water quality modelling in south carolina

8/9/2019 Water Quality Modelling in South Carolina

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Ecological Modelling 114 (1999) 137173

Spatial and temporal hydrodynamic and water quality modelinganalysis of a large reservoir on the South Carolina (USA)

coastal plain

Daniel L. Tufford *, Hank N. McKellar

Uni6ersity of South Carolina, Department of En6ironmental Health Sciences, 311 Health Sciences Bldg., Columbia, SC 29208, USA

Accepted 29 June 1998

Abstract

Two-dimensional, 31-segment, 61-channel hydrodynamic and water quality models of Lake Marion (surface are

330.7 km2; volume 1548.3106 m3) were developed using the WASP5 modeling system. Field data from 1985 to 199

were used to parameterize the models. Phytoplankton kinetic rates and constants were obtained from a related in sit

study; others from modeling literature. The hydrodynamic model was calibrated to estimates of daily lake volume; th

water quality model was calibrated for ammonia, nitrate, ortho-phosphate, dissolved oxygen, chlorophyll-a, biochem

ical oxygen demand, organic nitrogen, and organic phosphorus. Water quality calibration suggested the modcharacterized phytoplankton and nutrient dynamics quite well. The model was validated (Kolmogorov Smirno

two-sample goodness-of-fit test at PB0.05) by reparameterizing the nutrient loading functions using an independen

set of field data. The models identified several factors that may contribute to the spatial variability previously reporte

from other research in the reservoir, despite the superficial absence of complex structure. Sensitivity analysis of th

phytoplankton kinetic rates suggest that study site-specific estimates were important for obtaining model fit to fie

data. Sediment sources of ammonia (1060 mg m2 day1) and phosphate (16 mg m2 day1) were importan

to achieve model calibration, especially during periods of high temperatures and low dissolved oxygen. This sedimen

flux accounted for 78% (nitrogen) and 50% (phosphorus) of the annual load. Spatial and temporal variability in th

lake, reflected in the calibrated and validated models, suggest that ecological factors that influence phytoplankto

productivity and nutrient dynamics are different in various parts of the lake. The WASP5 model as implemented he

does not fully accommodate the ecological variability in Lake Marion due to model constraints on the specificatio

of rate constants. This level of spatial detail may not be appropriate for an operational reservoir model, but as research tool the models are both versatile and useful. 1999 Elsevier Science B.V. All rights reserved.

Keywords: Reservoir; Hydrodynamic model; DYNHYD; Velocity gradients; Water quality; WASP; Eutrophicatio

model; Phytoplankton productivity; Sensitivity analysis

* Corresponding author. Tel.: +1-803-7774114; fax: +1-803-7773391; e-mail: [email protected]

0304-3800/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved.

PII: S0304-3800(98)00122-7


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D.L. Tufford, H.N. McKellar /Ecological Modelling 114 (1999) 137173138

1. Introduction

Reservoirs are engineered structures, built to

benefit human populations. Among these benefits

are hydropower, recreation, sport and commercial

fisheries, flood control, and water supply. Any-

thing that impairs these uses has direct and no-ticeable impact. A common cause of impairment

to reservoir use is eutrophication, or increase in

lake productivity. Eutrophication is a natural pro-

cess that is not inherently negative. It easily be-

comes a problem in reservoirs because the main

tributaries import large nutrient loads over time

scales that are short relative to the ability of the

aquatic ecosystem to adapt to the loading. The

nutrient loads facilitate large populations of pri-

mary producers. These can impact uses such as

recreation and habitat maintenance or increase

the cost of uses such as drinking water (Ryding

and Rast, 1989).

Study of the causes and consequences of eu-

trophication and potential mitigating actions is

complex for any lake or impoundment. These

studies are often accomplished with the help of

models of various types. Models are essential

tools in studies of large reservoirs due to reservoir

complexity in terms of morphometry, hydrology,

ecology, and internal and external forcing

functions.

Impoundments created by damming major riv-ers may be more complex than natural lakes.

While streamflow into natural lakes may be of

limited quantity and impact, rivers import the

majority of the water, particulates, and dissolved

substances into most reservoirs. The river may

define circulation patterns in the reservoir through

its interaction with lake morphometry and by

advective transport and density gradients (Ford,

1990). Many of the external events influencing the

river (land use practices and weather, for exam-

ple) are seasonal in nature. This along with themorphometry of reservoirs allows establishment

of many different functional habitats, in addition

to the littoral, pelagic, and benthic zones shared

with natural lakes.

During the early stages of development of

mechanistic hydrodynamic models, Orlob (1975)

stated that circulation is an important determi-

nant of ecosystem response. This belief was reite

ated more recently (Falconer et al., 1991

reflecting its then and current role in motivatin

development and use of reservoir models wit

greater hydrodynamic complexity. Ecological sim

ulation models that include circulation processe

seek to understand their influence on temperaturzonation and vertical stratification, in-lake an

outflowing water quality, primary productivit

turbidity along with the light environment, hab

tat loss or creation, and hydraulic residence tim

variation as a result of sedimentation (Kim et al

1983; Martin, 1988; Riley and Stefan, 1988; Lun

and Testerman, 1989; Falconer et al., 1991; Ok

abe et al., 1993; Carrick et al., 1994; Leclerc et al

1995; Shen et al., 1995; Ziegler and Nisbet, 1995

Bailey and Hamilton, 1997; Hamilton an

Schladow, 1997; Schladow and Hamilton, 199

Soyupak et al., 1997).

Jorgensen (1994) reviews the role of ecologic

models in ecosystem understanding and environ

mental management. He states the case for th

necessity that models increase in complexity i

order to understand the system under study an

its stressors. This understanding is needed t

provide input to management and political dec

sions about actions to be taken as a response t

observed or expected conditions. Straskrab

(1994) discusses the management role many mod

els can fulfill. The difference between the use of model for ecological understanding and its use a

a management or technological tool is often sim

ply the perspective of the researcher. Ecologic

results may have management implications an

vice versa. Thus, understanding the hydrolog

ecology of a lake or reservoir is an importan

aspect of research in lacustrine environments.

Lake Marion, a large reservoir on the Sout

Carolina Coastal Plain, has been the object o

much study due to its geographic location an

economic importance to the state. Though it appears to have little of the morphometric complex

ity often associated with reservoirs, studies hav

shown it exhibits spatial zonation (Inabinet, 197

Pickett and Harvey, 1988). The causes of th

variability can be only partially understood from

those empirical studies. The objective of the re

search reported here is to synthesize availab


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D.L. Tufford, H.N. McKellar /Ecological Modelling 114 (1999) 137173 1

morphological, hydrologic, meteorologic, and wa-

ter quality data to simulate water transport and

water quality processes in Lake Marion. The

model was used to identify, characterize, and ex-

plore in-lake mechanisms that influence lake pri-

mary productivity. A large database of hydrologic,

environmental, and water quality data exists forLake Marion. This, coupled with relevant litera-

ture sources, facilitated simulation of the spatial

and temporal dynamics of the lake.

The model selected for this research was

WASP5, the Water quality Analysis Simulation

Program (Ambrose et al., 1993a,b,c). WASP5 is a

group of mechanistic models capable of simulating

water transport and fate and transport of water

quality constituents and toxic organics. The mod-

eling package is distributed and supported by the

US Environmental Protection Agency (USEPA,

1995). Various components of WASP5 have been

used to study a variety of lake, reservoir, and

estuarine issues including ecological characteriza-

tion, the effects of anthropogenic activities, and

the impact of mitigation measures (Ambrose,

1987; Lung et al., 1993; Nikanorov et al., 1994;

Bierman et al., 1994; Bierman and James, 1995;

James and Bierman, 1995; Lung and Larson,

1995). Reasons given for selecting WASP5 include

its linkage of hydrodynamics to water quality and

the broad range of water quality processes in-

cluded in the modeling framework. The WASP5components used in this study are DYNHYD5 for

simulation of reservoir hydrodynamics, and

WASP/EUTRO for water quality simulation.

2. Study area description

2.1. Drainage basin hydrology and hydrography

Lake Marion is in the lower portion of the

Santee River basin (Fig. 1), one of the largestdrainages on the US east coast. The lake and its

companion reservoir, Lake Moultrie, are collec-

tively called the SanteeCooper lake system (Fig.

2).

Lake Marion has three principal subdrainages:

1. the Saluda River, which originates in the

South Carolina Blue Ridge province;

2. the Broad River, originating in the North Ca

olina mountains, and;

3. the Catawba River, which also originates i

the North Carolina Mountains.

The rivers have been extensively dammed fo

hydropower; at one time more hydropower wa

generated here than on any other river system ithe world (Savage, 1968). The system now als

assimilates the wastewater for large and growin

urban areas, especially Charlotte, NC, th

Greenville/Spartanburg region of SC, and Colum

bia, SC.

