v/EPA
United States Office of Water (4305) EPA- 820-R-12-013
Environmental Protection August 2012
Agency
AQUATOX (RELEASE 3.1)
MODELING ENVIRONMENTAL FATE
AND ECOLOGICAL EFFECTS IN
AQUATIC ECOSYSTEMS
TECHNICAL NOTE 3: MODELING WATER
FLOWS WITH AQUATOX RELEASE 3.1
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Technical Note 3: Modeling Water Flows
with AQUATOX Release 3.1
Performed under
EPA Contract EP-C-06-029, WA No. 4-11
with
AQUA TERRA Consultants
and
EPA Contract EP-C-12-006, WA No. B-01
with
Horsley Witten Group
Submitted to
Marjorie Coombs Wellman
Office of Water/Office of Science and Technology
Standards and Health Protection Division
U.S. Environmental Protection Agency
Washington, DC 20460
Prepared by
Jonathan Clough
Warren Pinnacle Consulting, Inc.
Final version prepared under contract to
Horsley Witten Group
August 2012
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Technical Note 3: Modeling Water Flows with AQUATOX
Release 3.1
Acknowledgments 1
Disclaimer 1
Background 2
Single Segment Overview 2
Four Options for Modeling Water Volume in Single-Segment Mode 3
Evaporation 3
Stratification Considerations 4
Water Flows in Multi-Segment Mode 5
Water Inflows 6
Water Losses 9
Flow Balance Considerations 9
Stratification Considerations 10
Case Study: Modeling a River, Lower Boise River ID 10
Overview 10
Water-flow Model 11
Water-volume Model 12
Water-balance Model 13
Model Verification 13
Case Study: Modeling a Reservoir with Linked Hydrodynamics, Tenkiller Lake, OK 15
Overview 15
Data from Model Linkage 17
Water-balance Model 18
Vertical Mixing 19
Withdrawal and Entrainment 22
Model Verification 22
Case Study: Modeling a Reservoir without Linked Hydrodynamics, DeGray Lake, AR 24
Water Balance Model 25
Inter-segment Flows 27
Stratification Considerations 29
Model Verification 30
References: 32
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Acknowledgments
We wish to thank Marjorie Coombs Wellman and Brenda Rashleigh of the US EPAfortheir close reading
and useful comments. Ben Nydegger of City of Boise was instrumental in creating the Lower Boise River
water balance. Work was performed under EPA Contract EP-C-06-029, Work Assignments No. 4-11 and
5-11 with AQUA TERRA Consultants; Tony Donigian's help is gratefully acknowledged. This Note was
completed under Contract No. EP-C-12-006 to The Horsley Witten Group, Inc., Nigel Pickering, Work
Assignment Leader.
Disclaimer
This document was designed to help users properly characterize water flows within the AQUATOX
model. Anticipated users of this document include persons who are interested in using the model for
various purposes, including but not limited to researchers and regulators. The model described in this
document is not required, and the document does not change any legal requirements or impose legally
binding requirements on EPA, states, tribes or the regulated community. This document has been
approved for publication by the Office of Science and Technology, Office of Water, U.S. Environmental
Protection Agency. Mention of trade names, commercial products or organizations does not imply
endorsement or recommendation for use.
Pagel
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Background
Modeling water flows within AQUATOX is an important part of setting up an ecological simulation and
can also be the cause of confusion to a model user. This document attempts to clarify how to specify
water flows into and out of an AQUATOX simulation in both single-segment and linked-segment modes.
Each time AQUATOX has been applied to a linked system (Lower Boise River, ID; Tenkiller Lake, OK; and
DeGray Reservoir, AR) the nature and quality of available hydrodynamic data has necessitated a
different approach to obtaining and managing the input data. Given these technical complexities, this
document summarizes the different approaches taken so that similar methods can be utilized in new
model applications.
Single Segment Overview
When modeling water flows in a single segment, there are four basic options that are available by
double clicking on "Water Volume" at the bottom of the state variables list (Figure 1). Note also that for
single-segment simulations, water volumes can also be entered via the AQUATOX Wizard interface.
Inflow of Water
* Use Const. Loading of |1.3600E*4 cu.mid Convert
' Use Dynamic Loadings
Initial Condition:
CU.m Convert
Use Manning's Equation (streams only)
f" Keep Constant at Initial Condition Level
>' Calculate Dynamically
r Utilize Known Values (below)
Multiply loading by 1
Discharge of Water
Use Const. Discharge |
> Use a Time-Series
12/27/2008 4.2118e04
12728/2008 3.6980e04
12/29/2008 3.4532e04
12/30/2008 3.4520e04
> 12/31/2008 3.2546e04 v
+ I _ I A j Change
Multiply loading by
Evaporation I Get I nit. Cond. from Site Data
Stratification Options
O.K. X Cancel
Figure 1: Water Volume Entry Screen in AQUATOX
Page 2
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Four Options for Modeling Water Volume in Single-Segment Mode
The Manning's Equation Method (streams only): This method requires discharge data,
often available from USGS stream gages. The site's volume at each time step is then
estimated using Manning's Equation and the length of the stream segment. The inflows
required to maintain these volumes are also automatically calculated. Careful attention
should be given to the "Channel Slope" and "Manning's Coefficient" parameters entered
in the "Stream Data" screen (within the site underlying data screen.)
The Keep Constant at Initial Condition Level approach: This method requires inflow
data. Discharge is calculated based on inflow and evaporation.
Calculate Dynamically: In this case, volume is calculated based on time series of inflow,
outflow and evaporation.
Utilize Known Values: This method requires a time series of known volumes and inflow
data. Outflow is calculated taking evaporation into account.
At each time step, segment volume is increased by the inflow coming into the system, and reduced by
the outflow and evaporation. Site volumes, inflows and discharges may be entered using the time-
series inputs available on the left and the right of the "Water Volume" entry screen (Figure 1). Inputs
that are not relevant to the water volume choice selected are colored a dark grey and unavailable for
user entry.
As a simplification, in single-segment mode, inflows of water due to direct precipitation are ignored1.
However, nutrient and organic toxicant loadings associated with direct precipitation may be specified by
clicking on any of the nutrients (or toxicants) in the state-variable list, moving to the "direct
precipitation" entry box, and adding the mass loaded to the system in units of "g/m2 d."
