Basin Scale Hydrology Support Vector Machines

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION FEBRUARY

AMERICAN WATER RESOURCES ASSOCIATION

2005

BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS1

Abedalrazq F. Khalil, Mac McKee, Mariush Kemblowski, and Tirusew Asefa2

ABSTRACT: Water scarcity in the Sevier River Basin in south-central Utah has led water managers to seek advanced techniques for identifying optimal forecasting and management measures. To more efficiently use the limited quantity of water in the basin, better methods for control and forecasting are imperative. Basin scale management requires advanced forecasts of the availability of water. Information about long term water availability is important for decision making in terms of how much land to plant and what crops to grow; advanced daily predictions of streamflows and hydraulic characteristics of irrigation canals are of importance for managing water delivery and reservoir releases; and hourly forecasts of flows in tributary streams to account for diurnal fluctuations are vital to more precisely meet the day-to-day expectations of downstream farmers. A priori streamflow information and exogenous climate data have been used to predict future streamflows and required reservoir releases at different timescales. Data on snow water equivalent, sea surface temperatures, temperature, total solar radiation, and precipitation are fused by applying artificial neural networks to enhance long term and real time basin scale water management information. This approach has not previously been used in water resources management at the basin-scale and could be valuable to water users in semi-arid areas to more efficiently utilize and manage scarce water resources. (KEY TERMS: artificial neural networks; multi-sensor data; irrigation; water management; multi-time scale forecasting; streamflow.)

Techniques for predicting seasonal, daily, and hourly streamflows are utilized in this paper to address the need for accurate information about water deliveries on a short term scale and to formulate long term or seasonal plans for allocation of water and related resources. Streamflow prediction is used in applications as diverse as agricultural planning, reservoir, and watershed management. Ames (1998) has discussed the financial returns to agriculture and industry that could be derived from successful extended range streamflow forecasts. Short term and real time forecasts of flows in rivers and tributaries, and near real time recommendations for required operational decisions for canal diversions and reservoir releases can provide additional opportunities for improving system level water use efficiencies. These information needs – for long term and real time streamflow forecasts and near real time reservoir releases – require a substantial investment in acquisition and analysis of a wide range of temporally and spatially disparate data. These information needs are very much the case for the highly regulated Sevier River Basin of south-central Utah, which has been heavily instrumented in recent years and which provides both the motivation and case study area for this paper. Physically based hydrologic and hydraulic mathematical modeling approaches have been proposed for streamflow predictions, but complexities in these modeling processes and difficulties associated with obtaining the data that such models would require have limited the scope and applicability of these

Khalil, Abedalrazq F., Mac McKee, Mariush Kemblowski, and Tirusew Asefa, 2005. Basin Scale Water Management and Forecasting Using Artificial Neural Networks. Journal of the American Water Resources Association (JAWRA) 41(1):195-208.

INTRODUCTION Forecasting of streamflow at different temporal scales is of practical importance to several disciplines.

1Paper No. 03202 of the Journal of the American Water Resources Association (JAWRA) (Copyright © 2005). Discussions are open until August 1, 2005. 2Respectively, Graduate Research Assistant, Professors of Civil and Environmental Engineering, and Graduate Research Assistant, Department of Civil and Environmental Engineering, Utah Water Research Laboratory, Utah State University, Logan, Utah 84322-8200 (EMail/Khalil: [email protected]).

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA traditional methods. As a result, there is a need for the development of modeling approaches that capture the behavior of the system utilizing available data, are computationally robust, and could be used in real applications. One such approach is presented in this paper. The goals of the work reported in this paper are to:

STUDY AREA – SEVIER RIVER BASIN The Sevier River Basin in rural south-central Utah is one of the state’s major drainages (Figure 1). A closed river basin, it encompasses 12.5 percent of the state’s total area. From the headwaters 250 miles (402 km) south of Salt Lake City, the river flows north and then west 255 miles (410 km) before reaching Sevier Lake (Berger et al., 2002). The Sevier River Basin has five subwatersheds and is divided into two major divisions, the upper and lower basins, for the administration of water rights. The dividing point between the upper and lower basins is the Vermillion Diversion Dam. Average annual precipitation varies around 13.0 inches (33 cm), and the growing season ranges from 60 to 178 days (Berger et al., 2002; Utah Board of Water Resources, 2001). Most of the surface water runoff comes from snowmelt during the spring and early summer months. The primary use of water in the basin is for irrigation. The average annual

1. Provide analyses that can be used to improve decisions in river basin management through exploiting the wealth of available, diverse data regarding canals and streamflows, irrigation water orders, climate information, and earth and sea surface satellite imagery. 2. Provide decision relevant information that facilitates the on-farm management of water in both the short and long term.