The Santee River begins as the confluence o

the Congaree and Wateree Rivers approximatel

17.6 km upriver from the lake (Fig. 3). The Con

garee River begins at the confluence of the Broa

and Saluda Rivers, 85.5 km upriver in Columbia

The Wateree River originates 122 km upriver athe dam forming Lake Wateree (its principal trib

utary is the Catawba River) (Fig. 1).

Fig. 1. Santee River basin with study area indicated. T

overall Lake Marion watershed is 38000 km2. The study ar

(4860 km2) consists of the lower subbasins of the Congar

and Wateree Rivers and the immediate drainage to La

Marion.


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Fig. 2. The SanteeCooper lake system. Water enters the system from the Santee River (at the northwest). Most water leaves th

system via the Tailrace Canal; other outflows are the Santee River at Wilson Dam and the Rediversion Canal.

The Congaree and Wateree Rivers are large

alluvial systems while their tributaries within the

study area all originate in the upper and middle

coastal plain. Tributary basins exhibit a dendriticdrainage structure. Wharton et al. (1982) describe

three types of streams originating on the south-

east coastal plain; blackwater, spring-fed, and

bog-fed. All three are manifest in the study area

though blackwater is the more common form.

Organic matter (humics) dissolves during slow

flowing floodplain residence and groundwater

flow through rich floodplain deposits, giving the

water its characteristic tea color (Wharton et al.,

1982; Smock and Gilinsky, 1992). Overland flow

of rainfall runoff produces characteristic irregulardischarge peaks throughout the year. Baseflow is

maintained by often significant groundwater seep-

age. These streams typically have floodplains

though they are not as well developed as those of

higher order coastal plain rivers.

Mean annual rainfall in the study area is ap-

proximately 1200 mm. Although 40% of the an-

nual precipitation typically occurs in June, Jul

and August, high evapotranspiration during thos

months results in annual minima for discharge i

the streams and rivers of the area (Smock anGilinsky, 1992).

2.2. Lake Marion

The SanteeCooper lake system was formed i

1941 by damming the Santee River (for Lak

Marion) and with a combination of dikes an

dams impounding a large floodplain forest and a

existing canal system (for Lake Moultrie). Th

principal discharge from Lake Marion is the D

version Canal to Lake Moultrie. A regulathough relatively small, outflow from Lake Ma

ion at the Wilson Dam spillway reenters the San

tee River. Excess flood-flow also discharges from

the spillway into the Santee River. The princip

discharge from Lake Moultrie is the Tailrac

Canal which eventually drains into the Coope

River. In 1985 the Rediversion Canal was com


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Fig. 3. Water quality and discharge sampling station locations in Lake Marion and its immediate drainage.

pleted which diverts some of Lake Moultrie

outflow back to the Santee River. Downstream

control of lake hydrology (lake stage and resi-

dence time) occurs largely due to power genera-

tion and flood control requirements at Pinopolis

Dam. Other power generating stations are at

Wilson Dam and the Rediversion Canal.The Santee Swamp, at the upriver extreme of

Lake Marion (Fig. 3), is a remnant of an exten-

sive floodplain that existed prior to damming the

river. During extended periods of high flow the

current swamp is inundated upstream to the Wa-

teree River. Much of the year, however, only the

lowest elevations are underwater along with pre-

existing stream channels (Bates et al., 1992). An

area just upstream from the Rimini trestle is the

approximate extent of consistent free flowing

open lake. For purposes of this study the trestlewas used as the swamp/lake demarcation.

The Santee Swamp has a complex hydrology

dependent upon discharge characteristics of the

Wateree River and lake stage (Fig. 4). At high

flows some overbank floodflow from the Wateree

River enters the swamp. Cuts in the levee along

the Santee River allow additional discharge into

the swamp; this occurs essentially year round. Th

effect is that as the swamp and lake converg

water is flowing both in the main river channel a

well as along either side of it. The amount o

water entering the lake from the swamp is highl

dependent on time of year and antecedent cond

tions in the swamp. Backwater effects from thlake can inhibit downstream flow from the swam

(Bates et al., 1992).

Lake Marion is similar to many reservoi

formed by major rivers (Ford, 1990). Its upstream

end is shallow compared to the dam end (mea

depth 2.2 vs. 4.9 m). Water velocity slows rapid

as the Santee River enters the lake (Patterson an

Harvey, 1995). The river is constrained by natura

levees along its channel until 9 km downstream

from the trestle. Several cuts in the levees allo

water to leave the channel prior to their completsubmergence.

The upper portion of the lake is also the na

rowest and has several smaller tributary embay

ments. These factors result in a range of aquat

environments with varying water velocity, bottom

morphology, tributary origin, chemistry, and cla

ity (Inabinet, 1985; Pickett and Harvey, 1988


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Fig. 4. Hydrologic details of the Santee Swamp and upper Lake Marion. Arrows indicate direction of water flow.

This portion of the lake is the principal nursery

for the stripped bass, a major recreational fish in

the SanteeCooper lake system (Bulak et al.,

1995).

Below I-95 the lake widens and deepens, taking

on more lacustrine features. However, since it isstill relatively shallow and the water is always

moving, thermal stratification is transient and

does not occur at all in some years (Inabinet,

1985). There are several additional smaller tribu-

tary embayments at this end which are shallower

than the open lake and, due to the tributary

inflow, little hydrodynamic mixing occurs with the

open lake (Patterson and Harvey, 1995).

A prominent biotic feature in most of the shal-

low portions of the lake is dense and extensive

growths of aquatic macrophytes (Inabinet, 1985;Welch et al., 1986; Harvey et al., 1987). The

dominant macrophyte species have changed over

time (Inabinet, 1985; Welch et al., 1986), as has

the distribution (Welch et al., 1986; Harvey et al.,

1987). The upper portion of the lake receives the

majority of the river-borne sediment burden

(Cooney, 1988). As the sediment accumulates and

reduces water depth, additional macrophyte hab

tat is created (Harvey et al., 1987). Th

macrophytes have been the object of intensiv

biological and chemical control measures.

Reservoirs typically exhibit marked longitud

nal gradients in velocity and water quali(Kennedy and Walker, 1990; Thornton, 1990

Inabinet (1985) and Pickett and Harvey (198

observed this for Lake Marion in analyses of fu

annual cycle data from 1984 and 1985/86, respe

tively. Nutrient concentrations and trophic sta

indices tended to be higher and primary produc

tivity lower upstream than downstream. Wate

clarity as measured by Secchi depth tended t

increase along the same gradient. These finding

support the conclusion that like most reservoir

water clarity in Lake Marion is primarily a function of non-algal turbidity. Trophic state analys

indicates the lake is eutrophic throughout, thoug

there is a distinct decrease from the upper- t

lower-lake (Inabinet, 1985).

Pickett and Harvey (1988) also found clea

evidence of latitudinal gradients. At the upper en

of the lake these were related to complex bas


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morphometry associated with the convergence of

the Santee Swamp, the Santee River, and the

submerged floodplain. Lateral gradients were also

associated with tributary embayments at both the

upper and lower ends of the lake.

Episodes of large fish kills have been docu-

mented in the extreme upper lake. Bates andMarcus (1990) believe these were the result of a

complex series of hydrobiochemical processes that

ultimately produced oxygen starvation. The kills

occurred following sudden increases in hydraulic

flow through the Santee Swamp into the upper

lake after extended low flow periods. This caused

a large pulse of anoxic sediment and oxygen

depleted water into the lake. The resulting pockets

of water with little oxygen were too large and

occurred too suddenly for fish to migrate away

from the area.

Water quality sampling by the South Carolina

Public Service Authority (the state owned entity

that owns and runs the Santee Cooper system)

generally occurs monthly. Data collected from 29

stations were used in the research described here

(Fig. 3). Sixteen stations are from the lake and

embayments, twelve from tributaries, and one

from the Santee Swamp.

3. Model parameterization

Model parameterization had as an objective

that the final result would be suitable for studying

a broad variety of issues. Whenever possible, data

from a long term interval were used so the model

would represent an average profile of the lake

rather than short term conditions. Under these

criteria the model calibration interval selected was

July, 1985 through June, 1990. This range was

chosen because it provided the longest, continu-

ous record of chlorophyll-a (Chl-a) observations

for the full complement of lake sample stationsused in the model. July, 1993 through June, 1994

was used as the water quality model validation

interval.

Internally, the hydrodynamic model derives

daily estimates of variable boundary flows spe-

cified by the model user. These values are used at

each time step during the model day. The hydro-

dynamic equations are solved using a modifie

Runge-Kutta procedure (Ambrose et al., 1993c

DYNHYD5 averages results (flows and volume

to match the time step of the water quality mode

There are 11 tributary inflows and two outflows i

the Lake Marion implementation. A code modifi

cation was required to increase the number ovariable flows from five in the model as it

distributed by USEPA.

