United States EPA-600/3-81 -015
Environmental Protection April 1981
Agency
Research and
Development
Sampling Strategies for
Estimating the Magnitude and
Imprtance of Internal
Phosphorus Supplies in Lakes
Prepared for
Office of Water Regulations and
Standards
Criteria and Standards Division
Prepared by
Environmental Research Laboratory
Corvallis OR 97330
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EPA 600/3-81-015
April 1981
SAMPLING STRATEGIES FOR ESTIMATING THE MAGNITUDE AND
IMPORTANCE OF INTERNAL PHOSPHORUS SUPPLIES IN LAKES
By
Robert E..Stauffer
Water Chemistry Laboratory
University of Wisconsin
Madison, Wisconsin 53706
Project Officer
Spencer A. Peterson
Freshwater Division
Corvallis Environmental Research Laboratory
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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DISCLAIMER
This report has been reviewed by the Corvallis Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. 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 endorsement or
recommendation for use.
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ABSTRACT
The physical and chemical factors controlling sediment release and water
column cycling of phosphorus and other nutrients (internal loading) are
discussed within a "systems" framework. Applying the systems approach, time-
dependent nutrient storage within identified compartments, and fluxes between
compartments are identified and interpreted mechanistically. The lake
"system" is partitioned into four main compartments, the lake water,
atmosphere, tributary land drainage, and underlying sediments. The lake water
and adjacent sediments are further partitioned along the vertical axis to
reflect seasonal thermal stratification, and sedimentation processes. The
important mechanistic paradigms applied to the "system" include transport
phenomena in density stratified fluids subjected to wind power, and the
interacting geochemistries of iron, phosphorus, and sulfur in bicarbonate-
buffered natural waters. The purpose of the model is to identify the chemical
and morphological factors regulating phosphorus recycling in lakes, and lay a
mechanistic foundation for a general model of the phosphorus "economy" of the
epilimnion.
The magnitude and fate of sediment-released P into the overlying water
column depends on the physical-chemical mechanism of release. In highly
turbulent sediment interface environments of high redox potential, phosphorus
release depends on the difference between the "cross over" concentration of
the surficial sediment and the dissolved inorganic phosphorus concentration in
the overlying water column. The "cross over" concentrations are typically
much higher in calcareous than non-calcareous epilimnetic sediments, as a
consequence of different edaphic conditions in their respective drainage
basins. During summer, epilimnetic photosynthesis raises the pH and lowers
the free water dissolved inorganic P concentration below the sediment "cross
over" concentration: This condition promotes oxic sediment P release in
calcareous lakes.
In the more general case of quiescent, or bio-turbated sediments, the
magnitude and fate of sediment released P depends on the Fe/P stoichiometry of
release. If the atomic Fe/P ratio exceeds 1.8, phosphorus is nearly
quantitatively precipitated as ferric-phosphate when Fe2+ is oxidized by
dissolved oxygen during diffusion upward through the overlying water column.
As a consequence, phosphate released during stagnation into the anoxic bottom
waters of deep non-calcareous lakes plays no subsequent role in the phosphorus
economy of the trophogenic layer. However, in calcareous drainage lakes, low
Fe/P release ratios «1.0 typically occur because of selective sulfide
inactivation of Fe(II) (as the precipitate, FeS) at the sediment-water
interface. These alkaline lakes accumulate H2S instead of Fe2+ in the anoxic
hypolimnia, and hence, are called "sulfuretums". Calcareous lakes are prone
to become sulfuretums because of low Fe weathering rates in the alkaline
pervious soils of the drainage basin, the relatively high concentrations of
m
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sulfate in the hypolimnion available for reduction, and the high productivi-
ties and organic deposition rates for these lakes. Such lakes are efficient
at recycling sediment-released P back into the trophogenic layer(s) because a
chemical separation of Fe and P has occurred in the recycle pathway. In the
absence of Fe, P is not naturally precipitated in the presence of oxygen. The
purpose of alum treatments is to substitute aluminum inactivation of P in
lakes lacking strong Fe regulation.
A methodological section discusses essentials of lake sampling, chemical
analyses, estimation of vertical nutrient transport using flux gradient
calculations, and interpretation of lake chemical budgets. A chronology of
essential tasks is presented for the lake manager or scientific consultant
interested in documenting internal cycling of nutrients in lakes.
IV
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CONTENTS
Page
I. Introduction 1
II. Lakes as Physical Chemical Systems 2
A. Compartments-Linkages 2
B. Drainage Basin Fluxes 2
C. Time Dependent Density Partitioning of the Water Column .... 6
1. Introduction to Stratification: Convective Circulation . 6
2. Duration of Vernal Isothermal Circulation 7
3. Windwork-Forced Overturn 7
4. The Dynamic Spring Period 8
5. Classical Description of Stratification Thermocline ... 21
6. The Summer Thermocline: Windpower and Air Temperature
Stationarity: Heat Budget Equilibrium 21
7. Time Series for the Convective Circulation Depth: h (t) . 22
D. Biological Partitioning of the Water Column 23
E. Sediment-Water Relations 26
1. Overview 26
2. Sediment Bulk Chemical Composition 26
a) Physical Resuspension-Deposition Patterns 26
b) Phosphorus and Iron Fractions in Calcareous vs.
Non-Calcareous Lake Sediments .... 26
c) Summary of factors Controlling Fe vs. P Sedimentation . 30
3. Sediment Release of Dissolved Inorganic Phosphate .... 32
a) Fickian Diffusion Model 32
b) Chemical Factors Controlling Sediment Interstitial
Phosphate and Fe(II) Concentrations 33
c) Seasonal Model of Sediment Interstitial Fe and P
Concentrations 35
d) FeS and Sediment Extraction Schemes 38
e) Measurements of Sediment Phosphorus Release 38
F. Factor Interactions Among Lake Morphometry, Seasonal
Stratification, Sediment-Water Interactions and Redox 41
1. Hypolimnetic Volume Development 41
2. Effects of Sediment Contact Area at Intermediate Depths. . 45
3. Entrainment Transport of P into the Mixed Layer
Accompanying Thermocline Migration 52
III. Estimation 53
A. Sampling Equipment 53
B. Analytical Methods 56
1. Temperature 58
2. pH 58
3. Dissolved Oxygen 61
4. Major Cations 61
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5. Bicarbonate Alkalinity 61
6. Sulfate and Chloride 61
7. Iron and Manganese 61
8. Dissolved Sulfide 62
9. Nutrients: NN:P:Si 62
10. Chlorophyll a 63
11. Conductance 63
12. Sample Preservation in the Field 63
C. Lake Temperature Estimation 64
1. Temperature Seiches 64
2. Seiche Dampening 67
3. Other Wave Disturbances 68
4. Effects of Lake Morphometry on Temperature Estimation . . 68
5. Variance Components of a Simple Random Sample
(s.r.s) for hi 69
6. Bias in f(z} 70
7. Biases in AT(z) 71
D. Estimating Vertical Nutrient Fluxes 73
IV. Chronology of Tasks for Lake Managers 75
References 79
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I. Introduction
During the past decade a number of case studies have established sediment
phosphorus release (internal supply) as one important factor regulating the
seasonal and annual trophic condition of a lake (Burns and Ross, 1972; Larsen
et a_K , 1979; 1980; Cooke et al_. , 1977; Stauffer, 1974). Burns and Ross
(1972) showed that pelagic sediment releases of P and hypolimnetic accumula-
tion in Lake Erie's Central Basin resulted from prior onset of anoxic con-
ditions at the sediment-water interface. This prior onset of anoxia also
appeared to be a necessary condition for P release in Shagawa Lake, Minnesota
(Larsen et al_. , 1979; 1980). However, Stauffer (1974) showed that, unlike
lakes Erie or Shagawa, large scale P build-ups in the hypolimnion of Lake
Mendota, Wisconsin predate the onset of anoxic conditions. Furthermore,
Stauffer and Lee (1973) showed that P released into the hypolimnion of Lake
Mendota could be transported through the summer thermocline during cold fronts
in such magnitude as to be the dominant source of phosphorus to the epilimnion
during the entire stratification period. Subsequent investigations (Stauffer,
1974) showed that large scale vertical transport of nutrients accompanying
storms was also important in other calcareous drainage lakes of southern
Wisconsin. Blanton (1973) and Sweers (1970) have also noted the potential for
thermocline-migration-entrainment.
In the present paper I consider sampling strategies for estimating the
magnitude and importance of internal phosphorus supplies in lakes. More
specifically, I describe the following:
1
What physical and chemical measurements yield useful information about
both the magnitude and fate of sediment phosphorus release? How
analytically are these measurements made with the prerequisite precision
and accuracy at the least cost?
2. When should the measurements be made, both from an annual perspective and
within seasons? How are these decisions based on climatic factors, lake
morphology, and the relation of the lake to its drainage basin?
3. Where on the lake surface do you sample? How do you take and process
samples and (when necessary) preserve them for later analyses? How does
the spatial arrangement of sampling stations depend on antecedent weather
variables?
4. How do you process the data? In what ways can you use accumulating
information to revise and refine the lake sampling and analytical
strategies provided sufficient attention is paid to site-specific
climatic influences on the seasonal stratification cycle.
Extensive physical-chemical data from lakes in the cold-temperate climate
in the upper Midwest form the basis for the discussion of error analysis and
optimal sampling strategies. However, based on accumulating evidence about
underlying chemical principles and transport mechanisms, the results are
likely to be broadly adaptable to lake investigations throughout the world. A
brief section on climatic influences on physical limnology introduces some of
these considerations. The importance of internal phosphorus supplies depends
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on both the long term and seasonal balances between the external supply and
the internal, or recycled nutrient supply. Hence, this paper should be used
in conjunction with Reckow's (1980) treatment of external sources for
developing lake survey and management plans.
II. Lakes as Physical Chemical Systems
A. Compartments-Li nkages
Following the initiative of Chemical Engineering, it is useful to think
of a lake (the water), its adjoining sediments, and its upstream drainage
basin as comprising a compartmentalized physical-chemical system. This system
responds over the long term to the annual climatic cycle, and in the short
term to specific weather events which represent statistical "noise" in the
climatic cycle. The system components or compartments influence one another
through linkages. The linkages are controlled by climate and weather. For
our purposes we will be mainly concerned with time series interpretations of
nutrient accumulation (and loss) within identified compartments and the flux
rates between compartments.
B. Drainage Basin Fluxes
The most important influence on lake chemistry is the drainage basin.
Over the long term lakes reflect drainage basin influences, just as we are
"What we eat". Many seminal illustrations of this fact can be cited, going
back especially to Mackereth's (1966) classic paper on the English Lake
District. The drainage basin-lake relation is essentially a one-way linkage.
The drainage basin receives precipitation, chemically transforms this
precipitation during the rock and soil weathering process (c.f. Holland, 1978)
and the exports the precipitation excess (the difference between precipitation
and evapo-transpiration; c.f. Linsley et al. , 1958) either as groundwater
seepage inflow (to the lake) or tributary inflow. The lake receives the water
and its dissolved solutes as an irreversible (except by evaporation and
reprecipitation) inflow down the hydraulic gradient. Because precipitation
excess is an areal-dependent time series related to precipitation, air
temperature, air humidity, and vegetative development in the watershed, the
temporal importance of drainage basin solute export to the lake depends both
on (A.. - A )/A and the specific weather sequence. [Note: AQ is the lake's
surface area; A., - A is the land drainage to the lake.] It follows that no
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interpretation of changes in lake nutrient storage can exclude, a priori, the
assessed potential for drainage basin export of these nutrients. This is
important in designing sampling strategies for estimating sediment nutrient
release and its fate in the water column.
The concentrations of individual nutrients exported from the drainage
basin depend sensitively and uniquely on the specific history of rock-soil-
water relations following the precipitation event. Dissolved silica concen-
tration is determined by relatively rapid adsorption-desorption reactions
between the water and dominant clay minerals comprising drainage basin soils
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(Kennedy, 1971; Siever and Woodford, 1973; Mayer and Gloss, 1980). Thus,
direct rainwater and snow-melt run-off (off frozen ground) can be relatively
impoverished in Si02- Otherwise, concentrations range mainly from 8 to 15 mg
L-1 throughout most of the temperate zone over most of the year. Low con-
centrations are often indicative of silica sedimentation (removal) in an
upstream lake or reservoir as silica is used in macro amounts as an essential
nutrient for diatom growth.
Drainage basin export of inorganic nitrogen is mainly in the form of
nitrate, as ammonia is oxidized microbiologically to N03 and ammonia is both
effectively adsorbed by clay minerals and preferentially utilized by vege-
tation for growth. High dissolved ammonia concentrations represent local
pollution (ammonification of sewage or manure) or direct fertilizer run-off.
Nitrate is frequently highly enriched in surficial ground waters draining
improved agricultural land because of the ion's high downward mobility in
soils and heavy applications of inorganic nitrogen as fertilizer to agri-
cultural soils.
Phosphorus is relatively enriched in soil solutions of rich fertilized
agricultural topsoils (Schroeder, 1976). Low equilibrium concentrations are
typical of less fertile subsoils and severely leached soils rich in Fe and Al.
The analysis of soil "cross-over" or equilibrium concentration has been
described by Mayer and Gloss (1980) and Schroeder (1976). Drainage basin
export of potentially "biologically available phosphorus" (c.f. Oglesby and
Schaffner, 1978; Schaffner and Oglesby, 1978) is encouraged by large scale
erosion of surficial topsoil under low temperature conditions at a time when
drainage basin vegetative utilization of phosphorus has been minimal. In the
north temperate climates these conditions are best satisfied in the late
winter and early spring.
The expected time series for drainage basin water export can be estimated
by substracting potential evapo-transpiration from precipitation norms on a
seasonal basis (Linsley et al. , 1958). Seasonal accuracy is improved if
precipitation falling as snow is "stored" until the thaw. Noting the above,
and equating "potential evapo-transpiration" to estimates of Lake Mendota
evaporative losses (Linsley et aj., 1958, p. 118) during summer stratification
(Stauffer, 1980a), drainage basin water export can be constructed for the
"normal" year and for several recent years featuring observed departures from
precipitation norms (Figures 1, 2). Improved estimates could be generated
using carefully calibrated algorithms like the Stanford Watershed Model.
Obviously, it is preferable to have actual gaged estimates of tributary inflow
and actual solute concentration data (Cooke et al. , 1977; Larsen et aj.,
1979); however, such information is expensive to collect in a "provisional"
analysis of the lake system.
Examining Figures 1, 2, I note that expected drainage basin export of
"excess precipitation" is important in Wisconsin in the late fall and
especially in the later winter and early spring. In the "normal" year net
export is only ~1 cm month-1 during May and June and then turns negative until
mid-September. The summer is a period of accumulating soil-moisture deficit
for Wisconsin watersheds. From Table 1 we can calculate that each 1 cm of
drainage basin water export is equivalent to 1.19% of Lake Mendota1s total
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volume, and 2.20% of the epilimnion volume during typical mid-summer thermo-
cline conditions. Noting that the total-P concentrations in the rural
tributary waters of Lake Mendota (Lathrop, 1978) and Green Lake average ~40 mg
m-3 during summer base-flow recessions (Stauffer, 1974; 1979, unpublished
data), and that this is approximately the mean midsummer Mendota epilimnion
concentration, it is clear that in the "normal" year net additions of P to the
lake from the drainage basin during May-September are negligible. This also
applies to Green Lake and Fish Lake. Conversely, in the early spring and late
fall, total-P concentrations in the tributary waters both increase by an order
of magnitude, and are associated with high discharge. Recent exhaustive
monitoring studies of the Lake Mendota drainage basin (Lathrop, 1978) have
confirmed this marked seasonality in drainage basin phosphorus loading.
Silica and N03-N exports from the drainage basin during May-September are
quantitatively much more important than for P because of the very large Si/P
and N/P ratios in the base flow recession stream waters (Stauffer, 1974).
Additions of these nutrients are likely to be especially important during
summer months with well above normal precipitation (note May-June 1978 in
Figure 2). After entering the summer period of cumulative soil moisture
deficit along with the concomitant emergence of vegetative cover, even heavy
rains fail to mobilize much phosphorus in the pervious well-drained Wisconsin
soils.
The above analysis shows that the incremental additions of P from the
drainage basin can be ignored during thermal stratification unless the summer
is so wet as to initiate erosion, and/or point sources of P (for example,
municipal sewage) are important in the annual phosphorus budget. The seasonal
pattern of external P loading also applies to erosion of elastics in the
drainage basin. Because Fe is transported almost entirely as coatings on clay
minerals (Carroll, 1958; Stauffer and Armstrong, 1980a) in alkaline drainage
basins, the summer flux of Fe is also negligible in southern Wisconsin.
Conversely, in arid climates with summer thunderstorm influences, external
inputs of P and Fe accompanying elastics erosion can be maximum in the summer
months (Gloss et al. , 1980). In mediterranean climates the summer flux falls
to zero (Kennedy, 1971).
C. Time Dependent Density Partitioning of the Water Column
1. Introduction to Stratification: Convective Circulation.
Until now I have considered the lake water as one compartment in the
tripartite: drainage basin-lake water-lake sediment chemical systems.
However, treatment of the lake as an integral whole is appropriate only during
those periods when it is isothermal and freely circulating. Because of the
temperature-dependence of water density (c.f. Hutchinson, 1957) the addition
or subtraction of heat at either the lake's atmospheric boundary or sediment
benthic boundary acts to either induce or suppress water column circulation.
We are thus led to the following important definition: The true mixed layer
thickness or free convective circulation depth at any time t is denoted h (t),
and is that point in the water column (measured positively downward from the
lake surface) above which Ap/Az<0 for all z
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its maximum density at 4°C, once the lake cools below 4°C in the fall it
resists mixing and is subject to winter stagnation. Winter stagnation is
enhanced by ice cover because ice uncouples the lake from the forced circula-
tion influences of the wind.