Evaporation
New to Release 3.1, a user may also specify time-varying evaporation. Evaporation time-series and
constant values are not located on the water-volume screen, but instead are available in the "Site Data"
entry screen (Figure 2). For convenience, an "Evaporation" button is available at the lower left of the
water-volume screen for the user to quickly jump to the relevant entry screen.
1 If water volume added due to direct precipitation is a critical component of the water balance of a single-
segment model, this water volume may be added to the inflow waters. However, note that concentrations of
nutrients or toxicants associated with the inflow waters will also be added to your direct-precipitation water
loadings. Another possibility is to model your segment using the multi-segment interface and adding a
tributary input that represents precipitation of water. This method is discussed in Water Flows in Multi-
Segment Mode below.
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Note: If "Use Bathymetry" is NOT selected in the site
screen, mean depth is calculated as volume over
surface area, rendering this entry screen irrelevant
Site Mean Depth (m)
'' Utilize Constant Mean Depth
(Set in underlying Site Data)
>' Import/ Enter Dynamic Mean Depth
Evaporation of Water (m la)
<*' Utilize Constant Evaporation
(Set in underlying Site Data)
Import/ Enter Dynamic Evaporation
(m3i'd)
Pond
Lake
r Stream
( Reservoir
<~ Enclosure
Estuary
(~ Tributary Input
Edit Underlying Site Data
Load Site From DB
Remineralization
Reload Remin. From DB
Show Shading / Velocity
Figure 2: Site Data Entry Screen, including Time-Varying Evaporation
Evaporation may be specified in daily cubic meters lost or, alternatively, the mean evaporation from the
site database may be used. The entry in the database is given in inches per year and is converted to
cubic meters per day. This entry is part of the "underlying site data."
Mean Evaporation
22.44 in./year
Stratification Considerations
The "Stratification Options" button allows a user to modify default model behavior regarding
stratification by specifying dates of stratification, thermocline depth, or flow routing options. (Default
model behavior is to initiate stratification when the mean water temperature exceeds 4 deg C. and the
difference in temperature between the epilimnion and hypolimnion exceeds 3 deg C. Overturn occurs
when the temperature of the epilimnion is less than 3 deg. C, usually in the fall.)
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In single-segment mode, when a system becomes "stratified," the number of biotic and nutrient state
variables are doubled; one set of state variables represents the upper epilimnion layer and one
represents the lower hypolimnion layer. Water can mix between the upper and lower layers due to
turbulent diffusion and again when the system is completely mixed due to "overturn." However, the
overall water volume of the system is not changed because of stratification. The water volume inputs
represent the entire modeled segment and are not specific to either the upper or lower segment.
Water volume outputs also represent the water volume of the entire segment.
Within the "Stratification Options" menu, options to route water into and out of the epilimnion and
hypolimnion segments are available (Figure 3). Again, this does not affect the overall water volume of
the system, only how water is flowing through the system.
Inflow Options: (In the Case of Stratification)
C Route I nfl ow to E pi I i m nion
<" Route Inflow to Hypolimnion
'' Route Inflow to Both Segments (weight by volume!
Thermocline Depth
if Calculate from Max Depth and Site Length
t Use Constant Thermocline Depth of
Outflow Options: (In the Case of Stratification)
r Route Outflow from Epilimnion
C Route Outflow from Hypolimnion
< Route Outflow from Both Segs. (weight by volume)
i" Use Dynamic Thermocline Depth
Timing of Stratification:
' Stratify based on Epi. and Hypolimnion Temps, (default]
Stratification and Overturn By Date
Enter "1" for stratification and "0" for overturn.
(If only one year rs entered, an annual cycle is assumed.)
Figure 3: Stratification Options Including Flow Routing Options
Water Flows in Multi-Segment Mode
In the multi-segment model, each segment has multiple potential sources of water inputs as shown in
Figure 4. When a system is linked together, AQUATOX requires that the water volume be solved using
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the "Calculate Dynamically" method described above (on pg. 4). In other words, the user specifies all
inflows to and outflows from each segment, including evaporation, precipitation, and groundwater (if
important) and AQUATOX calculates the resultant volume of each segment.
Primary Boundary
Condition Loading
(Modeled as"lnflow"through
"water volume" screen.
Nutrients modeled as "inflow
loadings")
Inflows from
other
segment(s)in
the system
(Modeled as a
"Link")
Evaporation-
water leaves model
domain
(Mode led thro ugh
"SiteScreen"input)
Current Segment
Outflows to
other
segment(s)in
the system
(Modeled as a
"Link")
Tributary Inputs: Any Number of
Boundary Condition Loadings of Water
e.g. precipitation, tributary loadings,
ground water.
(Modeled as"Link"from 'Tributary Input"
segments. Nutrients in put as "inflow
loadings" within the "tributary input"
segments themselves)
Boundary Condition
Loss of Water
(Modeled as "Discharge"
through "watervolume"
screen)
Figure 4: Diagram of potential water inputs and losses from each segment within a linked system
Water Inflows
There are three primary sources of water inflows into an AQUATOX segment:
Primary boundary condition loading: This usually represents the primary source of water
coming into the segment that is not part of the modeled spatial domain. Inflows of water are
specified as "inflow loadings" through the water volume screen within the segment. (First
double click on the relevant segment to access its state variable list and then double click on
"water volume" in the segment's state variable list, as shown in Figure 5.) Nutrients, gases,
toxicants, organic and inorganic sediments, and biotic loadings within this water may be
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specified by double-clicking on the relevant state variable and specifying the concentration of
that loading within inflow water.
| Linked System Mode: "Duelling Diatoms in Venice Lagoon,als"
Jj
Jj
f* Show Segment Data f* Show Link Data
Linked System Name: |New Venice Link
Perturbed: 07-15-11 11:47 AM Control Run: No CM. Run Recot
[VL2]: Low Salinity
fVL3]: Medium Salinity
V14] High Salinity
[VL5]: Adriatic
First double click the
relevant segment
HideTribu
At
Data Op
Segment VL1: River
Single Segment of "New Venice Link"
Seg.Name EPA Release 3.1 Beta
River
Model Run Status:
Perturbed Run: 07-15-11 11:46 AM
Control Run: Wo Ctrl. Results Attached
State and Driving Variables In Stud)
Data Operations:
Program Operations:
DllQ
<ป
iT^t
m
P
initial Conds.
Chemical
Site
1 Setup
>\
Notes
<a Go Back
rhen double click
'Water Volume" J!
