Surface-water quality and flow Modeling Interest Group
Comparing Physics-Based and Neural Network Models for Simulating Salinity,
Temperature, and Dissolved Oxygen in a Complex, Tidally Affected River
Basin
by Paul A. Conrads1
and Edwin A. Roehl Jr.2
1Hydrologist
USGS, Water Resources Division
Stephenson Center, Suite 129
720 Gracern Road
Columbia, SC 29210-7651
Internet: pconrads@usgs.gov
Phone: (803) 750-6140
FAX: (803) 750-6181 |
2Vice President - Systems Development
OptiQuest Technologies, LLC
214 Pelham Davis Circle
Greenville, SC 29615
Internet: info@oqt.com
Phone: (864) 987-0717
FAX: (864) 234-7521 |
Editor's note:
This paper was written for the 1999 South Carolina Environmental Conference,
held in Myrtle Beach on March 15-16, 1999.
Citation:
Conrads, P.A. and Roehl, E.A., 1999, Comparing physics-based and neural
network models for simulating salinity, temperature, and dissolved-oxygen
in a complex, tidally affected river basin, in Proceedings of the
1999 South Carolina Environmental Conference, March 15-16, 1999, Myrtle Beach,
SC.
Contents
The U.S. Geological Survey participated in an evaluation of using neural
networks for modeling estuarine systems, and selected physics-based, dynamic
one-dimensional flow and water-quality models of the Cooper and Wando Rivers
for comparison. The results showed that the neural network models were more
accurate at simulating salinity, temperature, and dissolved oxygen of this
very complex estuarine system than physics-based models. They were also far
less costly to develop and can be easily integrated into commercial software,
such as spreadsheets, and real-time data acquisition and control systems.
However, the physics-based models may provide a better understanding of the
system's behavior and provide a better methodology for extrapolating to
environmental conditions that are not manifest in the historical data.
Beginning in 1992, the U.S. Geological Survey (USGS), in cooperation with
State agencies, initiated a study to apply the one-dimensional dynamic flow
model BRANCH (Schaffranek and others, 1981) and the dynamic mass transport
and water-quality model Branched Lagrangian Transport Model (BLTM) (Jobson
and Schoelhamer, 1987) to the Cooper and Wando Rivers (Conrads and Smith,
1996, 1997). As part of the study (Conrads and others, 1997), the real-time
gaging program for the Cooper River was expanded to include the Wando River
(fig. 1). Additional gages were also added for the Cooper River. The water
properties that were measured included water level, temperature, specific
conductance (used to calculate salinity), and dissolved-oxygen
concentration. Data from each station were collected at 15-minute intervals
and transmitted via satellite communication to a database at the USGS
District Office in Columbia, SC. The applied models were implementations of
existing finite-difference computer codes that were calibrated and validated
to match the flow, transport, and water-quality characteristics of the Cooper
and Wando Rivers.
Figure 1. Study Area.
In early 1997, the USGS participated in an evaluation of using neural
networks for modeling environmental systems. Unlike the finite-difference
models, which are based on the principles of physics and chemistry (referred
to as physics-based models), neural network models are inspired by the
learning behavior of animals and humans (Jensen, 1994). The type of neural
network model used in this study employs a set of mathematical relations with
adjustable coefficients to map a set of input variables into a set of output
variables. In a process called "training," neural networks implement a
"learning algorithm" that, for a given data set, iteratively searches for
coefficient values that provide a good generalized mapping of inputs to
outputs.
This paper compares the results of the BRANCH/BLTM modeling effort, in which
salinity transport, temperature, and dissolved-oxygen concentration were
simulated, to a subsequent application of neural networks. Other aspects of
the modeling approaches, such as time to apply the model, costs, and
deployment options, are also discussed.
The Cooper River is formed by the confluence of the West and East Branches of
the Cooper River at an area referred to as the "Tee" (fig. 1). The freshwater
inflows to the West Branch are controlled by the releases from Pinopolis Dam
on Lake Moultrie. The area above the Tee is characterized by meandering
natural channels bordered by extensive tidal marshes and old rice fields in
varying states of disrepair. Downstream of the Tee, industries are located
along the west bank of the river. The east bank is dominated by extensive
Spartina alterniflora salt marshes and contains numerous
dredge-material disposal areas. Saltwater in the Cooper River extends from
the Harbor upstream to several miles below the Tee. The Wando River is a
tidal slough that tapers from a width of about 0.5 mile at its mouth to a
narrow tidal creek 21 miles upstream from the confluence with the Cooper
River. Saltwater extends throughout the Wando River. The banks of the river
are dominated by extensive Spartina alterniflora salt marshes. The
Cooper and Wando Rivers are tidally affected throughout their entire reach,
and have a spring-tidal range of approximately 6 feet at their lower
reaches.