Figure 1. The Sevier River Basin in South-Central Utah.

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BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS ARTIFICIAL NEURAL NETWORKS

amount of water diverted for cropland irrigation is 903,460 acre-feet (1,114 million cubic meters, mcm). Of this amount, approximately 135,000 acre-feet (166.5 cmc) are pumped from ground water. About 40 percent of the diversions are return flows from upstream use (Berger et al., 2002). For a detailed description of the basin and much of the real time database utilized in this research, refer to Sevier Water Users Association (2004).

In this paper, artificial neural network (ANN) learning methods are used to develop basin scale management models. Artificial neural networks are practical information processing systems that provide methods for “learning” functions from observations. An ANN roughly replicates the behavior of the organic brain by emulating the operations and connectivity of biological neurons. This emulation, of course, is done in a mathematical form that is greatly simplified from the biological prototype. The advantage of ANNs in engineering and practical applications lies in their ability to learn and capture information from data that describe the behavior of a real system (Govindaraju and Rao, 2000; Hayken, 1994). An interesting property of ANNs is that they often work well even when the training data sets contain noise and measurement errors (Hammerstrom, 1993). Moreover, they have the capability of representing complex behaviors of nonlinear systems (Maier and Dandy, 2000). Artificial neural networks are characterized by their architecture, an activation function, and the learning rule and learning parameter set used in their construction. A common architecture is one embodied in feed forward backpropagation ANNs, which consists of layers of neurons in the network and different number of neurons in each layer (Skapura, 1995). It is composed of a sequence of layers that are classified as input, hidden, and output layers. Each layer consists of a set of one or more nodes, or “neurons.” The nodes in the input layer receive information from the outside world, process this information, and send output to the next layer of neurons in the network. Each neuron is connected to neurons in the preceding layer, from which it receives inputs, and to the neurons in the subsequent layer, to which it passes its output. The learning rule specifies the way in which weights will be determined during the training process, and this depends on the input, output, and activation values of the model. Each neuron has an activation function, which can be continuous, linear, or nonlinear functions [i.e., monotonic nonlinear function that saturates at finite value arguments like sgm(·) and tanh(·)]. The output signal that passes from one neuron to another in a subsequent layer is transformed by a weight, or “connection strength,” that modifies the signal before it reaches the receiving neuron. Thus, the output of a node in any layer is determined by applying a nonlinear transformation (the activation function) to the sum of the weighted inputs it receives from the neurons of the previous layer. Figure 2 shows an ANN model that takes input

BACKGROUND Real time integrated management of river basins can be important in achieving optimum allocation of scarce water resources. Researchers have proposed physical and stochastic approaches for prediction of streamflow at different time scales for management purposes. Complexities in the underlying physical processes and difficulties in acquiring needed data limit the utility of these approaches. The main functions of an integrated real time water resources management system are: water resources real time monitoring and data collection, information and knowledge mining, and prediction and real time decision support. Real time water resources management requires a heavily instrumented basin to monitor precipitation, runoff, climatic indices, and streamflow. The Sevier River Basin has been heavily instrumented with gages that measure all the aforementioned factors. Measurements of flows at several locations on the mainstem of the Sevier River, tributary flows and canal diversions, various meteorological data, reservoir volumes and releases, and other data are reported hourly, stored in a database, and made available via the internet. While the managers of the Sevier River water systems have utilized these data in raw form to improve overall system operations, much more could be done with these data to develop and implement advanced tools for forecasting and realtime management. The Sevier River is therefore a suitable study area to test tools that are not physically based, but that “let the data speak.” The emphasis of this manuscript is on integration of the available data by artificial neural networks to obtain decisionrelevant predictions of flows and reservoir operation recommendations at different time scales. These models will ultimately be integrated into a water resources information management system to be delivered to the operators of the reservoir and canal systems in the Sevier River Basin.

