PRECIPITATION-RUNOFF MODELING USING ARTIFICIAL NEURAL NETWORKS AND CONCEPTUAL MODELS

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1 PRECIPITATION-RUNOFF MODELING USING ARTIFICIAL NEURAL NETWORKS AND CONCEPTUAL MODELS By A. Sezin Tokar 1 and Momcilo Markus 2 ABSTRACT: Inspired by the functioning of the brain and biological nervous systems, artificial neural networks (ANNs) have been applied to various hydrologic problems in the last 10 years. In this study, ANN models are compared with traditional conceptual models in predicting watershed runoff as a function of rainfall, snow water equivalent, and temperature. The ANN technique was applied to model watershed runoff in three basins with different climatic and physiographic characteristics the Fraser River in Colorado, Raccoon Creek in Iowa, and Little Patuxent River in Maryland. In the Fraser River watershed, the ANN technique was applied to model monthly streamflow and was compared to a conceptual water balance (Watbal) model. The ANN technique was used to model the daily rainfall-runoff process and was compared to the Sacramento soil moisture accounting (SAC-SMA) model in the Raccoon River watershed. The daily rainfall-runoff process was also modeled using the ANN technique in the Little Patuxent River basin, and the training and testing results were compared to those of a simple conceptual rainfall-runoff (SCRR) model. In all cases, the ANN models provided higher accuracy, a more systematic approach, and shortened the time spent in training of the models. For the Fraser River, the accuracy of monthly streamflow forecasts by the ANN model was significantly higher compared to the accuracy of the Watbal model. The best-fit ANN model performed as well as the SAC-SMA model in the Raccoon River. The testing and training accuracy of the ANN model in Little Patuxent River was comparatively higher than that of the SCRR model. The initial results indicate that ANNs can be powerful tools in modeling the precipitation-runoff process for various time scales, topography, and climate patterns. INTRODUCTION The precipitation-runoff relationships are among the most complex hydrologic phenomena to comprehend due to the tremendous spatial and temporal variability of watershed characteristics, snowpack, and precipitation patterns, as well as a number of variables involved in modeling the physical processes. For many years, hydrologists have attempted to understand transformation of rainfall and snow to runoff in order to forecast streamflow for water supply, flood control, irrigation, drainage, water quality, power generation, recreation, and fish and wildlife propagation. The transformation of precipitation to watershed runoff involves many highly complex components, such as interception, depression storage, infiltration, overland flow, interflow, percolation, evaporation, and transpiration. Conceptual models provide daily, monthly, or seasonal estimates of streamflow for short- and long-term forecasting on a continuous basis. The entire physical process in the hydrologic cycle is mathematically formulated in the conceptual models. Thus, they are composed of a large number of parameters. The Sacramento soil moisture accounting (SAC-SMA) model is defined by 22 parameters in addition to 12 parameters required by the potential evaporation ( National 1996). The number of water balance (Watbal) model parameters can be much larger and can often exceed 50, or even 100, for larger basins with a large number of computational units (Markus and Baker 1994). The simple conceptual rainfall-runoff (SCRR) model has seven fitting coefficients and two storage elements (McCuen and Snyder 1986). Since there are numerous model parameters, and the interaction of these parameters is highly complicated, the optimization of the model parameters is usually accomplished by a trial-and-error procedure. Therefore, the accuracy of the model predictions is very subjective and highly dependent on the user s ability, 1 Hydro., Consultant, Nat. Weather Service, 1325 East-West Hwy., Silver Spring, MD Sr. Hydro., Michael Baker, Jr., Inc., Alexandria, VA. Note. Discussion open until September 1, To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on October 5, This paper is part of the Journal of Hydrologic Engineering, Vol. 5, No. 2, April, ASCE, ISSN /00/ /$8.00 $.50 per page. Paper No knowledge, and understanding of the model and the watershed characteristics. In conceptual models, precipitation, air temperature, and/or evaporation data are usually employed as input data. In addition, streamflow data are required for the calibration of the model. Although well-calibrated conceptual models provide reasonable