Adopting Hutchinson's (1957) descriptive terminology, temperate lakes of
sufficient depth are either dimictic if they circulate in the fall and early
spring, or monomictic if they circulate from the late fall through the early
spring. Winter stagnation under ice persists in southern Wisconsin approxi-
mately from mid-December to mid-April. In northern Wisconsin,
Minnesota, Michigan and New England the duration of ice cover is about one
month longer. Because of their greater heat capacities, large deep lakes have
delayed ice-on and ice-out dates.
2. Duration of Vernal Isothermal Convective Circulation
Following ice-out, and until the lake attains an average temperature of
4°C, net heat additions to the lake's upper layers by the direct absorption of
solar radiation or sensible heat transfer (warm air overlying cold water)
generate buoyancy instability and induce free convective circulation. These
convections penetrate to the lake bottom unless the bottom benthic layer is
significantly density stabilized by important accumulations of dissolved or
suspended solids [such lakes are called "meromictic", c.f. Hutchinson, 1957;
Judd, 1970; Walker, 1974, for example].
The duration of the vernal free convective circulatioji period depends
sensitively o_n two factors: (1) the lake's mean depth (z) and mean lake
temperature (T.) at ice-out; hence the heat (cal cm-2 surface area) required
to warm it to 4°C (100 (4-fL)*z); (2) the rate of lake heating following
ice-out. Because large windswept lakes usually cool to 1 to 2°C prior to
ice-on, large deep lakes require a long heating period to attain 4°C. Because
most of the heating is accomplished by solar radiation, and insolation
increases as we approach the summer solstice, the later the date of ice-out
the shorter the expected duration of the vernal convective circulation period.
Assuming a mean lake temperature of 2°C at ice-out, and a lake heating
efficiency of 70% (% of incident radiation including infra red band retained
over die! cycle, Stauffer, 1980a) approximately 0.6 days are required for each
meter of lake mean d_epth to attain the 4°C mark_during mid-April in Wisconsin.
For lakes Mendota (z = 12.4 m) and Big Green (z = 31.0) the expected lengths
of the vernal convective circulation periods are approximately 7 and 19 days
for mid-April insolation of -500 cal cm-2d-1.
3. Windwork-Forced Overturn
After the lake attains 4°C, further additions of heat create upper layer
buoyancy stabilization. Redistribution of this heat load downward requires
expenditure of gravipotential work in the water column (Birge, 1916). This
work is performed by the exogenous wind power time series above the lake. One
laboratory-based model of this heat redistribution assumes that a small (~1%)
but nearly constant fraction of the input kinetic energy of the wind is used
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to perform gravipotential work in the water column (Sundaram, 1973; Kato and
Phillips, 1969; Kraus and Turner, 1967). Actually a fully generalizable lake
transfer function model relating wind power to gravipotential work has never
been adequately formulated and tested. Provisional estimates on Lake Mendota
suggest that the work efficiency of the wind decreases by about 1 order of
magnitude (from 3 to 0.2%) between late spring and early fall, accompanying
the movement of the thermocline downward from ~3 to 15 m (thus further away
from the wind energy source, Stauffer, unpublished data). At any given time,
however, we do expect at least double the work for a doubling in input power.
Such "mechanistic" model of thermal stratification interprets stratification
as the dynamic interaction of two time series, namely the net heat (hence
buoyancy) flux across the air-water interface (cal cm-2 s-1) and the windpower
time series (ergs cm-2 s-1) (Sundaram, 1973; 1974; Tucker and Green, 1977).
4. The Dynamic Spring Period
If the date of ice-out is late (for example in May) the lake will not
have attained the 4°C mark until a date when the radiation time series is
already sinusoidally approaching its summer solstice maximum, and the wind
power time series has already undergone its precipitous mid-spring attenuation
in intensity (Stauffer, 1980b). Furthermore, the prevalence of extended
spring season sequences of very low power (Stauffer, 1980b), accompanying
atmospheric inversions over the lake surface, can result in the onset of
permanent (even if only partial) thermal stratification soon after termination
of the free convective circulation period. This tendency toward a short
forced (wind driven) vernal circulation is marked for lakes at higher
latitudes, lakes with small wind sheltered exposures, and especially lakes
with large shoal areas and isolated deep holes of small area! extent. The
extensive shoals trap the solar insolation in a narrow depth band, and
accelerate the rate of surface layer heating. Fish Lake (see Table 1)
typically stratifies in April for these last two reasons.
The specific lake heating process differs markedly from year to year
because of pronounced variability in the late spring windpower time series.
Figures 3-13 show the differential effects of wind during 1967, 1971-1973 on
the onset of stratification in Lake Mendota. A long period of abnormally low
windpower and warm sunny weather in mid-May 1972 resulted in full strati-
fication prior to May 25 (Julian Day 145) for both Lakes Mendota and Delavan.
A cool windy early June then deepened the thermoclines and cooled the
epilimnions of these two lakes. The very windy May in the following year
preserved nearly isothermal conditions in Lake Mendota until Julian Day 148.
In both 1971 and 1973 marked thermal stratification only developed with the
onset of sunny warm, relatively calm June weather. Conversely, June 1974 was
cold and windy and Lake Mendota did not develop a typical summer thermal
structure until early July. Strong stratification occurred early (May) in
both 1975 and 1977. Notice that strong stratification set in on Lakes
Mendota, Delavan and Green simultaneously following May 12, 1972. However,
Fish Lake was already strongly stratified by that early date.
(text continued on page 21)
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5. Classical Description of Stratification Thermocline
For lakes of sufficient depth, the spring dynamic heating period
eventually makes a gradual transition to "summer stratification". The clas-
sical description (c.f. Hutchinson, 1957) or model of this stratification
features a warm buoyant isothermal upper layer or epilimnion, which is
circulated by the wind, and which "floats" on the colder nearly homogeneous
hypolimnion bottom layer. The transitional layer separating the epilimnion
and hypolimnion is called the metalimnion or "thermocline" where the
temperature gradient exceeds l°C/m. Because of the density stabilization
within the thermocline, this layer is frequently considered to be a static
diffusional barrier to vertical transport of heat and/or solutes between the
hypolimnion and epilimnion, and vice versa.
The classical three layer description of summer thermal stratification is
a useful model until misused in limnological research. Misuse involves the
model's deficiencies. First the model has little to say about the complex
sequence of events affecting the lake between ice-out and early summer.
Second, it is a naively static interpretation of thermal stratification during
the summer and early fall period.
6. The Summer Thermocline: Windpower and Air Temperature Stationarity:
Heat Budget Equilibrium
The 2\ month period following mid June in Wisconsin is said to feature
weather "stationarity" because of the absence of significant time trends in
the important meteorological variables governing lake stratification and heat
budgets (wind energy, insolation, relative humidity, air temperature). More
generally, July-August is a stationary windpower minimum throughout the United
States east of the Rocky Mountains. The weather stationarity period arrives
earlier and persists later as we proceed along a transect from Wisconsin to
the Gulf of Mexico (Stauffer and Dominguez, 1980).
After late June in Madison, Wisconsin the epilimnion has normally
attained its "equilibrium" temperature of 23±1°C for the summer stationarity
period. The epilimnion is in approximate thermal equilibrium with the
atmosphere when daily heat losses via black body radiation and evaporation at
the surface balance incoming radiation corrected for the albedo (6%). For
lakes situated in humid temperate climates (3 PM relative humidity -40%; 3 AM
relative humidity ~80%) equilibrium is attained when the lake surface
temperature is 1-2°C warmer than the average daily air temperature (Stauffer,
1980a). [Note: Because latent heat transfer increases linearly with both
wind speed and the vapor pressure gradient (Deacon and Webb, 1962), lakes
situated in arid windy climates will have cooler surface temperatures at
equilibrium with the prevailing air temperature.]
During summer interludes of below normal air temperatures, above normal
windspeeds, and/or below normal insolation, the epilimnion tracks the
atmospheric trend and thus cools below its normal summer equilibrium
temperature. A subsequent warming trend can then initiate new heat accumula-
tions in the upper epilimnion and lead to the formation of multiple thermo-
clines. [This process has been well described by Lewis (1973) for tropical
21
-------
lakes. I follow his terminology.] Such weather trends during mid summer are
capable of shifting Lake Mendota's surface temperature over 7°C (approximately
20 to 27°C). During a Midwest warming trend it is not unusual to have a
high-lying daytime "breeze thermocline" positioned at 3 to 6 m and featuring a
temperature drop from ~25°C to 21°C. This overlies the main "storm thermo-
cline" beginning at z=8 to 10 m and 20 to 21 °C. The storm thermocline
encompasses an 8 to 10°C temperature drop in a 4 to 6 m depth interval.
During subsequent windy cooling trends the "breeze thermocline" is both eroded
and pushed downward until it is merged with the storm thermocline. Under
favorable circumstances multiple thermoclines persist in Lake Mendota for
several weeks.
The development of multiple thermoclines leads to a complex vertical
partition of the nutrient store in the lake, and complicates procedures for
estimating the magnitude and ultimate fate of internal (sediment-derived)
supply. The complications include the following: First, the higher lying
thermocline may partially overlap the trophogenic zone, hence sediment-derived
nutrients may be utilized before their accumulation is apparent. Second, a
high lying thermocline may persist long enough to initiate sediment phosphorus
release but be transitory enough to be missed in a crude monitoring program.
Third, the breeze thermocline is subject to large amplitude lateral tilts in
response to wind stress (see later section).
7. Time Series for the Convective Circulation Depth: h (t)
Because the joint lake water-lake sediment system loses heat by black
body (long wave) radiation and evaporative cooling only at the water's
surface, but gains heat by the absorption of solar radiation at depth, the
energy budget equation dictates that h (t) is >0. The depth of convective
circulation thus depends sensitively on: (1) the instantaneous balance
between insolation and combined surface heat losses; (2) the extinction coef-
ficients for light in the water column (c.f. Kraus and Rooth, 1961). During
still sunny conditions at mid-day the high insolation "overloads" the water
column by vastly exceeding surface heat loss rate. The result is a shallow
convective circulation depth (perhaps only a few mm if the lake surface is
cold and the insolation intense). However, at night, when insolation drops to
zero, the convective circulation depth deepens sufficiently to satisfy the net
surface heat exports (to the atmosphere) while maintaining a nearly isothermal
profile above h (t). After the lake attains summertime thermal equilibrium
with the atmosphere over a typical diel cycle (net daytime heating balanced by
net nighttime losses) the nocturnal convective circulation depth will coincide
with the lower boundary of the epilimnion, hence upper boundary of the
thermocline. Clearly, the diel maximum in h (t) is shortly after sunrise,
i.e., after the maximum duration of antecedent nocturnal cooling. Thermal
studies on Lake Mendota, Wisconsin (Stauffer, 1980a) show that typical net
heat losses between a mid afternoon sampling time of 1500 hr LST and 0700 LST
the following morning average 200-250 cal cm-2 lake surface during the summer
stationarity period. Assuming a vertical sided lake, a nocturnal loss of 250
cal cm-2, and an isothermal afternoon epilimnion 5.0 m in thickness, then
nighttime cooling will extend the isothermal mixed zone to 5.48 m by sunrise
of the following morning (Figure 14) if the temperature gradient in the
thermocline ts l°C/m. This example shows that the true diel mixed layer
22
-------
thickness is deeper than normally supposed based on mid-day or afternoon lake
surveys. Assuming the same initial stratification conditions, then under
conditions of sharply accelerated surface heat loss (as for example during
cold fronts with high winds) the die! shift in h (t) can be twice as large.
The vertical amplitude of h (t) migration is increased in lakes with extensive
shoal areas because of thefr reduced water column heat capacities relative to
lake surface area (heat losses are proportional to A ). An example is shown
in Figure 14.
The presence of weather cycles of longer than diel period (Stauffer,
1980b) guarantees that the summer time series of hc(t) is actually much more
variable than the diel example illustrated above. Consider, for example,
possible effects of the ~7 day cold front cycle on estimation of mixed layer
thickness. If, as is so often the case, the lake sampling program is rigidly
scheduled on a weekly basis, we have the maximum potential for statistical
confounding between effects of the potential weather cycle and the sampling
schedule. Stauffer (1980b) showed that following the cold front with its high
windpower, low insolation, and frequently reduced relative humidities (all
conditions favoring downward migration of h (t)), a period of high insolation
and very low power often ensues. During this several day power interlude, the
increased insolation and reduced evaporative cooling can result in reformation
of a high-lying thermocline and upward migration of h (t) from the upper
boundary of the deep storm thermocline. In a typical midwest lake like
Mendota or Shagawa Lake, Minnesota, h (t) can vary from a few cm to ~10 m
during the course of a few weeks in mid-summer. The importance of the h (t)
time series cannot be overemphasized in estimating the magnitude and
interpreting the fate of internal nutrient sources in stratified lakes!
D. Biological Partitioning of the Water Column
The upper biological compartment in the lake is the "euphotic" zone or
trophogenic layer. This extends from the lake surface to the "photo
compensation depth" (here called h ). At the compensation depth photo-
synthesis is just balanced by respiration over a typical diel cycle. This
lower boundary is frequently assumed to the depth of penetration of 1% of the
incident radiation (lake surface) in the visible region of the spectrum.*
The depth of the euphotic zone depends both on the lake surface albedo
and the extinction coefficients for light in the water column. The effective
albedo (fraction of incident radiation reflected) of snow-covered lake ice can
be very high (>.95), thus effectively suppressing primary production and
nutrient uptake under the ice. The albedo drops as the snow cover decreases,
and the ice takes on its bruised-blue color accompanying columnar recrystal-
lization in the weeks just prior to ice-out. After ice-out, albedo averages
Note: In small sheltered lakes photosynthetic bacteria are frequently
active at depths corresponding to ~0.1% of the visible incident light flux.
The effective utilization of such low light levels may depend on the low
water temperatures in such environments (reduces respiration rate)
(T. D. Brock, personal communication, University of Wisconsin, Department of
Bacteriology, April 1980).
23
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0.06 and is notably insensitive to meteorological conditions (Stauffer,
1980a). The ice albedo and available insolation are important environmental
factors limiting algal development and nutrient uptake prior to ice-out. This
is true because thermal stratification (below 4°C) under the ice preserves
algal cells close to the ice window for light.
After ice-out the extinction coefficients for light in the water column
control the depth of the euphotic zone. James and Birge (1938) (c.f.
Hutchinson, 1957 for summary) showed that the natural yellow-brown-stained
humic material in some forest or bog lakes is highly efficient in removing the
bluelight which is otherwise most penetrative in pure lake water. A lakewater
with 50 chloroplatinate units of natural color will have a photo compensation
depth (defined as 1% of the visible) of <1 m, even in the absence of any algal
or inorganic turbidity.
Under favorable circumstances the euphotic depth (plane of 1% remaining
visible) can be estimated as 2.5 times the secchi disk transparency (Tyler,
1968). This extrapolation is relatively imprecise, and is, in fact, inac-
curate if the spectral properties of the water below the secchi transparency
depth are different than in the upper portion of the water column. The
extrapolation is good if h
-------
E. Sediment-Water Relations
1. Overview
The sediment sub-system interacts with the overlying lake water by
exchanging heat and solutes on a seasonal basis, and by acting as a partly
reflecting-partly absorbing boundary for: (1) penetrative solar radiation; (2)
kinetic energy contained both in the wind driven circulation and gravity wave
field. The magnitudes of these exchanges depend on season and on the depth of
overlying water. The above factors act over time to control bulk sediment
chemical properties, sediment surface albedo, sediment temperature, sediment
redox state, and mixing intensity in the sediment surface-benthic boundary
layer.
2. Sediment Bulk Chemical Composition
a) Physical Resuspension-Deposition Patterns. Well consolidated
"grainy" sediments act as an intact shearing barrier which enhances turbulence
in the overlying water. Conversely, dissipation of energy contained in the
surface gravity waves acts to rework shallow water sediments until only heavy,
grainy particles remain. The darker-colored fine-grained particles are
resuspended by the turbulence in the shoals, transported laterally to the
pelagic lake region, and eventually irreversibly settled out. The depth of
wave influence depends on the amplitude of the waves (Tucker and Green, 1977),
hence on wind speed, wind duration, and upwind fetch length (Barber and
Tucker, 1962) accompanying storms in the recent historical period. Strong
wind influences imply sandy or pebbly shallow water sediments that are
chemically and biologically relatively inert. They are not important sources
for phosphorus.
As the depth of overlying water increases, the physical and chemical
character of the sediments changes because of this "sorting" effect of
turbulence. Total iron, P and Mn are usually strongly enriched in the deeper
water surficial sediments (expressed as ug/gm dry wt basis), as compared to
the shallow water sediments (c.f. Delfino et al. , 1969; Williams et al. ,
1971c) because fine grained particles settling into the deep water have large
surface to volume ratios. The surface coatings on clay minerals are sorption
active hydrous Mn(IV) and Fe(III) oxides (Carroll, 1958; Jenne, 1968).
b) Phosphorus and Iron Fractions in Calcareous vs. Non-calcareous
Lake Sediments. Following the initiative of soil science, limnologists have
sought to chemically classify the heterogeneous phosphorus and iron contents
of lake sediments. The classification is empirically based on chemical
extraction procedures which separate the total reservioir according to mineral
type and crystallinity. In particular, the extraction schemes focus on
defining a "potentially mobilizable" sediment P (or Fe) fraction. The
"potentially mobilizable" fraction is that portion which can be solubilized
and exchanged with the overlying water column, or taken up by rooted aquatic
plants under certain (specified later) redox, pH, and temperature conditions
which are potentially realized in the lacrustrine environment.
26
-------
The influence of overlying water depth on "potentially mobilizable" Fe
and P is much more pronounced (Williams et a 1. , 1971abc; Bannerman et aj_. ,
1974; Larsen et aK , 1980) than on elemental totals. This is particularly
true of non-calcareous drainage basins, where detrital heavy-grained hematite
and magnetite may accumulate in shallow water sediments. These "well ordered"
iron particles are not surface active with respect to phosphorus and play no
significant direct role in the phosphorus economy of the lake. For typical
bicarbonate-buffered non-calcareous drainage lakes in Vilas-Onedia Counties in
northern Wisconsin, Williams et al. (1971c) found that the "potentially
mobilizable" (CDB extractable) Fe/P atomic ratio partitioned into two groups.
