Stratification dynamics in wastewater stabilization ponds

;Vat. Res. Vol. 29, No. 8, pp. 1909-1923, 1995

Pergamon

0043-1354(95)00011-9

Elsevier Science Ltd. Printed in Great Britain

STRATIFICATION DYNAMICS IN WASTEWATER STABILIZATION PONDS RUOCHUAN

G U 1. a n d H E I N Z G. S T E F A N 2

~Department of Civil and Construction Engineering, Iowa State University, Ames, IA 50011 and 2St. Anthony Falls Hydraulic Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, M N 55414, U.S.A.

(First received June 1994; accepted in revised form January 1995) Abstract--Measurements show that wastewater stabilization ponds although often only 1-2 m deep stratify and destratify intermittently depending primarily on weather. Stratification can be observed in vertical profiles of water temperature, dissolved oxygen, pH and other water quality parameters. In three stabilization ponds of a small Minnesota town, stratification develops primarily by differential heating o f the pondwater through its surface and, in the absence of artificial aeration or mixing devices, by insufficient wind mixing. The resulting water temperature stratification affects other parameters in a variety of ways through chemical, microbial and planktonic kinetics and reduced vertical mixing. To gain a better understanding of stabilization pond water quality dynamics, temperature profiles were monitored at 20-min intervals, and a dynamic lake water quality model was modified and applied to simulate the temperature slratification. A 12-h timestep option was incorporated into the program in order to capture the diurnal variation in stratification. Measurements and simulations were made for three wastewater stabilization ponds at Harris, Minnesota. The level of agreement between field measurements and numerical simulations demonstrated that water temperatures and stratification dynamics in a shallow and small pond can be simulated on a diurnal timescale with a standard error from 1.0 to 1.5°C between simulation and measurements. The model includes wastewater inflow in the form of a vertical jet and water transfer betwe,,~n ponds in the form, 9t: non-surface inflow and outflow. Three types of stratification were identified and 1'.heirrespective durations were determined. Stratification occurred on about 55% of all days from 1 April lo 30 November. Information on pond stratification presented can be used to guide field studies and reactor modeling of ponds which can lead to further improvements in design and operation.

Key words--~aixing, numerical simulation, ponds, stratification, water quality, water temperature, wastewater stabilization

A a b c C

= = = = =

C~ = C2 = Ck = Cr = Di = E = Fr = Fr¢ = Frs = g = G= H = Hp = Hs = H~m~ = I = Kz =

maximum hypolimnetic diffusion coefficient (m2/s) N = Brunt-Vaisala frequency (s- t ) O = outflow flowrate (m3/s) P = precipitation flux (m3/s) q = entrainment flowrate from a horizontal water layer (m3/5) Q = flowrate or volume flux (m3/s) Qo = entrainment fiowrate (ma/s) Qj = inflow jet discharge (m3/s) Qp = interflow flowrate (m3/s) Qt = total flowrate (m3/s) s = percentage of sunshine t = time (s) T = temperature (°C) Tj = inflow jet temperature (°C) Tp = interflow temperature (°C) Uj = inflow discharge velocity (m/s) c = vertical velocity (m/s) V = volume (m 3) W = wind speed (m/s) z = vertical distance or elevation (m) Az = thickness of horizontal water layer (m) p = water density (kg/m 3) P0 = ambient water density (kg/m 3) pj = inflow jet water density (kg/m 3) Ap = density deference between jet and ambient pond water (kg/m 3)

gzmax =

NOMENCLATURE surface area o f a pond (m 2) constant coeJ:ficient constant coel~icient heat capacity (kJ/kg °C) minimum value of N at which K:m~xoccurs, taken to be 8.66 × 10 -3 (s -I) constant coefficient constant coelficient constant coefficient percentage of cloud cover inflow jet diameter (m) evaporation flux (m3/s) densimetric Froude number critical densimetric Froude number stable densimetric Froude number acceleration of gravity (m/s 2) flowrate of groundwater seepage (m3/s) pond depth (m) intruding depth o f interflow (m) total solar radiation (kcal/m 2 day) maximum solar radiation (kcal/m 2 day) inflow fiowrate (m3/s) vertical diffusion coefficient (m2/s)

*Author to whom all correspondence should be addressed. 1909

1910

Ruochuan Gu and Heinz G. Stefan I. I N T R O D U C T I O N

Stabilization ponds are an economical and efficient method of wastewater treatment in small communities. This form of wastewater relies upon the natural ability of a body of water to achieve self-purification, such as reducing the suspended solids, the bacterial content and the organic content, and returning the dissolved oxygen concentration to a desirable level. Overall efficiency of waste stabilization ponds is a function of many interacting processes. Connections and relationships between mixing, stratification and planktonic kinetics have been investigated in lakes and oceans, and the findings are related to processes in ponds. Wastewater stabilization ponds, however, differ from lakes in nutrient loading, oxygen demand, depth, size, water residence time, material residence time, flow control and therefore separate detailed studies in wastewater ponds are needed. To gain a better understanding of the important factors which control the effectiveness of various methods of stabilization pond management, a study of the physical, chemical and biological processes has been initiated. Reported herein are some observations and a simulation model for physical processes, primarily mixing and stratification. The physical limnology of the wastewater stabilization ponds at Harris, Minnesota, was investigated by Luck and Stefan (1990), including continuous recordings of water temperature and associated meteorological parameters, intermittent measurements of underwater light, dissolved oxygen and Secchi depth and observation of ice thicknesses and snow cover in winter. Alternating mixing and restratification of these ponds over periods of hours or days was observed. These dynamic physical processes which are in response to time-variable weather affect the water chemistry, microbial and planktonic processes. Intermittent stratification sometimes lasting several days has a strong effect on sediment/water interaction

and vertical transport of dissolved oxygen, nutrients and phytoplankton in the pond. Field studies are needed to study pond problems but numerical modeling of pond water quality dynamics is necessary to explore the improvement of pond operation and performance. In this paper the adaptation of the M I N L A K E water quality model (Riley and Stefan, 1988) to a pond is described. A jet inflow and mixing model is incorporated. Simulated results are compared with field measurements, and three types of stratification and their duration are identified. The model's ability to simulate observed temperature stratification dynamics in the Harris ponds, Minnesota, is demonstrated. Briefly discussed also are chemical, microbial, and planktonic kinetics under stratification conditions, and potential applications to design, operation and performance evaluation of waste stabilization ponds. 2. S I T E OF S T U D Y