forecast accuracy, their uses are limited only to a small number of watersheds due to the difficulties discussed. Artificial neural networks (ANNs) have been in existence since the 1940s, but since current algorithms have overcome the limitations of those early networks great interest in the practical applications of ANNs has arisen in recent decades (Wasserman 1989; Muller and Reinhardt 1990). Various ANN algorithms have an objective to map a set of inputs to a set of outputs. An ANN is described as an information processing system that is composed of many nonlinear and densely interconnected processing elements or neurons. ANNs have been proven to provide better solutions when applied to complex systems that may be poorly described or understood; problems that deal with noise or involve pattern recognition, diagnosis, abstraction, and generalization; and situations where input is incomplete or ambiguous by nature. It has been reported that an ANN has the ability to extract patterns in phenomena and overcome difficulties due to the selection of a model form such as linear, power, or polynomial. An ANN algorithm is capable of modeling the rainfall/snowmelt-runoff relationship due to its ability to generalize patterns in noisy and ambiguous input data and to synthesize a complex model without prior knowledge or probability distributions. The ANN model is calibrated using automatic calibration techniques. Thus, an ANN model eliminates subjectivity and lengthy calibration cycles. In the literature some of the hydrologic applications of ANNs include modeling of the daily rainfall-runoff process and snowmelt-runoff process, assessment of stream ecological and hydrological responses to climate change, rainfall forecasting, sediment transport prediction, pier scour estimation, and ground-water remediation (French et al. 1992; Trent et al. 1993a,b; Roger and Dowla 1994; Hsu et al. 1995; Markus et al. 1995; Poff et al. 1996; Tokar 1996; Shamseldin 1997; Tokar and Johnson 1999). 156 / JOURNAL OF HYDROLOGIC ENGINEERING / APRIL 2000

2 REVIEW Artificial Neural Networks An ANN is an information processing system that is composed of a number of processing elements (or neurons) analogous to biological neurons and interconnections (or weights) between these elements that imitate the synaptic strength in a biological nervous system (Fig. 1). In an ANN architecture, the neurons are arranged in groups called layers. Each neuron in a layer operates in logical parallelism. Information is transmitted from one layer to another in serial operations (Hecht- Nielsen 1990). A network can have one or several layers. The basic structure of a network usually consists of three layers the input layer, where the data are introduced to the network; the hidden layer(s), where data are processed; and the output layer, where the results for given inputs are produced (Fig. 2). The most distinctive characteristic of an ANN is its ability to learn from examples. Learning (or training) is defined as self-adjustment of the network weights as a response to changes in the information environment. When a set of inputs is presented, a network adjusts its weights in order to approximate the target output (observed or measured output) based on a certain algorithm. Learning in ANNs consists of three elements weights between neurons that define the relative importance of the inputs, a transfer function that controls the generation of the output from a neuron, and learning laws that describe how the adjustments of the weights are made during training (Caudill 1987). During learning, a neuron receives inputs from the input or previous layer, weights each input with a preassigned value, and combines these weighted inputs. The combination of the weighted inputs is represented as net = wx j ij i where net j = summation of weighted input for the jth neuron; w ij = weight from the ith neuron in the previous layer to the jth neuron in the current layer; and x i = input from the ith to the jth neuron. The net j is either compared to a threshold or passed through a transfer function to determine the level of activation (Fig. 1). If the activation of a neuron is strong enough, it produces an output that is sent as an input to other neurons in the successive layer. The hyperbolic tangent and sigmoid are often employed as transfer functions in the training of networks. In this study, the training of ANNs was accomplished by a back-propagation algorithm. Back-propagation is the most commonly used supervised training algorithm in the multilayer-feedforward networks. In back-propagation networks, information is processed in the forward direction from the input layer to the hidden layer(s) and