The distribution of water quality variables in space and time
is computed by solving the one-dimensional advection-dispersion
equation in which non-conservative constituent relationships
are considered to be governed, in general, by first order rates
(see equations on page 3-5).
The processes of chemical and biochemical transformations, including
interaction among various parameters as represented in the model
are shown in Figure 3.1 at the
end of this chapter. These constituents include dissolved oxygen,
carbonaceous BOD, phytoplankton, organic nitrogen, ammonia nitrogen,
nitrite nitrogen, nitrate nitrogen, organic phosphorus, dissolved
phosphorus, TDS, and temperature. The conceptual and functional
descriptions of the constituent reactions are based generally
on QUAL2E (Brown and Barnwell 1987); although in certain instances
they were updated based on the work of Bowie et al., (1985).
Mass balance equations are written for all quality constituents
in each parcel of water (see equations
on page 3-5). The reader is referred to Jobson and Scoellhamer
(1987) for a description of the Lagrangian formulation which
provides the basic framework for DSM2-Qual.
In applying the water quality model, changes in concentration
due to advection and dispersion, including changes due to tributaries
or agricultural drainage are first computed. Next, concentrations
of each constituent in each parcel of water are updated, accounting
for decay, growth, and biochemical transformations. New subroutines
developed for modeling non-conservative constituents are structured
in modular form to facilitate extension for simulation of additional
constituents (in the case that such needs arise in the future).
Subroutine KINETICS updates constituent concentrations at each
time step. A single or any combination of the eleven water quality
variables can be modeled to suit the needs of the user. KINETICS
is called by the parcel tracking subroutine of DSM2-QUAL for
every parcel at each time step. The model has also been extended
to simulate kinetic interactions in reservoirs (extended open
water bodies encountered in the Delta).
Subroutine CALSCSK builds a source/sink matrix within KINETICS
for each non-conservative constituent simulated. For simulation
of temperature, a subroutine that computes net transfer of energy
at the air-water interface has been adapted from the QUAL2E model
with some modification. Required meteorology data (obtained preferably
at hourly intervals) include dry bulb and wet bulb atmospheric
temperatures, wind speed, atmospheric pressure, and cloudiness.
Physical, chemical, and biological rate coefficients required
for KINETICS are read as input. Some of these coefficients are
constant throughout the system; some vary by location; and most
are temperature-dependent. A list of these coefficients and sample
values is provided in chapter 5.
The numerical scheme for updating kinetic interactions was
developed considering properties of Lagrangian box models that
are most accurate when time steps are small enough to define
the dominant temporal variations in flow and concentration. A
relatively simple scheme that takes advantage of small time stepsthe
Modified Euler methodis used to update concentrations.
Concentration updating is done at least once in every time step,
and more often if the parcel in question has passed a grid point
before the current time step is fully accounted for. In the latter
case, the reaction time step will be the increment of time remaining
to be accounted forless than the simulation time step
(typically 15 minutes). Consequently, reaction time steps remain
small, so the Modified Euler scheme for concentration updating
is appropriate. Since changes in concentration of any constituent
affect the other constituents, tests are included in DSM2-Qual
to check whether corrections to constituent concentrations are
The ability of the model to simulate the dissolved oxygen
sag on a reach of the San Joaquin River near Stockton was recently
demonstrated. DSM2-Qual was capable of capturing diurnal variations
of important constituents such as dissolved oxygen, phytoplankton,
temperature, and nutrients under the unsteady conditions of the
estuary. Variations were realistic, although lack of a large
temporal variation in observed data was somewhat of an impediment
to testing the model's full capacity to predict field conditions.
Tests of the model's capability to distinguish between alternatives
in terms of incremental changes in water quality were encouraging
(Rajbhandari 1995). The model has great potential for use as
a practical tool for analysis of the impacts of water management
To enhance the predictive capability of the model, sensitivity
analysis should be performed to determine the relative influence
of rate coefficients on model response. Calibrated values of
the rate coefficients which are most sensitive should be refined.
Also, subject to a consistent expansion of the database, future
extensions in the model to add additional variables (such as
zooplankton) are likely to result in improvement in model performance.
Extension of model to represent sediment transport capability
should also be investigated such that a dynamic interaction of
sediments with simulated constituents is possible. Other uses
of the model would be in providing the spatial and temporal distributions
of water quality variables for the Particle Tracking Model, so
that aquatic species can be more accurately modeled.
Bowie, G. L., Mills, W. B., Porcella, D. B., Campbell, C.
L., Pagenkopt, J. R., Rupp, G. L., Johnson, K. M., Chan, P. W.
H., and Gherini, S. A. (1985). Rates, Constants and Kinetics
Formulations in Surface Water Quality Modeling. 2nd Ed.,
US EPA, Athens, Georgia, EPA 600/3-85/040.
Brown, L. C., and Barnwell, T. O. (1987). The Enhanced
Stream Water Quality Models QUAL2E and QUAL2E-UNCAS: Documentation
and Users Manual. US EPA, Athens, Georgia, EPA 600/3-87/007.
Jobson, H. E., and Schoellhamer, D. H. (1987). Users Manual
for a Branched Lagrangian Transport Model. U.S. Geological
Survey, Water Resources Investigation Report 87-4163.
O'Connor, D. J. and Dobbins, W. E. (1956). Mechanism of
Reaeration in Natural Streams.
J. Sanitary Engrg. Div., ASCE, 82(6), 1-30.
Orlob, G. T. and N. Marjanovic (1989) Heat Exchange. Ch.
5 in Mathematical Submodels in Water Quality Systems, ed.
S.E. Jorgensen and M.J. Gromiec, Elsevier Pub.
Rajbhandari, H. L. (1995). Dynamic Simulation of Water
Quality in Surface Water Systems Utilizing a Lagrangian Reference
Frame. PhD Dissertation, Univ. of California, Davis, Calif.
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