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ST. ANTHONY FALLS LABORATORY Engineering, Environmental and Geophysical Fluid Dynamics

Project Report No. 479

Hydrothermal Simulation of a Stormwater Detention Pond or Infiltration Basin

by

William R. Herb, Michael Weiss, Omid Mohseni and Heinz G. Stefan

Prepared for Minnesota Pollution Control Agency

St. Paul, Minnesota

September 2006 Minneapolis, Minnesota

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The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age or veteran status.

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Abstract

A numerical simulation model has been developed to simulate the hydraulic and heat transfer properties of a stormwater detention pond. The model is dynamic (unsteady) and based on basic principles of hydraulics and heat transfer. It is driven by hourly climate and weather data. To calibrate and validate the pond model field data were collected on a commercial site (State Farm Insurance Company) in Woodbury, Minnesota. The relationship between pond inflow and outflow rates to precipitation was effectively calibrated using continuously recorded pond level. Algorithms developed for surface heat transfer in lakes were found to be applicable to the pond with some modification. A significant diurnal thermal stratification was simulated and measured in the pond which had 2.4m depth. Temperature differences from top to bottom were as high as 13oC during daytime hours. The outflowing water temperature was essentially equal to the pond surface temperature because the outlet was located near the pond surface. Outflow water temperatures were calculated with a RMSE of 1.4oC. Water clarity had little effect on the pond outflow temperatures but the pond bottom temperature was found to be highly sensitive to water clarity. For pond designs with outlet structures that take subsurface water, water clarity will introduce uncertainty to simulations of the pond temperature profile and the pond outlet temperature. Further work is required to consider other pond designs with alternate outlet structures, significant shading, and wind sheltering. Surface shading should include consideration of terrestrial vegetation (trees), emergent, submerged, and floating leaf aquatic vegetation, Algae need to be included in the water clarity. Wet ponds with subsurface outlet withdrawal and high surface shading from emergent or floating leaf plants may yield significantly lower outlet temperatures than typical wet pond designs.

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Table of Contents

NOTATIONS AND UNITS…………………………………………………………… 5 1. INTRODUCTION……………………………………………………………………7 2. MODEL FORMULATION/ MODEL COMPONENTS…………………………...8 2.1. Hydrology Inflow and outflow Water balance

2.2. Water Temperature Water temperature profile Surface heat exchange

3. MODEL INPUTS…………………………………………………………………...11 3.1. Climate data 3.2. Inflow data 3.3. Pond data 3.4 Soil data 3.5 Vegetation data 4. MODEL OUTPUT………………………………………………………………….12 5. MODEL CALIBRATION AND VALIDATION…………………………………12 5.1. Field data collection 5.2 Pond hydrology 5.3 Pond water temperature 5.4 Outflow temperature 6. MODEL SENSITIVITY ANALYSIS……………………………………………...27 7. CONCLUSIONS…………………………………………………………………….30 ACKNOWLEDGMENTS REFERENCES………………………………………………………………………...31 APPENDIX A. SOIL MOISTURE TRANSPORT MODEL………………………32 APPENDIX B. FORMULATION OF SURFACE HEAT TRANSFER EQUATIONS FOR A POND WATER SURFACE OR A BARE SOIL SURFACE……………………………………………………………………………..34

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NOTATION AND UNITS Nominal values are given in parenthesis, where appropriate. b = soil specific constant (-) Cfc = forced convection transfer coefficient (0.0014 for water, 0.003 for bare soil) Cnc = free convection transfer coefficient (0.0014) CR = cloud cover ratio (0 – 1) CSh = wind sheltering coefficient for heat transfer (-) CSm = wind sheltering coefficient for wind mixing energy (-) DA = available water in a soil layer (-) Dmix = mixed layer depth (m) Dsed = thermal diffusivity in sediment (m2/s) ET = evapotranspiration (m) ea = atmospheric vapor pressure (Pa) hconv = convective heat flux (W/m2) hevap = evaporative heat flux (W/m2) hli = incoming long wave radiation (W/m2) hlo = outgoing long wave radiation (W/m2) hn = net heat flux (W/m2) hrad = net incoming surface radiation (W/m2) hs = short wave radiation absorbed at surface (W/m2) hsp = short wave radiation that penetrates water column (W/m2) K = hydraulic conductivity (m/s) Ki = unsaturated hydraulic conductivity (m/s) Ks = saturated hydraulic conductivity (m/s) Kw = total light attenuation coefficient in water column (m-1) Kz = thermal diffusivity in water column (m2/s) Lv = latent heat of vaporization (J/kg) Rs = incoming solar radiation (W/m2) T = temperature (°C) Ta = air temperature (°C) Tak = air temperature (°K) Tsk = water surface temperature (°K) Tave = average water column temperature (°C) Tbot = bottom water temperature (°C) Tg = ground surface temperature (°C) Ts = surface water temperature (°C) Tsk = surface temperature (°K) us = adjusted wind velocity (m/s) u10 = wind velocity at 10 m above surface (m/s) α = surface albedo (0.087 for water, 0.15 for bare soil) β = fraction of solar radiation absorbed at water surface (0.4) ∆θv = difference in virtual temperature between ground and air (oC) ∆t = time step (h) ∆z = soil layer thickness (m)

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εw = emissivity of water surface (-) Фb = bubbling pressure head (m) Фi = unsaturated head (m) ρCp = sediment (density · specific heat) product (J/m3/°C) ραCp = air (density · specific heat) product (J/m3/°C) σ = Stefan Boltzman constant (W m-2 oC-4) θi = unsaturated soil moisture (-) θs = saturated soil moisture (-) θwp = wilting point soil moisture (-)