then to the output layer (Fig. 2). The objective of a back-propagation network is to find the weights that approximate target values of output with a selected accuracy. The least-mean-square-error method, along with the generalized-delta rule, is used to optimize the network weights in back-propagation networks. The gradient-descent method, along with the chain rule of the derivative, is employed to modify the network weights. Detailed information on learning rules and back-propagation is available (Rumelhart et al. 1986; Hecht-Nielsen 1990). Conceptual s Watbal I FIG. 1. Artificial Neuron (x n = nth Input; w nj = Weight from nth Input to jth Neuron in Ith Layer; Net j = Weighted Inputs of jth Neuron; f( ) = Transfer Function; and out j = Output of jth Neuron) FIG. 2. Schematic of Back-Propagation Network The Watbal model is a physically based model used for forecasting water yields in areas where runoff is dominated by snowmelt (Leaf and Brink 1973, 1976; Leaf and Alexander 1975; Markus and Baker 1994). It simulates winter snow accumulation, shortwave and longwave radiation balance, snowpack conditions, snowmelt, evapotranspiration, and subsequent runoff in time and space. Shortwave and longwave radiation represents the energy components available for snowmelt. In the Watbal model, shortwave radiation to snow or the ground surface beneath the forest canopy is controlled by a transmissivity coefficient, which varies with forest cover characteristics. The incident shortwave radiation as measured on a horizontal surface is adjusted based on the slope and aspect of each hydrologic response unit. Longwave radiation is computed by the Stefan- Boltzmann equation (Leaf and Brink 1973, 1975). Snowpack reflectivity varies with precipitation form, air temperature, and the energy balance. During the winter months, temperatures within the snow cover are simulated using the unsteady heat flow theory. The snowpack will yield snowmelt only when it becomes isothermal at 0 C, and its free water holding capacity is reached. Evapotranspiration is derived from the Hamon equation (Leaf and Brink 1973, 1975) for potential evapotranspiration reduced in proportion to the radiation actually received. The soil water content is computed for each time increment. The critical point, at which the soil water content begins to limit evapotranspiration, varies with time and forest tree species. Forest cover density plays an important role in the simulation model. It is the major descriptive parameter of the form, structure, and arrangement of forest stands, and therefore controls the energy balance, interception, and evapotranspiration. Reflectivity is described as a function of the forest stand reflectivity, forest opening reflectivity, and natural forest cover JOURNAL OF HYDROLOGIC ENGINEERING / APRIL 2000 / 157

3 density. Interception is given as a function of forest cover. The combined evaporation from snow surfaces and intercepted snow is a function of potential evapotranspiration, intermediate forest cover density, and forest cover density. Many other processes, such as snow redistribution, tree cutting, groundwater flow, etc., that are significant factors influencing runoff are also modeled in the Watbal model. SAC-SMA The SAC-SMA model is a conceptually based, lumped, rainfall-runoff model that represents spatially heterogeneous runoff processes for river basins at scales ranging from a few hundred to thousands of square kilometers. The SAC-SMA model is an operational rainfall-runoff model that is used in the National Weather Service river forecast system ( United States 1972). The model has six soil moisture states and 16 parameters, not counting the 12 monthly adjustment factors of potential evaporation. Most of the parameters have to be calibrated using historical hydrometeorological data. In this model, the watershed consists of two areas a pervious area that produces runoff only when precipitation exceeds a specific amount, and an impervious area that produces runoff regardless of the amount of precipitation. In pervious areas, the soil profile is divided into two vertical zones an upper zone and a lower zone. The upper zone represents the amount of water held in the interception and upper-soil layer, and the lower zone represents the amount of water retained in the lower zone and ground-water storage. Both zones are divided into two types of storage- tension water and free water storage. Tension water represents the field capacity, which is the amount of water held in the soil zones due to binding with soil particles. Once the tension water is satisfied, water starts accumulating in free water storage, and from there it moves either