The wastewater treatment facility at Harris, Minnesota, is typical of many new installations. It consists of three stabilization ponds. Each pond is rectangular in shape, having a fiat bottom with dimensions of 55 m by 92 m. The dikes containing each pond, rise at a slope of 1 : 4. The surface area of a full pond, 1.8 m deep, is 69 m by 107 m, or 7383 m 2. Wastewater is pumped underground through a 101.6 mm (4 in.) diameter pipe and discharged vertically in the center of pond 1 (Fig. 1). The inflow rate and the inflow water temperature were continuously measured at the pumping station during operation for about 1 year (Luck and Stefan, 1990). The average inflow rate was 0.0167 m3/s (185 gallons per minute). The actual inflow was intermittent at roughly 20 min intervals and for 2-3 min. This form of wastewater inflow produces a forced jet which upwells on the surface and spreads laterally on the

&Z

[NEARFIELD

i

d _ ~ ~ '

=

:Point ,

T

FARFIELD

Plunging',

~

/

]

--_::::-_--

i

,, ; I

,

:

'-#

;

!!1 1 ' T Jet

'

Intruding/ ading Flow ~ "

rature ,

/

t

P'rOtlle

/

Dj, Uj. Tj

Fig. 1. Flow pattern and jet behavior of the wastewater discharge in pond 1.

I

/

Stratification dynamics in wastewater ponds surface. Figure 2 schematically illustrates the water transfer system between ponds and inflow to pond 1 and outflow from pond 3. The pond has a maximum depth of 2 m. The outlet pipes withdraw water from an elevation approx. 0.6 m above the pond bottom. During the summer months the ponds are operated in series. As water accumulates in pond 1 it is intermittently transferred to pond 2, and eventually to pond 3. This water transfer is gravity driven with the flow rate controlled by the use of various sized gates in the control structures. In wintertime, the water flows freely between pond 1 and 2 as the control gate betwee, n them is kept open. Pond 3 is discharged intermittently, typically during the spring and again during the fall, into a ditch that flows into Goose Creek and tlaen into the St Croix River. During two years of field studies Luck and Stefan (1990) documented hydrothermal (physical) features in the Harris wastewater stabilization ponds in detail at time scales of rainutes. Based on the observed temperature (densJLty) stratification, inflow and weather, numerical simulations of temperature stratification dynamics, jet mixing and submerged outflow are possible using a modified version of the dynamic lake water quality simulation model MINLAKE. 3. MODEL FOR SIMULATION OF STRATIFICATIONAND MIXING DYNAMICSOF PONDS 3. I. Overview A pond is usually much smaller and more shallow than a lake and has high nutrient/suspended solids loading. Therefore modifications of the water temperature simulation model originally developed for lakes by Ford and Stefan (1980) and Stefan et al. (1982) and incorporated by Riley et al. (1988) into the M I N L A K E program had to be made for application to wastewater ponds. The M I N L A K E model was developed originally to simulate principal hydrotherreal, chemical and biological processes in a lake on a daily time scale over the open water season. The

output of the M I N L A K E program consists of daily vertical distributions of water temperature, dissolved oxygen, suspended solids, phosphorus and phytoplankton. Simulations can be carried out over periods of months. Morphometry, weather and inflow data are required as input. This process-oriented, deterministic water quality model solves the one-dimensional, unsteady vertical mass transport and heat transfer equations. Heat fluxes at the water surface are related to weather parameters. The thermal state of a lake is governed by the one-dimensional unsteady advection-diffusion equation OT v O(TA) Ot -~ A Oz

10"

PIPE

WEIR

=

1 ~( A

--

K~A

OT~+ S -~z ,] - pc

(1)

where A = horizontal area of lake at depth z, e = heat capacity, K~ = turbulent diffusion coefficient, S = heat source or sink per unit volume, T = temperature, t = time, v = vertical velocity, z = vertical coordinate, and p = density. The time step in the numerical simulation had to be reduced in order to capture the diurnal stratification and destratification dynamics of the shallow ponds. Inflow distribution was incorporated by a submodel which simulates jet entrainment from ambient water, depth of flow intrusion and forced mixing of the pond water. A sub-surface inflow and outflow submodel was developed to simulate the water transfer between ponds including effects on the stratification and water balance. A submodel for the heat exchange with lake bottom sediments was also incorporated into the pond model (Gu and Stefan, 1991a). The submodel was previously discussed by Gu and Stefan (1990). The effect of wind on vertical mixing in the pond is much less than in a lake. This had to be accounted for in the simulation, as discussed in the next section. In order to simulate the diurnal effects, i.e. the onset and the disappearance of temperature stratification in the pond, a time step smaller than one day had

2/

%"°'

PIPE

1911

POND 3

| 10"

PIPE X VALVE

lo'piPE

Fig. 2. Schematic of wastewater flow pathway in the Harris ponds.

lo'PIPE

1912

Ruochuan Gu and Heinz G. Stefan

to be used. Changing from the original time step of one day to one of 12 or 6 h required modification of the program and extension of input data. Details are given by Gu and Stefan (1991b).

3.2. Vertical thermal diffusivity in ponds Flow mechanisms contributing to vertical transport and mixing are currents, breaking internal waves, and internal shear instability or natural convection due to cooling. In the model vertical transport is simulated by turbulent vertical diffusion and the vertical diffusion coefficient Kz [equation (1)] has to be specified. The parameters to which K~ can be related are pond surface area, A, maximum depth, H, strength of stratification represented by BruntVaisala frequency, N, and wind speed, W. The diffusion coefficient, Kz, in the pond epilimnion (surface layer) was related to wind speed, W, by a function (Filatov et al., 1981; Riley and Stefan, 1987, 1988) K~ = Ck(0.6214W) b

(2)

where Ck and b are constant coefficients, W is in km/h and K~ is in m2/d. The hypolimnetic diffusion coefficient was determined from K~ = min[K~. . . .