The time step chosen for the hydrodynam

model was 120 s; for the water quality model

was 2 h. The models simulated a 365-day interv

beginning on January 1. Water quality and stream

discharge data were from the USEPA STORE

database (see http://www.epa.gov/owowwtr

STORET/zip/sthp.html for a description

Tufford (1996) has additional discussion of mod

parameterization.

3.1. Model geometry

Lake bathymetry is needed in multi-segmen

models to help establish segment geometry. Eac

segment must have a surface area and dept

which approximate the actual geometry of th

corresponding location in the lake. The number o

segments a model can have is conceptually con

strained, in part, by the scale at which reasonab

bathymetric estimates can be made.

Bathymetry for this model was derived bplanimetry of a bathymetric map of the lak

(Patterson and Logan, 1988). A principal obje

tive for this model was that it facilitate evaluatio

of spatial variability in the lake. Both lateral an

longitudinal segmentation was developed; se

ments are rectangular prisms. Segments were als

designed so that no more than one of the 1

monthly lake water quality sampling stations oc

cur in a segment. Other segment design criter

included that they should complement the natura

morphology of the lake and they should be alarge as possible while still meeting other criteri

This combination of constraints resulted in 3

model segments, each 50106 m3 at maximum

lake stage (Fig. 5).

DYNHYD5 uses a channel/ junction geomet

(Ambrose et al., 1993c). Channels move wate

between junctions. Most of the hydrodynam


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Fig. 5. Configuration of water quality model segments with segment number (underlined) and mean depth at full pool. Shading

included to help visualize depth gradients.

junctions correspond to segments in the water

quality model. The model requires additional

junctions that serve as sources and sinks for

boundary flows (Fig. 6). These extra junctions do

not map to water quality model segments. A

channel must be defined for each lake inflow and

outflow and to represent flow within the lake.

Internal flow paths were estimated based on a

previous tracer study of the lake (Patterson and

Harvey, 1995). The total number of channels is 61

(Fig. 6). Defined channels only indicate potential

flow paths. Actual advective flow is determined at

each time step based on hydraulic head differen-

tial between adjacent junctions.

3.2. Eutrophication constituents and kinetic rates

and constants

The water quality model can simulate kinetic

transport and transformation for up to eight eu-

trophication constituents (Fig. 7). Constituent

concentrations from sixteen lake stations wereused to set initial concentrations (5 year mean for

January) and to produce calibration charts (5 year

monthly means91 S.E.). Tributary and swamp

stations were used to obtain constituent inflow

concentrations during the model execution. Flow

weighted mean concentrations were derived for

segments with more than one tributary inflow.

Water quality parameters simulated were:

1. chlorophyll-a (Chl-a);

2. ammonia/um-N (NH3/4);

3. nitrite/nitrate-N (NO2/3);

4. ortho-phosphate-P (OPO4);

5. 5-day biochemical oxygen demand (BOD5);

6. dissolved oxygen (DO);

7. organic nitrogen-N (ON), estimated as tot

Kjeldahl nitrogen (TKN) minus NH3/4;

8. organic phosphorus-P (OP), estimated as totphosphorus (TOTP) minus OPO4.

WASP5 models phytoplankton production an

nutrient kinetics (Fig. 7) as temperature modifie

functions of rates entered by the model user (Am

brose et al., 1993a). Phytoplankton production

also modified by light and nutrient limitatio

Nutrient limitation is modeled using Michaelis

Menton kinetics. Nutrient species are taken u

during phytoplankton growth and released durin

respiration or at death according to atomic ratio

entered by the model user. Water quality constituent transport occurs principally by advection

Dissolved fractions are also subject to diffusio

and particulate fractions can settle and resuspend

Constituent loads enter the system in tributar

inflows, as point sources, or as nonpoint source

Inorganic nutrients can also enter by benth

release.


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Fig. 6. Channel/junction geometry of the hydrodynamic lake model. (a) Junctions with dashed outline do not appear in the wat

quality model; they exist as sources and sinks of water. (b) Channels are potential flow paths between junctions.

The initial values for most of the reaction rates

and constants were taken from water quality

modeling literature (Ambrose et al., 1993a; Bowie

et al., 1985), and when changed during calibra-

tion, the literature ranges were used as guides

(Table 1). Exceptions were the phytoplankton

growth rate, the temperature correction coefficient

to phytoplankton growth, and the half-saturatio

constants for nitrogen and phosphorus limitatio

to phytoplankton growth. Initial values for thes

were taken from work in Lake Marion by Suda

shan (1995) (Table 2).

The ammonia and phosphorus benthic flu

functions were determined by calibration. The


10/37


Fig. 7. Energy diagram of the processes in the eutrophication model of Lake Marion. Temperature (left out to simplify the diagram

modifies all processes except settling, sediment nutrient release, reaeration, extinction, and loading /export. The WASP5 model

capable of additional, and in some cases different, processes. Those indicated are implemented in the model described her

Acronyms are defined in the text.

were needed as additional sources of nutrientsinto the system. There was not a deterministic

derivation of the values entered, but they gener-

ally follow the rule that flux increases as tempera-

ture increases and dissolved oxygen decreases.

Their ranges are within those found in the

literature.

3.3. En6ironmental forcing functions

Four water temperature specifications (to facili-

tate spatial differentiation within the model) weredeveloped by cluster analysis (SAS/STAT PROC

CLUSTER, AVERAGE method; SAS, 1988) us-

ing the 5-year monthly mean temperatures at each

sample station. Segments without a sample station

were assigned a cluster based on proximity to a

segment with a station. Downstream proximity

was given the highest consideration.

Light extinction coefficient specifications wealso derived by cluster analysis. The monthly valu

was derived with Eq. (1) (Williams, 1980) from th

field data. These were modified by subtracting a

estimate of light extinction due to phytoplankto

(see Eq. 5.9, Ambrose et al., 1993a; Kirk, 1994

This was done because internally the water qualit

model adds this estimate to the extinction coeffi

cient entered by the model user.

Ke=1.1Secchi depth0.73

(Secchi depth in meters). (

Daily total solar radiation (TSR in W m2) wa

derived from Eq. (2), fitted from a long ter

record along the South Carolina coast (Summe

et al., 1980). The daylight fraction of the 24-

interval was obtained by proportion using sunrise

sunset for Charleston, SC (United States Nav

Observatory, 1977).


11/37


Table 1

Reaction rates and constants (and range of values tried during calibration) for the WASP eutrophication model

RangeValue SourceFunctionName

Water column dispersive transport Bowie et al. (1985)Dispersion 10 m2 s1

Bowie et al. (1985)Solids flow specification0.00.50.00.4 m day1Settling

Ambrose et al.1.03.0SOD1D 3.0 gO2 m2 Sediment oxygen demand

(1993a)day1

0.991.04 Temperature correction factor (TCF) for SOD1DSODTA Bowie et al. (1985)1.04

0.050.15 Bowie et al. (1985)Nitrification rate0.075 day1K12C

1.08 1.081.20 TCF for K12C Bowie et al. (1985)K12T

Half-saturation constant for O2 limit. on nitrification Bowie et al. (1985)KNIT 2.0 mg O2 l1

1.42.6 Maximum phytoplankton (PP) growth rateK1C 2.24 day1 Sudarshan (1995)

0.981.072 TCF for K1C Sudarshan (1995)1.03K1T

Ambrose et al.XKC 0.016 mg CHL-a Coefficient for extinction due to chlorophyll

m3 (1993a)

Sudarshan (1995)0.0150.0250.015 mg N l1 Half-sat. constant for N limitation to PP growthKMNG1

0.00320.02 Half-sat. constant for P limitation to PP growthKMPG1 Sudarshan (1995)0.005 mg P l1

0.050.35 PP respiration rateK1RC 0.2 day1 Bowie et al. (1985)

Bowie et al. (1985)TCF for K1RC1.0451.11.05K1RT

0.020.1 Non-predatory PP death rateK1D Bowie et al. (1985)0.04 day1

P-to-C ratio in PP Bowie et al. (1985)PCRB 0.025 mg P

mgC1

N-to-C ratio in PP Bowie et al. (1985)0.25 mg N mgNCRB

C1

Half-sat. constant for PP effect on mineralization Ambrose et al.0.0 mg C l1KMPHYT

(1993b)

Bowie et al. (1985)BOD deoxygenation rate0.10.30.3 day1KDC

Bowie et al. (1985)TCF for KDCKDT 1.04

Ambrose et al.Half-sat. constant for O2 limit. to BOD decomp.KBOD 0.5 mg O2 l1

(1993a)

O-to-C ratio in PP Default2.667 mg O2 mgOCRB

C1

0.020.2 Mineralization rate of DONK71C 0.06 day1 Bowie et al. (1985)

TCF for K71C Bowie et al. (1985)K71T 1.02 1.021.3

0.25,0.5 Fraction of dead PP recycled to DONFON 0.5 Ambrose et al.

