United States Environmental Monitoring Environmental Protection and Support Laboratory Agency P.O. Box 15027 Las Vegas NV 89114 Research and Development EPA Comparisons of Working Models Predicting Paper 704 Ambient Lake Phosphorus Concentrations ------- COMPARISONS OF MODELS PREDICTING AMBIENT LAKE PHOSPHORUS CONCENTRATIONS WORKING PAPER NO. 704 ------- COMPARISONS OF MODELS PREDICTING AMBIENT LAKE PHOSPHORUS CONCENTRATIONS by Stephen C. Hern, Victor W. Lambou and Llewellyn R. Williams Environmental Monitoring and Support Laboratory Las Vegas, Nevada 89114 Working Paper No. 704 NATIONAL EUTROPHICATION SURVEY OFFICE OF RESEARCH AND DEVELOPMENT U.S. ENVIRONMENTAL PROTECTION AGENCY September 1978 ------- FOREWORD The National Eutrophication Survey was initiated in 1972 in response to an Administration commitment to investigate the nationwide threat of acceler- ated eutrophication to freshwater lakes and reservoirs. The Survey was designed to develop, in conjunction with State environmental agencies, infor- mation on nutrient sources, concentrations, and impact on selected freshwater lakes as a basis for formulating comprehensive and coordinated national, regional, and State management practices relating to point source discharge reduction and nonpoint source pollution abatement in lake watersheds. The Survey collected physical, chemical, and biological data from 815 lakes and reservoirs throughout the contiguous United States. To date, the Survey has yielded more than two million data points. In-depth analyses are being made to advance the rationale and data base for refinement of nutrient water quality criteria for the Nation's freshwater lakes. ii ------- ABSTRACT The Vollenweider, Dillon, arid Larsen/Mercier models for predicting ambient lake phosphorus concentrations and classifying lakes by trophic state are com- pared in this report. The Dillon and Larsen/Mercier models gave comparable results in ranking 39 lakes relative to known ambient phosphorus concentrations. The Vollenweider model, which does not include a phosphorus retention capacity component, was unable to achieve the high rank correlations found with the other models. Trophic state predictions from the phosphorus loading models are compared with National Eutrophication Survey lake report designations. Disagreements of 14, 18, and 25 percent, respectively, were found with the Dillon, Larsen/ Mercier, and Vollenweider concepts. iii ------- COMPARISONS OF MODELS PREDICTING AMBIENT LAKE PHOSPHORUS CONCENTRATIONS The phosphorus loading - mean depth - relationship formulated by Vollenweider (1968) has been widely accepted and used to indicate the degree of eutrophy of lakes and evaluate the level of phosphorus loading to lakes. Dillon (1975) pointed out that there has been too little thought and criticism given to the limitations of the model by people using it. Subsequently, modifications of the basic mass balance equation have been derived to predict mean ambient lake phosphorus concentrations at equilibrium. Dillon (1975) utilizes phos- phorus areal loading (L), the retention coefficient for phosphorus (R), the hydraulic flushing rate (P), and mean depth (Z) in a plot of the form L (1-R) p versus Z to estimate trophic state. Vollenweider (1975) revised his original formula to include T , hydraulic residence time, so that areal phosphorus loading (L) is plotted against mean depth (Z) divided by T . Larsen and Mercier (1976) provide an alternative (to the prior