ฃป. Export Results
IB^ Export Control
I
Dissolved.orq. tpx...1:..IP.C.B1.254J
Total Ammonia as H
Nitrate as N
Total Soluble P
Carbon dioxide
Oxygen
Tot. Susp. Solids
Salinity
Refrac. sed. detritus
Labile sed. detritus
Susp. and dissolved detritus
Diatoms'!. [Phyt Diatom, Marine]
Diatoms2: [Phyt High-Nut Diatom]
Water Volume
Temperature
Wind Loading
Light
pH
Figure 5: Manner of accessing water volume loadings in linked-segment mode
Inflows from other modeled segments: These loadings can either be unidirectional "cascade"
water loadings, or bi-directional "feedback" water loadings. To specify such a loading, first a
"link" between the two modeled segments must be created ("Show Link Data" check-box then
"Add"). When the link is then edited, the user may specify water flows from one segment to
the next. Note that nutrients, toxicants, organic matter, biotic, and inorganic-sediment loadings
do not need to be specified as they are being calculated by AQUATOX within the other modeled
segment.
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Help ^H Edit Bed Loads
XSection of boundary!
Date
9/20/2006
9/21/2006
9/22/2006
9/23/2006
9/24/2006
9/25/2006
9/26/2006
9/27/2006
9/28/2006
9/29/2006
> 9/30/2006
|Loading A
2.3628e06
2.2620e06
2.201 BeOS
2.1317e06
2.0975e06
2.1146e06
2.1043eQ6
2.1285e06
2.1687e06
2.1553e06
2.1711e06
V>
Change
| Change |
(Water flow must be non-negative)
Note: water flows specified here are from one modeled (or tributary) segment
to another modeled segment. Additional boundary condition inflows and
outflows may be found in the water volume screen within each segment.
| Change |
X Cancel
Figure 6: Entry screen to edit water flows between segments
Tributary inputs: Any number of additional boundary-condition loadings of water may be
specified including point sources, non-point sources, direct precipitation, tributary loadings, and
ground water. First, an additional segment is added and designated as a "tributary input" type
in the site data-entry screen (Figure 2). The new tributary input must then be linked to the
segment in question by adding a "link" and specifying water flows from the tributary input into
the segment (Figure 6).
In order to specify nutrients, organic and inorganic sediments, toxicants, and biotic loadings that
are associated with the inflow water from the tributary input, these items are specified as part
of the inflow loadings to the tributary input itself. The tributary input segment is not part of the
model domain, but water flows and state variables associated with them are loaded into the
spatial domain of the model.
Using "tributary inputs" to break boundary-condition inflows of water into their components,
rather than aggregating all flows and dissolved and suspended state variables, has several
benefits. First, AQUATOX can determine the total loads of dissolved and suspended state
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variables and water to the modeled system rather than requiring the user to sum water flows
and to perform a complex weighted-average of nutrients, toxicants, gasses, and sediments.
Secondly, setting up scenarios that pertain to a single input then becomes much more
straightforward (e.g. "what would be the ecological effect if nutrients and organic matter from a
given wastewater treatment plant were to be reduced?"). The Lower Boise River example
discussed below made extensive use of tributary inputs to model dozens of tributaries,
groundwater, and point-source inputs to the model domain.
Water Losses
Primary boundary-condition loss: This represents the sum of non-evaporative water losses
from the segment. Because each segment is assumed to be well mixed, specifying different
locations for water losses is not required. This could represent withdrawal (to a location outside
the model domain) or the main-stem outflow for the stream segment furthest downstream
(with no linked segments below it). These outflows or withdrawals are specified as "discharge
of water" through the water-volume screen within the segment. (Figure 5.)
Outflows to other modeled segments: As was the case with inflows from modeled segments,
outflows to and from other segments can either be unidirectional or bi-directional. To specify
such an outflow, a "link" must be created and water flows added as specified above.
Evaporation: New to Release 3.1, a user may also specify time-varying evaporation for each
segment using the "Site Data" entry screen (Figure 2). Evaporative water losses can be
separated from the primary boundary-condition losses so that the state variable concentration
is properly computed.
Flow Balance Considerations
As discussed above, the entire water balance of the linked system must be externally specified by the
user, including both internal and external water flows. As we will discuss within this document, there
are many ways to set up such a water balance model ranging from simple spreadsheet models to
complex hydrodynamic modeling systems.
When a complex water balance is set up, it may prove to be overly time-consuming to enter all of the
flows and nutrient concentrations into the AQUATOX interface by importing many dozens of individual
time-series. For this reason, the "Excel Template Import Capability" was designed and implemented.
This allows a user to maintain all water and nutrient loadings in a single auditable Microsoft Excelฎ
template (Figure 7) that can then communicate directly with the AQUATOX interface. Using Excel
spreadsheets a user can both set up a new linked-mode simulation and also modify such a simulation for
scenario analysis. For more information about this capability, please see the section on "Excel Template
Import Capability" within the AQUATOX Help and Users Manual.
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A
1 Addition Type
2 Addition Name (ND Flag?)
3 Seg/Link ID (seg ID from)
4 Length km (seg ID to) (commend )
5 Vol 1C m3 (link type) (commentt)
6 SARA m2 (time series header)
7 [Mean Depth m (time series)
8 Max Depth m
9 Slope m/m
10 Manning's N
Til
12 (set inflow, disch to zero)
13 (calc dynamic)
it]
IE
B C
NewSeg
Seg 1
31
4.50
113.231
289.620
2.558
3.837
0.0023
0.043
NewSeg
Seg 2
32
13.03
243.304
456.152
1.875
2.612
0.0024
0.043
D E
Inflnw
S1 to S2
31
S2
Cascade
Date: Flow (m3/d)
1/1/1993 605,408
1/2/1998 594,241
1/3/199S 597,518
1/4/1998 591,794
1/5/1993 593,965
1/6/1993 598,360
1/7/1993 605,131
1/8/1998 596,413
Figure 7. Example spreadsheet used for flow data import
Stratification Considerations
Unlike single-segment mode, in linked-mode AQUATOX handles stratification by modeling each
vertically-stratified layer as a unique model segment. When segments are vertically stratified, they must
be linked together with a bi-directional "feedback" linkage. A stratification screen within each
segment's main interface allows a user to specify whether a segment is part of a vertically stratified pair
and, if so, whether it is the epilimnion or the hypolimnion segment. For more information see
"Stratification in a Linked System" within the AQUATOX Users' Manual.
