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A Review of Public Domain Water Quality Models for Simulating Dissolved Oxygen in Rivers and Streams

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A Review of Public Domain Water Quality Modelsfor Simulating Dissolved Oxygen in Rivers and Streams
Prakash R. Kannel
&
Sushil R. Kanel
&
Seockheon Lee
&
Young-Soo Lee
&
Thian Y. Gan
Received: 26 May 2006 /Accepted: 14 July 2010 /Published online: 31 July 2010
#
Springer Science+Business Media B.V. 2010
Abstract
The review discusses six major public domainwater quality models currently available for rivers andstreams. These major models, which differ greatly in termsof processes they represent, data inputs requirements,assumptions, modeling capability, their strengths and weak-nesses, could yield useful results if appropriately selected for the desired purposes. The public domain models, which aremost suitable for simulating dissolved oxygen along riversand streams, chosen in this review are simulation catchment (SIMCAT), temporal overall model for catchments (TOM-CAT), QUAL2Kw, QUAL2EU, water quality analysis simu-lation program (WASP7), and quality simulation along rivers(QUASAR). Each of these models is described based on aconsistent set of criteria-conceptualization, processes, input data, model capability, limitations, model strengths, and itsapplication. The results revealed that SIMCATand TOMCATare over-simplistic but usefultoquicklyassessimpactofpoint sources.TheQUAL2Kwhasprovisionforconversionofalgaldeath to carbonaceous biochemical oxygen demand (CBOD)and thus more appropriate than QUAL2EU, where macro- phytes play an important interaction. The extensive require-mentofdatainWASP7andQUASARisdifficulttojustifythetime and costs required to set up these complex models. Thus,asinglemodelcouldnotserveallwiderangeoffunctionalitiesrequired. The choice of a model depends upon availability of time, financial cost and a specific application. This reviewmay help to choose appropriate model for a particular water quality problem.
Keywords
Water quality models.Dissolved oxygen.SIMCAT.TOMCAT.QUAL2Kw.QUAL2EU.WASP7.QUASAR
1 Introduction
Mathematical model is described in different ways. Theencyclopedia of life support system described a model as anapproximate description of a class of real-world objects and phenomena expressed by mathematical symbolisms [1].
Concise Oxford Dictionary (1990) described a model as asimplified form of a system that assists calculations and predictions of a condition of a system in a given situation.The USEPA [2] described water quality models as tools for simulating the movement of precipitation and pollutants fromthe ground surface through pipe and channel networks,storage treatment units and finally to receiving waters. Chapra[3] described a mathematical model as an idealized formula-
tion that represents the response of a physical system to
P. R. Kannel (
*
)
:
T. Y. GanDepartment of Civil and Environmental Engineering,University of Alberta,Edmonton, AB T6G2W2, Canadae-mail: prakash.kannel@gmail.comP. R. KannelDepartment of Irrigation, Ministry of Irrigation,Kathmandu 44600, NepalS. R. KanelPegasus Technical Services, Inc.,46 E. Hollister Street,Cincinnati, OH 45219, USAS. LeeWater Environment & Remediation Research Centre,Korea Institute of Science and Technology,Seoul 130-650, South KoreaY.-S. LeeDepartment of Environmental Engineering,Kwangwoon University,Seoul 139-701, South KoreaEnviron Model Assess (2011) 16:183
–
204DOI 10.1007/s10666-010-9235-1
external stimuli. Similarly, Cox [4] described a water-quality
model means anything from a simple empirical relationship,through a set of mass balance equations, to a complexsoftware suite in which a user can simulate water quality instreams and rivers by supplying physical and chemical data.Dissolved oxygen (DO) is essential for survival of aquaticlife. The impacts of low dissolved oxygen concentrationsresult in an unbalanced ecosystem with fish mortality, odorsand aesthetic nuisances [4]. In river systems, the targeted
water quality can be achieved through a water qualitymanagement strategy, which involves the assessment of impacts of pollutants on the dissolved oxygen concentrationalong the river systems. Quantitative techniques started to beused to assess the impacts of pollutants on the river systemsin 1925 when Streeter and Phelps developed a model for simulating DO in the river systems.Withtheadvancementincomputertechnologyintwentiethand twenty-first centuries, there have been a number of significant developments in the field of water qualitymodeling that have resulted in a variety of models. There arenowmanywaterqualitymodelsbecauseofcontinuousstudiesand construction of new models for specific situations arisingaround the world [4]. However, a choice of a simulation
model should be based on a compromise between feasibilityand desirability [5]. In this paper, we have reviewed six most
widely used and freely available water quality models(simulation catchment, SIMCAT; temporal overall modelfor catchments, TOMCAT; QUAL2Kw; QUAL2EU; water quality analysis simulation program, WASP7; and qualitysimulation along rivers, QUASAR) for simulating dissolvedoxygen concentrations along the river systems and examinedtheir respective potential for use in applications.
