu -p o3 tf S3 o •H .p efl N •H rH 03 Sn CU S3 •H S CO pi fn O 43 ft CO O 43 PL, (U rH p «3 H •H 03 > 03 S3 P 0) p\| O S3 CO O H OO CD -P S3 (U •H O •H CH CH CU O 0 CU rH p! -p 03 H CD ft & CU EH =^ o3 => 43 CJ bO PL O 0 UA a W $3 O rH -p 03 N •H 1 d JH CU S3 •H s -p c cu •H rf -P Pi O5 SH O Vi ^ o3 -P CO S3 O o $3 O •H -P 03 fn p! •P 03 CQ > 0? T^ "a LIA 0 O t-^r f—-i 1 bO c , ?H O is S3 CU bO O fn -P •H 05 0 •H S3 03 bO S !H O =H >J -P •H O O rH cu > bO S3 •H rH -p -p cu CQ !>> c? tJ s LA O o PL, t> oJ ,-H £ ts CO pi SH O 43 ft CO o 43 PM cu H p 03 H •H oi 03 !§ r< O tH >» -p •H O O rH CU > bO S3 •H rH -p -p cu CQ 158 ------- CQ W H EH PS O O H EH S & EH CQ >H CQ t CO pr"\| \|_3 pQ CX EH £_\| CL) -P (I) £3 CD cd PH a •p CQ on PS 1 CM PS 1 H PS II -p i — i cd 1 r-^H O •tf cd\| H H tc~{ ft 0 o H O a o -p fl cd H ft 0 J? PH H ffi LA PS 1 _j^- PS 1 on PS PH O cd ca II -p x i — i PS CNl ^ 3 O I -=f I on cd H W H 0 fl + "£ + ^ ^ CO ^ O c{ ft fl fl CO (1) 0) O tlO tlQ r^H O O PH -P -P 0) •H -H H s a ^ cd cd 0) H •H -p -H a cd cd 0 H !> g -p cd -3" LA VO CO PS \| , X 0 LA PS + M PH V S s — ^ "^ C[_\| 1 V ^ 0 ft cd + ^t PS — <; i H O ft — x 0 LO 1 H + on PH <3j C\|_ \| PH ft cd — CQ 1 CO H PS -j- -{- s — ^ CM 0 PS u~\ <; PS PH PH ft LA cd PS -—• o + 0 cd > H -rl •H d ^ c^ H fi cd H •iH cd [> o\ 159 ------- TABLE A9. TIME VARIABLE SAGINAW BAY WASTE LOADINGS Time (days) 0 1 3 20 29 30 38 11 56 59 66 81* 86 96 100 ill* 131* lll 117 193 206 22T 255 295 311 325 353 365 [Org N] (Ibs/day) 36,100 36,100 19,700 18,900 175,000 125,000 31,900 ill, 800 70,900 19,500 187,000 26,000 53,800 113,000 87,100 36,800 111, 200 169,000 35,100 18,000 5,410 19,000 8,0l0 9^5 16,150 6,850 7,880 7,880 Time (days) 0 2 18 21 28 32 38 >9 52 56 59 65 73 80 87 91* 95 101 105 109 119 123 131* 135 lUl ll2 113 155 162 165 172 226 261 352 365 [NH^-N] (Ibs/day) 3,890 3,890 1,900 7,6liO 22,000 12,000 1,220 2,270 3,910 10,500 8,680 38,100 11,000 9,290 4,660 11,700 1,960 l,ll0 8,060 1,990 3,700 7,110 5,310 11,000 1,060 10,800 l,ll0 3,090 6,910 3,180 3,180 1,020 1,900 5,710 5,710 Time ( clays ) 0 1 8 21* 28 30 39 53 59 65 74 90 95 101 106 112 137 lll ].12 170 179 189 207 225 261 280 353 365 [NOj^-N] (Ibs/day) 15,200 15,200 2l,l00 207,000 515,000 258,000 66,700 73,700 92,500 106,000 128,000 66,200 230,000 127,000 127,000 11, 600 69,000 118,000 99,100 11, 200 10,000 9,280 2,990 2,520 3,960 U,990 U,2l0 l,2l0 (continued) 160 ------- TABLE A9 (continued) Time ( days ) 0 1 16 24 29 32 3k ^9 56 59 66 67 74 90 95 99 114 134 141 142 147 154 162 165 206 295 311 337 365 [Unavail-P] (Its /day) 4,060 4,060 2,570 14,700 54,300 12,200 3,830 1,830 8,210 9,920 65,600 21,500 6,470 4,630 24,900 11,200 7,960 3,990 37,600 14,300 5,520 3,380 11,200 4,870 l,84o 774 2,800 249 1,650 Time (days) 0 3 18 21 22 24 25 28 30 32 36 49 56 59 64 67 78 99 100 101 106 109 126 134 135 141 142 153 155 158 162 165 176 193 226 262 274 280 295 305 311 317 325 337 [PO^-P] (Ibs/day) 2,710 2,710 637 2,510 3,550 4,300 4,910 8,970 2,150 3,350 1,840 957 3,310 2,930 9,320 4,160 1,400 818 9,540 2,400 701 2,530 975 3,280 639 529 1,710 364 1,550 609 2,690 1,000 646 1,100 706 871 2,090 1,330 1,800 1,870 4,770 1,820 2,020 917 Time ( days ) 0 1 18 21 23 25 28 29 32 38 39 50 53 59 65 74 78 93 95 101 105 114 120 130 134 137 147 158 162 176 179 186 274 295 311 325 353 365 [Si] (Ibs/day) 94,000 94,000 46,700 111,000 338,000 216,000 324,000 687,000 164,000 76,600 115,000 47,400 230,000 169,000 767,000 251,000 138,000 265,000 444,000 41,500 271,000 75,600 72,600 92,400 70,200 246,000 91,100 42,800 91,100 53,200 32,200 83,400 40,700 30,900 65,800 35,900 34,800 34,800 161 ------- CQ C5 H^ ^H H P 5 O h3 ^: K ------- TABLE A12. FLOWS TO (Segment) FROM (Segment) FLOW (cfs) 1 2 2 2 boundary boundary 1 boundary 3 boundary 175,^60 2,000,^60 (north-south circulating-flow) 6,555 11,235 (Day 0-151) 1,561 (Day 181-365) 193,250 (Day 0 - 151) 183,576 (Day 181-365) 11,235 (Day 0-151) 1,561 (Day 181-365) 1,825,000 (north-south circulating flow) 163 ------- CQ O s 3 ffi 0 H • on s! 3 pQ 3 EH 0) O !-t 0) -P f-t H CM 1 -p OO a 0) 0) CQ 01 O OJ 0) -p c H J- I -P LA C 01 01 CQ 0) o o3 0) -P fl '— H H Q "fl oo a EH bQ P=H Ol VO CQ O H 0) 0 oj ^H O) -P S H CM 1 -p LA fl 01 a bO 0) CQ 0) 0 153 Ol -p H H 1 -P - 0) CQ 0) !>, a 03 •H Tj EH ~— CM CM CM CM ON ON ON H LA LA LA ON CM CM CM V£> H H H H LA LA LA LA on on on on H H H H CM -3- -=f -* on on on on j- j- j- _* ON ON ON ON VD VD VO VO t— t— t— C— ^ * rt ^ J~ ~j~ ^3~ -^~ on on on oo H H H H LA LA LA LA CO CO CO CO oo on on on r\ rt «N f\ LA LA LA LA H H H H J- _4- -3" J" 0000 on vo ON CM CM CM CM H H H H ON ON ON ON vo VD VO vo H H H H LA LA LA LA on oo on oo H H H H -4" -4" _^"j" ^" on on on on ^f J- J- ,3- ON O\ ON V£) VO VO t — t — t — «, .. ^ o -^1" -3" -3" on on on H H H LA LA LA CO CO CO on on oo » ~ ^ o LA LA LA H H H -4" J- J" O O O O CM LA CO H H H H CM OJ CM CM CM ON ON ON ON LA LA LA LA CM CM CM CM H H H H LA LA LA LA oo on en on H H H H —3" -^j~ ~3" ^- on on en oo _=i- -a- _ j- (3N 0\ VO VD t— t— O O •< " ^ j- y^" en on rH H 1A LA CO CO m on o o « •< IA LA H H "* J" 0 0 O 0 j- N- o on CM CM rn on CM ON LA CM H LA on H -J- oo _=)• ON \O t— «* ^f on H LA CO on * LA H "^ 0 vo oo CM ON LA CM H LA on H ^j- on j- ON VD t— « ^^f on H LA CO on A LA H "^ LA VD on 16U ------- CQ 1 P-i EH g cl? pr"\| CQ 3 w pq <3J EH LA -P C 0) £5 be CD CQ •p a OJ & 0) CQ on -p a M OJ CQ CM -p Pi g be 0) CQ H _p pj S Si (p CQ fH rf CD f-l cd PM , — 1 t— 0 OJ • • o o LA t— O OJ O 0 LA O LA VO H H t— O OJ LA O H t— on O OJ LA O H H OJ w -p rt 0) P! -H *— 00 0 -H -H — ' -p ------- TECHNICAL REPORT DATA (Please read Instructions on the reverse before completing) 1. REPORT NO. EPA-600/3-80-056 2. 3. RECIPIENT'S ACCESSION NO. 4. TITLE AND SUBTITLE Mathematical Models of Water Quality in Large Lakes Part 1: Lake Huron and Saginaw Bay 5. REPOF1T DATE JULY 1980 ISSUING DATE 6. PERFORMING ORGANIZATION CODE 7. AUTHOR(S) Dominic M. DiToro and Walter F. Matystik, Jr. 8. PERFORMING ORGANIZATION REPORT NO. 9. PERFORMING ORGANIZATION NAME AND ADDRESS Manhattan College Environmental Engineering and Science Program Bronx, New York 10471 10. PROGRAM ELEMENT NO. A30B1A 11. CONTRACT/GRANT NO. R803030 12. SPONSORING AGENCY NAME AND ADDRESS Environmental Research Labortory Office of Research and Development U.S. Environmental Protection Agency Duluth, Minnesota 5580^ 13. TYPE; OF REPORT AND PERIOD COVERED Final 14. SPONSORING AGENCY CODE ~~ ~~~ EPA/600/03 15. SUPPLEMENTARY NOTES Refer to Part 2: Lake Erie for supplemental information. 16. ABSTRACT This research was undertaken to develop and apply a mathematical model of the water quality in large lakes, particularly Lake Huron and Saginaw Bay (Part 1) and Lake Erie (Part 2). A mathematical model of phytoplankton biomass was developed which incorporates both phytoplankton and zooplankton as well as phosphorus, nitrogen and silica nutrient forms. Extensive water quality data for Lake Huron and Saginaw Bay was analyzed and statistically reduced. The model was then calibrated by comparison of computed results to these data. An exhaustive treatment of the kinetics employed for modeling the eutrophication process is presented. The sensitivity of the model to some of its key parameters is examined. In addition, responses of water quality in Lake Huron and Saginaw Bay system to variations in total phosphorus inputs are projected. 17. KEY WORDS AND DOCUMENT ANALYSIS DESCRIPTORS b. IDENTIFIERS/OPEN ENDE D TERMS c. COSATI Field/Group Mathematical models Water quality Great Lakes Lake Huron Saginaw Bay Ecological Modeling 08/H 18. DISTRIBUTION STATEMENT Release to public 19. SECURITY CLASS (This Report) Unclassified 21. NO. OF PAGES 180 20. SECURITY CLASS (Thispage) Unclassified 22. PRICE EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION IS OBSOLETE 166 -US GOVERNMENT PRINTING OFFICE 1980-657-165/0070 -------


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Laboratory
Duluth MN 55804
EPA-600/3-80-056
July 1980
Research and Development
Mathematical
Models of Water
Quality in  Large Lakes

Part  1
Lake Huron and
Saginaw Bay

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                RESEARCH REPORTING SERIES

Researcn repcfts of trie Office of Research arnj Dov'-jloorrent, U S Environmental
Protect on Agency, nave been grouped into nine series  These nine broad ca;e-
gones were estabhsned to facilitate further development and  application of en-
vironmental technology  Elimination of traditional grojpmg  was  consciously
planned to foster technology trans'er and a maximum interface in related fields
The nme series are

      1   Environmental  Health Effects Research
      ?  Environmental  Protection Technology
      3  Ecological Research
      <-  Environmental  Monitoring
      (:•  Socioeconomic Environmental Studies
      6  Scientific and Technical Assessment Reports (STAR)
      /'  Interagency Energy-Environment Research and  Development
      8   Special' Reports
      9  Miscellaneous Reports

This report has been assigned to the ECOLOGICAL RESEARCH series This series
describes research on the effects of pollution on numans plant and animal spe-
cies, and materials Problems are assessed for their long- and short-term influ-
ences  Investigations include forma'ion transport,  ard pathway studies to deter-
mine the fate cf pollutants and their ejects  This work provides the technical basis
for sett ng standards to minimize undesirable changes i  •. living organisms in the
aquatic  terrestrial  and atmospheric environments
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161

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                                              EPA-600/3-80-056
                                              July 1980
MATHEMATICAL MODELS OF WATER QUALITY IN  LARGE  LAKES
        PART 1:  LAKE HURON AND SAGINAW  BAY
                Dominic M. DiToro
              Walter F. Matystik, Jr.

                 Manhattan College
   Environmental Engineering and Science Program
               Bronx, New York 101*71
                 Grant No. R803030
                  Project Officer

               William L. Richardson
           Large Lakes Research Station
            Grosse lie Laboratory - EPA
               Grosse lie, Michigan
         ENVIRONMENTAL RESEARCH LABORATORY
        OFFICE OF RESEARCH AND DEVELOPMENT
       U.S. ENVIRONMENTAL PROTECTION AGENCY
              DULUTH, MINNESOTA 5580^4
          F;v:ronm,-iitc! Protection Agsncy
          '~"i V,  Librar
      ?l'- • Sojtii  Dearborn  Street
      Chicle, Illinois  60604

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                                DISCLAIMER
     This report has "been reviewed by the Large Lakes Research Station,
Grosse lie Laboratory, U.S. Environmental Protection Agency, and approved
for publication.  Approval does not signify that the contents necessarily
reflect the views and policies of the U.S.  Environmental Protection Agency,
nor does mention of trade names or commercial products constitute endorse-
ment or recommendation for use.
                                     11

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                                  FOREWORD
     The Great Lakes comprise 80% of the surface freshwater in North America
and provide 45 million people living in the basin with almost unlimited
drinking water and industrial process water.  Five thousand miles of shore-
line provides access for much of the tourist and recreation activity in the
surrounding basin.  Lucrative sport and commercial fisheries rely on these
waters as do the transport of tremendous quantities of raw and refined
commercial products and the disposal of residual, industrial and municipal
materials.

     This resource represents a complex system of competing water uses as
well as a delicate, interacting ecosystem.  Such a situation requires a
balance between the economic well being of the region with the health
related well being of the ecosystem.  To arrive at this balance a rational
and quantitative understanding of the interacting and competing components
is required.  In this way complex questions can be addressed and optimal
decisions made.

     Research sponsored by the U.S. EPA, ERL-D, Large Lakes Research Station
has in large part been directed toward this end.  Primarily the modeling
research has been conducted to synthesize surveillance and research data and
to develop predictive capabilities of the transport and fate of pollutants
in the Great Lakes.

     This report documents the results of a three year research project to
develop a water quality model for Lake Huron and Saginaw Bay.  The purpose
of including the kinetic formulations, data analysis, and verification
procedures is to provide sufficient detail that would not be available in
journal publications so that much of this methodology could be applied to
other water bodies throughout the world.  Also, it is our intent to document
the details for those Great Lakes' managers and researchers who have and
will develop, recommend and judge pollution control strategies based on this
research.

     Appreciation is extended to scientific reviewers at the University of
Michigan and the NOAA, Great Lakes Environmental Research Laboratory.  The
report has also received extensive review by several Canadian and State
agencies.

                                      William L. Richardson, P.E.
                                      Environmental Scientist
                                      ERL-D, Large Lakes Research Station
                                      Grosse He, Michigan  48138
                                    iii

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                                  ABSTRACT
     This research was undertaken to develop and apply a mathematical model
of the water quality in large lakes, particularly Lake Huron and Saginaw Bay
(Part l) and Lake Erie (Part 2).

     A mathematical model of phytoplankton Momass was developed which incor-
porates "both phytoplankton and zooplankton as well as phosphorus, nitrogen
and silica nutrient forms.  Extensive water quality data for Lake Huron and
Saginaw Bay was analyzed and statistically reduced.  The model was then cali-
brated by comparison of computed results to these data.

     An exhaustive treatment of the kinetics employed for modeling the eutro-
phication process is presented.  The sensitivity of the model to some of its
key parameters is examined.  In addition, responses of water quality in Lake
Huron and Saginaw Bay system to variations in total phosphorus inputs are
projected.

     This report was submitted in fulfillment of Grant No. R803030 by Manhat-
tan College under the sponsorship of the U.S. Environmental Protection
Agency.  This report covers the project period March 26, 197^ to March 25,
1977.
                                     IV

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                                 CONTENTS



Foreword  ..............................  ill

Abstract  ...............................   iv

Figures ...............................   vi

Tables  ...............................  xii

Acknowledgement ...........................  xiv

     1.  Introduction ........................    1
     2.  Summary and Conclusions ...................    2
     3.  Recommendations .......................    7
     k.  Physical Features, Mass Loadings, and Segmentation .....    8
     5.  Estimation of the Seasonal Transport Regime .........   l6
     6.  Kinetics ..........................   27
     7.  Data ............................   57
     8.  Model Structure and Calibration ...............   85
     9.  Sensitivity Analysis ....................  125
    10.  Preliminary Applications ..................  135
References ..............................

Appendix ...............................  150

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                                 FIGURES

Number                                                                Page

   1     Segmentation of Lake Huron.  Top Layer (Epilimnion) and
         Bottom Layer (Hypolimnion) of Northern and Southern Lake
         Huron.  Segment 3 represents Saginaw Bay 	       2

   2.    Vertical Transport Calibration 	       3

   3.    Schematic Diagram of the Kinetic Interactions  	       3

   k.    Results of model calibration: Computed versus Observed
         Data in Southern Lake Huron and Saginaw Bay	       k
   5.    Final calibration computations for Southern Lake Huron,
         Lake Ontario, and Saginaw Bay phytoplankton chlorophyll.       5

   6.    Effect of Increases of Phosphorus Inputs to Southern
         Lake Huron.  Percent change in yearly average epilimnion
         concentration versus percent change in total phosphorus
         input (a) Chlorophyll, P_; (b) Total phosphorus, p  .  .  .       6

   T.    Lake Huron and Saginaw Bay Drainage Basin  .  „	       9

   8.    Annual distribution of Saginaw River flow and nutrient
         mass loading rates, 197^ 	  .....      12

   9.    Segmentation of Lake Huron.  Top Layer (Epilinnion) and
         Bottom Layer (Hypolimnion) of Northern and Soxithern Lake
         Huron.  Saginaw Bay is represented by one layer  ....      1^4

  10.    Typical surface circulation pattern for Lake Huron
         (after Ayers et al. (1956) [l6]	      IT

  11.    Comparison of Saginaw River mass discharge rai;es for
         chlorides and total phosphorus as estimated from weekly
         and monthly sampling data	      20

  12.    Vertical Transport Calibration 	      2k

  13.    Horizontal Transport Calibration 	      26

  ik.    Exponential Dependence of growth rate and respiration
         rate as a function of temperature.   Data are from [27].
         Straight lines correspond to the values of 8 as indicated     30
                                    vi

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                            FIGURES (continued)
Number
  15-     Ratio of growth rate to maximum growth rate vs. external
          phosphorus concentration for external phosphorus concen-
          tration for Scenedesmus sp. (37).   m'm = 1.33 day"1;
          qo = 1.6  f-mol/cell:  V  = k.8 f-mol/cell/hr :   K  = 18.6
          u                       m                        m
          yg PO  - P/£; K  = 0.73 f-mol/cell. (f-mol = 10" J 5 mol
                                                                        35
  l6.     Application of Algal growth and nutrient uptake equations
          (3k) to "batch kinetic data ........ ,  .......     38

  17.     The relationship between filtering rate of Diaptomus ore-
          genensis and prey concentration ( chlamydamonus and chlor-
          ella).   C'gm =2.0 m£/ animal/day"!  Kmg = 40,000 cells/
          m£.  Curve is equation (kO) ...............     k2

  l8.     Logarithm of normalized zooplankton respiration rate as a
          function of temperature.   Exponential temperature depen-
          dence in the range 6 = 1.06 - 1.2 as indicated.  For
          legend and references see [27] ..............     ^5

  19.     Variation of the ratio of estimated unavailable to total
          phosphorus and of dissolved organic to total dissolved
          phosphorus ratio with chlorophyll.  See Table 6 for
          legend ..........................     53

  20.     Comparison of observed and calculated ratio of unavail-
          able to total phosphorus for saturating (eq. 58b), first
          order (eq. 58a), and second order (eq. 58c)  nutrient re-
          cycle kinetics ......................     56

  21.     Sampling station locations for the major data sets used
          in this report.   These correspond to the tabulations in
          Tables 8-10 ......................     68

  22.     Comparison of data taken by CCIW,  CIS, and GLRD at
          approximately the same location in Inner Saginaw Bay.  . .     69

  23.     Comparison of data taken by CCIW,  CIS, and GLRD at
          approximately the same' location in Northern Saginaw Bay .     70

  2k.     Comparison of data taken by CCIW,  CIS, and GLRD at
          approximately the same location in Southern Saginaw Bay .     71

  25-     Model Calibration Data (Segment l) ............     72

  26.     Model Calibration Data (Segment l) ............     73


                                   vii

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                            FIGURES (continued)

Number                                                                Page
  27.     Model Calibration Data (Segment 2)	     76

  28.     Model Calibration Data (Segment 2)	     77

  29.     Model Calibration Data (Segment 2)	     78

  30.     Model Calibration Data (Segment 3)	     79

  31.     Model Calibration Data (Segment 3)	     80

  32.     Model Calibration Data (Segment k)	     8l

  33.     Model Calibration Data (Segment k)	     82

  3k.     Model Calibration Data (Segment 5)	     83

  35.     Model Calibration Data (Segment 5)	     84

  36.     Schematic diagram of the kinetic interactions incorpora-
          ted in the eutrophication model structure	     86

  37.     Calibration calculation for a recycle rate characteristic
          of Southern Lake Huron (bottom figure).  Saginaw Bay
          chlorophyll and nutrients comparison (top three figures)     88

  38.     Calibration calculation for a recycle rate characteristic
          of Saginaw Bay (bottom figure).  Southern Lake Huron
          chlorophyll and nutrients comparison (top three figures)     90

  39.     Calibration calculation for a recycle rate characteristic
          of Southern Lake Huron.  Saginaw Bay - Southern Lake
          Huron transport exchange rate set to zero	     91

  40.     Northern Lake Huron epilimnion calibration calculation.
          Comparison of observations and computations for phyto-
          plankton chlorophyll, zooplankton carbon, ammonia nitro-
          gen and soluble reactive phosphorus, 197^.  See figure
          for data symbol legend	     9^

  i»l.     Northern Lake Huron epilimnion calibration calculation.
          Comparison of observations and computations for nitrate
          nitrogen, total phosphorus, and reactive silica nitrate
          nitrogen total 	     95

  ii2.     Northern Lake Huron epilimnion calibration calculation.
          Comparison of observations and computation for observed
          Secchi disk depth and gross primary production, (1971)  •     97

                                  viii

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                            FIGURES (continued)

Number
 k3.   Computed versus Observed Data (So. Lake Huron epilimnion). .    98

 kk.   Computed versus Observed Data (So. Lake Huron epilimnion). .    99

 45.   Computed versus Observed Data (So. Lake Huron epilimnion). .   100

 k6.   Computed versus Observed Data (Saginaw Bay) .........   102

 1*7.   Computed versus Observed Data ( Saginaw Bay) .........   103

 U8.   Computed versus Observed Data (Saginaw Bay) .........   10^

 k9 .   Computed versus Observed Data (No. Lake Huron hypolimnion) .   106

 50.   Computed versus Observed Data (No. Lake Huron hypolimnion) .   107

 51.   Computed versus Observed Data (So. Lake Huron hypolimnion) .   108

 52.   Computed versus Observed Data (So. Lake Huron hypolimnion) .   109

 53.   Phytoplankton growth and death rates in Southern Lake Huron
       epilimnion and hypolimnion .................   110

 5k.   Nutrient limitation of growth rate.  Inorganic nitrogen
       (N/N + KmN) and reactive phosphorus (P/p + Kmp) terms, and
       their product (total reduction) ...............   112

 55.   Comparison of kinetic fluxes of unavailable phosphorus in
       Southern Lake Huron and Saginaw Bay.  Curves correspond to
       a _(l-f.)R  for phytoplankton respiration; a  (l-f )
        p.r    A  Z                                 pO    A
       (R  +R  ) for zooplankton respiration; a  (l-$)(l-f )R
         pn  P o                                pJr         A  j
       for unassimilated phytoplankton, and a  (l-e )(l-f )R,
                                             P w    C     /-i  4
       for unassimilated zooplankton ................   113

 56.   Cumulative plot of the components of total phosphorus in
       Southern Lake Huron and Saginaw Bay.  The curves correspond
       to reactive phosphorus; reactive & unavailable phosphorus;
       and total phosphorus , which includes algal and zooplankton
       phosphorus .........................
 57.   Seasonal distribution of phytoplankton growth and death
       rates showing light and nutrient limitation reductions .  .  .   Il6
                                    IX

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                            FIGURES (continued)


Number                                                               Page

 58.    Seasonal distribution of computed herbivorous zooplankton
       growth and death rates for Southern Lake Huron and Saginaw
       Bay growth rate, $a pFL; respiration rate, -R, ;  carnivore
       grazing, -R^. . .  ?	117

 59-    Lake Ontario calibration.   Application of saturating recycle
       kinetics.  Data from 196?  - 1972 CCIW cruises	121

 60.    Lake Ontario calibration.   Application of saturating recycle
       kinetics.  Data from 1967  - 1972 CCIW cruises	122

 6l.    Final calibration computations for Southern Lake Huron, Lake
       Ontario, and Saginaw Bay phytoplankton chlorophyll.  The
       phytoplankton and recycle  kinetic constants are the same in
       each calculation.  However Lake Ontario zooplankton kinetics
       are not those used for Lake Huron and Saginaw Bay	123

 62.    Sensitivity to phytoplankton kinetic constants.   Saturated
       growth rate @ 20°C, K  (middle).  Growth rate temperature
                               T—20
       dependence, 6, with K 6      constant at T = 13°C (bottom).