loading concepts) which avoids the criticism of Edmondson (1970) that the effect of an increasing phosphorus load upon a lake depends, in part, upon whether that increase re- sults from increases in influent flows, concentrations, or both. The Larsen/ Mercier formula plots mean tributary phosphorus concentration against phosphorus retention coefficient, called R experimental, computed in the same way as Dillon's R, i.e., r = *1 _ Total phosphorus leaving Total phosphorus entering It is interesting to note that in applying the above-mentioned formulas, each of the authors have selected to use levels of 10 and 20 yg/1 of ambient lake phosphorus to divide lakes into the three standard trophic classi- fications -- oligotrophic, mesotrophic, and eutrophic. To compare the three models, we selected 39 lakes sampled during 1973 by the National Eutrophication Survey (U.S. Environmental Protection Agency, 1975) which represented the entire range of water transparency as measured by Secchi disk. Table 1 demonstrates the variety of lakes selected. 1 ------- TABLE 1. THE NUMERICAL AVERAGE AND RANGE OF MEAN CHEMICAL, PHYSICAL AND BIOLOGICAL CHARACTERISTICS OF 39 LAKES, SELECTED FROM THOSE SAMPLED DURING 1973 BY THE NATIONAL EUTROPHICATION SURVEY PARAMETER MEAN RANGE Surface Area (km2) 40.75 0.23 263.05 Drainage Area (km2) 3502.6 4.3 38850.0 Mean Depth (m) 7.5 0.9 21.0 Maximum Depth (m) 21.6 1.5 57.8 Volume (m3 x 106) 379.28 0.45 2608.00 Hydraulic Retention Time (days) 251 1 2446 Secchi Disk (cm) 177.8 15.2 563.9 Total Phosphorus (pg/liter) 147 5 1120 Chlorophyll a^ (yig/liter) 53.9 1.4 456.6 The data used in this report are from the various individual National Eutrophication Survey (NES) lake reports for the lakes listed in Table 2, e.g., Report on Lake Lulu (EPA, 1976). Similarly, NES lake reports provide data for Lake Mead (EPA, 1977a) and Flaming Gorge Reservoir (EPA, 1977b) included as examples of the application of the formulas. Solution analyses based on 20 pg/1 were employed to place the three formulas on an equivalent basis by dividing the appropriate theoretical minimum eutrophic "loading" rate for a given lake (i.e., that which would produce an ambient lake concentration of 20 yg/1) into the actual "loading" rate determined for that lake. Hereafter, this ratio will be referred to as the "trophic ratio". Trophic ratios which exceed or equal 1.0 represent eutrophic loadings, whereas trophic ratios extending from 0.5 to less than 1.0 represent mesotrophic loadings and trophic ratios below 0.5 represent oligotrophic loadings, regardless of the formula employed. Table 2 lists the 39 lakes used in this study, ranked in descending order by total phosphorus concentration, and gives the mean total phosphorus concentration and mean Secchi disk value for each lake. In addition, the trophic states given in the individual NES lake reports are listed along with the trophic ratios calculated for the Larsen/Mercier, Dillon, and Vollenweider models and the trophic states predicted by the ratios. The trophic states indicated in the NES reports were based largely upon lake mean total phosphorus, chlorophyll a_, Secchi depth, hypolimnetic dissolved oxygen values and phytoplankton data (Allum et al., 1977). Spearman rank correlation coefficients (rs) were calculated for each trophic ratio against measured mean ambient phosphorus concentrations with the following results: Larsen/Mercier (.94), Dillon (.92), and Vollenweider (.82). The Larsen/Mercier