Also unlike the single-segment model, water flows must be specified between the two segments.
Overturn may be specified by a high degree of mixing between the two segments whereas periods of
stratification will have considerably lower flow. One possible source of inputs for vertical water flows
would be a 3D hydrodynamic model, though vertical stratification must be well calibrated within that
model and that model's output would likely need to be spatially and temporally aggregated before being
input to AQUATOX.
The specification of vertical water flows may be estimated as a function of temperature or oxygen data.
Methods used to derive these flows are documented in the reservoir case-studies presented below.
Case Study: Modeling a River, Lower Boise River ID
Overview
The Lower Boise River in Idaho is an example in which AQUATOX was used to model a long river span of
over 60 river miles (Figure 8). This site has considerable spatial variability with respect to water quality
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and river flows and was characterized using 13 main-stem segments. Some characteristics of the project
included
26 "tributary inputs"
Groundwater inputs
Wastewater treatment facilities
Input drains and tributaries
Extensive agricultural water withdrawals
"Xf/fr
&v&y!*-m* - .
Figure 8: Overview of segments in Lower Boise River AQUATOX implementation
Water-flow Model
To model the Lower Boise River (LBR), a complex water-flow accounting was created for this site with
the assistance of the City of Boise. Given all of the tributary inputs and withdrawals of water, nutrients
and organic matter were then integrated within the main-stem of the model.
The basic steps taken to implement the LBR model were to:
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1. Create a continuous accounting of water inputs and withdrawals from all of the wastewater
treatment plants and agricultural drains2.
2. Gather main-stem flow data from all relevant USGS gages.
3. Estimate groundwater flow contributions to each segment given available estimates from City of
Boise3.
4. Estimate flow rates for each segment using the simple equation presented here, all units being
in cubic meters per day (tributary inputs include groundwater contributions, agricultural drains,
and wastewater treatment plants):
OutputsSeg N = OutputsSeg w_! + y Trib. Inputs f Withdrawals
5. When gage data downstream were available these were used preferentially and were also used
to check the assumptions of the equation shown above.
6. The average daily flow for each river segment was then calculated, as the average of water flows
coming into the reach and water flows leaving the reach each day.
Water-volume Model
To estimate the water volume of each segment, the flows were used along with the river length and
Manning's equation. This was done within a spreadsheet, combining equations (4) and (5) from the
AQUATOX Technical Documentation:
, 0 x Manning \
Volume = x CLength x Width
where:
Volume = volume of segment (m3);
Q = (average daily) flow rate (m3/s) as derived from water-flow model;
Manning = Manning's roughness coefficient (s/m1/3 );
Slope = slope of channel (m/m);
Width = channel width (m); and
CLength = length of reach (m);
2 These data were primarily based on USGS water chemistry data and monitoring reports from National Pollutant
Discharge Elimination System (NPDES) permittees.
iroundwater flows derived
Base for the Boise Valley.
3 Groundwater flows derived from R.D. Schmidt's 2006 document, A Distributed Parameter Water Budget Data
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This equation provided a daily estimate of segment volume for each segment in the simulation.
Water-balance Model
To complete the process a "closed system" water-balance spreadsheet model was produced that
accounts for changes in volume as well as changes in inflows and outflows for each segment. The inflow
of each river segment was defined by its boundary condition loadings as well as any modeled water
inputs from the upstream reach. Then the outflow of each river segment was calculated as follows:
Outflow = Inflow + Inputs Withdrawals AVolume
where:
Outflow = flow rate over downstream boundary (m3/d);
Inflow = inflow from upstream boundary (m3/d);
Inputs, Withdrawals = boundary conditions used in the water flow model (m3/d);
AVolume = increase in volume from previous day derived from water
volume model (m3/d), can be negative.
In the main stem of the Lower Boise River, evaporation was assumed to be negligible and was set to
zero.
There were some complications to this approach, however, since in some cases, due to the influence of
the calculated volume for each segment, negative flows were derived, indicating a water flow from a
downstream to an upstream segment. Water flowing up the main stem did not match our conceptual
model for the site (i.e. did not seem realistic) and also adds complexity to the modeling. Negative flows
require bi-directional "feedback" which can cause model runtimes to increase. This problem primarily
occurred in the smaller upper reaches during low-flow conditions, probably due to uncertainty in the
water volume estimation based on Manning's equation.
To avoid this occurrence, any negative flows were added to the boundary condition inflow at the top of
the main stem. This process ensured that water flows could remain unidirectional and that the water-
volume model would be maintained throughout the study area.
Model Verification
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The results of the "water balance" model provided us with a second estimate of water flows, compared
with the "water flow" analysis above. In the "water flow" analysis water flows were estimated based on
inflows and outflows for each segment or gage data where available. In the water "balance" analysis,
the water volume for each segment was calculated using Manning's equation and outflows were
calculated as a function of changes in water volume combined with inflows. Because the latter analysis
balances the mass of water in the entire system and also takes into account segment volumes, flows
from one segment to another could differ somewhat from the water "flow" analysis.
To assess the importance of this difference, the average percent "error" was calculated for each
segment, comparing the "closed-system" flows with the flows derived using USGS data and the
estimated flow discussed above. In general, average errors were below 10% and highest at the boundary
of segments 11 and 12 (Figure 9). This percent error was deemed acceptable given the modeling
objectives at this site.
40%
Avg. Percent Error in Closed System Flows vs. Data Flows
(predicted - observed)/observed i.e. positive values are an "overprediction"
30%
20%
S
ฃ 10%
c
01
fc 0%
01
00
S -10%
-20%
-30%
-40%
TO
&
TO
&
TO
&
TO
&
se
10
TO
&
TO
&
TO
&
TO
&
E
o
JJ
o
CD
Figure 9: Percent Error Calculation for Alternative Flow Derivations
Finally, a continuous accounting of nutrient, algae, and organic-matter data for all tributary,
groundwater, and wastewater sources was associated with each water input when importing these into
the model (including point sources). The final main-stem results were compared to water column
observed data with generally favorable results (Figure 9).