(1993a)

Mineralization rate of DOP Bowie et al. (1985)0.22 day1 0.10.4K83C

TCF for K83C Bowie et al. (1985)K83T 1.08 1.081.2

Fraction of dead PP recycled to DOPFOP Set equal to FON0.5

TSR=((39451695cos((2pi/365)(day+11)))

27.9). (2)

3.4. Other parameterization issues

Constituent mass transfer into and out of seg-

ments in the water quality model occurs principally

by advection as specified by the hydrodynamic

model. Transfer also occurs as a result of dispersive

exchange and by settling; both were determine

during calibration of the hydrodynamic model.

dispersion coefficient of 10 m2 s1 was specifiebetween segment pairs 1/2, 5/6, 22/26, 25/27, an

27/29.

Reaeration coefficients were derived for th

model using estimates of wind speed (Banks, 1975

Estimates of wind speed (at 10-day intervals) wer

the 36-year mean of observations kept by NOAA

for Columbia and Charleston (USEPA, n.d.).


12/37


Two source code modifications were made to

the water quality model. The first modification

resulted from concern that in the model as dis-

tributed by USEPA the daily derivation of the

carbon-to-chlorophyll ratio underestimated the

light in the water column. Conversations with

the model developer resulted in adjustments tothe derivation to increase the light estimate.

The second code modification implemented an

estimate of saturating light intensity as a linear

function of incident light developed by Sudar-

shan (1995) during her work in Lake Marion.

This replaced the derivation already in the water

quality model; a function of water temperature

and phytoplankton physiological state. Sudar-

shan developed her equation using incident solar

radiation as photosynthetically active radiation

(PAR) in mol m2 day1 Eq. (3).

Is=0.12+(0.47Id) r2=0.63 (3)

where Is and Id are saturating and total daily

PAR, respectively, in mol m2 day1.

The model uses total solar radiation as Ly

day1. Documentation from LI-COR (1979) in-

dicated that 1 mol m2 day1 (400700 nm

wavelength)=5.733 Ly day1 (photosynthetic

radiant exposure). The proportion of total inci-

dent radiation that is PAR is about 0.48 (Kirk,

1994). With these conversion factors the equation

developed by Sudarshan (1995) was modified for

the model.

4. Surface water balance model

The Diversion Canal is the principal surfac

outflow from Lake Marion. It is ungauged sinc

its discharge is under direct control of Lak

Moultrie. To estimate its discharge a surface wa

ter budget model was developed. Flow measurments or estimates with daily frequency we

entered into the model as 10-day arithmet

means. This was because of a limitation in th

DYNHYD5 model. All other flows had monthl

measured or estimated values.

4.1. Stream discharge sampling

Discharge estimates for the Congaree (nea

Columbia) and Wateree (near Camden) Riv

were daily averages from US Geological Surve(USGS) continuous stage/discharge records. Th

accounts for drainage from 87% of the overa

basin area. The net effect of additional sma

tributary inflow, loss to extensive floodplain

and groundwater exchange downstream from

these recorders was probably small; it was no

included in these discharge estimates. Discharg

estimates from USGS stations near the Congare

and Wateree confluence and on the Santee Rive

upstream from the lake have been discontinue

due to uncertainty over backwater effects.Small tributary discharge estimates were ob

tained from monthly sampling by the South Ca

olina Department of Health and Environment

Control (SCDHEC) and the South Carolin

Public Service Authority (also known as Santee

Cooper, the state owned entity that owns an

operates the SanteeCooper lakes). Santee

Cooper also estimates daily discharge from th

spillway at Wilson Dam.

4.2. Santee swamp discharge estimate

It is estimated that Wateree River discharg

above 283.2 m3 s1 spills over into the Sante

Swamp (Pickett, 1992). It is also estimated th

10% of the Santee River discharge flows into th

Santee Swamp through cuts in the natural levee

which form the main channel upriver from th

Table 2

Estimated phytoplankton growth parameters and 95% confi-

dence intervals

Estimate 95% CIParameter

2.24 1.722.76Maximum growth rate

1.031.071.05Temperature correction

0.00430.0250.015Ks for Na

0.0010.0075Ks for Pa 0.0032

16.7623.8220.2Is (mol m2 day1)b

See text for discussion. From Sudarshan (1995).a MichaelisMenton half-saturation constant.b Saturating light intensity.


13/37


lake (Patterson and Harvey, 1995) (Fig. 4). Pick-

ett (1992) estimated that the annual average

travel time from the USGS gauging stations at

both Camden (Wateree River) and Columbia

(Congaree River) to the confluence is about 1

day. An additional lag of 1 day was introduced

to account for travel from the confluence to thelake. The estimated discharge into the lake from

the Santee River main channel is given by Eq.

(4).

Discharge=0.9(2 days prior to Congaree River

at Colombia+2 days prior to Wateree River

discharge at Camdenportion of Wateree

discharge\283.2 m3 s1)). (4)

Bates et al. (1992) estimated the annual mean

hydraulic travel time through the Santee Swamp

is 40 days. A travel time of 5 days for SanteeRiver levee cut water was assigned to introduce a

lag. The estimated flow of water from the swamp

into the lake is 10% of the 5 days prior Santee

River discharge, as described above, plus the

portion of the 40 days prior Wateree River dis-

charge \283.2 m3 s1, if any. The Santee River

main channel and the two Santee Swamp sources

were entered into the model as three separate

flows to facilitate modification to them to evalu-

ate research or management questions.

4.3. Small tributary discharge estimates

The natural log transform of the monthly

mean discharge (m3 s1) from each of the mea-

sured small streams was regressed against the log

transformed watershed area (m2) using SAS

PROC REG (SAS, 1988). This provided a

method to estimate the monthly discharge of two

unmeasured creeks Eq. (5). Of the six small lake

tributaries which were measured, the measure-

ment was taken upstream from the lake. Thedischarge regression model provided a method to

estimate their full basin discharge into the lake

(Table 3).

ln(q)=a+bln(A) where

Q=flow(m3 s1) A=subbasin area (m2).

(5)

4.4. Precipitation and e6aporation

Direct precipitation onto, and evaporatio

from, the lake surface was estimated based o

National Climate Data Center (NCDC) record

(NCDC, 1985a,b, 1986a,b, 1987a,b, 1988a,b

1989a,b, 1990a,b). Precipitation and evaporatioare the monthly mean of measurements fro

stations near Lake Marion. Estimated lake evap

oration was taken as 70% of the measured pa

evaporation. This is a standard open-water co

rection factor from pan measurements (Veih

meyer, 1964). Data are from 1985 to 1990. Th

net effect was evaporative loss every mont

(Table 4).

4.5. Lake 6olume estimates

The bathymetry map of the lake used for seg

ment geometry (Patterson and Logan, 1988) in

cluded a lake stage-volume curve which was use

to fit a 5th order polynomial to estimate volum

from stage Eq. (6). Volume has units of acr

feet; stage has units of feet. The stage interv

that can be used to predict volume with th

expression is 5077.5 feet (15.2423.62 m).

Volume=(16500.629481525.16547stage

+55.67088

stage

2

1.01081

stage

3

+0.00915stage4

0.0003stage5)1000, r2=0.999.