       Labels in the figures correspond to computer program vari-
       able designations	127

 63.    Sensitivity to phosphorus  system kinetic constants.
       Michaelis constant for phosphorus, K  (top).  Phosphorus to
       chlorophyll ratio,  a  (bottom) 	  128

 6h.    Sensitivity to recycle rate kinetic constant of phosphorus
       and nitrogen, phytoplankton chlorophyll, reactive phosphorus
       and nitrate nitrogen 	  130

 65.    Sensitivity to herbivore grazing rate.  Kinetic  constant and
       silica to chlorophyll stoichiometric constant a..p 	  132
                                                      t_) 1 ir

 66.    Sensitivity to phytoplankton settling velocity (top), satu-
       rating light intensity (middle) and stratifications (bottom),
       Southern Lake Huron epilimnion (left), Southern Lake Huron
       hypolimnion (center), Saginaw Bay (right)	13^

 67.    Fifteen year distribution  of and percent increase in yearly
       averaged phytoplankton chlorophyll a in Southern Lake Huron.
       Model is essentially at steady state in year 15	136

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                            FIGURES (continued)


Number                                                              Page

 68.    Effect of increases of phosphorus inputs to Southern Lake
       Huron.  Percent change in yearly average epilimnion concen-
       tration versus percent change in total phosphorus input (a)
       Chlorophyll, P_; ("b) Total phosphorus, p •  (c) unavailable

       phosphorus, p ; (d) Ratio of algal phosphorus to total

       phosphorus, P'/p^	139
                       "C

 69.    (Southern Lake Huron epilimnion)  Yearly average chlorophyll
       concentration versus total phosphorus loading to Lake Huron.
                                   XI

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                                  TABLES




NUMBER                                                                 PAGE




  1.   Nutrient Loadings 	    11




  2.   Segment Parameters  	    15




  3.   Heat Flux Input for Transport Verification	    23




  k.   Zooplankton Grazing Constants	    hi




  5.   Experimentally Determined Nutrient Recycle Rates   	    50




  6.   Data Used for Recycle Rate Analyses	    52




  T.   Historical Data Summary	    58




  8.   CCIW Lake Huron Surveys	    63




  9.   GLRD Lake Huron Surveys	    6h




 10.   CIS Saginaw Bay Surveys	    65




 11.   Survey Stations and Model Segments   	    66




 12.   Inter-Survey Station Comparisons  	    7^




 13.   Total Phosphorus Mass Balance 	   119




 Ik.   Effect of Various Nutrient Recycle Mechanisms  	   137




 15.   Results of Model Simulations  	   lUl




 Al.   Phytoplankton Growth  	   150




 A2.   Phytoplankton Respiration 	   152




 A3.   Herbivorous Zooplankton Growth  	   153




 AH.   Carnivorous Zooplankton Growth  	   15^




 A5.   Zooplankton Respiration 	   155




 A6.   Nitrification	156
                                    xii

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                            TABLES  (continued)




NUMBER                                                                 PAGE




 AT.   Mineralizations	157




 A8.   System Kinetic Derivitives	158




 A9.   Time Variable Saginaw Bay Waste Loadings	159




A10.   Main Lake Huron Waste Loadings	l6l




All.   Boundary Concentrations  	•	   l6l




A12.   Flows	162




A13.   Exchanges	163




Al^.   Segment Parameters   	   l6k




A15.   Time Variable Functions	1.6k
                                   xiii

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                              ACKNOWLEDGEMENTS
     This study could not "be undertaken without adequate data to serve as
input and for calibration purposes.  We therefore extend special thanks to
the Cranbrook Institute of Science, the Casiada Centre for Inland Waters, and
the Great Lakes Research Division of the University of Michigan for supplying
and permitting us to use their water quality data.  The cooperation of all
members and committees of the Upper Lakes Reference Group of the International
Joint Commission, particularly those who provided us with waste loading infor-
mation, is also gratefully acknowledged.

     The participation, helpful criticism, and support of our colleagues at
Manhattan College: Robert Thomann and Donald O'Connor, and at the EPA Grosse
lie Laboratory: Nelson Thomas, William Richardson, Victor Bierman, and Tudor
Davies (presently of EPA, Gulf Breeze, Florida) is greatly appreciated.
Special thanks are also due to Mrs. Eileen Lutomski for her typing of the
report manuscript.
                                     xiv

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                                  SECTION 1

                                INTRODUCTION
     The principle objective of this research project is to structure and
apply a numerical model of phytoplankton Momass in lake Huron and Saginaw
Bay in order to provide a framework for assessing, managing, and controlling
eutrophication problems in these areas of the upper Great Lakes.  This work
is part of a larger study which also addressed water quality problems in Lake
Erie, particularly the depletion of oxygen in the hypolimnetic waters of the
Central Basin.  Results of that study are reported separately in Part II of
this report.

     The continuing eutrophication of the Great Lakes, the largest single
freshwater system in the world, has been a widely recognized water quality
problem.  While the open lake waters of Lake Huron are classed as oligotro-
phic, Saginaw Bay, a shallow, short residence time embayment which serves as
a receiving body for a large percentage of the waste loadings entering Lake
Huron, is a highly eutrophic area exhibiting, for example, phytoplankton
chlorophyll concentrations which are an order of magnitude greater than those
found in Huron's open lake waters.  Recognizing the potential for large scale
water quality deterioration, the International Joint Commission appointed a
special committee in April, 1972, the Upper Lakes Reference Group, to deter-
mine whether the waters of Lakes Superior or Huron were being polluted on
either side of their respective international boundaries to an extent likely
to cause a degradation of existing levels of water quality in the Great Lakes
system.  While this project did not form a part of the Upper lakes Reference
Study, per se, it does provide a framework for responding to the reference
questions raised therein.

     The computation comprises a kinetic structure which characterizes the
interrelationship between phytoplankton, herbivorous and carnivorous zoo-
plankton, ammonia, nitrate, and unavailable nitrogen, dissolved ortho and
unavailable phosphorus, and silicate.  These constituents form the nine de-
pendent variables.  This formulation is then coupled to the water transport
in the Saginaw Bay/lake Huron system, the boundary concentrations and nutri-
ent waste loadings.  A new framework is developed which relates the rate of
recycle of nutrients from unavailable to available inorganic forms to the
phytoplankton biomass concentrations.  The model is calibrated by comparing
computed concentrations to observations.  Sensitivity analyses are presented
which indicate the extent to which the model's computations depend upon
values chosen for key parameters which affect the kinetic interactions of
the various model compartments.  Finally, applications of the model are pre-
sented which project water quality responses in southern Lake Huron and
Saginaw Bay to various management strategies for reducing total phosphorus
inputs to this system.

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                                  SECTION 2

                           SUMMARY AND CONCLUSIONS
     This research project develops a framework for an analysis  of  the  causes
and remedies of eutrophication of Lake Huron and Saginav Bay.  The  methodol-
ogy employed is based on a mathematical model which expresses  in quantitative
terms the mass "balance relationships which interrelate the nutrient mass
discharges to the lakes, the nutrient concentration in the lake,  the  phyto-
plankton and zooplankton response to these nutrients, and their  resulting
seasonal distribution.  The model calculations provide the method by  which
the fate and impact of present and projected levels of nutrient  discharges
can be evaluated in terms of their effect on the biomass of phytoplankton.
It is for this specific purpose that they have been constructed:  to provide
a quantitative method by which nutrient management plans can be  evaluated.

     It is concluded, based on this investigation, that the phytoplankton
biomass, nitrogen and phosphorus concentrations in Lake Huron  and Saginaw Bay
can be adequately modeled using the formulation presented.  This is suggested
by the fact that the computations reproduce observed concentrations fairly
well in both Saginaw Bay and the open waters of Lake Huron where concentra-
tions of most variables span almost an .order of magnitude and  conditions
range from eutrophy to oligotrophy.

     Mass balance calculations are based on three components:  estimates of
the rate of nutrient mass discharges to the lake; estimates of the  vertical
and horizontal transport regime; and estimates of the nutrient,  phytoplank-
ton, an^zooplankton kinetics.  This report is concerned with  the latter  two
components; the mass discharge rates have been estimated "by the  Upper Lakes
Reference Study group. [98]  The mass balance calculations; are made for each
                                      BOTTOM .LAYER
  Figure 1.
                         kl
                 0-15m«t«rslmilnl>l»>
                 0-Mtom isigin* B>>>
Segmentation of Lake Huron.  Top, Layer  (Epilimnion)  and
Bottom Layer (Hypolimnion) of Northern  and Southern  Lake
Huron.  Segment 3 represents Saginaw Bay.

-------
of the five  segments,  illustrated in fig. 1, which represent  the epilimnion
and hypolimnion  of  Northern and Southern lake Huron,  and  Saginaw Bay.   The
transport regime between these segments is evaluated  using convenient conser-
vative tracers,  primarily temperature.  As shown in fig.  2 the vertical
exchange coefficient  is established from the seasonal distribution of temper-
ature.  The  lines in  the figure are the result of a temperature balance cal-
culation employing  the vertical exchange coefficient  illustrated in the fig-
ure.  A similar  calculation for Saginaw Bay using both temperature and
chloride concentration establishes the horizontal exchange between Saginaw
                                        Bay and Southern Lake  Huron.
        EPILIMNION
                NoftfHni tjlw Huron
                            HYPOLIMNION
  9.0
 -6.0
    J'F'M'A'M'J'J'A'S'O'N'O
                        J'F'M'A'M'J'J'A'S'O'N'D
                SouttMm Lite Huron
                            HYPOLIUNION
* 9.0


« -5.0
    J'F'M'A'M'J1J'A'S'O'N'D
                        J'F'M'A'M'J'J'A'S'O'N'D
                                 The kinetics of the computation
                            are illustrated j.n fig. 3.  The phyto-
                            plankton are represented by their
                            chlorophyll concentration; the zoo-
                            plankton are partitioned into herbiv-
                            orous and carnivorous groups.  The two
                            major nutrient cycles considered are
                            the phosphorus and nitrogen cycle.
                            Both unavailable and available forms
                            are considered and as shown subse-
                            quently the rate of recycle of una-
                            vailable to available phosphorus is a
                            focal point of the analysis.  These
                            kinetics are expressed in mathematical
                            terms and, together with the transport
                            regime and the mass discharges , they
                            comprise the mathematical model that
                            is  the basis of the calculation.
Figure 2.
Vertical Transport
Calibration
          Figure  3   Schematic Diagram of the Kinetic  Interactions

-------
     The critical step in the development of this or any model  is  calibra-
tion; the comparison of computed concentrations for each of the nine  vari-
ables considered in each of the five segments of the lake.  The ability of
the model to reproduce present conditions is a necessary prerequisite in
establishing its validity.  An example of the calibration results  for Saginaw
Bay and the Southern Lake Huron epilimnion is shovn in  fig. k.   The concen-
                      SAQINAW BAY
SOUTHERN LAKE HURON
                 J'F'M'A'M'J'J'A'S'O'N'D
                 J'F'M'A'M1J'J'A'S'O'N'D
                       M1J'J'A'S'O'N'D
         25
         t- 0 0.40
         5g
           z 0.00
                 J'F'M'A'M'J'J'A'STQTN'D
8.0
4.0
0.0
0.016
0.008
0.000
0.004
0.002
0.000
0.40
0.20
0.00
I"
-_-^"T|?l
J 'F 'M'A'M1 J
r
• ml
FT]
J 'F'M'A'M1 J
NL-f-"^LM-
' J 'A'S'O'N'D
[ i I i if
1 f f " p-
' J ' A ' S ' 0 1 N ' D
n
^ ..* 0 T £
J 'F'M'A'M1 J
'J'A'S'O'N'D
ii T!
iiJL J T ,_J—
J^_l_p
j 'F'M'A'M' j
rrf#!«
' J 'A'S'O'N'D
     Figure k.  Results of model  calibration:  Computed  versus  Observed
                Data in Southern  Lake  Huron  and  Saginaw Bay.

trations of nutrients and phytoplankton  in these regions are  quite different;
Saginaw Bay is almost an order  of magnitude  more enriched in  phosphorus and
chlorophyll than the main lake  and the computation  responds accordingly.
These and the other calibration results  are  used to assess the probable
range of applicability of the model to projected conditions.   In particular
the calibration and other analyses described in  section 6 indicate that the
recycle rate in Southern Lake Huron is considerably slower than in Saginaw
Bay.  The effect has important  implications  in the  projected  response of
Lake Huron to increased phosphorus discharges.
     In order to  further verify  this  phenomenon a previous analysis of Lake
Ontario was modified to include  this  new  recycle rate  formulation.   The

-------
         SOUTHERN LAKE HURON
   8
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a.
      JTFTMTA'MIJ'J'A'S'O'N'D

              LAKE ONTARIO
5>
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      J 'F'M'A'M1 J ' J 'A'S'O'N'D
              S4G//VXHV
   40
   20
      J 'F'M'A'M1 J1 J

Figure 5
                                        result is that it is  possible  to
                                        reproduce the phytoplankton chloro-
                                        phyll and nutrient seasonal distri-
                                        butions for Southern  Lake  Huron and
                                        Lake Ontario epilimnia and Saginaw
                                        Bay using the same phytoplankton and
                                        nutrient kinetic  structure and con-
                                        stants as shown in figure.  5.  This
                                        simultaneous applicability suggests
                                        that the model employed in this cal-
                                        culation has a more general validity
                                        and its use in making projections is
                                        supported.

                                             A sensitivity analysis is pre-
                                        sented in order to assess  the  effects
                                        of varying kinetic constants on the
                                        computation.   In  particular it
                                        appears that although the  shape of
                                        the seasonal distribution  is strongly
                                        affected by the zooplankton kinetics
                                        the peak and yearly average concen-
                                        trations are rather insensitive.
                                        Therefore the projections  for  these
                                        measures of eutrophication are not
                                        invalidated by the uncertainties in
                                        the zoopla'nkton kinetic  coefficients.
                                             Projection  calculations for var-
                                        ious  phosphorus  mass discharge rates
                                        are presented  in section 10, an ex-
                                        ample of which is  shown in fig. 6.
                                        The importance of  phosphorus recycle
                                        is  shown in the  projected yearly
                                        average  chlorophyll change to be
                                        expected from  changes in yearly aver-
                                        age phosphorus inputs.  For satura-
                                        tion  kinetics, which are suggested by
                                        the calibration  results, a doubling
                                        of  the phosphorus  loading is pro-
                                        jected to increase the yearly average
                                        chlorophyll over 300$ whereas for
first-order recycle a doubling would be  projected.  This implies that South-
ern Lake Huron is quite senstive to  changes in phosphorus  loading and it
would respond more dramatically than strictly linearly to  increases in phos-
phorus inputs.  More detailed projection calculations  including Saginaw Bay
are included in section 10.   The results indicate than an  annual load of
total phosphorus to Lake Huron of 3600 metric tonnes/yr. will maintain exist-
ing chlorophyll levels in Southern Lake  Huron achieving  non-degradation.  It
is also projected that phosphorus reductions  at  municipal  sewage treatment
plants in the Saginaw Bay area to effluent  concentrations  of 1 mg/£ which
will reduce the Saginaw Bay  load by  600  tonnes/yr. will  result in yearly
           Final calibration compu-
           tations for Southern Lake
           Huron, Lake Ontario, and
           Saginaw Bay phytoplankton
           chlorophyll.

-------
                              SOUTHERN LAKE HURON EPILIMNION
                       r=  >
                       K
                     UJ f)
                       8
                     ZK
                       <
                       ui
                       >
                                          50          100
                                 PERCENT CHANGE IN TOTAL
                                    PHOSPHORUS INPUT

Figure 6.  Effect of Increases  of Phosphorus Inputs to Soiithern Lake Huron.
           Percent change  in yearly average  epilimnion concentration versus
           percent change  in total phosphorus  input (a) Chlorophyll, P_;
           (b) Total phosphorus,  p .


average chlorophyll concentrations of about  1.1 yg/Jl in Southern Lake Huron
and 10.T Ug/& in Saginaw Bay.   These results have been used by a United
States-Canadian Task Group for  purposes of developing total phosphorus load-
ing objectives to the Great Lakes as part of the re-negotiation of the 1972
Water Quality Agreement [104],

-------
                                 SECTION 3

                              RECOMMENDATIONS
     Due to the significance of the role which nutrient recycle plays in the
Lake Huron and Saginaw Bay ecosystem, experimental investigations should "be
undertaken to provide additional insights into the factors affecting these
mechanisms.  Furthermore, since classical phytoplanktoij growth kinetics do
not reproduce well what appears to be significant observed chlorophyll a_
concentrations in the cold and dark hypolimnion waters of Southern Lake
Huron, further studies of this deep chlorophyll phenomenon are recommended
to determine whether, for instance, low light adaptation, transport, migra-
tion, or some combination thereof contributes to this observed effect.  In
addition, a verification of the model developed hereunder should be per-
formed utilizing Saginaw Bay waste loadings which were lowered subsequent
to this study as part of a remedial phosphorus reduction program.  Some
long term model simulations incorporating yearly variations in waste load-
ing are also recommended to determine if present observations can be repro-
duced.  Such verification exercises would provide an additional degree of
validity to the model as it presently stands.

-------
                                  SECTION h

             PHYSICAL FEATURES, MASS LOADINGS, AND SEGMENTATION


     A major legacy of Pleistocene glaciation is the formation of the Great
Lakes [l], the largest freshwater system on earth.  Lake Huron is the second
largest of these Great Lakes and is the fifth largest lake in the world [2].
Saginaw Bay is an inland extension of the western shore of Lake Huron pro-
jecting southwesterly midway into the southern peninsula of Michigan [3].

     Lake Huron is connected to Lake Michigan by the Straits of Mackinac,  to
Lake Superior by the St. Mary's River, and to Lake St.  CLair by the St. Clair
River.  Lake Huron with Saginaw Bay and the combined drainage basin is shown
on fig. T.
GEOMORPHOLOGY

     Lake Huron's water surface is 1?6 meters (579 feet) above sea level.
The total water surface area, including Georgian and Saginaw Bay, is 59,570
km2 (23,000 mi2) [^,5].  The lake drains a total land and water area of
193,700 km2 (7^,800 mi2) [k], two-thirds of which is land drainage.  Meas-
ured from low water datum, Lake Huron has a maximum depth of 229 meters
(750 feet) [U],  Averaged over the lake, the mean depth is reported as 53-59
meters [^,5].  Total water volume of Lake Huron is 3535 km3 (8H8 mi3) [U,5].
The length of the lake is 330 km (205 miles) with its breadth being 292 km
(l8l miles) [5].  Total shoreline including islands is 5,088 km (3162 miles)
[51.

     Saginaw Bay is a shallow arm of Lake Huron h2 .km (26 miles) wide and
approximately 82 km (51 miles) long.  The bay's 2960 km2 (11^3 mi2) of
surface area are equally divided between an inner and outer bay divided by a
constriction where the bay narrows to 21 km (13 miles).  The shallower inner
zone has a mean depth of k.6 meters (15 feet) while the outer bay mean depth
if lU.6 meters (H8 feet).  The maximum depth is ^0.5 meters (133 feet) in
the outer bay [3].
HYDROLOGY

     Lake Huron is in the central portion of the Great Lakes Basin, southeast
of Lake Superior and east of Lake Michigan.   It receives outflow from Lake
Superior through the St. Mary's River, a channel 112 km (70 miles) long.
Lake Huron also receives outflow from Lake Michigan via the Straits of
Mackinac.  The straits of Mackinac provide a broad and deep connection
between Lake Michigan and Lake Huron, being more than three miles wide at

-------
                                                 MINNESOTA

                                                    WISCONSIN
STRAITS OF
MACKINAC
                                                            INDIANA
                                                      UNITED STATES
                                                        SCALE IN MILES

                                                        0 10 20  30 40 50
     Figure  7.   Lake  Huron  and  Saginaw Bay Drainage Basin

-------
their narrowest point and ranging in depth to more than 6l meters (200 feet).
Direction of currents in the Straits alternates from east to west depending
upon meteorology.  Net flow, however, is to Lake Huron [h].   It should be
noted, however, that flow reversal with depth during the stratified season
has been observed in the Straits of Mackinac [100].   This phenomena, in turn,
has been determined to have a significant effect on the estimation of trans-
port through the Straits [101].   Outflow from Lake Huron is via the St.  Clair
River at its southernmost tip.

     The average flow (1860-1970) to Lake Huron from the St. Mary's River
draining Lake Superior is 2123 m3/sec (75000 cfs).  The flow across the
Straits of Mackinac from Lake Michigan is estimated to be 1^72 m3/sec
(52,000 cfs); while that leaving via the St. Clair River is 5,303 m3/sec
(187,300 cfs) [h].   The average annual precipitation (1900-1970) on Lake
Huron's water surface is 79 cm (31 inches) [^,5], and the average annual
evaporative loss has recently been estimated at 66 cm (26 inches)[l|].

     The Saginaw River is the major source of drainage flowing to Saginaw
Bay.  Formed by the convergence of the Shiawassee, Tittabawasee, Cass, and
Flint Rivers, the Saginaw River is 35 km (22 miles)  long and enters the bay
at its southwestern end.  The average annual water levels in Saginaw Bay are
controlled by the Lake Huron water level.  The bay itself, however, exhibits
very short term, rapid and large fluctuations as a result of wave runup,
wind driven tides,  and seiches [3].  Some of these propagate down the Saginaw
River and cause flow reversal.   Flows typically range from ik to 227 m3/sec
(500 to 8000 cfs) throughout a year with an average value estimated to be
109 m3/sec (3850 cfs) [3].
MASS INPUTS

     The earliest comprehensive mass loading data for Saginaw Bay is avail-
able from the 1965 survey by the FWPCA of Michigan tributaries.   They are
based on Saginaw River and other bay tributary measurements of total and
ortho phosphorus, and nitrate, ammonia and organic nitrogen.  No Lake Huron
estimates for the comparable period are available, however.  Johnson [6]
summarizes some typical Saginaw Bay loadings from its major tributaries based
on the 1965 surveys.

     The Great Lakes Water Quality Board [7»8,9] has made estimates of the
1972 to 197^ overall lake loadings for total phosphorus and total nitrogen.
Estimates of loadings under reduction policies are also included.  The break-
down of the total nutrient loading into various nitrogen a.nd phosphorus forms
and their spatial distribution are not estimated.

     In view of the lack of comprehensive and detailed mass loading informa-
tion for Lake Huron and Saginaw Bay, a major effort was instituted in order
to rectify this situation.  As part of the Upper Lakes References Study of
the IJC, one of the aims of which is to document the present water quality
status of Lake Huron, "data collection programs and studies were proposed for
the purpose of determining the loading of materials to the lakes which could
adversely affect their water quality" [10].  Sources studied included munici-

                                     10

-------
pal, industrial and tributary point sources as well as other land and atmos-
pheric inputs  (nonpoint sources).  These studies provide the necessary com-
prehensive mass loading data without which it is impossible to perform mean-
ingful mass balance calculations.

     In addition to total nutrient mass loading information it is necessary
to know the forms of the nutrient, the important division being available or
unavailable for phytoplankton growth.  The division into the various nutri-
ent forms: ammonia, nitrite plus nitrate, and organic for nitrogen; and
soluble reactive and unavailable (total minus reactive) for phosphorus, were
determined based on information which was available for Province of Ontario
and State of Michigan tributary loadings.  Atmospheric loads were evenly
divided between ammonia and nitrate for nitrogen, while'all atmospheric
phosphorus was considered to be in the soluble reactive form.

     For Lake Huron proper, average annual mass loadings suffice because of
its large volume and long residence time for nutrients.  However for Saginaw
Bay more detailed information is necessary, since the bay is highly respon-
sive.  Based on the 197^- surveys of Saginaw Bay (Section VI), which had a
few stations at the mouth of the Saginaw River, USGS flow data, and State of
Michigan water quality stations, Richardson and Bierman [11] computed load-
ings to Saginaw Bay from the Saginaw River, its major contaminant source.
Figure 8 shows these loadings as a function of time together with the Sagi-
naw River flow.  As can be seen, all parameters are highly correlated to the
flow, as would be expected, with spring runoff flows yielding the highest
loading rates.  Flow is relatively small in the latter half of the year as
are the loadings.

     The mass loading estimates used in the subsequent calculations are a
combination of the Lake Huron loadings computed by the Upper Lakes Reference
Group and the time variable Saginaw Bay loadings.  Both are computed using
197^ data.  Table 1 summarizes the total nitrogen and phosphorus loadings
which are used in the Lake Huron/Saginaw Bay computation.


	TABLE 1.  NUTRIENT LOADINGS	

Location                     Total Phosphorus           Total Nitrogen
                          (tonnes/yr)  (ibs/day)     (tonnes/yr)  (#/day)
Northern Lake Huron
Southern Lake Huron
Saginaw Bay
TOTALS
1,281
1,297
1,315
3,893
(7,739)
(7,832)
(7,9^5)
(23,516)
58,186
35,773
17,678
111,637
(357,^1)
(216,066)
(106,773)
(67^,280)

SEGMENTATION

     Five  segments are chosen to represent the significant regions of the
.Lake Huron - Saginaw Bay system described in the preceding section.  The


                                     11

-------
          1974 SAGINAW RIVER LOADINGS TO SAGINAW BAY
      J F MAMJ J A SON D
JFMAMJJASOND
Figure 8.   Annual  distribution of Saginaw River flow
           and nutrient mass loading rates,
                          12

-------
choice is a compromise between a realistic characterization of the major fea-
tures of the biological and chemical variations and the constraints of compu-
tation and simplicity, with the emphasis on the latter requirements.

     Three surface segments are considered: Northern Lake Huron, a large open
expanse of water which tends to be deeper and colder than other portions of
the lake and receives the inputs from Lake Superior and Lake Michigan and
from major Canadian tributaries feeding the North Channel and Georgian Bay;
Southern Lake Huron bounded by the Canadian and Michigan shorelines which
approach one another to form the St. Clair River outlet channel.  It is
influenced, to some degree, by the Saginaw Bay flow sweeping down its western
shoreline.  Concentrations of biological and chemical parameters tend to be
slightly higher than in the open lake waters to the north.  Saginaw Bay
receives the loading from the Saginaw River.  Its waters are significantly
enriched as compared to the oligotrophic waters of the rest of Lake Huron.

