EPA 600/R-??/???
December 2008
www.epa.gov
WASP8 Temperature
Model Theory and User's Guide
Supplement to Water Quality Analysis
Simulation Program (WASP) User
Documentation
Tim A. Wool
U.S. EPA, Region 4
Water Management Division
Atlanta, Georgia
Robert B. Ambrose, Jr., P.E.
U.S. EPA, Office of Research and Development
National Exposure Research Laboratory
Ecosystems Research Division
Athens, Georgia
James L. Martin, Ph.D., P.E.
Mississippi State University
Starkville, Mississippi
U.S. Environmental Protection Agency
Office of Research and Development
Washington, DC 20460
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WASP Temperature Module
User's Guide
NOTICE
The U. S. Environmental Protection Agency (EPA) through its Office of Research and Development
(ORD) funded and managed the research described herein. It has been subjected to the Agency's
peer and administrative review and has been approved for publication as an EPA document. Mention
of trade names or commercial products does not constitute endorsement or recommendation for use.
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WASP Temperature Module
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ABSTRACT
The standard WASP eutrophication and toxicant modules use water temperature to determine rates
of reactions that are influenced by temperature. In many cases there is not enough spatial and
temporal water temperature data to adequately parameterize a water quality model. The WASP
Temperature Module can be used to predict water column temperature based upon atmospheric
conditions and heat exchange between the surface, subsurface and benthic layers of the water body.
Furthermore, WASP has methods for transferring the predicted water temperatures to other WASP
sub models via a transfer interface file.
This supplemental user manual documents the temperature algorithms, including the kinetic
equations, the additional model input and output, and a series of model verification tests.
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WASP Temperature Module User's Guide
Table of Contents
1 Introduction 1
2 Model Theory 2
2.1 General Mass Balance Equation 2
2.2 Water Quality Kinetics 3
2.2.1 T emperature 3
3 Model Input 13
3.1 Model Parameters 13
3.2 Model Constants 15
3.3 Kinetic Time Functions 17
4 References 21
List of Figures
Figure 1 Segment Parameters for Temperature Module 13
Figure 3 Global Constants for the Temperature Module 15
Figure 4 Constants for Temperature Calculation 16
Figure 5 Constants for Fecal Coliform Calculation 17
Figure 6 Kinetic Time Functions for Temperature Module 18
List of Tables
in
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WASP Temperature Module User's Guide
Table 1 Description of Segment Parameters for Temperature Module 14
Table 2 Global Constants for Heat Module of WASP 15
Table 3 Temperature Kinetic Constants for Heat Module of WASP 17
Table 4 Fecal Coliform Kinetic Constants 17
Table 5 Environmental Time Functions for the Temperature Module 19
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WASP Temperature Module
User's Guide
1 Introduction
The Water Analysis Simulation Program (WASP, Ambrose et al 1993) is a dynamic compartment
modeling system that can be applied to a variety of water bodies. The flexibility afforded by WASP
is unique. WASP permits the modeler to structure one, two, and three dimensional models; allows
the specification of time-variable exchange coefficients, advective flows, waste loads and water
quality boundary conditions.
One of the other unique advantages to WASP is its modular structure which permits tailing
structuring of the kinetic processes, all within the larger modeling framework without having to
write or rewrite large sections of computer code. The two primary operational WASP models,
toxicants and eutrophication, are reasonably general and are intended to simulate two of the major
classes of water quality problems: conventional pollution (involving dissolved oxygen, biochemical
oxygen demand, nutrients and eutrophication) and toxic pollution (involving organic chemicals and
sediment). In addition, kinetic models have been developed for mercury (MERC4, Martin 1992) and
for simulation of metals in general (META4, Martin and Medine 1996).
With the release of WASP8 the capability of simulating water temperatures has been added to both
the toxicant and eutrophication module. Temperatures affect many of the kinetic rates in all versions
of WASP and are often important in their own right. WASP8 has been developed to allow the
dynamic simulation of processes affecting water temperatures, including surface heat exchange, ice
formation and breakup. The temperature routines are based upon those in the U.S. Army Corps of
Engineers CE-QUAL-W2 model (Hydraulics and Environmental Laboratories 1984, Cole and
Buchak 1994).
This manual is intended to describe the basic relationships used to predict variations in each of the
five state variables simulated by Heat Module as well as describe the model input requirements.
This manual is intended as supplement to the WASP manual (Ambrose et al 1993), and the reader is
referred to that manual for a more complete description of WASP model theory and input
requirements. In addition, the basic relationships used to predict temperature variations, as
described in the following section, were taken from Cole and Buchak (1995).
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WASP Temperature Module
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2 Model Theory
2.1 General Mass Balance Equation
The basic equations solved by all versions of WASP are those based upon laws of conservation.
The primary laws of conservation used in the development of water quality models include those for
energy, mass and momentum. For example, the hydrodynamic models DYNHYD and RIVMOD are
based upon conservation of momentum and water mass. Previous versions of WASP were based
upon the conservation of water and constituent mass. The Heat Module model is also based upon
conservation of water and constituent mass (for salinity, coliform bacteria, and the arbitrary
constituents), as well as the law of conservation of energy, for heat transfer. These laws form the
underlying principals of much of modern science and engineering as well as water quality modeling.