(6

4.6. Di6ersion canal discharge estimates

The estimate of daily diversion canal outflo

was then the net difference of the daily volum

change9all other measured or estimated flow

Eq. (7).Discharge=(previous day lake volume

current day lake volume)

+Santee River main channel discharge

+Santee River discharge through swamp

+Wateree River discharge through swamp


14/37


Table3

Drainagebasinareas(km2)andpredictedmonthlymeandischarges(m3

s1)forthe

smalldirecttributariesofLakeMarion(upperpan

el)andstatisticsforthemonthlyregressionmodels(allP-valuesB0.0

001)usedto

predictthedischarges(lowerpanel)

Area

Jan

Feb

Mar

Ap

r

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

WybooSwampCreek

45

0.4

9

0.6

7

0.6

1

0.4

4

0.3

0

0.2

4

0.25

0.2

6

0.4

2

0.3

3

0.3

5

0.5

5

103

1.5

1

1.8

2

1.6

3

1.2

9

0.9

7

PotatoCreek

0.9

3

0.85

1.0

0

1.2

3

1.1

4

1.4

6

1.6

6

TawcawCreek

102

1.1

6

1.4

4

1.3

0

1.0

1

0.7

4

0.6

8

0.64

0.7

4

0.9

6

0.8

5

1.0

5

1.2

8

97

0.1

2

0.1

9

0.1

8

0.1

2

0.0

7

JacksCreek

0.0

5

0.06

0.0

5

0.1

1

0.0

7

0.0

6

0.1

4

61

1.1

1

1.3

8

1.2

4

0.9

6

0.7

0

SpringGroveCreek

0.6

5

0.61

0.7

0

0.9

2

0.8

1

0.9

9

1.2

3

12

0.4

2

0.5

8

0.5

3

0.3

8

0.2

6

ChapelBranchCreek

0.2

0

0.22

0.2

2

0.3

6

0.2

8

0.2

9

0.4

8

39

0.6

8

BigPoplarCreek

0.8

9

0.8

1

0.6

0

0.4

2

0.3

6

0.36

0.3

9

0.5

7

0.4

7

0.5

3

0.7

6

225

2.6

8

3.0

3

2.6

8

2.2

3

1.7

6

HalfwaySwampCreek

1.8

6

1.58

1.9

9

2.1

2

2.1

3

3.0

3

2.9

0

34

0.3

7

0.5

1

0.4

7

0.3

3

0.2

2

0.1

7

H.S.unnamedtriba

0.19

0.1

9

0.3

2

0.2

4

0.2

4

0.4

2

8.5

4

10.5

2

9.4

6

7.3

6

5.4

5

5.1

4

Totaldischarge

4.76

5.5

3

7.0

1

6.3

2

8.0

2

9.4

1

0.7

59

0.5

35

0.6

89

0.6

83

0.6

22

r2

0.6

64

0.507

0.6

42

0.5

55

0.7

43

0.8

46

0.6

67

19.2

3

16.9

2

16.6

1

18.4

4

20.4

9

23.5

8

21.27

Intercept

23.3

4

18.4

5

21.3

7

24.4

4

18.6

1

1.0

51

0.9

37

0.9

15

1.0

01

1.0

95

1.2

59

1.130

Coefficient

1.2

50

0.9

98

1.1

51

1.3

28

1.0

23

a

HalfwaySwampCreekunnamed

tributary.


15/37


Table 4

Precipitation (P), evaporation (E), and net (PE) used in the hydrodynamic model. Also shown are comparisons of evaporatio

among the current model and three literature estimates

Net (PE) E (current) EbEaP E Ea

(mm year1)(mm year1)(mm day1)(mm day1) (mm month1)(mm day1) (mm month1)

41Jan 342.2 2.8 0.2

61Feb 2.3 2.9 0.2 3181Mar 2.5 4.6 0.7 36

114Apr 361.8 6.5 1.5

38 137May 2.3 7.1 1.6

160Jun 3.2 7.5 1.4 37

168Jul 392.7 7.8 1.7

Aug 5.2 6.0 0.3 37 152

140Sep 3.9 4.9 0.3 35

112Oct 353.9 4.3 0.1

33 76Nov 2.3 3.2 0.3

Dec 2.0 2.2 0.1 33 48

425 1290 1325Total 1092

a

Van der Leeden et al. (1990).b Morton (1983).

+(precipitationevaporation)

+small tributary discharges

Wilson Dam spillway discharge. (7)

5. Methods

5.1. Calibration and6

alidation

Hydrodynamic model calibration was per-

formed by adjusting the estimated, 5-year mean

boundary flows. The calibration objective was

that the daily modeled volume would be within

5% of the estimated 5-year daily mean volume.

Hydrologic estimates are discussed in a subse-

quent section. The calibrated model specifically

simulated hydrologic conditions during the cali-

bration interval. Under this implementation the

only meaningful validation would be of the datacollection and derivation methods; none was

performed.

The water quality model was calibrated by

comparing measured monthly mean concentra-

tions (91 S.E.) to the modeled monthly mean.

This was done for each of the eight constituents

for each model segment with a corresponding

water quality sampling station. Calibration wa

accomplished by adjusting rates and constan

within the limits of literature values for biochem

cal processes in the lake. Rates controlling phyto

plankton kinetics were kept within ranges derive

from field work in Lake Marion by Sudarsha

(1995) (Table 2).

For validation the calibrated model boundar

loads were set to field values for January, 199through August, 1994. The validation interval wa

July, 1993 to June, 1994. This corresponds to th

field work interval from which Sudarshan (1995

estimated the phytoplankton growth kinetics. Th

model was parameterized to run from Januar

1993 because the hydrodynamic flows and vo

umes simulate a January 1 begin date.

Each of the 16 segments with correspondin

sample stations were individually assessed for va

idation using the KolmogorovSmirnov two-sam

ple goodness-of-fit test (Conover, 1980; Reckhoet al., 1990). Parameters evaluated were Chl-a an

the inorganic nutrient species. The model pr

dicted values corresponding to station samplin

days were used as one sample. The station sam

ples themselves were the second sample. Statio

sampling did not occur every month at all station

during the validation interval (range was 5 12


16/37


Table 5

Phytoplankton production kinetic constants, their values in the calibrated model, and values in the sensitivity analysis

Constant Calibrated Values in sensitivity analysis

2.24Max growth 1.51.0 2.0 2.5

0.080.010.015N half-sat 0.040.02

0.08P half-sat 0.005 0.0005 0.001 0.01 0.04

The KolmogorovSmirnov test is a nonparamet-

ric test that converts the two samples to their

empirical distribution function (EDF). The princi-

ple is that if the two samples are from the same

underlying population, their EDFs should be

close to each other. The test statistic is derived as

the maximum vertical distance (y-axis) between

the two EDFs. A P-value is determined based on

the sample sizes. The null hypothesis is that the

two samples are taken from the same underlying

distribution. For this research the hypothesis was

rejected at P50.05. The test was performed using

PROC NPAR1WAY (SAS, 1988) with the EDF

option.

5.2. Tracer simulations

The water quality model can simulate a conser-

vative chemical that is subject only to transport,

boundary, and loading processes (Ambrose et al.,

1993a). Two types of tracer simulations were exe-cuted during this study. In the first, a steady unit

concentration of 1 mg l1 was included as a

boundary concentration in all inflows. Significant

deviations from that concentration anywhere in

the reservoir would indicate a source or loss of

chemical not associated with surface advective

flows.

The second type of tracer simulation was exe-

cuted as a way of estimating hydraulic travel time

through the reservoir during high and low flow

scenarios. This was accomplished by introducinga pulse (simulated as a point source load) of 50 t

of tracer into junction 12 (water quality model

segment 1) on model day 62 (775 m3 s1) and 192

(222 m3 s1). The day of the occurrence of the

peak tracer concentration in junction 42 (water

quality model segment 31) minus the entry day of

the tracer was considered hydraulic travel time.

The quantity of tracer in the pulse was est

mated by trial-and-error. Significant dilution oc

curs as the pulse move downstream. Determinin

the location of the peak tracer cloud, versus jun

tions with steadily diminishing residual concentr

tions, was not possible during simulations wit

lesser quantity. The tracer did not move down

stream as a single pulse because of the comple

flow structure in the model (Fig. 6).

5.3. Sensiti6ity analysis

Model response to calibrated values of con

stituent boundary loading and rate constants wa

evaluated by two series of sensitivity analyses. Th

first series proportionately altered the nitroge

and phosphorus loads (both organic and ino

ganic) in the calibrated model by factors of 0.5

1.5, and 2.0 times. The nitrogen and phosphoru

simulations were each run separately, then thewere combined. Results were plotted as the pro

portion change (from the calibrated model) i

constituent concentration (abscissa; 1.0=cal

brated model) and the proportion change (from

the calibrated model) in mean growing seaso

Chl-a concentration in the segments 1 and 6 (ord

nate; 1.0=calibrated model). Growing season

defined as May through September.

The second series of sensitivity analyses in

volved altering the values of the phytoplankto

maximum growth rate and the nitrogen and phophorus half-saturation constants (Table 5). Th

range of values used corresponds to the rang

found in Bowie et al. (1985). The effect of bot

increases and decreases was simulated. Howeve

the calibrated values for all three constants wer

near an extreme from the literature source s

there was some limitation in available choice


17/37


Results of the second series were plotted as the

rate constant value (abscissa) and a sensitivity

index Eq. (8).

Sensitivity index (SI)

=(D Chla)}(calibrated mean Chla)

(D rate constant)}(value of constant in calibrated model) (8)

where D Chl-a is the change in growing season

mean CHl-a, and D rate constant is the change in

value of the rate constant.

6. Results and discussion

6.1. Hydrodynamic model calibration

The hydrodynamic model was calibrated with amaximum volume difference of 3.3% (Fig. 8). The

lake starts the year at its annual low volume. Late

in January it begins a rapid increase to its annual

maximum in late March. This corresponds to the

period of highest discharge of the Congaree and

Wateree Rivers (Fig. 9) and graphically depicts

the reservoir function as a flood control structure.