KzmaxC N - ']

3.3. Inflow jet entrainment and mixing The inflow of wastewater to pond 1 forms a strong vertical jet. Figure 1 illustrates schematically the flow pattern produced by the wastewater discharge in pond 1 during the summer. The entrainment by the jet, the spreading and the plunging due to differences in densities between the incoming and the ambient pond water were analyzed to develop a simple jet mixing model as follows. The jet entrains much ambient water from the bottom portion of the pond. The jet reaches and overshoots the water surface because of the shallow water depth and high initial jet momentum. The condition for overshooting is the exceedance of a critical densimetric Froude number for the round jet, Frc (Gu and Stefan, 1991a)

H3/2 Frc = 0.087 D~/--~

(4)

in a stratified pond, where H = total water depth and Dj = jet diameter. Jet densimetric Froude number is defined as Fr =

Uj

(5)

(3)

where K~ax = maximum hypolimnetic diffusion coefficient estimated from surface area of the lake and C = minimum value of N at which the K~maxoccurs, taken to be 8.66.10 -3 s -l (Jassby and Powell, 1975). Effects of the stratification parameter N on K~ in the hypolimnion are also discussed by Ward (1977) and Hondzo et al. (1991). Equations (2) and (3) suggest that wind speed is of dominant importance for epilimnetic diffusion, and that stratification affects the vertical diffusion in the hypolimnion. Effects of pond surface area on K~ are hidden in the empirical coefficients Ck and b (epilimnion) and K~m~x (hypolimnion). The empirical coefficients Ck and Kzmaxare calibration parameters for the model. A Ca value in the range of 0.14).3 is suggested based on the model calibration. For Kzmax a value of 0.1 m2/d was used. In lakes these values would be larger. When the model is applied to ponds of different sizes, the dependence of epilimnetic K. on surface area A has to be considered. A strong correlation exists between vertical diffusion coefficient and lake surface area (Ward, 1977; Hondzo et al., 1991). Ward concluded that lake surface area is the dominant factor for vertical hypolimnetic diffusion. Hondzo et aL (1991) gave a K., vs A T M correlation based on data for six Minnesota lakes. Dimensional analysis performed by Ward (1977) on 15 lakes gave a linear relationship, K= vs A 0.5, for lake hypolimnia. Similarly, a K~ vs A °'7s correlation was obtained by Gu and Stefan (1991 b) for lake epilimnia with a reference parameter A °5/H, the ratio of approximate lake fetch to maximum depth.

in which Uj = discharge velocity, Ap = (P0 - P j ) = density difference between jet and ambient pond water at the discharge. For the wastewater discharge in Harris Pond 1, one obtains Fro=6.5 with Dj = 0.10 m and H = 1.8 m. For a typical temperature difference of 7°C, the density difference is Ap = 0.9 kg/m 3. With Uj = 1.44 m/s Fr is estimated as Fr = 48. Since this value is much larger than Fro the discharge jet is predicted to emerge on the water surface, as was indeed observation in the field. Following impingement and radial spreading on the water surface, the much diluted inflow sinks (plunges) into the pond (Fig. 1). A horizontal intruding-spreading interflow is formed where buoyancy is neutral, i.e. where current density is identical to ambient water density (equilibrium layer). A densitytemperature function p ( T ) (Gu and Stefan, 1988) is used to determine the depth of the interttow layer by neutral buoyancy. If information is available, density due to total solids can also be taken into account in the water density calculation. The discharge configuration in Fig. l is termed "stable" because the interflow water is not recirculated into the buoyant jet. Based on theoretical and experimental studies of an axisymmetric (round) turbulent buoyant jet discharged vertically into a stagnant shallow water body, Lee (1980) indicated that there would be no recirculation if the jet densimetric Froude number Fr [equation (5)] is less than the value H Fr~ = 4.6 - - .

Dj

(6)

Stratification dynamics in wastewater ponds For the wastewater discharge in Harris pond 1, Frs = 82. The jet flow in pond 1 satisfies the stability criterion. If Fr is greater than Frs due to either shallow water (H) or low buoyancy (Ap) or high initial momentum (Uj), an unstable discharge configuration is formed. In this situation, recirculation cells are set up near the jet discharge, leading to re-entrainment into the discharge. It was also suggested by Lee (1980) that in deep water and under stable discharge conditions, the spreading layer thickness on the surface was about one tenth of the tc,tal depth (0.1H). Therefore the depth over which jet entrainment contributes to dilution of the jet is estimated to be on the order of 0.9//. A simplified model for jet entrainment in the nearfield and mixing in the farfield is formulated for incorporation into the pond temperature stratification simulation model. The entrainment rate of ambient water by the vertical jet is determined from the jet flowrate as a function of distance from the orifice (Albertson et al., 1948)

__e Qj=

1 + l'0133C2w+zj 1.9735C

.

(7)

in which Q = volume flux at vertical distance z above the efflux, Qj = jet discharge, (72--coefficient, in the range from 0.081 to 0.111. The total entrainment by the jet over height 0.9H is estimated as Q, = Q ~ - Qj

(8)

or

I,.0,33c2 +,.9735c ( )21. Entrainment from an individual horizontal water layer of thickness Az at height z is q = dQ Az dz

1913

from the layer. The interflow is added to the equilibrium layer. The temperature in the equilibrium layer is modified by the incoming water. 3.4. Water transfer The water balance in a stabilization pond can be evaluated by the equation dV dt

--

=I-0

+_G -E+P

(14)

where V = storage volume of the pond, t = time, and L O, G, E, and P = flowrates of inflow, outflow, groundwater or seepage, evaporation and precipitation, respectively. The change in pond storage, dV, can be estimated from the depth-volume function using intermittently measured stages as input. Wastewater inflows to a pond are typically recorded at the pumping station. These records include flowrate, and temperature of the pumped wastewater inflow, from which the inflow volume, /, is calculated. Rainfall (precipitation) data are available from the weather station. The groundwater seepage, G, is neglected in this study because the ponds are lined. Outflow, O, can be estimated using equation (14). Evaporation is calculated from the evaporation heat flux in the water temperature model. Inflow to pond 2 is equal to outflow from pond 1, and similarly inflow to pond 3 is the same as outflow from pond 2 (Fig. 2). Outflow temperature from the pond is assumed to be water temperature in the pond at the level of withdrawal. Sub-surface inflows and outflows were incorporated in the simulation through model subroutines. In summary the numerical simulation with this simple water transfer model accomplishes the following: (1) determines the layer from which water is taken or to which water is added, (2) calculates the volume of withdrawal or addition for each layer in the pond and (3) computes the final temperature in each layer after mixing with inflowing water.