The Group A ratios ranged from 3.3 to 9.7 and averaged 6.5; these were
associated with the deeper water sediments in all of the study lakes. The
Group B ratios ranged from 21 to 85 and were associated with shallower water
sediments (3-10 m) below the depth of direct wave influence. The high ratios
are extremely unfavorable for desorption of P. The much lower ratios found in
Group A are also representative of calcareous drainage lakes from southern
Wisconsin. However, in the calcareous lakes, the CDB extractable Fe/P ratio
did not change with depth of overlying water, although deeper water sediments
contain considerably larger quantities of both extractable Fe and P (Table 2).
In calcareous lakes, a significant, although still minor percent (14-33%)
of the total inorganic P is present in the form of apatite [Ca5(P04)3X, where
X is OH or F , i.e., hydroxy or fluoro apatite] (Table 2). Because the lake
waters and sediment interstitial waters are generally supersaturated with
respect to apatite, this phase does not dissolve and is an unimportant source
of P for sediment-water exchange. The apatite has been shown to be mainly of
detrital origin (drainage basin erosion) both here (Syers et a]_. , 1973) and in
Lake Erie (Williams et a!. , 1976). The authigenic formation of apatite is
kinetically hindered in many lake systems.
Apatite is quantitatively unimportant in non-calcareous lake sediments of
Wisconsin, in part because the small detrital fluxes of the mineral slowly
dissolve in the slightly acidic-lower-Ca sediment environment. Thomas and
Dell (1978) have described this diagenic relationship for Lake Superior sedi-
ments. Williams et al. (1971a) noted that oxalate extractions of sediment P
include the apatite fraction whereas CDB extractions do not. Because the
apatite in calcareous sediments is inert, the oxalate extraction overestimates
"potentially mobilizable" P. In non-calcareous sediments lacking apatite, the
oxalate and CDB extraction schemes yield essentially the same sediment P
fraction.
As was inferred in the classical sediment-water investigations of Einsele
(1936; 1938) and Mortimer (1941; 1942), the extraction studies of Williams et
al., (1971abc) have shown that potentially mobilizable sediment P is
associated with amorphous Fe in both the calcareous and non-calcareous lake
classes. Aluminum is a negligible "natural" control on P, in part because it
is tied up as primary and secondary alumino-silicate minerals. Amorphus
A1(OH)3 formed after alum treatments is very effective at adsorbing phosphate.
Like the apatite fraction, the quantitatively important organic-P. fraction in
the upper historical sediments is relatively refractory over the seasonal time
scales of interest here.
27
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u aj o
? re .C
S- ro <
"~ 're 4-
gj X O
U ^
S « c
re _2 °
"re "0 <->
X - "
° « £
01 o "
_C a, 0
T 10
U OJ
jp 'ro ^
** U /x
«
ro ro J°
_j S- S-
e x x
o aj ^
^~ 't
ro.ro Q
"ro TT 'ro T;
a r x ro
r^ ° s-
ro o~»
5 r S- . U
(5 0 r -r-
01 » ro E
ro GO zj o
.c o cr 4->
to ro o cu <:
* -K- *-
28
-------
The data of Table 2, while valuable, is at best, narrowly representative
of Wisconsin lakes; it is inadequate for describing the stoichiometric
relations between Fe and P in lakes of diverse geologic and cultural settings.
Only "drainage" lakes are represented in the calcareous class, and of these
only Lake Geneva has escaped intensive agricultural and/or urban-based
cultural eutrophication. Lake Geneva is the second deepest lake in the state
and has a small land drainage area. It is significantly spring-fed. Present
day summer hypolimnetic oxygen depletion rates (Stauffer, 1978, unpublished
data) are indistinguishable from measurements made by Birge in 1907 (Birge and
Juday, 1911). By contrast, closely-neighboring Lake Delavan is the most
impacted by cultural eutrophication among the lakes listed in Table 2. In
addition to extensive agricultural and suburban drainage (see Table 1) it has
been severely impacted by direct sewer discharges from Elkhorn city (popula-
tion 1970 = 40,000) for many years (Stauffer, 1974). The "Yahara Lakes"
studied (Mendota, Monona, Wingra) currently receive varying amounts of agri-
cultural and urban drainage (c.f. Ahern, 1976; Kluesner, 1972; Lathrop, 1978),
and in the past municipal sewage (Mendota, Monona) (Sonzogni and Lee, 1974).
In light of these historical impacts it is interesting that Lake Geneva
has the highest sediment extractable Fe/P ratio, while neighboring Lake
Delavan has by far the lowest ratios among all the lakes studied by Williams
et aJL (1971c). If accurate, the 11 m Delavan ratio is only 40% greater than
the stoichiometry of vivanite, Fe3(P04)2'8H20, the lowest stoichiometry iron
phosphate mineral stable in reducing sediment environments, and a known
diagenic product in both calcareous and non-calcareous lake sediments
(Tessenow, 1974; Emerson, 1976; Emerson and Widmer, 1978; Anthony, 1977).
Furthermore, the Delavan ratios are less than one half of lower bound
stochiometric ratios for P04-P adsorbed on amorphous preformed hydrous Fe(III)
oxides at neutral pH (Einsele, 1936; 1938)! Under alkaline pH the adsorption
of P04-P on these oxides is still less favorable (Einsele, 1936; 1938).
The second lowest extractable Fe/P sediment ratios apply to eutrophic
Lake Wingra. Williams et a 1. (1970) found that Lake Wingra sediment has by
far the lowest tendency to adsorb added P04-P among all the lakes they studied
(Delavan was not studied), and desorbed the largest fraction of this adsorbed
P during a subsequent desorption step.
The non-calcareous lakes studied from the Northern Highlands State Forest
(Table 2) are representative of bicarbonate-buffered natural forest drainage
and seepage lakes experiencing negligible or only minor (except Minocqua West)
cultural influence. Trout Lake retains the hypolimnetic oxygen relations
(Stauffer, unpublished data, 1978) reported earlier by Birge and Juday (1911).
Minocqua West formerly received sewage from the towns of Woodruff and
Minocqua. The Wisconsin lakes investigated have low natural color (chloro-
platinate units) hence are unrepresentative of lakes subjected to drainage
from acid sphagnum bogs and tamarack-spruce swamps. Both the total and
soluble Fe/P ratios from lakes and streams in this latter class (Table 3) are
an order of magnitude higher than the sediment extractable ratios for non-
calcareous lakes reported in Table 2 (Stauffer and Armstrong, 1980a). Four
meromictic lakes in crystalline drainage basins of southern Norway are
noteworthy for their high sediment atomic Fe/P (totals) ratios (c.f. Table 4)
(Kjensmo, 1967). Similar conditions have been reported from the Experimental
29
-------
Lakes Area of Western Ontario (D. W. Schindler, personal communication, 1979).
Crystal Lake is among the most oligotrophic lakes of the state and yet has the
lowest extractable Fe/P ratio among the non-calcareous lakes. The lake has
negligible drainage basin influence except direct atmospheric deposition on
the lake surface, hence extremely low Fe, Si02, and Ca sediment deposition
rates (Twenhofel and Broughton, 1939) and almost undetectable free water
concentrations of Fe, Si02 and SRP (Stauffer, R.E., unpublished data, 1978).
Table 3. Concentrations of Fe, Mn, P in Representative Surface
Waters of the Forested Northern Highlands Region,
Wisconsin and Northern Minnesota.
Sample Sources
(date)
1.
2.
3.
4.
5.
6.
Allequash Cr. , WI*
9/3/79
Stevenson Cr. , WI
9/3/79
Cranberry Cr. , WI
9/12/79
Burntside R. , MN*
8/3/79
Armstrong Cr. , MN
8/3/79
Helmet Lake, WI
9/4/79
UA
FA
UA
FA
UA
FA
UA
FA
UA
FA
UA
FA
Fe
mg m-3
340
(260)
910
(700)
5,780
(1,980)
75
<35
1,100
(835)
725
(590)
Total
Mn
mg m-3
46
(31)
31
(31)
46
(62)
17
<8
405
(370)
46
(46)
P
mg m-3
21.5
(14.0)
14.0
13.0
41.5
35.5
2.0
3.0
15.0
14.0
15.5
13.5
Fe/P
(atomic)
8.7
10.2
36.0
30.0
77.0
31.0
19.0
41.0
33.0
26.0
24.0
Low color, lack bog drainage.
UA = unfiltered acidified; FA =
filtered acidified.
The extractable
Lake's 12
estimated
(see Table 2 notes) for Shagawa
too high given the important hematite
Range forming part of its drainage
non-extractable Fe and P at lesser overlying
eutrophication of the lake has markedly decreased the
surficial sediments (Larsen et al., 1979; 1980).
Fe/P ratio
m and 14 m deep holes may be
mineralization in the Vermillion Iron
basin, and the large fraction of
water depths. Cultural
Fe/P ratio in the
c) Summary of Factors Controlling Fe vs. P Sedimentation. Sum-
marizing, the main geochemical determinants of sediment Fe-P relations are as
follows. The extractable Fe/P sediment ratio reflects both the relative
strengths of the external sources for non crystalline Fe vs. P, and the
30
-------
Table 4. Total Iron, Manganese, and Phosphorus in Representative
Calcareous vs. Non-calcareous Deep Water Lake Sediments*
Sampling
Lake Depth (m) max
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A. Calcareous
PI
MendotaDL
MendotaBL
P
Monona
Monona
Wingra
B. Non-Calcareous
Trout-South
Trout-North6
Minocqua-SW Bay
B**
Firefly Lake
Devils6
uw
Shagawa (EEDH)W
ww
Shagawa (BPDH)
I/
Store Tryvann
if
Bjordammen
Skennungen
I/
Store Aaklungen
C. Average World
Igneous Rock
23.2
18.6
19.5
16
3.4
34
28
13.7
12.6
13.1
12.0
13.0
15.5
13.0
17.0
32.0
NA
24.5
24.5
19.5
19.5
6.0
35.5
28.5
14.0
14.0
14.0
12.5
14.0
16.0
13.5
17.8
32.5
NA
Organic
Carbon
84.0
77.0
---
74.W
71.0
157W
---
160^
250t
75W
123L
123
220
248
220
240
NA
Fe
mg G-1
19.0
22.0
18.0
18.5
8.5
66.0
68.0
60.0
14.2
36.0
58.0
49.0
75.0
75.0
97.0
121.0
51.0
Mn
mg G-1
1.5
1.05
.8
.75
.56
4.0
3.8
1.95
0.25
0.46
0.97
1.27
3.8
7.5
0.7
1.05
0.93
mg
1.
1.
1.
1.
7.
10.
9.
2.
2.
6.
4.
3.
3.
2.
2.
1.
P
G-1
95
60
75
.80
63
6
.0
.3
.85
40
0
5
8
5
6
5
31
Atomic Ratios
Fe/Mn
12.5
20.7
22.1
24.3
15.0
16.2
17.6
30.3
55.9
77.0
58.8
38.0
19.4
9.8
136.0
113.0
54.0
Fe/P
5.4
7.7
5.7
5.7
7.5
4.8
3.8
3.6
2.8
8.3
5.4
6.1
10.9
11.9
20.5
26.3
21.6
Mn/P
0.44
0.37
0.26
0.24
0.50
0.30
0.22
0.12
0.05
0.11
0.09
0.16
0.56
1.21
0.15
0.24
0.39
* Surficial sediments collected by dredge except Mendota (top 5 cm of cores at overturn).
** Firefly Lake formerly called Weber Lake.
t 15 meter sample from East Basin used for organic C (Williams et aj. , 1970).
t Value for edaphically, morphologically similar Crystal Lake (Williams et a_L , 1970).
Data source: B-Bortleson (1970), BL-Bortleson and Lee (1972), K-Kjensmo (1967), L-Larsen et al_. (1980),
W-Williams et a]_. (1970), WW-Waddington and Wright (1974) except for organic C.
31
-------
relative tendencies of these two elements to be immobilized by sedimentation.
High drainage basin pH's (calcium related), low concentrations of dissolved
humic coloring material in drainage streams, low erosion rates, and selective
enhancement of the soluble phosphate flux via agricultural fertilization or
sewage additions all act to decrease the Fe/P ratio by enhancing the drainage
basin flux of P relative to Fe. The Fe is contributed by erosion of elastics
(calcareous agricultural soils) or acidic chemical weathering involving humic
materials (Northern Highlands). In the lake environment, high pH favors
selective precipitation of Fe because phosphate sorption (on Fe(III) oxides)
is unfavorable under alkaline conditions. Detrital apatite is unimportant in
the phosphorus economies of calcareous lakes. In non-calcareous sediments it
may slowly dissolve and release a Fe-active P component.
Within the lake the sediment resources of "potentially mobilizable" Fe
and P usually increase dramatically in proceeding from the shallow to the
deepest water sediments. The effect of overlying water depth is particularly
striking in the final few meters. In those non-calcareous lakes that have
received study the potentially exchangeable Fe/P ratio also shifts
dramatically downward as the deep hole sediments are approached. In the
calcareous lakes that have received study the reservoir of exchangeable Fe and
P increases with depth but at a lesser rate than the non-calcareous lake
class. Importantly, the Fe/P ratio is little affected, if at all.
3. Sediment Release of Dissolved Inorganic Phosphate
a) Fickian Diffusion Model. In principle the diffusion flux of
phosphorus and other sediment solutes across the sediment-water interface can
be described by Pick's first law,
, (z) _ K (z) Ts
Js ~ Ks fi
where J has units: mM solute S cm-2 s-1, K is the effective diffusivity for S
along the z axis (units: cm2 s-1) and Ts/Tz is the solute concentration
gradient applicable to the interface. [In practice difficulties arise from
trying to estimate the effective diffusivity and concentration gradients at
the interface.] The Fickian model shows that flux is proportional both to the
mixing intensity and the solute concentration gradient. Modeling sediment P
release over space and time, thus, depends on knowledge of environmental
control over these two parameters.
The concentration gradient depends on the solute concentration in the
overlying water and the concentration in the sediment interstitial water. The
latter is usually more important in determining the gradient. The
interstitial inorganic phosphorus (IIP) concentration depends on the
stoichiometric balance between Fe and P, redox, temperature, and diffusivi-
ties, at the interface, in the overlying water, and in the bulk sediment. The
factors are inter-related. First I present a chemical model for interstitial
phosphorus and Fe concentrations.
32
-------
b) Chemical Factors Controlling Sediment Intersitital Phosphate
and Fe(II) Concentrations. The importance of sediment redox potential on Fe,
P, Mn, and Si02 sediment mobility was shown in the classical studies of
Einsele (1936; 1937; 1938) on the non-calcareous Schleinsee in southern
Germany and Mortimer (1941; 1942) on non-calcareous lakes of the English Lake
District. When Eh falls below ~+100 mv associated with the disappearance of
detectable dissolved oxygen, Fe(III) present as amorphous hydrous oxide
(CDB-Fe or oxalate-Fe fractions) is reduced and Fe(II) comes into solution.
The solubilization of Fe also solubilizes the associated inorganic phosphate.
Under low redox, interstitial concentrations of Fe(II) and P04 increase
jointly until a solubility product involving reduced Fe is exceeded. The
stoichiometric balance between Fe(II) and P04 in the interstitial water
depends on the Fe:P stoichiometry of the oxidized iron undergoing reduction
and dissolution, pH, and the availability of H2S for forming FeS as a Fe(II)
sink.
Ferrous iron readily precipitates with H2S to form amorphous FeS, and the
more highly ordered mackinawite (FeS), at pH's near neutrality (Einsele, 1938;
Berner, 1964; 1967; 1970; Nriagu, 1968; Davison and Heaney, 1978; Stauffer and
Armstrong, 1980a). In the presence of S° formed by partial H2S oxidation,
these kinetically unhindered sulfide precipitates undergo a slow diagenesis to
pyrite (FeS2) which is a final stable iron reservoir in reducing environments
(Berner, 1970). At pH 7.3 (a value representative of late summer conditions
in the benthic hypolimnetic boundary layers of stratified calcareous lakes
(Stauffer and Armstrong, 1980a) chemical equilibrium with respect to amorphous
FeS implies only 12 pg Fe(II) L-1 present associated with 3.2 mg S(-II),
actual late summer deep water concentration (Delfino, 1968; Stauffer and
Armstrong, 1980a). Furthermore, pH's in the benthic hypolimnion boundary
layer of bicarbonate-buffered non-calcareous lakes undergoing sulfate
reduction increase to a value close to 7.15 (Davison and Heaney, 1978;
Stauffer and Armstrong, 1980a) because of alkalinity increases associated with
sulfate reduction (Goldhaber and Kaplan, 1973; Berner, 1970; Scholkovitz,
1973). Thus, for bicarbonate-buffered benthic environments, pH>6.5 and
usually >7.0; both FeS solubility product considerations, and broad environ-
mental experience (Stauffer and Armstrong, 1980a) prove that such anoxic
hypolimnion waters can be classified as either sulfide rich or Fe(II) rich,
but never simultaneously rich in both Fe(II) and total dissolved sulfide.
After the onset of anoxia the concentrations of Fe(II) and/or P04
increase until finally the ion activity product of Fe(II) and P04 exceeds the
solubility product of a kinetically unhindered reduced iron phosphate mineral.
Further increase in interstitial water concentrations of these solutes then
stops. Vivianite, Fe3(P04)2v8H20, is the least soluble reduced iron phosphate
mineral. Because its formation is frequently kinetically hindered, reduced
surficial lake sediments normally attain a metastable equilibrium with some
unidentified amorphous gel-like solid phase which is more soluble than
vivianite. In accordance with the solubility product principle, interstitial
water equilibrium with respect to reduced iron phosphates can be attained for
infinitely varying Fe(II)/IIP ratios. If the concentration of Fe(II) is held
low by significant H2S at near neutral pH's, the IIP concentration will be
high. Conversely, high Fe(II) concentrations imply lower IIP at constant pH.