2 Model Review
The selected six water quality models SIMCAT, TOMCAT,QUAL2Kw, QUAL2EU, WASP7, and QUASAR arereviewed with a consistent set of criteria: conceptualization, processes, input data, model capability, limitations, modelstrengths, and its application.2.1 SIMCATThe SIMCAT is a stochastic, one dimensional (1D), steadystate and deterministic model. SIMCAT was developed byAnglian Water [6], one of the leading providers of water andwastewater services in the United Kingdom (UK). It has been widely used in UK for over 20 years and is recognizedas being a cost-effective, practical water quality management tool. It describes the quality of river water throughout acatchment by Monte Carlo simulation approach to predict the behavior of the summary statistics of flow and water quality, such as mean and a range of percentiles [7]. An
extensive review of SIMCAT is available at Cox [4].
2.1.1 Conceptualization
In SIMCAT, the river system being modeled is divided intouser-defined reaches into any length, generally taken to be thedistance between tributaries or other points of interest. Themodelcanrepresentmorethanoneinfluenceinanyonereach.A diffuse runoff can be specified as a flow rate and quality.The model represents the river reaches as a continually stirredtank reactors in series (CSTRS) model. The model does not use an advection
–
dispersion transport equation, but assumes perfect and instantaneous mixing throughout the reach, withsolutes moving at the same velocity as the water. A mass balance is performed at the top of each reach. The flow andsolute mass-balances for a reach are:
Q
0
¼
Q
i
þ
Q
t
þ
Q
e
Q
a
ð
1
Þ
and
C
0
Q
0
¼
C
i
Q
i
þ
C
t
Q
t
þ
C
e
Q
e
C
i
Q
a
Δ
C
;
ð
2
Þ
where
Q
is the flow,
C
is the concentration of the determinant and the subscripts
o
,
i
,
t
,
e
and
a
refer to the reach outflow, theupstream input, tributary inputs, effluent discharges, andabstractions, respectively. Internal transformations such as physical, chemical or biological processes are represented bythe term
Δ
C
. An empirical velocity
–
flow relationship (
V
=
aQ
b
, where
V
is the velocity,
Q
is the flow rate and
a
,
b
areconstants) is used to derive the velocity of the water in a reach.The calculated velocity is used to compute the residence time.
2.1.2 Processes
The solute concentrations are subjected to first-order decays tocalculate the concentrations of the determinants that will enter thenextreach.Thedeterminantsbeingmodeledmaybetreatedeither conservatively or as having first-order decay, and themodel includes chloride (conservative), biochemical oxygendemand (BOD; first order), ammonium (first order). Chemicalfate and advective transport in SIMCAT is described by:
dC dt
¼
kC
;
dt
¼
dxv
and
C
x
¼
C
0
e
k
:
xv
;
ð
3
Þ
where
C
is the concentration,
k
is the rate of decayconstant,
x
is the distance, and
v
is the velocity. In the caseof DO modeling, the atmospheric re-aeration is includedand the method of Elmore and Hayes [8] is used toestimate the DO saturation concentration as expressed bythe equations,
dC dt
¼
k
r
L
þ
k
a
C
s
C
ð Þ ð
4
Þ
184 P.R. Kannel et al.
and
C
S
¼
14
:
652
0
:
41022
T
þ
0
:
0079910
T
2
0
:
000077774
T
3
;
ð
5
Þ
where
C
is the DO concentration,
C
s
is the saturationconcentration,
L
is the BOD,
k
r
is the rate of removal of BOD,
k
a
is the re-aeration rate coefficient, and
T
is thetemperature in degrees Celsius.