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA values x1, x2, ... xl and generates an output signal y1, y2, ... yK. A multi-layer ANN is described as “feedforward” when the connections are directed from the input layer, forward through the network, to the output layer.

“backpropagation” (Rumelhart et al., 1986) is used for training ANNs, by which w is modified in such a way to find a set of w that minimizes the error. For details about ANNs, interested readers are referred to Govindaraju and Rao (2000) and Schalkoff (1997).

RELEVANT DATA SETS The development of the predictive learning model requires the precise identification of the relevant data. In the next sections, a brief description of the relevant data sets will be provided. The relevancy evaluation is judged subjectively. In other words, this paper utilizes the available data that could be related to the given model from a hydrologic perception. Streamflow Streamflow is the result of interactions between many hydrologic events, such as precipitation, snowmelt, evapotranspiration, infiltration, and ground water recharge, with anthropogenic influences, such as irrigation activities. Continuous historical streamflow data were obtained for different sites. Data appropriate for use in seasonal streamflow predictions are available in the form of average daily flows from 1976 to 2002. Short term predictions can be supported by daily and hourly streamflow data that are available in both daily and hourly form from 2000 to 2003. Irrigation Demands Figure 2. Typical ANN Structure.

Irrigation demands represent the quantities of water that farmers request be delivered to their headgates. Such requests are made one day in advance of the expected time of deliveries to take place. Data on irrigation demands for various canals in the Sevier River Basin are available for the years 1952 through 2002.

The activation functions are evaluated through two steps. First, the activation is calculated as the inner product of the input vector, x = [x1, x2, ... xl]T, and the l

weight vector, w = [w1, w2, ... wl]T, u =

∑ wi , xi .

Sec-

i

ond, the output, y, is evaluated as a function f(u) of the activation. Optimal values for the weight vector are determined by minimization of an objective function that measures the error between the model’s output and the measured behavior of the real system “Empirical Risk Minimization.” Typically, the error for query t may be defined as the difference between the observed or measured target response, T(t), and the model’s response, y(t). Generally, a method called JAWRA

Temperature Temperature can directly affect the rate of snowmelt, which in turn contributes to streamflow. The inclusion of temperature data as a predictor can enhance the model. Historic daily and hourly temperature data are available at many SnoTel and weather stations. 198

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BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS neurons in each hidden layer, which is usually accomplished through a trial-and-error process. Finally, the resulting ANN model must be evaluated, or “tested,” in terms of the quality of its predictions.

Sea Surface Temperature Anomaly Satellite derived measurements of sea surface temperature anomaly (SSTA) data can be useful in making seasonal predictions of streamflow. Sea surface temperature influences continental precipitation patterns, and hence provides information about the quantity of water that will become available for storage in reservoirs. Incorporation of SSTA measurements over a broad temporal scale can therefore be relevant to the study of basin-scale water management issues. A long, statistically homogeneous record of sea surface temperature anomalies is available (Kaplan et al., 1998) on a 5-degree-by-5-degree grid covering the majority of the world’s oceans for the period 1856 to present. Details of the statistical development of these data are beyond the scope of this paper. Readers are referred to Kaplan et al. (1997) for a description of the methodology.

Seasonal Streamflow Prediction Model Seasonal predictions of future streamflow and reservoir volumes can play a vital role in planning and decision making in river basins. In the case of the Sevier River Basin, ranchers must make decisions to purchase livestock early in the year, well before information is available about how much water will be supplied in the summer and fall for irrigation and production of feed for those livestock. Financial commitments made early in the water year can result in substantial economic losses if the winter snow pack and resulting spring runoff do not subsequently supply enough irrigation water. Seasonal predictions were made in this study for flows on the Sevier River at the Hatch gage, which is high in the upper basin. The quantity of water that flows through this gauge represents a large portion of the total water available to the basin. The streamflow at this gauge changes from season to season due to the interactions of a multitude of factors. Regional and local meteorological conditions and snowpack in the mountains will obviously influence streamflows. Previous work has shown that ANNs are appropriate to capture the complex nonlinear relationships among these phenomena. For a more complete review of the uses of ANNs in water resources applications, refer to Maier and Dandy (2000) and Govindaraju and Rao (2000). The approach adopted here in building a model for forecasting seasonal streamflow quantities is based upon a multi-sensor data driven approach that uses an ANN as a learning machine. Inputs to the model consist of previous seasonal streamflows, SSTA data, and SWE data from the SnoTel stations at Harris Flat and Midway Valley. The cumulative quantity of water that flows past the Hatch gage in a season provides information on the overall status of the basin with respect to water availability and the response of basin hydrology to climatic forcings. The SWE input to the model is the average of the monthly SWE over the previous 12 months. Sea surface temperature anomaly data are input to the model in the form of the 12 previous monthly average SSTA values. The relationship between inputs and outputs of the seasonal ANN model, then, can be expressed as