If the pH drops, the concentrations of both Fe(II) and IIP must rise to
33
-------
satisfy the iron-phosphate and_FeS solubility products because of increasing
protonation of the P0| and HS ions as H increases. Lowering the pH's can
preclude attainment of FeS equilibrium for the available H2S supply (see
below) and thus uncouple Fe from its sulfide control. Acidic conditions thus
mobilize both Fe(II) and P04 simultaneously in the sediment environment (c.f.
Patrick et aj. , 1973). Lower pH accounts for the coexistence of high con-
centrations of both H2S and Fe(II) in mildly acidic (pH 5 to 6) lakes with
acid-bog drainage in the Northern Highlands region of Wisconsin (Stauffer and
Armstrong, 1980a). Meromictic Lake Mary is an example.
For pH's >7.0, the Fe(II) vs. H2S "chemical exclusion principle" dictates
that the interstitial dissolved Fe/P crossing the sediment-water interface
depends on the rate of production of H2S accompanying sulfate reduction as
compared to the rate of supply of Fe to the interface. If sedimentation of
drainage basin export Fe(III) is unimportant during stratification (this was
shown to be true for seepage and drainage lakes in the Midwest during the
typical summer) then the Fe can only be supplied from below the sediment-water
interface.
Einsele (1938) showed that the oxidation of 10 mg L-1 Fe(II) to Fe(III)
at pH 6 to 7 in the presence of 5.5 mg L-1 P04-P resulted in the formation of
a yellow-white ferriphosphate precipitate of strengite-1ike composition (Fe/P
= 1:1). These experiments were performed both in lake and artificial water
systems with realistic bicarbonate buffering and Fe(II) initial concentrations
ranging up to -10 mg L-1. The experimental domain was high but still
representative of some reduced hypolimnetic and sediment interstitial waters.
Furthermore, if Fe(III) as chloride salt solution was added to an adequately
buffered natural water containing P04 the result was stoichiometrically the
same. However, if Fe(III) was added to buffered water, or if Fe(II) was
allowed to oxidze in the absence of P04, and immediately following the
formation of the brownish hydrous Fe(III) oxide, P04 was added, the atomic
Fe/P stoichiometry of the precipitate was changed to ~6:1 at pH's near
neutrality. The adsorption precipitate did not alter to the ferriphosphate
composition with aging. These observations by Einsele, and his related
observations on FeS formation, are probably the most important chemical
observations ever made on lakes. Tessenow (1974) conducted similar experi-
ments using lower Fe(II) and P04 initial concentrations (1-2 mg L-1) and
obtained a precipitate with Fe/P = 1.7 at neutral pH. The ratio shifted
slightly (to 1.8) at pH = 8.0. The precipitate was interpreted as approaching
Fe2(OH)3P04 composition.
Based on the work of Einsele (1938), and the more conservative findings
of Tessenow (1974), iron can quantitatively immobilize P04 as ferriphosphate
in the upper water oxidation zone only if atomic Fe/P > 1.8. In other words,
the potentially free migrating P04 (in terms of Fe chemical control) is given
approximately by:
P°4-p(free) = P°* (initial) ' °'55 Fe(n>(initial): if the R'H-S^°
= 0:otherwise (actually a few pg L-1)
34
-------
The above equation is inaccurate for very low initial concentrations
because the P04 concentration never falls completely to zero (Stauffer and
Armstrong, 1980a).
c) Seasonal Model of Sediment Interstitial Fe and P Concentrations.
The foregoing principles can be used along with other environmental variables
to model sediment interstitial chemical composition on a seasonal basis. This
chemical model provides insights into experimental studies of sediment release
of P and lake budget studies on the ultimate fate of released P in the
overlying waters. First, it is important to recognize that the sediment-water
interface is not a razor-sharp diffusion boundary but rather a micro-
stratified chemical interaction zone, whose thickness and position changes
with season.
Assume, initially, following Mortimer (1971), that the "surface oxidized
layer" is 1 cm thick, i.e., Eh falls to 0 mv at this level and, hence oxygen
diffuses in 1 cm before being completely consumed. These conditions apply to
mesotrophic Lake Windermere during winter (T , = 4°C). If these same sedi-
ments are close enough to the lake surface to oe warmed to 24°C accompanying
subsequent summer stratification, then, still assuming molecular diffusion
rates, the new oxidized microlayer will have been reduced to 1-2 mm thickness.
This reduction occurs because the temperature change decreases saturation
oxygen concentration in the overlying water but enhances the 02 diffusion rate
commensurately (Lerman, 1979, p. 96). Meanwhile the rate of sediment BOD
increases by perhaps an order of magnitude. The seasonal temperature shift
alone has moved the upper boundary of the sediment reduced zone much closer to
the sediment-water interface.
Now assume that algal production in the trophogenic layer commences and
loads the surface of the sediment with readily decomposable organic matter.
[Burns and Ross (1972) described algal-organic mats up to 2.5 cm thick being
laid down on the surface of Lake Erie's Central Basin sediments.] The new
organic layer adds an organic mat interface above the pre-existing historical
sediment-water interface, and vastly increases the BOD rate at the new
interface. The increase in "system" BOD rate is large because oxidation is
"zero order" with respect to 02 until low concentrations are reached, and
because the BOD of the historical sediments involves relatively refractory
organics (that is why they are still around). Because the only oxygen source
in the sediment-water "system" is the bulk water column, the 0 mv Eh boundary
shifts upward to the upper levels of the organic layer. Below this level S04
reduction commences in the middle-lower parts of organic layer, as S04 is the
preferred electron acceptor after the consumption of initial 02 and minor
amounts of N03. Sulfate reduction is thus imposing a sulfide layer between
the Fe-rich historical sediments and the overlying water column. Phosphate is
generated in this multi-layered system both by mineralization of the organic
matter (Richards, 1965; Richards et a 1. , 1965) and diffusion up from the bulk
historical sediments. Because the deposited algal remains are rich in P (~1%
dry wt, Redfield et al. (1963)) but contain negligible Fe, remineralization
yields a very low Fe/P ratio. Furthermore, the sulfide layer intercepts
Fe(II) diffusing along with IIP from the sediments and precipitates it
selectively as FeS. Phosphorus produced by remineralization is physically
remote from a potential Fe interaction zone and IIP diffusing upward is
35
-------
liberated from its earlier Fe association. The overall result is a release of
P into the bulk water column unassociated with Fe, and its relatively rapid
transport up through the water column. This release occurs even if the
overlying water column is saturated with dissolved oxygen!
The above scenario can be modified to reflect varying temperature
conditions, eddy diffusivity rates for 02 in the bulk water column, different
02/S04 initial ratios, and varying organic deposition rates. Because 02 is
completely consumed before S04 reduction commences, a high 02/S04 initial
ratio may limit the sulfide production rate below the interface. Also colder
water temperatures following complete fall turn-over will displace the sulfide
boundary deeper into the sediment for reasons specified earlier. In marine
waters (very high S04) the organic deposition rate is the critical parameter
limiting sulfide production in the upper sediments. In sulfate-poor lakes in
crystalline drainage basins the low S04 concentration in the overlying water
(~3~5 mg L-1) is limiting unless the lake is unproductive.
If the 0 mv Eh potential is near the surface of the historical sediment
but the sulfate reduction rate is low, Fe(II) will come into solution in
larger quantities than can be precipitated by the available H2S supply.
[Lowering the pH serves to decrease the effectiveness of the available H2S
supply.] In such cases the Fe/P ratio diffusing across the sediment-water
interface may closely approximate the interstitial Fe/P ratio in the absence
of sulfide influence. The ratio may approximate the CDB-extractable Fe/P
ratio of the sediments, or be skewed if vivianite or similar minerals are
forming with fixed compositions. In non-calcareous sediments the vivianite
reaction will lead to interstitial Fe/P ratios that are larger than CDB or
oxalate extractable Fe/P. In lake sediments with abundant FeS, P04 can
"dominate" Fe(II) in the surficial sediments and vivianite formation can
decrease the interstitial Fe/P ratio. Sediment composition (the potentially
mobilizable Fe and P fractions), temperature, pH and rate of sulfide produc-
tion are clearly the important variables determining the sediment Fe/P release
ratio.
The "sulfide intercept" model just described may surprise some lim-
nologists who are used to thinking rigidly of the "surface oxidized
microlayer" as a "diffusion barrier" to phosphate release. The diffusion
barrier model described by Mortimer (1971) is just the high Fe-low sulfate
reduction end member condition of a much more general and valid model of
sediment diagenesis. Stuiver (1967) showed that significant sulfate reduction
occurred in the Linsley Pond (Connecticut) hypolimnion before the hypolimnion
became anoxic. Einsele (1941) showed that fertilization of the non-calcareous
Schleinsee with P04 caused a marked increase in organic production and hence
an earlier onset of hypolimnetic anoxia as compared to prior years. However,
the hypolimnetic release of Fe(II) decreased by 67% because of the formation
of FeS stimulated by S04 reduction. These observations led Hasler and Einsele
(1948) to propose lake fertilization with sulfate to stimulate P04 return from
the sediment without associated Fe(II). This potentially uncouples the P
cycle from its Fe-oxidation immobilization during the overturn. Ohle (1954)
reiterated the theme. Hutchinson (1969) noted that enhanced sulfate reduction
in Linsley Pond in recent years had accompanied post 1930's increases in lake
sulfate content, a downward shift in the hypolimnetic Fe(II) release rate, and
36
-------
a pronounced upward shift in the H2S and P04-P accumulation in the summer
hypolimnion. More recently Stauffer and Armstrong (1980a) have shown that the
Fe/P ratio of all calcareous lakes, and productive non-calcareous lakes,
shifts downward during the summer as compared to winter stratification, and
that the sulfuretum principle accounts for the especially high trophic
efficiencies of calcareous lakes, generally. It has long been held that
sulfide immobilization of Fe accounts for the high P04 contents of anoxic
coastal fjords, ocean trenches and marine sediment interstitial water. The
sulfuretum principle is probably partly responsible for the productivity of
marine estuaries.
Studies of the sulfate-sulfide budgets of Lake Mendota (Nriagu, 1968;
Stauffer and Armstrong, 1980a) and additional hypolimnetic sulfide data
reported by Delfino (1968) and Delfino and Lee (1971), show that production of
H2S at the sediment-water interface is sufficient to ensure a net hypolimnetic
(z>15 m) accumulation of 10-15 g S(-II) m-2 in the two month period following
mid-July each year. This accumulation does not include sulfide formed but
then oxidized by oxygen diffusing through the thermocline, nor sulfide
immobilized as FeS and FeS2 during the stratification period. However, the
Mendota hypolimnetic accumulation is three times greater than the known
sedimentary accumulation rate of FeS on an annual basis during the post-
cultural period (Nriagu, 1968). Furthermore, the hypolimnetic excess is
stoichiometrically (FeS) equivalent to al1 of the oxalate Fe fraction
(including pre-existing FeS) in the top 3-4 cm of the hypolimnetic sediments
of the lake. The sulfide production situation in Lake Delavan is even more
extreme; hyoplimnetic concentrations at summer's end exceed 6 mg L-1 (Stauffer
and Armstrong, 1980a). Sediment Fe capacity considerations thus conclusively
show that H2S production overwhelms Fe by a huge margin in the calcareous
drainage lakes of southern Wisconsin. Furthermore, studies of sediment
interstitial waters both in Mendota and the eutrophic calcareous Greifensee
(Switzerland) show that sulfide production exceeds the potential Fe(II) dif-
fusion rate in the upper 2 cm of the sediment by two orders of magnitude
(Stauffer and Armstrong, 1980a)! The calcareous drainage lakes are thus
"Sulfuretums". The same applies to mesotrophic calcareous seepage lakes
(Stauffer and Armstrong, 1980a).
Under winter ice conditions sulfate reduction is low because of the very
much reduced BOD loads placed on the deep-water sediments. Near the end of
the ice-cover period we thus expect and find higher Fe/P ratios in the benthic
boundary layer of calcareous lakes than during summer stratification (Stauffer
and Armstrong, 1980a). This seasonal shift also applies to highly productive
non-calcareous lakes. The ol igo-mesotrophic clear water non-calcareous lakes
of Northern Wisconsin have very low summer sulfate reduction rates because of
limited S04 concentrations in the overlying waters (4 vs. 30 mg L-1) and/or
the much lower primary production-organic sedimentation rates as compared to
the calcareous lakes (Stauffer and Armstrong, 1980a).
In completely oxidized littoral zone sediments P04 adsorption-desorption
can control interstitial water concentrations and release into overlying
water. The high pH's and low overlying water concentrations (P04) encourage
release during the summer. The low concentrations in the overlying* water
37
-------
necessary to support a concentration gradient are maintained by algal uptake.
Release is most efficient with calcareous phosphate-enriched naturally Fe-poor
sediments like Lake Wingra (Bannerman, 1973).
d) FeS and Sediment Extraction Schemes. The extractable sediment
Fe/P ratios reported in Table 2 are misleading because they depend on
procedures which were originally developed for aerated soils, not sediments;
the extraction classification ignores the very important competitive (vs.
P04-P) complexing of Fe by H2S in anoxic lake sediments. Williams et ajL
(1971c) noted that oxalate extracts amorphous FeS, hence so does CDB (because
CDB-Fe nearly equalled oxalate-Fe in calcareous sediments rich in FeS).
Because Nriagu (1968) found that most sedimentary reduced sulfur in the post-
cultural deep water sediments of Lake Mendota is present as FeS (not pyrite),
the oxalate of CDB-Fe fractions estimate mainly FeS for the sulfur-rich gytta
sediments in the calcareous drainage lakes. This is important because FeS has
no affinity for P04. Nriagu (1968) reported that fully 27% of the total Fe in
Mendota1 s post-cultural deep water sediments is tied up as FeS on an annual
basis. Subtracting the FeS fraction from the oxalate-Fe reported for these
same sediments by Williams et al. (1971c) leaves only 8-22% of the total Fe
reservoir as the potentially phosphate-active iron fraction. Assuming an
intermediate percentage (15%) I calculate an atomic: (oxalate-Fe minus FeS)/
CDB-P = 2.2 for Mendota instead of the 6.1 misleadingly shown in Table 2.
e) Measurements of Sediment Phosphorus Release. Direct measurements
of sediment phosphorus release have been made either i_n situ using "sediment
release chambers" (Sonzogni et aj. , 1977; Larsen et al. , 1980) or in the
laboratory using incubated sediment-lake water columns (Holdren and Armstrong,
1980). The laboratory technique, while seemingly less direct, is actually
much more useful, both because it is cheaper, and because the pertinent
environmental variables can be carefully manipulated and controlled to deter-
mine factor dependency of phosphorus (and other solute) release. [Note: It
is important that lake water be used from the lake studied to preclude
"unnatural" sediment-water chemical interactions.] The laboratory technique
thus allows scientific exploration of a wide diversity of sediment-water
environments, both germane to the heterogeneous sediment environments of a
given lake, and potentially duplicative of remote or potentially existing
(after lake change or dam construction, for example) lake sediment environ-
ments. For these reasons, and because of the extraordinarily interesting
results, the recent study of Holdren and Armstrong (1980) deserves extensive
comment and interpretation.
Holdren and Armstrong (1980) showed decisively that epilimnetic (3 to 6 m
overlying water depth) sediments of calcareous drainage lakes (Wingra and
Mendota) differed markedly from the non-calcareous lake sediments (Minocqua,
Little John, Northern Highlands region) in terms of oxic SRP release rates.
Laboratory attempts to reproduce truly anoxic conditions using N2 flushing
were not successful, as residual 02 concentrations <0.8 mg L-1 always resulted
in the overlying water. Previously, Mortimer (1941; 1942) experienced some
difficulty in maintaining a truly anoxic environment in the laboratory.
38
-------
For the non-calcareous lake sediments, lowered redox (overlying water)
was a necessary condition for observing significant sediment P release. At
16-18°C oxic release rates were <0.6 mg SRP m-2 d-1, and usually significantly
lower. Furthermore, as initial SRP concentrations in the overlying waters
were low, final concentrations were < 40 mg P m-3. Slightly higher release
rates (up to 3.8 mg SRP m-2 d-1 at 16~18°C) were obtained under N2 atmosphere
(but retaining 0.8 to 3.9 mg 02 L-1). Release rates were negligible for water
temperatures of 3-4°C, even if initial overlying water concentrations were < 1
mg m-3.
For the calcareous lakes the results were entirely different. Sediment P
release increased dramatically with increasing core temperature and especially
with level of benthic invertebrate activity. Invertebrate active Mendota
cores collected throughout midsummer of two different years, and incubated at
environmentally representative temperatures of 21-23°C, released vast
quantities of SRP (20 to 83 mg P m-2 d-1), irrespective of stirring rate of
overlying water 02 concentration. However, in the presence of the biocide,
formalin, the oxic release rate (23°) dropped from 25 to 0.7 mg P m-2 d-1 in a
specific core-core comparison. Final SRP concentrations in the oxic overlying
water reached 688 mg m-3! The IIP concentrations in the summer collected
cores were generally high (>1000 mg IIP m-3). [Note: These cores came from
the epilimnion.]
By contrast, Mendota cores collected in midwinter and incubated at 2-4°C
slowly liberated SRP (0.56 mg P m-2 d-1), if overlying water SRP concentra-
tions were initially low (<55 mg m-3; this is low for Mendota during turn-
over). If initial overlying water SRP concentrations were higher (>100 mg
m-3, or representative of mean lake conditions after fall turnover), core SRP
release rates were negligible or even negative (as low as -2.0 mg P m-2 d-1).
The sediments during the winter resting period had the capacity to remove P.