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1. INTRODUCTION Urbanization affects the temperature of cold water resources, streams and rivers in particular. Cold-water streams typically exist in well-shaded watersheds with large water inputs from groundwater. They are ecologically significant because they support coldwater fisheries and other wildlife that would be unable to survive in warmer streams. Coldwater streams are threatened by the conversion of land from existing agricultural use or natural conditions to urban use. Urban expansion usually requires removing crops and trees and replacing them with parking lots, roads, lawns, and buildings. These changes affect shading, heat transfer, and hydrology within the watershed. Currently, there are few tools available to project to what extent stream temperatures are influenced by development in the watershed. The main focus of this research is to create a model that would be useful for making decisions on land use and zoning in the watersheds of coldwater streams, to ensure that urbanization does not negatively impact the fragile nature of these ecosystems. Ease of use is essential if the model is to be used for planning and permit decisions. The ideal model would be able to accept standard climate data (solar radiation, air temperature, relative humidity, and wind speed) along with parameters concerning land usage to predict the changes in surface and subsurface runoff temperatures, and ultimately, stream temperature. One small but significant portion of this overall model is the creation of a sub-model that can predict the outflow rate and temperature from stormwater detention basins/ponds after a rainfall event. This report is intended to give an overview of the heat transfer processes that take place in a small and shallow water body such as a detention pond. With the information on heat transfer processes a model is developed to predict the temperature dynamics, i.e. the temperature variation with depth and time in a pond. The bulk of the paper is devoted to the description of the necessary equations, and their use on a specific example . The intent is to develop a model that can be operated with standard climate data and hydrologic input to predict the change in water temperature in a pond. The hydrologic input will have to come from runoff models. A computational simulation model was developed to quantify the effect of a stormwater detention pond on the temperature of surface runoff. The model is also applicable to infiltration basins. The model is designed to

1. Quantify the outflow temperature and flow rate from a stormwater detention pond,

2. Quantify the water temperature in an infiltration pond, and the infiltration rate.

Future applications of the model will most likely serve to 3. Explore the benefits of alternative pond designs, e.g. outlet structures, on outflow

temperatures,

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4. Determine the influence of shading, wind sheltering and water clarity on pond outlet temperatures,

5. Estimate the impact of infiltration ponds on groundwater temperatures. 2. MODEL FORMULATION/ MODEL COMPONENTS Similar to previous 1-D models of lakes (Ford and Stefan 1980, Hondzo and Stefan 1993) and wastewater detention ponds (Gu and Stefan 1995) the model divides a storm water detention or infiltration pond into a system of horizontal water layers, and simulates the time-variable (hourly to daily) water temperature as well as in- and outflow rates for each layer. Given the geometry of all storm sewers discharging to a pond, the hydrology of the inflows, and the design of any outlet structure, the model projects the rate and temperature of the outflow from the pond. Pond bathymetry and weather data are required to run the model. The model uses and solves equations that describe flow and heat transfer processes in the pond. Several features and processes represented in the pond model are shown in Figure 2.1.

groundwater flow ground heat

transfer

atmosphere

water

soil

Tin, Qin

storm sewer

Tout, Qout

atmospheric heat transfer

outlet structuretemperature

dept

h

Shading, Sheltering

Figure 2.1. Schematic of storm water pond and model features 2.1. Hydrology Inflow and outflow. Simulation of inflows to the pond from storm sewer pipes and outflow from the pond through an outlet structure are included in the model. In a wet pond a minimum water level is maintained at all times, whereas a dry pond or an infiltration basin drains completely some time after a rainfall/runoff event. To prevent seepage, wet ponds have liners (clay or geosynthetic liners), unless they intercept a shallow aquifer. The flow from a storm sewer into a pond is typically a jet-like buoyant flow that entrains ambient water and becomes diluted as it advances into the pond. Dilution is estimated based on

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algorithms developed by Fang and Stefan (199x). The inflow is added to a water layer based on density of the diluted inflow and the density (temperature) stratification of the pond. In the current model formulation the outflow is from a structure that has a circular opening in a vertical wall, and an emergency overflow weir. The elevations of these outlets above the pond floor have to be specified in the model input because they affect the outflow rate. For circular outlet ports, the following equation is used to model the outflow rate (Qout) as a function of pond level and port area (Aport).

(2.1) ⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆⋅∆=

portportportout D

hMinhgACQ23,0.12

where Cport is the port coefficient, g is the acceleration of gravity, ∆h is the difference in elevation between the pond surface and the bottom of the port, and Dport is the port diameter. The Min (minimum) function adjusts the outflow for cases where the pond level drops below the top of the port, i.e. only a fraction of the port contributes to outflow. For this case, the outflow rate varies according to a weir equation and is proportional to ∆h1.5. For an overflow weir of width B at the crest, the model outflow rate Qout as a function of pond level H can be calculated from the equation (2.2) Qout = Cw B H3/2

where Cw is the weir coefficient that will typically range from 2.5 to 3.9, and can be determined from weir geometry (e.g USBR 1987). Water balance. The pond water volume is calculated for each time step based on inflow and outflow rates, precipitation, evaporation, and infiltration from the pond into the ground. From the water volume, the water depth and surface area of a pond are then calculated based on a pond’s bathymetry which can be specifies in a table. The number of layers in the pond model is adjusted as the water level changes, so that the layer thickness stays within a specified range (e.g. 0.1 to 0.5m). If the pond depth reaches zero, the water content of the underlying soil is calculated using a multi-layer model described in Appendix A1. Moisture transfer between layers is calculated using a modification of Darcy’s law, and saturated soil at the groundwater table as a lower boundary condition. In this way, the pond model may be applied to both dry detention ponds and infiltration basins.