Snow Water Equivalent Information about snow can be critical for forecasting spring runoff and water levels in streams. Snow serves as storage of water supplies at the beginning of the season. Daily data on snow water equivalent (SWE), which is the equivalent depth of water obtained when the snow is completely melted, are available from several SnoTel sites in the Sevier River Basin, including the three shown in Figure 1. Precipitation Daily precipitation measurements are available at different locations across the Sevier River Basin. The precipitation data used in this manuscript were obtained from the Kimberly Mine SnoTel station, and the Richfield airport weather station, as it is the nearest station to the locations at which streamflow predictions are desired.

MODEL FORMULATION AND APPLICATION Developing an ANN model for a particular application requires designing the network architecture for capturing the dynamical characteristics of the system being simulated from data that are available to describe the problem domain. The structure of an ANN requires identification of the input and output vectors. It also requires selection of the number of hidden layers and specification of the number of JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

Qt+6 = Γ(I)

(1)

where Qt+6 is the expected quantity of water (cfs) coming to the basin through the Hatch gage for six 199

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA be sufficient to meet the needs of nine irrigation canals that divert water from the river downstream of the reservoir, these canals all lie between the Clear Creek confluences and the Vermillion Diversion Dam (see Figure 1). If too little water is released, it is likely that the lower canals will not receive enough water. If too much water is released, some might be spilled to the lower basin; water that is spilled is considered “lost” by the users in the upper basin, who, in accordance with the complicated system of water rights on the Sevier, are entitled to it. Vermillion Diversion Dam, shown in Figure 1, is the administrative dividing point between the upper and lower Sevier River. Efficient daily management decisions about the operation of the reservoir, then, can result in reduction of water losses and improved deliveries to users. This will translate into increased overall farm production for the upper basin. Modeling all the climatic, hydrologic, and hydraulic physical processes involved to provide near real time forecasts of river and canal flows and, ultimately, required reservoir releases would involve solution of a complex system of nonlinear, partial differential equations. Implementation of such a model would need a substantial amount of data, a skilled modeler, and powerful computing devices. There is uncertainty involved in the reservoir releases owing to the variations in the influencing processes throughout the season and the travel times from the reservoir to the last demand that range from

months from time t, I is the vector of inputs to the ANN, and Γ is the ANN nonlinear transformation of inputs to outputs. The input vector can be expressed as – I = [Qt-6 St-12 Tt-12]T

(2)

where Qt-6 is the total quantity of water (cfs) flowing past the Hatch gage in the last six moths, St-12 is the average SWE (in) calculated over the 12 months prior – to time t for each SnoTel station, and Tt-12 represent a vector of average monthly SSTAs (˚C) for the previous 12 months. The SSTA data were obtained for six different stations (see Figure 3). Therefore, six ANN models were built using one individual SSTA station at a time (see Figure 3). Detailed descriptions of the model performance for the SSTA station that proved to be the most significant are presented in the results section. Daily Reservoir Release Prediction Model The need for daily prediction is of great importance to manage irrigation canals and reservoir releases in river basins. Piute Reservoir was selected to test the applicability of ANNs for supplying information for daily reservoir management (see the Middle Sevier portion of Figure 1). Each day, the operator of the Piute Reservoir must set releases at a level that will

Figure 3. Significant Sea Surface Temperature Anomaly Measurement Locations.