     Figure 9 presents the segmentation.  Segment 1 encompasses the northern
Lake Huron epilimnion.  Its depth ranges from the surface to 15 meters
(^9-2 feet) which is the approximate thermocline depth as well as the eupho-
tic zone depth (l$ surface light penetration depth).  The lower boundary of
segment 1 is the line of kh° 30' north latitude or roughly a line across the
lake connecting a point 8 km (5 miles) north of Oscoda on the Michigan
shoreline to a point just north of Southhampton on the Province of Ontario
shoreline.  Georgian Bay and the North Channel are not included as part of
the segment.

     The epilimnion of southern Lake Huron comprises segment 2, also 15
meters deep.  It is bounded to the north by segment 1 and it also interacts
with the Saginaw Bay model segment to the west.  Segment 2 is the outflow
segment as its southern boundary is the St. Clair River outflow channel.

     Segments k and 5 comprise the northern and southern Lake Huron hypolim-
nion, respectively.  They are both 50 meters (l6k feet) deep and are situa-
ted directly below their respective epilimnion segments with their outer
ring boundary being the 15 meter depth contour of the lake.  Together, they
form the second vertical layer of the model.  Inclusion of hypolimnetic seg-
ments is required to characterize the thermocline formation, its effects on
vertical transport, and the effect of phytoplankton sinking and net trans-
port of biomass and associated nutrients to the sediment.

     Saginaw Bay is represented by segment 3.  It encompasses all of the
inner bay and part of the outer bay.  The mean depth of this segment is 6
meters (19-7 feet) slightly deeper than the reported inner bay mean depth of
k.6 meters, since some of the outer and deeper portions of the bay are also
included.  Saginaw Bay is characterized by only one vertical layer since
only in the outer reaches of the bay does a well formed thermocline persist
in the summer and fall.

     Table 2 lists the individual segment depths, surface areas, and vol-
umes.  These were obtained by using navigational charts [12,13], measuring
the areas of concern with a planimeter, and converting using map scales.
When the volumes for the North Channel and Georgian Bay are added to the

                                     13

-------
 TOP LAYER
 0-15 meters (main lake)
 0-bottom (Saginaw Bay)
BOTTOM LAYER
15 meters-bottom
Figure 9-    Segmentation of Lake  Huron.  Top Layer  (Epilimnion) and
             Bottom Layer (Hypolimnion) of Northern  and Southern Lake
             Huron.  Saginaw Bay is represented "by one layer.

-------
total values for the five segments the result is within 3-5% of reported
values [4,5] for total lake volume.
                        TABLE 2.  SEGMENT PARAMETERS

Segment Depth
meters (feet)
1 15
2 15
3 6
4 50
5 50
(49.2)
(49.2)
(19-7)
(164.1)
(164.1)
Surface Area
km2 (mi2)
24,882
14,780
1,815


41,477
(9,608)
(5,707)
(701)


(16,016)
Volume
km3
373.4
221.7
10.8
1141.1
619.7
2366.7
(mi3)
(89.6)
(53.2)
(2.6)
(273.8)
(148.7)
(567-9)
                                    15

-------
                                  SECTION 5

                 ESTIMATION OF THE SEASONAL TRANSPORT REGIME
     The available estimates of the nutrient mass discharge rates to Lake
Huron and Saginaw Bay are presented in the previous section as well as the
relevant geomorphology and hydrology.   These provide the volumes, flows, and
material input rates to the surface segments.  In order to calculate the
resulting concentrations, it is necessary to know the transport rate between
the segments.  Three segment boundaries are considered: the Northern-Southern
Lake segment boundary; the Saginaw Bay-Lake Huron boundary, and the thermo-
cline.  The estimates of the transport are based on observations of the mag-
nitude and direction of the currents and the analysis of the distribution of
conservative tracers.  The former are used for the estimate of the Northern-
Southern Lake exchange whereas suitable tracers are available for the Saginaw
Bay exchange and thermocline transport.
LAKE HURON CIRCULATION PATTERNS

     Many factors affect the currents in the Great Lakes.   Although primarily
wind driven, currents are also affected by temperature, which can form den-
sity gradients in the lake; by basin geometry which modifies the currents;
by the Coriolis force, an apparent force due to the rotation of the earth;
by incoming flows; and by wave effects.  A detailed discussion of the com-
plexities involved and governing equations is available [L^].

     Although current patterns in Lake Huron appear not to be well under-
stood [15]> generalized patterns have been observed.  Several investigators
[6,l6,lT] have characterized a circulating flow from Lake Huron entering
Saginaw Bay at its northwestern shore and exiting along the southeastern
shore at least under some prevailing wind direction.  Flow from the Saginaw
River hugs the southern shore and then exits to Lake Huron [3].  The pre-
vailing circulation seems to be counterclockwise.  However, it should be
noted that all of the investigators agree that the circulation is sensitive
to changes in wind speed and direction which result in short term and rapid
fluctuations.

     Another major feature of Lake Huron circulation which has been observed
is a circulating flow between the northern and southern open lake waters
which occurs towards the eastern shore near the center of the lake.  Figure
10 illustrates the features of Lake Huron and Saginaw Bay transport described
above.

     Recent intensive studies undertaken as part of IJC's Upper Lakes Refer-
ence Study [102] have significantly enhanced knowledge of Lake Huron currents


                                     16

-------
                                      SCALE IN MILES
                                      0  10  20 30 40
Figure 10.   Typical surface circulation pattern  for  Lake Huron
             (after Ayers et al.  (1956)  [l6]).
                              17

-------
especially winter circulation patterns.  These winter studies show patterns
of flow similar to the circulation of epilimnion water during summer as well
as a counterclockwise circulation of waters across the international boundary
as shown on fig. 10.
METHODOLOGY

     The estimation procedure for transport involves calculating the distri-
bution of suitable tracers and comparing them to observations.   This is only
possible for the Saginaw Bay exchange with the southern Lake Huron segment
since there exist sufficiently large gradients for chlorides, temperature,
and total phosphorus.  The northern-southern lake circulation is difficult to
estimate since no strong gradients exist.  The values used are consistent
with observed surface velocities [16].  The magnitude of the vertical mixing
is established by calibrating a temperature balance calciilation to the large
gradients which exist between epilimnion and hypolimnion segments.  The per-
iod of intense stratification, during which no appreciable mixing appears to
occur, commences in July and continues through October.  Vertical exchanges
that are consistent with the temperature observations are determined and used
to parametize the seasonal vertical mixing pattern.

     The equation which governs the concentration of a conservative tracer in
any segment is determined from a mass balance around that segment which takes
into account flow into and out of the segment, dispersive exchange, and
boundary inputs:

           dc.
        V. —- = £ Q..c. + I E!.(c.-c.) + W.                             (1)
         i dt    .  ij J      ijx j  i'    i
                 J         J

where:  c.  = concentration in the i   segment (M/L3)
        V.  = volume of the i   segment (L3)
        Q.. = volumetric flow rate from segment j to segment i
         1J   (L3/T)
        E!. = volumetric exchange rate between segments i and j
         1J   (L3/T)
        W.  = rate of mass input into the ±'  segment (M/T)

The flow rates, Q.., are thought of as the unidirectional flows due to the
                 i J
net advection through the segment boundaries.  Thus the Saginaw River flow
and the north to south Lake Huron flow described in Section ^, Hydrology,
are represented by these terms.  The exchange flows are the result of the
horizontal circulating flows which are bi-directional, as illustrated in fig.
10, and whatever other mixing processes occur between adjacent segments.  For
the boundary at the location of the thermocline, the exchange coefficient is
related to the vertical dispersion coefficient, E.., via the expression E!. =

E..A..1%. . where A.. is the interfacial area and £.. is the length between
 ij ij  ij        10                              !J
the segment midpoints [l8].  This relationship applies if the segment sizes

                                     18

-------
are small enough so that finite difference approximations to derivatives are
reasonable.  For the large segments considered in this study, the relation-
ship is only approximate.

     The estimation of the Saginaw Bay-Southern Lake Huron exchange coeffi-
cient is based on the solution of equation (l) using chlorides as the conser-
vative tracer.  In addition, total phosphorus is considered although as shown
subsequently some removal occurs due to particulate phosphorus settling.
Finally, a temperature analysis is presented to further confirm the estimated
exchange rate.  The equation used for the chlorides and total phosphorus ana-
lysis is:

           dc
                                                                         (2)
where Q2s(t) is the observed Saginaw river flow and Ws(t) is the observed
mass loading rate from the Saginaw River.  These are obtained from the EPA
and the IJC Upper Lakes Reference Group studies as outlined in Section k.
Comparison to Saginaw Bay loadings calculated by the University of Michigan
(Canale, personal communication) are shown on fig. 11.  It is interesting to
note that the weekly sampling data is necessary to resolve a number of sharp
peaks which contribute to the total loading.

     The methodology for using temperature as a tracer is a simplification of
a full thermal balance calculation.  Heat storage in a lake is dependent on
many factors including short and long wave solar radiation incident to the
water surface; reflected solar radiation; long wave back radiation; sensible
heat transfer to the atmosphere; and energy of condensation and evaporation.
The net result of these is a net heat flux to the lake which can be thought
of as a forcing function for temperature.  Thus instead of developing rela-
tionships for each of the terms which comprise total heat storage using
observations for solar radiation, water reflectivity, air temperature, cloud
cover, wind speed, vapor pressure and the like, which is a complex task
requiring large amounts of data, heat storage is computed directly from
observed temperature data.  Mean temperatures for each segment (i) for each
cruise (k),T., , are computed using the 197^ survey data.  Because of the
            liC
relatively uniform spacing of the observations volume-weighted means were a
refinement that was judged to be unnecessary.  Total heat content change in
the lake, AH , between cruise k and & is then computed using:



        AHT =.   AHi =  *  Vi (Tlk-Tl£) P °P
where:
        AH. = change in heat content for the ith segment between
              cruise k and £ (calories)

        V.  = volume of segment i (cm3)


                                     19

-------
            ro
           -D
             10
            c

              8
           LJJ
           Q

           cc

           3
           i

           0
         cc
         O

         Q-
         00
         O
         X
         a.
            D
            O
            .c
 6


 4


 2


 0


10


 8


 6


 4


 2


 0
                  	EPA

                  	UNIVERISTY OF MICHIGAN
                JIFIM'A'M[JIJTATSTO
                J  ' F ' M ' A ' M '  J  ' J'A'S'O
Figure 11.  Comparison of Saginaw River mass dischsirge rates

            for  chlorides and total phosphorus  as  estimated

            from weekly and monthly sampling data.
                                20

-------
        T.  = volume average temperature in segment i on the
         ik
              kth cruise  (°C)
        T. g = volume average temperature in segment i on the
         1    Jlth cruise  (°C)

        C   = heat capacity of vater (cal/g-°C)

        p   = density of water (g/cm3)

The total lakewide daily average surface heat flux, J   between the cruise

dates , which represents the net amount of energy input over the surface area
of the lake, can then "be determined using:
where:

        A     = total lake surface area (cm2)
         s
        At .  = time between the kth and &th cruise (days)
        J     = areal heat flux (cal/cm2-day )

     In order to apportion the net heat flux to the surface segments of Lake
Huron and Saginaw Bay a number of assumptions are possible.  The simplest is-
to assume that the flux is uniformly distributed over the entire lake.  How-
ever, certain of the mechanisms which cause this heat flux are dependent on
the water surface temperature which is quite different for Saginaw Bay and
Lake Huron.  Thus a correction for this effect is necessary.  The method is
based on the assumption that the equilibrium temperature, E, is the same for
Saginaw Bay and Lake Huron.  This is reasonable since the equilibrium tem-
perature does not depend on the water depth, but only on meteorological vari-
ables, which can be presumed to be relatively uniform lakewide.  In addition
it is assumed that the net heat flux can be computed using a surface heat
transfer coefficient coefficient.  This approximation can be justified by
linearizing the equations for long wave back radiation (Stephan-Boltzman
equation) and the equations that depend on the saturated vapor pressure at
the water surface temperature [19].  The result is that the net heat flux at
location i, J. , is related to the local surface temperature by the equation:


               J. = K(E-Tp                                              (5)

where :

     K  = surface heat transfer coefficient (cal/cm2-day-°C)

     E  = equilibrium temperature (°C)

     T!  = surface water temperature of segment i (°C)


                                    21

-------
The prime denotes surface as opposed to volume  average temperature.   Con-
sider this equation applied to the total lake surface:


               JT = rz JiAsiK(E-T1)
                     s i

where T" is the lakewide average surface temperature.  If  it  is assumed that
the heat transfer coefficient is also constant,  for the  same  reasons  that
the equilibrium temperature is assumed constant, then a  relationship  is
obtained between the segment specific and the lakewide average heat flux by
subtracting eq. (6) from eq. (5):

               J. = JT - K(T^-T')                                       (T)

The correction depends on knowing the segment average and  lakewide average
surface temperatures, which are available from  the cruise  data, and the sur-
face heat transfer coefficient.   For Lake Huron it has been estimated to be
K = 50-65 cal/cm2-day-°C [20],  In units comparable to surface gas transfer
coefficients this corresponds to K/pC  = 0.5 -  0.65 m/day.  The computed
lakewide and segment specific heat fluxes resulting from application  of this
procedure are given in Table 3.   The heat balance equation using the  ad-
justed net heat fluxes becomes:
                  dT.
               V. T+ = Z Q. .T.  + E E! .(T.-Tj  + i i                   (8)
                i at    j "U j    .   ^ 0 L>   ^-g-
where:
Calibration
               H. is the average depth of segment  i.  (cm)
     The methodology outlined above is used to  determine  the  degree  of  hor-
izontal and vertical transport necessary to match observed concentration
gradients in the lake.  Figure 12 shows the results  of this analysis for
vertical transport.  The temerature gradients between the northern and
southern Lake Huron epilimnia and hypolimnia are  matched  fairly well using
the computed segment specific heat fluxes (Table  3)  and incorporating a
vertical exchange coefficient of 10 m2/day (107-6 ft2/day) during periods
of non-stratification.  There is no vertical exchange in  the  model during
periods of complete lake stratification.  This  seasonal trend is  simulated
with a temporally varying vertical exchange coefficient as shown  on  figure
12.  Surface temperatures which are most sensitive to the vertical mixing
are well reproduced using this vertical variation.  Hypolimnion tempera-
tures are overestimated in Northern Lake Huron  segment but are well  repro-
duced for Southern Lake Huron with the exception  of  the rather erratic  late
August value.

     A circulating flow equivalent to 2.2 cm/sec  across the northern and
southern lake epilimnia is incorporated and is  consistent with surface

                                    22

-------
         TABLE 3.  Heat Flux Input for Transport Verification

Time
(days)
97-5
127.5
ll*2.5
157.5
172.5
187.5
202.5
217.5
232.5
21*7.5
262.5
277.5
292.5
307.5
322.5
337-5
355.0
Lakewide Average
Heat Flux
2
(gm-cal/cm -day)
120.37
336.77
510.81
553.65
1; 1*1*. 03
298.92
211.36
86.38
39.21*
6.82
-7-71
-77.27
-99.71*
-188.77
-23l*. 09
-1*06.57
-815.50
Segment
139-32
371.02
51*5.06
612.35
502.73
327.22
239-66
136.93
89.79
55.32
1*0.79
-30.17
-52.6U
-157.77
-203.09
_l*0l*.57
-813.75
Segment Specific Heat
2
(gm-cal/cm -day)
1 Segment 2
121* . 62
317.97
1*92.01
1*82.60
372.98
277 . 22
189.66
19.78
-27.36
-65.68
-80.21
-15^.87
-177.31*
-238.27
-283.59
-1*21.07
-830.25
*
Flux
Segment 3
-159.28
21.07
195.11
327.95
218.33
87.62
0.06
-61*. 37
-111.51
-70.18
-81*. 71
-91.52
-113.99
-211*. 27
-259.59
-329.57
-738.75

* K = 50 cal/cm2-day-°C
                                     23

-------
              TEMPERATURE VERIFICATION OF VERTICAL TRANSPORT
               EPILIMNION
                               Northern Lake Huron
o
o
cc
D
cc
LU
a.
23.0




 9.0



-5.0
    J 'F'M'A'M > TT
                              N MD
                                    o
                                    o

                                    111
                                    CC.
                                       ? 8.0
                                    <  4.0
                                    cc
                                    LU
                                    a.

                                    uj  0.0
                                                  HYPOLIMNION
                                                       l ' J 'A'S'O'N'D
                EPILIMNION
                              Southern Lake Huron
o
o

LU
DC
a.
23.0
   9.0
   -5.0
       J 'F'M'A'M "
                                    o
                                     -  8-0
                                    <  4.0
                                    cc
                                    LU
                                    a.


                                    LU  0.0
                                                  HYPOLIMNION
                                          J 'F'M'A'M'.n J ] A'S'O'N'D1
                   _ji±i  5
                   <0
                   uj O
                       j'F'M'A'M'j'J'A'S'O'N'D
               Figure 12.   Vertical Transport  Calibration
                                    2k

-------
current magnitudes given by Ayers, et al. [16].  The horizontal exchange
between the respective epilimnia and hypolimnia Of northern and southern
Lake Huron is set at 900 cm2/sec based on estimates of horizontal diffusivi-
ties by Csanady [21].  Unfortunately there are no strong horizontal gra-
dients here with which to calibrate these exchanges.

     Figure 13 shows the horizontal transport calibration for exchange
between Saginaw Bay and southern Lake Huron.  The marked gradients for chlor-
ides, temperature, and total phosphorus can be used to obtain consistent mass
transport coefficients which give a consistent agreement between observation
and calculation.  The temperature calculation which is begun after the ice
has melted is quite sensitive to the magnitude and timing of the exchange
coefficient since Saginaw Bay is shallow and the heat flux markedly affects
the computed temperature profiles.  This is balanced by the loss of heat
via the exchange flow.

     Other estimates of the exchange flow are available, in addition to the
Saginaw River advective flow which is inputted as a time-varying flow
between 11,235 cfs (3l8 m3/sec) and l,56l cfs (kk m3/sec) in order to repro-
duce the seasonal trend shown previously on fig. 2.  The counterclockwise
circulating flow from Lake Huron to Saginaw Bay is the major mechanism of
this exchange.  Danek and Saylor ]22] have estimated a typical exchange rate
between the inner and outer bay of 3700 m3/sec (130,6^7 cfs) based on cur-
rent meter and Lagrangian measurement during 197^•  The Upper Lakes Refer-
ence Group [23] approximates the annual average exchange from the inner to
the outer bay at 800 m3/sec, and from the entire bay to Lake Huron at 5»000
m3/sec.  Richardson [2U], using a sixteen segment model of Saginaw Bay,
matched 197^ chloride profiles using an advective transport across inner
and outer bay segment interfaces of 30^-686 m3/sec (10,737 - 2*1,229 cfs)
during a thermal bar period and 1370 - 1750 m3/sec (W,388 - 6l,8lO cfs)
for the remainder of the year.  The magnitude of the counterclockwise cir-
culation from Lake Huron to Saginaw Bay for this calibration ranges from an
equivalent of U25 m3/sec (15,000 cfs) to 1,133 m3/sec (UO.OOO cfs) with
this exchange flow increasing in the spring and continuing through the sum-
mer as shown on fig. 13.  Although there are differences in the magnitudes
of the exchange rates estimated by various workers, the agreement shown on
fig. 13 for three independent tracers indicates that the values used herein
are consistent with observations.

-------
          SOUTHERN LAKE HURON
                SAG IN AW BAY
u  23.0
   9.00

LLJ
Q.

5

^ -5.00
I 8.0

CO*
LLJ

94.0

o


o 0.0
^,0.016
to
D
oc
        J 'F'M'A'M1J 'J IAT S
                                      CJ
                                      oc
                                      D
oc
LLJ
O.
        J 'F 'M1 A1!^1 J ' J ' A'S'O1 N'D
   20.0
    0.0
  -20.0
I 40.0

co"
LLJ


E 2°'°
O
_l

o 0.00
                     'J'A'S'O'N'D
                                                    J  I I A

                                                    4
                     ll  ILU
        J'F'M'A'M'J'J'A'S'O'N'D
CL
c/)
O
  .0.008
  0.000
        J'F'M'A'M'J'J'A'S'O'N'D
        J'F'M'A'M'J1J'A'S'O'N'D
            <


            CO
              < 3 40,000
              CD LL,
                z 20,000
                         J'F'M'A'M'j'J'A'S'O'N'D
               Figure 13.  Horizontal Transport Calibration
                                    26

-------
                                 SECTION 6

                                 KINETICS
     The interactions between the biological, chemical, and physical vari-
ables of concern must be specified in a way consistent with the conservation
of mass equations that are the basis of this analysis. The transport com-
ponents  of these equations have been estimated in the previous section.
The method to be used in this section, which is derived from physical chem-
istry, seeks to specify the rates of change of reacting species in terms  of
their concentrations.  The application of these equations to essentially
biological reactions has a long history [25] and is, in fact, currently a
very active and fruitful guide for designing investigations and analyzing
the resulting data.

     The principle concern in the analysis of eutrophication phenomena is
the growth and death of photosynthetic microorganisms.  The framework for
their kinetic equations derives from the work of Monod and it is this formu-
lation which forms the basis of the work to be discussed subsequently.

GROWTH AND DEATH RATES

     The fundamental kinetic equation for microorganisms in terms of their
biomass, X, expresses their rate of growth as a function of a growth rate,
y, and a death rate, b:


          f=yx-bx                                                  (9)

The growth rate is a function of nutrient concentration and, for photosyn-
thetic organisms, light intensity, and both y and b are affected by temper-
ature.  In laboratory reactors the death rate is normally due only to endo-
genous respiration, the maintenance energy reaction necessary to keep the
cell functioning, while in the natural settings predation by higher order
organisms can substantially increase it, as shown subsequently.

     Consider, first, the simplest situation with y and b constant, that  is
there are abundant nutrients and the temperature and light intensity are
constants.  The solution to the kinetic equation is


          X(t) = X(o) e(y~b)t                                          (10)


and exponential growth or decay of microorganism biomass is predicted. In
fact, such behavior is commonly observed in both laboratory reactors and
natural waters.  Examples of sustained exponential growth for the Lake
Ontario and Lake Erie phytoplankton populations have been documented and


                                     27

-------
analyzed [26].  However, other modes of population behavior are possible
since the growth and death rates are not always constants but can vary sub-
stantially due to temperature, light, nutrient, and predation effects.

Temperature Dependence ofJReactionJRate Constants

     The temperature at which a reaction occurs has a significant influence
on the reaction rate.  This is true whether the reaction is simple (ideal
gas) or a complex chain of biological reactions.  For the case of chemical
reactions at equilibrium it is known from thermodynamics that the equilibrium
constant, K  , has an exponential temperature dependence.  The usual formula
is:        e(1

          d In K     AH°
          	££ = _JL                                                /-,-, \
             dT        2                                                ^-"--L/
                     RT

which upon integration and assuming that AH , the enthalpy change of the
reaction, is constant, yields,

                      AH°
                    	r_
          K   = K' e  RT                                                (12)


where K' is the integration constant, R is the universal gas constant and T
is the absolute temperature.  For the rate constants, k, Arrhenius proposed
the analogous relationship

          d In k      E
which leads to an exponential temperature variation.  E is called the acti-
vation energy of the reaction.

     Since the absolute temperature scale is somewhat inconvenient, the
Arrhenius temperature variation equation can be recast in a more useful
form.  If

          k(T) = k' e-E/RT                                              (HO

and T = T   + (T -20.) where T  is temperature in centigrade and T   =

293.l6°K then Eq. (ik) becomes:

                      (T -20)
          k(T) = k2Q 0  C                                               (15)

with
                       E/RT
          k2Q  = k' e-     20                                           (16)
                                     28

-------
                  + E/RT?n
            6  = e+     20                                              (IT)

where the approximation (l + e)~  =l-e for e « 1 has been used.  The
normal range of 6 for chemical and biological reactions, over the range of
interest (5  - 35°C) is 1.01 to 1.15, corresponding to an activation energy
of 1.7 to 2k kcal/mole.

     The temperature dependence of biological reactions is often reported in
terms of Qio, the ratio of the reaction rate at 20 C to that at 10 C.  It is
clear from the definition of 6 that Qio = 910.  Thus a Qio = 2 implies that
6 = 1.072, a common value for biological reactions.

     The exponential temperature dependence of algal growth and respiration
rates is clearly seen in fig. 1^, a plot of log \i and log b versus T.  The
sources of this data have been presented previously [27].  A detailed study
of marine phytoplankton growth rate temperature dependence has been presented
by Eppley [28] which indicates that the maximum growth rates vary with 9 =
1.065.

     It is well known, however, that a continually increasing growth rate
with temperature is not realistic and, as higher temperatures are reached,
the growth rate abruptly stops increasing and begins decreasing usually more
sharply than it increased [29].  This effect can be important if species-
specific calculations are being made.  However for biomass as the dependent
variable, the growth rate of an aggregration of species continues to rise
until a maximum is reached at which no species can function.  This is
clearly shown in Eppley's fig. 7 [28] for which there exist species that can
grow at maximal rates to beyond 25°C.  Since the maximum temperatures reached
in Saginaw Bay do not exceed this value, the decrease in growth rate due to
high temperatures is not included in this calculation.

Light Dependence

     For photosynthetic organisms, a relationship between growth rate and
incident light energy is to be expected and this dependency has been studied
quite intensively.  However, until recently it is not growth rate that has
been measured but primary production:  the rate at which either Oa is
evolved, or C02 is assimilated.  If the carbon synthesis reaction of algae
is taken as equivalent to growth, which is correct for carbon as the measure
of biomass, then the primary production rate is a measure of the growth rate.
This assumption can be inaccurate'for short term experiments, especially if
environmental conditions are markedly varied during the measurement or for
different measures of biomass.  However, it provides a convenient starting
point for the analysis.