For all materials that act according to the laws of conservation, if some transformation or change
occurs, the total amount of the material present after the change or transformation must be identical
to that present before. For mass, in order to account for processes affecting the transformation the
balance equation must account for material entering and leaving through direct and diffuse loading;
advective and dispersive transport; and physical, chemical, and biological transformations. For a
coordinate system where the x- and y-coordinates are in the horizontal plane and the z-coordinate is
in the vertical plane, the mass balance equation around an infinitesimally small fluid volume is:
+Sl+Sb+S
K
where:
Ux,Uy,Uz
Ex,Ey,Ez
Sl
Sb
C
t
concentration of the water quality constituent, mg/L or g/m3
time, days
longitudinal, lateral, and vertical advective velocities, m/day
longitudinal, lateral, and vertical diffusion coefficients, m2/day
direct and diffuse loading rate, g/m3-day
boundary loading rate (including upstream, downstream, benthic, and
atmospheric), g/m3-day
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WASP Temperature Module
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Sk = total kinetic transformation rate; positive is source, negative is sink,
g/m3-day
The mass balance equation as written above is based upon constituent concentrations, which refers
to the mass of that dissolved or suspended in a given volume of water. Similarly, temperature may
be considered a measure of the amount of heat energy contained in a volume of water, and the
relationship between heat energy and temperature is given by:
H = V(p„CrT)=VC,
where H is the heat content, Cp the specific heat of water (at a given pressure) and T the
temperature, where the quantity in parenthesis may be considered the "concentration" of heat (Ch).
Replacing the constituent concentration with the heat concentration in the above equation results in
the heat balance equation, which is solved by Heat Module for water temperatures.
By expanding the infinitesimally small control volumes into larger adjoining "segments," and by
specifying proper transport, loading, and transformation parameters, WASP implements a
finite-difference form of equation (. The basic equation is applied to a set of expanded control
volumes, or "segments," that together represent the physical configuration of the water body. The
network may subdivide the water body laterally and vertically as well as longitudinally. Benthic
segments can be included along with water column segments. If the water quality model is being
linked to the hydrodynamic model, then water column segments must correspond to the
hydrodynamic junctions. Concentrations of water quality constituents and temperatures are
calculated within each segment. Transport rates of water quality constituents are calculated across
the interface of adjoining segments.
2.2 Water Quality Kinetics
The balance relationship described in the previous section is solved by WASP for all state variables.
The basic relationship is the same regardless of the state variable. Differences occur between
WASP submodels in the number of state variables and the in the processes which are included in the
total kinetic transformation rate (Sk) for each state variable. All versions of WASP share the same
main program, which computes all terms except for Sk. That term is computed in a separate module
(WASPB) which is specific to the submodel (EUTRO, TOXI).
2.2.1 Temperature
The processes included in the total transformation rates for temperature include surface and bottom
heat exchange. Surface heat exchange is calculated by either a full heat balance or of through use of
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WASP Temperature Module
User's Guide
equilibrium temperatures and coefficients of surface heat exchange (Brady andEdinger, 1975). The
surface heat budget is described below and is taken from Cole and Buchak (1994).
2.2.1.1 Surface Heat Exchange
The source and sink term for heat includes loadings from external sources, such as thermal
discharges, as well as heat exchange across the air-water interface. The sources and sinks term for
water temperature due to surface heat exchange may be written as
dVT H „ A,
dt lxCkange OCr,
where V is volume (m3), As is surface area (m2), T is temperature (°C), t is time, p the density of
water (997 Kg m"3 at 25 °C), Cp is its specific heat (4179 J Kg"1 °C_1 at 25°C), and Hn (Watts m"2) is
the net thermal energy flux. The net thermal energy flux includes the effects of a number of
processes. The net thermal energy flux (Hn, Watts m"2), may be expressed as
Term-by-term surface heat exchange is computed as:
Hn = Hs + Ha + He + He " ( Hsr + Har + Hbr )
where
Hn = the net rate of heat exchange across the water surface, Wnf2
Hs = incident short wave solar radiation, W m-2
Ha = incident long wave radiation, Wnf2
Hsr = reflected short wave solar radiation, Wnf 2
Har = reflected long wave radiation, Wnf 2
Hbr = back radiation from the water surface, Wnf 2
He = evaporative heat loss, Wm~2
He = heat conduction, Wm~2
In Heat Module, the surface heat exchange processes depending on water surface temperatures are
computed using previous time step data and are therefore lagged from transport processes by the
model time step. The short wave solar radiation (Hs) is either measured directly or computed from
sun angle relationships and cloud cover. The long wave atmospheric radiation is computed from air
temperature and cloud cover or air vapor pressure using Brunts formula.