The volume steadily declines after reaching its

peak. This is due to low tributary inflows, sea-

sonal high power requirements, and to increase

storage capacity during the tropical storm season(Inabinet, 1985). Discharges begin to increase

again in late summer and early autumn, resulting

in higher volume. During December, even though

river inflow is relatively high, volume rapidly de-

Fig. 9. Mean daily discharge of the Congaree and Water

Rivers during the study period.

creases in preparation for the flood control r

quirement after the beginning of the year.In general, the model tracks the significant an

nual volume trends very closely. Principal di

crepancies are that it does not increase in volumas quickly as the lake early in the year and once a

maximum volume the model declines more gradu

ally. But it is sensitive to even short term fluctuations such as the volume increase at about da

230 and the brief dip beginning at day 270. Th

lag is likely an artifact of the 10-day and monthaveraging of the tributary flows.

The measured volume was estimated from ac

tual lake stage as recorded by SanteeCooper. Aempirical stage-to-volume relationship in such a

enormous, irregularly shaped basin has some unknown error in its accuracy. This suggests thcloser correspondence between measured an

modeled volumes may not necessarily bring th

model into closer agreement with actual lakvolume.

Fig. 8. Volume comparison of the calibrated hydrodynamic

model to the estimated 5-year daily mean volume. Daily

proportional difference is also shown.

Fig. 10. Comparison of tracer concentration when the hydr

dynamic model has evaporation included versus not include

Data represents junction 23, as an example.


18/37


6.2. Effect of e6aporation

During execution of the conservative tracer

model a deterministic deviation from uniform

concentration occurred. This resulted from evapo-

rative loss from the lake surface. Tracer does not

leave the lake with evaporation so it is concen-trated in the lake by the evaporative loss. A model

run with evaporation removed from the hydro-

dynamic model eliminated the evaporative con-

centration (Fig. 10).

Table 4 includes some literature values based

on mechanistic models of lake evaporation for a

geographic range that includes the study area.

The evaporation used in this model is an underes-

timate by at least 2.5 times compared to them.

James and Bierman (1995) estimated open water

rainfall as 80% of the land station gauges for theirmodel of Lake Okeechobee; the current model

used 100%. In combination these literature values

suggest the net evaporation used in this model

may be conservative. If so, the evaporative con-

centration effect may be more pronounced, and

significant, than the current results indicate.

Evaporation was left in the hydrodynamic

model for use with the water quality model. The

numbers used were empirical estimates of the net

monthly open water evaporation and rainfall

(Table 4). The effect is less important at theupriver extreme (maximum of 1% in junction 12

and 2% in junction 13 versus 6% in junction 23

and 10% in junction 41). This may reflect the

influence of residence time on the opportunity fo

evaporation to occur. The maximum evaporativ

effect may have little impact on lake water qualit

constituents. However, since the estimate use

here was at the low end of literature estimates, th

effect may be considerably greater than that ob

served in this model. Under any estimate, it likely the effect would only be significant in th

downstream portion of the lake.

6.3. Water 6elocity and settling rates

The model suggests the existence of longitud

nal velocity gradients in the lake (Fig. 11). This

often seen in reservoirs (Ford, 1990) and wa

observed in Lake Marion during a tracer stud

(Patterson and Harvey, 1995). Velocity gradien

can influence sedimentation of tributary particulate burden (Thornton, 1990); heavier particles a

lost first followed by lighter material as velocit

further reduces downstream. Settling also can be

significant loss to water column phytoplankto

and nutrient stocks (Kennedy and Walker, 1990

The water quality model component of th

WASP5 system includes settling flow specific

tions to account for loss and resuspension o

sediment, phytoplankton, and particulate nutrien

fractions. These values were determined by cal

bration using literature ranges as a guide (Fi12). In the upper- and mid-lake junctions (13 an

22) there is no settling during the period of max

mum velocity early in the year (Figs. 11 and 12

Fig. 11. Comparison of water velocities estimated by the

hydrodynamic model for three junctions (13, 22, and 41)

indicating the upstream-to-downstream gradient.

Fig. 12. Particle settling velocities for three junctions (13, 2

and 41). Rates were estimated by model calibration.


19/37


Fig. 13. Annual modeled velocity profile in junctions just upstream (17) and downstream (18, 20, and 22) from I-95.

Settling increases as velocity declines in midyear

before reducing again late in the year. Settling in

the lower lake is uniform throughout the year.

Water velocity is also much less than in upstream

portions of the lake. This result suggests a

threshold advection velocity, below which most

particulate material in the lake is capable of set-

tling out. However, it cannot be inferred from this

that all suspended sediment is removed from the

lake water by settling prior to outflow. Residence

time is a factor. In a study from 1983 to 1985, the

USGS reported a suspended sediment trap effi-

ciency of about 73% for Lake Marion (Cooney,

1988).Turbulence may be a factor in settling as well.

The model does not numerically account for pro-

cesses that reduce net sedimentation such as tur-

bulence and horizontal advection so rate estimates

must incorporate these effects. The upper portion

of the lake is relatively shallow with variable

bottom topography. This along with greater ve-

locity variability may increase turbulence. These

factors do not exist in the lower lake.

The I-95 bridge across the lake restricts open

flow to a single, main channel that is approxi-mately 47% of lake width at the southern end of

the bridge. This constriction appears to create a

velocity gradient (Fig. 13) with a significant in-

crease in the junction (18) immediately down-

stream from the bridge. The gradient is greatest in

magnitude during periods of high flows (compare

Figs. 9 and 13); the first 70 days of the year are

especially pronounced. It is uncertain what effec

this has although it may lead to enhanced particu

late settling upstream from the bridge and r

Fig. 14. High flow tracer simulation results. Peak tracer con

centration indicated by darkest shading.


20/37


Table 6

Hydraulic residence time estimates (days) for Lake Marion from the WASP5 model (shown are four hydrologic extremes and annu

mean)

Min. flow Min. volMax. flow Max vol. Annual mean

1519.3 1399.5Vol.106 m3 1495.4 1506.31555.8

365 n/a22691Day of year 66

177 522Outflow (m3 s1) 682 384501

176 410Inflow (m3 s1) 797 511 406

466177 395506Mean-flow (m3 s1) 739

Retention

99 35Whole lake 23 36 44

843 56168Jacks Creek 105

18 5Tawcaw Creek 4 5

9812041609Potato Creek 162

45Wyboo Swamp 32 46 141

duced residence times just below the bridge. The

early year period is also the time of greatest

sediment transport into the lake from the water-

shed (Patterson et al., 1996), so enhanced settling

may exacerbate basin filling in the upstream por-

tion of the lake. This inference seems to contra-

dict the discussion of calibrated settling flows,

immediately above. Both may apply to the results

observed if differing particle size fractions are

involved. The heaviest sediment particles may not

play a significant role in water column nutrient

dynamics but they are most likely to settle in the

upstream portion of the lake.

6.4. Hydraulic tra6el time

USGS conducted a tracer study in Lake Mar-

ion in 1984 (Patterson and Harvey, 1995). They

estimated tracer travel time through the lake (be-

ginning in the Wateree River upstream from the

Santee Swamp) during periods of high and low

inflow from the Congaree and Wateree Rivers.

For logistical reasons they divided the lake into

three sections; their lower two sections togethercorrespond to the lake as described for the current

research. As a comparison, a similar tracer slug

simulation was run with this model. Travel time

from the Rimini trestle to the Diversion Canal at

high flow (775 m3 s1) estimated by the model is

17 days (Fig. 14). USGS (810 m3 s1) estimated

13 days. The low flow (222 m3 s1) travel time for

the model is 53 days; for USGS (240 m3 s1) it

40 days. The differences are fairly small conside

ing the significant differences in method betwee

the two estimates. This result is a confirmation o

the volume calibration discussed above; the mod

appears to lag the lake in its hydrologic respons

The tracer result also provides evidence of lim

ited hydrologic exchange between the open lak

and the small tributary embayments (Fig. 14

also found by Patterson and Harvey (1995). Th

embayment toward the upstream end of the lak

receives less tracer and retains it well after th

peak tracer concentration has moved downstream. Similarly, the embayment just past th

middle of the lake retains tracer after the pea

concentration has moved past it. The embaymen

at the downstream end of the lake has not r

ceived any appreciable amount of tracer as th

peak concentration first reaches the diversio

canal.