laterally or vertically. In the upper zone, free water moves laterally to the streams as interflow and vertically to the lower zone as percolation. The free water from the lower zone either constitutes the base flow or feeds to the groundwater storage. SCRR The conceptual rainfall-runoff model, SCRR, that was developed by McCuen and Snyder has three storage components surface, ground water, and the unsaturated zone (McCuen and Snyder 1986). The rainfall first enters to the surface and ground-water systems depending on the model parameter that defines the fraction of infiltrated water into the ground. Water that enters to the surface storage contributes to the stream systems using a unit hydrograph with a time base of four time intervals. The unit hydrograph ordinates are based on a model parameter that distributes the surface runoff. The schematic of the model is presented in Fig. 3. Daily precipitation, air temperature, and streamflow data are employed for the calibration of the model. The objectives are to approximate a combination of the following: total measured runoff, peak discharges, timing of peak discharges, soil moisture state at the beginning of the record, recession of the storm events, and bias in the flow during dry periods. Since there are multiple objective functions, the calibration can be accomplished by the subjective optimization technique. CASE STUDIES The numerical algorithm based on ANNs was applied to three watersheds in the continental United States (Table 1). Historical measurements of precipitation (P), temperature (T), snow-water equivalent (SWE), and stream discharge (Q) are available for the Fraser River, the Raccoon River, and the Little Patuxent River watersheds. Fraser River The ANN technique was used to develop a one-step, monthly flow forecast model for the Fraser River in central Colorado. The Fraser River is a mountainous, subalpine river, with steep slopes, coniferous vegetation, and large snowpack accumulation in wintertime. The discharge of the Fraser River is dominated by snowmelt in the late spring and early summer. The Fraser River flows into the Colorado Big Thompson reservoir system. Therefore, timely and accurate forecasts of monthly river volumes result in significant economic benefits. In the Fraser River watershed, data are available for the periods of and In calibration of the ANN and Watbal models, only data for high-flow months, May, June, and July, were employed. The Watbal model was calibrated using the data for the entire record, and tested using data for the period from 1981 to 1983 and However, the ANN model was trained using only data extending from 1951 to 1980, and then tested for the period from 1981 to 1983 and A standard back-propagation algorithm and the sigmoid transfer function were applied in training of the networks. A one-hidden-layer network with two hidden neurons was used, and the number of iterations for the training varied from several hundred to several thousand, depending on the particular month. The watershed runoff was modeled as follows using ANN: Q(t)=f{Q(t 1), P(t 1), SWE(t 1), SWE(t 2), T(t 1)} where Q(t) and Q(t 1) = streamflows at times t and t 1, respectively; P(t 1) = precipitation at time t 1; SWE(t 1), SWE(t 2) = snow water equivalents at times t 1 and t 2, respectively; T(t 1) = air temperature at time t 1; General Information for Basins Used in Case Stud- TABLE 1. ies FIG. 3. Flowchart for Simple Conceptual Rainfall-Runoff, SCRR (McCuen and Snyder 1986) Parameter Station Fraser River Near Granby, Middle Raccoon River Little Patuxent River Near Bayard, Colo. Iowa Latitude Longitude Drainage area (km 2 ) Mean annual discharge (m 3 /s) Period of record Near Guilford, Md. 158 / JOURNAL OF HYDROLOGIC ENGINEERING / APRIL 2000

4 and t = one month. The testing results for the ANN and Watbal models are presented in Table 2. The ANN model provided higher streamflow forecast accuracy compared to the forecasts of the Watbal model for highflow months based on the ratio of root-mean-square error (S e ) to the standard deviation of the observed data (S y ), and coefficient of determination (square of the correlation coefficient) between the predicted and observed discharges ( ). The ratio of for testing the ANN model was significantly lower for May and July, and about the same for June, as illustrated in Table 2. These results indicate that the ANN model has a higher accuracy than that of the Watbal model for forecasting monthly streamflows in the Fraser River, despite the fact that the testing data set was included in the calibration of the Watbal model. The ANN model is also simpler, and takes less time to calibrate compared to the Watbal