2.1.3 Input Data
Flow and quality data are entered at the top of the main river.All tributaries, effluent discharges and abstraction in thesystem are assigned to the appropriate reaches. As the modelisastochasticandusestheMonteCarlomethod;theinputsarenotsinglevalues,butdescriptionsofthe statisticaldistributionfor that determinant. The model accepts distribution descrip-tions as annual means and standard deviations, from proba- bility distributions such as Constant (or Uniform), Normal,Lognormal, 3-Parameter lognormal, Pearson and Log-Pearson Type III Distributions, and others.
2.1.4 Model Capability
The SIMCATcan be used to model up to 600 reaches and upto 1400 features such as rivers, discharges, abstractions,diffuse pollution, and weirs. The model can be run in four different ways: The first technique uses the data as provided bythe userand isused for manualcalibration;the second usesauto-calibration algorithms to check the flow and quality; thethird sets effluent quality in order to achieve required river water quality objectives; and the fourth sets effluent standardsthatwouldpermitnodeteriorationinwater quality.Themodelcan be run for auto-calibration. For using the auto-calibration,the model feeds in extra flows as a function of the river lengthuntil the simulated flows match those observed in the river at flow gauges. It then calculates a series of adjustments to thequality parameters in order to match simulated and observedwater quality. The model produces summary statistics (meansand 90th or 95th percentiles) for each determinant for eachreach.The model estimates the confidencelimitsofthe resultsassuming that the distributions are normal or lognormal. Themodel simulates: biochemical oxygen demand, dissolvedoxygen, ammonia, and user defined parameters. The modelcan be used to simulate other conservative or first order decay parameters.
2.1.5 Limitations of Model
The approach of modeling used in SIMCAT is over-simplistic though it is quick. It is limited by the fact that there is no allowance for temporal variability and noaccounting of photosynthesis, respiration, sediment oxygendemand, and variation of re-aeration rate with flow. Thus, it is unlikely that the DO model will produce satisfactoryresults for productive rivers. However, it is suitable for modeling determinants in freshwater that do not rely onsediment interactions. It provides the user with annualstatistics and the model can quickly run the effects of changes in effluent discharge conditions.
2.1.6 Strengths and its Application
The SIMCAT is likely the best used among existingavailable models and often requires limited data. It isreadily applied at a catchment scale. It is used as a routinetool by trained non-specialist staff and it allows rapidassessment of management options [7]. It was used for
integrated water quality and environmental cost-benefit modeling for the management of the river Tame in UK [9] and for integrated catchment planning study for the four river catchments (Ehen, Kent, Derwent, and Eden) in the North West of England [7].2.2 TOMCATThe TOMCAT was developed by the UK water utilitycompany, Thames Water, in the early 1980s [10] to assist in
the process of reviewing effluent quality standards at allThames Water sites in order to meet river-water qualityobjectives. An extensive review of TOMCAT is available at Cox [4].
2.2.1 Conceptualization
The conceptualization for TOMCAT is identical to that inSIMCAT, i.e., a steady state CSTRS model, and the modeltake a Monte Carlo stochastic approach. However, TOMCATallows for more complex temporal correlations.
2.2.2 Processes
Theprocessequationsdescribingtheconcentrationsofsolutesare identical to SIMCAT, except for those used to simulate thetemperature and DO. The river temperature (
T
) is assumed totend towards the air temperature (
T
air
). The DO modelincorporates nitrification, atmospheric re-aeration and theoxidation of BOD as described by equations,
dT dt
¼
K
T
T
T
air
ð Þ ð
6
Þ
and
dC dt
¼
C
s
C
ð Þ
K
a
dLdt
4
:
57
d
NH
4
½
dt
;
ð
7
Þ
Public Domain Water Quality Models 185
where
K
T
is the first-order rate coefficient,
C
is theconcentration of DO,
K
a
is the re-aeration rate coefficient,
C
s
is the saturation concentration of DO,
L
is the BODconcentration and [NH
4
] is the ammonium concentration.The re-aeration rate coefficient is determined from a
‘
user-supplied
’
re-aeration parameter (
K
u
), the river width (
W
) andthe cross-sectional flow area of the channel (
A
) i.e.:
K
a
=
K
U
×
W
/
A
. Temperature dependency is included as a linear increase in
K
a
with increase in temperature.