     Let P(l) be the rate of primary production and P  be the observed maxi-

mum rate of primary production at high light intensity.  Further assume that
the biomass of the population is constant throughout the measurements as
light intensity varies.  For this situation a number of expressions have

                                    29

-------
  SnON330QN3
HlMOdE)
 0)
 Si

 -p
 05
 JH
 0)
 ft
 s  •
 0) Ti
 -p 

 ri (L)
 O £1
 •H -p
 -P
 n5 O
 Jn -P
 •H
                                             
-------
"been proposed that relate P(l)/P  to light intensity.  The original sugges-
tion by Tailing [30] is:        m


          P(I) = P    (l/Ik)                                            (18)
                  m
where I  is related to the slope of the photosynthesis-light relationship
       jfi
low intensities:

          L- -  1 (dP)
           k    m     I=o

This expression predicts a continuously increasing rate as intensity in-
creases.  However, it has been observed that at higher intensities the rate
decreases.  An expression with this property, proposed by Steele [31] is;
               =e                                                   (20)
           max    s

which reaches a maximum at I = I .  As has been shown [27], this behavior is
                                S
observed and the shapes are comparable to eg.. (20).  The relationship between
I  and I  is easily found from eq. (l9)5 namely I  = e I .   Although these
 K      S                                        S      K.
expressions are somewhat different, it happens that for applications where
depth-averaged primary production is required, they produce nearly equivalent
expressions.

     The light intensity in a body of water usually changes with depth as an
exponentially decreasing function of depth.  Thus

                     -K z
          I(z) = IQ e  e                                                (21)

For a particular volume segment of depth, H, for which the biomass is uni-
formly distributed in depth the average primary production and, by inference,
the average growth rate is calculated from the expression:


          P             H
              =r=/   P[l(z)]dz                                    (22)
           m            o

where f is the fraction of daylight, the photoperiod, and r is the reduction
factor due to the non-optimal light distribution.  But from eq. (21):

          dz = - dl/K I                                                (23)

so that;


                                     31
-------
                         P(DdI
The evaluation of this integral is straightforward for both expressions of
P(l).  For eq. (l8), the average yields:
               f
              n
              X I
where ^  = l(o)/I  and ^  = l(H)/I .   For eq. (20), the average yields:
       o         K-      o         ^
                       n

          r = FIT   e    ~ e
               e

where a  = l(o)/I  and OL. = l(H)/I .   A direct comparison is possible since
       O         S      il         S
I  = e I .  For depths at which aR and ^  •*• 0 the comparison is shown below
where f/K H = 1 for convenience of presentation:


          I /I           Tailing Eq.  (25)         Steele Eq. (26)
           O  S

           3.0                 2.80                    2.58

           2.0                 2.39                    2.35
           1.0                 1.73                    1.72
           0.5                 1.11                    1.07

           0.25                0.6U                    0.60

The differences are quite small with the effect of decreasing primary pro-
duction in Steele' s eq. (20) amounting to less than 10% for the highest
incident intensity.

     It is also interesting to note that for either expression the difference
between normalized surface intensities of 3.0 and 2.0 is small indicating
that changes in I  when the surface intensity is large have only a small
                 s
effect.  However the converse is true for small I /I  where the reduction is
                                                 o  s
almost proportional.  This is confirmed in section 9 which illustrates the
sensitivity of the solution to I .  In practice the measured incident solar
                                S
radiation is the total daily flux: I  .   Since this includes the dark period
as well, the mean daily radiation intensity is l(o) = I  /f.  This is the
                                                       cL v
quantity used in evaluating the light reduction factor (see Table

                                     32
-------
Nutrient Dependence
     The nature of the dependence of phytoplankton growth rate on nutrient
concentration is a topic for which a large "body of experimental information
exists.  For this investigation the principle nutrients of concern for Lake
Huron and Saginaw Bay are inorganic phosphorus and nitrogen.  Recent inves-
tigations of the growth kinetics of single species in chemostats have concen-
trated on the dependence of growth rate, y, as a function of internal cellu-
lar concentrations, q, of phosphorus [32] and nitrogen [33].

     For investigations of single nutrient limitation of algal growth, the
following expression has been found to apply to observed growth rate y
          fe — r
where y' is the theoretical maximum growth rate at infinite cell quota, q is
the internal cell quota in units of mass of nutrient per cell, and q  is the
minimum cell quota for that nutrient.  Thus the growth rate is a saturating
function of the internal "available" nutrient concentration q - q .   The
external concentration, S, together with the internal concentration, deter-
mines the cellular uptake rate of the nutrient, v.  For a specific internal
concentration the relationship of uptake to external concentration is found
to be:
                                                                        (28)
a Michaelis-Menton function with half saturation constant K .
                                                           m

     In order to examine the implications of these equations,  consider the
situation that occurs at steady state.  For this situation an  equilibrium
is established between the internal cell quota and cell growth so that :

          v = yq                                                        (29)

and nutrients are assimilated only insofar as they are required for cell
growth.  For this case, it is possible to express cell growth  rate as a
function of external nutrient concentration [3k].  Using eqs.  (27), (28),
and (29) to solve for q yields:
               m
               s
                                                                        (30)
where
          "V " rhr                                                 (31)
                   Ku
                    V
                     m
                                    33
-------
              y'q K
               mo m
                                                                        (32)
Thus if these parameters are in fact constant,  the Monod theory applies.
However, it has been found that V  varies inversely with q, i.e. more rapid
nutrient assimilation occurs for small internal cell quota, and, therefore,
the behavior is more complex than a purely Michaelis-Menton expression.  For
example, for phosphate limited Scenedesmus, the uptake velocity is found to
be [371
               V  S       K.
          V =   m          X
              K  + S    K. + i                                          (33)


where i is the internal nutrient concentration of total inorganic polyphos-
phate and K. is a half saturation constant for this dependency.

     For this type of behavior the relationship of growth to external nutri-
ent concentration is no longer exactly given by eq. (30).  However, if K  is
                                                                        S
defined appropriately, the differences are of no practical importance [36]
and eq. (30) applies as a very good approximation.  This is illustrated in
fig. 15 which compares eq. (30) to that which results from using the cellular
nutrient expression for growth, eq. (27); the cellular and external nutrient
equation for uptake, eq. (33) with i = q - q ; and assuming cellular equili-

brium, eq. (29).  The difference is of no practical importance.

     However, the Monod behavior occurs only if eq. (29) holds,which essen-
tially specifies that there is no dynamic luxury uptake.  Rather the uptake
of nutrients is occurring in quantities sufficient to meet the cell quota at
that growth rate.  Thus depending on the conditions of the experiments or in
the prototype, Monodfs theory may apply only approximately, and only for
conditions approaching equilibrium for the internal cell quota.   An estimate
of the time scale for this condition to be reached, based on a dynamic per-
turbation analysis [36], indicates that it is at least 1/U y  where y  is
the non-nutrient limited growth rate of the population.  Thus, except for
short-term laboratory growth rate experiments, it is expected that cellular
equilibrium is a reasonable approximation.

     The major difficulty with Monod1s theory of microorganism growth as
applied to phytoplankton is that the variation of cell stoichiometry is not
taken into account in the uptake expressions for nutrients.  The problem is
compounded by the lack of a clear choice of the proper biomass or aggregated
population variable for a natural assembledge of plankton [36].   From a
practical point of view the population variable for which a sufficient
quantity of data exists for the Great Lakes is chlorophyll-a and the appro-
priate stoichiometry is the nitrogen and phosphorus to chlorophyll-a ratios.
It is well known that these ratios vary considerably with external nutrient
concentration and past population history.  Large ratios correspond to excess


                                     31*
-------
      1.0
      0.8
     0.6
   I
     0.4
      0.2
       0
         0.1
MONOD THEORY
                   CELLULAR
             EQUILIBRIUM THEORY
          1.0
    s, jug P04-p/i
10.0
Figure 15.  Ratio of growth rate  to maximum growth rate  vs. external
           phosphorus concentration for external phosphorus concen-
           tration for Scenedesmus jsp. (37).  rn'rn = 1.33 day"1;
           qo = 1.6 f-mol/cell;  V^ ^4.8 f-mol/cell/hr; K  = 18.6
                                m
                                                       m
           yg PO^ - P/£;  K± =-0.73 f-mol/cell.  (f-mol = ICT1 5 mol
           PO^-P).
                                35
-------
nutrients and small ratios correspond to that nutrient limiting the growth
rate.  Thus the choice of the relevant ratio can be made with the situation
of interest in mind.  Since the population to be discussed subsequently is
primarily phosphorus limited, the stoichiometry chosen can reflect these
facts.  The operational consequences of this choice is that the population
stoichiometry  under non-limiting conditions will be underestimated but the
maximum chlorophyll concentrations under limiting conditions should be
correctly estimated.  Hence there is a tradeoff between a probable lack of
realism during a portion of the year versus a correct estimate of population
chlorophyll during the period of nutrient limitation.  Since this is usually
the critical period, and most questions to be answered are usually sensitive
to the maximum population size, this choice is a practical expedient.

     A more detailed discussion of these issues, together with tabulations of
the experimentally determined ratios is given  elsewhere [37].  What is im-
portant to realize is that the kinetics which finally emerge are essentially
empirical since they are applied to natural populations vith chlorophyll as
the aggregated population variable whereas their basis is derived from single
species experiments.

APPLICATION TO BATCH KINETICS

     Let P be the phytoplankton chlorophyll concentration and a  , a p, etc.

be the stoichiometric ratios of nitrogen, N, and phosphorus, p, to chloro-
phyll.  The rate of assimilation of inorganic nitrogen isi then a.^ GpP where

G  is the population growth rate and GpP is the rate of increase of popula-

tion chlorophyll.  The assimilation rate of phosphorus is a pGpP, and so on
for all the constituents of the population.

     The kinetic equations which result from these considerations are :
where D  is the endogenous respiration rate, Si is the dissolved silica con-
centration and a    is the silica to chlorophyllstoichiometric ratio of
the population.  For this application to batch kinetics recycle has been
neglected.  As shown subsequently it is of prime importance for the actual
situation in the Great Lakes.

     An application of these equations has been made for a series of batch
phytoplankton growth experiments using a natural assemblage of phytoplankton
from the estuary of San Francisco Bay [38].  This population is exclusively

                                     36
-------
nitrogen limited.  The calculation of the maximum growth rate for the popula-
tion rate is based on the temperature and light intensity used for the exper-
iments.  As shown previously, the effect of temperature on algal growth and
respiration is well represented by an exponential relationship below the
optimum temperature.  The effect of a non-optimal light intensity is to
reduce this growth rate from its maximum.  If it is assumed that these
effects are multiplicative, it follows that:

                   T-20
                                                                         (35)
and that :


          L  - K6T-2°                                                  (36)
Note that the depth-averaged form of the light reduction equation is not used
since the reaction vessel is completely illuminated.

     A control and two different initial conditions for the nutrients, 0.2
mgN/£ and 0.5 mgN/£ were examined.  The results for these experiments
together with the calculations are presented in fig. 16.  It is clear that
the limiting nutrient is inorgan nitrogen since its concentration is calcu-
lated to decrease to below the half saturation constant, K „, as the algae

grow to their peak.  The behavior of the phytoplankton biomass and nitrate
nitrogen are well represented by the calculations.  The uptake of dissolved
silica is less well represented and the silica to chlorophyll ratio repre-
sents a compromise for the observations.  The uptake of phosphate is not in
agreement with the observations.  The phosphorus continues to decrease
beyond that required for the growth, as indicated by the decrease of both
algae and inorganic phosphorus during the later portion of the experiment.
This luxury uptake cannot be explained in the terms of the Monod theory and
constant stoichiometric coefficients, and, as pointed out previously, the
variation of the stoichiometry of the microorganisms during short term
experiments is perhaps the most frequently encountered effect which violates
the assumptions of the Monod theory.  Nevertheless the predicted behavior
with respect to the limiting nutrient is reasonable and supports the use of
these kinetics for calculation of changes in chlorophyll as a function of
nutrient concentrations.

ZOOPLANKTON KINETICS

     A major factor in the reduction of phytoplankton biomass after the
spring bloom in the Great Lakes is the predation pressure exerted by the
herbivorous zooplankton.  In order to quantify this effect and relate it to
the magnitude of the phytoplankton and zooplankton populations present it is
necessary to develop an additional set of kinetic relationships.  The basis
for these equations are not the substrate-microorganism formulations appli-
cable to dissolved nutrients and bacteria or algae but rather the relation-
ships that have been developed to describe the behavior of larger predatory
organisms such as fish.  The principle difference is the mode of feeding.

                                     37
-------
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TIME, days
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     012345
            TIME, days
012345
       TIME, days
Figure l6.   Application of algal growth and nutrient uptake
            equations  (3*0 to batch kinetic data
                             38
-------
Phytoplankton are the prey and the predators are the herbivorous and omnivor-
ous zooplankton.  The classical equations of predator-prey interaction are
those of Volterra [253 which, for phytoplankton-herbivorous zooplankton
interactions, take the form:

     dZ
         = (G-Z                                                 (3T)
with the growth rate G _ , given by:
                      /i-L


     G   = a   e C  P                                                   (38)
where Z  is the herbivorous zooplankton biomass, a   is the zooplankton/
       1                                          ^-T
phytoplankton stoichiometric ratio which, as in this case with zooplankton
biomass in carbon units, corresponds to the carbon/chlorophyll ratio of the
phytoplankton.  The interaction coefficient £ C  can be thought of as a
                                               O
specific filtering rate C , with units &/mg C-day corresponding to the spe-
                         &
cific (i.e. per unit biomass) filtering rate of the zooplankton population,
and e, the assimilation efficiency.  For raptorial feeding these interpreta-
tions do not apply and the coefficient must be regarded as empirical.  The
loss rate, D  , is due to both respiration and higher order predation.
            ZiJL

Growth Rate

     The filtering rate defined above varies as a function of the concentra-
tion of the prey, the size of the grazing organism, and the temperature [39].
These effects are quite significant and are taken into account using the
available data to suggest functional forms and the range of the parameters
that are reasonable.

     To relate these terms to the more classical analysis of zooplankton
feeding and growth, consider the ration, R, the weight of food consumed per
animal per unit time.  Investigations of the feeding of crustacean zooplank-
ton indicate that the relationship of the ration to increasing food concen-
tration is to increase in proportion to the increasing but small food concen-
trations but then to level off and reach a maximum, R , as food concentra-
tion continues to increase.  This type of behavior, observed in the feeding
behavior of fish by Ivlev, can be described by the equations [39»^0,4l]:


     R = Rm (1 - e-5P)                                                  (39)

In terms of the growth equation (38), this suggests that the filtering rate
is decreasing as the food concentration increases.  If a hyperbolic function
is used to represent this behavior as done previously [29], then the ration
changes as
                                     39
-------
                        C'  P K

                          mg

where C'  is the maximum filtering rate (A/animal-day) and K   is the half
       gm                                                   mg
saturation constant for filtering.  By matching the maximums and the initial
slopes of these two expressions the relationships:

                          1
                    V ' 5Em

are derived.  Table h, adopted from Sushchenya [39] illustrates some repre-
sentative values.  The value of the half saturation constant varies widely
with lower values in the range of 1-10 yg Chl-a/& and appears to depend
strongly on the species of both phytoplankton and zooplankton involved.

     The hyperbolic dependence of the specific filtering rate on phytoplank-
ton concentration is illustrated in Fig. IT-  The data from Richman [1*2] for
Diaptomus oregonensis feeding on Chlamydomonas and Chlorella is well repre-
sented by eq^i (1*0) with K   = 1*0,000 cells/ml corresponding to an estimated

K   = 8 mg wet. wt./£ (11-32 yg Chl-a/£).
 mg

     The relationship of the ration to body weight of the animal follows an
equation of the form:


                    R = a W5

at constant food concentration and temperature.  A review of the available
values for 3 indicates that it varies from a low of $ - '3.6 to a high of
3-0.9 with the higher values predominating [1*1].  This suggests that the
ration, defined per unit zooplankton biomass, R/W, is less dependent on the
absolute body weights of the population since:


                    f=aW3-1                                           (1*1*)


and 1-3 is in the range of 0.1 to 0.1*.  For a 10 fold increase in W, the pre-
dicted change in R is a factor of 3 to 8 increase whereas the change in R/W
is only a 21 to 60$ decrease.  Thus for a formulation that aggregates the
zooplankton population into a biomass concentration, the specific ration R/W
is the useful parameter, since it is closer to being constant with changes in
body weight.  This useful fact gives some support to the validity of aggre-
gating the zooplankton in terms of biomass rather than as individuals, a pro-
cedure which is, as with the phytoplankton, a practical expedient Specific
filtering rates have been summarized [27] arid vary in the range 0.1 - k.O
&/mgC/day with the majority of the rates in the vicinity of 1-2 £/mgC/day.

                                     1*0
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     The temperature dependence  of the  filtering rate has been summarized
 [27] and the  results indicate that,  in  contrast to all other biological rates
 included in the kinetics, the dependence  is linear with temperature, with a
 zero filtering rate at  0°C a reasonable simplification.  Thus the specific
 filtering  rate is  specified at 20°C  and multiplied by T/20°C to account for
 its temperature dependence.

     The assimilation efficiency, e, has  been reported in the range of hO-90%
 [4U],   The efficiency is the fraction of  the food ingested which is not
 excreted but  is used for growth  and  metabolism.  It has been observed to de-
 crease  with increasing  ration [39] and  increasing food concentration [k3]-
 Since ration  increases  with food concentration it seems reasonable to incor-
 porate  this effect as dependent  on food concentration using a hyperbolic
 relationship  of the form:  e=eK   /(K  +P)by analogy to the grazing de-

 pendence with K    as the half saturation  constant.
               me
     The result of the  above considerations is that the growth rate of the
 herbivorous zooplankton, G „, grazing on phytoplankton at concentration P is
 of the  form:


     G  =  app e(P) C (P,T)P                                             (1*5)
      L   Lr      g
 where

             me
 and
                         mg

 The parameters to be  specified are the maximum grazing rate at 20°C, C   :
                                                                      gm
 the grazing  half saturation  concentration of phytoplankton, K  ; the maximum
 assimilation efficiency, £  ; and its half saturation constant, K   ; and the
 zooplankton  to phytoplankton stoichiometric ratio, a   .
                                                    OJr
 Death Rate

     The  components of the death rate included in this formulation of herbi-
 vorous  zooplankton kinetics  are the loss of biomass due to metabolism as
 measured  by  respiration, and that due to predation by carnivorous  zooplank-
 ton.

     The  respiration  rate of zooplankton as measured by their 0  consumption

 has been  found to be  a strong function of both organism weight and tempera-
ture [^5].   The dependency on organism weight is analogous to that found for

                                     43
-------
grazing rates, eq. (^3), with the exponent in the same range.  Thus the spe-
cific respiration rate, the rate per unit biomass rather than per animal,
can be expected to be more nearly constant with respect to organism weight
although some variation has "been found [^l].   For organisms from temperate
waters that rate varies from ^.6 to 2.3 y£0^,/mg dry wt./hr. for a 10 fold
change (0.1-1.0 mg dry wt. /animal) in organism weight.

     The temperature variation of the respiration rate is an exponential
function with 0 found to be in the range of 6 = 1.060 to 1.120 as shown in
Fig. 18, a plot of the log of the ratio of specific respiration rate at T °C
to that at 20°C.  The legend, source, and references for these data have
been given previously [27].  Thus respiration loss rate can be represented
by the equation:

          RZ1 = K3 93T"2°                                               (U8)

where R    the respiration rate in per day units, is available from the spe-
       /il
cific oxygen consumption rate if the fraction of the dry weight that is car-
bon and the respiratory quotient (RQ = ACOp produced/AOp consumed) are known.
For reasonable values of these ratios (hO% C/dry wt.  and RQ = l) the observed
rates are in the range 0.06 to 0.2 day"  [^l].   The observed values of the
zooplankton respiration rate, K   are somewhat  less than the equivalent phy-
toplankton respiration rates which is consistent with the observation that
specific rates appear to decrease slightly with organism size or weight.

     Other experimentally observed effects which have not been explicitly
included in the kinetics is the possible existence of a phytoplankton con-
centration at which grazing ceases [^6] and the effect of nocturnal grazing
as opposed to continuous or daily average grazing [1*7].  Perhaps the rather
large range in observed parameters for the present paramerization reflects
these effects as well as the specifics of the grazing experiments themselves,
e.g. short versus long term experiments and starved versus normal zooplank-
ton.

     The other major component of herbivorous zooplankton mortality is pre-
dation by the carnivorous zooplankton population.  The importance of carniv-
orous grazing pressure in Lake Ontario is evident from the calculations of
Thomann et al. [U8].  An interesting example of this effect has been ob-
served and quantified [^9] for Daphnia grazing  on phytoplankton, measured as
chlorophyll, and being preyed upon by Leptodora.  The relevant constants
derived from the data are:  a.™, e  C   = 0.025  £/ygC/day; zooplankton res-
                             Cr  m  gm
piration rate = 0.088 day" ; and Leptodora filtering rate of 9.5 m£/animal/
day, all of which are within reported ranges for these parameters.  The for-
mulation of the carnivorous grazing adopted in  this analysis is entirely
classical [25] and corresponds to the Volterra  predator-prey formulation
without saturating effects.  That is the death  rate by predation takes the
form C 0(T)Z^ where the grazing rate is linear  in temperature and Z  is the
carnivorous zooplankton biomass.
-------
                                                      LO
                                                      CN
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     The growth and death rates for the carnivors in turn determine their pop-
ulation size:

     dZ

     d!T= (GZ2-DZ2)Z2

The growth rate follows from the filtering rate and an assimilation effi-
ciency e:


     GZ2 = £Cg2(T)Zl


The death rate is the sum of respiration losses and an empirical constant,
K , which accounts for higher order predation so that:

               rp Of)
     DZ2 = VlT   + K5


At this level of resolution Thomann et al. [hQ] have shown that, at least
computationally, higher order dynamic predator-prey equations do not materi-
ally influence the dynamics of the lower members of the food chain on an
annual cycle.

NUTRIENT RECYCLE

     The recycling of nutrients, that is, the transformation from unavail-
able particulate and soluble organic forms to the available soluble inorganic
forms, is the critical step in completing the cyclic nutrient pathways in
aquatic systems.  The purpose of this section is to present evidence that the
rate of this recycle reaction for phosphorus in the lower Great Lakes is re-
lated to the size of the phytoplankton population.  It is also shown that
under simplifying assumptions the rate of recycle, together with the growth
rate of the algae determines the fraction of the total phosphorus concentra-
tion which is present as either plankton, or in unavailable or available
forms.

     The importance of phosphorus recycle is well known.  If no significant
recycle occurred, the plankton would rapidly deplete the available form, and
the unavailable form being generated by the algal metabolic losses and zoo-
plankton excretion processes would build up and eventually account for all
the phosphorus present, thus terminating the cycle.  However since recycle
does in fact occur, the balance between the three forms of nutrients is
maintained.

     The observational and experimental investigations of recycling have
been described by a number of investigators [50,5l]-  The two major processes
which contribute to the recycle are the predation by zooplankton and the
metabolic losses of the algae and zooplankton themselves.  The role of bac-
teria in the subsequent transformation has recently been documented [52].
                                     1*6
-------
     Normally, healthy algal cells are not usually attacked by proteolytic
"bacteria but if the cells are deprived of essential nutrients and/or suffi-
cient light the cells become permeable and soluble nutrients leak out.  The
phenomena can be quite rapid with up to QQ% of the cell phosphorus and 20% of
the cell nitrogen being released in 2-3 days [50].  The remainder of the cell
nutrients are in the form of particulate cell fragments.  The phenomena
occurs as the population is stressed, possibly declining, and using its cellu-
lar constituents in its metabolism.  In this report, the process is termed
respiration, since it is most pronounced in dark conditions which character-
ize the oxygen consumption (e.g. the dark bottle of primary production
studies) and nutrient release experiments that quantify the rates.

     A nutrient release process also occurs during zooplankton grazing of
algal populations.  For example, during active feeding, Calanus retained Yl%
of the algal phosphorus for growth and excreted the remainder, 23% as fecal
pellets and 60% as soluble phosphorus.  For nitrogen 27% was retained while
3Q% was excreted as fecal pellets and 36% as soluble nitrogen [53].  A simi-
lar result for natural marine zooplankton populations has been observed where
60% of the total excreted phosphorus is in the -form of phosphate [5^]-  Thus
the result of algal respiration, mortality, and zooplankton grazing is to
release nutrients in both soluble and particulate forms.  A portion of the
soluble nutrients are in the available form with the remainder present as
organic compounds.

KINETIC FORMULATION

     The detailed characterization of the forms of nutrients in natural
waters: inorganic or organic, particulate or dissolved, requires extensive
data that, at the low concentrations in Great Lakes waters, are difficult to
obtain.  Perhaps the most difficult differentiation is between detrital and
phytoplankton-bound nutrient since no simple separation is possible.  In
order to characterize the recycle process and at the same time not compli-
cate the formulation to the point of impracticality, it appears that the
division of the nutrient into three forms: plankton-bound, available, and
unavailable is a reasonable first step.  The available phosphorus form is
directly measured as soluble reactive phosphorus.  A portion of the unavail-
able phosphorus is measured as dissolved organic phosphorus.  The total
phosphorus is also measured.

     The formulation of the kinetics of recycle requires an equation which
specifies the rate at which the unavailable nutrient is transformed to the
available form.  To be specific, let p , p  and p. be the concentrations of

total, unavailable, and inorganic (= available) phosphorus respectively.
The concentration of phosphorus associated with a concentration, P, of algal
chlorophyll, is a  P where a   is the phosphorus to chlorophyll ratio of the

population.  Similarly, if Z is the zooplankton carbon concentration, then
a  Z is the zooplankton phosphorus.
 PZ>

     Consider a situation in which transport and external sources can be
neglected, i.e. a purely kinetic setting.  The kinetic equations which des-
cribe phytoplankton and zooplankton growth and death, and phosphorus uptake
-------
and recycle, with the modification that a fraction (l-p) of respired and
excreted phosphorus is directly available, have the form [27,^8]


     P = (G  - D  - C Z)P                                             (52a)
           r    r    g


     z = (GZ - DZ)Z                                                   (52b)


     pu = pDpP' + p(CgZP' - GZZ') + PDZZ' - Kpu                       (52c)


     p  = (l-p)D P' + (l-p)(C ZP' - G Z') + (l-p)D Z'  - G P'  + Kp     (52d)
      1         i            g       A            Zj.rU


where G , D  are the epilimnion averaged growth and respiration rates for

phytoplankton; G , D  are the growth and death rates for zooplankton; C
                L   L                                                  g
is the zooplankton grazing rate; p is the fraction of respired and excreted
phosphorus that is in the unavailable form; P' = a  P and Z'  = a  Z, the

phosphorus equivalents of phytoplankton chlorophyll and 2;ooplankton carbon;
and K is the recycle rate of unavailable to available phosphorus, which is
assumed to be first order with respect to p .   In this notation total phos-

phorus is given by:  p  = p. + p  + P1 + Z'.  For steady state conditions
the derivatives are all equal to zero and either eq. (52c) or eq. (52d)
yields the following relationship:

           K   pu   pi   7'
     (l+-£-)-^+-i + f-=l                                       (53)
          P P  PT   PT   PT
For the case that the fractions of the total phosphorus that are either in
the available form, p./p^, or bound as zooplan]

small relative to one, eq. (53) simplifies to:
the available form, p./p^, or bound as zooplankton biomass, Z'/p ,  are both
where:

     "£

the dimensionless ratio of recycle rate to the growth rate - fraction
unavailable product.