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Seg 3 (PERTURBED)
Run on 10-1-07 12:41 AM
Obs PO4at Glenwood (mg/L)
Tot. Sol. P (mg/L)
TPatGB, City of Boise (mg/L)
TP(mg/L)
0.0^
2/27/1999 8/28/1999 2/26/2000 8/26/2000 2/24/2001 8/25/2001
Figure 10. Simulated and observed total phosphorus at Veteran's
Case Study: Modeling a Reservoir with Linked Hydrodynamics, Tenkiller
Lake, OK
Overview
In 2008-2009, Tenkiller Ferry Lake in Oklahoma was selected as the location for a nutrient criteria
modeling case study. The AQUATOX model domain comprised approximately 43 million square meters,
modeled with five horizontal segments (Figure 11). All segments other than the riverine segment were
assumed to undergo vertical stratification. Therefore, a total of nine segments were utilized within
AQUATOX:
Riverine
Transitional Epilimnion
Transitional Hypolimnion
Lacustrine A to Lacustrine B to Lacustrine C Epilimnion (3 segments)
Lacustrine A to Lacustrine B to Lacustrine C Hypolimnion (3 segments)
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1974 EPA-Na'jontl
EutrophictOon Survey Sit*
1985-86 Unitod States
Army Corps of Engineers
Survey Site
1992-93 EPA - dean
Lakes Program Survey
Site
5 km
Figure 11: Longitudinal segments and sampling stations on Tenkiller Ferry Lake, Oklahoma.
Base map from (Oklahoma State University 1996)
Boundary-condition water flows for this study area were available from a linked HSPF and EFDC model
simulation calibrated for the years 1992-1993 (Figure 12). The original intention was to model
horizontal and vertical water flows between AQUATOX segments using EFDC results. This proved to be
possible with horizontal flows, but not vertical flows, as detailed below.
Page 16
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20,000,000
(20,000,000)
(40,000,000)
1/1/1992
4/10/1992
7/19/1992
10/27/1992
2/4/1993
5/15/1993
8/23/1993
12/1/1993
-Flow, Series: Illinois & Baron Rivers(m3/d) Flow, Series: Dam Release (m3/d)
Flow, Series: Caney Creek (m3/d) Flow, Series: Local Runoff (Rev) (m3/d)
Figure 12: Boundary condition water flows from EFDC and HSPF
Data from Model Linkage
The EFDC modeling team provided a water balance for the entire site that did not precisely match the
river flow input data from HSPF. To solve this problem, the flows for the Illinois and Baron rivers were
calculated using the EFDC total boundary condition inputs and subtracting the water inputs from Caney
Creek. In this manner, a model was produced in which the boundary-condition inputs plus the change in
system volume are equal to boundary-condition outputs for each day of the simulation4. Similarly,
EFDC-derived outflows over the Tenkiller Dam were used preferentially to alternative data sources.
EFDC model runs were also used to derive horizontal water flows from Riverine to Transitional, from
Transitional to Lacustrine A, and throughout the three lacustrine segments.
4 Initial modeling by the EFDC team used "cell-center" velocities to estimate water flows over AQUATOX
boundaries. This resulted in a model that would not balance the mass of water in a reasonable manner.
"Cell edge" velocities were then utilized, which resulted in a much better fit. This illustrates the
importance of precision and difficulty of setting up linkages between models.
Page 17
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Water-balance Model
The volume of the river segment was estimated using EFDC inflows and Manning's equation as shown
on page 12 of this document. Outflow from the river segment could then be calculated as a function of
boundary condition river inflow minus any gain in river volume.
Initial condition water volumes for non-riverine segments were derived using information from EFDC
regarding the total volume of the site and then distributing this using the surface area and mean depth
of each segment. Multiplying the estimated surface area by the mean depth provides mean-volume
estimates for each segment. For each segment, percentages of the whole-site mean volume can be
derived. Multiplying these percentages by the initial condition water volume for the entire study area
provides an estimate of initial-condition water volume for each segment.
Using the derived data discussed above, a spreadsheet was used to solve the water volume for each
segment on each day as follows:
Volseg = VolsegT^ + InfloWSUpper segment + RunoffEFDC - Outflow EFDC
where:
Vol = Segment volume in cubic meters;
Inflows = inflow from upstream segment or boundary condition (m3/d);
Runoff EFDC = runoff water from EFDC water balance (m3/d);
Outflow EFDC = horizontal movement of water from EFDC (m3/d).
The resulting predicted water volumes by horizontal segment (m3) are shown in Figure 13.
Page 18
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450,000,000
400,000,000
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
100,000,000
50,000,000
Nov-91 Feb-92 May-92 Sep-92 Dec-92 Mar-93 Jun-93 Oct-93 Jan-94
Riverine
-Transitional
Lake A
LakeB
-LakeC
Figure 13: Predicted Tenkiller water volumes in each horizontal AQUATOX segment
Vertical Mixing
The original intention was to use vertical flows as specified from the EFDC linkage to specify site
stratification and overturn. However, vertical flow fields between segments based on EFDC predicted an
unrealistically high mixing rate of at least 20% per day and were essentially linear over time for each
segment. This did not match site data that showed significant temperature and oxygen stratification by
depth and strong seasonal differences in stratification regime5.
Because of this, vertical mixing was computed offline from observed temperature data and, for the
Transition segment, from dissolved oxygen data. An example is provided here from the Lacustrine C
segment.
1. Based on mean temperatures and temperature ranges for the epilimnion and hypolimnion
segments, a temperature time-series was synthesized for both segments using equation (24)
from the AQUATOX Technical Documentation (Figure 14).
' This mis-match could have been a function of how EFDC defined thermocline depth. Due to variable water depth
in each cell a certain degree of "churning" between segments might have been predicted simply due to water
volume changes in the overall system. Whatever the cause, this problem again highlights the potential
complexities in linking fine-resolution spatial models with models of a coarser spatial resolution.
Page 19
-------
o
1/1/1992 7/1/1992 12/30/1992 6/30/1993 12/30/1993 6/30/1994
Figure 14: Estimated Temperatures differences between Vertical Segments for Lacustrine C
2. Within the spreadsheet, vertical dispersion is calculated in square meters per day, using
equation (18) from the AQUATOX Technical Documentation:
VertDispersion = Thick
\ HypVolume
rpt-l rpt+1
L hypo ~ L hypo
where:
^ ThermoclArea Deltat Tept - T\yi
ipo
VertDispersion
Thick
HypVolume
ThermoclArea
Deltat
1, T
hypo
Tepf,
vertical dispersion coefficient (m2/d);
distance between the centroid of the epilimnion and the centroid of the
hypolimnion, effectively the mean depth (m);
volume of the hypolimnion (m3);
area of the thermocline (m2);
time step (d);
temperature of hypolimnion one time step before and one time step
after present time (deg. C); and
temperature of epilimnion and hypolimnion at present time step
(deg.C).