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WASP Temperature Module
User's Guide
Water surface back radiation is computed from:
Hbr = ^(Ts+ 273.15)4
Where
8 = emissivity of water, 0.97
g* = Stephan-Boltzman constant, 5.67 x 10~8 Wm~2 EK~4
Ts = water surface temperature, EC
Evaporative heat loss is computed as:
He = f(W) (e, - ea)
where
f(W) = evaporative wind speed function, Wm~2 mm Hg'1
es = saturation vapor pressure at the water surface, mm Hg
ea = atmospheric vapor pressure, mm Hg
Evaporative heat loss depends on air temperature and dew point temperature or relative humidity.
Surface vapor pressure is computed from the surface temperature for each surface segment.
Surface heat conduction is computed as:
Hc = Cc W (Ts - Ta)
where
Cc = Bowen's coefficient, 0.47 mm Hg EC1
Ta = air temperature, EC
Short wave solar radiation penetrates the surface and decays exponentially with depth according to
Bears Law:
Hs (z) = (1 - P) Hs e"72
Where
Hs(z) = short wave radiation at depth z, Wm~2
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WASP Temperature Module User's Guide
P = fraction absorbed at the water surface
r| = extinction coefficient, m1
Hs = short wave radiation reaching the surface, Wm~2
In the equilibrium temperature approach, a temperature is computed at which the net surface
exchange is equal to zero. The linearization of the net heat balance and this definition of the
equilibrium temperature allows the net rate of surface heat exchange, Hn, to be expressed as:
Hn = ~ Kaw (Tw " Te)
where
Hn = rate of surface heat exchange, W m"2
Kaw = coefficient of surface heat exchange, Wm~2 EC'1
Tw = water surface temperature, EC
Te = equilibrium temperature, EC
Seven separate heat exchange processes are summarized in the coefficient of surface heat exchange
and equilibrium temperature. The linearization used in obtaining equation ( has been examined in
detail by Brady, et al. (1968), and Edinger et al. (1974).
2.2.1.2 Sediment Heat Exchange
Sediment heat exchange with water is generally small compared to surface heat exchange and has
often been neglected. However, investigations on several reservoirs have shown the process must be
included to accurately reproduce hypolimnetic temperatures primarily because of the reduction in
numerical diffusion (Cole and Buchak 1994). The formulation used to compute bottom heat transfer
is similar to that used in the equilibrium temperature approach for surface exchange:
Hsw "Ksw (Tw _ Ts)
Where:
Hsw = rate of sediment/water heat exchange, W m"2
Ksw = coefficient of sediment/water heat exchange, Wnf 2 EC'1
Tw = water temperature, EC
Ts = sediment temperature, EC
Cole and Buchak (1994) indicated that values of 7 x 10"8 W m"2 EC"1 for Ksw have been used in
previous applications and that average yearly air temperature is a good estimate of Ts.
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WASP Temperature Module User's Guide
2.2.1.3 Ice Cover
Ice formation can affect the heat balance, mixing characteristics, and water quality in lakes and
reservoirs. For example, once a lake freezes over, sensible heat losses and evaporation nearly cease
and net radiation is strongly outward, resulting in more or less steady ice growth during early winter
months (Lerman 1978). In addition, other processes which are often negligible during ice-free
periods, such as heat flux from the bottom, become important in the heat cycle. Ice essentially
shields the lake against wind mixing and retards light penetration, depending upon the thickness of
the ice and snow cover. Surface reaeration is also retarded during periods of ice cover and in many
shallow eutrophic lakes anoxic conditions often occur following long periods of ice and snow cover
and may result in winter fish kills.
Ice cover is described to the eutrophication submodel of WASP. Heat Module computes ice cover,
based on relationships included in the CE-QUAL-W2 model (Cole and Buchak 1994). The ice
model is based on an ice cover with ice-to-air heat exchange, conduction through the ice, conduction
between underlying water, and a "melt temperature" layer on the ice bottom (Cole and Buchak 1994,
Ashton, 1979). The overall heat balance for the water-to-ice-to-air system is:
Ah . . . .
A Lf (Ti-Te)-hwi (Tw-Tm)
where
pi = density of ice, kg m3
Lf = latent heat of fusion of ice, J kg1
Ah/At = change in ice thickness (h) with time (t), m sec1
hai = coefficient of ice-to-air heat exchange, Wnf 2 EC'1
hwi = coefficient of water-to-ice heat exchange through the melt layer, Wm2 EC'1
Ti = ice temperature, EC
Tei = equilibrium temperature of ice-to-air heat exchange, EC
Tw = water temperature below ice, EC
Tm = melt temperature, OEC
The ice-to-air coefficient of surface heat exchange, hai, and its equilibrium temperature, Tei, are
computed the same as for surface heat exchange in Edinger, et al. (1974) because heatbalance of the
thin, ice surface water layer is the same as the net rate of surface heat exchange presented previ-
ously. The coefficient of water-to-ice exchange, hwi, depends on turbulence and water movement
under ice and their effect on melt layer thickness. It is a function of water velocity for rivers but
must be empirically adjusted for reservoirs.