     For rapid recycle relative to growth or for a small p, the unavailable
fraction excreted or respired, 6 » 1, and only a small portion of total
-------
phosphorus is in the unavailable form.   Conversely for slow recycle relative
to growth or a large unavailable excreted or respired fraction,  6 < 1,  and
most of the phosphorus is in the unavailable form.  Thus the dimensionless
parameter, S, is the important characteristic of the kinetics which deter-
mines the distribution of total phosphorus for the case that the available
and zooplankton fractions are small relative to the algal and unavailable
fractions.

     The magnitude of the recycle rates from various laboratory  experiments
are listed in Table 5.  The range is 0.01 to 0.06 day"1 corresponding to half
lives of approximately 12 to TO days.   The temperature coefficients are
within the expected range for heterotrophic bacterial reactions.   For G =

0.05 to 0.2 day"1 which is characteristic of the summer average  epilimnion
values and p = 0.5 as an estimate of the respired and excreted fraction that
is unavailable, the range of 6 is 0.1 - 2.5 corresponding to a range in p  /p
of 30% to 90%.  The large unavailable fraction corresponds to a  low recycle
rate and a high algal growth rate and therefore, at steady state, a high
respiration plus grazing rate, whereas fast recycle and slow growth result in
the low fraction unavailable.  It is probable that under this condition the
available and zooplankton fractions become significant, the approximations
p./Pm <<: 1 an(i Z'/Pm <<: 1 are no longer reasonable, and eq. (3)  is not  appli-
cable.  This suggests that p /p  may not decrease as low as 30%.

     For these kinetic equations and assumptions it is also possible to cal-
culate the algal phosphorus fraction and the chlorophyll a/total phosphorus
ratio, P/P-,.  The latter follows from the approximation: a pP +  p  - p   and
eq. (5*0 '•


               r^rrfr                                           (56)
               PT   apP ±   °

The importance of the stoichiometric coefficient a   is clearly  evident in
this equation as is the effect of 6.

RECYCLE RATE AND CHLOROPHYLL CONCENTRATION
     The relationship, eqs. (5*0 and (55)» between recycle rate,  K, the
fraction of respired and excreted phosphorus that is unavailable, p, and
the ratio of unavailable to total phosphorus suggests that the observed
variations in the latter be used to investigate variations in the former.
As mentioned previously no direct measurement of unavailable phosphorus is
available since the detrital and algal particulate phosphorus are not sep-
arable.  However if only soluble phosphorus is considered then unavailable
phosphorus is equivalent to dissolved organic phosphorus which can be esti-
mated as total dissolved minus soluble reactive phosphorus, and  the ratio
p /p  for soluble phosphorus can be calculated.  Alternately if  a phosphorus
to chlorophyll ratio is assumed then the algal bound phosphorus  can be  esti-
mated and a direct calculation of p p   is possible with the additional
assumption that Z' is negligible.
-------














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     Both of these methods can be used to estimate p /p .   This has been done

for the various data sets for which the appropriate measurements are avail-
able.  The procedure is to average the epilimnion observations during the
period of stratification for the years indicated.  The well mixed basins,
Western Lake Erie and Saginaw Bay, are analyzed for the periods employed for
the rest of that lake.  The idea is to conform to the assumptions of the
simple analysis of the previous section, namely steady state and constant
parameters, by using long time averages.  Admittedly, this is rather crude
but the results are quite interesting.

     The data used for the calculations are given in Table 6.  Plots of the
ratio of soluble unavailable to total soluble phosphorus and the ratio of
estimated total unavailable to total phosphorus versus chlorophyll a_ are
shown in fig. 19.  The results suggest an inverse relationship between the
unavailable fraction of both the soluble and total phosphorus and chloro-
phyll.  The exceptionally large Saginaw Bay value for the soluble fraction
is probably the result of the influence of inputs which have been neglected
in the simple analysis of the previous section.

     For the computations that follow the relevant plot is that relating
total unavailable phosphorus to total phosphorus, consistent with the phos-
phorus species considered in the theoretical analysis.  The decrease in the
fraction unavailable: from p /p  =0.8 for the low chlorophyll basins, to

p /p  = 0.7 for the intermediate basins (^ 5 yg Ch£-a£) to p /p  = 0.65 for

the basins with higher chlorophyll concentrations, suggest that the recycle
rate is influenced by the chlorophyll &_ concentration.

     This 20 percent change in the ratio of p /p  over an order of magnitude

increase in chlorophyll a^ takes on added significance when one considers that
there is only minor variability in the data given in Table 6.  For Lake
Ontario, for instance, the standard error is within 1.0 - 8.5% of the mean
values listed for the component variables of the calculation, total, dis-
solved, and available phosphorus and chlorophyll ji, with an average of some
1,000 data points from four lakewide cruises used as part of the computation.

     That such a relationship should exist can be seen from the following
reasoning:  If the agents of the recycle reaction are heterotrophic bacteria
which convert unavailable phosphorus to available phosphorus as a byproduct
of their metabolic activity, and if the major source of carbon for the
energy and synthesis reactions of the bacteria is the detrital carbon pro-
duced by the algal respiratory and excretion reactions, it is reasonable to
expect that the bacterial biomass increases as the source of this detrital
carbon, namely the standing stock of algae, increases.  Evidence that bac-
terial biomass increases as chlorophyll a_ increases has been reported for a
series of Canadian Lakes [58] and for Lake Huron [59]-  Although the rela-
tionships are different for the different sets of data, the trend is clear
in both cases.  Evidence from other studies [60,61,62] indicates that the
seasonal trends of chlorophyll and bacteria, although not in perfect phase,
tend to follow the same pattern.
                                    51
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             1.0
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Figure 19.   Variation of the ratio of estimated unavailable to  total
            phosphorus and  of dissolved organic to total dissolved
            phosphorus ratio with chlorophyll.  See Table 6 for legend.
                                53
-------
     On the other hand, it is also known that certain species of algae can
metabolize dissolved organic phosphorus directly [50] in which case the quan-
tity of unavailable phosphorus would tend to decrease as chlorophyll in-
creases.  Hence if either or both these mechanisms are active the result is
an increased recycle rate as chlorophyll increases.

     Alternately, the decrease in the ratio of unavailable to total phos-
phorus as chlorophyll increases could be related to a decrease in, p, the
unavailable fractions respired and excreted.  The mechanism is related to
the fraction of algal phosphorus that is labile and quickly available (l-p)
and that which is structurally bound and unavailable, p.  In oligotrophic
situations it is probable that a smaller fraction is labile and p is larger
than in eutrophic settings where p is smaller.  This suggests that p would
decrease as chlorophyll increases.  Based on eqs. (5^) and (55), it is not
possible to distinguish between K increasing and/or p decreasing as chloro-
phyll increases since they occur as a ratio (eq.  55).

     All these mechanisms are known to occur and influence the relationship
between unavailable to total phosphorus and chlorophyll.  The question is:
how to modify the equation structure to account for the observations.  A
number of approaches are possible.  Bacterial biomass can be included direct-
ly as a state variable with a governing differential equation [103].  The
problem is that in most cases observations of bacterial biomass are not
available and the kinetic constants obtained from a calibration with unob-
served state variables are likely to be quite tentative and uncertain.

     The inclusion of state variables which partition the internal algal
pools of phosphorus is also possible [99] but again these cellular concentra-
tions are unobservable and add to the uncertainty of the calibration, while
also increasing the realism of the formulation.

     An alternate approach, which has the attraction of simplicity, is to
establish an empirical relationship between recycie rate and chlorophyll.
As shown subsequently this adds only one more unknown kinetic coefficient
to the formulation and no unobservable state variables.  For this reason
this latter approach seems appropriate.

     With the data in fig. 19 interpreted as suggesting that the recycle
rate is chlorophyll dependent with p constant it is nece:ssary that the func-
tional form of the dependence be established.  The relationships which span
the expected dependency for the recycle rate coefficient are:

     First order recycle:   K = K'(T)                                  (57a)

     Second order recycle:  K = K"(T)P                                 (57b)

     Saturating recycle:    K = K'(T) -—^-^                          (5Tc)
                                       mr
with conventional 6 temperature dependence for the rate constants K'(T) and
K"(T).  First order kinetics, which are the conventional formulations for
the transformation of organic to inorganic nutrient forms in estuaries [63]
-------
and previous lake models [U8] assume a recycle rate constant that varies with
temperature only.  Second order recycle assumes that the rate of recycle is
proportional to the phytoplankton biomass present as well as the amount of
unavailable nutrient.  In laboratory experiments, pure cultures with bacte-
rial seeding appeared to follow a second order dependency [56].  Saturating
recycle is a compromise between these two mechanisms :  a second order depen-
dency at low chlorophyll concentrations when P « K  , where K   is the half
    J              * J                             jjj.,,5        jjjp
saturation constant for recycle, and first order recycle when the chlorophyll
greatly exceeds the half saturation constant.  Basically this parameteriza-
tion slows the recycle rate if the algal population is small but does not
allow the rate to increase continually as chlorophyll increases.  The assump-
tion is that at higher phytoplankton chlorophyll concentrations other factors
are rate limiting the recycle kinetics so that it proce'eds at its maximum
first order rate.

     Two tests of these forms for the recycle kinetics have been made.  The
first utilizes the expected relationship between p /p  and & = K/pG  given by
eg.. (5^)«  The growth rate G  is calculated using the conventional expres-
sions and the results of seasonal calculations, [37,^8] and p = 0.5 is used
for all basins.  In addition it is assumed that 0 = 1.08 for this reaction.
Using the information in table 6, it is possible to calculate 6 for each
hypothesized recycle mechanism:

                              T_?n
                            , Q-L-^U
     First Order:      6 = ^-^ -                                      (58a)
                              T-20
     Saturating:       6 = £~ -     P+                               (58b)
                               P     mr

                              T_?0
                           TT"fi
     Second Order:     6 = ^-^ - P                                    (580)
and to compare the observed ratio, p /p , for this basin with the expected
ratio:  l/(l+6).  The results are shown invfig. 20 for K' = O.Oh day"1,
K   = 5 yg CM-a/Jl, and K" = 0.008^3 day-1/yg Ch£-a/£ which appears reason-
able from the calculations to be discussed subsequently.  Consistent results
are obtained only if the saturating recycle formulation is used to calculate
6.  Neither first nor second order kinetics are appropriate since the obser-
vations are not consistent with the expected theoretical result, namely that
P /Pm = 1/1+6.  Thus in order to be consistent with observations in the var-
ious basins it is necessary to adopt a saturating recycle rate as the func-
tional dependency on chlorophyll.

     The second test of this formulation is a comparison of seasonal calcu-
lations and observations in the various basins which is discussed below.
                                     55
-------
            SATURATING RECYCLE     FIRST-ORDER RECYCLE
       0.9
       0.8
       0.7
       0.6
       0.5
           -  ON
                              WB
         0.1     0.2       0.5    0.1     0.2
                       6                          6

                        SECOND-ORDER RECYCLE
             0.9
            0.8
             0.7
             0.6
             0.5
                    0.5     1.0
• EB
                                     • CB
                                                  >s»
               0.1     0.2
 0.5
1.0     2.0     4.0
Figure 20.    Comparison of observed and calculated ratio of unavailable
             to total phosphorus for saturating (eq.  5&"b), first  order
             (eq.  58a), and second order (eq.. 58c) nutrient recycle
             kinetics.
-------
                                  SECTION 7

                                    DATA
     The credibility of model calculations is determined, in large measure,
by their agreement with observations.  Besides the obvious constraints that
the model should behave reasonably well and predict general patterns such as
spring phytoplankton growth, this is perhaps the only external criteria which
is available to determine the validity and hence the utility of a complex
eutrophication model.  A comparison to actual data indicate if the approxima-
tions used in the model adequately represent the real situation.  With this
in mind, a detailed review of available data for Lake Huron and Saginaw Bay
is presented and from these data a set of aggregated data were generated for
use in calibration.

HISTORICAL DATA

     Prior to 1971» not much comprehensive limnological data had been gath-
ered for Lake Huron, and those data which were available fell short of pro-
viding the substantial data base necessary for water quality modeling efforts.
Data for Saginaw Bay were even more scarce.  One observer, reviewing histori-
cal data for the bay, noted that "presently, the necessary data for verifica-
tion (of water quality models) does not exist."[3]

     The data summary presented in Table 7 encompasses all of the major Lake
Huron surveys which were available for review.  One of the earliest surveys
of Lake Huron was that undertaken by Ayers, et al. [l6] in the summer of 195^-
This survey consisting of three cruises during which a few chemical para-
meters were measured (Ca, Mg, Si02), but of prime interest are the measure-
ments of current magnitudes and directions made using drift bottles.  To date,
this is still one of the best sources of flow patterns for Lake Huron and its
applicability to this modeling effort has been discussed in relation to
transport regime estimation (section 5).  Drift bottle current measurements
were also made by the U.S. Fish and Wildlife Service in 1956 [6k].  Other
analyses of Lake Huron circulation are also available [65,66,67].

     Commencing in I960 and continuing through 1970, the Great Lakes Insti-
tute (GLl) of the University of Toronto conducted several surveys of Lake
Huron [68].  These consisted of temperature, geophysical, meteorological,
internal wave and synoptic surveys.  GLI data reports [69-73] include com-
prehensive weather information and lakewide temperature data.

     In 1965, the FWPCA sampled Saginaw Bay and the Southern Lake Huron tri-
butary area [7^K  The stations in the bay were sampled twice a month during
the summer and fall of 1965.  These data are available through STORET.  Data
from similar surveys made by the FWPCA during the period 1967-1970 [75,76,77,
78] were also reviewed through STORET.  In addition, tributary measurements,


                                     57
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coupled with the lake surveys [79-85]  and combined with USGS flow data, can
provide mass loading information.

     In 1968, the Canada Centre for Inland Waters (CCIW) commenced synoptic
surveys of Lake Huron.  Their Limnological Data Reports [86,87] provide data
from cruises in August of 1968 and September and November of 1969.  Two
cruises in 1970 were made during May and October.  These surveys included
data for several parameters and the spatial and depth coverage of the lake
is extensive.  Another 1970 cruise was conducted by the Great Lakes Research
Division of the University of Michigan [2] concentrating mainly in Saginaw
Bay and the Michigan shoreline region.

     In order to properly calibrate a eutrophication model, data sets which
include phytoplankton chlorophyll and nutrient data measured over the entire
lake, in depth, and with adequate temporal coverage are needed.  The histor-
ical surveys discussed above are not adequate for this purpose because they
failed to meet one or several of 'these criteria.

Calibration Data
     The data base used for calibration of the model is derived mainly from
three sources:
     (l)  Canada Centre for Inland Waters (CCIW)
     (2)  Great Lake Research Division (GLRD), University of Michigan
     (3)  Cranbrook Institute of Science (CIS)
     These sampling surveys together with a compilation of background mate-
rial and an evaluation of sources and characteristics of material inputs
form an integral part of the IJC Upper Lakes Reference Study [10], which
should be consulted for a more detailed review of procedures and results.

     Data from the CCIW cruises are available for two survey years , 1971 and
197^.  Table 8 lists the sampling dates and parameters measured on these
cruises.  The 1971 surveys [88] sampled at least 78 stations per cruise and
the 197^ surveys [89] sampled ^5 stations, excluding the Morth Channel.  Both
surveys have only one sampling station in inner Saginaw Bay.  Chlorophyll-a ,
primary production, and phytoplankton composition for the 1971 cruises have
been analyzed [90,91,92] and zooplankton distribution for these same cruises
have also been studied [93].

     The 197^ GLRD Lake Huron surveys [9^] sampled a range of 36-UU stations
for eight cruises.  These stations are concentrated in southern Lake Huron
and the outer reaches of Saginaw Bay.   Sampling dates and parameters meas-
ured on these cruises are listed in Table 9>
     Table 10 lists the cruise dates and measured parameters for the
CIS surveys of Saginaw Bay [95].  These surveys form the most comprehensive
study which has been undertaken for Saginaw Bay and fills many voids in the
historical data base for the bay.  A total of 59 bay stations were sampled,
some of which are at the mouth of the Saginaw River , including 4 water intake
stations.
                                     62
-------
             TABLE 8.  CCIW LAKE HURON SURVEYS

YEAR
1971
1971
1971
1971
1971
1971
1971
1971
1974
1974
1974
1974
1974
1974
1974
CRUISE
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
DATE
4/19-4/28
5/17-5/25
6/15-6/28
7/19-7/27
8/23-8/30
9/27-10/4
10/27-11/3
11/29-12/6
V23-4/28
5/14-5/18
6/22-6/28
7/22-7/28
8/26-9/2
9/30-10/6
12/4-12/10
PARAMETERS MEASURED
ON ALL CRUISES
Secchi, Temperature, Turbidity,
pH,
Specific Conductance, Chlorides,
D.O. , Silica
NH -N, N02+N0 -N, N02-N,
* *
Inorganic Carbon Total Carbon ,
*
Organic Carbon , Chlorophyll,
Total P, Dissolved P,
Reactive P.
Secchi , Temperature ,
Specific Conductance, pH,
Alkalinity, Particulate
*
Organic Carbon , D.O.,
Total P, Soluble P, Reactive
P, total particulate
* *
Nitrogen , NO +NO -N, total N ,
SO, , Chlorides, Silica, Chlorophyll

Not measured on all cruises.
                            63
-------
TABLE 9.  19T1* GLRD  LAKE HURON SURVEYS

CRUISE
1
2
3
U
5
6
7
8
DATE
U/28-5/3
5/1U-5/17
6/OU-6/08
6/17-6/25
7/17-7/22
8/26-8/31
10/08-10/12
11/10-ll/lU
PARAMETERS MEASURED
ON ALL CRUISES
Secchi, Temperature,, pH,
Conductivity, SiO , NO -N,
NH -N, Total P, Sol\ible
P, SO^, Chlorides, Chlorophyll
Phaeopnytin fraction,
Alkalinity, carbon uptake,
particle counts

-------
TABLE 10.  1971* CIS SAGIMAW BAY SURVEYS

CRUISE
3
U
5
6
7.
8
9
10
11
12
13
Ik
15
16
DATE
2/18-2/21
3/25
U/17-H/20
U/28-V30
5/13-5/17
6/02-6/05
6/18-6/22
7/08-7/10
7/25-7/27
8/25-8/27
9/18-9/20
10/06-10/08
ii/n-n/iU
12/16-12/18
PARAMETERS MEASURED
ON ALL CRUISES
Temperature, Secchi,
Conductivity, DO, pH,
Alkalinity, NH -N,
Kjeldahl-N, N02+N0 -H,
Total P, Dissolved P
Dissolved Ortho-P, Ca,
Mg, Na, K, Chlorides,
SO. , Silics, Chlorophyll,
Phaeophytin





                  65
-------
        TABLE 11.  SURVEY STATIONS AND MODEL SEGMENTS

Model
Segment
No.
1

2






3





1*

Depth
Range
(Meters)
0-15

0-15






0-6
(all depths
measured
used for
bay sta-
tions)
15-bottom
(only val-
1971
CCIW*
37-^8
50-100
1-5,
7-30,
33-36,
U9



31,32





Same as
Seg. 1
197^
**
CCIW
108-13^
157-167
101-105
107
166




106





Same as
Seg. 1
19TU
GLRD
ND

1-7,
9-11,
13-15 ,
20-26,
36-58,
60,
63-65 ,
ND





ND

197^
CIS
ND

U2-53
57,58





2-1+0,
56
59



ND

         ues @ > 15
         meter depth
         used)
        15-"bottom
        (only val-
         ues @ > 15
         meter depth
         used)
Same as
Seg. 2
Same as
Seg. 2
Same as
Seg,. 2
Same as
Seg. 2
*   CCIW  Permanent Station Numbers

**  Chlorophyll Values for 197^ are integrated samples
    (usually to 20m) these values are used for the top
    layer (0-15m) segments only

ND  No Data
                               66
-------
     Figure 21 shows the lake coverage provided by the surveys cited.  Sagi-
naw Bay, northern, and southern Lake Huron are adequately covered by the
sampling stations as a group.  They are used collectively since the CCIW
data gives adequate coverage of the northern and southern lake but not of
Saginav Bay, CIS surveyed only in the bay, and GLRD concentrated the south-
ern lake and outer bay.  Taken together, the 197^ surveys provide the most
comprehensive Lake Huron water quality to date and their utility for the
calculations to be presented below cannot be overemphasized.  Without such
comprehensive data, calculations of this complexity could not be adequately
calibrated.

Data Reduction

     The data base resulting from an aggregation of the.surveys is quite
large.  Altogether there are a total of 35 cruises and approximately -225
individual sampling stations measured over a range of depths.  The first
step in processing these data is to match the sampling stations to the model
segmentation.  Using cruise maps from each of the four surveys, the individ-
ual stations are assigned to the appropriate model segment as shown in Table
11.  The cruise mean and standard deviation for each variable utilizing all
stations within a segment are computed.  These values for each survey are
then overplotted and the result is a set of calibration data for each model
segment for all parameters being considered.

     Aggregation and statistical reduction of data described above has been
found to be appropriate and, in fact, quite necessary.  As an illustration
of the variation which may be encountered when dealing with data not only
from different locations but different agencies as well, plots were made of
surface values for several parameters measured by different groups at essen-
tially the same location in the lake.  Three separate comparisons are pre-
sented.  Table 12 lists the overlapping stations and figs. 22-2H show the
results.  Parameters near the limit of sensitivity of the test employed:
reactive and total dissolved phosphorus, ammonia, and to a certain extent,
chlorophyll show large variations whereas the nitrate measurements are in
virtual agreement.  Total phosphorus and reactive silica are in agreement
for certain stations but not at others.  The possible causes of these varia-
tions are differences in sampling methods if a consistent difference is
obtained; for example, soluble reactive phosphorus at the northern and
southern Saginaw Bay comparison stations; and changes in actual concentra-
tions over short time scales due to the transient nature of the circulation
and mass loading for the locations chosen.

     The latter effect must be smoothed out of the data since the calcula-
tions are not designed to reproduce short time scales but rather the longer
monthly and seasonal changes.  Thus aggregation of stations, comparison to
several sources where they exist, and statistical reduction to means and
standard deviations are necessary in order to smooth the variations encoun-
tered.

     The results of the aggregation and statistical reduction of the 1971
and 197^ data sets are shown in figs. 25-35 for all the segments considered.
The comparison is made between the two years and between the different


                                     67
-------
             1971 CCIW
1974 CCIW
             1974 GLRD
 1974 CIS
Figure 21.   Sampling station locations  for the major data sets used
            in this report.  These correspond to the tabulations in
            Tables 8-10.
                               68
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Figure 26.    Model Calibration Data (Segment 1)
                      73
-------
                 TABLE 12.   INTER-SURVEY STATION COMPARISONS


AGENCY
'7^ CCIW
CIS
'Ik CCIW
CIS
GLRD
'Ik CCIW
CIS
GLRD
STATION
NO.
006
028
007
Ok9
kk
005
052
in

LATITUDE LONGITUDE
^3°51'30" 83°1|0T12"
1*3051-35" 83°U0.25»
1|1|012'2V 83°23'00"
lll|o-L2t]4o" 83°22'liO"
kk°ll'k2" 83°20'36"
l+k°Qk'l6" 83°05'08"
^l^°0l+'10" 83°0l|!50"
W°03'18" 83°02'5U»

LOCATION
Inner Sagi-
naw Bay
Northern
Saginaw Bay

Southern
Saginaw Bay


agency sources if they overlap.   The primary purpose of this comparison is
to investigate the differences in the two years data as well as the differ-
ences "between the segments.

     Figures 27 and 28 for the southern Lake Huron epilimnium show a seasonal
pattern, especially in 197^  for which there is "both CCIW and GLRD data.  At
this level of aggregation the comparisons between the two different data
sets are quite reasonable and they compliment each other nicely.   The general
trends are apparent and consistent with expected seasonal patterns:  lower
nutrient concentrations and  secchi depths as the plankton population devel-
ops, with the recovery of nutrient concentrations after the fall overturn.
Zooplankton biomass data, however, is quite variable between the two years
as is C1*1 primary production.  Differing techniques are the probable cause,
although the data does set the range for these variables.
     Figures 30-31 for Saginaw Bay show much more marked seasonal patterns
but again no marked difference between the two years (the CCIW soluble reac-
tive phosphorus for 1971 appears suspect).  CCIW and CIS data are comparable
for 197^ with the increased temporal and spatial coverage clearly delinea-
ting the seasonal features: a bimodal chlorophyll distribution, sustained
nitrate uptake, fairly constant total phosphorus concentrations, a marked
silica uptake during the spring diatom bloom with a recovery during the sum-
mer and fall and an essentially constant secchi depth during the ice-free
period.

     Hypolimnion data for the northern and southern lake segment show prac-
tically constant values for nearly all variables and no differences between
the two years.  A seasonal pattern for soluble reactive and total dissolved
phosphorus is suggested by the data which, when combined with the chloro-
phyll data for southern Lake Huron suggested seasonal algal activity in
-------
these deep waters.  This feature of the data will "be discussed subsequently
in light of the model calculations for these segments.