3. Percent mixing per day is then estimated as follows:
VertDisp x ThermoclArea
Percent Mixing = ^
2 (ZMean) x Volume
Page 20
-------
where:
VertDisp = vertical dispersion coefficient (m2/d);
ThermoclArea = area of the thermocline (m2);
ZMean = mean depth (m);
Volume = Segment Volume (m3).
4. In this modeling exercise, the entire system was assumed to undergo overturn at the same time.
Therefore, if the temperature difference between vertical segments in the Lacustrine C segment
was less than 3 degrees centigrade, the entire system was assumed to be well-mixed. In this
case, percent mixing for all segments was estimated at 25% per day.
5. Offsetting upward and downward flows were then estimated as the percent mixing each day
multiplied by the volume of the entire horizontal segment on that day. These time series were
then entered as flows associated with upward and downward links between vertical segments.
Within the transitional segment, available temperature data at depth were quite limited. However,
oxygen data were available (Figure 15). In this case, we calculated vertical dispersion in square meters
per day, using equation (18) from the AQUATOX Technical Documentation, but substituting oxygen
differences for temperature differences.
Dissolved Oxygen
Data
Fit to Epilimnion
^Seasonal Fit to Hypolimnion
Data
* Observed Epilimnion DO
A Observed Hypolimnion DO
1/1/1992
7/1/1992 12/30/1992 6/30/1993 12/30/1993
Figure 15: Oxygen differences between transitional epilimnion and hypolimnion layers
The above example shows how vertical mixing can be derived based on either oxygen or temperature
Page 21
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data, if only one or the other is available. Vertical differences in concentrations for both oxygen and
temperature can provide a strong indication of how well-mixed a segment is. However, if high-
resolution temperature data are available, they are generally better to use in such an analysis as
temperature is a more "conservative" variable. In other words, oxygen concentrations are subject to
effects from sediment oxygen demand and microbial degradation (among other effects) and these
effects have the potential to complicate the analysis.
Withdrawal and Entrainment
The final complexity addressed within this water-balance model pertains to the withdrawal of water
from the reservoir. All withdrawals over the Tenkiller Lake dam were assumed to come from the upper
(epilimnion) segment. For this reason, some water needed to be routed from hypolimnion to epilimnion
segments to prevent epilimnion segments from becoming "water-volume zero."
Our model application assumed that entrainment from the hypolimnion was spread equally between
the three lacustrine segments. To manage this within the spreadsheet the quantity of outflow that
would have come from the hypolimnion if the water withdrawals were weighted by volume was
calculated.
u + *D A n w,i.,7 Volume'
Entrainment Required = Dam Withdrawal
' ฐ''Um'eEpilimnion+Hypolimnion
This quantity was then divided by three and added to the upward flux of water from the hypolimnion to
the epilimnion for each of the three lacustrine segments.
This procedure also required some specification of additional horizontal flows in the upper layer after
water had been entrained. The horizontal flows from Lacustrine A to Lacustrine B and from Lacustrine B
to Lacustrine C within the epilimnion were also increased to allow the entrained water to exit the
system at the top of the Lacustrine C segment. Horizontal flows within the hypolimnion segments were
reduced by this entrainment quantity because the water that would be flowing through the hypolimnion
had been entrained in the epilimnion layer.
Model Verification
There are no specific flow or water-volume data available to verify this particular water balance model,
however, using this set of horizontal and vertical flows, AQUATOX does a nice job of estimating oxygen
concentrations including seasonality and vertical differences. For example,
Figure 16 shows good correspondence between predicted and observed oxygen concentrations in
segment Lacustrine B.
Page 22
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Lake BEpi. (CONTROL)
Run on 07-8-0910:17 AM
12/28/1991 4/26/1992 8/24/1992 12/22/1992 4/21/1993 8/19/1993 12/17/1993
LakeB Hyp. (CONTROL)
Run on 07-8-0910:17 AM
12/28/1991 4/26/1992 8/24/1992 12/22/1992 4/21/1993 8/19/1993 12/17/1993
Figure 16: Comparison of Oxygen Simulations in Lacustrine B Hypolimnion vs. Epilimnion
Page 23
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Case Study: Modeling a Reservoir without Linked Hydrodynamics,
DeGray Lake, AR
In 2010 and 2011, the AQUATOX model was used in a proof-of-concept analysis of the environmental
relationships of a representative reservoir, DeGray Lake, Arkansas. Calibration and verification over an
eight-year period were based on hypolimnetic dissolved oxygen, nutrients, overall phytoplankton
biomass, chlorophyll a, and biomass of algal groups and fish species.
The model spatial domain was represented by three horizontal segments (Figure 17) and six segments
overall due to vertical stratification (Figure 18).
STA. 10
STA. 8
STA. 2
ST/U3
012345
iiii i
km
Figure 17. Riverine, transition, and lacustrine zones modeled for DeGray Lake
(R, T, and L), respectively (Groeger and Kimmel 1987)
Page 24
-------
inflow
(epi. withdraw)
inflow
(hyp. withdrawal)
precip. evap.
I t
Riverine
Epilimnion
Riverine
Hypolimnion
precip. evap.
i t
Transitional
Transitional
Hypolimnion
precip. evap.
I t
Lacustrine
Epilimnion
Epilimnetic
withdrawal
Lacustrine
Hypolimnion
Hypolimnetic
withdrawal
I Boundary condition Segment to Segment Linkage
1 Tributary Input ^ Vertical Mixing, Turb. Diffusion
Figure 18: DeGray Reservoir Water Flows within AQUATOX
Water Balance Model
While a hydrodynamic model of water flows was not available for DeGray lake, a very useful resource
was available for the calibration period: a table that estimates the water balance for the entire
calibration period of 1974-1980 (Table 1), including adjustments for ungaged flow into the lake (Table 2)
(Ford and Stein 1984).