Ice temperature in the ice-heat balance is computed by equating the rate of surface heat transfer
between ice and air to the rate of heat conduction through ice:
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WASP Temperature Module
User's Guide
1 (T T A — -ki(Ti - Tin)
hai (Ti- TeiJ :
h
where
ki = molecular heat conductivity of ice, W m'1 EC'1
When solved for ice temperature, Ti, and inserted in the overall ice-heat balance, the ice thickness
relationship becomes:
ALf Ah_(TM - Tei )
At
h 1
+
ki hia
hwi (Tw " Tm )
from which ice thickness can be computed for each longitudinal segment. Heat from water to ice
transferred by the last term is removed in the water temperature transport computations.
Variations in the onset of ice cover and seasonal growth and melt over the waterbody depend on
locations and temperatures of inflows and outflows, evaporative wind variations over the ice surface,
nd effects of water movement on the ice-to-water exchange coefficient. Ice will often form in
reservoir branches before forming in the main pool and remain longer due to these effects.
A second, more detailed algorithm for computing ice growth and decay has been developed for CE-
QUAL-W2 (Cole and Buchak 1994) and is include in Heat Module. The algorithm consists of a
series of one-dimensional, quasi steady-state, thermodynamic calculations for each time step. It is
similar to those of Maykut and Untersteiner (1971), Wake (1977) and Patterson and Hamblin (1988).
The detailed algorithm provides a more accurate representation of the upper part of the ice
temperature profile resulting in a more accurate calculation of ice surface temperature and rate of ice
freezing and melting.
The ice surface temperature, Ts, is iteratively computed at each time step using the upper boundary
condition as follows. Assuming linear thermal gradients and using finite difference approximations,
heat fluxes through the ice, qi, and at the ice-water interface, qiw, are computed. Ice thickness at
time t, 9(t), is determined by ice melt at the air-ice interface, A9ai, and ice growth and melt at the
ice-water interface, A9iw. The computational sequence of ice cover is presented below.
Initial ice formation. Formation of ice requires lowering the surface water temperature to the
freezing point by normal surface heat exchange processes. With further heat removal, ice begins to
form on the water surface. This is indicated by a negative water surface temperature. The negative
water surface temperature is then converted to equivalent ice thickness and equivalent heat is added
to the heat source and sink term for water. The computation is done once for each segment
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WASP Temperature Module
User's Guide
beginning with the ice-free period:
„ _-Tw„PwCPwh
C70
A Lf
where
CPw
Pi
Lf
h
pw
90
thickness of initial ice formation during a time step, m
local temporary negative water temperature, EC
layer thickness, m
density of water, kg m3
specific heat of water, J kg1 EC'1
density of ice, kg m
latent heat of fusion, J kg1
.-3
Upper air-ice interface flux boundary condition and ice surface temperature approximation: The ice
surface temperature, Ts, must be known to calculate the heat components, Hbr, He, He, and the ther-
mal gradient in the ice since the components and gradient all are either explicitly or implicitly a
function of Ts. Except during the active thawing season when ice surface temperature is constant at
0 EC, Ts must be computed at each time step using the upper boundary condition. The approximate
value for Ts is obtained by linearizing the ice thickness across the time step and solving for Ts.
dt
where
Ki
Tf
n
thermal conductivity of ice, Wm1 EC'1
freezing point temperature, EC
time level
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WASP Temperature Module
User's Guide
Absorbed solar radiation by the water under the ice. Although the amount of penetrated solar
radiation is relatively small, it is an important component of the heat budget since it is the only heat
source to the water column when ice is present and may contribute significantly to ice melting at the
ice-water interface. The amount of solar radiation absorbed by water under the ice cover may be
expressed as:
HpS = Hs (1-ALBi) (l-A) e"/,e(t)
where
Hps = solar radiation absorbed by water under ice cover, Wm~2
Hs = incident solar radiation, Wm~2
ALB; = ice albedo
Pi = fraction of the incoming solar radiation absorbed in the ice surface
yi = ice extinction coefficient, m'1
Ice melt at the air-ice interface. The solution for Ts holds as long as net surface heat exchange,
Hn(Ts), remains negative corresponding to surface cooling, and surface melting cannot occur. If
Hn(Ts) becomes positive corresponding to a net gain of heat at the surface, qi must become negative
and an equilibrium solution can only exist if Ts > Tf. This situation is not possible as melting will
occur at the surface before equilibrium is reached (Patterson and Hamblin, 1988). As a result of
quasi-steady approximation, heat, which in reality is used to melt ice at the surface, is stored
internally producing an unrealistic temperature profile. Stored energy is used for melting at each
time step and since total energy input is the same, net error is small. Stored energy used for melting