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2.2. Water temperature Water temperature profile. The vertical temperature profile of the water in the pond and the underlying soil is calculated for a series of discrete layers at 1 hour time steps. The temperature is assumed to be horizontally uniform in the pond and the underlying soil. The computations use the finite difference model developed for MINLAKE (Ford and Stefan 1980, Hondzo and Stefan 1993). There are three principal steps in determining the temperature profile in the pond water column and the underlying soil. 1. The 1D (vertical) heat diffusion/conduction equation is solved for the water/sediment column. 2. Any density instabilities are removed by a convective mixing algorithm. 3. The surface mixed layer depth and temperature are calculated using the surface wind mixing algorithm (Ford and Stefan 1980). The heat diffusion/convection model uses measured or calculated heat fluxes between the water surface and the atmosphere as an upper boundary condition, and a known temperature in the ground as a lower boundary condition. Mean annual air temperature +1 or 2oC at 10 m depth in the underlying soil, or a known groundwater temperature at a more shallow depth are appropriate boundary temperatures. Formulations for the hypolimnetic vertical diffusion coefficient (Kz) developed for lakes (Hondzo and Stefan 1993) were found to be inappropriate for a stormwater pond, because the Kz vs. lake area relationship yields a value of Kz smaller than molecular diffusion. For the pond simulations, Kz was set equal to molecular diffusion. The temperature of the outflow is calculated based on the vertical temperature profile of the pond and the depth of the outlet port below the pond surface, using an algorithm similar to that used in the reservoir model RESQUAL II (Stefan et al. 1982). Surface heat transfer Heat transfer from the water surface to the atmosphere is calculated for each time step based on components of long and short wave radiation, evaporation, and convection, as described in Appendix A2. Climate data consisting of solar radiation, precipitation, air temperature, relative humidity, and wind speed at 1 hour time intervals are required as model input. For the case of a vegetated land surface as found in dry ponds or infiltration basins, the surface heat transfer and evaporation components are adjusted, as summarized below and detailed in a separate document (Herb et al. 2006). The effect of vegetation is included in the surface heat transfer model and the evaporation rates used for the water balance. Several forms of vegetation can affect a pond or an infiltration basin: (1) terrestrial, littoral (e.g. trees and bushes along the shoreline of a lake or grass growing in an infiltration pond). (2) emergent aquatic (e.g. cattails and rushes emerging from the water surface), (3) submerged aquatic (e.g. macrophytes growing in the pond). The model

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accounts for several effects between vegetation and heat exchange: (1) incoming solar radiation reaching the water or dry pond surface is reduced based on a vegetation density parameter to account for shading by plants; (2) long wave radiation from the atmosphere is replaced by long wave radiation from the plant canopy, based on an estimated canopy temperature, where appropriate, (3) evaporative and convective heat flux between a dry pond surface and the atmosphere are altered by vegetation. 3. MODEL INPUT Required inputs to the pond model include the following: 3.1. Climate data Air temperature (°C), relative humidity (%), wind speed (m/s), and solar radiation (W/m2) at one hour time intervals are required for the period to be simulated. Latitude, longitude, and elevation of the site to be simulated are also required for the algorithm to estimate cloud cover. 3.2. Inflow data One hour time series of inflow rate (m3/s), temperature (°C), velocity (m/s) and inflow depth (m) are required model input. The inflow point is specified as the vertical position of the inflow (invert elevation in m) with respect to the pond bottom. Up to three separate inflows can be specified. 3.3. Pond data Pond area (m2) versus elevation above pond bottom (m) is required in table format. Water clarity has to be specified as Secchi depth (m). To estimate shading and wind sheltering of the pond, information on the topography, trees and buildings surrounding a pond is required. From these a sheltering coefficient and a shading coefficient have to be determined and put into the model. 3.4. Soil data Several soil properties have to be specified: hydraulic conductivity (m/s), porosity, field capacity, wilting point, density (kg/m3), thermal conductivity (Wm-1oC-1) and specific heat (Jm-3 °C-1) 3.5. Vegetation data For grass and bushes in dry ponds or infiltration basins the following parameters are specified: canopy density (0=no foliage, 1=fully dense canopy), canopy albedo and emissivity, canopy aerodynamic roughness, and root depth. The model components are in place to simulate surface heat transfer in the presence of vegetation, however, at the time of this report, these model components have not been verified for water surfaces. For trees on the shoreline and for emergent vegetation such as cattails a shading coefficient and a wind sheltering coefficient are specified. At the time of this report, relationships between vegetation characteristics, e.g. tree height, and the wind sheltering and shading coefficients have not been established.

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4. MODEL OUTPUT The following quantities are computed and stored for each hourly time step:

1. The temperature profile in the water column and underlying sediment 2. Pond water depth and mixed layer depth 3. Outflow rate and temperature

5. MODEL CALIBRATION AND VALIDATION To calibrate and validate the pond model and its components, field data were collected, and the model was applied for the wet stormwater detention pond located at the State Farm office complex in Woodbury, Minnesota (Figures 5.1 and 5.2). The pond is unshaded and has an outlet structure that withdraws surface water. A single inlet pipe drains the asphalt parking areas of the facility. Simulations were made for the period April 1 to September 30, 2005. Measured pond water temperatures and pond levels were available for verification for the period June 3 to August 25, with a gap from July 28 to August 4. Wind speed and direction and precipitation were also recorded at the station installed in the pond (Figure 5.2).

Figure5.1. Aerial photograph of the State Farm office facility in Woodbury, MN. The stormwater detention pond is the dark elongated water body north of the building complex near the center of the photograph. I-94 and Radio Drive are north and west of the facility, respectively.