model. Middle Raccoon River Various ANN models were trained to simulate daily rainfallrunoff relationships for the Raccoon River near Bayard, Iowa. The loss of life and property in this region due to the Great Flood of 1993 led to a need for improved predictions to support flood/drought management and damage mitigation ( The Great 1994). The SAC-SMA model is currently used by the National Weather Service for rainfall-runoff calibration and operational forecasting ( National 1996). The calibration accuracy of the ANN was compared to the calibration accuracy of the SAC-SMA model. In this study, four different ANNs were trained using the back-propagation algorithm. In training of networks, the hyperbolic tangent was used as an activation function. The networks were trained and tested using NeuralWorks software (Professional 1993). A one-hidden-layer network was used for training of each model. The number of neurons in the hidden layer was 10 for models 1 3 and 25 for model 4. The ANN architecture for each model was determined by a trial-anderror process. The models are represented by (6) Q(t) =f{p(t 1), P(t 2), P(t 3), T(t)} Q(t) =f{p(t), P(t 1), P(t 2), P(t 3), T(t)} Q(t) =f{p(t), P(t 1), P(t 2), P(t 3), P(t 4), T(t)} Q(t) =f{p(t 1), P(t 2), P(t 3), T(t), Q(t 1)} (6) where Q(t) = streamflow at time t; P(t 1) = precipitation at time t 1; and T(t) = temperature at time t; note that t is in days. The calibration period for both the ANN and the SAC- SMA extends from 1978 to The results are presented for the entire calibration period and for average-, dry-, and wet-year data sets, separately shown in Tables 3 and 4. 4 has a slightly lower S e to S y ratio, about 0.40, when compared to the SAC-SMA model. s 1 3 had higher S e to S y ratios, ranging from 0.64 to 0.67, compared to both model 4 and the SAC-SMA model. As shown in Table 3, the SAC-SMA model reproduced observed standard deviation fairly well, while the ANN models provided less variation of streamflow values. The SAC-SMA model underestimated the minimum and maximum streamflows in the record, at about 69% and 11% of their observed values, respectively. While the ANN models closely approximated the maximum streamflow in the record, they significantly overestimated the low flow values. A poor performance of the ANNs in forecasting low flows is consistent with the results reported in recent literature (Tokar 1996; Markus 1997). The sensitivity of model training accuracy to the content of data was assessed using three data sets within the training data. TABLE 2. Statistical Indices for Testing ANN and Watbal s Developed Using Monthly Streamflow in Fraser River, Colo. May June (6) July (7) (8) (9) Watbal ANN observed discharge, respectively. represents coefficient of determination TABLE 3. Statistical Indices for Calibration of ANN and SAC- SMA s for Middle Raccoon River, Iowa S y S e Observed SAC-SMA observed discharge, respectively. represents coefficient of determination TABLE 4. Statistical Indices for Training, Dry, and Wet Years Using ANN and SAC-SMA for Middle Raccoon River, Iowa Dry (6) Wet (7) SAC-SMA observed discharge, respectively. represents coefficient of determination Three years were selected based on the mean annual daily discharge values average, dry, and wet years. As illustrated in Table 4, the SAC-SMA model provided slightly higher accuracy for the average year compared to the ANN models. However, the SAC-SMA and models 1 3, with high S e to S y ratios, fail to approximate the dry-year data as well as model 4. In addition, model 4 provided the lowest S e to S y ratio for the wet year. As shown in Table 4, model 4 also had the highest accuracy for the three years compared to the SAC-SMA and models 1 3. These results are explained by the addition of Q(t 1). In model 4, the values of Q(t 1) provided information that was not contained in precipitation and temperature. Little Patuxent River The Little Patuxent River is located in Maryland. It is a rainfall-dominated stream exhibiting the behavior of a stable ground-water and perennial runoff stream type (Poff et al. 1996). The streamflow regime in the Little Patuxent River consists of high flows from December to May. The highest precipitation variations are observed during the dry months, June through September, that are characterized by flash flood events. The ANN technique was used to model daily rainfallrunoff in the watershed. Networks defined by various combinations of rainfall, temperature, and discharge at present and JOURNAL OF HYDROLOGIC ENGINEERING / APRIL 2000 / 159