Sediment IIP concentrations were also generally low (20 to 25 mg IIP m-3) in
the winter. Cores collected in late April and incubated aerobically at
intermediate temperature (9.5°C) acted similarly to the winter cores.
Moderate stirring of the overlying water decreased winter and spring core
release rates (or even turned them negative) but accelerated summer oxic
release rates.
Lake Wingra was similar to Lake Mendota except that the summer oxic
release rates were much lower (2.5 to 3.0 mg P m-2 d-1). Initial sediment IIP
levels were also much lower (~29 mg m-3) in these shallow (3.5 m) wind
disturbed sediments. The IIP levels in the Lake Wingra incubated cores rose
to 150 to 490 mg m-3 during the course of the incubations.
Specific weather factors probably influence the Wingra-Mendota release
comparison. The Wingra sediments were gathered on 28 June 1974, following
cold and windy May-June months. Conversely the Lake Mendota cores were
obtained from 5.5 to 6 m water depth in mid July-mid August of 1973 and 1974.
The wind energy drops off in these months, both in these and the normal years
(Stauffer, 1980b), and 5 to 6 m is close to the breeze thermocline position.
It is also worth noting that the Mendota release rates from July 1973 were
threefold higher than July 1974. The warm summer of 1973 was noted for its
high epilimnion P04 contents and algal standing crops following the extra-
39
-------
ordinarily high drainage basin export of P during the wet spring months and
low April-May phytoplankton activity. It is thus apparent that greater
over-lying water depth, warmer calmer antecedent conditions, and an
accelerated organic deposition rate in the 1973 mid-summer period, could be
contributing to an order of magnitude higher Mendota release rate as compared
to Wingra release rate.
The non-calcareous lake sediment release rates of Holdren and Armstrong
(1980) agree with Sonzogni et aj_. (1977) and Larsen et a\_. (1980) observations
on Shagawa Lake, Minnesota and Mortimer's (1941; 1942) experience with Lakes
Windermere and Eswaithe Water in the non-calcareous English Lake District.
These Fe-rich sediments release negligible SRP under aerobic conditions.
The measurements of sediment P release by Holdren and Armstrong (1980)
conform closely to expectations based on the previously discussed "mechanistic
boundary layer model" involving sulfide inactivation of Fe(II). The model
predicts high aerobic release rates for high antecedent organic carbon loading
on the sediment, and high temperatures. These conditions correspond closely
to the mid-summer measurements on Mendota (especially 1973). The importance
of the invertebrates is that they increase the effective surface area of the
sediment-water interface with their burrowing, while preserving the sulfide
barrier near the channels necessary to immobilize Fe(II) and preserve SRP in
solution once it encounters 02. Goldhaber et a^. (1977) have described
sediment pyrite formation adjacent to the burrows of marine bio-turbated
sediments with appreciable organic loadings. Bio-turbation perforates the
sediment boundary and extends it, but preserves the sulfide microlayer
"structure" of the sediment benthic boundary layer. Resuspension of sediments
by violent stirring in the presence of 02 indiscriminately destroys the
sulfate reduction zones in the benthic boundary because the sulfate reducers
are obligate anaerobes and are inhibited by such randomized perturbations of
the sediment environment. Both the model and actual observation converge on
the P release suppression effect of violent stirring. In strictly anoxic
chambers stirring enhances SRP release because SRP retention in the overlying
anoxic water does not depend on immobilizing Fe(II) as FeS. This explains
Spear's (1970) anoxic experiments on Lake Mendota sediments, and is compatible
with the experience of Mortimer (1941; 1942), who found that SRP was quickly
precipitated (by oxidizing Fe(II)) if dissolved oxygen was let into a
previously anoxic system.
The IIP measurements of Bannerman (1973) and Holdren and Armstrong (1980)
during winter vs. summer are compatible with the sulfide inactivation model.
Table 5 shows that during summer sulfide suppresses Fe(II) and ensures a low
interstitial Fe/P ratio in calcareous lakes, but not the Fe-rich sulfide poor
non-calcareous lakes. Serruya et al_. (1974) made similar observations on
calcareous Lake Kinneret; Emerson (1976) observed sulfide inactivation of
Fe(II) in the Greifensee. The model applies to epilimnetic sediments under
02-saturated overlying water if the organic sedimentation rate and sediment
temperature are high enough.
In mid winter and early spring sediment-water relations suggest
adsorption-desorption behavior of oxidized sediments. The winter sediment-
release behavior of Mendota and Wingra sediments suggests a SRP "cross-over"
40
-------
concentration of 50 to 100 mg SRP m-3. This is representative of equilibrium
concentrations found both by Mayer and Gloss (1980) and Schroeder (1976). The
implied low "cross-over" concentrations for the Fe-rich Northern Highlands
lake sediments are consistent with the edaphic conditions in that nutrient-
poor area.
Table 5. Fe/P Gradients in
Calcareous (C) vs.
the Benthic Boundaries of Stratified
Non-Calcareous (N) Lakes.
Level*
(cm)
-2 to -35
+1
+3
+5
+45
Fe/P (Atomic)
Greifenzee
0.06
0.08
0.56
6.0
63.0
(C)
E
E
E
E
E
Mendota
0.04
0.08
0.17
0.24
""
(C)
S
H
H
H
Minocqua
19.4
34.0
34.0
65.0
""
(N)
S
H
H
H
Notes:
* Zero at sediment-water
E: Emerson (1976)
H: Holdren (1977)
S: Stauffer (unpublished)
interface; values increase downward into sediment.
F. Factor Interactions Among Lake Morphometry, Seasonal Stratification,
Sediment-Water Interactions and Redox
1. Hypolimnetic Volume Development
The activity of the sediments in the internal phosphorus cycle of a lake
depends on lake basin morphometry and the superimposed seasonal cycle of
thermal stratification. One important measure is the ratio of main or storm
thermocline depth to lake mean depth (Figure 15). If the lake is shallow and
expansive (large fetch and A ) and set in a windy climatic regime, then the
potential thermocline depth may be deeper than the maximum lake depth. This
is true of Lake Winnebago, Wisconsin (A = 55,730 hectares; z 6.4 m). In
o max
this situation (diagrammetrically shown in Figure 15A), the sediment-water
interface everywhere has the temperature, pH, and redox condition of the mixed
layer. Typically, this implies warm (22 to 25°C) alkaline (pH 8 to 10)
aerobic conditions, a high organic carbon sedimentation rate (if the lake is
productive) and release of sediment nutrients directly into the trophogenic
layer.
As the lake progressively deepens, the main thermocline depth will form
above the deep water sediments fijst as shown in Figure 15B, and finally as
shown in Figure 15C. Clearly, as z increases, the distance from the sediment-
water interface to the thermocline boundary increases, the hypo!imnetic volume
41
-------
22*
T(z)
SEDIMENT 22'
Om
8m
Main Thermocline
12m
B
10° SEDIMENT
i Main Thermocline.
V = 1108.8
M
c
SEDIMENT
'40m
Figure 15. Schematic cross sections for lakes.
42
-------
13° 15° 19° 22° c
14m
13° 15° 19° 22° c
14m
Figure 15. (continued)
43
-------
increases, and the temperature of the deep-water sediments decreases
asymptotically to 4°C, both because of the delayed onset of the 4° isothermal
condition after ice-out (see Section II-C), and because heat transported
through the main thermocline is dispersed into a much larger water volume.
The lower temperatures (closer to the 4° maximum density point for pure
water), and decreasing temperature gradients (3T/3z) in the deeper lakes
hypolimnion, imply low density stabilization of the deep hypolimnion and
hence, enhanced rates of eddy diffusivity (Quay et aj. , 1980; Li, 1973;
Stauffer, 1980hi). For Green Lake 9T/8z approaches 0.01°C m-1 and K
increases by two orders of magnitude at 50 m as compared to the thermoclinl
(Stauffer, 19801). This enhanced vertical transport rate, coupled with lower
sediment temperature and the increased initial oxygen storage (proportional to
Vu), Imply that the pelagic sediment surface of deep water lakes will remain
aerobic even late in the stratification period. This will be true even if the
productivity of the mixed layer and organic sedimentation rate are the same
for all three scenarios (Figure 15A-C).
In the well-mixed scenario (Figure 15A) sediment release of P is enhanced
by the high temperature, high pH, high organic sedimentation rate, biological
utilization of P in the overlying water, and effective stirring rate above the
sediment. However, as shown by Holdren and Armstrong (1980), and inferred
from the sediment chemical exchange model proposed in Section II-E, aerobic
sediment release of P is effective only for the calcareous lake or marine
sediments. During the summer, immobilization of Fe(II) by sulfide results in
a low Fe(II)/IIP ratio in the surface sediment interstitial water of these
alkaline Fe-poor lake sediments, as shown by Holdren (1977) and Bannerman
(1973) for the Yahara Chain lakes in Madison, and by J. Wiersma (personal
communication, University of Wisconsin-Green Bay) for calcareous Lake
Winnebago sediments. The periodicity in the windpower time series associated
with cold fronts (Stauffer, 1980b) affects P release from shallow water
sediments by interspersing low power periods with high power periods. During
low power, concentrations of IIP build up in the surficial sediments; the high
power acts to release this suddenly to the overlying water where it is
utilized by the algal standing crop. In non-calcareous lakes the high
interstitial Fe(II)/IIP ratio acts to immobilize the P accompanying transport
and Fe(II) oxidation, and prior to algal utilization.
In the intermediate depth scenario (Figure 15B), aerobic sediment P
release is potentially slower than in Figure 15A because of the colder
temperature (~10°C). However, the restricted size of the hypolimnion implies
that anoxia sets in early in the stratified period. During the anoxic period,
sediment release of P is accelerated, especially for non-calcareous lakes. In
calcareous lakes, the sulfide interception of Fe(II) again leads to a very low
Fe/P ratio in the hypolimnion. Because of this low ratio, P is transported by
eddy diffusion away from the sediment-water interface and up into the
thermocline region. In the absence of Fe there is no important chemical
mechanism for P reprecipitation even in the oxic metalimnion. The rate of P
transport through the thermocline depends on the metalimnetic P gradient and
the eddy diffusivity for solutes. The metalimnetic P gradient will be
negligibly small if the euphotic zone overlaps the main thermocline. This
happens in small calcareous seepage lakes and in Green Lake, Wisconsin in late
summer (Stauffer, 1980hi). Non-calcareous lakes of intermediate depth
44
-------
accumulate P in the hypolimnion only after the onset of anoxia! Release of P
(and Fe(II)) occurs at the anoxic sediment-water interface. These solutes
migrate upward by eddy diffusion until dissolved oxygen is encountered. The
oxygen oxidizes the Fe(II) and causes chemical reprecipitation of the P (see
Section II-E).
In the deeper lakes hypolimnetic volume development is great enough so
that this layer never goes completely anoxic (unless the lake is meromictic
like the Black Sea). Sediment phosphorus release and storage in the oxic
hypolimnion of a non-calcareous lake is never important. In calcareous Green
Lake large quantities of both SRP and Si02 are released into the hypolimnion
and stored until fall turn-over (Stauffer, 1980i).
2. Effects of Sediment Contact Area at Intermediate Depths
The scenarios in Figure 15A-C portray a steep sided lake with little
sediment-water contact area until the flat floor of the pelagic basin is
reached. Clearly, z/z is close to unity, and much larger than the ratio
fflSX _ _
0.5 or less found for most lakes. Large z and z/z__u values are typical of
fflclX
lakes occupying caldera and tectonic grabens (c.f. Hutchinson, 1957). Deep
graben lakes (Lake Tahoe, California) and caldera lakes (Crater Lake, Oregon)
are typically infertile because of the restricted drainage basins, and the
remoteness of the deep-water sediments from the trophogenic layer. As the
depth increases we have, in the limit, the one-dimensional model of the
infertile tropical ocean. For shallower lakes with sediment "shelf" areas we
must consider sediment contact area at the intermediate water depths.
Consider a partition of lake volume and associated sediment contact area
accomplished by truncating horizontal planes positioned at integral meter (j)
depths below the lake surface elevation. Define the ratio: RA(j) =
A (j)/A(j), as the sediment contact area divided by the lake area exactly j
miters below the surface. Because the layers are exactly 1 m thick, RA(j) is
also the ratio of sediment contact area to water volume for the jth element of
the depth partition. Also, the inverse of RA(j) is the number of cubic meters
of layer slice volume in contact with 1 m2 sediment contact area. The RA(j)
values are measures of potential sediment-water interactions for different
lakes, and for different depth zones within the same lake. For a vertically
sided lake the RA(j) ratios are zero until the flat bottom floor is reached,
hence there is JTO influence of sediment contact area on the water chemistries
of the intermediate layers.
Geologic processes (responsible for the origins of, and morphological
changes in lake basins accompanying lake aging) lead to important typologies
for the RA(j) vectors of many lakes. Two important morphological changes
accompanying aging are the preferential development of the littoral sediment
zone by shore reworking and macrophyte colonization, and the faster rate of
sediment filling of the deep holes as compared to the pelagic slope sediments.
As a result, RA(z) is typically moderately large for the shallower littoral
zone, then drops off to a pronounced minimum at the intermediate lake depths,
45
-------
and finally increases exponentially to a maximum value exceeding 1.0 as z
nicix
is approached. Of course, the RA(z) minimum is lower,_and the depth range of
this minimum broader, for lakes with large z and large z/z ratios.
IT13X
One common depth-dependent pattern for glacial lakes is shown in Figure
16. All five lakes have a metalimnetic minimum in RA(z). Note the prominent
littoral zone sediment contact area in Fish Lake, followed by the sharp drop
in RA(z) at the intermediate lake depths. Green Lake (see also Figure 17) has
notably low RA(z) values throughout the metalimnion and upper hypolimnion.
The minimum ratio is 0.015 at 18 m; this implies 67 m3 or volume for each m2
sediment contact area at this depth. Furthermore, RA(z) does not increase
again beyond 0.030 (the minimum RA(z) value for Lake Mendota, see also Figure
18) until a water depth of 45 m is reached. Lake Delavan is a conformal lake
basin with larger amounts of sediment contact area at all depths (see Figure
19).
Unlike the typical conformal Wisconsin kettle lake left in thick glacial
drift, or glacially dammed lakes in soft sedimentary strata (Green Lake, New
York Finger Lakes), lakes in glacially sculptured hard rock drainage basins
often have exceedingly complex, topographically aligned morphologies,
including numerous islands, irregular shorelines, and irregular isolated deep
holes. This complicates estimation of internal phosphorus supplies. Two
examples are Shagawa and Burntside Lakes in NE Minnesota in the drainage of
the Burntside River (Schults et al., 1976). Burntside Lake has at least seven
isolated prominent deep holes; Shagawa Lake has three holes set in a profundal
plane of 6-10 m overlying water depth. In vivid contrast to Lake Mendota,
Shagawa Lake has a prominent RA(z) maximum at intermediate water depths
(Figure 20). As suggested by Larsen et al. (1980) and shown by Stuaffer and
Armstrong (1980b) this metalimnetic maximum is fundamental in regulating the
magnitude and fate of internal phosphorus supplies in Shagawa Lake.
Employing the RA(z) values and pertinent data on sediment solute release
rates, it is possible to calculate the direct potential effect of sediment
release on the chemistry of each layer slice below the lake's surface. I call
the effect "direct" because it depends on release and lateral dispersion
within the layer slice and not on vertical transport (possibly impeded by
density stabilization within the thermocline). If we assume, for example, the
frequently observed anoxic sediment release rate of ~10 mg SRP m-2 d-1
(Holdren and Armstrong, 1980; Burns and Ross, 1972; Larsen et aj. , 1980), that
release rate, continuing for a week, would raise the average P concentration
at the 8 m level in Green, Mendota, Delavan, Fish, and the West Basin of
Shagawa Lake by 1.3, 2.0, 7.8, 6.4, and 70.0 mg m-3, respectively. We see that
the release contribution of metalimnetic sediments is small in the two deepest
lakes (Green, Mendota) but potentially huge in Shagawa Lake because of the
extensive sediment shelf contact area at the 8 m level.
The above analysis assumed that phosphorus, once released, acted in a
chemically conservative fashion (i.e., no biological uptake or chemical
precipitation at the 8 m level). Furthermore, a chemical profile at the deep
hole station would provide "average" layer phosphorus concentration only if
lateral transport and dispersion instantaneously equalized the solute
concentration everywhere within the layer slice. The first assumption
46
-------
035
0.30-
RA vs. Z
a DELAVAN
o MENDOTA
n GREEN
o DEVILS
FISH
0.25-
0.20-
<
CC
0.15
0.10
0.05
i
16
T~
18
i
22
T"
6
i 1 1
8 10 12
DEPTH « Z , m
14
20
24
Figure 16. Ratio of sediment contact area to lake
area for five southern Wisconsin lakes.
47
-------
o
c
n-
to
o
o
o>
Ji^
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c
Ol
0)
J-
CJ3
S-
o
Q.
03
o
S-
4->
O)
>>
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-------
< H
OC UJ
< -I
£
Jj
cc t-
1,1
UJ
1 -I
IK 2
- ,
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49
-------
in
c
o
c
m
(0
O)
CJ
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S-
o
a.
ro
u
r*
J-
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>>
-P
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s_
=>
en
50
-------
CM
s- m
o o
4- -P
(f>
(0 0)
CD C
J- C
0)
-^
m
to
m 3
* vy
51
-------
(conservatism) very nearly holds if: (1) the 8 m layer is deeper than the
true depth of the euphotic layer, hence biological uptake to support photo-
synthesis is negligible (see Section II-D); (2) the atomic Fe/P sediment
release ratio is significantly below 1.0 p_r the 8 m layer slice is everywhere
anoxic. If this latter condition is violated, oxygen will be encount'ered
during the lateral transport of P away from the anoxic sediment-water
interface. At this contact, Fe(II) diffusing with the P will rapidly
(minutes) oxidize to Fe(III) and immediately chemically bind the P04-P. The
length of time required for this initially colloidal Fe(III)-bound phosphate
to form a settlable precipitate increases (to days) as the ionic strength of
the water decreases to values characteristic of non-calcareous lakes in
northern Wisconsin, northern Minnesota and the Canadian shield region of
Canada (Koenings, 1976; Koenings and Hooper, 1976; Stauffer and Armstrong,
1980a).