(10) 4. MODEL APPLICATION

or in numerical form

4.1. Concepts and input data

qt = Q(zi + ½Az~)- Q(zi - ½Azi), i = 1, 2 . . . . . I (11) where I = total number of layers contributing to entrainment and zi = elevation of layer i. It is assumed that there is no entrainment into the plungingintruding-spreading flow beyond the jet region (nearfield). Flowrate and temperature of the interflow are therefore approximated, respectively, as Qp = Qt

(12)

~', (q, Ti) + TjQj TD= i=' Qe+Qj

(13)

and 1

The volume of each layer in the pond is modified in each timestep by subtracting the water entrained

In a pond system, effluent water quality from the last of the wastewater stabilization ponds is of greatest concern since it has impact on water quality in the effluent receiving stream. Therefore, a simulation model for stratification dynamics in Harris pond 3 was developed, calibrated and verified first. After the addition of jet mixing and water transfer to the model, pond 1 and pond 2 could also be simulated. Eventually the entire pond system could be simulated as it is operated, starting with pond 1, transiting with pond 2 and ending with pond 3. This simulation procedure takes account of the unique jet dynamics and mixing processes in pond 1 and characteristics of water transfer between pond 1 and 2, as well as 2 and 3. Field measurements showed that water quality characteristics in pond 1 and pond 2 are similar but pond 3 has clearer water and weaker stratification

1914

Ruochuan Gu and Heinz G. Stefan

than the other two. The main season for pond or lake water quality problems is summer. The periods from 1 August to 30 November 1989 and from 7 April to 31 October 1990 were therefore selected for the simulation of pond 1. Temperature stratification in pond 3 was simulated for the period from 1 August to 31 October 1989 and from 7 April to 31 October 1990. The simulation for 1989 served to calibrate the model. Model validation was made against the 1990 data, Input requirements for the water temperature profile simulations include the initial conditions, pond morphometry, the meteorological data file and the inflow/outflow data file. All data files must be organized for the half day time steps. Meteorological input data include solar radiation, air temperature, dew point temperature, wind speed and direction and precipitation. Estimates of cloud cover were made from solar radiation measurements using the relationships (Baker and Enz, 1979) Cr = 100 - S

(15)

and S = a

Ms

x 100

(16)

nsmax

where Cr = percentage of cloud over, S = percentage of sunshine, a = coefficient, Hs = total solar radiation and H .... = maximum solar radiation (clear day). The mean value of coefficient, a, was determined from Twin City weather data for 1971-1972 and 1982 to be 0.952. Hsmaxis used as an input weather parameter in the meteorological data file. Calculation of Cr is incorporated into the program. For the Harris ponds data were available for meteorological parameters (measured at 2min intervals and averaged over 20 min intervals), light attenuation, Secchi depth and

pond stage or depth. The weather records were displayed graphically in the report by (Luck and Stefan, 1990). Measurements came from a weather station located between pond 1 and pond 2 Luck and Stefan (1990). Measured values of the light attenuation coefficient include the effect of suspended solids, mainly detritus and phytoplankton. There were no direct measurements of outflow flowrates from pond 3. These flowrates were therefore evaluated from the water budget equation [equation (14)] and the volume-depth relation. 4.2. Model calibration

Figure 3 shows an example of simulated and measured water temperature profiles in pond 3. Simulations begin with 1 August 1989. Field data are from measurements made at 6:00 a.m. The applicability of the simulation model to the pond is demonstrated by the small error between field data and model simulated water temperatures. Analysis of 110 pairs of data gave a regression slope of 0.99, a regression coefficient of 0.98, and a standard error of 0.56°C. Definitions of parameters used in the statistical analysis were listed by Gu and Stefan (1991a). Values of the maximum hypolimnetic diffusion coefficient, wind function coefficient and wind sheltering coefficient, which were defined by Riley and Stefan (1988), were calibrated to be 0.1 m2/day, 20 and 0.1 respectively. The coefficient Ck in equation (2) for K~ was set to be 0.2. Strong diurnal cycles of temperature stratification during the summer period are evident in the field data recorded by Luck and Stefan (1990). During day time, absorption of solar radiation in the surface layers caused a temperature stratification to occur. The stratification gradually became stronger, beginning in the morning, and reaches a maximum in mid-afternoon. An isothermal surface mixed layer

0

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0.2 0.4

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0,8 1.0 1.2

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1.4

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DATA, AUG. 13 MODEL, AUG. 13

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DATA, SEPT. 2 MODEL, SEPT. 2 DATA, OCT. 13 MODEL, OCT. 13

I

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30

35

40

T E M P E R A T U R E (°C)

Fig. 3. Temperature stratification simulation with a timestep of one day: pond 3, 1989.

Stratification dynamics in wastewater ponds developed by convective cooling during the night. To gain insight into the cycle of daytime stratification and night mixing, which is paralleled by strong vertical gradients of dissolved oxygen and other water quality parameters, a half-day timestep referred to earlier had to be used in the simulation. Shown in Fig. 4 are the measured and simulated temperatures at 6:00 a.m. and 6:00 p.m. over a period of approximately two months in late summer/early fall. The morning temperatures (6:00a.m.) were measured after night cooling and coincide with the lower boundary of the simulated temperatures. The evening temperatures (6:00 p.m.) were measured after a day of heating and form the top boundary. The temperature difference between morning and evening has its maximum value (up to 5°C) in the surface layers, is less with depth and becomes very small (0 to 0.5°C) at the bottom. The values in Fig. 4 are for depths of 0.04 m and 0.60 m below the water surface.