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Figure 5.2. Ground level photograph of the State Farm stormwater detention pond, viewing from west to east, and close-up of the measurement station installed in the pond. 5.1. Field data collection The pond is a wet pond with the bathymetry shown in Figure 5.3. Surface outflow stops when the maximum pond water depth is about 2.4m. The pond has a clay-liner to prevent water loss by infiltration. Surface water inflow is from the State Farm office complex and includes an upper and a lower parking lot. The surface area of the pond when it is not overflowing is about 5000 m2 (1.2 acres). The instrumentation installed for the field study comprised a central measurement station and a number of discrete temperature loggers. The central measurement station in the pond, shown in Figure 5.2, was comprised of 1) an anemometer, wind direction sensor, and tipping bucket rain gage mounted on a pole near the center of the pond, (2) a thermistor chain (7 thermistors) attached to the same pole, (3) a pressure sensor to record pond water level, and (4) a Campbell Scientific data logger. Several Vemco Minilog and Onset Hobo temperature loggers were used to record water temperature at 2 minute intervals at the pond inlet and outlet structures and 2 stormwater catchments in the parking lots. An additional 2 temperature loggers were buried in the surface of the asphalt parking lot to record pavement temperature at 2 minute intervals. The instrumentation in the pond was operated from June 3 to August 25. . The weather data and the water temperature data from the thermistor chain were measured every minute and averages were recorded on the Campbell data logger every 10 minutes. Water temperatures were measured with YSI model 55032 thermistors with a time constant of about 10 seconds. Wind speed was measured by a R.M. Young model 03001 anemometer and wind direction instrument.

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Figure 5.3. Bathymetry of the State Farm storm water detention pond, courtesy of Ellerbe Becket, Inc. The contours are at 1 foot intervals. The inlet structure is on the left, and the outlet structure is on the right. 5.2. Pond hydrology The pond has an outlet structure with an 8” diameter circular opening for normal operation, and an emergency overflow weir. Using pond level measurements, a relationship between pond level and outflow rate Qout was established according to Equation 2.1, with Dport = 0.203 m.

(2.1) ⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆⋅∆=

portportportout D

hMinhgACQ23,0.12

The port coefficient Cport in Equation 2.1 is nominally 0.4 to 0.9 for a circular port in a thick wall, depending on inlet shape, pipe attachments and obstruction by debris. Cport was calibrated to a value of 0.46. The time history of the outflow rate was then calculated using the measured pond level and Equation 1. A rate of storage change Qnet was calculated from the measured pond levels using Equation 5.1. (5.1) dtdhhAQnet /)(= where A(h) is the pond surface area at level h, and dh/dt is the rate of change of pond level. The inflow rate Qin was calculated as the sum of storage change and outflow:

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(5.3) Qin = Qnet + Qout The total inflow volume during a rainfall event was related to the measured precipitation for larger precipitation events, as shown in Figure 5.4. The slope of the linear regression gives the calibrated impervious (without water loss) surface area as 98,500 m2, or about 24 acres. The inflow time history during a rainfall event, i.e. the inflow rate for each 1 hour time period, was then calculated from the measured precipitation data. It was assumed that all the precipitation reached the pond within the hour in which it fell. To run the model from April to October 2005, a composite precipitation record was made using precipitation from the Minneapolis/St. Paul International Airport for most periods, but substituting the measured rainfall at the State Farm site when it was available (June 3 to August 30). The simulated pond level is compared to the measured pond level in Figure 5.5. Agreement between the simulated and measured pond level values is quite good, with a RMSE (root mean square error) of 3.7 cm. During the first two weeks in July, there are no rainfall events, so that the change in pond level is due entirely to evaporation (infiltration is assumed to be negligible, because the pond has a clay-liner). The slopes of the measured and simulated pond levels are in good agreement during this period, implying that the model is predicting evaporation accurately.

y = 98.514xR2 = 0.932

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30 35

Total Event Precipitation (mm)

Tota

l Pon

d In

flow

(m^3

)

Figure 5.4. Calculated inflow volume to the State Farm stormwater pond vs. measured total precipitation for 10 storm events in 2005.

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2

2.2

2.4

2.6

2.8

3

3.2

3.4

4/1 5/1 6/1 7/1 8/1 8/31 10/1

Date

Pond

Lev

el (m

)SimulatedMeasured

Figure 5.5. Simulated and measured water level in the State Farm stormwater detention pond vs. time, April 1– October 1, 2005. The RMSE of the simulated pond level is 3.7 cm. 5.3. Pond water temperature Before temperature profile calculations for the pond could be made the parameters used to calculate surface heat transfer and heat flux through the water column were calibrated. The focus of the temperature calibration was on parameters that would be expected to be different for a small pond compared to a lake, e.g. the wind sheltering coefficient. As a starting point, default parameter values for surface heat transfer, density stratification and wind mixing were taken from the MINLAKE model. The initial wind sheltering coefficient was set equal to one (no sheltering). A composite wind data set for the simulation period was created by starting with data from the University of Minnesota St. Paul campus (with no scaling factor), and then substituting wind measurements from the State Farm pond when available. The State Farm data were multiplied by a constant scaling factor of 1.6, which was determined by plotting St. Paul data versus State Farm data during the State Farm measurement period (R2 = 0.60). There are two separate wind sheltering coefficients used in the heat transfer model. The parameter CSH is used to adjust the measured wind velocity for calculation of the convective and evaporative surface heat transfer components, while the parameter CSM is used to adjust the wind velocity for calculation of the kinetic energy available for wind mixing in each time step. Good agreement between simulated and measured water surface temperatures was achieved when CSH =1.5 and CSM = 1.0 was applied to the composite St. Paul/State Farm wind data. The high value of CSH can be attributed to the