The multi-stage process defined by: (1) initial sediment Fe(II)/P
release; (2) lateral diffusion away from the sediment shelf into deeper water;
(3) Fe(II) oxidation in the oxygen enriched waters furthest from the sediment
shelf; (4) Fe(III) binding to phosphate; and (5) coagulation and settling of
the precipitate into deeper water; probably explains the very great enrichment
of CDB or oxalate extractable Fe and P in non-calcareous stratified lakes of
northern Wisconsin and Minnesota. Conversely, because the sediment Fe/P
release ratio is very low in the calcareous lakes, the outlined multi-stage
process for deep sediment enrichment is less effective for those two elements
in calcareous lakes (Stauffer and Armstrong, 1980a).
3. Entrainment Transport of P Into the Mixed Layer Accompanying
Thermocline Migration
Figures 15D and E illustrate lake cross sections where sediment "shelves"
are present either in the epilimnion (3 m; scenario D) or within the
metalimnion (7 to 9 m; scenario E). Scenario D corresponds most nearly to
Fish Lake; here littoral zone sediment release of P and lateral transport into
the pelagic zone is much more important than vertical transport of P through
the thermocline during summer stratification (Stauffer, 1974; Erickson, 1980).
The dominance of lateral transport from the littoral occurs because the
littoral is extensive; vertical eddy diffusivity is very small (~10-3 cm2 s-1)
within the geographically confined and highly stabilized thermocline of this
small lake (A = 88 hectares), and because low epilimnetic total-P concentra-
tions, low wa°ter color, and a shallow storm thermocline (~5 m) combine to
allow the euphotic zone to completely overlap the metalimnion (Stauffer,
1974). Algal uptake of P in the metalimnion itself leads to low P vs. z
gradients in the upper metalimnion (Stauffer, 1974). The net effect is a
short circuiting of P directly into algae prior to its arrival in the mixed
layer.
Scenario E corresponds to the West Basin of Shagawa Lake. Initially the
mixed layer boundary (ht) is at 5 m. A severe cold front sequence then
deepens this to 9 m and cools the mean temperature of the epilimnion to ~19°C.
Such mid-summer "events" have been described for the geographically extensive,
wind-exposed West Basin by Larsen et aj. (1980) and Stauffer and Armstrong
52
-------
(1980b). Note that the large scale migration of the thermocline directly
entrains the former metalimnion water, including the solute-enriched benthic
boundary layer (~ 1 m thick) immediately above the shelf sediments (diagram-
metrically: areas A! and A2 in Figure 15E). In addition, following the usual
pattern, heat is irreversibly added by eddy diffusion to the deeper waters of
the basin (z>9 m) (c.f. Stauffer and Lee, 1973; Stauffer, 1980h; Stauffer and
Armstrong, 1980b for more detailed discussion).
Following the cold front, rewarming of the mixed layer occurs during the
low wind power interlude, a new thermocline is set up above the 5 m plane, and
the former metalimnetic shelf is again hydraulically partitioned off from the
mixed layer. However, because of the higher water temperatures and very high
RA(z) ratios (~1.0 for Shagawa West Basin metalimnion), oxygen depletion of
the 7-9 m stratum proceeds rapidly and again triggers the release of
sediment-P. If this release period is long enough, the next episode of
thermocline deepening again entrains phosphorus rich water into a mixed layer
(Stauffer and Armstrong, 1980b). In non-calcareous Shagawa Lake profile
sampling the deep holes fails to estimate the water column P "storage" in the
vicinity of the extensive shelf.
The situation in Lakes Mendota and Delavan is substantially different.
In these "sulfuretum" lakes the upper metalimnetic phosphorus gradient exceeds
100 mg SRP m-4 by late summer, irrespective of oxygen concentration in the
upper metalimnion! Furthermore, very active migration of the thermocline and
eddy diffusion through the middle of the metalimnion transports large
quantities of NH3-N and SRP in both lakes during the summer stratification
period (Stauffer and Lee, 1973; Stauffer, 1974; Stauffer, 1980h). Both
morphometric and chemical differences between these two eutrophic calcareous
lakes, and non-calcareous Shagawa Lake, de-emphasize metalimnetic contact
sediments in the two calcareous lakes. In Shagawa Lake they are critical
(Stauffer, 1980h; Stauffer and Armstrong, 1980b).
III. Estimation
A. Sampling Equipment
By connecting the intake tube of a peristaltic pump to an underwater
conductance-thermistor probe, lake water samples can be easily obtained from
thin (~5 cm) depth strata in the thermocline region and even in close
proximity to the sediment-water interface. Filtered sample splits can be
obtained on-station without air contacting the sample. The probe identifies
the i_n situ sample temperature to within ±0.01°C and the conductance to ±1
pmhos. The temperature covariate is essential for accurate descriptions of
solute transport processes in stratified lakes. The conductance can be used
as a solute covariate for rapid exploratory surveys of lake sediment shelf
areas (see later discussion).
A portable "Masterflex" peristaltic sampling pump (Horizon Ecology Co.,
Chicago, IL) is fitted with a Model 7015 pump head and si 1icone tubing. The
inlet tube of the pump-head is serially connected to 50' sections of Tygon
tubing (manufacturer recommendation, ID = 0.1925", OD = .3915"). The
53
-------
requisite number of sections depends on the desired sampling depth. The inlet
end of the Tygon sampling tube is connected to a stainless steel flow-through
weight (Horizon Co.)) which is taped to the conductance-thermistor probe of a
Whitney precision electronic conductance thermometer (Figure 21). The Whitney
cable is used for depth referencing. The pump's outlet tube is conveniently
connected via a T, plug and needle valves, Swagelok fittings, and Teflon
connecting tube, to a Nucleopore 57 mm Swin-Lok pressure filter apparatus, to
allow collection of a filtered (0.4 urn pore size) sample split within seconds
of collecting the unfiltered split, and without the water sample ever
contacting the air. The valves are used for controlling pressure across the
filter. Customized large diameter pressure-filter assemblies are required for
large sample sizes (>250 ml, Ball et aj. 1976).
The pump is rated at 700 ml min-1 when fully charged and without the
added impedance of the pressure filter assembly. From the dead-volume of the
tubing (18.8 ml m-1), the calculated water transit delay is 1.64 s m-1. The
calculated intake velocity at the two 7 mm orifices in the flow-through weight
is 15.2 cm s-1. Assuming a cone-shaped flow field with angle a=90° extending
away from the intake orifices, the calculated mean velocity through the cone's
base, 5 cm from the orifice drops to 0.1 cm s-1 (Figure 21). This value is an
order of magnitude lower than typical hypolimnetic bottom currents in Lake
Mendota (John Col man, Water Chemistry Laboratory, UW-Madison, personal com-
munication).
The Whitney thermometer probe precisely estimates i_n situ water temp-
erature at the probe orifice. The accuracy is improved by considering the
time delay for water transit through the tubing. The highly accurate and
precise estimates of sample i_n situ temperature find utility in estimating
hypolimnetic solute concentration gradients in the presence of isotherm tilts,
and in estimating eddy diffusion transport in stratified lakes (Sweers, 1970).
The accuracy and precision of the z sample coordinate depends both on the
boat being securely anchored, and also on the surface roughness. Under
optimal weather conditions the variance in z is likely to be ~1 cm2 for the
~30 seconds required to collect a 250 ml unfiltered sample at any predeter-
mined depth. Because the intake orifices of the flow-through sampling weight
generates a flow field whose axis is orthogonal to z (Figure 21), the sample
is obtained from a thin water slice. The vertical thickness of the slice
depends on the temperature (hence density) gradient at level z, in accordance
with the Richardson number characterizing laminar or turbulent flows in
density stratified fluids. I have routinely obtained perfectly clear pump
samples from within 5-10 cm of the sediment-water interface of Lake Mendota in
overlying water depths of 24 m.
An important asset of the described procedure is the ability to obtain
either filtered or unfiltered sample splits without transfer steps and without
the sample contacting the air. This capability is necessary in chemical
studies of iron, manganese, phosphorus, arsenic and sulfur in the bottom
boundary layer. Heaney and Davision (1977) and Stauffer and Armstrong (1980a)
have emphasized the importance of sampling procedures in studying redox-
sensitive chemical species.
54
-------
TYGON CONNECTING
TUBE
ORIFICES TO
TO WHITNEY
THERMISTOR
V = 0 1 cm / sec
PUMP
FLOW - THRU WEIGHT
Figure 21.
Probe configuration for combined conductance,
temperature, and peristaltic pump sampling.
55
-------
The described procedure is also
Van Dorn and other messenger-tripped
of testing an aggregate 48 samples
Mendota in approximately 3h hours,
person is required for the sampling.
from below the 12 m thermocline. For
1 min per 250 ml sample is required;
are obtained simultaneously.
costwise more efficient than the use of
bottle samplers. Thus, on the first day
were obtained from six stations in Lake
including boat travel time. Only one
All but five of these samples were taken
sampling at the 30 m depth approximately
the temperature and conductance profiles
The procedure works equally well during the winter. Only a small auger
hole is required for inserting the electronic probe-tube assembly and the
Whitney cable can be securely clamped to a 2x4" or aluminum strut to preserve
"down-hole" position. In this way it is possible to obtain detailed solute
concentration profiles in the 1 m benthic boundary layer where concentrations
are increasing exponentially with depth (Figure 22). This is impossible using
conventional "Van Dorn" type sample bottles. Use of the pressure filter
assembly on the outlet tube of the peristaltic pump allows collection of a
filtered sample split as in summer. If the air temperature is much below 0°C,
the tubes should be dry before first setting up in the field. Otherwise, ice
formation will plug the tubes. Because the lake water "down-hole" temperature
is usually 2°C, water drawn up by the pump will not freeze in the tubes
provided the pump is left running! A 12 volt lead-acid car battery should be
brought along for ensured electric power during cold weather.
B. Analytical Methods
The lake manager must be thoroughly acquainted with analytical methods if
s/he expects to obtain useful physical-chemical information on lake trophic
state and external and internal nutrient fluxes and storage. Important
classes of parameters include the following:
1. General physical-chemical "Master Variables":
dissolved 02
Temperature, pH,
2. Major cation-anion balance: Ca, Mg, Na, K, carbonate alkalinity; S04, Cl
3. Redox sensitive transition metals acting as "Master Variables" in the
lake chemical system: Fe, Mn
4. Dissolved sulfide
5. Macro-nutrients frequently biologically limiting (c.f. Verhoff, 1973;
Gerhart and Likens, 1975 for discussion of limiting nutrient concept); N,
P, Si
6. Algal standing crop variable: chlorophyll a
7. Ionic strength proxy variable: i_n situ conductance.
56
-------
6 DO
MENDOTA
3-9-78
24
-12
ISI
U
ISI
he
\ ** o
1
5
3
0
0 * *0
&ed I ment
1*1
2
10
6
Mn
3
15
9
* (
1
P Fe
Mn
S\O2
Figure 22.
Solute concentration profiles for Lake Mendota, March 9, 1978.
57
-------
1 . Temperature.
Accurate and precise temperature data are essential for defining the
progress of thermal stratification, and for calculating inter- layer fluxes of
heat and solutes using the "flux-gradient" algorithm (Section III-D). Lake
temperature is obtained using an electronic HI situ thermometer probe
(3-element thermistor or platinum wire resistance typejl The errors depend on
the instrument's consistent calibration against precision NBS references and
on the inherent quality of the electronics. The requisite accuracy and
precision depends both on the lake and on the time interval over which eddy
diffusivities have to be calculated. In general, anajytical quality must
increase as the lake gets smaller (A ) and deeper (both z and z /z), and as
0 McLX
the time interval shortens. For lakes with medium areal extent and medium
depth (example: Mendota), the minimum acceptable accuracy and precision is
a = ±0.05°C throughout the temperature range of interest and over the
cl " "
duration of the summer stratification measurements. During the dynamic spring
heating period lesser instrumental capability is required, however, this early
period is of less interest to the lake manager interested in internal nutrient
supplies. For smaller lakes (maximum fetch <2 km) with z >15 m, the
/v 'v'
requisite accuracy and precision must each improve to a = 0.01°C. The
a
"Montedoro Whitney" company sells thermometers attaining these high standards
(Stauffer, 1980hi). For deeper lakes (z >35 m) in the medium size range (10
IT)3X
to 100 km2) a ±0.01 °C instrumental capability is also required during the
summer stationarity period (c.f. Stauffer, 1980hi). Table 6 shows the monthly
rates of summer heating of the lower hypolimnetic waters, and the minimum
hypolimnetic temperature gradient for representative lakes in Wisconsin. The
Table gives some idea of the temperature "signal" you are attempting to
measure.
2. £H
Accurate pH data from the metalimnion-hypolimnion are useful for inter-
preting the Ca, Fe, Mn, S, and P cycles in lakes. Unless the lake is acidic
and dystrophic (c.f. Hutchinson, 1957) pH data from the epilimnion has limited
utility (it usually reflects the temporal balance between C02 uptake for
photosynthesis, respiration, and C02 invasion from the atmosphere (Emerson,
1975ab).
pH measurements are recommended in the thermocline region where dissolved
oxygen is approaching zero (solute oxidation-P adsorption zone), in the middle
of the hypolimnion, and especially 25 to 50 cm above the sediment-water
interface in the deep hole region. The latter measurement yields pH informa-
tion relevant to the sediment-water solute release and sulfate reduction zone.
If the lake is significantly bicarbonate-buffered, these pH measurements can
be expected to fall in the narrow range, 6.75 to 7.6, late in the stratifica-
tion period. The deep benthic boundary layer experiencing sulfate reduction
normally has a narrower pH range (7.1 to 7.5; Stauffer and Armstrong, 1980a;
Davison and Heaney, 1978).
58
-------
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59
-------
The following procedure is capable of providing j_n situ pH estimates
accurate within ±0.05 pH unit. The actual pH measurements should be made in
the laboratory on field preserved samples (see below). The field procedures
used for obtaining and preserving the samples are critical if accurate i_n situ
values are to be expected. Unwanted oxidation of redox sensitive solutes
(Mn(II), Fe(II), H2S) lowers the pH, while gas exchange with the atmosphere
(esp. C02 and H2S) has the effect of raising the pH. Fortunately, these
changes can be avoided.
Collect the pH samples using Pyrex "Winkler" D.O. bottles and a
peristaltic pump. Flush the bottle by overflowing several bottle volumes with
sample by holding the outflow tube (bypass the filter) orifice near the bottom
of the Winkler bottle. Slowly withdraw the tube, thus filling the bottle
neck; then immediately seal the bottle with the ground glass stopper. Secure
the stopper with glass-tape. Place the bottle in an iced darkened cooler and
leave refrigerated until just prior to the laboratory-based pH determination.
Begin the laboratory portion of the analysis as soon as practical (within a
few hours).
In the laboratory allow the samples to warm to room temperature, while
remaining tightly stoppered in the dark. Select suitably dilute reference
buffers (near pH 7) that narrowly span the expected pH range. Acclimate the
buffers to the same known laboratory temperature (preferably 20 to 25°C to
improve electrode response). After calibrating the high quality glass pH
electrode in the buffers, condition it for a few minutes in a sample of the
lake's epilimnion water (approximately same ionic strength as hypolimnion
samples) before making the pH determinations on the deeper water samples.
Finally, determine the pH (at lab temperature) of the deeper water samples by
inserting the pH electrode immediately after removing the glass stopper seal.
The electrode will nearly fill the hole and come to equilibrium before sig-
nificant gas exchange or oxidation can take place. Back calculate the i_n situ
pH at the i_n situ temperature for the bicarbonate system following Davison and
Heaney (1978).
Field i_n situ direct pH measurments are not recommended for all of the
following reasons: (1) High quality pH instrumentation is easily damaged in
the field; (2) it is difficult to bring buffers and water samples to a common
temperature in the field; (3) the pH electrode responds sluggishly and some-
times erratically at low temperatures, hence an accurate buffer calibration is
difficult; (4) if pH measurements are attempted in a "flow-thru" cell con-
nected to the peristaltic pump's outflow tube, additional problems (in
addition to (2), (3) above) are encountered with water "streaming potential"
and/or pH shifts accompanying sample oxidation or degassing; and (5) winter
field measurements add impossible further complications; such measuremnts are
important and yet no more difficult to make using the bottle preservation-
laboratory technique outlined here.
60
-------
3. Dissolved Oxygen (P.O.)
Standard procedures are adequate except for D.O. concentrations <0.2 mg
L-1. The potentiometric i_n situ measurements are easily obtained and of
requisite accuracy and precision, provided the instrument is accurately
calibrated. Winkler titrations are also acceptable (c.f. APHA, 1971).
4. Major Cations
Flame atomic absorption spectrometry should be used on HCl-acidified
sample splits (see below) following standard procedures. The analytical
coefficient of variation c.v. ~ ±1%.
5. Bicarbonate Alkalinity
For moderately well-buffered typical lake waters (alk.>0.5 mN) with low
borate and ammonia concentrations, standard acid titration suffices (APHA,
1971). Depending on the initial pH, borate, NH3, and even silicate can add
acid titration alkalinity, however, this is rarely a problem except for
geothermal waters at high pH. For poorly buffered natural waters, and
especially for highly colored lake and stream waters, accurate carbonate
alkalinity measurements are very difficult for the inexperienced analyst.
Hire a chemical consultant.
6. Sulfate and Chloride
For most situations the "cation exchange" method is by far the best S04
technique from the standpoint of cost and low analytical error. See Stainton
(1974) and especially Stauffer (1980g) for a careful analysis of the potential
analytical biases and optimal analytical strategies. Note that sulfide
present in a natural water sample can be bacteriologically oxidized to S04 if
allowed to stand. Chloride is readily determined either by standard "Mohr"
titration (APHA, 1971) or by "cation exchange" (Stainton, 1974; Stauffer,
1980g).