5 TABLE 5. Statistical Indices for Training and Testing Using ANN and SCRR s for Little Patuxent River, Md. Training Testing Training Testing ANN SCRR model observed discharge, respectively. represents coefficient of determination TABLE 6. Statistical Indices for Training and Testing, Dry, and Wet Years Using ANN ( 4) and SCRR s for Little Patuxent River Watershed, Md. Parameter Wet Training Dry (a) SCRR Wet Testing Dry (6) (7) (b) ANN observed discharge, respectively. represents coefficient of determination previous time periods were trained and tested to simulate streamflow using different ANN configurations. Based on average precipitation, three data sets representing average, wet, and dry years were selected for training and testing in order to identify the rainfall-runoff behavior in the Little Patuxent River watershed. For training of the networks, 1979, 1980, and 1984 were selected as the wet, dry, and average years. Similarly for testing, 1989, 1991, and 1992 were chosen as the wet, dry, and average years. The testing data were not directly used in the training; however, in order to avoid overtraining of the networks, networks were tested using a test set. For different combinations of the input variables, networks were trained using a one-hidden-layer network (Tokar 1996). The training of networks was accomplished using the back-propagation algorithm of NeuralWorks (Professional 1993). The hyperbolic tangent was selected as an activation function in training of the networks. The selection of the best-fit model was accomplished by a trial-and-error process (Tokar 1996). The best-fit model was the network with 10 hidden neurons, and is given below Q(t) =f{p(t), P(t 1), T(t)} (7) where t is in days. The SCRR model for the Little Patuxent River watershed (Tokar 1996) was calibrated under the supervision of R. H. McCuen, who originally developed the SCRR model (McCuen and Snyder 1986). For the conceptual model, the values are 0.66 and 0.67 for calibration and verification, respectively. As indicated in Table 5, the forecast accuracy for SCRR is relatively poor compared to that of the ANN model, with low values of 0.46 and 0.42 for training and testing, respectively. As shown in Table 6, the ANN model provided a significantly higher training accuracy for the average and wet years compared to that of the SCRR, whereas SCRR illustrated better training accuracy for the dry year. However, the ANN model demonstrated significantly higher testing accuracy for the three years. CONCLUSIONS In the literature, the ANN methodology has been reported to provide reasonably good solutions for circumstances having complex systems that may be poorly defined or understood using mathematical equations, problems that deal with noise or involve pattern recognition, and input data that are incomplete and ambiguous by nature. Because of these characteristics, it was believed that ANN could be applied to model precipitation-runoff relationships. The ANN rainfall-runoff models exhibit the ability to extract patterns in the training data. The ANNs were applied to forecast monthly streamflows in the Fraser River basin, and daily streamflows in the Raccoon River basin (calibration only) and the Little Patuxent River basin (calibration and testing). For the Fraser River, the ANN provided more accurate monthly streamflow forecasts than did a physically based model. Similarly, for the Raccoon River, the best-fit ANN model has reasonable calibration accuracy when compared to that of a conceptual model. Such performance is a result of adding the streamflow at t 1 as an input to the ANN model. Finally, in the Little Patuxent River basin, the best-fit ANN model provided higher training and testing accuracy compared to that of the simple conceptual rainfallrunoff model. These examples demonstrated that ANNs can accurately model nonlinear relationships between hydrologic inputs, rainfall, snow water equivalent, temperature, and output streamflow. The ANN models provided a systematic approach and shortened time spent on training of models compared to the conceptual models. Although the models were applied to only three watersheds, the results presented here were encouraging, and demonstrated a high potential for the application of neural networks to various precipitation-runoff modeling scenarios. APPENDIX. REFERENCES Caudill, M. (1987). Neural network primer: Part I. AI Expert, (December), French, M. N., Krajewski, W. F., and Cuykendall, R. R. (1992). Rainfall forecasting in space and time using a neural network. J. Hydro., 137, The Great Flood of (1994). NOAA Natural Disaster Survey Rep., National Weather Service, Office of Hydrology, Silver Spring, Md. Hecht-Nielsen. (1990). Neurocomputing. Addison-Wesley, Reading, Mass. Hsu, K, Gupta, V. 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