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short lengths over which the wind is acting. The air above the pond does not saturate with moisture and heat over the short pond fetch, leading to higher transfer rates than are typical for larger lakes. Simulated time series of the water temperature at the pond surface and the pond bottom, and the depth-averaged temperature of the pond are given in Figure 5.6 for the entire simulation period. Time series of simulated and measured pond surface temperatures are compared in Figure 5.7. Simulated and measured hourly pond surface water temperatures are plotted against each other in Figure 5.8. The overall RMSE (root mean square error) for the hourly simulated surface temperature is 1.1 °C. Agreement of measured and simulated bottom temperatures was more difficult to achieve, for two reasons: 1) the thermistor used for measuring bottom temperature had a +4°C error at final calibration and 2) the bottom temperature is sensitive to water clarity, which may vary significantly at weekly to monthly time scale. The simulated sensitivity of bottom water temperature to water clarity is illustrated in Figure 5.9. This sensitivity is caused by solar radiation reaching the pond bottom and heating the sediment water interface. Because of the large calibration error of the bottom thermistor, water temperature measurements at 0.6 m above the bottom were used instead to test the model accuracy. Using calibrated water clarity/attenuation coefficient values, the simulated and measured water temperature at 0.6 m above the pond bottom are in good agreement (Figure 5.10, top panel). For comparison the simulated and measured bottom temperatures are shown in the bottom panel. Simulated values diverge from measured values to about 4 °C lower, consistent with the thermistor error measured at final calibration. Although the large drift/calibration error renders the bottom thermistor recordings useless for comparison with the simulated bottom temperatures, the measured diurnal fluctuations in bottom temperatures were useful to calibrate the water clarity/ radiation attenuation parameter Kw. It was observed that daily fluctuations in bottom temperature were strongly dependent on water clarity. In a shallow water body with moderate water attenuation, significant heat energy reaches the bottom and heats the sediment water interface. The top panel of Figure 5.11 gives a clear indication of the diurnal bottom temperature variations at the pond bottom due to heating by solar radiation; the slow/longterm temperature variations have been filtered out by subtracting mean daily temperature from the raw 10-minute bottom temperature data. A calibrated, seasonally variable water clarity parameter Kw was obtained by matching the measured and simulated diurnal bottom temperature fluctuation time series, The calibrated water clarity values are slightly higher than values extracted from Secchi disk (SD) readings in the pond (Figure 5.12), using Equation 5.4, but the conversion of SD to Kw has its own limitations, particularly the empirical coefficient 1.6. (5.4) Kww = 1.6/SD

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0

5

10

15

20

25

30

35

4/1 5/1 6/1 7/1 8/1 8/31 10/1Date

Tem

pera

ture

(C)

SurfaceDepth averagedBottom

Figure 5.6. Simulated surface water temperature in the State Farm storm water detention pond, April – September 2005.

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23

28

33

38

6/1 6/16 7/1 7/16 8/1Date

Tem

pera

ture

(C)

SimulatedMeasured

Surface TemperatureRMSE=1.0 °C

Figure 5.7. Simulated and measured surface water temperature in State Farm storm water detention pond, June – July 2005.

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y = 1.028x - 0.7314R2 = 0.8563

15

20

25

30

35

15 20 25 30 35

Measured Surface Temp (C)

Sim

ulat

ed S

urfa

ce T

emp

(C)

Figure 5.8. Simulated versus measured hourly surface water temperature in State Farm storm water detention pond, June – August 2005.

0

5

10

15

20

25

30

35

4/1 5/1 6/1 7/1 8/1 8/31 10/1

Date

Tem

pera

ture

(C)

Kw=0.5 m-1

Kw=1.5 m-1

Kw=1.0 m-1

Figure 5.9. Simulated bottom water temperature in the State Farm storm water detention pond for varying water clarity (light attenuation coefficient Kw), April – September 2005.

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0

5

10

15

20

25

30Te

mpe

ratu

re (C

)Temperature 0.6 m above bottom

0

5

10

15

20

25

30

4/1 5/1 6/1 7/1 8/1 8/31 10/1

Date

Tem

pera

ture

(C)

SimulatedMeasured

Bottom Temperature

Figure 5.10. Simulated and measured water temperature at the pond bottom (lower panel) and 0.6 m above bottom (upper panel). The measured bottom temperature data shown are raw data, with no correction for the known calibration error. The drift of the temperature sensor occurred near the end of June.

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-2

-1

0

1

2

T-Ta

ve (C

)

Measured

-2

-1

0

1

2

T-Ta

ve (C

)

Simulated with calibrated Kw

0

3

6

9

12

Win

d Sp

eed

(m/s

)

0.0

0.5

1.0

1.5

10 m

in P

reci

pita

tion

(cm

)

0

250

500

750

1000

6/1 6/11 6/21 7/1 7/11 7/21 7/31

Date

Sola

r Ra

diat

ion

(W/m

2 )

Figure 5.11. Measured and simulated bottom water temperature fluctuation (10-minute bottom temperature minus daily average bottom temperature) in the State Farm stormwater detention pond, June – July 2005. Also shown are measured wind speed and precipitation (both affect vertical mixing of the pond), and solar radiation.

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0.0

0.5

1.0

1.5

2.0

6/1 6/15 6/29 7/13 7/27 8/10 8/24

Date

Kw

(m-1

)Measured (Kw=1.6/SD)Calibrated

Figure 5.12. Clarity/light attenuation coefficient of the pond (Kw) versus time. The “measured” points were obtained from Secchi depth (SD) measurements and the empirical equation Kw=1.6/SD. The “calibrated” values were obtained by matching measured and simulated daily temperature fluctuations at the pond bottom. Incorporated in the temperature profile simulation is the surface mixed layer calculation. The surface mixed layer depth is calculated from wind speed, wind direction and water temperature stratification (density stratification) in the pond (Ford and Stefan 1980). The simulated mixed layer depths agree reasonably well with measured values (Figure 5.13). The “measured” mixed layer depth was calculated from the measured and recorded water temperature profiles as the depth below the surface where the temperature was 0.5 oC lower than the surface value. In that case the RMSE of the simulated mixed layer depth was 0.53 m. Measured and simulated temperature profiles at 6-hour intervals on three arbitrarily selected days are given in Figure 5.14. The model appears to capture not only the seasonal variation of surface temperature, but also the seasonal variation in the temperature profile.