7. Iron and Manganese
These elements exist both as oxidized (Fe(III) and Mn (IV)) particulate
phases and as reduced dissolved species under low redox conditions (Fe(II) and
Mn (II)). Several analytical techniques are available for the direct deter-
mination of the "reduced" forms of these elements (c.f. Delfino and Lee
(1969); Davison (1977); Shapiro (1966); Lee and Stumm (I960)). However, from
the perspective of the lake manager or consultant it usually suffices to know
both the total and total dissolved concentration. These are readily obtained
by flame atomic absorption spectrometry on FA (field filtered and acidified)
or UA (unfiltered acidified) sample splits. Low concentrations can be
determined following the complexation-solvent extraction scheme of Kennedy and
Zellweger (1973). Kennedy and Zellweger (1974) note that 0.4 urn pore size
61
-------
filtrates seriously overestimate the true "dissolved" Fe and Mn components in
natural waters of high redox potential. This analytical bias is not a problem
in the anoxic hypolimnion waters; here the filtered acidified sample split
estimates Mn(II) and Fe(II) in the environment.
8. Dissolved Sulfide
Outlined below is a modified ZnS-iodine-thiosulfate technique based on a
standard procedure (APHA, 1971). For hypolimnetic waters with relatively high
concentrations of dissolved sulfite (>0.5 mg L-1, and preferably greater),
collect a 250 ml sample as for D.O. Analysis using a peristaltic pump and
immediately "fix" the sulfide by adding zinc acetate (c.f. APHA, 1971). The
precipitated ZnS is later quantitatively recovered on a glass fiber filter in
the laboratory and the filter reacted with an excess of standardized iodine in
acid medium. Finally, the excess iodine is titrated with standard thio-
sulfate. Iodine consuming organics in the precipitate can give an important
positive interference, especially for colored Fe-rich non-calcareous waters
where the dissolved sulfide concentration is low. The technique works
especially well for calcareous "sulfuretums".
The ZnS precipitate formed above can also be solubilized using an
alkaline-ascorbic acid anti-oxidant buffer and the sulfide determined
potentiometrically using a sulfide-specific electrode (Baumann, 1974). Other
useful techniques have been developed by Cline (1969) and Davison (1977). The
latter is good for low concentrations of sulfide but requires specialized
polarographic equipment.
9. Nutrients: N:P:Si
Inorganic nitrogen is generally present in the form of ammonia (NH3-N) or
nitrate (N03-N). Nitrite is rarely present in significant concentrations
relative to the other two forms. Ammonia is readily determined at environ-
mental levels (and especially within the hypolimnion) using the popular
phenol-hypochlorite colorimetric procedure which has been adapted to auto-
analyzers (Strickland and Parsons, 1968). The N03-N concentrations
encountered in stream flow in sedimentary regions, and over winter in lakes,
can be determined using the brucine procedure (Kahn and Brezinski, 1967). Low
nitrate levels require a reduction step (Cadmium column, for example) to
nitrite followed by diazotization (Strickland and Parsons, 1968).
Soluble reactive phosphorus (abbreviated SRP) determinations are based on
the ascorbic acid reduction molybdenum-blue procedure (Murphy and Riley, 1962;
see also Strickland and Parsons, 1968 for a popular variant). Very low SRP
concentrations can be determined following Stephens (1963). Total-P and total
soluble P (TSP) fractions are determined colorimetrically in the same fashion
after first liberating organically bound P by persulfate digestion in an
autoclave (Menzel and Corwin, 1965). The particulate-P fraction can be
determined indirectly by arithmetic difference, or preferably, directly by
62
-------
digesting participates caught on a 0.4 nm nucleopore filter (Erickson, 1980).
A high quality spectrophotometer equipped with 5 cm cuvettes is required for
most environmental P determinations.
The phosphorus analytical procedure is less straightforward than commonly
supposed. As a result, environmental P data can be analytically biased by
hundreds and even thousands of percent. Arsenic present as arsenate (As(V))
reacts with molybdenum to give a positive interference (Johnson and Pilson,
1972; Stauffer, 1980e). The lake management consultant must verify whether or
not arsenic is a potential analytical interference in the study lake because
arsenic levels have been elevated in many Midwestern lakes from long histories
of sodium arsenite treatments for weed control.
Silica is also an insidious potential P interference because of the very
high Si/P ratios in many P-poor natural waters. Silica forms a positive
colon'metric interference if the H and H /Mo ratios are too low (as for
example, specified by Strickland and Parsons (1968)); and/or the color is
developed at elevated temperature in an auto-analyzer variant of the basic
procedure (see Stauffer, 1980ef; 1980f for details).
Reactive silica concentrations are readily determined following the
Fanning and Pilson (1973) refinement of the Mull in and Riley (1955) colori-
metric procedure (c.f. Strickland and Parsons, 1968).
10. Chlorophyll a
Chlorophyll a is determined by solvent extraction of algal cells caught
on a glass fiber filter. See Stauffer e_t al. (1979) for a streamlined
procedure and discussion of potential extraction biases using acetone (90%).
11. Conductance
Edmondson (1956) introduced the useful procedure of measuring conduc-
tivity iji situ. Modern high quality combination temperature-conductance
instruments (for example, Montedoro Whitney Model CTU4) are highly accurate
and precise. Frequently, the u) situ conductance is adjusted to a temperature
of 25°C based on the measured iji situ temperature and the known conductance
properties of NaCI solutions. For low temperatures, the differential ion
mobilities (with respect to temperature shifts) cause a small but consistent
bias for calcium bicarbonate lake waters.
12. Sample Preservation in the Field
Both filtered and unfiltered sample splits should be acidified with 1 ml
cone. HC1/250 ml sample in the field for analysis of major cations, Mn, Fe,
and nutrients. Hydrochloric acid is the ideal acid for this purpose because
it causes no later analytical interferences. The acid prevents biological
63
-------
uptake of nutrients, sorption on the walls of the polyethylene sampling
bottles (Heron, 1962) and the chemical precipitation of CaC03 or Fe, Mn,
following oxidation (c.f. Bray et aJL , 1973; Heaney and Davison, 1977).
C. Lake Temperature Estimation
1. Temperature Seiches
After the onset of thermal stratification, we have in the simplest
possible case, that the lake's surface is flat calm and the internal isotherms
are level. Internal gravipotential energy is then at a minimum. I will call
this (rare) situation "isotherm equilibrium". At equilibrium, any point
,*.
estimate T(x,y,z,t ) over A is an unbiased estimator for T(z,t ) and the
total measurement error reduces to the analytical error. "Isotherm
equilibrium" represents an end-member situation where all perturbing
influences of wind, atmospheric pressure gradients, etc., have receded into
the distant past.
In general, temperature is a function of x, y, in addition to z, because
of advection of water through open lake systems, and more importantly, because
of the immediate and delayed responses of the lake's internal isotherms to the
wind "set-up". During period of intense solar radiation and surface warming,
the wind transports the warm buoyant lenses of epilimnion surface water to the
downwind end of the lake, creating a lateral surface temperature gradient.
The stress-dependent lake surface tilting is known as the "set-up" and has
amplitude (c.f. Hutchinson, 1957, p. 284):
dh 2c T .67 T
o j_ s a j_ a fy\
dx ~
3g Pifii g Pifii
where T is lake surface wind stress (dynes cm-2), g is the gravitational
acceleration (980 cm2 s-1), px is the density of the epilimnion (G cm-3), fix
is the true mean (over A ) depth of the mixed layer (cm), and cg = 1 + Tb/ta
(T, = bottom stress).
Accompanying the "surface seiche" is a large amplitude reverse tilting of
the upper pycnocline and the associated upper metalimnion isotherms. Except
under conditions of extreme stress, when the tilt of the upper metal imnion
isotherms intersects the lake surface (upwelling), the isotherms identified
with the bottom of the metalimnion remain more nearly level. The resulting
cross sectional view is called the "metalimnion wedge". The relatively small
density difference between the epilimnion and hypolimnion (p2~Pi) implies that
the tilt of the upper pycnocline:
dhj 2c T .67 t
* = §§ § (3)
3g(o2 - Pl)fii g(p2 -
64
-------
has an amplitude ~370 times that of the surface tilt for typical summer
conditions on Lake Mendota. The linear tilt or "wedge" model is a useful
idealized representation of an actual lake's internal response to an imposed
wind stress. Pycnocline displacement increases linearly with T , and with
distance outward from the tilt axis node. The node is the equilibrium
position. The upper pycnocline tilt can have sigmoidal character, and dif-
ferential bottom effects can lead to asymmetry about the tilt node (c.f.
Hutchinson, 1957, p. 344; Dutton and Bryson, 1962). In the event a higher
lying "breeze thermocline" develops, the upper thermocline is tilted by the
wind stress, while the lower one remains nearly stationary. The tilt amplitude
is large because both hj and p2 - pi are small in this case (c.f. Figure 23).
Equation 3 shows that at constant stress, the amplitude of tilt (upper
pycnocline) is greatest in the late spring, when the thermocline is shallow
and the temperature (hence density) difference between epilimnion and
hypolimnion is still small (Table 7). During summer, tilt displacements are
minimum because of the maximum expected density difference. In the fall, the
deep thermocline is furthest removed from the perturbing wind stress. If we
consider as well the seasonal variations in over lake wind stress (Stauffer,
1980b), the expected tilt amplitudes are reduced still more for the summer, as
compared to the late spring. Midday lake stresses in excess of 1.0 dynes cm-2
are unusual during summer and 3-hourly stress estimates exceeding 2.0 dynes
cm-2 were not observed (Madison, WI) during 10 years of summer record (1966-
1975). During the height of summer stratification, the maximum calculated
tilt displacements at the ends of the 9.0 km WSW-ENE fetch axis are 1.5 to 2 m
(from the nodal plane). During the expected die! stress maximum of 0.8 dynes
cm-2 (between 1200 and 1500 hrs), we would expect approximately a 190 cm
difference in elevation for the end points of the upper pycnocline under the
summer conditions specified in Table 7.
Table 7. Calculated Displacements for the Mendota Upper Pycnocline for
Representative Conditions of Wind Stress and Stratification.*
Season and Stratification Conditions
w i nu our ess
(Dynes/cm2)
0.4
1.0
2.0
Late Spring1
328
820
1,640*
Mid Summer2
96
240
480
Fall3
228
570
1,140
* Pycnocline intersects lake surface.
Note: Displacements are calculated for the 9.0 km (WSW-ENE) maximum fetch,
and represent the elevation difference (cm) of the pycnocline at the
ends of that axis.
Lake stratification conditions:
1 Te = 20°, Th = 10°, hi = 500 cm, p2 - Pi = 0.00150
2 T = 25°, T. = 11°, hi = 1000 cm, p2 - Pi = 0.00256
e *- ' h
h
65
3 T = 17°, T, = 12°, hj = 1500 cm, p2 - pi = 0.00072
-------
cu
c
u
o
c
o
s-
OJ
Q.
Q.
(V
o
O)
CO
1/1
Ol
S-
-p
c
r
3:
o
CD
ra
a>
a
ro
CM
ai
0)
66
-------
Removal of the causal wind stress initiates the short period-low
amplitude surface seiche and the long period, large amplitude internal
(temperature) seiches. For temperature estimation, the surface seiche is of
negligible importance. The long period internal waves are very important
because of their invisibility to a surface observer, large displacements, and
broad spectrum of periodicities.
The periods (P.) of the internal oscillations based on a two layer model
range upward to that observed for the uninodal seiche and can be calculated
approximately using Equation 4 (Hutchinson, 1957, p. 336).
pi =
- PI)
tl/h2 + I/hi
(4)
where £, is fetch
(cm)
*-,: ic. icv-t-u length
pycnocline to the lake bottom.
and h2 here is the mean distance from the
For Mendota the uninodal seiche period during
mid summer is 10.5-11 hours (Stewart, 1965). The uninodal seiche has the
largest amplitude, contains a disproportionately large fraction of the total
internal wave energy, and is the slowest to dissipate its stored energy
through viscous dampening (Mortimer, 1953). The relative importance of the
uninodal and binodal temperature seiches depends on basin morphometry and the
depth of the thermocline (Mortimer, 1953). The uninodal seiche periods are
proportional to fetch and are long relative to the time required for sampling
a medium sized lake.
2. Seiche Dampening
The rate of dampening of internal seiches has apparently not been
extensively studied. Mortimer (1953) found approximately 23% dampening with
each cycle of the uninodal seiche in the North Basin of Lake Windermere. The
dampening rate increases with decreasing z because of the increasing drag of
the bottom T, . Donelan et aj. (1974) note that t, is proportional to the mean
square bottom current velocity
t. =
(5)
67
-------
Simons (1973) has reported a bottom drag coefficient, C. = 2.5*10-3 for Lake
Ontario, for u. units (cm s-1). Thus, if as a very rough approximation, we
assume the r.m.s. bottom current decreases approximately as 1/z (for A
constant), T. and hence the dampening rate should decrease approximately as
1/z2. Clearly, we would expect a rapid rate of seiche dampening for Lake
Mendota, and a slow rate for Green Lake, Wisconsin.
3. Other Wave Disturbances
In addition to the seiches, very short period temperature fluctuations
(time scale 1-15 minutes) are almost invariably superimposed on the longer
period temperature oscillations. These "progressive waves" have low spatial
coherence. Stewart (1965) investigated them on Lake Mendota and noted periods
ranging generally from 1 to 5 minutes.
Surface gravity waves also affect temperature (and solute) sampling by
imposing partially periodic and partially random fluctuations in the
observer's surface reference position. The amplitude of the effective
vertical fluctuations depends both on wave amplitude and the wave dampening
efficiency of the sampling boat. Even during windy conditions, and white-
capping, much of the periodic component can be "averaged out" during handling
of the sampling line leaving a residual error of 10-20 cm. During calm con-
ditions the error is negligible (<1 cm).
4. Effects of Lake Morphometry on Temperature Estimation
For constant stress over the water surface, increasing fetch linearly
increases maximum tilt displacement (Equation 3), hence the initial seiche
energy-m2-surface area increases as £f. For isomorphic lakes S.^ increases
with A^ and S2s r s(hx) is proportional to AQ (Stauffer, 1980h). The
proportionality holds only at initial time because we would expect faster
rates of seiche dampening in the smaller shallower lakes, than in large deep
ones [Note: s.r.s. denotes simple random sample; s2 = sample variance].
The effect of increasing A on S2 (hx) is actually more subtle than
indicated above because of the influence of the lake surface on the wind
velocity and, thus, surface stress. For small (A^l km2) lakes in heavily
wooded or hilly environments, the surface stress is drastically reduced by the
shelterbelt effect (Henderson-Sellers, 1977). Furthermore, the shorter
roughness length for water as compared to adjacent land surfaces (Deacon and
Webb, 1962), and the influence of the bulk Richardson number (Rb), ensure that
differential accelerations occur over large lakes than smaller ones (Stauffer,
1980b). The ratio of the wind velocity at reference height 10 m over water
(u10) to the velocity at an adjacent land station is frequently called the
"wind factor" (c.f. Stauffer, 1980b). As the wind stress is roughly propor-
tional to u20, the initial S2s r g (h^) for two adjacent lakes differ
68
-------
according to the 4th power of the ratio of their wind factors. Two adjacent
lakes can have different wind factors because substantial fetch (up to 50 km)
is required for the full acceleration to a new steady-state velocity, and
because the wind factor increases as R. decreases. Because large deep lakes
have larger heat budgets than small ones, they lag the solar heating cycle
more than smaller lakes (Hutchinson, 1957). The extended lag results in an
extension of positive Rb values into the mid summer and accounts for the very
small wind factors (~1.0) commonly observed over the Great Lakes in July
(Richards et al., 1966). Conversely, in the fall, the very great heat storage
of the larger lake leads to a prolonged episode of lapse conditions (Rb<0) and
consequently large wind factors (-2.0) for long fetch lengths. Clearly, for
two adjacent lakes with radically different mean depths and fetches, there is
a seasonal influence on the ratio of their wind factors. The ratio is likely
to be close to 1.0 during the late spring because of the compensating effects
of fetch length and Rb values. In the late summer and fall, however, both the
increased fetch and the more negative Rb value selectively accelerate the wind
over the larger deeper lake.
5. Variance Components of a Simple Random Sample (s.r.s.) for ht
If the lake surface is sampled for hj using simple random sampling
(probability proportional to area), then the sample variance S2 (hl5t) at
time t is given approximately by:
S!.r.s.(hl>t} = Sf.w.^i'1) + ^.w.^i'^ + Sg.w.(h't} + Sl(hl't} (6)
The error components partition into expected mean squares due to long period
temperature seiches, short period internal waves, and surface gravity waves.
The last component is a pure analytical measurement error. For a s.r.s. of
size n, the expected mean square error is simply S2/n (Cochran, 1963).
Although unbiased, a simple random sample is extremely inefficient
statistically because the mean square is concentrated in the first term of the
R.H.S. of Equation 6. This partitioning suggests that our considerable
knowledge about temperature seiches should be exploited in constructing a
stratified or systematic sample. One technique which can be employed on small
lakes is to anticipate the "set-up" by conditioning the sampling design on
antecedent wind conditions. If the lake is known to be in a state of "set-up"
based on observable strong and unidirectional winds prior to, and during
sampling, then the reverse thermocline tilt implies that a single station in
either the downwind or upwind lake region results in a strongly biased
estimate of h^. If a single sample is to be selected, a station near the
lake's midpoint and hence tilt node should be sampled. The bias depends on
the station's distance from the tilt node and the amplitude of the tilt. For
a symmetric tilt, pairs of stations, each equidistant from the node provide a
strong sampling design.