ice is expressed as:
A CP,^ 0(t) = ALf A0ai
where
Cpi = specific heat of ice, J kg1 EC'1
Gal = ice melt at the air-ice interface, m1
Formulation of lower ice-water interface flux boundary condition. Both ice growth and melt may
occur at the ice-water interface. The interface temperature, Tf, is fixed by the water properties. Flux
of heat in the ice at the interface therefore depends on Tf and the surface temperature Ts through the
heat flux qi. Independently, heat flux from the water to ice, qiw, depends only on conditions beneath
the ice. An imbalance between these fluxes provides a mechanism for freezing or melting. Thus,
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WASP Temperature Module User's Guide
_ T d6>lw
q, - qiw " A Lf
where
9iw = ice growth/melt at the ice-water interface
The coefficient of water-to-ice exchange, Kwi, depends on turbulence and water movement under
the ice and their effect on melt layer thickness. It is known to be a function of water velocity for
rivers and streams but must be empirically adjusted for reservoirs. The heat flux at the ice-water
interface is:
qiw = h™ ( Tw(t)-Tf )
where
Tw = water temperature in the uppermost layer under the ice, EC
Finally, ice growth or melt at the ice-water interface is:
A0L = -
A Lf
Ki 1 " h™ (Tw-Tf)
e
2.2.1.4 Density
Water densities are affected by variations in temperature and solids concentrations given by :
p = pT + A ps
where
P
pT =
ApS =
density, kgm3
water density as a function of temperature, kg m3
density increment due to solids, kg m3
A variety of formulations have been proposed to describe water density variations due to
temperatures. The following relationship is used in Heat Module (Cole and Buchak 1994,Gill,
1982):
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WASP Temperature Module User's Guide
pJw = 999.8452594 + 6.793952x 10"2 Tw
-9.095290xl0"3Tw + 1 001685xl0"4Tw
-1.120083 xlO"6 Tt + 6.536332 xlO"9xT^
The affect of dissolved solids, expressed as either salinity or total dissolved solids, on density is
also included. Density effects due to TDS is given by Ford and Johnson (1983):
APtd s = (8.221 x 10"4 - 3.87 x 10"6 T w + 4.99 x 10"8 Tw) Otos
where
OTDS = TDS concentration, gm~3
and for salinity (Gill, 1982):
Apsal = (0.824493 - 4.0899xl0"3 Tw + 7.6438xl0"5 T«
- 8.2467 x 10"7 T3w + 5.3 875 x 10"9 Tt) Osai
+ (-5.72466 x 10"3 +1.0227 x 10"4 Tw
-1.6546xl0"6 Tl,) Osd + 4.8314x10~4Osai
where
Osal = salinity, kgm
-3
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WASP Temperature Module
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3 Model Input
The data required to support the application of a model of the thermal module include initial
conditions (segment parameters, environmental time functions and kinetic constants. Each
of these is briefly described in the sections below.
3.1 Model Parameters
Parameters are spatially-variable characteristics of the water body. The definition of the
parameters will vary, depending upon the structure and kinetics of the systems comprising
each model. The input format, however, is constant. The number of parameters that is
specified must be input for each segment. Figure 1 and illustrate where the user would
define and enable segment specific parameters. If a segment parameter is not defined by the
user, it is considered to be inactive.
Parameter Data
Parameter
System
Used
Scale Factor
lHarpeth River
LSPC203PERO
3HarpethRiver
4JonesCreek
1
Temperature of Segment [|C or Multiplier]
None
a
1.0000
1.0000
1.0000
1.0000
2
Solar Radiation Multiplier [unitless or watts/m2]
None
HI
1.0000
1.0000
1.0000
1.0000
3
Solar Radiation Time Function [1-4]
None
H
1.0000
1.0000
1.0000
1.0000
4
Light Extinction for Segment [per meter or multiplier]
None
IB
1.0000
1.0000
1.0000
1.0000
5
Air Temperature of Segment [°C or Multiplier]
None
0
1.0000
1.0000
1.0000
1.0000
6
Pointer to Air Temperature Time Function
None
El
1.0000
1.0000
1.0000
1.0000
7
Wind Speed Multiplier [unitless or m/sec]
None
0
1.0000
1.0000
1.0000
1.0000
8
Pointer to Wind Speed Time Function
None
m
1.0000
1.0000
1.0000
1.0000
9
Cloud Cover Multiplier [unitless or fraction]
None
m
1.0000
1.0000
1.0000
1.0000
10
Pointer to Cloud Cover Time Function
None
m
1.0000
1.0000
1.0000
1.0000
11
Dew Point Temperature Multiplier [unitless or °C]
WTEMP
m
1.0000
1.0000
1.0000
1.0000
12
Pointer to Dew Point Time Function
WTEMP
m
1.0000
1.0000
1.0000
1.0000
13
Multiplier for Shading Coefficient [unitless or fraction]
None
a
0.0000
0.0000
0.0000
0.0000
14
Pointer to Shading Time Function
None
B
0.0000
0.0000
0.0000
0.0000
15
Wind Sheltering Coefficient Multiplier [unitless or fraction]
WTEMP
B
0.0000
0.0000
0.0000
0.0000
16
Pointer to Wind Sheltering Time Function
WTEMP
m
0.0000
0.0000
0.0000
0.0000
17
Water Velocity [m/sec or Multiplier]
None
B
0.0000
0.0000
0.0000
0.0000
18
Ice Cover [Fraction Cover or Multiplier]
None
B
0.0000
0.0000
0.0000
0.0000
19
Sediment Cobble Concentration [mg/L]
None
B
0.0000
0.0000
0.0000
0.0000
20
Zooplankton Population
PHYTO
H
0.0000
0.0000
0.0000
0.0000
4 1 1 ~
Copy | [ Paste
II
Fill/Calc
11 «
II
Cancel
Figure 1 Segment Parameters for Temperature Module
Not only does the used have to define the segment specific parameters, the user must enable
the parameter and adjust the scale factor if need be.