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0

0.5

1

1.5

2

2.5

3

6/15 6/20 6/25 6/30 7/5 7/10 7/15Date

Mix

ed L

ayer

Dep

th (m

)

SimulatedMeasured

Figure 5.13. Simulated and measured mixed layer depth in the State Farm stormwater detention pond, June 15 - July 15, 2005. The RMSE is 0.53 m for the entire measurement period.

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0.0

0.5

1.0

1.5

2.0

2.5

15.00 20.00 25.00 30.00 35.00 40.00

Dep

th (m

)

Temperature (1 division = 5 °C differential)

Midnight 6 am 6 pmNoon

Sim.Meas.

June 15

0.0

0.5

1.0

1.5

2.0

2.5

Dep

th (m

)

Midnight 6 am 6 pmNoon

Sim.Meas.

July 13

0.0

0.5

1.0

1.5

2.0

2.5

Dep

th (m

)

Midnight 6 am 6 pmNoon

Sim.Meas.

August 11

Figure 5.14. Simulated and measured water temperature differential versus depth at 6 hour time increments for June 15, July 13, and August 11, 2005. The horizontal axis gives relative temperature, with each temperature profile offset by 5 °C for each 6 hour increment.

25

5.4. Outflow temperature For the purpose of this study, the most important simulation result is the pond outflow temperature and outflow rate. A time series of simulated outflow temperatures (using the calibrated water clarity values) is compared to measured values in Figure 5.15. Because the pond outlet pipe is located only a short distance below the pond surface, the measured outflow temperature is often the same as the measured pond surface temperature. The simulated outflow temperatures are also the same as the simulated surface temperatures most of the time. The simulated outflow temperatures tend to underpredict the highest measured outflow temperatures (28 to 32oC) and to overpredict the lowest measured ones (18 to 22oC) (Figure 5.16). The model is therefore not conservative in the high temperature prediction. Overall, the RMSE is 1.25°C. If water temperatures are simulated using a fixed water clarity, Kw = 1.2 m-1 instead of seasonally variable Kw values, the simulated outflow temperatures remain almost the same, and the RMSE rises by only 0.03oC to a RMSE of 1.28 °C. In this case study, the calibrated Kw value is not needed to improve pond outflow temperature. The pond inlet and outlet temperatures can be used to calculate the total heat energy transferred from the parking lot to the pond, and the heat energy exported through the pond outlet. The total heat export from surface runoff (gro) for some period of time can be calculated as: (5.5) ( ) ( ) [ ]2

ropro mJdtTrefTqCg ∫ −ρ= where Tro and Tref are the runoff and reference temperatures, q is the flow rate per unit runoff area, and ρCp is the product of density and specific heat. A reference temperature of 20 C was chosen to represent a critical stream temperature, so that positive heat export would raise stream temperature above 20 °C. The total heat export from parking lot to the pond and from the pond outlet was then calculated on a monthly basis using Equation 5.5. The results are shown in Figure 5.17. The heat export from the parking lot is negative in April and May, positive in June, July, and August, and close to zero in September. In all cases, the heat export from the pond exceeded the heat export from the parking lot. This increase in thermal energy is due to the heat added to and stored in the pond from the atmosphere. For June, July, and August, the heat export from the pond was 11% higher than the heat export from the parking lot.

26

10

15

20

25

30

35

6/9 6/16 6/23 6/30 7/7

Date

Out

flow

Tem

pera

ture

(C)

0

0.02

0.04

0.06

0.08

0.1

Out

flow

Rat

e (m

3 /s)

Measured OutletSimulated OutletOutflow rate

10

15

20

25

30

35

7/20 7/27 8/3 8/10 8/17Date

Out

flow

Tem

pera

ture

(C)

0

0.02

0.04

0.06

0.08

0.1

Out

flow

Rat

e (m

3 /s)

Meas. Outlet Temp

Sim. Outlet Temp

Outflow rate

Figure 5.15. Simulated and measured pond outlet temperature and pond outflow rate versus time, using the calibrated water clarity values (The outflow temperature is plotted only for time periods when the outflow rate is non-zero).

27

y = 0.8278x + 4.3978R2 = 0.843

15

20

25

30

35

15 20 25 30 35

Measured Outlet Temperature (C)

Sim

ulat

ed O

utle

t Tem

pera

ture

(C)

Figure 5.16. Simulated versus measured outlet temperature for 1 hour averaged data. The RMSE is 1.37 °C.

-3

-2

-1

0

1

2

3

April May June July August Sept

Tota

l Hea

t Exp

ort (

MJ/

m2 )

Pond InletPond Outlet

Figure 5.17. Total monthly heat export of parking lot runoff and of pond outlet, using a 20 °C reference temperature.