     The similarity of the tvo years data in the large main lake segments is
to some extent expected since the hydraulic detention times of the lake is
in excess of twenty years and differences in mass loadings, if they existed,
would not appreciably change the concentrations over the three year period
"between the two sets of observations.  For these comparisons it is clear
that the 197^ data set is comprehensive and well suited for an analysis based
on the kinetics and transport discussed in the previous sections.
                                     75
-------
     1971 DATA
1974 DATA
— 9 ^^
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Figure 27.    Model  Calibration Data  (Segment 2)
                      76
-------
                   1971 DATA
                                                        1974 DATA
H  E

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              Figure 28.   Model Calibration Data (Segment  2)
                                    77
-------
      1971 DATA
1974 DATA
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-------
       1971 DATA
1974 DATA
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                      79
-------
     1971 DATA
1974 DATA
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Figure 31.    Model Calibration Data (Segment  3)
                      80
-------
      1971 DATA
1974 DATA
AMMONIA
NITROGEN, mg/l
3 0 O
§ s 2

NITRATE
NITROGEN, mg/l
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Figure 32.    Model Calibration Data  (Segment U)
                      81
-------
      1971 DATA
1974 DATA
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TOTAL DISSC
CA- PHOSPHORU
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Figure 33-   Model Calibration Data  (Segment k)
                      82
-------
      1971 DATA
1974 DATA
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Figure 3k.    Model Calibration Data (Segment  5)
                       83
-------
        1971 DATA
1974 DATA
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Figure 35-  Model Calibration Data (Segment 5)
-------
                                 SECTION 8

                      MODEL STRUCTURE AND CALIBRATION
     In the preceding sections the necessary components of the eutrophication
model have been discussed:  tha transport between the segments; the mass
loadings to the segments; and the kinetics within the segments.  It remains
to combine these elements into a consistent set of equations and to estimate
the values of certain kinetic coefficients by calibrating the model against
the data set described in section J.

MODEL STRUCTURE

     The variables included in the model calculations are dictated primarily
by two f-'-'.cts: the available data, and their importance as either variables
of concern, e.g. phyloplankton chlorophyll, or as a component of the kine-
tics, e.g. unavailable phosphorus.  The eight dependent variables of the
calculations are shown in fig. 36.  The phytoplankton biomass that develops
in a body of water depends on the interactions of the transport to which
they are subjected and the kinetics of growth, death, and recycling.  Phyto-
plankton biomass growth kinetics are a function of water temperature, inci-
dent-available solar radiation, and nutrient concentrations, specifically
inorganic nitrogen and phosphorus.  Phytoplankton also endogenously respire
and are predated by herbivorous zooplankton which grow as a consequence.
They, in turn, are predated by carnivorous zooplankton whose biomass also
increases.  Zooplankton grazing and assimilation rates are functions of tem-
perature and, for the herbivorous zooplankton, the phytoplankton biomass as
well.  Zooplankton respiration is temperature dependent.  The nutrients,
which result from phytoplankton and zooplankton respiration and excretion,
recycle from unavailable particulate and soluble organic forms to inorganic
forms, ammonia and orthophosphate for nitrogen and phosphorus respectively.
The recycle kinetics are temperature dependent and the rate is also influ-
enced by the algal biomass present as discussed previously.

     The spatial scale of the computation approaches a whole lake scale with
the northern and southern regions of the lake, and the epilimnion and hypo-
limnion, differentiated.   Saginaw. Bay is also explicitly included.  The time
scale chosen for the calculation,  which characterizes the main features of
phytoplankton growth, is seasonal:  the spring growing season'during which
the plankton utilize and are eventually limited by available nutrients as
well as zooplankton grazing; the summer minimum; the secondary period of
growth due to the fall overturn and/or nutrient regeneration and finally the
winter decline.  Variations of the environmental parameters on a time scale
of less than bi-weekly are not considered.  Thus although it is known, for
example, that phytoplankton exhibit diurnal variations, such variations are
-------
                                                               O

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                                                                0)
86
-------
not characterized in this calculation.

     The numerical aspects are straightforward: it is time variable computa-
tion and uses a finite difference scheme to solve the differential equations
by explicit forward time differencing.  A time step of 0.5 days is used.  The
model has eight dependent variables or systems and five segments, which com-
prise 4 5 comprtments, a compartment being equivalent to one differential
equation, which must be solved simultaneously.  The computational burden is
not excessive; it requires ^ 22 central processer unit (CPU) seconds of CDC
6600 computer execution time for a one year model simulation.  Additional
peripheral processing approximately doubles the above figure.  These figures
include rather complete graphical displays of the results.

     A complete presentation of the equations, the coefficients, and the
forcing functions, boundary and initial conditions used in the subsequent
calculations are presented in Appendix I.  This is a complete specification
of the model developed during this project.

MODEL CALIBRATION

     The calibration is begun by assigning estimates of the coefficients
which govern the kinetics based on field and/or laboratory information as
well as prior studies.  Successive adjustments of the coefficients are made
until reasonable agreement is achieved between computed results and observed
conditions.  This process is critical to a modeling effort.  It is not enough
that governing equations are written and solved.  The results must be com-
pared with observed conditions for all variables in all model segments.  Only
then can any degree of confidence be assigned to the results.

     As shown in Section 7, Lake Huron and Saginaw Bay waters differ by more
than an order of magnitude in some biological and chemical parameters.  Thus
the model must simultaneously reproduce the conditions in a locally eutrophic
area as well as large oligotrophic areas.  This section contains a discussion
of the problems encountered in attempting this calibration over an order of
magnitude in the variables, the basis for incorporation of kinetic effects
outlined in section 6, and insights gained during calibration procedure.

Recycle Rate

     Early in the process, it became clear that phosphorus availability was
a focal point of the analysis.  Figure 37 illustrates the problem.  In fig.
37(a) a relatively low first order recycle rate for unavailable phosphorus
(K1 = .0084 day"1) results in computed chlorophyll concentrations which match
observed concentrations of phosphorus and chlorophyll fairly well in southern
Lake Huron but not in Saginaw Bay.  The observed peak concentrations in the
bay are not reproduced, and the computed fall profile is substantially below
the data.  That this is due to low inorganic phosphorus availability is sug-
gested by the fact that the effect is most apparent in the fall when recy-
cling provides the major source of available nutrients due to low mass load-
ings during this period (fig. 8).  The available phosphorus pool, replenished
by recycle in mid-June, is rapidly depleted as a fall peak forms, thereby
limiting further growth.
                                    87
-------
                                 SAG IN AW BAY
UJ  __

>  ^

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                 0.032
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             O LLJ

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             J ' F ! M ' A
                                      J  J ' A  S
                                        .
                        j' F' M ' A  M ' j' PA'S
                           SOUTHERN LAKE HURON
Figure 37.  Calibration calculation for a  recycle rate  characteristic

           of Southern lake Huron (bottom figure).   Caginaw Bay chlor-

           ophyll and nutrients comparison (top three  figures).
-------
     Figure 38 illustrates the opposite case.  Using a relatively high first
order recycle rate (K1 = .031 day"1), the computed chlorophyll concentrations
match observed values in Saginaw Bay but are much too high in southern Lake
Huron.  Inorganic nutrient concentrations, especially soluble reactive phos-
phorus during the beginning and towards the end of the year are also high in
comparison to observed values, indicating too rapid recycling of phosphorus.
Note that the late fall and winter observations of soluble reactive phos-
phorus are critically important in determining the recycle rates.

     A number of alternate hypotheses were examined in order to account for
this discrepancy.  For example at the low recycle rate Saginaw Bay chloro-
phyll is computed to be lower than observed.  It might be possible that the
transport across the Saginaw Bay-Lake Huron boundary is too large and the
plankton are being flushed out too rapidly.  Although the magnitude of the
exchanging flow is set by the transport analysis based on conservative
tracers (as described in section 5), it is possible that the phytoplankton
calculation is more sensitive to this exchange rate than the conservative
tracer calculation.  The results, using the low first order recycle rate
(K1 = . 0081| day"1) which is suitable for southern Lake Huron, and with no
exchanging flow between the bay and open lake, are that computed chlorophyll
concentrations are comparable to observed magnitudes but computed total phos-
phorus and Kjeldahl nitrogen concentrations are more than double observed
values (fig. 39).  The chlorides and temperature calculations would also
exhibit the same lack of agreement with observations.  Thus inaccurate basin-
lake exchanges are not the source of the problem.

     Other possible hypotheses were investigated.  For example, as shown in
section 6, eq. (56), the phosphorus to chlorophyll ratio, a  , is important
in determining the quantity of total phosphorus that is assimilated and
becomes algal chlorophyll.  However if it is varying it would be expected
that the ratio is larger in Saginaw Bay where the quantity of inorganic
phosphorus is larger than in Lake Huron.  But this just compounds the diffi-
culty since, as shown by eq. (56), and the sensitivity calculations in
section 9, this would lower the computed chlorophyll in Saginaw Bay which is
contrary to the direction required if the low recycle rate that appears
reasonable for Lake Huron is used.  Thus the conclusion that the recylce
rate is different in these two regions becomes inescapable.

     One possible solution to this dilemma would be to assign a different
recycle rate to each segment.  This, however, defeats the purpose of the
calculations which are ultimately to be used to evaluate the effects of
changes in mass loadings.  For example if the loadings to Saginaw Bay were
lowered substantially, with the high degree of mixing between the bay and
the lake, Saginaw Bay would approach concentrations similar to those in the
open lake waters.  Then areas of similar properties .would have different re-
cycle rates since the rate had been assigned by segment.  Similarly, if the
mass loadings to the open lake waters of Lake Huron were increased to such
a degree as to approach concentrations existing in Saginaw Bay, the model
would have an unrealistically low recycle rate in these segments.

     The fundamental problem with specifying site-specific kinetic constants


                                    89
-------
                       SOUTHERN LAKE HURON
                    J'F'M1A'M1J'J
         UJ _

         H E  0.004
         < co'
         LU 13
         QC OC
         LU O  0.002

         gi
         3 °
         o J  o.ooo
         co °-
              0.04
              0.02
               0.00
J'F'M'A'M'J'J'A'S'O'N'D
                    J'F'M1A'M1J'J'A'S'O1N'D
                             SAG IN AW BAY
              _     J'F'M'A'M1J'J'A1S'O1N'D

Figure 38.  Calibration calculation for a recycle rate characteristic

          of Saginaw Bay  (bottom figure).  Southern Lake Huron chlor-

          ophyll and nutrients comparison (top three figures)
                            90
-------
        S
          40
      .  .
     O O
          20
>  o

£  i  o
   O
     _


   p f 0.032
   o  *
   < w
   m ^

   S O  0.016
             J'F'M'A'M'J'J'A'S' O'N T D


   3
   o ?  o.ooo
   CO ""
         J'F'M'A
'A'S'O'N'D
             J'F'M'A'M'J'J'A'S'O'N'D
             J'F'M'A'M1J'J'A'S'O'N'D
Figure 39-   Calibration calculation for a recycle rate

           characteristic of Southern Lake Huron.

           Saginaw Bay-Southern Lake Huron transport

           exchange rate set to zero.
                      91
-------
is that it defeats the purpose of the kinetic formulation, which is to prop-
erly characterize processes, independent of the particular geographical
location in which they are occurring.  The more srce-specific the kinetic
constants are, the less realistic is the modeling framework since the model
is "being calibrated to one particular situation, rather than to the class of
situations to which it is designed to apply.  This theme is returned to sub-
sequently in the discussion of the application of the modified recycle kine-
tics to Lake Ontario.

     The varying recycle rates are accounted for in the present calculation
by relating the recycle rate to the chlorophyll concentration.   At higher
chlorophyll concentrations the recycle rate increases up to a limit that is
consistent with observed laboratory rates.  As shown in section 6, the
available data from various regions in the Great Lakes supports this hypoth-
esis.  Saginaw Bay with its higher chlorophyll concentrations would there-
fore have a higher recycle rate and the inorganic phosphorus available for
growth would be resupplied more quickly thus supporting a larger population.
It should be noted that the same hypothesis is applied to the recycle of
nitrogen and, since the recycle mechanisms are assumed to be the same as for
phosphorus, the same rates are used.  Initial calculations with the nutrient
recycle rate directly proportional to phytoplankton concentrations (i.e. a
second order recycle rate) indicated that this mechanism would provide the
inorganic nutrient flux necessary to support observed growth in Saginaw Bay.
Subsequent investigations described in the kinetics section (6) indicates
that the recycle rate saturates with respect to chlorophyll concentration,
and the calculations presented subsequently incorporate this formulation.

Zooplankton Kinetics

     As discussed in section 6, the two mechanisms incorporated in zooplank-
ton growth expression are a reduction in filtering rate and in assimilation
efficiency as chlorophyll concentrations increase.  Whereas the formulation
for Lake Ontario included only assimilation efficiency decreases it was
found that the same grazing rate did not apply to both Saginaw Bay and Lake
Huron.  A rate suitable for Lake Huron was invariably too large for Saginaw
Bay.  As soon as the spring bloom began in Saginaw Bay, herbivorous zooplank-
ton growth would increase to such an extent that they would exert too much
grazing pressure on the phytoplankton, reducing their concentrations to
below observed peak values.

     Perhaps this effect appeared so dramatically in the Saginaw Bay-Lake
Huron calculations because of the order of magnitude difference in chloro-
phyll concentrations in the two regions.  Zooplankton grazing at the high
rates required to produce the observed population biomass in Lake Huron,
would overgraze the Saginaw Bay population.  The modification to the zoo-
plankton feeding expression which reduces the grazing coefficient as chlor-
ophyll increases is an attempt to parameterize this effect.  Whether the
effect is physiologically actually taking place, or whether this is just a
method of computationally accounting for the different species of zooplank-
ton in the very different regions awaits further investigation.
                                    92
-------
Primary Production
     Primary production investigations of Lake Huron and Saginaw Bay are
available [91] arid provide additional supporting data for the calibration.
Both in situ and shipboard measurements can be used for comparisons to calcu-
lations.  The relevant expressions are directly available from the kinetic
equations for biomass growth.  Since these assume that growth, carbon and
other nutrient assimilations are simultaneous and, on the weekly time scale
of the calculation this is reasonable, the in situ gross carbon assimilation
rate is a,  G P where a   is the carbon/chlorophyll-a ratio of the biomass.
         L-ir JT         U.T
For shipboard measurements the time and depth averaged light reduction factor
is not appropriate so that the instantaneous rate reduction expression, eq.
(26), evaluated at the light intensity of the incubator is used instead.  The
temperature and nutrient factors are assumed to be at their in situ values,
which is consistent with the experimental procedure.

     The primary production data are, therefore, direct measurements of a
rate, and a critical rate, in the kinetic equation of phytoplankton growth.
And, unlike all the other data which measure the quantities at the time and
location of sampling, and from which rates are inferred via the calibration,
the primary production gives an estimate of the assimilation rate directly.
Further the primary production exhibits a thirty fold variation between
Southern Lake Huron and Saginaw Bay.  This large difference is a stringent
test of the calculations since if the kinetics can reproduce these variations
one's confidence in their validity increases.

Calibration Results
     Figures ^0 to ^2 show the comparison of computed profiles to observed
data for the northern Lake Huron epilimnion segment.  For these and all sub-
sequent calibration plots the data are cruise averages +_ the standard devia-
tion.  Phytoplankton chlorophyll-a concentrations peak at approximately
2 yg/£ in early June, and are limited by the rate of phosphorus recycle.  The
decline to a mid-August minimum is due mainly to grazing pressure exerted by
the herbivorous zooplankton.  They in turn are grazed by the carnivors which
develop a significant population commencing in early August leading to a
decline in the herbivors and subsequent fall phytoplankton growth.  Not quite
enough fall phytoplankton growth is achieved, however, and it is apparently
due to the combination of excess grazing, since the herbivors still maintain
enough of a population to exert pressure throughout the fall, and perhaps to
an underestimation of fall recycle rate.  Ammonia concentrations are both
computed and observed to be in the range of 5-10 ug N/£.  The low concentra-
tion is maintained by algal uptake and nitrification sinks.  Available phos-
phorus is computed to be reduced to below the half saturation constant of
0.5 yg POr-P/5- which then severely limits growth.  The abnormally high obser-
vations in April 197^ are unexplained and are not consistent with 1971 obser-
vations.

     Nitrate nitrogen concentrations range between 0.2 and 0.3 yg N/£ as
shown in fig. 35.   The fall depression of nitrate is not reproduced by the
calculation.  It may represent a larger uptake of nitrate in the fall by a
species with a larger nitrogen to chlorophyll ratio than the spring bloom

                                     93
-------
             H co 8.0
 o- E 4.0
 O o

 x °
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O ^,0.16
£  E

3 § 0.08
                 0.00
             <  EO-04
                       J'F'M'A'M1J'J"A'S'O'N'D
                                           HERBIVOROUS
                                             CARNIVOROUS
                       J ' F MVIrATMTJTJ 'A'S rOTN ' D

            uu
                  0.02
                  o.oo
               E  0.004
            LU D
            cr or
              O 0.002
            o £ o.ooo
            CO
                       J'F'M'A'M'J'J'A'S'O'NTD
          J"F'M'A'M1J'J'A'S'O'N'D
Figure  i*0.  Northern  Lake Huron Epilimnion Calibration Calculation.
           Comparison of observations and computations for phyto-
           plankton  chlorophyll,  zooplankton carbon, ammonia nitro-
           gen and soluble reactive phosphorus, 197^.  See figure
           for data  symbol legend.
-------
NITRATE


NITROGEN, mg/


PPP
O N) £*
OOO
                     J 'F 'M'A'M1 J ' J 'A'S'O1 N'D
          _l CO


          *s
          gg
            Q.
            CO
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                    J 'F'M'A'M1 J ' J 'A'S'O'N'D
C

ro
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mg
->
•
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                    J'F'M'A'M'J'J'A'S'O'NTD
Figure hi.  Northern Lake Huron Epilimnion Calibration Calculation.

          Comparison of observations and computations for nitrate

          nitrogen, total phosphorus, and reactive silica nitrate

          nitrogen total.
                            95
-------
variety.

     Total phosphorus concentration is calculated to remain essentially con-
stant at 5 Ug PO, -P/Si throughout the year.   Some seasonal variation is ob-

served in the data, together with the high April 197^ observation.   Varia-
tions in mass discharge rate cannot account for these fluctuations  since the
mass in the segment is much larger than the annual loading to the segment.
Perhaps a transient settling of detrital particles into the hypolimnion dur-
ing the latter part of the year is the cause, since an increase in  unavail-
able phosphorus is calculated to occur during this period.

     The reactive silica profile is computed by considering just silica up-
take of the population.  Since they are primarily dia,toms a reasonable com-
parison is expected.  The silica cycle is not included, however, and the
computation is not meant to be representative of the actual recycle mech-
anisms.  The reasonable agreement is taken to mean that over a one  year
period, the recycle source of silica is not critical at these concentrations.
Note, however, that the computed curve is decreasing below the observations
by year's end so that the effects of recycle would be very important for
adequate multi-year calculations of silica.

     Figure k2a compares computed and observed Secchi disk depth.  The effect
of increased chlorophyll during April through June in lowering the  transpar-
ency and the increase due to reduced populations during July and August are
in reasonable agreement with observations.

     The comparison to observed primary production data is shown in fig. U2b.
The data are for 1971 [91] in contrast to the other variables.  However the
comparison in section 7 of 197-1 and 197^ data support the comparability of
both these years.   The computation overestimates the spring and underesti-
mates the fall primary production.  A smaller carbon to chlorophyll-a ratio
is suggested by the spring data.  With the discrepancies in the later part of
the year related to the discrepancy in computed and observed chlorophyll.
The final carbon to chlorophyll ratio is a compromise for both seasons.

     The results for the southern Lake Huron epilimnion (segment 2), are
shown in figures h3 to k5.  Phytoplankton growth exhibits the same  behavior
as in northern Lake Huron epilimnion but both the computed and observed
spring concentrations are slightly higher and in better agreement.   Zooplank-
ton growth is also similar and the fall peak is again limited by herbivore
grazing and phosphorus limitation with nitrogen limitation not being a fac-
tor.  Calculated zooplankton biomass concentrations exceed that estimated to
be present based on the 1971 data but is lower than the 197^ estimates (see
fig. 18)  which are not included in this figure.  The general state  of both
biomass estimates and the calculation is unsatisfactory.  The uncertainty in
both the observations and the relevant kinetic constants is sufficiently
large so that the level of credibility of this portion of the calculation is
uncertain and probably low.

     Calculated ammonia nitrogen is within the range of the observations and
is similar to the northern segment result.   The available phosphorus calcula-


                                     96
-------
tr
     • 12.0  -
     I
     LU
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     CJ
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CC Q.
         8.0
         4.0
         0.0
           j IF'M'A'M'J ' j 'A'S'O'N'D
 Figure k2.  Northern Lake Huron  Epilimnion Calibration
            Calculation.  Comparison of observations and
            computation for observed Secchi disk depth and
            gross primary production, (1971)-
                      97
-------
                0 8.0
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                 0.16
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               TOTAL
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                  HERBIVOROUS

                     CARNIVOROUS
                      J'F'M'A'M1J'J"A'S'O'N'D
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                      J'F'M'A'M'J'J'A S1 OnrN "D
J'F'M'A'M'JU'A'S'O'N1^
Figiire 1+3.   Computed versus Observed Data (So. Lake Huron epilimnion)
                              98
-------
           LU

           O    0.40
           DC
              05
              £ 0.20
           QC

           £    0.00
                                    iii-J
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Figure hk.   Computed versus Observed Data (So.  Lake Huron epilimnion)
                                   99
-------
               J'F'M'A'M'J'J'A'S'O'N'D
Figure k$.  Computed versus Observed Data (So. Lake Huron
          epilimnion).
                       100
-------
tion agrees with the observed 1971 data but not the substantially higher
values observed in 197^.  No ready explanation of this discrepancy is avail-
able.  Nitrate nitrogen data again shows a fall depression which is not
reproduced by the calculation.  Total phosphorus data are somewhat erratic
if all the data are overplotted as in this figure.  The individual year's
data as shown in fig. 27 do not appear to have any strong seasonal trends
although there is a suggestion of a fall decrease as in the northern lake
epilimnion data.  The silica profile follows observed patterns although it
appears that more uptake is required.  Transparency as measured by Secchi
depth, agrees well and computed gross primary production falls within the
range of observed data for both 1971 CCIW data and 197^ GLRD data as shown
in fig. 1*5.

     The Saginaw Bay calculation is shown in figures k6 to 48.  Notice the
difference in plotting scales used for these computed profiles and observa-
tions to those used for the open lake segments presented above.  Phytoplank-
ton and reactive phosphorus concentrations are approximately 15 times
greater, zooplankton populations are approximately 5 times higher, while
inorganic nitrogen, ammonia and nitrate values are approximately U times
higher than in the main lake segments.  Thus Saginaw Bay spans almost an
order of magnitude change in the concentration of most variables.

     Both the data and the calculation show two peaks in Saginaw Bay phyto-
plankton with the spring pulse declining during the beginning of July.  A
broad fall peak extending through November is indicated by the data.  The
calculated concentrations taper off progressively in the fall with a signi-
ficant population decline starting at the end of October.  Fall growth limi-
tation is due to both zooplankton grazing and phosphorus limitation.  It can
be seen on figure k^c that the calculated total phosphorus also is low at
the end of the year.  This suggests that a significant phosphorus source at
the end of the year may not have been accounted for.  This may be due to
resuspension of sediment phosphorus or a mass discharge which eluded measure
ment.
     Zooplankton biomass is reproduced quite well as can be seen in fig.
The magnitude of a pulse at the end of July which limits phytoplankton growth
is reproduced although the calculated biomass is slightly in excess of that
observed in the fall.  Computed ammonia concentrations are slightly high
during the spring as are the Kjeldahl nitrogen calculations.

     The problem may be due to an overestimation of the detrital nitrogen
mass loading rate or increased settling of particulate nitrogen during the
spring.  Nitrate uptake as calculated and observed is shown in fig. ^7a.  The
agreement is quite remarkable.  Soluble reactive phosphorus data are quite
variable although the calculation appears to be below the observations for
significant portions of the spring.

     Secchi disk observations are compared to calculations in fig.  48b.  The
small variations due to algal chlorophyll are not significant.  The February
measurement is through the ice cover and therefore is not representative of
the total light available since the attenuation due to the ice is not meas-
ured.  The primary production data for the summer and fall are well repro-

                                    101
-------
                  J ' F 'M'AMVll J ' J 'A'S'O1 N'D
          ^ 0.80
       <   0.40
       N
          <
            0.00
                                TOTAL
                  J'F'M'Anvl1 J'J'A'S'O1N'D
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Figure h6.   Computed versus Observed Data (Saginaw Bay)
                           102
-------
x
<
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       0.00
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       0.40



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            J'F'M'A'M1J"J'A'S'O'N'D
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Figure ^7.  Computed versus Observed Data (Saginaw Bay!
                      103
-------
       o    4.0
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            0.0
                J'F'M'A'M'J1J'A'S'O'N'D
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                J'F'M'A'M'JTJ 'A'S'O1N'D
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Figure U8.  Computed versus Observed Data (.Saginaw Bay)
                       10 It
-------
duced.  The low values observed in the spring during the height of the diatom
bloom are unexplained and appear suspect.

     The bottom layer segments representing the northern and southern lake
hypolimnia are in reasonable agreement with observations.  Figures ii9 and 50
show the computed profiles compared to observations for the northern Lake
Huron hypolimnion.  No chlorophyll data for comparison are available as the
CCIW measurements are integrated samples only in 197^ and surface concentra-
tions in 1971.  Calculated concentrations average only 0.3 yg/& on a yearly
basis due to light limitation as the hypolimnion is well below the euphotic
zone.  Computed profiles for the other variables agree reasonably well with
observations.

     The comparison of the computation and observed data for the southern
Lake Huron hypolimnion is shown in figs. 51 and 52.  In fig. 51a, it can be
seen that the model calculates phytoplankton chlorophyll-a concentrations
substantially lower than the observations by GLRD in 197^.  Nitrate and reac-
tive phosphorus concentrations agree reasonably well, so there are no nutri-
ent limitation problems.  Total inorganic nitrogen and available phosphorus
are both well above their respective half saturation constants.  The reason
for the lower computed profile can be seen in fig. 53, which presents the
phytoplankton growth rate which results after light and nutrient limitations
are imposed on the saturated temperature dependent rate.  The comparison
shown is between the epilimnion and hypolimnion segments in the southern
lake.  It can be seen that in the epilimnion, light limitation accounts for a
30 to 80 percent decrease in the saturating rate with nutrient limitation
also being significant.  In the hypolimnion, however, light limitation
amounts to greater than a 99-9% reduction in the saturating rate.  Nutrient
limitation is unimportant as is zooplankton grazing in comparison to light
effects.