Similar procedures were used for both modeling techniques. Data from
"boundary stations," gaging stations located at the external boundaries of
the study area (stations 021720011, 02172037, 02172040, 02172066, 021720694,
021720695, and 021720710), were inputs to the models. Data from "internal
stations," gaging stations that were represented as internal nodes on the
finite-difference grid of the physics-based models (stations 02172019,
02172050, 02172053, 021720675, 021720696, and 021720698), were the model
outputs. The models computed hydraulic properties and water-quality
constituent values for internal stations that were then compared with
measured values.
Modeling was completed in two phases. The first phase calibrated and
validated the unsteady-flow model (BRANCH) and the branched Lagrangian
transport model (BLTM) to simulate the movement of a conservative constituent
(salinity) in the system. The scope of the second phase was to calibrate and
validate the water-quality model (BLTM) to simulate the fate and transport of
non-conservative constituents, such as nutrients, biochemical oxygen demand
(BOD), and dissolved oxygen.
Several types of data were required to apply, calibrate, and validate the
transport and water-quality models. A large data-collection effort was
completed during 1992-95 (Conrads and others, 1997). The data included:
- continuous water level, specific conductance, temperature, and
dissolved-oxygen concentration at the upstream and downstream
boundaries and at an interior location;
- tidal-cycle measurements of streamflow and nutrient concentrations at
boundaries and selected interior locations;
- channel geometry;
- municipal and industrial discharge-flow rates and effluent
concentrations; and
- meteorological data including equilibrium temperature, solar radiation,
and wind speed.
In the BRANCH and BLTM models, rivers are represented as a series of cross
sections and channel lengths, which define segments, junctions, and
branches. The BRANCH model computes hydraulic properties at each cross
section. The BTLM model uses the water-quality reaction kinetics found in the
QUAL2E model (Brown and Barnwell, 1987) to simulate the fate and transport of
nutrients, BOD, and dissolved oxygen. It computes water temperature, nutrient
concentration, BOD, algal biomass, and dissolved-oxygen concentration at
every cross section. The schematization of the BLTM for the Cooper and Wando
Rivers uses 30 branches, 7 external boundaries, 16 internal junctions, and
112 cross sections.
The BRANCH model was calibrated by adjusting flow-resistance coefficients,
gage datums, cross-sectional areas, storage volumes, and dispersion-rate
model parameters until simulated and measured (or calculated) values met a
predetermined calibration goal. The calibration and validation periods for
the BRANCH model for water level, streamflow, and salinity were July 30-31
and September 24-25, 1993. Because the model was ultimately used to simulate
the fate and transport of conservative and non-conservative constituents,
emphasis was placed on the salinity-transport simulations during the
calibration and validation. Months were spent getting satisfactory
simulations of water levels, streamflow, and salinity transport to
characterize the mass transport in the system.
Calibration of the BLTM model was accomplished by adjusting rate kinetics and
model parameters that control the dynamics of photosynthesis, nitrogen and
phosphorus cycling, BOD decay, sediment oxygen demand, and reaeration. The
calibration and validation periods for the BLTM water-quality model were
April 8 to May 8 and August 1-30, 1993.
The models were validated by using measured data different from those used
for calibration. The parameters used to calibrate the hydraulic and
mass-transport models were not changed in the validation process. The
calibration and validation process took approximately two person-years to
accomplish.
The approach of the neural network model evaluation followed the boundary and
internal station input/output representation used for the BRANCH and BLTM
models. However, unlike the BRANCH and BLTM models that were calibrated by
systematically adjusting various model parameters, the neural network models
were "trained" on the measured time-series data. The type of neural network
employed is called a "back-propagation" network (Jensen, 1994) and is
especially good at fitting high dimension, continuously valued functional
approximations to data.
A requirement for training and evaluating neural networks is that model data
be arranged into input/output vector pairs representing the variables of
interest. A vector pair having one or more missing measurements cannot be
used for training a model and an input vector with a missing measurement
cannot be evaluated by a developed model. Therefore, the efficacy of
implementing a neural network model is highly dependent on the quantity,
historical range, and quality of the data used for their development.
Bifurcating the modeled data set into "training" and "test" sets provides
verification of a model's accuracy. A model trained on the training set can be
evaluated by comparing its predictions to the measured values of the test
set. The resulting empirical model is subject to the same statistical
characterizations of accuracy and applicability as physics-based models. For
this study, the data were bifurcated into 80% training data and 20% test data
by random number selection.
The first neural network implementation focused on developing a model that
would apply all of the 3.5 years of available time-series data to evaluate
the feasibility of performing long-term simulations (Roehl and Conrads,
1999). This departed from the more temporally restricted calibration
procedure used for BRANCH and BLTM models, which had been focused on modeling
"critical conditions" that cause dissolved-oxygen concentrations to be low.