Page 25
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Table 1. Water balance for DeGray Lake in 1974, 10s m3 (Ford and Stein 1984)
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Bee
Year
Direct
Precipi-
tation
7,32
2.90
4,13
7.72
9,15
16,71
3.27
11.45
9.09
s.ai
11.19
5.79
94.53
Highway
84
Inflow
55,69
18.32
29.98
92.68
36.65
187.11
4,95
a. 38
31.04
19.15
128.74
47,60
660,29
Ungaged
Inflow
26 , 18
a. 61
14.09
43.56
17.23
87.94
2.33
3.94
14.59
9.00
60.51
22,37
310.35
Outflow
106.29
54,70
50,28
7.35
145.23
260.82
31,78
14.34
59,27
70.70
150.58
152,62
1103,96
Evaporation
1.78
2.23
3.03
4.88
5-32
6,32
6,73
5,53
3.33
2,73
1.98
1,52
45.38
Error
18.15
11,42
8.53
-7,93
12.41
-27 . 78
-3.84
-1,21
2.74
-0.64
-20.25
6.21
-2.19
Volume
Change
-0.73
-15.68
3.43
123,80
-75.11
-3.16
-31,81
2.69
-5.13
-40 . 10
27-65
-72,17
-86,36
Table 2. Factors for adjusting the ungaged inflow into DeGray Lake to eliminate water imbalances
(Ford and Stein 1984)
fear
1974
1975
1976
1977
1978
1979
1980
* Corrected ungaged inflow
= factor F x Highway 84
inflow.
I
0.4?
0.42
0.16
0.21
0.39
0.53
0,68
As in other studies, an Excel spreadsheet was developed to account for water flows. An example of this
spreadsheet is shown in Figure 19. The first step required was to build a boundary condition model for
the reservoir in which "what goes in" minus "what is retained in the reservoir" precisely matches "what
comes out." The water balance tables from Ford and Stein nearly solve this problem but there is an
"error" column in which their estimates do not balance the volume of water precisely.
Page 26
-------
1
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Year
Checksum
Direct
Precipi-
tation
7.32
2.9
4.13
7.72
9.15
16.71
3.27
11.45
9.09
5.81
11.19
5.79
94.53
94.53
Highway 84
Inflow
55.69
18.32
29.98
92.68
36.65
187.11
4.95
8.38
31.04
19.15
128.74
47.6
660.29
660.29
Ungaged
Inflow
26.18
8.61
14.09
43.56
17.23
87.94
2.33
3.94
14.59
9
60.51
22.37
310.35
3m35
Outflow
106.29
54.7
50.28
7.35
145.23
260.82
31.78
14.34
59.27
70.7
150.58
152.62
1103.96
1103.96
Evap.
1.78
2.23
3.03
4.88
5.32
6.32
6.73
5.53
3.33
2.73
1.98
1.52
45.38
45.38
Error
18.15
11.42
8.53
-7.93
12.41
-27.78
-3.84
-1.21
2.74
-0.64
-20.25
6.21
-2.19
-2.19
Volume
Change
-0.73
-15.68
3.43
123.8
-75.11
-3.16
-31.81
2.69
-5.13
-40.1
27.65
-72.17
-86.36
-86.32
Checksum
-0.73
-15.68
3.42
123.8
-75.11
-3.16
-31.8
2.69
-5.14
-40.11
27.63
-72.17
-86.36
-86.36
Difference
0.00
0.00
0.01
0.00
0.00
0.00
-0.01
0.00
0.01
0.01
0.02
0.00
0.00
0.04
Figure 19. Excerpt from DeGray Lake Water Flows Spreadsheet
To account for these error terms, adjustments were made to the most uncertain columns within the
table, starting with "ungaged inflow." If too much error exists, the corrected ungaged inflows could
become negative, so the next choice for an adjustment was using "direct precipitation." Finally, outflow
was determined to be the third most uncertain term for any remaining error in the water balance. By
adjusting these three factors, a water-volume mass balance could be produced.
An additional complication to the water-volume mass balance was the difference between daily water
flows and monthly water-balance estimates. Any discrepancy between daily outflow totals and monthly
water-balance outflow estimates was corrected by modifying the monthly water-balance outflows and
also the monthly water-balance error term. This procedure assumed that the sum of daily values is a
more accurate total than the estimated monthly totals.
Inter-segment Flows
Initial-condition volumes for the three zones were taken from Nix and coworkers (1975). Areas were
estimated from the Esriฎ shape file for the reservoir using ArcViewฎ. Volumes and areas were
apportioned among the three zones (Table 3) using the relationships of Junge (1966) described in the
AQUATOX Technical Documentation, where:
VolFrac =
AreaFrac -
Z
f. (]
ZMax
Z Z 9
-// P) 1 p / p
(1 - r) + r ( )
ZMax ZMax
Z 2
ZMax
Z }3
ZMax
3.0 + P
where:
Page 27
-------
AreaFrac
VolFrac
ZMax
Z
P
fraction of area of site above given depth (unitless);
fraction of volume of site above given depth (unitless);
maximum depth (m);
depth of interest (m); and
characterizing parameter for shape (unitless); P is between -1.0 and 1.0.
Table 3. Estimated volume (m3), and area (m2) for each of the segments
Segment
Riverine
Transition
Lacustrine
Tot Vol
9.40E+07
3.01E+08
3.78E+08
ZMean
5
5
5
ZMax
15
25
47
P
-1
-1
-1
VolFrac
0.704
0.488
0.286
Vol(Epi)
6.61E+07
1.47E+08
1.08E+08
Vol(Hyp)
2.79E+07
1.54E+08
2.70E+08
AreaFrac
0.56
0.36
0.20
Area(Epi)
1.08E+07
2.13E+07
1.45E+07
Area(Hyp)
6.00E+06
7.68E+06
2.93E+06
After this procedure, precipitation and evaporation could be distributed as a function of surface area. In
addition, the fraction of total water volume that each segment represented could be calculated and was
estimated as follows:
Riverine volume fraction: 12% of the total
Transition volume fraction: 39% of the total
Lacustrine volume fraction: 49% of the total
The fractions of total volume for each segment were assumed to remain constant throughout the model
simulation.
Having an accounting of the water volume for each day of the simulation from the water balance
calculations, and an accounting of the volume fraction for each segment, the volume for each segment
for each day could be calculated.
The next step was to account for all flows into each segment which, along with the change in volume for
each day, could be used to calculate outflows from each segment. Inflows to each segment included
boundary condition loadings, ungaged water loadings, and precipitation. Losses included evaporation
and boundary condition withdrawals (Figure 18).
As was the case in other model applications, occasional adjustments needed to be made for negative
flows. For example, during a low-flow period of 1974 dam withdrawals were calculated to be small
negative values (when accounting for inflows minus losses). During these periods, dam withdrawals
were simply set to zero; the water volume of the entire system was then slightly lower than would be
suggested by the water volume balance derived above, but the differences were negligible.