6.5. Hydraulic residence time

Hydraulic residence time can influence reservomixing processes, nutrient availability, and phyto

plankton dynamics (Thornton, 1990). A short re

idence time (rapid flushing rate) can decrease th

opportunity for phytoplankton production. It ca

also result in additional nutrient import from th

watershed resulting in increased production afte

a temporal lag. If longitudinal zonation develop


21/37


Fig. 15. Segment 02 calibration charts. Monthly monitoring data (5-year mean91 S.E.) and monthly mean model results.

due, in part, to long residence times, it can be

reduced during periods of increasing flushing

rates.

Previous estimates of Lake Marion residence

time are variable. Inabinet (1985) estimated an

annual mean residence time of 31.1 days using a

mean outflow of 577 m3 s1 and volume of

1548.31106 m3. Patterson and Harvey (1995

as part of their tracer experiments, made tw

estimates of residence time, one each during hig

and low flow periods. Both used a lake volume o

1664.55106 m3. The estimate based on mea

inflow during the tests was 73 days at low flo

(266 m3 s1) and 23 days during high flow (82


22/37



m3 s1). Retention based on their actual tracer

results was 60 days at low flow and 20 days at

high flow.

With WASP5 a modeled estimate of lake vol-

ume and discharges are known at any interval.

Internally, WASP5 estimates retention time for

each segment using its current volume and mean

of segment inflow and outflow. Retention times a

the whole-lake scale were derived using tha

method (Table 6). Because of the extreme time

for the embayments their volume was not in

cluded in the whole lake estimates. Estimate

given are at principal hydrologic extremes and a

annual mean. Times range from 23 days at hig


23/37



flow during March to 99 days at low flow dur-

ing August. The annual mean is 44 days. Peri-

ods of high flow and low volume tend to

coincide resulting in rapid flushing in the cool

months. Discharge is high (and residence time is

low) even at maximum volume, however, indi-

cating the longest residence times occur only

during periods of very low flow. This result sug

gests that tributary discharge is a dominan

forcing function in Lake Marion. From the ea

lier discussion this effect is subject to modific

tion spatially and temporally, creating

heterogeneous hydrologic environment in th

reservoir.


24/37


Fig. 18. Incident light curve used in the water quality model and comparison of three estimates of saturating light intensity. See te

for discussion.

6.6. Water quality model calibration

The water quality model calibration demon-

strated the capability of the model to simulate the

spatial heterogeneity that occurs in the lake. (See

Table 1 for summary of reaction rates and coeffi-

cients.) Figs. 1517 are example calibration charfor segments 2 (upstream), 10 (mid-lake), and 3

(downstream), respectively. The model tracks Ch

a dynamics well in each segment even though th

annual pattern was different for all three. Th

model also simulates the annual cycle of the re

maining constituents well. Discrepancies are on

of two types: a divergent month or two occurs i

an otherwise close correspondence (NH3/4 in seg

ment 10, for example) or the model diverges i

magnitude but the annual pattern was general

correct (NO2/3 in segment 2, for example).Some discrepancies may reflect the existence o

a process in the lake that was not conceptualize

in the model. For example, DO simulation tend

to be very accurate. This probably indicates tha

DO dynamics are controlled more by water tem

perature and reaeration than by water colum

biochemistry. In segment 2, however, the mod

misses a significant dip in September. Fish kill

believed to be caused by DO exhaustion, we

recorded in that area of the lake at that time o

year during the study period (Bates and Marcu1990). The kills occurred after an extended dr

period followed by a heavy rain and flood surg

through the Santee Swamp. A large pulse o

reduced organic material entering the upper lak

from the swamp may have caused the DO dip.

The DO depression can be simulated with th

model by introducing a BOD5 load of 350

Fig. 19. Comparison of Chl-a results when using three differ-

ent estimates of saturating light intensity. The calibrated

model was used as the base. Shown are data for segment 2

(upper), segment 10 (middle), and segment 30 (lower).


25/37


day1 from the swamp into segment 2 during the

September interval. At the flow rate into segment

2 specified in the hydrodynamic model (mean

discharge of 34.41 m3 s1) this BOD5 load

corresponded to a concentration of 117.7 mg l1.

The mean concentration of BOD5 into the seg-

ment based on measured boundary conditionswas 1.4 mg l1. A simulation run in which the

inflowing water had no DO did not have an

observable effect on model results.

This BOD5 test result raised a question as to

whether or not a load from outside the lake could

have been the sole cause of the DO reduction

observed in the field data. Even assuming a flood

surge of 10-times the modeled swamp discharge

(an unrealistically high value) the field data for

BOD5 should approach 11.8 mg l1. Decaying

vegetation, carried as bed-load and undetected as

BOD5, may be a partial explanation for these

results. In-lake effects also seem likely. Senescence

of extensive macrophyte beds in the segment is

one possibility. That a large BOD5 flux had oc-

curred in the lake was suggested by the observa-

tion of BOD5 spikes during September in

segments 10 and 30 (Figs. 16 and 17).

Another possible source of discrepancies in the

calibrated model was that most of the biochemical

rates and constants have a single value for the

entire lake. This does not allow for possible eco-

logical differences among regions. Differencesmay result from physical characteristics such as

depth or water velocity, or biochemical character-

istics such as phytoplankton assemblages or ex-

tent of macrophyte coverage.

Phytoplankton, for example, adapt their physi-

ology to differing physical environments (Kirk,

1994) so even assuming community homogeneity

throughout the lake there still may be some varia-

tion based on adaptation. Inabinet (1978) found

evidence of longitudinal variability in species oc-

currence in the lake. The significance of his resultsare difficult to interpret because he only noted

presence or absence so relative densities cannot be

assessed. But this does suggest differences among

areas in the lake that may be reflected in the rates

and constants in a mechanistic model.

The hydrodynamic model suggests a cause for

the discrepancy in the phytoplankton results in

downstream segments 10 and 30 during Februar

Approximately 50% of the I95 crossing of th

lake is a built on a land bridge, resulting in

constriction. The constriction may cause poolin

upstream from the bridge and a significant in

crease in velocity just downstream from th

bridge. This increase may have a washout effect ithat area of the lake; the effect is greatest durin

the highest flows early in the year. If this effec

exists, as suggested by the hydrodynamic model,

would seem the water quality model should r

spond to it. A possible explanation is that th

actual velocity increase may be much greater i

the lake than in the model. This could be e

plained by the 10-day averaging of flows used t

parameterize the hydrodynamic model.

6.7. Phytoplankton kinetics

Phytoplankton production is dependent o

availability of nutrients and favorable environ

mental conditions, light and temperature (Fig. 7

The water quality model takes the supplied phyto

plankton maximum growth rate and modifies

with a temperature correction factor and light an

nutrient limitation factors Eq. (9).

Rg=GmaxFtF1Fn (9

where: Rg is the effective phytoplankton growt

rate, Gmax is the maximum growth rate, Ft is thtemperature correction factor, Fl is the light lim

tation factor and Fn is the nutrient limitatio

factor.

The nitrogen and phosphorus nutrient limit

tion factors are derived using the MichaelisMen

ton construct with half-saturation constan

supplied in the model input file. The mod

derives the light limitation factor as a function o

incident light, light extinction in the wat

column, water column depth, saturating light in

tensity, and the daylight fraction of the currenday. Temperature correction may range above o

below unity; the other three factors are all b

tween 0 and 1. The model selects the lowe

nutrient limitation factor for adjustment of th

growth rate. This reflects the empirical and labo

ratory observation that the growth rate is dete

mined by the availability of the nutrient i


26/37


Fig. 20. Annual curve showing sediment OPO4 flux determined by calibration. DO curve included to show inverse relationshi

Fig. 21. Annual curve showing sediment NH3/4 flux determined by calibration. DO curve included to show inverse relationshiRates for segment 16 are 1.5 times those indicated here.

shortest supply (Hecky and Kilham, 1988). The

phytoplankton growth rate for a given model day

was adjusted below maximum as a result of nutri-

ent or environmental limitations.

Kinetic rates and constants in models of differ-

ent aquatic systems vary due to physical and

biochemical differences among environments

(Bowie et al., 1985). If rates are not known for a

specific environment they are estimated duringmodel calibration. Recognition of the variability

in, and uncertainty of, key rates was the prime

motivating factor in a related project that evalu-

ated phytoplankton growth kinetics in situ (Su-

darshan, 1995). She estimated the phytoplankton

maximum growth rate, the temperature correction

factor, and the nitrogen and phosphorus half-sat-

uration constants using a nonlinear curve fittin

technique. The results of that work provided guid

ance within which calibration of other parameter

in the model proceeded. The final model was at o

within the 95% confidence interval of all ra

estimates developed by Sudarshan (1995).