1915

The diurnal cycle of stratification and mixing and its variation with depth can be more clearly seen in Fig. 5. The analysis of errors between field data and model simulations for 1989 was based on 800 pairs of water temperature data (Table 1). Slope of model to data regression is 1.00. Regression coefficient is 0.96. The standard error of estimate is 1.04°C. These statistics indicate good agreement between field data and numerical simulations with a half-day timestep.

4.3. Model verification Following standard practice, the model is verified by returning the calibrated model over a different simulation period than that used for calibration. Comparison of water temperature model results to field data for a second simulation period (7 April to 31 October 1990) indicates that the calibrated model

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MEASURED6:00AM + • MEASURED6:00 PM SIMULATED

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~

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PROBE#3 AT DEPTH0 60 M 5

0 210

2,~.0 230

2~t0 250 260 270 JULIAN DAY, 1989

280

290

300

Fig. 4. Morning and evening water temperatures from 1 August to 31 October 1989 at depths of 0.04 and 0.60 m in pond 3.

R u o c h u a n G u a n d H e i n z G . Stefan

1916

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TEMPERATURE(°C)

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TEMPERATURE(°C)

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T E M P E R A T U R E (°C)

Fig. 5. E x a m p l e s o f m o r n i n g a n d e v e n i n g w a t e r t e m p e r a t u r e profiles in p o n d 3.

can simulate other time periods as shown in Fig. 6. Water temperatures records for the upper probes are missing because pond 3 was drained to 0.61 m at the beginning of June 1990 (Julian day 152) and filled back to 1.6 m at the end of that month (Julian day 18i). During that period, the upper probes were exposed to air. Pond water depths were measured only every 1 to 3 Weeks and water depths on days between measurements were linearly interpolated.

Generally, the fit between measured and simulated water temperatures was proper during the draining and filling periods. Analysis of errors between field data and model simulations based on 1904 pairs of water temperature data for pond 3 gave a slope of model to data regression of 1.00, a regression coefficient of 0,94 and a standard error of estimate of 1.46°C (Table 1). Similar values obtained for pond 1 are also listed in Table 1.

Table I. Results of statistical error analysis for comparison of field data and model simulations

Pond 1 1 3 3

Period

Timestep (h)

Number of data point

Mean temperature field ("C)

Mean temperature model (°C)

Standard error (°C)

Slope of regression sr

Regression coetlieient r2

I/8-30/11/89 7/4-31/10/90 1/8-31/10/89 7/4-31/10/90

12 12 12 12

1566 2337 800 1904

13.52 18.24 19.25 19.64

13.98 18.10 19.23 19.42

1.33 1.36 1.04 1.46

0.96 1.00 1.00 1.00

0.97 0.95 0.96 0.94

Stratification dynamics in wastewater ponds

1917

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+

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li0

130 150 1"70 190 2i0 250 250 230 2!~0 310 JULIAN DAY, 1 990

Fig. 6. Morning and evening water temperatures from 1 April to 31 October 1990 at depths of 0.30 and 1.20 m in pond 3.

4.4. Simulation of stratification dynamics with jet mixing A strong vertical jet is produced by the inflow of wastewater to pond 1. Entrainment of ambient water by the vertical water jet is a function of the total pond water depth as described in equation (6) and illustrated in Fig. 7. The calculated ratio of entrainment, Q=, to the inflow, Qj, iis in the range of 5-10 for 1989 and 8-10 for 1990. The temperature in the intrudingspreading layer (Fig. I) depends on both inflow and ambient water temperature. Temperature of the spreading water (Fig. 8) is mainly determined by the ambient water temperature because of the high entrainment rates. Figm'e 8 also shows the simulated depth at which the flow intrudes and spreads after plunging, i.e. the depth of equilibrium layer. That depth can be seen to vary significantly in time. The inflow spreads close to the bottom when the inflowing

water is colder (heavier) than the pond (ambient) water. The role of jet entrainment and mixing in the temperature stratification of pond 1 can be seen by a comparison of temperature vs. depth profiles simulated with and without the jet model (Fig. 9). When the wastewater inflow is colder than the ambient pond water, as is typical for the summer, the inflow plunges to the bottom of the pond (Fig. 8) and temperature stratification in the pond seems to be enhanced (Fig. 9) compared to a pond without a jet discharge. A warmer than ambient discharge into the pond also enhances the stratification. The jet discharge into pond 1 appears to enhance stratification by placing the inflow to its equilibrium depth. Jet mixing does not appear to compensate for this effect fully. Simulated pond temperatures including jet mixing and water transfer are presented in the form of time series and compared to measured temperatures for

Ruochuan Gu and Heinz G. Stefan

1918 WATER DEPTH

(rn)

(Qe + Qj)/Qj

2.4

12 []

2.2 .

2

.

.

.

MEASURED DEPTH 11

SIMULATED DEPTH

.

.

.

.

.

10

1.8

9

1.6

8

1.4

7

1.2

6

1 200

I 220

i 240

I 260

L

~

280

300

I 320

5 340

JULIAN DAYS, 1989 Fig. 7. Calculated entrainment by inflow jet and measured and simulated water depth: pond 1, 1 August to 30 November 1989.

probes placed at different depths in pond 1. Probe Nos 1-6 were located at 0.04, 0.20, 0.40, 0.60, 0.80, 1.00 m depth, respectively. Probe No. 7 was fixed at the pond bottom. Results shown in Figs 10 and 11 suggested that the computed and measured water temperatures in the pond agree closely. Statistical results from error analysis of field data and modeled water temperatures are given in Table 1. Poorer agreement was achieved with weaker stratification; upper (top) layer temperatures were underestimated and lower (bottom) temperatures overestimated. This may be related to insufficient information on concentration of solids and algae and hence light attenuation in the pond. Pond 1 had high solid concentrations which contribute to high light attenuation resulting in strong stratification. Values of attenuation coefficients are from 3 to 11 (m -m) for pond 1, in contrast to a range of 1.5-3.5 (m - l ) for pond 3. Better results for pond 3 than pond 1 were obtained in the model calibration and verification as shown in Table 1. In the numerical prediction, a constant attenuation coefficient for the whole simulation period was used and effects of time variable solids and algae concentrations have not been simulated. An improvement may occur after the model is extended to include time variables of chemical and biological components. 5. EVALUATIONOF SIMULATIONRESULTS Pond water temperatures, simulated, or measured by probes distributed from the water surface to the pond bottom, were presented in form of temperature versus time plots in Figs 4, 6, 10 and I 1. These figures, as well as the composite pond water temperature