The 1992-95 data were converted from 15-minute to 30-minute intervals by
simply not using the extra values. The time-series for all but a few
variables contained numerous large gaps where data was not taken or sensors
had failed, resulting in a need to fill in the gaps to obtain a satisfactory
number of complete input/output vector pairs spanning the 3.5 years. This was
accomplished by developing more than 90 neural network models to generate
synthetic data, which were appended to the actual data. Variables that had
relatively large numbers of measurements were used as inputs to models whose
outputs were variables with fewer measurements. A model was developed using
the "appended data set" which was then compared to the physics-based models.
This work required approximately two person-months with most of the time
spent on formatting the raw data received from the USGS and building the
appended data set.
A second implementation was performed to directly compare the prediction
accuracy of the two approaches. This involved developing a series of models
that focused on the same critical condition periods that were used to
evaluate the BRANCH and BLTM models. The training and test sets omitted the
use of synthetic data, and covered periods as follows: water level and
salinity - July 1 to October 21, 1992, water temperature - April 1 to October
15, 1993, and dissolved-oxygen concentration - August 1 to October 1, 1993.
These periods were much longer than those used to calibrate the physics-based
models to insure that the neural network models would learn the range of
hydrodynamic and biochemical behaviors exhibited by the estuarine system.
This work required approximately one person-week.
The neural network model (second implementation using the datasets that
include the calibration and validation periods of the BRANCH and BLTM models)
more accurately simulated the salinity, water temperature, and
dissolved-oxygen concentrations of the Cooper and Wando Rivers than the
BRANCH/BLTM models. Typical results are shown in figures 2 and 3. The reach
on the Cooper River between station 021720675 and 02172053 is of particular
water-quality concern. It is the location of the freshwater and saltwater
interface and dissolved-oxygen "sag" in the system. Computed and measured
salinity concentrations for two stations on the Cooper River are shown in
figure 2. At the downstream station (021720675), both models satisfactorily
simulate the salinity concentrations; however, the BRANCH/BLTM simulation has
a timing error of 60 minutes. The root mean square error (RMSE) of the neural
network simulation was 1.25 parts per thousand (ppt) as compared to 3.14 ppt
for the BRANCH/BLTM simulations. Farther upstream at station 02172053, the
neural network model more accurately simulates the range of salinity values
(RMSE 0.36 ppt) than the BRANCH/BLTM, which is only able to simulate the
lower range of salinity (RMSE 1.97 ppt).
Figure 2. Computed and measured salinity (in parts per thousand) for
two stations on the Cooper River.
Figure 3. Computed and measured water temperature and dissolved-oxygen
concentration at station 021720675 on the Cooper River.
Similar results are seen in the water temperature and dissolved-oxygen
concentration simulations at station 021720675 (fig. 3). The BRANCH/BTLM
water-temperature simulations are within two degrees Celsius of the measured
temperatures (RMSE 1.48 degree Celsius). The neural network is able to
simulate the water temperature to within a degree or less (RMSE 0.31 degree
Celsius). The BRANCH/BLTM dissolved-oxygen simulations are within the range
of the measured values but do not simulate the dynamics of the measured
concentration (RMSE 0.81 milligram per liter (mg/L)). The neural network
model is able to quite accurately simulate the tidal dynamics of the measured
dissolved-oxygen concentration (RMSE 0.27 mg/L).
The evaluation of the BRANCH and BLTM models and neural network models
highlighted the strengths and weaknesses of the two modeling approaches in a
number of categories:
- Data Requirements - neural network models are developed
directly from data; therefore, for a system to be adequately modeled
there must be sufficient data available to fully describe the
behaviors of interest. In the Cooper and Wando River systems, a neural
network trained only for "critical conditions" will have little
ability to perform for other conditions. In a physics-based model,
knowledge and information contained in the modeling program may in
some circumstances provide for a lower data requirement; however, the
data must still be adequate for calibration and testing. The
physics-based models used 30-day datasets for calibration and
validation; whereas, the neural network model used datasets of four to
seven months for training and testing. Alternatively, the neural
network models required only 12 to 15 variables to achieve the very
accurate predictions shown above. This was far fewer than the number
used for the physics-based models and underscores how highly
correlated the boundary station measurements were with the internal
station measurements, and the trade off between numbers of variables
and time-series length.
- Temporal and Spatial Interpolation - the BRANCH and BLTM models
are able to generate time series of constituents of concern at any
point along their finite difference grid. This connotes both temporal
(time) and spatial (location) interpolative capability. The neural
network models as configured for this study were unable to interpolate
spatially and could only make predictions at the internal stations.
However, other work by the authors in modeling 3D ground-water flows
indicates that neural network models can perform combined temporal and
spatial interpolation as well.