The Sudarshan (1995) estimate of a linear rela

tionship for predicting saturating light intensit

from incident solar radiation was coded into thphytoplankton growth kinetics module. She foun

that the saturating intensity increases as inciden

radiation increases. Saturating intensity is a con

struct used to account for the field and laborator

observation that phytoplankton growth increase

with increasing light intensity up to a certain leve

Above that level light toxicity causes growth rat


27/37


Table 7

Mineralized nutrient loads in the calibrated model

Santee River Sediment ProportionAnnual load

(kg)

851 883 3 931 503 4.62N as NH3/40.785 018 103N as NH3/4 3 931 503

and NO2/3765 092 383 561P as OPO4 0.50

ences to Smith and DiToro during this discussio

refer to the WASP5 implementation.

The Sudarshan and Smith derivations of satu

rating intensity are similar during the growin

season but diverge during periods of low inciden

intensity (Fig. 18). The similarity between Smit

and Sudarshan was reflected in the resultingrowth (Fig. 19). Differences tend to be in th

months associated with low incident radiation (se

especially segment 30). This result suggests th

relationship developed by Sudarshan (1995) wa

more sensitive to the actual light environment i

Lake Marion, though this sensitivity did not ap

pear to have a significant impact on model result

The default fixed value for saturating intensit

was always greater than the derived intensity (Fi

18). The growth results for both Smith and Suda

shan are different from DiToro (Fig. 19). DiToris not fully comparable since the phytoplankto

kinetic is different in other respects in addition t

the saturating light intensity. However, the rela

tive absence of effect in segment 2 suggests th

upstream area is not as sensitive to the ligh

conditions as the downstream area.

6.8. Internal nutrient loading

Nutrient calibration required inclusion of ben

thic sources of both phosphorus (as OPO4) annitrogen (as NH3/4). Rates are comparable t

literature ranges (Ryding and Forsberg, 197

Thomann and Mueller, 1987) and increase durin

midyear (Figs. 20 and 21). The inverse relation

ship between benthic release rates and DO con

centration suggests higher sediment flux durin

periods of low DO and high temperature.

The relationship between temperature, low DO

and sediment nutrient release is much studied an

discussed in the literature. Aerobic sediment flu

has been reported by several researchers (Rydinand Forsberg, 1977; Premazzi and Provini, 198

Thomann and Mueller, 1987) although the flu

during anaerobic conditions is greater. Of thos

who report values for an annual cycle, relea

rates are higher during warm seasons (Baccin

1985; Recknagel et al., 1995). Lee et al. (1977

explicitly concluded that release appears affecte

reduction (Kirk, 1994). This effect is referred to as

photoinhibition. The critical light level is known

as the saturating light intensity.

The Sudarshan (1995) formulation replaced the

derivation already in the module. The Smith

(1980) derivation is a function of incident light,

temperature, light available in the water column,

and the phytoplankton carbon-to-chlorophyll ra-tio. It derives a time-integrated light limitation to

growth based on the varying amount of light

available in the water column during the day. An

alternate method in WASP5 is to use a fixed value

for saturating light intensity (default was 300 ly

day1) based on work by DiToro et al. (1971).

This method develops a light limitation factor as a

single instantaneous estimate for each day. (See

Ambrose et al., 1993a for a discussion of the

WASP5 implementation of these kinetics.). Refer-

Table 8

P-values for the KolmogorovSmirnov validation test

OPO4Segment NH3/4CHL-a NO2/3

0.541 0.0021 0.5410.006

0.541 0.1142 0.203 0.056

0.019 0.0100.5183 0.034

0.699 0.2064 0.0060.000

0.758 0.0015 0.010 0.001

0.518 0.2706 0.002 0.001

0.270 0.2708 0.964 0.627

0.699 0.0009 0.076 0.2060.441 0.03110 0.893 0.441

0.2700.08814 0.9640.270

0.001 0.13716 0.270 0.270

0.1640.015 0.001 0.00326

0.1640.015 0.164 0.05527

1.0000.0140.40128 0.329

0.015 0.7590.16429 0.401

1.0000.0820.32930 0.329


28/37


29/37


Fig. 23. Segment 02 validation charts. Field data (+) and model results.

are well described in the model, likely due to the

field work that estimated important rate values.

An alternative explanation is that phytoplankton

production is not sensitive to the difference in

nutrient loading values used in this validation.

Validation was especially weak in the upstream

segments (1,3,4,5). The explanation may be due,

in part, to the nutrient load into the lake (Fig.26). During the validation run the phosphorus

load was less and the nitrogen load was greater

than during calibration (Fig. 26 represents load

from the Santee River only). Differing nutrient

levels may have altered system primary produc-

tion and nutrient cycling. Downstream areas of

the lake are apparently under less direct riverine

influence.

Another view of this issue considers actual

lake hydrology in the calibration and validation

intervals. The hydrodynamic model used in bothcalibration and validation of the water quality

model was developed using hydrologic data from

1985 to 1990. The annual discharge of the Con-

garee and Wateree Rivers during the calibration

interval was 22% greater than during the valida-

tion interval (Fig. 27). So the nutrient loads dur-

ing the validation run (Fig. 26) are likely

overestimates of what actually occurred becau

the modeled discharge was greater than the mea

sured discharge during the interval. The use of

longer term discharge dataset in the hydrody

namic model would probably not solve th

problem; it may exacerbate it (Fig. 27). This ha

implications for future modeling studies of LakMarion. To obtain reasonable results it may b

necessary, depending on the modeling objective

to recalibrate the hydrodynamic model represen

ing the specific hydrologic conditions during th

model interval.

The validation results suggest hydrodynamic

and riverine nutrient loads are dominant forcin

functions in controlling nutrient status in Lak

Marion. This is especially significant in light o

the earlier discussion of the apparent importanc

of benthic sources of nutrients to lake productivity. Phytoplankton productivity was influence

by other factors as well; light and temperatur

based on results discussed earlier. A high degre

of spatial zonation was also suggested, confirm

ing results from the model calibration and othe

research in Lake Marion (Inabinet, 1985; Picke

and Harvey, 1988).


30/37



6.10. Sensiti6ity analysis

Altering nitrogen loading in the model suggests

that most of the lake has ample nitrogen for

phytoplankton growth (Fig. 28). Upper-lake (seg-

ment 2) growing season mean Chl-a concentra-tions are substantially attenuated by nitrogen

reduction, but at the other simulated levels the

entire lake was unaffected. The result for segment

2 may be due to the riverine nature of that

segment; nutrients are either used by phytoplank-

ton for growth or they are transported down-

stream. A reduction in any nutrient load reduces

the opportunity for photosynthetic assimilation

and growth.

The model exhibits greater sensitivity to alter-

ations in phosphorus loading than to nitrogenloading (Fig. 28). Again this is reflected more in

segment 2 than in either the mid- or lower-lake

segments (10 and 30, respectively). This result for

segment 2 tends to support the above observation

from the nitrogen loading test, and further sug-

gests phosphorus limitation in the upstream

segment.

The effect of decreasing both nutrients load

was not different from the phosphorus result, bu

increasing both had a cumulative effect. In up

stream segment 2, doubling phosphorus alone r

sulted in a 60% increase in growing season mea

Chl-a concentration; when both nutrients wedoubled the effect was an 80% increase. Th

incomplete utilization of the additional nutrien

load may result from relatively short residenc

times. Also that of the total boundary nutrien

loads, 60% of the nitrogen and 26% of the pho

phorus are in the immediately bioavailable mine

alized forms. The result in segments 10 and 3

(mid- and lower-lake) suggests colimitation t

phytoplankton growth by both nutrients.

The validation test discussed earlier raised th

question of whether or not the changed nutrienload could have produced a detectable differenc

in Chl-a concentration from the calibrated mode

Nitrogen loading during validation was propo

tionately 1.2 times greater than during calibration

phosphorus loading was 0.55 times the amount i

the calibrated model. According to the sensitivit

results (Fig. 28) a significant reduction in Chl


31/37



concentration would be expected, especially in

upstream segment 2. This was the situation (Fig.

29), suggesting that the model can be used to

project the effect of changing nutrient loads that

actually occur, or may occur, in the study area.

The second sensitivity analysis evaluated modelresults with respect to values of three kinetic rate

constants that are key to phytoplankton produc-

tion in the WASP5 model. A negative value of the

sensitivity index indicates the corresponding rate

constant value reduces growing season mean Chl-

a concentration relative to the calibrated model; a

positive value indicates an increase (Fig. 30).

(Note that conceptually the SI for the calibrated

model is zero, but arithmetically it is undefined;

see Eq. (8).) Results for the analysis of the nitro-

gen half-saturation constant are not presentedbecause variation from the calibrated model was

extremely small.

The three areas of the lake respond to the rate

changes in varying magnitudes. Segment 2 ex-

hibits the greatest range, further suggesting the

highly dynamic environment of this riverine sec-

tion of the lake. For all three segments and for

both rate constants, the value of the constant

water quality modelling in south carolina

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