profiles in Figs 5 and 9, show the presence of strong temperature stratification dynamics clearly. Solar radiation causes daytime heating of the surface layers and contributes mainly to the temperature stratification of the ponds. A completely or partially mixed state is brought about by nighttime cooling. Air temperature also is a factor affecting heat exchange through the surface and pond temperature stratification. Naturally, more mixing occurs during periods of stronger winds. Based on the variability of the thermal structure of the ponds over months as described by the variation of temperature distributions with time and depth, the ponds experience three types of stratification. They can be (I) completely mixed during consecutive day and night, or (II) stratified during the day and mixed during the night or (III) continuously stratified during several days and nights. The number of days for which each type of stratification and/or mixing was observed or simulated is given in Table 2. Each type of stratification can appear several times in a month. The total number of days for each of the three types of stratification, measured (m) and simulated (s), were compared for an overall evaluation of simulations of dynamic stratification processes (Table 2). A error is defined as the difference between the measured and simulated number of days in a year for each type of stratification. The relative error is the normalized absolute error with respect to the measured days. As listed in Table 2, the maximum absolute error is 9 days and the minimum error is 0; the relative error reaches its maximum at 63% and minimum at 0%. The mean relative errors for type I, II and III stratification, respectively, are calculated

Stratification dynamicsin wastewater ponds

TEMPERATURE

MEAN ~ T E R TEMP. DATA M E A S U R E D , e:O0 pm

r-l

M E A S U R E D , 6:00 a m _

. -

A

~

20 "'

J ,/~l,

/ / I I [I

~:

15

Hp)/H

(H -

"~

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30

('C)

1919

r.

.~..~

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~ ~, ..,.,,~A .... .4t ~fv,--rft~t'V

lwll[ [

1

[ [

0.8

"%"

0.4

P~

,

"

10

Tp

0

200

220

240

260

280

300

320

340

JULIAN DAYS, 1989 TEIvllPERATURE (°C)

(H - Hp)/H

351

1

• Ill

i

30

(H- Hp)IH /

TD

i

08

,

25

20

¢ .,•

15

rj

,~

~'~

;~

~

0.6

..

0.4

10 0.2 5

0 80

0 100

120

140

160

180

200

220

JULIAN DAYS, 1990 Fig. 8. Measured jet inflow temperature Tj, simulated spreading flow temperature Tp and intruding interflow depth (H-Hp)/H in pond 1. from results for pond I and pond 3 in 1989 and 1990 (total 596 days). The numerical model simulated type I, i.e. complete mixing during day and night with only 2% overprediction. Type I occurred on 268 days based on the field data and 273 days according to the model. Type II, i.e. day stratification and night mixing, was underpredicted with an average error of 16% (me~.sured 169 days and simulated 141 days). The model :simulated type III, i.e. stratification during consecutive days and nights with an average 14% error (measured 159 days, simulated 182 days). These results may be probably improved

by reexamining the effects of wind and night cooling on mixing.

6. EFFECTSOFSTRATIFICATIONONPOND WATERQUALITY Current methods of design, operation and performance evaluation of waste stabilization ponds usually assume that the ponds are well-mixed reactors (James, 1987; Pearson et aL, 1987), However, existence of stratification in the ponds has been recognized and observed (Luck and Stefan, 1990; Pearson et al.,

Ruochuan Gu and Heinz G. Stefan

1920 0

--

DATA, 6:00 AM DAY 184

0.2-

MODEL WITH JET 0.4 --

MODEL WITHOUT JET

0.6-

o

DATA 6.00 PM DAY 200 B~

MODEL WITH JET

E 0.8 .1I- 1 . 0 ix uJ a 1.2-

MODEL WITHOUT JET

1.41.61.8-

2.0

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

lO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

I

I

I

I

I

26 27 28 29 30

W A T E R T E M P E R A T U R E (°C) Fig. 9. Water temperature profiles simulated with jet and without jet, pond 1, 6:00 a,m., 3 July and 6:00 p.m., 29 August 1990. 35 A