28

6. MODEL SENSITIVITY ANALYSIS To summarize the influence of different model parameters on simulated pond water temperatures, simulations were made with increased values of nine input parameters. A 10% increase was made for individual parameters, one at a time. The nine independent input parameters and their nominal values (in parenthesis) are: Cfc = surface heat/moisture transfer coefficient for forced convection (0.0014) Cnc =coefficient for natural convection (0.0015) CSh = wind sheltering coefficient for heat transfer (1.5) CSm = wind sheltering coefficient for wind mixing energy (0.2) εw = water emissivity (0.97) Kw = total light attenuation coefficient in water column (1.0 m-1) Kz = thermal diffusivity in water column (1.44 E-07 m2/s) ρCp = sediment (density · specific heat) product (2.6 E+06 J/m3/°C) Dsed = thermal diffusivity in sediment (4.0 E-07 m2/s) The effect of the parameter increase on four dependent variables was calculated. The response variables and their nominal or reference values (in parenthesis) are: Ts = pond surface temperature (24.1 °C) Tave = average water column temperature (22.6 °C) Tbot = bottom water temperature (19.7 °C) Dmix = surface mixed layer depth (0.95 m) For the State Farm stormwater detention pond the outlet water temperature can be assumed equal to the surface water temperature (Ts). To quantify the sensitivity we calculated the mean values and the diurnal amplitudes of the simulated dependent variables for the period June 1 to September 30. The sensitivity was expressed as the change in the mean values in response to a 10% change in a parameter value. The changes are given in Table 6.1 in a matrix of dependent variables on the horizontal versus parameters on the vertical. The sensitivities can be summarized as follows: Mean surface temperature (Ts) is most sensitive to water surface emissivity (εw) and wind sheltering expressed by the transfer coefficients (Cfc) and (CSH). The sensitivities to Cfc and to CSH are identical, because both are multipliers in the forced convection terms. For average water column temperature (Tave), and water temperature amplitudes - with the exception of the water surface temperatures – the emissivity (εw) and the light attenuation coefficient (Kw) are the most influential parameters. Bottom water temperature (Tb), of the typically shallow stormwater detention ponds are most sensitive to Kw, due to the shading effects discussed previously.

29

Mixed layer depth (Dmix) is also significantly influenced by emissivity (εw) and water clarity (Kw). In addition, mixed layer depths are also sensitive to the wind sheltering coefficient for wind mixing (CSM). Table 6.1. Simulated response of three water temperatures and the surface mixed layer depth in the State Farm stormwater detention pond to nine model parameters. Each value in the table is the change in the response variable to a 10% increase in value of the parameter listed in the first column.

Change in Mean Value, June - September Parameter Ts (°C) Tave (°C) Tbot (°C) Dmix (m) εw -0.9635 -0.7971 -0.3410 0.0394Cfc -0.2604 -0.2199 -0.0561 0.0049CSh -0.2604 -0.2199 -0.0561 0.0049Cnc -0.1098 -0.1004 0.0506 0.0004Dsed -0.0176 0.0018 0.0296 -0.0010Kw -0.0172 -0.2573 -1.0578 -0.0465Kz -0.0142 -0.0111 0.0245 -0.0008CSm -0.0132 0.0300 0.1506 0.0284ρCP -0.0008 -0.0143 -0.1280 -0.0046

Change in Mean Daily Amplitude, June - September Kw 0.1087 -0.0275 -0.1247 -0.0618Cnc 0.0508 0.0168 0.0239 0.0065CSm -0.0423 0.0195 0.0258 -0.0274εw -0.0400 -0.0121 0.0492 0.0792Cfc -0.0305 0.0028 0.0284 0.0058CSh -0.0305 0.0028 0.0284 0.0058ρCP -0.0065 -0.0037 -0.0023 -0.0023Dsed -0.0057 -0.0044 0.0145 0.0207Kz 0.0042 0.0014 -0.0092 -0.0096

Emissivity of water is well known, while the light attenuation may vary significantly with season and from one pond to another. Secchi depth measurements can therefore become an important input in pond water temperature modeling. The independent input parameters are ranked in order of importance in Table 6.2.

30

Table 6.2. Ranking of nine model parameters for their effect on simulated water temperatures or mixed layer depths. To be listed in this table, a 10% change in the parameter value must result in more than 0.06oC mean temperature change, more than 0.04oC diurnal temperature change or more than 0.02m mixed layer depth change.

7. CONCLUSIONS A model has been developed to simulate the hydraulic and heat transfer properties of a stormwater detention pond. A case study was conducted for a pond on a commercial site (State Farm Insurance Co.) in Woodbury, Minnesota. The relationship between pond inflow and outflow rates to precipitation was effectively calibrated using continuously recorded pond level. Algorithms developed for surface heat transfer in lakes were found to be applicable to the pond with some modification. To reproduce the measured pond surface temperature, it was necessary to increase the wind sheltering coefficient for heat transfer to 1.5, suggesting that the short fetch produces unsaturated atmospheric boundary layers that give relatively high rates of evaporation and convective heat transfer. The pond bottom temperature was found to be highly dependent on water clarity, and conversely, measured bottom temperatures provides a record of water clarity for shallow water bodies. In the State Farm pond, with an outlet structure near the pond surface, the sensitivity to water clarity had little effect on the simulated pond outflow temperatures which were calculated with a RMSE of 1.37oC.Pond outflow temperatures were essentially equal to pond surface temperatures. For pond designs with outlet structures that take subsurface water, water clarity will introduce uncertainty to simulations of the pond temperature profile and the pond outlet temperature. Further work is required to consider other pond designs with alternate outlet structures, significant shading, and wind sheltering. The sensitivity of water column temperature to water clarity suggests that the analysis of surface shading should include consideration of terrestrial vegetation (trees), emergent, submerged, and floating leaf aquatic vegetation, and algae. For example, wet ponds with subsurface outlet withdrawal and high surface

Mean Value, June - September Rank Ts (°C) Tave (°C) Tbot (°C) Dmix (m) 1 εw ( - ) εw (-) Kw (-) Kw (+) 2 Cfc ( - ) Kw (-) εw (-) εw (+) 3 CSh ( - ) Cfc ( - ) CSm (+) 4 Cnc ( - ) CSh ( - ) ρCP (-) 5 Cnc ( - )

Mean Daily Amplitude, June - September 1 Kw (+) Kw (-) εw (-) 2 Cnc (+) εw (+) Kw (-) 3 CSm (-) CSh (-) 4 εw (-) Dsed (+)