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BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS Creek, a tributary of the Sevier River, is an example of an uncontrolled tributary stream that discharges into the river in such a way that its diurnal fluctuations make downstream water management more difficult. In the spring and early summer, snowmelt in the Clear Creek watershed can produce runoff quantities with substantial diurnal fluctuations. The irrigators in the upper basin are entitled to capture and use flows from Clear Creek, but they have limited capabilities to do so. Instead, they must let flows from Clear Creek enter the mainstem of the Sevier, and then divert these waters downstream. If they fail to do so, the excess flows received at Vermillion that cannot be diverted and locally used will be spilled from the Vermillion Diversion Dam and lost from the upper basin. Clearly, capture of Clear Creek waters will require coordination of releases from Piute Reservoir, upstream, with diversion of irrigation water into canals, downstream. This coordination will be best facilitated with advanced forecasts about likely diurnal fluctuations in Clear Creek flows. The design of an appropriate hourly prediction model requires the use of data that reflect the physical forces that cause streamflow in these tributary streams to fluctuate throughout the day. These include hourly total solar radiation, previous day streamflow, precipitation, and air temperature. An hourly model is required to provide information on the diurnal fluctuations in the river flows due to tributary inflows. The nonlinear mapping equations used to capture the relationships between inputs and outputs of a hourly ANN model can be expressed as

two to three days depending on the quantity of flow in the river and on antecedent flow conditions. In the face of uncertainty, the Piute Reservoir operator needs a tool to help decide on a near real time basis how much water to release to meet water orders to canal operators located downstream of the reservoir. In other words, a common requirement for managing the reservoir that is operated on an “on-demand” basis is the anticipation of the quantity of water that must be released while accounting for losses and travel time. The Piute Reservoir operators would like to set the diversion gates once per day and maintain a constant flow into the canal over the following 24hour period. Therefore, the desired output of the ANN model is simply the daily quantity of water that should be released from the Piute Reservoir. The information that should be made available to the ANN model through the neurons in the input layer should include the data that describe current, and perhaps recent historical, flow conditions in the river and canals. This information is readily available from the on-line database maintained by the Sevier River Water Users Association (2004). Input to the ANN should also include the orders that have been received by the canal managers for water deliveries along the length of the river. The relationship between inputs and outputs of the daily ANN model, then, can be expressed as ODt = Γ(I)

(3)

where ODt is the rate flow of water (cfs) to be released on day t, I is the vector of inputs to the ANN, and Γ is the ANN nonlinear transformation of inputs to outputs. The input vector can be expressed as – – I = [Dt-1 Q t-l O t]T

Qt = Γ(I)

(4)

where Qt is the rate of flow (cfs) past the Clear Creek gage for the coming 24 hours, and t = (1,2,..., 24). I is the vector of inputs to the ANN, and Γ is the ANN nonlinear transformation of inputs to outputs. The input vector can be expressed as

where Dt-1 is the average release flow (cfs) from the – previous day, Q t-l is a vector composed of the average flows (cfs) from the previous day at the flow gages – along the river, and O t is a vector of water orders (cfs) to be delivered during day t. The use of previous day canal flow information and orders for next day water deliveries produces an input layer with 14 neurons.

– – – – – I = [Q t-24 Tt-24 R t-24 S t-24 P t-24]T

(6)

– – – where Q t-24, Tt-24, and R t-24 are averages of the vectors of hourly streamflow (cfs) at the Clear Creek gage, air temperature (˚C), and solar radiation (kW/m2), respectively, for the 24 hours previous to the – – prediction time; S t-24 and P t-24 are averages of the vectors of wind speed (mph) and precipitation (in), respectively, for a period of 24 hours before time t. Precipitation data were provided from the Kimberly Mine SnoTel station (see Figure 1).

Hourly Streamflow Predictions In some situations, unregulated tributary streams can cause flows to fluctuate in the main river over a diurnal pattern that is difficult to predict and that causes management problems in planning for diversions in locations downstream of the tributary. Clear

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(5)

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA RESULTS AND DISCUSSION

shows the number of neurons in each layer, the optimal transfer function, and the learning rule used for each model.

Model Specifications Obtaining an optimal level of performance for any learning machine entails a considerable number of design choices, especially for ANN learning. The characteristics of an optimal architecture are a model that produces acceptable predictions, has good generalization abilities, and requires a minimal number of calibrated parameters (i.e., degrees of freedom). The approach for selecting an optimal architecture benefits from a rigorous statistical analysis and expert knowledge. Splitting the data into two sets, where the machine is trained on one and tested on the other to avoid underestimating the true error, has a twofold disadvantage: the problem of having sufficient data for training, and the possibility of statistical dependence between the two subsets (Blum et al., 1999). Moreover, since the available data are scarce, k-fold cross-validation can be used to overcome these deficiencies. In k-fold cross-validation, the data set is partitioned into k mutually disjoint folds (subsets) S j ∀ j ∈ {1, 2,..., k} (Shakhnarovich et al., 2001). For each Sj, the model is trained on all folds except Sj. The final error is estimated as ErrCV × k =

1 K

Figure 4. RMSE (five-fold cross-validation) and 95 Percent Confidence Bounds as a Function of Number of Hidden Nodes.