model provided the best estimation of the relative rank of the lakes based on ambient phosphorus concentrations. It was followed closely by the Dillon model. Both of these models take into consideration the phosphorus retention capacity of lakes. These models are 2 ------- TABLE 2. COMPARISON OF LAKE AMBIENT PHOSPHORUS PREDICTION MODELS AND TROPHIC CLASSIFICATIONS WITH ACTUAL AMBIENT LAKE CONDITIONS. THE 39 LAKES COMPARED ARE RANKED IN DESCENDING ORDER BY MEAN SUMMER AMBIENT PHOSPHORUS CONCENTRATION MEAN MEAN AMBIENT AMBIENT SECCHI NES LARSEN/KERCIER DILLON V0LLENWE1DER LAKE NAME TOTAL-P DEPTH TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC RANK (STATE) (pq/1) (cm) STATE* RATIO* STATE* RATIO* STATE* RATIO* STATE* 1 Lake Lulu (Fla.) 1120 23 E 259.90 - E A 75.62 - E 2 Sloeurn Lake (111.) 882 20 E 61.77 - E 74.00 - E 29.42 - E 3 Lake Hancock (Fla.) 608 30 E 79.90 - E A A 4 A11igator Lake (Fla.) 429 58 E 38.92 - E A A 5 Fox Lake (in.) 322 23 E 10.81 - E 3.40 - E 12.66 - E 6 Highland (Silver) Lake (111.) 258 20 E 14.61 - E 15.38 - E 5.43 - E 7 Horseshoe Lake (111.) 256 25 E 11.81 - E 12.00 - E 1.96 - E 8 Kill en Pond (Del.) 216 66 E 5.58 - E 5.67 - E 9.25 - E 9 Lake Loramie (Ohio) 204 15 E 18.57 - E 18.67 - E 5.02 - E 10 Crab Orchard Lake (111.) 184 58 E 7.40 - E 7.33 - E 7.42 - E 11 Duhernal Lake (N.J.) 179 61 E 3.17 - E 3.33 - E 18.92 - E * E = eutrophic, M = mesotrophic, 0 = oligotrophia and a = insufficient data to make estimate of trophic ratio. (Continued) ------- TABLE 2. COMPARISON OF LAKE AMBIENT PHOSPHORUS PREDICTION MODELS AND TROPHIC CLASSIFICATIONS WITH ACTUAL AMBIENT LAKE CONDITIONS. THE 39 LAKES COMPARED ARE RANKED IN DESCENDING ORDER BY MEAN SUMMER AMBIENT PHOSPHORUS CONCENTRATION (Continued) MEAN MEAN AMBIENT AMBIENT SECCHI NES LARSEN/MERCIER DILLON VOLLENWEIDER LAKE NAME TOTAL -P DEPTH TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC RANK (STATE) (wq/D (cm) STATE* RATIO* STATE* RATIO* STATE* RATIO* STATE * 12 Lake Charleston (111.) 164 23 E 8.57 - E 7.50 - E 15.91 - E 13 Lake Apopka (Fla.) 161 29 E 19.17 - E 22.00 - E 3.94 - E 14 Marsh Lake (Ind.) 115 127 E 5.80 - E 5.92 - E 4.54 - E 15 Saluda Lake (S.C.) 73 68 M 1 .84 - E 1.88 - E 5.07 - E 16 Arkabutla Reservoir (Miss.) 58 64 E 11 .28 - E 11.39 - E 2.58 - E 17 Barren River Reservoir (Ky.) 49 123 E 3.35 - E 2.32 - E 2.10 - E 18 Lake Chesdin (Va.) 40 120 E 2.20 - E 2.21 - E 2.24 - E 19 Lay Lake (Ala.) 39 104 E 4.84 - E 4.20 - E 5.72 - E 20 Cherokee Lake (Tenn.) 37 141 E 2.28 - E 2.43 - E 3.61 - E 21 Hickory Lake (N.C.) 34 114 E 2.04 - E 1 .74 - E 3.13 - E 22 Walter F. George Reservoir (Ga.) 30 no E 3.12 - E 3.25 - E 3.44 - E * E = eutrophic, M = mesotrophic, 0 = oligotrophic and a = insufficient data to make estimate of trophic ratio. (Continued) ------- TABLE 2. COMPARISON OF LAKE AMBIENT PHOSPHORUS PREDICTION MODELS AND TROPHIC CLASSIFICATIONS WITH ACTUAL AMBIENT LAKE CONDITIONS. THE 39 LAKES COMPARED ARE RANKED IN DESCENDING ORDER BY MEAN SUMMER AMBIENT PHOSPHORUS CONCENTRATION (Continued) RANK LAKE NAME (STATE) MEAN AMBIENT TOTAL-P (uq/1) MEAN AMBIENT SECCHI DEPTH (cm) NES TROPHIC STATE * LARSEN/MERCIER TROPHIC TROPHIC RATIO* STATE* DILLON TROPHIC TROPHIC RATIO* STATE* VOLLENWEIDER TROPHIC TROPHIC RATIO* STATE* 23 Moultrie Lake (s.c.) 25 134 E 1 .51 - E 1.55 - E 1.70 - E 24 Lake Hopatcong (N.J.) 25 231 E 1 .32 - E 1 .00 - E 0.34 - 0 25 Tims Ford Reservoir (Tenn.) 25 240 E 2.22 - E 2.70 - E 1.11 - E 26 Lake Minnehaha (Fla.) 22 140 E 2.11 - E A A 27 Murray Lake (S.C.) 20 218 E 1 .56 - E 1.56 - E 1.49 - E 28 Chatuge Lake (Ga.) 17 310 M 1 .06 - E 1.10 - E 0.56 - M 29 Liberty Reservoir (Md.) 15 381 M 0.71 - M 0.76 - M 1.80 - E 30 Wanaque Reservoir (N.J.) 14 467 M 1 .31 - E 0.96 - M 0.48 - 0 31 Maxinkuckee Lake (Ind.) 14 221 M 1.20 - E 1.33 - E 0.75 - M 32 Dale Hollow Reservoir (Ky.) 13 318 M 0.49 - 0 0.47 - 0 0.49 - 0 * E = eutrophic, M = mesotrophic, 0 = trophic ratio. oligotrophic and A = insufficient data to make estimate of (Conti nued) ------- TABLE 2. COMPARISON OF LAKE AMBIENT PHOSPHORUS PREDICTION MODELS AND TROPHIC CLASSIFICATIONS WITH ACTUAL AMBIENT LAKE CONDITIONS. THE 39 LAKES COMPARED ARE RANKED IN DESCENDING ORDER BY MEAN SUMMER AMBIENT PHOSPHORUS CONCENTRATION (Continued) LAKE NAME (STATE) RANK 33 Lake Wallenpaupack (Penn.) 34 Martin Lake (Ala.) 35 John W. Flannagan Reservoir (Va.) 36 Deep Creek Lake (Md.) 37 Summersville ' (W.Va.) 38 Harveys Lake (Pervn.) 39 Tygart Reservoir (W.Va.) MEAN AMBIENT TOTAL-P (wq/1) MEAN AMBIENT SECCHI DEPTH (cm) NES TROPHIC STATE* DILLON VOLLENWEIDER LARSEN/MERCIER TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC TROPHIC RATIO* STATE* RATIO* STATE* RATIO* STATE* 13 434 M 1.10 - E 1.12 - E 0.50 - M 13 230 M 1 .04 - E 0.96 - M 1 .35 - E 11 366 M 0.66 - M 0.69 - M 1 .92 - E 11 366 M 0.39 - 0 0.38 - 0 0.34 - 0 10 549 M 0.83 - M 0.83 - M 1 .28 - E 9 564 M 0.55 - M 0.59 - M 0.54 - M 5 320 M 0.95 - M 0.94 - M 2.02 - E * E = eutrophic, M = mesotrophic, 0 = oligotrophic and a = insufficient data to make estimate of trophic ratio. ------- very similar, as areal phosphorus loading (L) divided by mean depth (Z) approximates mean tributary concentration. The major difference between the models is the flushing rate (P) employed by Dillon. The Vollenweider model, which does not contain a phosphorus retention capacity element, produced the poorest estimate of the ambient phosphorus concentration. Comparison of NES trophic state assignments to various phosphorus model predictions revealed a 14, 18, and 25 percent disagreement, respectively, for the Dillon, Larsen/Mercier, and Vollenweider concepts. The Dillon and Larsen/Mercier models predicted the same trophic state in 33 of 35 lakes. The only exceptions were Martin Lake and Wanaque Reservoir where the trophic ratios, although very close, lay on opposite sides of the somewhat arbitrary borderline. Nine of the 35 Vollenweider trophic state predictions differed from the Dillon model predictions, while 8 differed from the Larsen/Mercier model estimates. Generally, the Dillon and Larsen/Mercier models not only predicted the same trophic state but their respective trophic ratios were quite similar. By comparison, the Vollenweider model porvided less consistent trophic state results and greater variation in trophic ratios. Wanaque Reservoir was classified as eutrophic, mesotrophic, and oligo- trophy by the models. However, the Dillon and Larsen/Mercier trophic ratios were actually very close (0.96 and 1.13, respectively). Even though all of the models produced relatively high Spearman rank correlation coefficients, these models must be used with caution as the com- parisons given in Table 3 illustrate. For the two western reservoirs, the Vollenweider model predicted a much higher eutrophic loading rate than the other models. Both of these reservoirs have high phosphorus retention capacities (associated with high suspended sediment deposition) -- Lake Mead (0.93), and Flaming Gorge