69
-------
During relatively calm conditions the lake is not set-up, and it will be
difficult to predict a priori the tilt of the thermocline based on antecedent
wind conditions. In general, as the lake's surface area and mean depth
increase, the slow dampening rates for past wind disturbances, and the long
lags required to achieve new steady-state circulations under a new stress,
make it increasingly difficult to anticipate the set-up. Without prior
knowledge of the thermocline tilt, any measurement hx (x,y,t) is approximately
unbiased for h\ because the seiches are oscillatory. However, Var hj (x,y,t)
increases with the mean square (over time) amplitude of tilt at (x,y).
Because of the salience of the uninodal tilt, the lake's extremities should
individually produce estimators h^x.y.t) of fix with the largest variance. As
in the case of the set-up, the mean of two stations synoptically sampled which
are positioned symmetrically about the tilt node, should provide an estimate
of hi with a sharply reduced variance. As it is frequently impractical to
sample two stations synoptically, the elapsed time between sampling members of
station pairs must be kept short, relative to the half period of the uninodal
temperature seiche. One of the inherent dangers in transect sampling is that
the elapsed time between sampling station pairs near the ends of the transect
can easily approach the half-period of the uninodal temperature seiche.
Obviously, a pair of sampling boats can be employed to great advantage to make
the sampling of individual station pairs nearly synoptic.
6. Bias in T(z)
The simplest and most commonly employed procedure for estimating the
lake-average temperature profile is Equation 7, where n is the number of
individual profiles sampled.
T(z) = I T.(z) (7)
n n
Sweers (1968) noted that the "average temperature curve", f(z) can provide
s\
biased estimates of the true "equilibrium" temperatures (T(z)) under
conditions of tilted isotherms. As the temperature profile at isotherm
equilibrium is required for calculating eddy diffusivitives, the potential
bias in T(z) can be an important nuisance. Sweers showed that for two
conformal sigmoidal T(x,y,z) curves whose metal imnion midpoint depths (z )
vary by a meters, the statistic T(z) is negatively biased for z -a
-------
The bias jn f(z) can be estimated as the difference between z (T)-1 (the
inverse) and f(z), as Z(t)-1 is a very nearly unbiased estimator for the
equilibrium temperature profile (Sweers, 1968). In contrast to T(z), which
can be computed directly from the raw T(z) data taken at integral meter
depths, the Z(T) vectors are determined either graphically or using
interpolating polynomials. Interpolation is difficult to do quickly by
computer because of the rapidly changing slopes T'(z) and variable depths of
the upper pycnocline (over A ). Thus, it is a matter of some practical
utility to identify the conditions leading to unacceptably large T(z) biases.
The bias in T(z) clearly depends both on the tilt amplitude, and on the
sampling design, i.e., the spatial relationships of the sampling stations to
the tilt node.
As shown by Figure 24, high amplitude thermocline tilts can occur during
powerful cold fronts in late spring, even on lakes of modest fetch (~10 km).
In mid-summer, however, the appreciably greater values in (p2~Pi) and hls and
the lower expected wind power inputs (Stauffer, 1980b) reduce the typical
afternoon tilt amplitudes. Under these latter conditions, the biases in f(z)
are confined to a 2 m depth interval and have expected magnitudes <0.3°C for a
5-station balanced sampling design including the tilt node (assumed to be the
lake's midpoint) and the ends of the longitudinal (tilt) and transverse axes
(Stauffer, 1980h).
7. Biases in AT(z)
The difference statistic, AT(z) = T(z,t1)-T(z,t ), is used for estimating
metal imnion and hypolimnion heat gains over time and in estimating vertical
eddy conductivity using the flux-gradient method (Powell and Jassby, 1974;
Jassby and Powell, 1975). Potential biases in AT(z) are thus of concern. A
related statistic is the "mixing ratio" R(z) defined by Equation 8 and used by
Stauffer and Lee (1973) for estimating entrainment transport of phosphorus
resulting from thermocline migration. If the thermocline has been static over
the
R(z) =
{fe(to,tl) - f(z,to)}
time interval (tx-t ), and if the mean square thermocline tilts are equal on
the two sampling dates, then AT(z) is unbiased. However, if h1(t1)>h1(t ), as
happens when a powerful cold front activates entrainment, then the metalimnion
temperature changes are in general biased. The sign of the bias function
depends on depth and boundary translation; the magnitude of the bias function
depends sensitively on the boundary translation and the difference in mean
square thermocline tiljbs for the two sampling dates (Stauffer, 1980h).
Statistical biases in AT(z) clearly militate against lake sampling during, or
immediately following, a powerful wind storm, if the objective is to document
the effect of the storm on the equilibrium temperature structure.
71
-------
(D
- E
CSJ
r^.
CT)
01
3 0)
o s-
O) CT
i- -r-
Ol U_
>
s- na
L_ i oJ
m 22
I I I 4J v->
Q 3 c
f^ O
_l S-
M-
c
Ol "O
Ol r
S- O
CJ3 O
C\J
0>
i-
in
72
-------
D. Estimating Vertical Nutrient Fluxes
The vertical transport of P and/or other dissolved solutes through the
thermocline is usually modeled as a "Fickian" eddy diffusion process. The
model is generalizable for describing solute transport through any horizontal
plane centered j meters below the lake surface.
Js(z) = K;(Z) * as/az (9)
where J (z) is the flux of solute S (units, mg cm-2 s-1) through the plane of
area A centered z meters below the surface; 3S/3z is the solute concentration
gradient at level z (units, mg cm-4); and K'(z) = K (z) + K (z) is the
effective diffusivity for solute S at level z. Note: K'(z) is the sum of the
temperature and solute dependent "molecular diffusivity" K (z) and the "eddy
diffusivity" K (z). The eddy diffusivity term depends on turbulent water
motions and is considered to be heat or solute independent (i.e., the solutes
are passively carried by the fluid). The eddy diffusivity component depends
strongly on wind energy inputs to the lake surface and on the local density
stabilization of the water column (Stauffer, 1980h; Quay et al., 1980). The
molecular diffusivity term is ~10-5 cm2 s-1 for dissolved ions and two orders
of magnitude larger (~10-3 cm2 s-1) for heat (Turner, 1968; Lerman, 1979; Quay
et al_. , 1980). The solute diffusivity increases with temperature and
decreases with increasing ion size.
The extreme divergence between the molecular diffusivity rates for heat
and solutes causes lake estimation problems if K'(z) approaches the molecular
rate for heat (~10-3 cm2 s-1). Because heat is used as our conservative
tracer for vertical diffusion in lakes (Jassby and Powell, 1975; Quay et al. ,
1980; Stuaffer, 1980h), K'(z) estimated from heat penetration measurements
seriously overestimates vertical solute transport if Kl(z) approaches the
molecular value.
In the middle of the summer thermocline of small lakes (A <100 hectares),
K'(z) approaches the molecular rate (Quay et aT_. , 1980; Stauffer, R. E. ,
unpublished data). In such lakes heat transfer measurements can only be used
to define an upper bound on K'(z) or 10-3 cm2 s-1 within the summer thermo-
cline. This inequality can still be very useful for excluding vertical P
fluxes as having importance in these lakes with only modest metalimnion P
gradients (Erickson, 1980). If the lake has a small thermocline diffusivity
and a very steep P concentration gradient, it will be difficult to resolve the
exact magnitude of the vertical flux. In this case a qualified scientific
consultant should be hired.
73
-------
For larger lakes "Mke Mendota or Green, the mid summer thermocline
minimum K'(z) value averlges 1 to 2 * 10-2 cm2 s-1, and increases by at least
an order of magnitude during severe storm events (Stauffer, 1980hi; Sweers,
1970). If the lake is shallower and has less density stabilization within
the thermocline, the thermocline minimum in K'(z) will increase dramatically
(Stauffer, 1980h). This holds true for the wind swept western basin of
Shawaga Lake and explains the high vertical flux rates of P within that lake
(Stauffer and Armstrong, 1980b). In situations where K'(z)» 10-3 cm2 s-1,
the flux of solutes can be computed using the flux gradient model as the
product: K.(z) * 3S/3z.
Stauffer and Lee (1973) introduced a ratio based algorithm for
calculating solute transport during storm events. Stauffer (1980h) shows that
this "non-Fickian" model is computationally more stable than the flux-gradient
algorithm for flux estimates across the important boundary hi_. If the solute
behaves essentially conservatively within the upper metalimnion region, the
two algorithms yield essentially the same result. If the solute is non-
conservative within the upper metalimnion (for example: Fe, or P if the Fe/P
ratio is sufficiently large), then the non-Fickian assumptions of the ratio
"Mixing Model" lead to larger vertical flux estimates than the flux-gradient
algorithm (Stauffer, 1980h).
The calculation of K|(z) depends on a number of assumptions. First, we
assume that large scale advection of heat and solutes into the hypolimnion-
metalimnion from the drainage basin streams is absent. In reservoirs this
assumption is frequently invalid. Furthermore, during abnormally wet erosive
summer periods, turbid density currents can add heat and solutes to the lake
below the boundary hx (Bryson and Suomi , 1951). Second, the K|(z) calculation
algorithm must correct for light penetration and adsorption within the water
column and at the sediment water interface (Jassby and Powell, 1975), and also
for the penetration of heat into the sediments as one component of the
hypolimnetic heat storage during stratification (Stauffer, 1980h). Dutton and
Bryson (1962) recognized this potential water-sediment heat exchange and
proposed that heat transport through the thermocline was largely the result of
reversible thermocline temperature seiches in Lake Mendota. Stauffer (1980h)
shows that this is not an important mechanism for explaining heat fluxes
through the Mendota thermocline, or in lakes generally. This possibility was
also excluded by Quay et al . (1980) for their study lakes in the Experimental
Lakes Area of western Ontario, Canada.
The Fortran computer program "LAKETRANS" developed by the author and
reported in Stauffer (1980h) can be used for computing thermal diffusivities
and solute transport in stratified lakes. The algorithm corrects both for
light penetration and sediment heat penetration effects. The sediment-water
heat exchange subroutine is based on lake studies by Birge et al_. (1927) and
Likens and Johnson (1969). Vertical solute fluxes are computed both using the
flux-gradient model and the reservoir "Mixing Model" reported by Stauffer and
Lee (1973).
74
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IV. Chronology of Tasks for Lake Managers
A. Acquire important available data source materials on the lake and its
drainage basin.
1. Local Climatological Summaries for the drainage basin (N.O.A.A.,
U.S. Department of Commerce, Asheville, NC).
a) Monthly precipitation norms
b) Monthly mean daily air temperature and humidity
c) Monthly average wind speeds.
2. Accurate lake bathymetric map (consult state Department of Natural
Resources).
3. Lake drainage basin/land use map, including town sites. If this is
unavailable, use large scale topographic maps (U.S. Geological
Survey) to construct one by drawing in drainage divides.
4. Summary of local hydrologic studies by the U.S. Geological Survey
and similar agencies, or private consultants.
a) Stream gaging
b) Lake or pan evaporation measurements
c) Ground water studies
d) Lake surface level records.
5. Published scientific studies of the lake (usually university based).
B. Determine expected seasonal external nutrient loading (see Reckow, 1980).
1. Estimate the monthly water export from the drainage basin.
2. Based on estimates of lake volume and lake epilimnion volume
(see below), estimate the hydraulic "residence" time of the
epilimnion.
C. Estimate lake hypsometric relations using the bathymetric map.
1. Convert the bathymetric map to metric units.
2. Determine lake area at each of these bathymetric contour lines.
(The easiest and most accurate technique is to cut a map copy along
the contour lines and weigh each of these components using an
analytical balance.)
75
-------
3. Interpolate the lake area A(j) at each "integral" meter depth below
mean lake surface level.
4. Calculate the sediment contact area, A (j), j meters below lake
surface, using the central difference formula:
A(j-l) -
As(j) =( 2~
5. Calculate RA(j) = A (j)/A(j) for each meter depth. Graph this
o
relationship vs. depth.
D. Determine provisional lake stratification relations.
1. From the climajtic norms, dates of ice-on, ice-out [Note: use local
sources], and z determine the approximate timing and duration of the
vernal free convective overturn period.
2. Estimate the "equilibrium surface water temperature", based on mean
daily air temperature and relative humidity during the summer
"weather stationarity period". Estimate the approximate duration of
summer thermal stratification (mixed layer temperature > "equili-
brium value" - 2°C).
E. Lake physical chemical measurements
1. Estimate lake average concentrations of reactive Si02, N03-N, NH3-N,
Total-P, and Total Soluble P as soon as possible after ice-out and
during the convective circulation period. (Compute the vernal
nutrient availability ratio (N03-N + NH3-N):TSP:Si02- If the atomic
N:P ratio is >14, the lake is likely to be "stoichiometrically
phosphate" limited. This will almost certainly happen if the lake
is "seepage dominated" in a hydrologic sense.) During the vernal
"overturn" period "lake average" concentrations can be estimated by
six samples: two samples each at three widely spaced sampling
stations "covering" the pelagic zone of the lake. (One sample at
each station from near the surface and one from mid water column
depth.) Retain several of the vernal overturn samples for major
.cation-anion analysis.
2. Obtain detailed temperature and solute concentration profiles from
the central basin-deep hole sampling station at the following three
times:
a) Soon after (within a week) the lake temperature at 2 m depth in
the pelagic region has attained the summer "equilibrium
temperature" -2°C.
76
-------
b) In mid-summer, preferably at the approximate date of hypo-
limnion onset of anoxia (if this occurs).
c) Near the end of the summer, prior to significant irreversible
cooling and thickening of the mixed layer (mixed layer
temperature still within 3°C of summer equilibrium value.
3. During the three summer lake surveys collect the following informa-
tion:
a) Temperature every meter to the bottom.
b) Oxygen every meter from hx to the bottom.
c) Total-P. Every other meter except within the main thermocline
and in the bottom 4 m of the lake (in the latter two depth
zones sample every meter). If the lake is 20 m or less in
maximum depth, sample every meter.
d) Si02: same as c) above.
e) NH3-N: same as c) above.
f) N03-N: same as c) above until oxygen decreases to below 0.1 mg
L-1; then terminate N03-N profile.
g) Total Mn: same as c) above.
h) Total Fe: same as c) above.
i) Total soluble Fe: every meter within the bottom 4 meters.
j) Total soluble P: two samples within epilimnion; two samples
within the main thermocline; the bottom two samples of the
profile.
k) SRP: epilimnion samples.
1) Sulfide: after definite evidence of formation need sample only
in late summer within the bottom 4 m to check on FeS solubility
control.
m) pH: bottom of hypolimnion if the lake is non-calcareous and
the studies are intended to be of scientific interest.
n) Secchi transparency depth.
Note: If the lake has a complicated non-conformal bathymetry, with
separate deep holes far removed from the approximate lake
center point, and is non-calcareous, a detailed "sampling
design" will be required to obtain sufficiently accurate lake-
average survey data. Hire a consultant well grounded in both
77
-------
statistical sampling theory and lake hydrodynamics. A
consultant should also be retained if the lake surface area
exceeds ~50 km2.
4. Using the analytical results of the three summer lake surveys, and a
sophisticated computer program like "LAKETRANS", compute the solute
partition by depth, changes in heat and solute storage over time and
estimated fluxes among layers of the vertical lake partition.
Compute the ratios of Fe:Mn:Tp:NH3-N:Si02 accumulated in the
hypolimnion and metalimnion during the two stratification intervals.
Note the Fe/P atomic ratio for the bottom of the hypolimnion and
within the metalimnion during the two stratification intervals.
5. Resample the lake closely following complete fall turnover. Use the
same spatial sampling design specified during the vernal sampling.
Compute total lake storage of total P and reactive Si02 as the
product of lake volume and mean analytical concentration. Compare
these mass estimates with the spring and summer sampling periods.
6. Resample the lake at mid depth at several sites immediately after
ice-on (few days delay for safety). The concentration of solutes
will be the lake-average value prior to the onset of winter stag-
nation and solute release at the sediment-water interface.
78
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References
Ahern, J. 1976. Impact and management of urban stormwater runoff. M.S.
Thesis. University of Wisconsin-Madison. 207 p.
Anthony, R. S. 1977. Iron-rich rhythmically laminated sediments in Lake of
the Clouds, northeastern Minnesota. Limnol. Oceangr. 22:45-54.
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examination of water and wastewater, 13th ed. Washington, D.C.
Bachmann, R. W., and C. R. Goldman. 1965. Hypolimnetic heating in Castle
Lake, California. Limnol. Oceanogr. 10:233-239.
Ball, J. W. , E. A. Jenne, and J. M. Burchard. 1976. Sampling and preserva-
tion techniques for waters in geysers and hot springs, with a section on
gas collection by A. H. Truesdell. Proceedings First Workshop on
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Bannerman, R. T. 1973. Interstitial inorganic phosphorus in Lake Wingra
sediments. M.S. Thesis, University of Wisconsin-Madison. 120 p.
Bannerman, R. T., D. E. Armstrong, G. C. Holdren, and R. F. Harris. 1974.
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Great Lakes Res. p. 158-178.
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Hill (ed.), The Sea, vol. 1. Interscience. New York.
Baumann, E. W. 1974. Determination of parts per billion sulfide in water
with the sulfide-selective electrode. Anal. Chem. 46:1345-1347.
Berner, R. A. 1964. Stability fields of iron minerals in anaerobic marine
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Berner, R. A. 1967. Thermodynamic stability of sedimentary iron sulfides.
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Berner, R.A . 1970. Sedimentary pyrite formation. Amer. J. Sci. 268:1-23.
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Birge, E. A, and C. Juday. 1911. The inland lakes of Wisconsin. I. The
dissolved gases and their biological significance. Bulletin Wis. Geol.
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Birge, E. A., C. Juday, and H. W. March. 1927. The temperature of the bottom
deposits of Lake Mendota; A chapter in the heat exchanges of the lake.
Trans. Wis. Acad. Sci. 23:187-232.
Blanton, J. 0. 1973. Vertical entrainment into the epilimnia of stratified
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Bryson, R. A., and V. E. Suomi. 1951. Midsummer renewal of oxygen within the
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