Page 28
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Stratification Considerations
Vertical stratification added some additional complexity to the modeling of DeGray Lake. The model
was assumed to go through periods of stratification and overturn as a function of calendar date. For all
three zones stratification was assumed to occur on March 7 of each year, and overturn on December 1,
based on data from James and Kennedy (1987). Within this paper, there was a suggestion that
stratification progresses downstream through each reservoir with time (i.e. stratification occurs up-
reservoir first), but given the available data, the simpler case was used.
Vertical mixing was set to 50% per day during well-mixed periods. Otherwise, vertical mixing was
calculated as a function of through-flow as shown in Equations (19) and (20) of the AQUATOX Technical
Documentation:
VertDispersion = 1.37 x 104 x Retention"2-269
and
Volume
Retention =
TotDischarge
where:
VertDispersion = vertical dispersion coefficient (m2/d);
Retention = retention time (d);
Volume = segment volume (m3).
TotDischarge = discharge from segment (m3/d).
Several additional assumptions were utilized when specifying vertical water flows:
Hypolimnetic withdrawal was assumed to start on March 15, 1979, prior to that there was
epilimnetic withdrawal (Wlosinski and Collins 1985a, Dewey and Moen 1987)
Inflow was assumed to be directed to the hypolimnion during stratification and to the
epilimnion during well-mixed periods. (Actually, inflow was to the metalimnion, but that layer
was combined with the hypolimnion. As a simplification within AQUATOX, the metalimnion is
never explicitly modeled.)
Ungaged inflow was assumed to be routed directly to the epilimnion and was equally distributed
between riverine and transition segments.
Due to imbalance in precipitation, evaporation, and water loadings, the volume of epilimnetic
segments could get bigger as simulations progress. These imbalances were reset to the original
epilimnetic and hypolimnetic proportions during turnover or storms, whenever mixing exceeded
25%.
Page 29
-------
The final segment-by-segment water balance is presented below, in Figure 20.
As with other multi-segment applications, all water inflows, links between segments, nutrient, toxicant
and organic matter concentrations could have been entered manually into the interface as specified in
the section on Water Flows in Multi-Segment Mode above. It was more convenient, however, to utilize
the "Excel Template Import Capability." This allowed us to maintain all water and nutrient loadings in a
single Excel template that could then communicate directly with the AQUATOX interface both for initial
model setup and for editing model assumptions. For more information about this capability, please see
the section on "Excel Template Import Capability" within the AQUATOX Help and Users Manual.
400,000,000
350,000,000
300,000,000
g- 250,000,000
13
U
~u 200,000,000
I
> 150,000,000
100,000,000
50,000,000
-RE
-RH
TE
-TH
LE
LH
^
A A
^ ,,
-------
Riverine Epi (Control)
Run on 03-6-11 7:04 AM
3/30/1974 9/28/1974 3/29/1975 9/27/1975 3/27/1976 9/25/1976
Riverine Hyp (Control)
Run on 03-6-117:04 AM
Trans Epi (Control)
Run on 03-6-11 7:04 AM
3/30/1974 9/28/1974 3/29/1975 9/27/1975 3/27/1976 9/25/1976
Trans Hyp. (Control)
Run on 03-6-117:04 AM
TY
ffi
Oxygen (mg/L)
| o Obs DO(mg/L) |
9/28/1974 3/29/1975 9/27/1975 3/27/1976
D
Lake Epi (Control)
Run on 03-6-11 7:04 AM
3/30/1974 9/28/1 974 3/29/1975 9/27/1 975 3/27/1 976 9/25/1 976
Lake Hyp (Control)
Run on 03-6-1 17:04 AM
3/30/1 974 9/28/1 974 3/29/1 975 9/27/1 975 3/27/1 976 9/25/1 976
Figure 21. Simulated and observed dissolved oxygen in epilimnion and hypolimnion of riverine (A, B), transition
(C, D), and lacustrine (E, F) segments
Page 31
-------
References:
Dewey, M.R., and I.E. Moen. 1987. Entrainment of Larval Fish from DeGray Lake, Arkansas,
During Epilimnial and Hypolimnial Discharges . Proceedings of the DeGray Lake Symposium
Technical Report E-87-4, March 1987. Final Report, p 437-460.
Ford, B., and A. B. Stein. 1984. The Hydrometeorology of DeGray Lake, Arkansas, Miscellaneous
Paper E-84-3. U.S. Army Engineer Waterways Experiment Station, Vicksburg MS.
Groeger, A. W. and B. L. Kimmel. 1987. Spatial and seasonal patterns of photosynthetic carbon
metabolism in DeGray Lake. Waterways Experimental IN Kennedy, R. H. and J. Nix [eds.],
Proceedings of the DeGray Lake Symposium. Technical Report E-87-4, US Army Engineer
Station, Vicksburg, Miss.
James, W. F., and R. H. Kennedy. 1987. Patterns of Sedimentation at DeGray Lake, Arkansas.
Pages 461-501 in R. H. Kennedy and J. Nix, editors. Proceedings of the DeGray Lake
Symposium, Technical Report E-87-4. U.S. Army Engineer Waterways Experiment Station,
Vicksburg MS.
Junge, C. O. 1966. Depth distributions for quadratic surfaces and other configurations. Pages
257-265 in J. Hrbacek, editor. Hydrobiological Studies. Vol. 1, Prague.
Nix, J. F., R. L. Meyer, E. H. Schmitz, J. D. Bragg, and R. Brown. 1975. Collection of Environmental
Data on DeGray Reservoir and the Watershed of the Caddo River, Arkansas. IWD No. Y-l,
U.S. Army Engineer Waterways Experiment Station, Vicksburg MS.
Schmidt, R. D., Cook, Z., Dyke, D., Goyal, S., McGown, M., and Tarbet, K. (2006). A Distributed
Parameter Water Budget Data Base for the Lower Boise Valley. US Bureau of Reclamation
Pacifica Northwest Region, Idaho Department of Water Resources.
Wlosinski, J. H., and C. D. Collins. 1985. Confirmation of the Water Quality Model CE-QUAL-R1
Using Data from Eau Galle Reservoir, Wisconsin. Army Engineers Waterways Experiment
Station, Vicksburg, Mississippi.
Page 32
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