The ANN model is constructed once the model structure is selected. Construction of an ANN model involves “training” the network with known input/ output data available from the real system, and then “testing” the resulting model against other data not used in training (the withheld sample). In this manuscript, ANNs are developed using Neural Works Professional II/Plus (NeuralWare, Inc., 2000) and the Matlab® toolbox “NetLab” (Bishop, 1995; Nabney, 2001).

k

∑ Q(S j , X ), S j ⊄ X

(7)

j =1

where Q(Sj,X) is the statistic of interest for evaluation of an ANN model trained using X and tested on Sj. In this paper, a set aside sample of data is used (i.e., validation data set) to test the model plausibility. To avoid data splitting, the training data sets were used in a cross-validation context to build the ANN model. The problem of choosing a suitable architecture for ANNs lies in specifying the activation function and the number of neurons in the hidden layer. Trial-anderror analysis resulted in selection of a suitable activation function for each model. Selection of the number of hidden nodes in ANNs is a most difficult but important step. The root mean square error (RMSE) from the five-fold cross-validation error was used to select the optimal number of hidden nodes (Rivals and Personnaz, 2000). The number of hidden nodes was increased, starting from only one, and evaluated the five-fold cross-validation error (mean and variance). The optimal number of hidden nodes was selected at the point where the decrease in the fivefold error becomes insignificant (see Figure 4 for the case of the hourly model). Table 1 provides a summary of the characteristics of the seasonal, daily, and hourly models that have been discussed. The table JAWRA

Performance Criteria The objective of the training phase in building an ANN is to produce a set of connection weights that causes the outputs of the ANN, y(t), to match as closely as possible the observed system outputs, T(t), for every set of training patterns. Achievement of this objective is typically measured by the correlation coefficient, R2, defined as  2  R =  

 ( y − y) T − T  t  y − y) T −T  ( t t 

∑ ∑

(

∑(

)

)

2

(8)

– where –y and T are the means of y and T, respectively. The correlation coefficient is not a measure of the predictive capabilities of the model since it is sensitive to 202

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BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS TABLE 1. Model Structures Summary.

Model

Input Layer

Hidden Layer 1

Hidden Layer 2

Output Layer

Transfer Function

Learning Rule*

Seasonal Model

15

10

–

01

sig(.)

∆-Rule

Daily Model

14

14

3

01

tanh(.)

NCD

Hourly Model

07

06

–

24

sig(.)

∆-Rule

*The learning rules are the delta rule (∆-Rule), and the normalized cumulative delta (NCD). A discussion of these rules can be found in Neu*ralWare (2000).

outliers and spurious data. Therefore, the coefficient of efficiency, E, has been widely used, defined as

∑ t (T − y)2 E = 1− ∑ t (T − T )2

Seasonal Streamflow Prediction Model Performance Figure 5 illustrates the relationship between the model predictions and the actual data. Using SSTA data from the East Atlantic station produced the optimal performance. The correlation coefficient of the model is 0.88 and the coefficient of efficiency is 0.76. Adequacy of the seasonal ANN could provide a very useful utility to the water users in making decisions in regard to the basin operations. Figure 6 provides a scatterplot, together with ±20 percent error bounds, of model predictions versus actual system behavior. It should be noted that in the total training data set corresponding to the period 1981 to 2002, the small number of patterns could be a direct reason for the ANN to exhibit relatively poor predictions at some points (i.e., the peak flows). It also could be attributed to a lack of sufficient data included in the inputs to the ANN model to fully represent the hydrology of the watershed for these events. It is worth mentioning that the lack of accuracy of ANNs in predicting peaks and valleys in hydrologic time series is one of the major concerns facing users of ANN technology in the hydrologic community. For techniques to improve peak flow estimation in ANNs, readers are referred to Sudheer et al. (2003). Successful seasonal forecasts of water quantity should help answer difficult questions such as, “Will there be sufficient water to meet competing demands in the Sevier River Basin?” and “How far will one be able to stretch the water that will become available?”