31

shading from emergent or floating leaf plants may yield significantly lower outlet temperatures than typical wet pond designs. ACKNOWLEDGMENTS This study was conducted with support from the Minnesota Pollution Control Agency, St. Paul, Minnesota. Bruce Wilson was the project officer. REFERENCES Edinger, J., D.W. Duttweiler and J.C. Geyer (1968). The response of water temperature to meteorological conditions. Water Resources Research 4(5): 1137-1145. Edinger, J., D.K. Brady and J.C. Geyer (1974). Heat exchange and transport in the environment. Report No. 14, Electric Power Research Institute, Cooling Water Discharge Research Project (RP-49), Palo Alto, CA, 125 pp. Fang, X. and H. G. Stefan (2000). Dependence of Dilution of a Plunging, Submerged Discharge Over a Sloping Bottom on Inflow and Bottom Friction, Jour. of Hydraulic Research, 38(1): 15-26. Fang, X. and H. G. Stefan (1991). Integral Jet Model for Flow From an Open Channel into a Lake or Reservoir, Project Report No. 315, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, 206 pp. Fang, X. and H.G. Stefan (1996). Long-term lake water temperature and ice-cover simulations/measurements. Cold Regions Science and Technology 24: 289 – 304. Ford,D.E. and H.G.Stefan (1980). Thermal prediction using integral energy model. J. Hydraulics Division ASCE 106(1): 39 -55. Gu, R. and H.G. Stefan (1995). Stratification dynamics in wastewater stabilization pond. Water Research 29(8): 1909 – 1923. Herb,W.R., B.Janke, O.Mohseni and H.G.Stefan (2006). All-weather ground temperature simulation model. Project Report 478, St. Anthony Falls Laboratory, University of Minnesota, 53pp. Hondzo, M and H.G. Stefan (1993). Lake water temperature simulation model. J. Hydraulic Engineering ASCE 19(11): 1251-1273. U.S. Department of the Interior, Bureau of Reclamation (USBR). (1987). Design of Small Dams. Third edition, 860pp. Wilson, B.N., 2002. Class Notes for Hydrologic Modeling of Small Watersheds. Dept. of Bio-systems and Agricultural Engineering, University of Minnesota, St. Paul, Minnesota.

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APPENDIX A. SOIL MOISTURE TRANSPORT MODEL In a “dry pond”, i.e. a stormwater detention pond or an infiltration basin that fills with water during a rainfall/runoff event, but falls dry sometime thereafter, the soil below the pond bottom is intermittently submerged or drying out. The soil below a dry pond is unsaturated down to the (shallow) groundwater table. During the dry periods it is necessary to account for the soil moisture and heat transport in the soil.

∆ziδzi

θi, Φi, Ki

θi+1, Φi+1 , Ki+1

∆Di

Figure A.1. Schematic of the numerical discretization for soil moisture simulation. Soil moisture is modeled over depth using a layer structure. The transport of moisture between layers is modeled using a discretized version of Darcy’s law:

(A.1) ⎟⎟⎠

⎞⎜⎜⎝

⎛δ

Φ−Φ+=

∆∆ +

i

i1iiz

1Kt

D

where ∆D (m) is depth of water moving between layers i and i+1 in the time step ∆t (h), K (m/s) is the average hydraulic conductivity, Φ (m) is potential (head), and δzi (m) is the distance between the center of layers i and i+1. The average conductivity is estimated as:

(A.2) 1ii

1i1iiizz

KzKzK

+

++∆+∆∆+∆

=

The average hydraulic conductivity and the potential head in each layer are estimated from the soil water content θ from the previous time step:

(A.3) 3b2

s

isi KK

+

⎟⎟⎠

⎞⎜⎜⎝

⎛θθ

= and b

wps

wpibi

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

θ−θ

θ−θΦ=Φ

33

where Ks is the saturated hydraulic conductivity (m/s), Φb is the bubbling pressure (head) (m), θwp is the wilting point soil moisture, and b is a soil specific constant (Wilson, 2002). If water is ponded at the surface, infiltration into the top soil layer is estimated as Ks∆t. Plant evapotranspiration is withdrawn from each layer over the specified rooting depth weighted by the available water in each layer, DAi:

(A.4) ii

ii

DAETDAET

ETDADAETDAET

=>

=<

:

:

(A.5) ( ) iwpii zDA ∆θ−θ= where DA and ET are the total available soil water depth and total plant transpiration, respectively.

34

APPENDIX B. FORMULATION OF SURFACE HEAT TRANSFER EQUATIONS FOR A POND WATER SURFACE OR A BARE SOIL SURFACE. The net vertical heat transfer at a water or land surface includes components due to long wave radiation, short wave (solar) radiation, evaporation, and convection. The heat transfer formulations used in this study are based on those given by Edinger et al. (1968 and 1974) for lake and reservoir surfaces, but are applied to both land and water surfaces by adjusting parameters appropriately. Parameter values are given in the list of notations where appropriate. The following equations have been used for the heat fluxes h. Bare soil (dry pond) surface (B.1) convevapradnet hhhh −−=

(B.2) ( )( )asat33.0

vncsfcvaevap qqCuCLh −θ∆+ρ=

(B.3) ( )( )ag33.0

vncsfcpaconv TTCuCch −θ∆+ρ=

(B.4) lolisrad hhhh −+= (B.5) ( ) ss R1h α−=

(B.6) ( )( ) 4ak

08.0ali TeCR167.0CRh −⋅+σ=

(B.7) 4sklo Th εσ=

(B.8) us = CSh u10 Water surface For a water surface, the same surface heat transfer formulation is used, except for solar radiation. Unreflected solar radiation is split into a surface heat flux, hs, and a penetrating radiation, hsp, which acts as a heat source term in the water column. (B.9) ( ) ( ) ss R11h β−α−= (B.10) ( ) ssp R1h βα−=