(") 30-

~~~÷

c~

MEASURED 6:00 A M

+

MEASURED 6:00 PM

--

SIMULATED

v

+

LU

+

25-

÷

W 15-

j

10-

DEPTH 0 2 0 . POND 1 0 2OO

~o

2~,o

2~o

2~o

360

3~,o

340

320

340

35¢O

[]

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g 26

MEASURED 6:00 A M

O TEO ÷

U.I

MEASURED 6:00 PM

~ 20UJ e¢"

10-

o'-

200

220

240

260

,

280

300

JULIAN DAY, 1989 Fig. 10. Morning and evening water temperatures from 1 August to 31 October 1989 at depths o f 0.2 and !.0 m in pond 1.

Stratification dynamics in wastewater ponds

f.

PROBE,,,AT

~" 30V

DEPTH

LU

POND ~

+

+. ,.14, .,-+ ~ ,.

'41- '4"

JB..II.

0.04 M .

-~

1921

?.

l~r.I'l.d-~-~l~

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÷ MEASURED6:00 PM SIMULATED

0 90 1i0 130 1~i0 170 190 21"0 230 250 270 2 ~ 35 30 re't'U'lt" 25

310

PROBE#4 AT DEPTH0.60 M POND1

.

,

~

~

~

1,]

:i:I:: SIMULATED

5] ~

O9o 1i0 1~0 1~0 1-~0 190 2i0 2~0 2~0 z?02~o alo JULIAN DAY, 1990 Fig. 1 !. M o r n i n g a n d e v e n i n g w a t e r t e m p e r a t u r e s f r o m 7 A p r i l to 31 O c t o b e r 1990 at d e p t h s o f 0.04 a n d 0.6 m in p o n d 1.

1987; Llorens et aL, 1992; Curtis et al., 1994; Soler et al., 1991). Pearson et al. (1987) suggested that diurnal variations of pond effluent quality, and dissolved oxygen and temperature with depth (vertical

profiles) should be measured at least once during each sampling season for performance evaluation of waste stabilization ponds. The importance of stratification and mixing has previously been mentioned but its

Table 2. Number of days with specific measured and simulated stratification and mixing characteristics Year Pond Type m 1989 1

3

1990 1

3

April s m

May s m

June s m

July s m

I II III I II III I II III I II III

20 0 4

17 3 4

]2 6 13 12 1 18

12 5 14 12 1 18

7 10 5 29 l 0

8 6 8 28 2 0

4 13 14 12 17 2

7 9 15 14 II 6

August s m

September s m

October s m

5 17 9 8 23 0

8 12 11 10 15 6

12 16 2 11 I1 8

14 13 3 10 10 10

20 9 2 22 6 3

18 9 4 23 6 2

6 11 14 5 0 26

7 I0 14 5 0 26

16 12 2 7 6 17

14 I1 5 13 4 13

25 6 0 23 4 2

20 10 I 23 4 2

12 0 18

November December s m s m 10 0 20

Note: " m " , "s", " a " and " r " indicate measured, simulated, absolute and relative values, respectively.

Total s a

Error r%

49 42 31 41 40 I1

50 34 38 43 31 18

- I -2 8 19 -7 -22 -2 -5 9 22 -7 -63

90 58 52 88 29 65

85 54 61 95 22 65

5 5 4 6 - 9 - 16 --7 -8 7 23 0 0

1922

Ruochuan Gu and Heinz G. Stefan

significance has not been sufficiently stressed in manuals on pond design (James, 1987). The frequency (55% of the time in the relatively new Harris ponds) and strength (type I, lI, and III) of stratification have mostly been unknown and unused. Results and information presented here, coupled with a knowledge of chemical and microbial kinetics under stratification conditions, may be used to determine the maximum and equilibrium algal crops, and vertical distributions of particulate and dissolved materials that can occur in waste stabilization ponds. Significant impact of thermal stratification of ponds or shallow lakes on the water quality kinetics, including algae growth, were demonstrated by several investigators (Stefan et al., 1976; Llorens et al., 1992; Soler et al., 1991; James, 1987; Ganf, 1987; Curtis et al., 1994; Luck and Stefan, 1990; Happey, 1970). Examples of the strong interaction of stratification and water quality in waste stabilization ponds are diurnal dissolved oxygen stratification varying from anoxic conditions to supersaturation within less than 2 m depth and within 24 h (Luck and Stefan, 1990), daily migration of zooplankton consuming algae, and nutrient recirculation from sediments in a pond. Higher near-surface temperatures and the presence of a thermocline which prohibits mixing between bottom layer (hypolimnion) and surface layer (epilimnion), usually result in the variation of biochemical parameters such as phytoplankton, dissolved oxygen, and pH with depth (Soler et al., 1991; Lloren et al., 1992). Temperature and light limitation of phytoplankton growth is particularly important when nutrient supply is abundant as is the case in waste stabilization ponds. Stefan et al. (1976) found that in a eutrophic lake, equilibrium concentration of algae went down (10-3 g/m 2 POC) with increased mixed layer depth (2-6 m) because of the effect of selfshading, combined with respiration. When artificial mixing/aeration was applied, the phytoplankton concentrations in the mixed layer were 0.0-0.5 g/m 2 POC for a mixed layer depth of 9 m and 0.5-1.5 g/m 2 POC for a 6 m depth. It is also well-known from other limnological studies that stratification will enhance the growth of algae in the surface layer because of high available light intensity. Stratification also produces high effective settling rates of detritus due to reduced stirring or mixing. After strong winds, resuspension of stirred bottom sediments increases turbidity and light attenuation, thus reduces algal productivity. After very strong winds, increases in chlorophyll-a concentrations within the water column have been observed and attributed to stirring of superficial sediments containing viable phytoplankton and nutrients (Ganf, 1974). It can be concluded that stratification effects on waste stabilization pond are represented by DO depletion, enhanced algae growth, more nutrient recycling, and better settling efficiency of detritus. Ultimately stratification dynamics and effects on water quality kinetics should be given consideration

in design, operation and performance evaluation of waste stabilization pond systems. Selective withdrawal from the last pond (pond 3 in the Harris ponds study) and design of a deeper pond 3 may be necessary to take advantage of vertical distributions of water quality parameters. Artificial mixing/ aeration is suggested for the secondary ponds to create a mixed condition for reduced algal growth, but not recommended for the primary pond because of adverse effects on settling efficiency. Water transfer from pond to pond could be designed with consideration of withdrawal depth relative to stratification. Biomanipulation of zooplankton grazing of phytoplankton in ponds is constrained by stratification because of its close link to oxygen availability. In the operation of waste stabilization pond systems, the following actions can be related to stratification dynamics: (1) timing of discharge for water transfer between ponds; (2) timing of release (selective withdrawal) from the secondary or last ponds; and (3) timing of artificial mixing/aeration, For the performance evaluation of a stratified waste stabilization pond with diurnal variation of water quality, time and depth of sampling need to be planned carefully as suggested by Pearson et al. (1987). As the stratification study shows, variations in a pond are very rapid, and well-mixed conditions can not be assumed. If this is not considered in water quality sampling in ponds and interpretation of results, erroneous conclusions are likely. This study of stratification dynamics may also raise questions if pond stratification should be enhanced or destroyed, and how and when. To answer these questions, process simulations for not well-mixed reactors including stratification dynamics as described herein are needed. With this goal it is necessary to further study chemical kinetics in waste stabilization ponds and to incorporate them into the simulations to represent the strong impact of stratification on chemistry. Biological kinetics also need to be added to improve modeling as migration of zooplankton in response to DO and presence or absence of macrophytes are significantly affected by stratification. 7. SUMMARY