     Based on the relationship developed by Beeton [17] from studies on Lake
Huron, the extinction coefficient can be approximated as 1.9/Secchi depth.
The epilimnion segment with an average Secchi depth of 6 meters has an
extinction coefficient of .32 meter  , yielding an equivalent euphotic zone
depth of approximately 15 meters.  Thus less than 1% of the surface irradia-
tion is available at a depth of 15 meters, the upper bound of the hypolimnion
segment.  This lack of available radiation causes the large computed reduc-
tion in the depth average growth rate in the hypolimnion.  Since the computed
respiration rate exceeds the computed growth rate as shown in fig. 53b, the
phytoplankton kinetics are, on balance, causing a net loss of biomass.  The
slight increase calculated in the hypolimnion is due to vertical transport
via mixing and settling from the epilimnion with the former predominating as
shown subsequently.

     The phenomenon of a significant standing crop of phytoplankton in the
meta- and hypolimnetic layers has come to be termed as "deep chlorophyll"
and has been observed in recent lake studies [96].  The kinetics, as present-
ly structured, are unable to characterize this effect since they are based
on the hypothesis that severe light limitation will result in minimal phyto-
plankton growth.  If the deep chlorophyll phenomena are reasonably well
verified by further observation, the kinetics may be adjusted to incorporate

                                     105
-------
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Figxire ^9-   Computed versus Observed Data (No. Lake Huron hypolimnion)
                               106
-------
        E  0.016
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Figure 50.  Computed versus Observed Data (No. Lake Huron)
                       107
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                       J "F'M'A'M1 J  J "A S  0 N'D
                ^» 0.40 -

             uu

             
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3CA^r,wC c,, ,™ TOTAL DISSOLVED TOTAL
REACTIVE SILICA, PHOSPHORUS, mg/l PHOSPHORUS, mg/l
mg Si02/l ooo ooo
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Figure 52.  Computed -vers-us  Ohs-erved Data.
             ftypolimnion)
                  (So. Lake  Huron
109
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                            110
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the effect in some manner such as the inclusion of a light adaptive mechanism.
The present kinetics do not deal with this phenomena.

Analysis of the Computation

     Figures 5^ to 58 present a detailed analysis of the calculation des-
cribed above.  The analysis is presented as a comparison between the open
lake waters, as characterized by southern Lake Huron, and Saginaw Bay.  This
yields further insight into the behavior of the model and the system under
study.

     The effects of nutrient limitation of phytoplankton growth is shown on
fig. 5^.  Nitrogen is not an important factor in limiting growth in southern
Lake Huron, since total inorganic nitrogen concentrations average more than
0.25 mg/£ and provide an abundant source for plankton growth.  On the other
hand, phosphorus limitation is significant yielding up to a 60 percent reduc-
tion in the saturated growth rate.  This is expected since available phos-
phorus concentrations in southern Lake Huron are very close to the Michaelis
half saturation constant of 0.5 yg P/&.

     Saginaw Bay is not nitrogen limited during spring growth but there is a
limitation effect during fall growth with reductions up to 30 percent in the
growth rate resulting.  Phosphorus limitation dominates, however, especially
during spring growth where 60 percent reductions result.  The replenishment
of the available phosphorus pool can be seen as a sharp increase in the
limitation term from the beginning of June to mid-July coinciding with the
decline in the phytoplankton standing crop and the recycling of unavailable
phosphorus.

     The sources of unavailable phosphorus available for conversion to forms
utilized for growth of phytoplankton is shown in fig. 55-  In southern Lake
Huron the principal source is from respiring phytoplankton.  Phytoplankton
grazed but not assimilated by the herbivorous zooplankton contribute signi-
ficantly to the unavailable phosphorus pool in mid-July when the herbivore
population is at a maximum.  This is true in Saginaw Bay also where excreted
phytoplankton phosphorus contributes significantly to phosphorus available
for recycle at the peak of herbivorous phytoplankton growth.  Zooplankton
respiration and excreted zooplankton phosphorus also provide unavailable
phosphorus and their relative importance can be seen.

     The unavailable phosphorus flux is higher in Saginaw Bay by nearly an
order of magnitude.  This is due to the higher concentrations of phytoplank-
ton phosphorus which provides the main kinetic source.  The rates are also
slightly higher in Saginaw Bay due to the warmer temperatures, but the prin-
cipal effect is the larger standing stock.

     The phosphorus concentrations which develop as a result of phytoplank-
ton uptake and the recycle mechanisms are shown in fig. 56.  The figure pre-
sents the available phosphorus, then the available plus unavailable phos-
phorus , and finally the total phosphorus which includes the algal phosphorus
as well.  Note the larger proportion of unavailable phosphorus in southern
Lake Huron when compared to Saginaw Bay.  This is primarily the result of


                                    111
-------
                       SOUTHERN LAKE HURON
          z
          o
              1.0
li  0.6

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LU

E  0.2

D
Z
                    NO LIMITATION
                             N/(N + KmN]
                            TOTAL REDUCTION
                  J'F'M'A'M1J'JT AISlQ'N'D
                            SAG IN AW BAY
           jl  1.0
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           LU
           E  0.2
                               /VO LIMITATION
                                     TOTAL REDUCTION
                  JTF'M'A'M1J'J'A'S"O'N'D
Figure  5^.  Nutrient limitation of growth rate.  Inorganic nitrogen

           (N/N + KmN) and reactive phosphorus  (P/p + Kmp) terms,

           and their product (total reduction)
                              112
-------
                           SOUTHERN LAKE HURON
*
DC

O
                    10



                   0.1



                 0.001
          I    0.00001
          CL

          UJ  >
             PHYTOPLANKTON RESPIRA TION



ZOOPLANKTON RESPIRATION
                                           UNASSIMILA TED


                                           ZOOPLANKTON
                           UNASSIMILA TED PHYTOPLANKTON
          O

          X
                       J 'F 'M1 A'M1 J ' J 'A'S'O1 N'D
                                 SAG IN AW BAY
          10



         0.1



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     0.00001
                        J"F"M1A'M1J'J'A'S'O1N'D
Figure 55.   Comparison of kinetic fluxes  of  unavailable phosphorus in

            Southern Lake Huron and Saginaw  Bay.   Curves correspond

            to a  (l-f )R  for phytoplankton respiration: a _(l-f.)
               Pr    "•  L                                pC    A

            (E  +R  ) for zooplankton respiration: a  (1-8)(l-f )R
             ?n  ?L                               pp         A3

            for unassimilated phytoplankton, and a „(!-£ )(l-f )R,
                                                pC    c     A  4

            for unassimilated zooplankton.
                                113
-------
                       SOUTHERN LAKE HURON
PHOSPHORUS, mg /I
U.UUD
0.004
0.002
0.000
TOTAL PHOSPHORUS
=___^-

^,

7 	 —
	
UNA VA/LABLE PHOSPHORUS
SOLUBLE REACTIVE PHOSPHORUS
J 'F 'M'A'M1 J
1 J
'A'S'O
N'D
                            SAGINAW BAY
            -  0.06
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            oc
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                                      TOTAL PHOSPHORUS
UNAVAILABLE
 PHOSPHORUS
   SOLUBLE REACTIVE
       PHOSPHORUS
      J'F'M1A'MTJ'J'A'S'O1N'D
Figure 56.   Cumulative plot of the components of total  phosphorus in
            Southern Lake Huron and Saginaw Bay.   The curves corres-
            pond to reactive phosphorus; reactive & unavailable phos-
            phorus; and total phosphorus, which includes algal and
            zooplankton phosphorus.
-------
the variable recycle rate which is small in southern Lake Huron and large in
Saginaw Bay.

     An analysis of the phytoplankton growth and death rates is presented in
fig. 57.  It can he seen that light limitation is more of a factor in Sagi-
naw Bay than it is in southern Lake Huron.  This is expected since the Secchi
depth averages 6 meters in the open lake but only 1 meter in Saginaw Bay.
Nutrient limitation in Saginaw Bay can be seen to be minimal at the end of
June when recycle has replenished the available nutrient pool.   Respiration
dominates the phytoplankton death term for most of the year in both areas
until the herbivorous zooplankton build a significant population and grazing
becomes the major factor.  These terms peak in both areas at the time of
maximum herbivorous zooplankton.  In Saginaw Bay, it can be seen from the
rapid rate of increase in zooplankton grazing as a major factor in phyto-
plankton decline, that if no limitation were placed on zooplankton grazing
rate as discussed earlier, they would develop large populations which is
inconsistent with observations and also exert too much grazing pressure.  In-
stead of the herbivorous zooplankton growth rates leveling off in Saginaw
Bay, as shown in fig. 58 "the rate would continue to increase.  Zooplankton
respiration rates are about equal in Saginaw Bay and southern Lake Huron with
the slight difference due to warmer Saginaw Bay waters affecting the tempera-
ture dependence.  Carnivore grazing is seen to be much more significant in
Saginaw Bay where more of a standing crop of herbivores are maintained which
stimulates carnivore growth and causes the grazing pressure.

     The calculations presented above compare reasonably well with observed
data for the variables of concern in the different areas of Lake Huron.  An
analysis of the results has also been presented highlighting some of the
important mechanisms such as nutrient limitation, nutrient recycle, and phy-
toplankton and zooplankton growth and death rates.  These processes strongly
affect the seasonal distribution of the phytoplankton and nutrients and the
calibration is sufficiently sensitive to the values of the kinetic constants
so that it is possible to make reasonable estimates of their magnitudes.

     There is an important process, however, for which the calibration of
the seasonal model is insensitive because its time scale is longer than
seasonal.  It is the loss of particulate phosphorus to the sediments.  The
issue of whether Lake Huron is in equilibrium with its current mass inputs
of phosphorus depends on the magnitude of the flux of phosphorus to the sedi-
ment s.

Phosphorus Sedimentation and Lake-wide Mass Balance

     The loss of total phosphorus from Lake Huron is primarily the result of
sinking of particulate phosphorus into the sediments.  The principle forms of
phosphorus considered in this calculation are algal-bound phosphorus, un-
available phosphorus and soluble reactive phosphorus, with zooplankton-bound
phosphorus a small fraction of the total.  Algal phosphorus and the particu-
late portion of the unavailable phosphorus each have a sinking velocity which
eventually leads to a fraction of this material being incorporated into the
sediment.  This mechanism is represented in the calculation by a sinking
velocity across the epilimnion-hypolimnion interface and the same velocity


                                    115
-------
                                   SOUTHERN LAKE HURON
O "J
    -  0.1
    >
    5  0.01
     0.001
                 REDUCTION DUE TO LIGHT LIMITATION
           SATURATED GROWTH RATEl_
             RESULTANT
            GROWTH RATE
                         REDUCTION DUE TO
                        NUTRIENT LIMITATION
           J'F'M'A'M1J'J'A'S'O'N'D
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            RESULTANT
           GROWTH RATE
                                        SAGINAW BAY
                        REDUCTION DUE TO
                       NUTRIENT LIMITA TION
           JIF'M'A'M'J'J'A'S'O'N'D
                                                 0.001
                                                      j'F'M'A'M1J'J'A'S'O'N'D
    Figure 57-   Seasonal distribution  of phytoplankton  growth  and
                  death rates showing light and nutrient  limitation
                  reductions.
                                      116
-------
                          SOUTHERN LAKE HURON
          LLJ
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          Q
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                          GROWTH RA TE
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               , TO CARNIVORE
                  GRAZING
                      J 'F 'M' A'M' J ' J 'A'S'O' N'D
                                SAG IN AW BAY
                       DEATH RATE DUE
                        TO CARNIVORE
                          GRAZING
                                  GROWTH RATE
                      J'F'M'A'M'J'J'A1 S "0] N'D
Figure 58.
 Seasonal distribution of  computed herbivorous  zooplankton
 grovth and death rates for Southern  Lake Huron and Saginaw
 Bay growth rate, 3a  R •  respiration rate, - R, ; carnivore
 grazing, _R       cr -5                     4'
                             117
-------
across the sediment-water interface.   For the coarse vertical segmentation
used, i.e. two layers, the seasonal calculation of phytoplankton is not very
sensitive to the absolute magnitude of the algal settling velocity as shown
subsequently in section 9 so that it  is not possible to infer this velocity
from the calibration.  Rather it is necessary to know the flux of phosphorus
from independent estimates.   The settling velocities are then suitably ad-
justed to reflect these estimates.

     Robbins [97] has estimated the net phosphorus settling into the mud
layer of fine grained sediments for Saginaw Bay to be 360 tonnes P/year.
For southern Lake Huron, a loss to the sediments is estimated at 782 tonnes
P/year.   Utilizing loss rates corresponding to an algal settling velocity of
0.05 m/day and a settling velocity of unavailable phosphorus of 0.1 m/day in
open lake waters, the model computes  a yearly loss of 363 tonnes P/year for
Saginaw Bay and 8^8 tonnes P/year for Southern Lake Huron.

     A comparison is also possible to an estimate of the lakewide sedimenta-
tion loss based on the Upper Lakes Reference Study mass balance [98] for
total phosphorus.  Their reported difference between inputs and outputs for
the whole lake is hhkO tonnes/yr and  for the main lake is 26^0 tonnes/yr.
Thus, there is a loss in Georgian Bay and the North Channel, areas not in-
cluded in this model, of 1800 tonnes/yr.  Adding this to the model's computed
total sedimentation loss of 2626 tonnes/yr yields kh26 tonnes/yr.  The lake-
wide estimate of sediment loading including anthropogenic and natural sources
is ^750 tonnes/yr [98],  It is important to realize that these computed sedi-
mentation fluxes are made using the same loss rates in1 both Saginaw Bay and
Lake Huron.  The difference is due to different concentrations of settleable
phosphorus.

     Table 13 summarizes these results and includes a corr.parison to the IJC-
ULRS mass balance of main Lake Huron.  The most recent IJC-ULRS estimates of
total phosphorus loading are very close to those used in this calculation.
The major loss in the main lake segments is via the settling of unavailable
phosphorus whereas in Saginaw Bay the principal mechanism is phytoplankton
settling.  The model computes total outflow that is lower than that measured,
although it agrees with the concentrations in southern Lake Huron whose
waters exit via the St. Glair River.   This apparent discrepancy may be due to
local inputs to the St. Glair River.   With the settling velocities used in
the calculation, Lake Huron is slightly out of equilibrium with respect to
its present loading, amounting to a buildup of 36^ tonnes of phosphorus
during 197^- or approximately a 10% change.  Considering the uncertainties of
the estimates it is reasonable to conclude that the lake is essentially in
equilibrium.

Application to Lake Ontario

     In order to further strengthen the calibration of the Saginaw Bay-Lake
Huron model, and to investigate the generality of the proposed recycle kine-
tic structure an application to Lake Ontario is presented.   In terms of
nutrient and chlorophyll concentrations, Lake Ontario is intermediate between
Saginaw Bay and Lake Huron.   It, therefore, is an ideal test case for the
modified recycle kinetics, and in fact served as a guide for the ultimate
choice of the half-saturation constant for recycle.

                                     118
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     Two major modifications have been made to the recycle kinetics when
compared to those used initially in Lake Ontario [U8].  The recycle rates for
nitrogen and phosphorus are assumed to be the same, and the rate changes with
changing chlorophyll concentration as described previously.  Also a fraction
of the nutrient fluxes due to respiration and excretion are assumed to be
immediately available.  The result of these kinetics when applied to Lake
Ontario with all other parameters the same as in the previous calibration
[kQ] is shown in fig. 59&.  As can be seen the predicted fall peak is low
when compared to observed values from 19&7 thru 1972 CCIW cruises of Lake
Ontario.  Computed reactive phosphorus concentrations are within the range of
observed data but computed nitrate nitrogen values are larger than observed
towards the end of the year.  This is due to the low fall phytoplankton popu-
lation that is calculated and consequently too little nitrate utilization.

     The second calculation, figure 59t>, illustrates the result of not only
incorporating the changes outlined above but also the phosphorus to chloro-
phyll ratio of the Lake Huron/Saginaw Bay model of 0.5 Pg P/Vg ChJl-a.  Both
the calculated spring and fall phytoplankton peaks are too large.  Reactive
phosphorus utilization is not as great as in the previous example and it can
be seen that the low calculated nitrate concentrations indicate that nitro-
gen has become limiting.

     The results of this exercise indicate that the carry-over of the kine-
tic changes affecting the nutrient cycles from the Lake Huron/Saginaw Bay
model to the Lake Ontario model do not have drastic effects on the computa-
tion, although the chlorophyll verification is not as good as the original
model.  Figure 60 shows a final calibration^for Lake Ontario with the Lake
Huron nutrient kinetics.  It utilizes a phosphorus to chlorophyll ratio of
0.5 yg P/y Ch£-a and a slightly lower initial condition for reactive phos-
phorus (10 ygPOij- P/& versus 1^ ugPOit- P/£) used previously.  The results
are quite reasonable although the spring peak is slightly larger than ob-
served.  It is reassuring that reactive phosphorus compares fairly well in
the hypolimnion as well.  This is due to the proportional recycle effect.
Phytoplankton concentrations are not as high in the hypolimnion as in the
epilimnion and therefore the recycle rate is lower.  This low rate prevents
a buildup in the lower layer.  Figure 6l presents the final chlorophyll-a
calculations for southern Lake Huron, Lake Ontario, and Saginaw Bay.

     These calculations embody the same phytoplankton growth and respiration
kinetics, and the same recycle kinetics.  The range over which these kine-
tics apply is approximately an order of magnitude in chlorophyll-a concen-
tration and almost two orders of magnitude in primary production.  It is
remarkable that not only the same equation structure applies but also that
the same kinetic constants are applicable.  This observation suggests that
the kinetic constants and functional relationships have a fundamental basis.

     A set of constants that result from a single calibration of a single,
rather homogeneous, setting are usually not regarded as certain until some
verifications are performed using independent data.  The kinetics employed
in the calculation displayed in fig. 6l have not been verified in this
sense.  However they have been shown to have general applicability to three
separate regions with widely varying characteristics.  This display of con-

                                    120
-------
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                     122
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                      SOUTHERN LAKE HURON
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6l.   Final calibration computations for Southern Lake Huron, Lake
     Ontario, and Saginaw Bay phytoplankton chlorophyll.  The
     phytoplankton and recycle kinetic constants are the same in
     each calculation.  However Lake Ontario zooplankton kinetics
     are not those used for  Lake Huron and Saginaw Bay.
                               123
-------
sistency argues rather strongly that the results are more than just a cali-
brated calculation (or as it is sometimes put, a curve fit)  but rather that
they have a certain generality.  This is somewhat surprising and gratifying
if one considers that the processes have been idealized greatly in an attempt
to make their quantitative description tractable.

     By the same token the zooplankton kinetic constants used are different
for Lake Ontario than the Lake Huron/Saginaw Bay calculation and it is
reasonable to conclude that this generality cannot be claimed for these kine-
tics.  As shown in the next section, the zooplankton responses are very sen-
sitive to the magnitude of the coefficients employed which also suggests
that the structure is not as robust as the phytoplankton kinetics.
                                    12k
-------
                                  SECTION 9

                            SENSITIVITY ANALYSIS
     One of the means available for testing the quantitative framework em-
ployed in this study is to perform a series of calculations in which the
sensitivity of a model to its coefficients is determined.  These coefficients
are chosen within the range of reported values , and are the result of many
calibration runs.  However there is frequently a range of values which may
be assigned and it is important to know what effect, if any, adjusting these
coefficients has on the resulting computations.

     The coefficients chosen for investigation are those which affect primary
variables and are related to important aspects of the calibration procedure.
Since phytoplankton chlorophyll is a key variable, several coefficients
directly related to its kinetics are investigated:

     l)  phytoplankton growth rate: K

     2}  phytoplankton respiration rate: K_

     3)  temperature dependence of phytoplankton growth rate: 6

     U)  zooplankton grazing rate: K~

     5)  phytoplankton settling velocity: wp

     6)  saturating light intensity for phytoplankton growth: I0
                                                               o

     Coefficients affecting the inorganic nutrient systems, particularly
phosphorus, are also investigated:

     l)  Half saturation constant for available phosphorus: K
                                                ^            mp
     2)  Phosphorus to chlorophyll ratio: a

     3)  Rate of recycle of unavailable phosphorus and nitrogen to available
         forms : 1C and K
Other effects investigated are:

     l)  vertical transport (stratification) effects

     2)  silica to chlorophyll ratio: a .
                                       Dli

     The results of these sensitivity runs are presented as a series of plots
showing the effect of parameter changes compared to the calibrated model
results previously presented.   Normally, sensitivity effects are investigated
by +_ 50 percent changes in the value used for model calibration, thus brack-
eting the results.
                                    125
-------
     Figure 62 shows the effect of varying the phytoplankton growth rate
term, KI.   Using a value of 2.08 day"1 reproduces the bimodal phytoplankton
growth curve in Southern Lake Huron and Saginaw Bay fairly well.   When the
rate is increased to 3.12 day l, initial growth occurs earlier with the
higher growth rate compensating for temperature limitation during these
colder months causing a broader spring pulse in both areas.   Lowering the
rate to 1.0^ day"1 has dramatic effects on both areas.  In Southern Lake
Huron, the spring peak occurs late and the magnitude of both this and the
fall peak is lower.  The spring pulse in Saginaw Bay is ir.uch lower with the
lower rate being unable to overcome the combination of temperature, light,
nutrient limitation effects and transport losses.

     The effects of varying the phytoplankton endogenous respiration rate,
K£, is also shown in fig. 62.  Lowering the rate from .05 to .025 day"1
increases the concentration of phytoplankton chlorophyll both in  Southern
Lake Huron and Saginaw Bay as one might expect since a sink of phytoplankton
is reduced.  Increasing the rate causes more loss due to endogenous respira-
tion to occur and lower phytoplankton concentrations result.  It  is interest-
ing to note that the timings of the pulses and declines are virtually unaf-
fected.

     Figure 62c illustrates the effect of varying the temperature dependence
of phytoplankton growth.  Since the effects of the saturated growth rate, KI ,
and the temperature dependence, 9i, are compounded in the growth  rate term,
and in order to isolate the effect of temperature dependence the  saturated
growth rates term for the three examples are set to be the same at 13 C.
This corresponds to the approximate temperature during spring bloom.

     As can be seen, lowering 61 from 1.068 (KI = 2.08 day"1) to  1.03^ (KI =
1.65 day  ) increases the growth rate during colder periods and spring
growth starts earlier in both Southern Lake Huron arid Saginaw Bay.  Increas-
ing 61 to 1.102 (KI = 2.59 day :) results in the opposite effect, a delayed
spring pulse which is less broad.  The timing and magnitude during the fall
period are virtually unaffected in both areas of the lake.

     Since phosphorus limitation has been shown to be an important mechanism
during the calibration process, the next series of sensitivity runs addresses
parameters affecting this process.  Figure 63a shows the effect of varying
K  , the half saturation constant for inorganic phosphorus, and a   , the
phosphorus to chlorophyll ratio.  Increasing the half saturation  constant
from 0.5 yg P/i to 1.0 and 2.0 yg P/£ has virtually no effect on  Saginaw Bay,
where concentrations of soluble reactive phosphorus average approximately
5 yg/&, well above the half saturation value.  There is a sufficient inor-
ganic phosphorus supply available for spring growth to commence as soon as
temperature and light conditions warrant it.  In Southern Lake Huron, how-
ever, soluble reactive phosphorus concentrations average near 0.5 yg P/&
which is right at the K   value of the calibrated model.  Any increase in
                       mp
this value results in a higher degree of nutrient limitation.  At 1.0 yg P/&
spring growth starts later since higher temperature and better light condi-
tions are needed to overcome the added nutrient limitation.  At 2.0 yg P/&
this effect is even more pronounced.  Soluble reactive phosphorus concentra-

                                     126
-------
          SOUTHERN LAKE HURON
                                           SAGINAWBAY
   8.0

   4.0


-  0.0
          K1C	3.12day-'
            	2.08
            •-•••1.04
                   j' j 'A'S'O'N'D
                               40.0


                               20.0


                                0.0
                                    J'F'M'A'M'J'J
             EFFECT OF VARYING PHYTOPLANKTON RESPIRATION RATE
   8.0
oc
O
  K2C	0.075 day-'
    	0.050
    •—• 0.025
g  4.0

£  0.0
z
Q.
O
   8.0


   4.0


   0.0
J'F'M'A'M'J'J'A'S'O'N'D
                                      40.0


                                      20.0


                                       0.0
                                           J'F'M'A'M'J'J'A'S'O'N'D
           EFFECT OF VARYING PHYTOPLANKTON GROWTH RATE
                  TEMPERATURE DEPENDENCE
          KIT	1.112
            	1.069
            ---1.034
       J'F'M'A'M'J'J'A'S'O'N'D
                               40.0

                               20.0

                                0.0
                                    j 'F 'M'AMVP J'
   Figure 62.  Sensitivity to phytoplankton kinetic constants.  Saturated
             growth rate % 20°C,  K^  (top).  Respiration rate @ 20°C, Kg

             (middle).  Growth rate  temperature  dependence, 6, with
                 m on
             KG      constant at T  = 13°C (bottom).  Labels in the fig-

             ures correspond to computer program variable designations.
                                  127
-------
              EFFECT OF VARYING MICHAELIS CONSTANT FOR PHOSPHORUS
              SOUTHERN LAKE HURON                   SAG IN AW BAY
       8.0

       4.0


       0.0
          KMP	0.001 mgP/l
            	0.0005
            ••-••0.002
           J'F'M'A'M'J'J'A'S'O'N'D
QJ —
>£:
^J«
!" 0.004


  0.002
Deo
CO Q.
     o.OOO
           J 'F'M'A'M1 J ' J 'A'S'O'N'D
                              40.0


                              20.0


                               0.0


                             0.032


                             0.016


                             0.000.
                                            J'F'M'A'M'J'  ' "A'S'P'-N'D
                                             ,   ,  .  ,-—,         ". T
                                            J'F'M'A'M'J'J 'A'S'O' N'D
              EFFECT OF VARYING PHOSPHORUS-TO-CHLOROPHYLL RATIO
      8.0
      0.0
  e 0.004
UJQ 0.002

Dt/5
OX 0.000
CO Q.
  PCHL - • - - 0.001 mg P/»*g CHL a
     	0.0005
     •••••0.002
J ' F ' M' A' M I J ' J ' A ' S ' 0 *N ' D
           J ' F 'M'AiM'   J
                               ' N ' D
                                       40.0


                                       20.0


                                        0.0


                                      0.032


                                      0.016


                                      0.000
                                              J ' F ' My A1 M ' J ' J 'A'S'O'N'D
                                                 j  A'S'O'N'D
     Figure 63.   Sensitivity  to phosphorus system kinetic constants,
                 Michaelis  constant for phosphorus, K   (top).