Table 1 provides a detailed description of the segment parameters that are available for the
heat module.
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WASP Temperature Module
User's Guide
Table 1 Description of Segment Parameters for Temperature Module
Name
Description
Pointer to Cloud Cover Time
Function
Flag designating the time-variable cloud cover function to be used for
the segment. The four cloud cover time functions are defined by the user
in the Environmental Time Function Data Entry Screen
Cloud Cover Multiplier (unitless
or fraction)
Segment clouds cover multiplier. Cloud Cover varies over space and
can be either actual cloud cover (as a percent of clear sky) or a
normalized function, depending on the way the user defines the time
function.
Pointer to Wind Speed Time
Function
Flag designating the time-variable wind speed function to be used for the
segment. The four wind speed functions are defined the Environmental
Time Function Data Entry Screen.
Wind Speed Multiplier (unitless
or m/sec)
Segment wind speed multiplier. Wind speed varies over space and can be
either wind speed (m/sec) or a normalized function, depending on the
way the user defines the time function.
Pointer to Air Temperature Time
Function
Flag designating the time-variable air temperature function to be used
for the segment. The air temperature functions are defined the
Environmental Time Function Data Entry Screen.
Air Temperature Multiplier
(unitless or °C)
Segment air temperature multiplier. Air Temperature varies over space
and can be either air temperature (°C) or a normalized function,
depending on the way the user defines the time function.
Pointer to Dew Point Time
Function
Flag designating the time-variable dew point temperature function to be
used for the segment. The dew point temperature functions are defined
the Environmental Time Function Data Entry Screen.
Dew Point Temperature
Multiplier (unitless or °C)
Segment dew point temperature multiplier. Segment Dew Point Multiplier
varies over space and can be either the dew point temperature (°C) or a
normalized function, depending on the way the user defines the time
function.
Wind Sheltering Coefficient
Multiplier (unitless or fraction)
Segment wind sheltering coefficient multiplier (a fraction, from 0 to 1).
The wind sheltering coefficient varies over space and can be either an
actual sheltering coefficient or a normalizedfunction, depending on the
definition.
Pointer to Wind Sheltering Time
Function
Pointer designating the time variable wind sheltering coefficient to be
used for segment. This coefficient is used to adjust the effects of the
wind. Its physical basis is that surrounding terrain often shelters the
waterbody so that observed winds taken from meteorological stations are
not the effective winds reaching the waterbody. Since prevailing wind
direction and vegetative cover vary with time, the user has the option to
vary the wind sheltering coefficient with time as well as space. The four
sheltering coefficients time functions available are defined in the
Environmental Time Function Data Entry Screen.
Light Extinction Coefficient
Multiplier (unitless or 1/m)
Segment extinction coefficient multiplier (m'1). Light Extinction varies
over space and can be either an actual extinction coefficient or a
normalized function, depending on the definition.
14
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WASP Temperature Module
User's Guide
3.2
Model Constants
The definition of the constants will vary, depending upon which state variables you elect to
use in the temperature module. The kinetic constants screen in the WASP interface breaks
the available constants down into three separate constant groups.
Listed below are the three constant groups with a description of each kinetic constant.
Figure 2 illustrates the kinetic constant data entry screen for global constants. To switch
between the constant groups, chose using the drop down picklist. Note the user is specifies
the values for the constants, but also needs to check the "Used" radio button. Failing to
check this box will keep the interface for sending this information to the model.
H Constants
Constant Group
Global Constants
Constant System
1 Fresh water = 0, Marine Water = 1 None
2 Latitude, degrees None
3 Longitude, degrees None
Used
a
m
IS
i
35.993
-87.003
Copy | | Paste | | Fill/Calc | | Use Defaults |
Figure 2 Global Constants for the Temperature Module
Table 2 provides a list of the kinetic constants for the global constants group.
Table 2 Global Constants for Heat Module of WASP
Constant
Waterbody type (1= fresh water, 2=salt water)
Heat exchange option (l=fuU heat balance,
15
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WASP Temperature Module
User's Guide
2=equilibrium temperature)
3
Ice Switch (0 = no ice solution, l=ice solution,
2=detailed ice solution)
4
Fraction of solar radiation absorbed in the ice surface
5
Latitude, degrees (Used of the Solar Radiation
Generator)
6
Longitude, degrees (Used of the Solar Radiation
Generator)
7
Julian Day at Start of Simulation (Used of the Solar
Radiation Generator)
Figure 3 illustrates the kinetic constants for the temperature prediction module. Note the
user is specifying the values for the constants, but also needs to check the "Used" radio
button. Failing to check this box will keep the interface for sending this information to the
model.