Measurements and simulations of temperature stratification were made for three wastewater stabilization ponds at Harris, Minnesota. They were chosen for study because they are of modern design, had well-defined boundary and inflow conditions, were easier to monitor than larger ponds and were considered typical of a small community. The temperature stratification dynamics in these ponds were impressive in terms of the occasional strength of the stratification stability as well as its rapid variability in time. Vertical temperature differentials of up to 8°C over the first meter of depth were observed and simulated. Variations in surface temperatures (0.04 m depth) from 6:00 a.m. to 6:00 p.m. reached also about

Stratification dynamics in wastewater ponds 8°C. At 1 m depth temperature fluctuations were typically I°C or les,; in summer and fall. Three types of temperature stratification behavior occurred from April to October: continuously well-mixed conditions during 268 days (45% of 596 days), stratification during day and complete mixing during night during 169 days (28% of 596 days studied) and continuous stratification over several consecutive days and nights during 159 days (27% of 596 days). A dynamic lake water quality model driven by daily weather parameters was modified and applied to the simulation of temperature stratification in wastewater stabilization ponds which are typically shallow ( l - 2 m ) and smaller in surface area than lakes. A 12-h timestep was incorporated into the program in order tc, capture the diurnal variation in stratification. The important role of pond area and depth in determining the vertical diffusion coefficient became apparent in the course of this study. The level of agreement between field measurements and numerical simulations demonstrates that water temperatures and stratification dynamics in a pond, with a small surface area and shallow depth, can be simulated on a diurnal timescale with a standard error from 1 to 1.5°C. The model was calibrated against 3 months of water temperature data measured at 7 depths every 20 min. Model verification was made against similar temperature data for 7 months. The model includes wastewater inflow in the form of a vertical jet and wal:er transfer between ponds in the form of non-surface inflow and outflow. Jet dynamics, jet entrainment and mixing processes, and their effects on the temperature stratification of shallow ponds can be simulated by the model. The simulation o[" intermittent stratification and destratification lays a necessary base for further simulation of other water quality parameters. The adaptation of the temperature simulation to chemical and biological parameters, such as dissolved oxygen, suspended solids, phosphorus and chlorophyll can follow the procedures used in the lake models. Additional components such as hydrogen ion, alkalinity, inorganic carbon, and daphnia can also be incorporated through new subroutines which are being developed. With full understanding of water quality stratification dynamics in waste stabilization ponds, recommendations may be developed for operational water quality monitoring, location and design of inlets and outlets, timing and location of release, etc. In other words, it is suggested that the information presented will be of considerable value towards improving the existing knowledge on design, operation and performance of wastewater stabilization ponds. [rEFERENCES Baker D. G. and Enz Y. W. (1979) The availability and dependability of solar radiation at St Paul, Minnesota, climate of Minnesota, Part XI. Tech. Bull. No. 316, Agricultural Experiment Station, Univ. of Minnesota, St Paul, Minn. W R 29/8--H

1923

Filatov N. N., Rjanzhin S. V. and Zaycev L. V. (1981) Investigation of turbulence and Langmnir circulation in Lake Ladoga. J. Great Lakes Res. 17, I-6. Ford D. and Stefan H. G. (1980) Thermal prediction using integral energy model. J. Hydraulic Div., ASCE 106, 39-55. Ganf G. G. (1974) Incident solar irradiance and underwater light penetration as factors controlling the chlorophyll-a content of a shallow equatorial lake (Lake George, Uganda). J. Ecol. 62, 593-609. Gu R. and Stefan H. G. (1990) Year-round temperature simulation of cold climate lakes. Cold Regions Sci. Technol. 18, 147-160. Gu R. and Stefan H. G. (1991a) Mixing of temperaturestratified lakes, reservoirs or ponds by submerged jets. Project Rep. No. 318, St Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minn. Gu R. and Stefan H. G. (1991b) Numerical simulation of stratification dynamics and mixing in wastewater stabilization ponds. Project Rep. No. 316, St Anthony Falls Hydraulic Laboratory, Univ. of Minnesota, Minneapolis, Minn. Happey C. M. (1970) The effects of stratification on phytoplanktonic diatoms in a small body of water. J. Ecol. 58, 635-65 I. Hondzo M., Ellis C. and Stefan H. G. (1991) Vertical diffusionin a small stratified lake: data and error analysis. J. Hydraul. Engng ASCE 117, 1352-1369. James A. (1987) An alternative approach to the design of waste stabilization ponds. Wat. Sci. Technol. 19, 213-218. Jassby A. and Powell T. (1975) Vertical patterns of eddy diffusion during stratification in Castle Lake, California. Limnol. Oceanogr. 20, 530-543. Luck F. N. and Stefan H. G. (1990) Physical limnology of the Harris wastewater stabilization ponds: July 1989 to October 1990. Project Rep. No. 309, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minn. Minnesota Pollution Control Agency and Consulting Engineers Council of Minnesota (1989). Report on evaluation of Minnesota water balance test. Pearson H. W., Mara D. D. and Bartone C. R. (1987) Guidelines for the minimum evaluation of performance of full-scale waste stabilization pond systems. War. Res. 21, 1067-1075. Riley J. M. (1988) User's manual for the dynamic lake water quality simulation program 'MINLAKE'. External Memorandum No. 213, St Anthony Falls Hydraulic Laboratory, Univ. of Minnesota, Minneapolis, Minn. Riley J. M. and Stefan H. G. (1987) Dynamic lake water quality simulation model 'MINLAKE'. Project Rep. No. 263, St Anthony Falls Hydraulic Laboratory, Univ. of Minnesota, Minneapolis, Minn. Riley J. M. and Stefan H. G. (1988) MINLAKE: a dynamic lake water quality simulation model. Ecol. Modeling 43, 155-182. Soler A., Saez J., Llorens M., Martinez I., Berna L. M. and Torrella F. (1991) Changes in physicochemical parameters and photosynthetic microorganisms in a deep wastewater self-depuration lagoon. Wat. Res. 25, 689-695. Stefan H. G. and Ford D. (1975) Temperature dynamics in dimictic lakes. J. Hydraulic Div., ASCE 101, 97-114. Stefan H. G., Dhamotharan S. and Schiebe F. R. (1982) Temperature/sediment model for a shallow lake. J. Environ. Engng Div., ASCE 108, No. EE 4. Stefan H. G., Skoglund T. and Megard R. O. (1976) Wind control of algae growth in eutrophic lakes. J. Environ. Engng Div., ASCE 102, 1201-1213. Ward P. R. B. (1977) Diffusion in lake hypolimnia. Proc. 17th Congr. Int. Assoc. Hydraulic Res. 2, Baden-Baden, Germany.