                 Phosphorus to chlorophyll ratio, a   (bottom).
                                   128
-------
tions follow the inverse pattern.  Since limited growth implies less nutri-
ent uptake, it follows that higher concentrations of inorganic phosphorus are
computed, with increasing values of K

     The effects of varying the phosphorus to chlorophyll ratio, a   = PCHL,

are investigated in fig. 63t>.  This coefficient effectively governs how much
available phosphorus is utilized to produce a unit of chlorophyll a_.  As a

is increased the available supply of inorganic phosphorus will be depleted
more rapidly.  The calibrated model uses a value of 0.5 yg P/yg ChJl-a.  It
can be seen that doubling and redoubling this value to 1.0 and 2.0 yg P/yg
ChJl-a has drastic effects on the calculation since two and four times the
amount of phosphorus is being utilized by the phytoplankton for growth.  In
Southern Lake Huron a spring pulse of the magnitude observed is never gener-
ated and the fall peak suffers as well.  Soluble reactive phosphorus concen-
trations are depleted to below the half saturation value and growth becomes
severely limited.  In Saginaw Bay the effect is equally dramatic.  The
spring peak is only about 15 yg/£ chlorophyll a_ using a   = 1.0 yg Ch£-a/

yg POij-P and less than 10.0 yg/£ at a value of 2.0.  These concentrations
are well below observations.  The increased rate of depletion of the soluble
reactive phosphorus pool is also clearly seen.  At a   = 2.0 yg P/yg Ch£-a

the available pool is essentially depleted by the end of March and phyto-
plankton growth levels off.  Some initial buildup of reactive phosphorus due
to pulses of phosphorus from the Saginaw River (Section h) occurs at a   =

1.0 yg P/yg Ch£-a but not enough to sustain a spring phytoplankton pulse of
the magnitude observed.  Thus, although a phosphorus to chlorophyll a_ rate
of 0.5 yg P/yg Ch£-a is at the low end of the range of reported values, the
concentrations of inorganic phosphorus in the open lake waters are small.
Further the standing crop of phytoplankton which must be supported in Sagi-
naw Bay is large.  The computation is able to simultaneously reproduce ob-
served conditions in both areas only for a value of a   at this level.

     The importance of a correct phosphorus to chlorophyll a_ stoichiometric
coefficient is clear from these sensitivity calculations.  It is also sug-
gested by eq. (56) of section 6 which indicates that the quantity of the
total phosphorus that appears as chlorophyll is inversely proportional to
the stoichiometric coefficient.  The Lake Ontario results, see fig. 59 and
60, also support this inverse relationship.  One of the principal drawbacks
of Monod kinetics is that this ratio is assumed to be fixed.  However it is
well known that this ratio is quite variable and depends on the ambient
phosphorus concentration.  Thus it appears that an important refinement
would be a kinetic structure which reflects this variability.  Bierman's
Saginaw Bay calculation [99] is one such structure, and a detailed analysis
of this phenomena is available [37]•   The choice of a minimum ratio is con-
sistent with the discussion in section 6 and the observed data.

     The coefficient governing the rate of recycle of nutrients from the
unavailable to an available inorganic form is assumed to apply to both the
unavailable phosphorus and nitrogen.   Figure 6k shows the results of sensi-
tivity calculation with doubled and halved coefficients, K7 = KS, the


                                   129
-------
1
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                                        130
-------
recycle rates of organic nitrogen and unavailable phosphorus, respectively.
Increases in the recycle rate result in higher calculated phytoplankton
chlorophyll and soluble reactive phosphorus concentrations as expected from
the theoretical analysis in section 6.  As the calibrated rate 0.0k day"1 is
increased to 0.08 day"1 more nutrient replenishment and utilization occurs
vith larger populations resulting.  As a lower rate (0.02 day M the con-
verse is true and lower concentrations result.  The nitrate profile in
Southern Lake Huron is virtually unaffected by changes in the rate of re-
cycle since the recycled nitrate is a small fraction of that already present,
while in Saginaw Bay differences occur during the time of reduction in the
spring phytoplankton pulse.  These reflect a combination of the change in
recycle flux and nitrification effects.  The ammonia profile in both areas
reflects the respective change in concentration due to increases or de-
creases in the recycle rates.

     The effects of changes in herbivorous zooplankton grazing rates is
shown on figure 65a.  It can be seen that timing of phytoplankton growth and
decline is greatly affected by changes in zooplankton grazing.  This is true
in both Southern Lake Huron and Saginaw Bay.  Total zooplankton (herbivores
plus carnivores) response also shows marked changes with a lower rate
resulting in a delayed pulse in Southern Lake Huron and a delayed and
smaller pulse in Saginaw Bay.  The higher grazing rate results in earlier
growth and more cropping of the spring phytoplankton crop in both areas of
the lake.

     The model is very sensitive to changes in the herbivorous zooplankton
grazing rate as well as the other zooplankton kinetic coefficients.  With
many factors affecting grazing it is difficult to specify what the actual
grazing, efficiency, and limitation coefficients should be.  However, the
model is able to reproduce observed conditions fairly well.  The coefficients
governing the zooplankton systems in this model should not, therefore, be
thought of as strictly unique.  In fact there appears to be considerable
uncertainty at the level of the kinetic structure itself.  When a calculation
is unduly sensitive to coefficients about which little is known, or which are
known to vary over orders of magnitude, then considerable caution is required
in interpreting the results of the calculation.  This appears to be the case
with the zooplankton formulation used in these calculations.

     However it is important to note that although the shape changes markedly
the peak concentrations of phytoplankton chlorophyll are essentially the same
over a four-fold change in filtering rate coefficient and the yearly average
concentrations are not dramatically different.  Therefore although the shape
of the seasonal distribution is markedly affected, the characteristic concen-
trations which are important in projected conditions are not as sensitive to
this parameter of the zooplankton kinetics, and it is probable that for peak
and average concentrations, the projected conditions are reasonably reliable.

     Figure 65b illustrates the effect of varying a    the silica to chloro-
                                                   oiP
phyll ratio.  Although the model is able to match open lake silicate concen-
trations it fails to reproduce observed concentrations in Saginaw Bay.  The
reason is that without the inclusion of a diatom group the proper uptake rate


                                     131
-------
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                                 132
-------
is not calculated.  Also remineralization of silica is not taken into account.
Varying a.,.^ does not help the situation in the bay, since rapid depletion is
         oljr
calculated even at a lower stoichiometric coefficient.  Since the calculation
is not structured to represent the silica cycle in Lake Huron/Saginaw Bay,
this exercise serves to demonstrate that a diatom species must be added to
the calculation if observed conditions are to be reproduced.  It also illus-
trates that an incorrect kinetic structure cannot be tuned arbitratily to fit
observations.  Thus a calibrated model is an indication that the kinetic
structure and constants are not inconsistent with the observations.  For
silica it is clear that both recycle and selective uptake by diatoms are
required for calibration.

     The final sensitivity results, fig. 66, illustrate the effects of phyto-
plankton settling velocity, saturating light intensity, and stratification.
As shown earlier, the model is unable to reproduce observed chlorophyll con-
centrations in the hypolimnion of Southern Lake Huron.  Increasing the phyto-
plankton settling velocity has no effect on the results in the hypolimnion
with the increased downward flux of plankton adding little to concentrations
in this large volume of water.  The increased rate does affect the Saginaw
Bay calibration, however, as can be seen.  A lower settling rate results in
expected higher concentrations.

     Increasing the vertical mixing during stratification and allowing more
phytoplankton to exchange into the lower layer is another, although unlikely,
mechanism by which higher concentrations in the hypolimnion might be calcu-
lated.  However, there is virtually no effect on the phytoplankton chloro-
phyll distribution in the lower layer when stratification effects are re-
moved.  Thus, changes in transport in the form of phytoplankton settling
velocity and vertical exchange as well as a lower saturating light intensity
cannot account for high hypolimnetic chlorophyll concentrations.  Once the
mechanisms for survival at these deep, dark, and colder depths are known
perhaps they can be incorporated into the model structure.

     The sensitivity calculations outlined above have shown what the effects
of changes in kinetic coefficients have on the calculated results.  For the
phytoplankton and recycle kinetics, even large changes in coefficient values
do not produce any computational difficulties and yields results which are
plausible.  Unfortunately the same is not true of the zooplankton kinetics.
The coefficients finally chosen are based on the results of numerous cali-
bration runs, application to Lake Ontario and the constraints provided in
the available experimental information.  By examining the effects of changes
in these coefficients through a sensitivity analysis, one is able to respond
to questions of effects of uncertainty in these values.
                                    133
-------
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                                           134
-------
                                 SECTION 10

                          PRELIMINARY APPLICATIONS
     The calculation of the response of Lake Huron to increase in phosphorus
mass inputs is one of the objectives of this study.  In addition to their
value for management decisions these calculations also provide considerable
insight into the workings of the kinetics.

     Simulations are presented for a time span of 15 years.  This is consid-
erably shorter than the hydraulic detention time for the whole lake of 22.6
years.  However the model does not incorporate the volumes associated with
Georgian Bay and the North Channel which reduces the hydraulic detention time
of the five segments to 1^.1 years.  Phosphorus removal via settling consid-
erably lowers the time to steady state.  A fifteen year time span appears to
be reasonable as shown in fig. 67 which shows the change in yearly average
phytoplankton chlorophyll _a concentrations in Southern Lake Huron during a
fifteen year time span.  This projection, based on the final calibrated ver-
sion of the model presented earlier and the present inputs of nutrients,
shows yearly average phytoplankton chlorophyll &_ concentrations in Southern
Lake Huron increasing from 1.33 yg/& at the end of the first year to 1.52
ug/£ at the end of the fifteenth year, a lh% increase.  The concentration
can be seen to level off, approaching dynamic equilibrium with the percent
change approaching zero.  All projections presented subsequently are fifteen
year runs.

     Table 1^ summarizes the results for a series of such calculations.  The
values presented cover three phosphorus loading increases for the three
different recycle mechanisms, with each simulation lasting fifteen years.
There are differences in the base line for each case with respect to phos-
phorus loading and equilibrium chlorophyll concentrations and direct com-
parisons of absolute magnitudes are difficult.  Therefore the results are
converted to percentage changes for ease in comparison of the effects of the
differing recycle mechanisms.  As shown in fig. 68a, the first order recycle
kinetics predict a strictly proportional increase in algal chlorophyll rela-
tive to a change in total phosphorus input.  However both saturating and
second order recycle kinetics predict a more rapid change in algal chloro-
phyll.  This effect is due entirely to the changing quantity of unavailable
phosphorus as the recycle rate increases.  The total phosphorus concentra-
tions are changing in almost direct proportion to the increasing mass input
as shown in fig. 68b.  However whereas the change in unavailable phosphorus
is proportional for the first order kinetics, fig. 68c, the change is less
for saturating kinetics and almost zero for second order kinetics.  As a
result the proportion of total phosphorus that is algal phosphorus changes
dramatically for second order kinetics, almost as dramatically for saturating
kinetics, but very little for first order recycle kinetics, fig. 68d.
                                    135
-------
     1
11
13
15
                               YEAR
Figure 67.   Fifteen year distribution of and percent increase in
            yearly averaged phytoplankton  chlorophyll a  in  Southern
            Lake Huron.   Model is  essentially at  steady  state in
            year 15.
                               136
-------
      TABLE lit.  EFFECT OF VARIOUS NUTRIENT RECYCLE MECHANISMS
           AND INCREASING PHOSPHORUS LOADING:  LAKE HURON

Percent
Change
in Total
P Load


+ 100$



+ 50$



BASE


Total P Load (Ibs /day)
Sedimentation Loss(lbs/day)
Yrly Avg Chlorophyll (ug/&)#
Unavailable P/Total P#
Total P Load (its /day)
Sedimentation Loss (ibs /day)
Yrly Avg Chlorophyll (ug/£)#
Unavailable P/Total#
Total P Load (Ibs /day)
Sedimentation Loss(lbs/day)
u
Yrly Avg Chlorophyll (yg/£)
Unavailable P/Total P#
Nutrient
First
Order
Recycle
Rate
U8.27U
27,558
5.5U
0.80
36,205
20,7^9
it. 07
0.79
2it,137
13,950
2.66
0.78
Recycle Mechanism
Saturating
Recycle
Rate
itU,338
28JU5
it.9it
0.87
33,253
22,768
2.73
0.89
22,169
l6,13it
1.12
0.01
Second
Order
Recycle
Rate
it8,27it
23,210
10.38
0.56
36,205
19,928
6.27
0.7l'
2it,137
15,762
2.05
0.82

Southern Lake Huron Epilimnion Values
                               137
-------
     As shown in section 6, the saturating kinetics appear to be the most
realistic formulation for the Great Lakes.  At chlorophyll concentrations
that are large relative to the half saturation constant for the recycle
reaction, K   = 5 Ug Ch£-a/&, saturating kinetics behave as first order

kinetics with roughly proportional changes in chlorophyll for changes in
total phosphorus loading.  However in the range of chlorophyll characteristic
of Lake Huron, the behavior is more like the second order recycle kinetics
with its accelerated response to small loading changes.

     This effect is quite important from a management point of view.  The
response of Lake Huron to small increases in total phosphorus loading is
expected to be larger than strictly proportional.  In fact the effect is more
like a fourfold change in chlorophyll for a twofold change in phosphorus
loading as shown in fig. 68a.  The degree of reliability of these calcula-
tions under projected conditions is unknown at present.  "So verification of
computational framework, in the sense of and independent computation of
future widely different conditions and a check against field data, has been
made.  A two-fold difference in projected chlorophyll percent change exists
between first order recycle kinetics and saturating kinetics (fig. 68a).
Although saturating kinetics appear to be the probable mechanisms the sensi-
tivity of the projections to this assumption is large and, therefore, this
should be taken into account in utilizing these projections for management
decisions.

     The results of a more extensive series of simulations for increasing
phosphorus loadings are shown in fig. 69.  These calculations represent the
results from the final calibrated model using the saturating recycle kine-
tics.  An almost exponential increase is expected until 5 Pg Ch£-a/& is
reached, after which the increases are more proportional to increasing load-
ing.  These results clearly indicate that a positive feedback mechanism
exists at low chlorophyll concentrations.  As phosphorus load increases not
only does total phosphorus concentration increase but the fraction of un-
available phosphorus decreases and the ratio of algal phosphorus to total
phosphorus increases, compounding the increase in chlorophyll.  For more
eutrophic lakes this effect would not be observed since the recycle kinetics
are saturated and behave as first order kinetics.  However for Lake Huron,
small increases in phosphorus loading produce significant changes in algal
chlorophyll.

     The effect of loading reductions to Lake Huron are examined based on
various waste management alternatives as outlined by the IJC.  These plans
consist of removing 60%, 83%, and a theoretical 100% of the controllable
phosphorus input to Lake Huron.  This results in actual removals of 3^.2%,
^7-3%, and 57% respectively, of the total load assuming ^3% of the input is
from uncontrollable (non-point) sources.  Effects of implementation of 80%
phosphorus removal in the State of Michigan are also investigated as well as
what type of waste load management is necessary to meet EPA's goal of non-
degradation.

     The results of these simulations are presented in table 15.  The assump-
tions implicit in this analysis are: phosphorus load rediictions are instan-

                                     138
-------
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               SOUTHERN LAKE HURON "EQUILIBRIUM'
                     CHLOROPHYLL a vs. TOTAL
                       PHOSPHORUS LOADING
            10.0
             5.0

             4.0

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             1.0
          Q_
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Figure 69.
      0              5,000           10,000

         TOTAL PHOSPHORUS  LOAD TO
          LAKE HURON, metric tons/year
(Southern Lake Huron  epilimnion)  Yearly average chlorophyll
concentration versus  total  phosphorus loading to Lake Huron.
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-------
taneous; the transport regime is the same as that used in the base run
including the time variable flow from the Saginaw River and the bay-lake
exchange; and relative fractions of available and unavailable phosphorus for
the loadings remain the same as that used in the calibrated model.  Since
Saginav Bay is sensitive to short term fluctuations because of its short
hydraulic detention time these assumptions become importsjit and since the
actual changes to be expected in these phenomena are unknown over the period
of the simulation, results presented for Saginaw Bay should be viewed with
this in mind.  The effects on Southern Lake Huron are important since they
directly address the first and fourth reference questions, of the Upper Lakes
Reference Study: to what extent are the waters of Lake Huron being polluted
on either side of the boundary to cause degradation of existing levels of
water quality in the lake and what are the effects of preventative measures.
These calculations enable one to gain some insight into these issues.

     The results of the simulations indicate that the allowable phosphorus
loading which maintains present water quality is 3600 tonnes/year.  This
will maintain a level of 1.31 Ug/£ chlorophyll a_ in Southern Lake Huron
epilimnion on a yearly average basis.  Implementating an 80% phosphorus
removal in Michigan yeilds levels of 1.1 yg Ch£-a/£ in the southern lake
as well as a 15$ reduction in yearly averaged total phosphorus concentra-
tions amounting to a decrease of 0.9 yg P/&.  The lowest concentrations
result from the IJC plan which postulates a reduction for the Saginaw Bay
load to 569 tonnes/yr.. Here chlorophyll a_ levels in Southern Lake Huron
are held to 1.0 yg/£ after 15 years.  There is also an accompanying 39%
decrease in the peak spring chlorophyll as well as an 18$ decrease in total
phosphorus concentrations.  Results in Saginaw Bay are mcst dramatic under
this scheme showing an almost 50$ reduction in yearly averaged chlorophyll
a_ values to 8.5 yg/£ and a spring peak reduction to 13.5 yg/£.  Total phos-
phorus concentrations show a 50$ reduction to 17 yg P/£.  More detailed
results of these calculations are given in table 15.

     It is important to emphasize that the absolute values of these pro-
jected concentrations are not certain to the three and four digits reported
in the tables.  The absolute error associated with these projections is
unknown at present.  Rather it is the relative changes that have more
validity and it is these results that should be used as a guide in formu-
lating the phosphorus reduction plans for Lake Huron and Saginaw Bay.  An
important issue that should be addressed in future work is the relative
errors that can be associated with projections, that is what is the probable
range of projected concentrations based on the present uncertainty of the
mass discharges, the observed data, and the transport and kinetic para-
meters .
-------
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102.  International Joint Commission.  1977.  The Waters of Lake Huron and
      Superior, Volume II (Part B) - A Report to the IJC "by the Upper Lakes
      Reference Group, pp. 295-350.

103.  Verhoff, F.H., C.F. Cordiero, W.F. Echelberger and M.W. Tenney.  1973.
      "Modeling of Nutrient Cycling in Microtiial Aquatic Environments" in
      The Aquatic Environment:  Microbial Transformations and Management
      Implications.  eds. L.G. Guarria and R.K. Ballantiie EPA U30/6-73-008,
      pp. 13-50.

10k.  International Joint Commission.  1978.  Fifth Year Review of  Canada-
      United States Great Lakes Water Quality Agreement Report of Task
      Group III.

105.  International Joint Commission.  1977.  The Waters of Lake Huron and
      Superior, Volume II (Part A) - A Report to the IJC by the Upper Lakes
      Reference Group, p. 59 (Table 3.1-1), p. 64 (Table 3.1-6).
                                     150
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TABLE A9.
TIME VARIABLE SAGINAW BAY WASTE LOADINGS

Time
(days)
0
1
3
20
29
30
38
1*1*
56
59
66
81*
86
96
100
ill*
131*
ll*l
11*7
193
206
22T
255
295
311
325
353
365







[Org N]
(Ibs/day)
36,100
36,100
19,700
18,900
175,000
125,000
3*1,900
ill, 800
70,900
19,500
187,000
26,000
53,800
11*3,000
87,1*00
36,800
111, 200
169,000
35,100
18,000
5,410
19,000
8,0l*0
9^5
16,1*50
6,850
7,880
7,880







Time
(days)
0
2
18
21
28
32
38
>*9
52
56
59
65
73
80
87
91*
95
101
105
109
119
123
131*
135
lUl
ll*2
11*3
155
162
165
172
226
261
352
365
[NH^-N]
(Ibs/day)
3,890
3,890
1,900
7,6liO
22,000
12,000
1*,220
2,270
3,91*0
10,500
8,680
38,100
11,000
9,290
4,660
11,700
1,960
l*,ll*0
8,060
1,990
3,700
7,11*0
5,31*0
11,000
1,060
10,800
l,ll*0
3,090
6,910
3,180
3,180
1,020
1*,900
5,710
5,710
Time
( clays )
0
1
8
21*
28
30
39
53
59
65
74
90
95
101
106
112
137
ll*l
].1*2
170
179
189
207
225
261
280
353
365







[NOj^-N]
(Ibs/day)
1*5,200
1*5,200
2l*,l*00
207,000
515,000
258,000
66,700
73,700
92,500
1*06,000
128,000
66,200
230,000
127,000
127,000
1*1*, 600
69,000
118,000
99,1*00
1*1*, 200
10,000
9,280
2,990
2,520
3,960
U,990
U,2l*0
l*,2l*0







                             (continued)
160
-------
TABLE A9 (continued)

Time
( days )
0
1
16
24
29
32
3k
^9
56
59
66
67
74
90
95
99
114
134
141
142
147
154
162
165
206
295
311
337
365















[Unavail-P]
(Its /day)
4,060
4,060
2,570
14,700
54,300
12,200
3,830
1,830
8,210
9,920
65,600
21,500
6,470
4,630
24,900
11,200
7,960
3,990
37,600
14,300
5,520
3,380
11,200
4,870
l,84o
774
2,800
249
1,650















Time
(days)
0
3
18
21
22
24
25
28
30
32
36
49
56
59
64
67
78
99
100
101
106
109
126
134
135
141
142
153
155
158
162
165
176
193
226
262
274
280
295
305
311
317
325
337
[PO^-P]
(Ibs/day)
2,710
2,710
637
2,510
3,550
4,300
4,910
8,970
2,150
3,350
1,840
957
3,310
2,930
9,320
4,160
1,400
818
9,540
2,400
701
2,530
975
3,280
639
529
1,710
364
1,550
609
2,690
1,000
646
1,100
706
871
2,090
1,330
1,800
1,870
4,770
1,820
2,020
917
Time
( days )
0
1
18
21
23
25
28
29
32
38
39
50
53
59
65
74
78
93
95
101
105
114
120
130
134
137
147
158
162
176
179
186
274
295
311
325
353
365






[Si]
(Ibs/day)
94,000
94,000
46,700
111,000
338,000
216,000
324,000
687,000
164,000
76,600
115,000
47,400
230,000
169,000
767,000
251,000
138,000
265,000
444,000
41,500
271,000
75,600
72,600
92,400
70,200
246,000
91,100
42,800
91,100
53,200
32,200
83,400
40,700
30,900
65,800
35,900
34,800
34,800






161
-------










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                              TABLE A12.   FLOWS
   TO
(Segment)
  FROM
(Segment)
   FLOW
   (cfs)
   1

   2

   2

   2


boundary
boundary

   1

boundary

   3
                 boundary
  175,^60

2,000,^60 (north-south circulating-flow)

    6,555

   11,235 (Day 0-151)
    1,561 (Day 181-365)

  193,250 (Day 0 - 151)
  183,576 (Day 181-365)

   11,235 (Day 0-151)
    1,561 (Day 181-365)

1,825,000 (north-south circulating flow)
                                    163
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                                   TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing)
1. REPORT NO.
   EPA-600/3-80-056
                              2.
                                                            3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
 Mathematical Models  of  Water Quality in Large  Lakes
 Part 1:  Lake Huron  and Saginaw Bay
                                                            5. REPOF1T DATE
                                                               JULY 1980  ISSUING DATE
             6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)

 Dominic M. DiToro and Walter F. Matystik, Jr.
                                                            8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
 Manhattan College
 Environmental Engineering and Science Program
 Bronx, New York  10471
             10. PROGRAM ELEMENT NO.
                A30B1A
             11. CONTRACT/GRANT NO.

                R803030
12. SPONSORING AGENCY NAME AND ADDRESS
   Environmental Research Labortory
   Office of Research and Development
   U.S. Environmental Protection Agency
   Duluth, Minnesota   5580^
             13. TYPE; OF REPORT AND PERIOD COVERED
                Final
             14. SPONSORING AGENCY CODE   ~~  ~~~
                  EPA/600/03
15. SUPPLEMENTARY NOTES
 Refer to Part 2:  Lake  Erie for supplemental  information.
16. ABSTRACT

This research was undertaken to develop and  apply a mathematical model of the water
quality in large lakes,  particularly Lake Huron and Saginaw Bay  (Part 1) and Lake
Erie (Part 2).

A mathematical model  of  phytoplankton biomass  was developed which  incorporates both
phytoplankton and zooplankton as well as phosphorus, nitrogen and  silica nutrient
forms.   Extensive water  quality data for Lake  Huron and Saginaw Bay was analyzed
and statistically reduced.   The model was then calibrated by comparison of computed
results to these data.

An exhaustive treatment  of  the kinetics employed for modeling the  eutrophication
process is presented.  The  sensitivity of the  model to some of its key parameters
is examined.  In addition,  responses of water  quality in Lake Huron and Saginaw
Bay system to variations in total phosphorus inputs are projected.
17.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                              b. IDENTIFIERS/OPEN ENDE D TERMS
                           c.  COSATI Field/Group
 Mathematical models
 Water quality
 Great Lakes
 Lake Huron
 Saginaw  Bay
 Ecological Modeling
     08/H
18. DISTRIBUTION STATEMENT

 Release to public
19. SECURITY CLASS (This Report)
  Unclassified
21. NO. OF PAGES
       180
20. SECURITY CLASS (Thispage)
  Unclassified
                           22. PRICE
EPA Form 2220-1 (Rev. 4-77)
                      PREVIOUS EDITION IS OBSOLETE
                                             166
                                                         -US GOVERNMENT PRINTING OFFICE 1980-657-165/0070
-------