.$! U5EPA WASP - Ej/States/TennesseB^Harpeth/Models/WASP/Harpeth.wif q II B | !3
- t m *.«:¦= ** ^ £ v A" J- o *
Constants | a ^ I
Constant Group
Constant
System
Used
Value
Default
Minimum
1 Heat exchange option (0=full heat balance, l=equilibrium temperature)
WTEMP
D
0
0
0
2 Coefficient of bottom heat exchange. Watts m-2 "C-l
WTEMP
m
0.4
0.4
0
3 Sediment (ground) temperature, °C
WTEMP
m
27
10
0
4 Ice switch (0 = no ice solution, l=ice solution, 2=detailed ice solution)
WTEMP
H
0
0
0
5 Temperature above which ice formation is not allowed, °C
WTEMP
e
1
1
0
6 Minimum ice thickness before ice formation is allowed, meters
WTEMP
H
0.005
0.005
0
7 Initial ice thickness, meters
WTEMP
E
0
0
0
8 Coefficient of water-ice heat exchange, Watts m-2 CC-1
WTEMP
n
0
10
0
* | w
~
[ Copy | ( Paste | | Fill/Calc | [ Use Defaults ]
[ Cancel [
Figure 3 Constants for Temperature Calculation
The kinetic constants that are defined by the user to predict water temperature are presented
16
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WASP Temperature Module
User's Guide
in Table 3.
Table 3 Temperature Kinetic Constants for Heat Module of WASP
Constant
1
Observed solar radiation time function multiplier
2
Coefficient of bottom heat exchange, Watts m-2 °C-1
3
Sediment (ground) temperature, °C
4
Initial ice thickness, meters
5
Ratio of reflection to incident radiation (albedo of ice)
6
Coefficient of water-ice heat exchange
7
Fraction of solar radiation absorbed in the ice surface
8
Solar radiation extinction coefficient for ice
9
Minimum ice thickness before ice formation is allowed, meters
10
Temperature above which ice formation is not allowed, °C
3.3
3.3 Kinetic Time Functions
The definition of the kinetic time functions will vary depending upon the structure and the
kinetics of the systems comprising each model. Listed below are the 21 time functions
available in Heat Module. All of the time functions operate in conjunction with a parameter
"pointer" in segment parameter definition (Section 3.1). Figure 4 illustrates the
environmental time function user entry screen for WASP. Note the user selects which time
functions will be considered and must check the "used" radio button for the information to
be passed to the model. For each time function being defined the user must provide a time
series of data ().
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WASP Temperature Module
User's Guide
4 Time Functions
WJE
Time Function
Used
Interpolation
Data Source
PCOOE
Station ID
Plot
9
1
Velocity Function (rrv'sec)
CI
linear
None
Moment/value pairs for Solar
adiation -1 (VI
fraction Daily light (fraction)
Linear
None
500-
¦ .
Water Temperature Function (*C)
13
linear
None
Solar Radiation • 1 (W/m2)
IB
Linear
¦ SOLAR RAO
1087X304.TN403280.TN40328
Solar Radiation - 2 (W/m2)
Linear
None
Solar Radiation-3 (W/m2)
Lmear
None
Solar Radiation - 4 (W/m2)
Air 7 emperature Function 1CC)
Air Temperature Function 2 (-C)
E
Lmear
None
Weather
None
AIR TEMP
Y087X304_TW403280_TNW328
Air Temperature Function 3 ("Q
linear
None
Air Temperature Function 4 CQ
None
Wind Speed Function 1 (rn/wc)
Wtnd Speed function 2 (m/sec)
Wind Speed Function 3 (m/'sec)
IS
H
L-
None
None
WIND SPIED
WB7X304.TN403280.TNW328
9
I
1
-
1
I
n
Linear
None
Rackabon - 1 C»V/hi2)
!»-
Datetone Value *
s
200 -
100 -
1/1/199314)0 AM
1 a.'1999 2.00 AM
67.396
54 AH
LI
LI/1999 3.00 AM
67396
1/1/199? 4 SO AM
1/1/1999 500 AM
80.178
1/1/1999 64)0 AM
1/1/1999 74)0 AM
8 1/1/1999 BOO AM
94J22
80.178
134.792
9 1/1/1999 900 AM
60.173
10 1/1/199910:00 AM
11 1/1/199911430 AM
12 1/1/199912.-OOPM
60.173
106504
13 1-1/199914# PM
94122
0-
I OK
Date
1 C—'
rf H « <
> » X ^ a
Figure 4 Kinetic Time Functions for Temperature Module
Brief descriptions of the environmental time functions are given in .