- Extrapolating Beyond Range of Data - extrapolation is using a
model to make a prediction for a "new" process state that is
appreciably different from those manifest in the data used to
calibrate and test the model. Neural network models can be designed
to extrapolate to some degree; however, collecting data that
characterizes a new state of interest and retraining the model is the
preferred course. Physics-based models may be better at extrapolating
if the physics of the new state is similar enough to the physics of
the model.
- Providing Process Understanding - preparing data, and
configuring, calibrating, and testing computer models is a highly
analytical endeavor from which fundamental understanding is derived.
This is true for both types of models because their performance cannot
be evaluated without a qualitative understanding of the physics of the
modeled system. The model with the best accuracy over the broadest
range of process conditions will best augment qualitative
understanding with quantitative details that are necessary for
regulating, controlling, and optimizing a process.
- Development Time and Costs - the time involved to apply the
neural network model to the Cooper and Wando Rivers was approximately
a tenth of the time to apply the BRANCH and BLTM models. The time
difference is significant in terms of cost and timeliness of obtaining
results. There are two large costs in applying models (1) collecting,
processing, and archiving data and (2) paying personnel to apply the
models. Neural network models offer a significant saving to the
personnel costs. The implementation of the neural network to simulate
3.5 years of data demonstrated a cost-effective approach to performing
long-term simulations that maximized all the data, not just the
calibration and validation periods of the physics-based models. Often
water-resource managers need answers to their water-quality questions
in months, not years. Neural networks can often provide answers more
quickly than physics-based models.
- Deployment Options - the neural network models execute several
orders of magnitude faster than the BRANCH and BLTM models. Unlike
physics-based models that perform multiple iterations every time step
to compute the output values, trained neural networks execute without
iteration. Therefore, the neural network models can be deployed as
compact programs that are suitable for integrating with optimization
routines and real-time information and control systems. The neural
network models can be readily disseminated to a large number of
water-resource managers by integrating into commonly used spreadsheet
software.
Applying neural network models to highly complex hydrologic systems offers
great potential for analyzing large amounts of time-series data and for
assessing the impact of various hydrologic conditions. The results of this
study indicate that neural network modeling can be an effective modeling tool
under the right circumstances. This technique was well matched to modeling
the Cooper and Wando Rivers because of the large amount of high-quality data
provided by the USGS real-time monitoring program. The 3.5 years of data used
for this effort increased the likelihood that the range of behaviors modeled
would be representative of the environmental system currently and for the
foreseeable future. In addition, the execution time of the neural network
models is several orders of magnitude faster than the BRANCH and BLTM models,
and the neural network models can be readily integrated into spreadsheet
programs to provide an extremely cost effective and user-friendly deployment
vehicle.
Brown, L.C. and Barnwell, T.O., Jr., 1987, The enhanced stream water quality
models QUAL2E and QUAL2E-UNCAS--Documentation and user manual: Athens,
Georgia, U.S. Environmental Protection Agency, Environmental Research
Laboratory, EPA/600/3-87/007, 189 p.
Conrads, P.A., Cooney, T.W., and Long, K.B., 1997, Hydrologic and
water-quality data from selected sites in the Charleston Harbor Estuary and
tributary rivers, South Carolina, water years 1992-95: U.S. Geological Survey
Open-File Report 96-418, 987 p.
Conrads, P.A. and Smith, P.A., 1996, Simulation of water level, streamflow,
and mass transport for the Cooper and Wando Rivers near Charleston, South
Carolina, 1992-95: U.S. Geological Survey Water-Resources Investigations
Report 96-4237, 51 p.
---- 1997, Simulation of temperature, nutrients, biochemical oxygen demand,
and dissolved oxygen in the Cooper and Wando Rivers near Charleston, South
Carolina, 1992-95: U.S. Geological Survey Water-Resources Investigations
Report 97-4151, 58 p.
Jensen, B.A., 1994, Expert systems - neural networks, instrument engineers'
handbook third edition: Chilton, Radnor PA, p. 48-54.
Jobson, H.E. and Schoelhamer, D. H., 1987, Users manual for a Branched
Lagrangian Transport Model: U.S. Geological Survey Water-Resources
Investigations Report 87-4163, 73 p.
Roehl, E.A. and Conrads, P.A., 1999, Real-time control for matching wastewater
discharges to the assimilative capacity of a complex, tidally affected river
basin: 1999 South Carolina Environmental Conference, Myrtle Beach, March
15-16, 1999.
Schaffranek, R.W., Baltzer, R.A., Goldberg, D.E., 1981, A model for
simulation of flow in singular and interconnected channels: U.S. Geological
Survey Techniques of Water Resources Investigations, Book 7, Chap. C3,
100 p.
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