(9)

A model with E = 0.9 has a mean square error of 10 percent of the variance of the observed data. It is, however, sensitive to significant outliers. To overcome the susceptibility to extreme values, the Index of Agreement, d, can be used. It is defined as follows

d = 1−

∑t (

∑t T − y

) (

y−T + T −T

(10)

)

It is less sensitive to large values. To quantify the error in terms of the units of the variable, one could use the RMSE. It is defined as

RMSE =

N −1

∑ t ( T − y) 2 ,

t = 1,..., N

(11)

Bias and mean absolute error are also physical measures. Bias is the average of the differences between observed and predicted values, while mean absolute error is the average of the absolute of the residuals. For more details about goodness-of-fit measures, see David and Gregory (1999). A complete assessment of the model should also include scatterplots with error bounds. The performance of the ANN model is evaluated during the ANN testing phase using scatterplots of y(t) versus T(t). The magnitude of the scatter of [T(t), y(t)] about a 45 degree line can be examined using error bounds to assess the deviation of predicted outputs from measured system behavior.

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Daily Prediction of Required Reservoir Releases Figure 7 presents a time series plot comparing the ANN model release forecasts and the actual diversions for the irrigation seasons of 2000, 2001, and 2002. This figure shows good model performance in predicting the required releases from the reservoir.

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Figure 5. Time Series Performance of the ANN Model in Predicting Seasonal Quantity of Water.

Figure 6. Scatterplot of Model Predictions Versus Actual Flows.

Figure 8 provides a scatterplot, together with ±20 percent error bounds, of model predictions versus measured releases for the validation data used in the 2000, 2001, and 2002 irrigation seasons. The correlation coefficient for this scatterplot had a value of R2 = 0.98 and the coefficient of efficiency = 0.95. To utilize JAWRA

the model in near real time, the predicted reservoir releases can be provided to the reservoir operator, and then it is possible for the operator and experts to analyze, judge, and evaluate the results of the ANN model according to their own knowledge and experience. 204

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Figure 7. Time Series Performance of the ANN Model in Predicting the 2000, 2001, and 2002 Irrigation Season Releases.

Figure 8. Scatter Plot of Model Predictions Versus Measured Releases for the 2000, 2001, and 2002 Irrigation Seasons.

The results indicate that the model forecast can be used to address the conflicting goals of satisfying downstream demands with high certainty while at the same time conserving water in the reservoir for use later in the season.

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Hourly Streamflow Prediction Model Results A hourly streamflow prediction model has been built to forecast the substantial diurnal fluctuation for the Clear Creek watershed. The total data available for building this model are from the spring runoff 205

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA periods of 2000 through 2003. As shown in Figure 9, it is possible to predict 2003 hourly flows at Clear Creek during the first months of the irrigation season when diurnal fluctuations play a strong role in determining flows in the creek.

As shown in Figure 10, the predicted flows versus the actual flows illustrate very good model performance. Hourly streamflow predictions provide useful management information for the Sevier River Basin managers and farmers in dealing with diurnal fluctuations of tributary streams. It is worth mentioning here that the model was able to accurately simulate the rapid rise in streamflow that occurs at sunrise, as well as other diurnal fluctuations in flow.

SUMMARY AND CONCLUSIONS To improve water management for the Sevier River Basin, an extensive, basin wide automated system has been installed that records and stores data on a hourly basis to enable real time information processing. Moreover, Internet based communications and control systems are in place to allow managers to remotely manipulate all reservoir releases and canal diversion gates at will. Operators of the basin wide system and water users alike have begun to view the resulting information and control system as an integrated tool for basin wide management (Berger et al., 2002; Bret et al., 2002). In most river basins, and particularly in the Sevier, water supply is managed at different temporal and spatial scales, and decisions made by different managers are not always well coordinated. This is

Figure 9. Model Performance Evaluated Using Coefficient of Efficiency and RMSE (2003 irrigation season).

On average, the linear correlation between the actual and the predicted flow is 0.97 and the RMSE is 9.43 cfs (0.27m3/sec). Different trials with different data sets proved that the hourly predictions would not be as good unless all the relevant data – previous streamflow, total solar radiation, air temperature, and precipitation – were employed.