18
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WASP Temperature Module
User's Guide
Table 4 Environmental Time Functions for the Temperature Module
Environmental Time Functions
1
Time-variable cloud cover function (1). Cloud Cover can be either a normalized
function or an cloud cover (percent), depending upon the definition of the segment
parameter multiplier
2
Time-variable cloud cover function (2), unitless or percent
3
Time-variable cloud cover function (3), unitless or percent
4
Time-variable cloud cover function (4), unitless or percent
5
Time-variable wind-speed function (1). Wind Speed can be either a normalized
function or an actual wind speed (m sec-1), depending upon the definition of the
segment parameter multiplier.
6
Time-variable wind speed function (2), unitless or m sec-1.
7
Time-variable wind speed function (3), unitless or m sec-1.
8
Time-variable wind speed function (4), unitless or m sec-1.
9
Time variable air temperature function (1). Air Temperature can be either a
normalized function or an air temperature, depending upon the definition of the
segment parameter multiplier.
10
Time-variable air temperature function (2), unitless or EC.
11
Time-variable air temperature function (3), unitless or EC.
12
Time-variable air temperature function (4), unitless or EC.
13
Time-variable dew point temperature function (1). Dew Point Temperature can be
either a normalized function or a dew point temperature, depending upon the
definition of the segment parameter multiplier.
14
Time-variable dew point temperature function (2), unitless or EC.
15
Time-variable dew point temperature function (3), unitless or EC.
16
Time-variable dew point temperature function (4), unitless or EC.
17
Time-variable extinction coefficient function (1). Light Extinction can be either a
normalized function or an actual extinction coefficient in nr1, depending upon the
definition of the segment parameter multiplier.
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WASP Temperature Module
User's Guide
18
Time-variable extinction coefficient function (2), unitlcss or m '.
19
Time-variable extinction coefficient function (3), unitlcss or m '.
20
Time-variable extinction coefficient function (4), unitlcss or m '.
21
Time-variable wind sheltering coefficient function. The Wind Sheltering Coefficient
can be either a normalized function or an actual sheltering coefficient (0 to 1),
depending upon the definition of the segment parameter multiplier.
4
20
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WASP Temperature Module
User's Guide
4 References
Ambrose, B, Jr., P.E., T. A. Wool, and J.L. Martin, "The Water Quality Analysis Simulation
Program, WASP5. Part B: the WASP5 Input Dataset, Version 5.00," U.S.
Environmental Protection Agency, Center for Exposure Assessment Modeling,
Athens, GA, May, 1993.
Ambrose, B, Jr., P.E., T. A. Wool, and J.L. Martin, "The Water Quality Analysis Simulation
Program, WASP5; Part A: Model Documentation," U.S. Environmental Protection
Agency, Center for Exposure Assessment Modeling, Athens, GA, June, 1993.
Ashton, G.D. 1979. "Suppression of River Ice by Thermal Effluents", CRRELRpt. 79-30,
US Army Engineer Cold Regions Research and Engineering Laboratory, Hanover,
NH.
Brady, D.K., Graves, W.L., and Geyer, J.C. 1969. "Surface Heat Exchange at Power Plant
Cooling Lakes", Cooling Water 2, Discharge Project No. 5, Publication No. 69-901,
Edison Electric Institute, New York, NY.
Cole, T.M. and E.M. Buchak. 1994. ACE-QUAL-W2: A Two-Dimensional, Laterally
Averaged, Hydrodynamic and Water Quality Model, Version 2.0, User Manual,®
Draft Instruction Report, Station, Vicksburg, MS
Edinger, J.E., Brady, D.K., and Geyer, J.C. 1974. "Heat Exchange and Transport in the
Environment", Rpt. No. 14, EPRI Publication No. 74-049-00-34, prepared for
Electric Power Research Institute, Cooling Water Discharge Research Project
(RP-49), Palo Alto, CA.
Ford, D.E., and Johnson, M.C. 1983. "An Assessment of Reservoir Density Currents and
Inflow Processes", Technical Rpt. E-83-7, US Army Engineer Waterways
Experiment Station, Vicksburg, MS.
Gill, A.E. 1982. "Appendix 3, Properties of Seawater", Atmosphere-Ocean Dynamics,
Academic Press, New York, NY, pp 599-600.
Martin,J.L. "MERC4, A Mercury Transport and Kinetics Model, Beat Test Version 1.0:
Model Theory and User's Guide," Prepared for the U.S. Environmental Protection
Agency, Center for Exposure Assessment Modeling, Athens, GA, July 1992.
Martin, J.L. and A. J. Medine. AA Dynamic model of Metal Speciation and Transport in
Surface Waters (META4): Model Description,® Draft manuscript, AScI
Corporation, Athens, GA.
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WASP Temperature Module
User's Guide
Maykut, G. N. and N. Untersteiner. 1971. "Some results from a time dependent,
thermodynamic model of sea ice", J. Geophys. Res., 83: 1550-1575.
Patterson, J.C. and Hamblin, P.F., "Thermal Simulation of a Lake with Winter Ice Cover",
Limnology and Oceanography, 33(3), 1988, P. 323-338.
Wake, A. 1977. "Development of a Thermodynamic Simulation Model for the Ice Regime
of Lake Erie", Ph.D. thesis, SUNY at Buffalo, Buffalo, NY.
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