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
                db    o
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

-------
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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     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

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                        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

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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

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          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

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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

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     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

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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

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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

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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

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     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

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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

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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

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                          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

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                    13° 15°     19°  22° c
                                    14m
                         13°  15°    19°  22°  c
                                   14m
Figure 15. (continued)
                              43

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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

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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

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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-
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 DEPTH  « Z , m
14
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24
       Figure  16.   Ratio  of sediment contact area to  lake
                    area  for five southern Wisconsin lakes.
                                47

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        51

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(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



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3
0
0 * *0
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1*1
2
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6
Mn

3
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Mn
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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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     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

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     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

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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

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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

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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

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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

-------
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                                                               Q.
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                                                               o

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                                                               Ol
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                                                               3:

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66

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     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

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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

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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

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     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

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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

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     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

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     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

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     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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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.

APHA  (American  Public Health  Association).   1971.   Standard methods for the
     examination of water and wastewater, 13th ed.  Washington, D.C.

Bachmann,  R.  W., and  C.  R. Goldman.   1965.   Hypolimnetic  heating in Castle
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Ball, J. W. ,  E.  A.  Jenne,  and  J.  M.  Burchard.   1976.  Sampling and preserva-
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Bannerman,  R.  T.    1973.   Interstitial  inorganic  phosphorus in  Lake Wingra
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Bannerman,  R.  T.,  D.  E.  Armstrong, G.  C.  Holdren,  and  R.  F.  Harris.  1974.
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Barber, N.  F. ,  and  M.  J.  Tucker.   1962.  Wind  waves, p. 664-699.  In:  M. N.
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Berner,  R.  A.    1967.  Thermodynamic  stability  of  sedimentary iron sulfides.
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     0.1 M NaCl system.  Environ.   Sci.  Technol.  4:517-519.

Williams, J.  D.  H., J.  K.  Syers,  R.  F.  Harris, and D.   E.  Armstrong.   1971a.
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Williams, J.  D.  H,  J.  K.  Syers,  D.  E.  Armstrong, and  R.   F. Harris.   1971b.
     Characterization of  inorganic phosphate in noncalcareous lake sediments.
     Soil Sci. Amer. 35:556-561.

Williams,  J.  D.  H. ,  J.  K.  Syers,  S.   S.   Shukla,  R.  F.   Harris,  and  D.  E.
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Williams,  J.   D.   H. ,  J.   M.  Jacquet, and  R.  L.  Thomas.    1976.   Forms  of
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                                                       * US GOVERNMENT PRINTING OFFICE 1981 -757-064/0316

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