Reservoir (0.82). These examples reinforce the concept that the Dillon and the Larsen/Mercier models give comparable results. However, the Larsen/Mercier model requires less information [(P) flushing rate and (Z) mean depth are not required] and produced the highest Spearman rank correla- tion coefficient (rs). Also, the Dillon model required mean depth information which is neither uniformily available nor necessarily accurate, without an extensive bathymetric survey. The mean depth of the lake is the only independ- ent variable which sets the level of the theoretical eutrophic "loading" rate in the Dillon model. In the Larsen/Mercier model the independent variable which controls the theoretical eutrophic loading rate is the phosphorus retention capacity. 7 ------- TABLE 3. COMPARISON OF THREE MODELS TO PREDICT MEAN AMBIENT LAKE PHOSPHORUS CONCENTRATIONS AT EQUILIBRIUM IN TWO RESERVOIRS CALCULATED MODEL VALUE TROPHIC STATE LEVELS EUTROPHIC OLIGOTROPHY TROPHIC RATIO PREDICTED TROPHIC STATE oo Lake Mead, Nev./Ariz. Vollenweider 6.23 g/m2/yr Larsen/Mercier 372 yg/1 Dillon 1.47 g/m2 Flaming Gorge, Wyo./Utah Vollenweider 1.35 g/m2/yr Larsen/Mercier 93.5 wg/1 Dillon 0.41 g/m2 0.78 g/m2/yr 298.5 yg/1 1.18 g/m2 0.76 g/m2/yr 152.6 yg/1 0.68 g/m2 0.39 g/m2/yr 149.5 yg/1 0.59 g/m2 0.38 g/m2/yr 76.9 yg/1 0.34 g/m2 7.98 1 .29 1 .24 Eutrophic Eutrophic Eutrophic 1.77 Eutrophic 0.60 Mesotrophic 0.60 Mesotrophic ------- LITERATURE CITED Allum, M.O., R.E. Glessner, and O.H. Gakstatter. 1977. An evaluation of the National Eutrophication Survey data. Working Paper No. 900. Assessment and Criteria Development Division, Corvallis Environmental Research Laboratory, Corvallis, Oregon. 75 p. Dillon, P.J. 1975. The phosphorus budget of Cameron Lake, Ontario: The importance of flushing rate to the degree of eutrophy of lakes. Limnol. Oceanogr. 20:28-39. Edmondson, W.T. 1970. Book review (Water Management Research). Limnol. Oceanogr. 15:169-170. Larsen, D.P. and H.T. Mercier. 1976. Phosphorus retention capacity of lakes. J. Fish. Res. Board Can. 33:1742-1750. U.S. Environmental Protection Agency. 1975. National Eutrophication Survey Methods 1973 - 1976. Working Paper No. 175. Environmental Monitoring and Support Laboratory, Las Vegas, Nevada, and Corvallis Environmental Research Laboratory, Corvallis, Oregon. 91 p. U.S. Environmental Protection Agency. 1976. Report on Lake Lulu, Florida. Working Paper No. 263. Environmental Monitoring and Support Laboratory, Las Vegas, Nevada, and Corvallis Environmental Research Laboratory, Corvallis, Oregon. 30 p. U.S. Environmental Protection Agency. 1977a. Report on Lake Mead, Nevada and Arizona. Working Paper No. 808. Environmental Monitoring and Support Laboratory, Las Vegas, Nevada, and Corvallis Environmental Research Laboratory, Corvallis, Oregon. 91 p. U.S. Environmental Protection Agency. 1977b. Report on Flaming Gorge Reservoir, Utah and Wyoming. Working Paper No. 885. Environmental Monitoring and Support Laboratory, Las Vegas, Nevada, and Corvallis Environmental Research Laboratory, Corvallis, Oregon. 67 p. Vol 1enweider, R.A. 1968. Scientific fundamentals of the eutrophication of lakes and flowing waters, with particular reference to nitrogen and phosphorus as factors in eutrophication. Organ. Econ. Coop. Dev., Paris. Tech. Rep. DAS/CSI/68.27:159 p. Vollenweider, R.A. 1975. Input - output models with special reference to phosphorus loading concept in limnology. Schweiz. Z. Hydro!. 37:53-83. 9 ------- |