Figure 10. Daily Predicted Versus Actual Flow at 10 p.m. for Clear Creek.

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BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS particularly difficult given long travel times and uncertainties in system behavior. The models described in this manuscript represent a first attempt to exploit the real time database available on the Sevier River to address the range in information needs of stakeholders and managers. A seasonal model provides prediction of future water availability in the upper basin to reduce the vulnerability of water users to unforeseen water shortages. This information will help them avoid financial commitments that must be made early in the water year but that could result in substantial economic losses if future water supplies become limited. A daily reservoir release model was designed to improve on-demand flexibility in reservoir operation. Efficient daily management decisions about reservoir releases reduce water losses and improve deliveries to downstream irrigators. A hourly model of uncontrolled tributary flows allows water managers to accurately anticipate diurnal flow conditions and consequently integrate both upstream reservoir releases with numerous downstream canal diversions. These models exploit the real time database with the coordinated input of water demand information by diverse canal and reservoir operators to provide both short term and long term decision relevant information. In these functions, they constitute a foundation of an integrated framework for basinscale management of the available scarce water resources. The ANN model was able to successfully transform measured input vectors into reasonably accurate forecasts of outputs for the three models. Large amounts of data, including multi-sensor data in the form of meteorological and streamflow data, were integrated into an ANN framework to develop useful models for water management problems. The adequacy of the ANN models is demonstrated by the quality of their forecast. This shows that construction of real time

monitoring and management systems can be accomplished to provide more efficient utilization of the basin’s water resources. This paper demonstrates the applicability of ANNs to learn relationships between easy to measure streamflow, meteorological, and satellite data to enhance basin scale management. The performance of ANN techniques in extracting useful information is satisfactory (see Table 2). Overall, the resulting models are easily used and have been found to provide useful and efficient forecasts without resorting to the development and application of complex, computationally demanding physically based models that require expensive data collection efforts to support them. In the future, such models could also provide a substantial potential contribution to computer controlled basin automation by linking them to the basin database. This is being considered in the Sevier River Basin, and, if implemented, might reduce the cost of management and more fully exploit the available database for the basin. This leads us to optimistically share the view voiced by one of the water users in the Sevier River Basin that: “…when something goes down and I have to go back to the old way of doing things, it is like being blind after being able to see” (Berger et al., 2002, p. 25-11).

ACKNOWLEDGMENTS The authors wish to thank Dr. Roger Hansen of the U.S. Bureau of Reclamation, Provo, Utah, for the extremely valuable contributions he has made to the work reported in this paper. Thanks are also due to Dr. Luis Bastidas and Connely K. Baldwin for their valuable insights and help. The authors are grateful to the Sevier River Water Users Association, the U.S. Bureau of Reclamation, and the Utah Water Research Laboratory at Utah State University for providing funding in partial support of the work reported here. Thanks are also due to anonymous reviewers for their insightful comments.

TABLE 2. Key Statistics of Model Performance in the Training and Testing Phases.

Statistics

Training

Correlation Coefficient

0.93

Coefficient of Efficiency

0.86

Index of Agreement

Seasonal Testing

Daily

Hourly Testing

Training

Testing

Training

0.88

0.99

0.98

0.99

0.97

0.76

0.98

0.95

0.98

0.91

0.96

0.94

0.99

0.99

0.99

0.97

RMSE

19.58 mcf 0.55 mcm

20.59 mcf 0.58 mcm

20.16 cfs 0.57 cms

38.13 cfs 1.08 cms

4.25 cfs 0.12 cms

9.43 cfs 0.27 cms

Bias

-3.44 mcf 0.097 mcm

-4.24 mcf -0.12 mcm

0.00 cfs 0.00 cfs

1.84 cfs 0.05 cms

0.00 cfs 0.00 cfs

-3.84 cfs -0.1 cms

Mean Absolute Error

14.00 mcf 0.4 mcm

15.67 mcf 0.44 mcm

13.25 cfs 0.38 cms

27.38 cfs 0.78 cms

2.86 cfs 0.081 cms

5.91 cfs 0.17 cms

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KHALIL, MCKEE, KEMBLOWSKI, AND ASEFA LITERATURE CITED

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