2.2.3 Input Data
Input data required are two types to run TOMCAT. The first is fixed values, generally physical parameters; the second isthe flow and quality data. The flow and quality data aregiven as means and standard deviations of a normaldistribution or of logged data, percentage points on anonparametric distribution, or as single values. Boundaryconditions of flow and quality are supplied as single or seasonal distributions at events, and a number of reach parameters are supplied for each user-defined reach. Theseinclude: reach length, mean cross-sectional area, depth,catchment number for estimating the (diffuse) catchment runoff, scale factor for runoff (i.e., the proportion of thetotal runoff for the catchment which the reach receives per kilometer), ultimate BOD concentration, BOD decay rate parameter, ultimate ammonium concentration, ammoniumdecay rate parameter, oxygen exchange rate parameter,thermal equilibrium rate constant. The observed data areincluded for the purpose of calibration in the form of seasonal distributions. Unfortunately, this means that themodel cannot be used in a predictive framework in terms of flow, although this is not what the model was designed for.
2.2.4 Model Capability
The TOMCAT can be used for simulating the current conditions of flow and water-quality in the catchment, but the model can also be used to assess the requirements for making improvements to the quality of water in thecatchment. This model provides the user with monthlyand annual statistics. The model can quickly run the effectsof changes in effluent discharge conditions. It is also able tosimulate the action of storm water overflows by
‘
diverting
’
effluent discharges to an alternative outlet if the flows riseabove a certain threshold.
2.2.5 Limitations of Model
The TOMCAT model has limited functionality in terms of the processes included but the use of seasonal statistics doesallow for potentially greater accuracy than could beachieved in the similar SIMCAT model. The model allowsthe user to obtain the results of each model run so that statistical analyses may be carried out using techniques that are not built in to the model. However, the model is lessaccurate than SIMCAT in the way it simulates the flowvelocity as it relies solely on the cross-sectional area of theriver. The TOMCAT is suitable for modeling determinantsin freshwater that do not rely on sediment interactions andwhere the simple processes are a reasonable approximation.The photosynthesis, respirations are not included in thismodel.
2.2.6 Strengths and its Application
The process representation is more simplistic than QUA-L2E, and is less data intensive. The use of seasonalstatistics does allow for potentially greater accuracy thancould be achieved in the similar SIMCAT model. Wherelittle data is available, TOMCAT is a more appropriatemodel for modeling down-the-drain chemicals at a catch-ment scale than QUAL2E [11]. The model was used in
modeling orthophosphate concentrations in the river Thames [12].
2.3 QUAL2EUThe QUAL2EU [13], enhanced stream water quality model
with uncertainty analysis, is a United States EnvironmentalProtection Agency (USEPA) model for conventional pollu-tants in branching streams and well-mixed lakes. It was first released in 1985 and the USEPA has used and improved thismodel extensively since then [4]. The QUAL2E is the result
of a historical development of oxygen (O), nitrogen (N) and phosphorus (P) models [14]. The starting point was the
pioneer Streeter
–
Phelps model [15] describing the DO and
BOD relationship. It was later extended to simulate thespatial and temporal variations in water temperature andconservative mineral concentrations in addition to BOD andDO concentrations resulting to the model QUAL1. Finally,the phosphorus cycling, nitrogen cycling, algae and manyother variables were added in creating the QUAL2 modelfamily [16]. Extensive use of QUAL2 had uncovereddifficulties that required correction in the algal-nutrient-light interactions. With incorporating a number of modifications,the enhanced version of QUAL2 was renamed QUAL2E.The QUAL2E was further enhanced and was calledQUAL2EU. The QUAL2EU compiles the best features of the available QUAL2E version on which was added theuncertainty analysis option [13]. This 1D steady state model
(which can also be run as dynamic model) is a very helpfulwater quality management tool. It can be used to study theimpact of waste loads on in-stream water quality. It also can be used to identify the magnitude and quality characteristicsof non-point waste loads as part of a field-sampling program.
186 P.R. Kannel et al.
It allows users to perform uncertainty analysis:sensitivityanalysis, first-order error analysis, and Monte Carlo simula-tion. A complete theory and documentation of QUAL2E/ QUAL2EU is available at Brown and Barnwell [13].
2.3.1 Conceptualization
The basic equation used to describe the behavior of a pollutant in the river is one dimensional conservativeadvection-dispersion equation. Its assumptions are: sol-utes are completely mixed across the cross section,advective transport is within the mean flow and disper-sive transport is proportional to concentration gradient.Most determinants are simulated as first-order decays but DO, nitrate, phosphate and algae are represented in moredetail. The model does include sediment processes, but only as a sink for substances or as a source of oxygendemand. Coliforms are modeled as non-conservativeconstituent. A simple first-order decay function is used,which only take into account coliform die-off. These andnon-conservative constituent are modeled as first order decay depending upon temperature.The conceptual representation of a stream used in theQUAL2EU is a stream reach that has been divided into anumber of sub-reaches (computational element) equivalentsto finite difference elements. For each computationalelement, a hydrologic balance in terms of flow, a heat balance in terms of temperature, and a materials balance interms of concentration is written. Both advective anddispersive transports are considered in the materials balance. The model uses a finite-difference solution of themass transport and reaction equations and it specificallyuses a special steady-state implementation of an implicit backward difference numerical scheme, which gives themodel an unconditional stability [17]. In each compartment,
the model computes the major interactions between up to15 state variables. The basic equation used in QUAL2EU todescribe the behavior of a pollutant in the river is one-dimensional conservative advection-dispersion equation(Eq. 8),
@
C
@
t
¼
@
A
x
D
L
@
C
@
x
A
x
@
x
@
A
x
UC
ð Þ
A
x
@
x
þ
dC dt
þ
Δ
S
;
ð
8
Þ
where
C
is the concentration of the determinant,
A
x
is thecross-sectional area,
D
L
is the dispersion coefficient,
x
isthe distance along the element,
U
is the mean velocity,
t
isthe time and
Δ
S
is the net concentration influence of external sources and sinks. The transformations occurringto individual determinants independent of advection,dispersion and external inputs are defined by the term
dC/dt
and these changes include physical, chemical and biological processes that occur in the stream.
2.3.2 Processes
Most determinants are simulated as first-order decays but DO, nitrate, and phosphate are represented in more detailand there is also an algal model as described by Fig. 1.Algae use chlorophyll-a as the indicator of algal biomass.The accumulation of biomass is calculated as a balance between growth, respiration, and settling of the algae. Themaximum growth rate is modeled as being light andnutrient limited. The algal model consists of growth by photosynthesis, respiration and the settling of algae onto thesediments of the riverbed, i.e.:
dAdt
¼
m
A
r
A
s
1
D A
;
ð
9
Þ
where
A
is the algal biomass concentration,
t
is the time,
μ
isthe algal growth rate,
ρ
is the respiration rate,
σ
1
is the settlingrate, and
D
is the depth. Ultimate carbonaceous biochemicaloxygen demand (CBOD
u
) is modeled as a first-order degradation process in QUAL2EU [18], which also takesinto account additional removal by settling and does not affect the oxygen balance as,
dLdt
¼
K
1
L
K
3
L
;
ð
10
Þ
Fig. 1
Schematic diagram of interacting water quality state variablesin QUAL2EU (
ORG-N
organic nitrogen,
ORG-P
organic phospho-rous,
DIS-P
dissolved inorganic phosphorous,
CBOD
carbonaceous biochemical oxygen demand,
SOD
sediment oxygen demand,
NH
3
ammonia,
NO
3
nitrate,
NO
2
nitrite,
Chla
chlorophyll
a
) [13]
Public Domain Water Quality Models 187

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