Multitemporal Scale Hydrograph Prediction Using Artificial Neural Networks

An artificial neural network (ANN) provides a mathematically flexible structure to identify complex nonlinear relationship between inputs and outputs. A multilayer perceptron ANN technique with an error back propagation algorithm was applied to a multitime-scale prediction of the stage of a hydrologically closed lake, Devils Lake (DL), and discharge of the Red River of the North at Grand Forks station (RR-GF) in North Dakota. The modeling exercise used 1 year (2002), 5 years (1998-2002), and 27 years (1975-2002) of data for the daily, weekly, and monthly predictions, respectively. The hydrometeorological data (precipitations P(t), P(t-1), P(t-2), P(t-3), antecedent runoff/lake stage R(t-1), and air temperature T(t)) were partitioned for training and for testing to predict the current hydrograph at the selected DL and RR-GF stations. Performance of ANN was evaluated using three combinations of daily datasets (Input I = P(t), P(t-1), P(t-2), P(t-3), T(t) and R(t-1); Input II = Input-I less P(t), P(t-1), P(t-2), P(t-3); and Input III = Input-II less T(t)). Comparison of the model output using Input I data with the observed values showed average testing prediction efficiency (E) of 86 percent for DL basin and 46 percent for RR-GF basin, and higher efficiency for the daily than monthly simulations. (KEY TERMS: artificial neural network; Devils Lake; Red River; flood forecasting; lake stage prediction; temporal scale.) Melesse, Assefa M. and Xixi Wang, 2006. Multitemporal Scale Hydrograph Prediction Using Artificial Neural Networks. Journal of the American Water Resources Association (JAWRA) 42(6):1647-1657. INTRODUCTION Artificial Neural Networks Neural networks, expert systems and fuzzy logic are the three branches of artificial intelligence. An artificial neural network (ANN) is a nonparametric attempt to model the human brain that uses machine learning based on the concept of self-adjustment of internal control parameters. Artificial neural networks are flexible mathematical structures that are capable of identifying complex nonlinear relationships between input and output datasets. The main differences between the different types of ANNs are arrangement of neurodes (network architecture) and the many ways to determine the weights and functions for inputs and neurodes (training) (Caudill and Butler, 1992). Training in ANN refers to pattern recognition using weight estimation and transfer function. The multilayer perceptron (MLP) neural network was designed to function well in nonlinear phenomena. A perceptron is a connected network that simulates an associative memory. The most basic perceptron is composed of an input layer and output layer of nodes, each of which is fully connected to the other. The multilayer in MLP refers to the use of the input, hidden, and output layers in the ANN analysis. A feed forward MLP network consists of an input layer, an output layer, and one or more hidden layers between them. Each layer has some number of neurons on it, input layers with input neurons and output layers with output neurons. 1Paper No. 05098 of the Journal of the American Water Resources Association (JAWRA) (Copyright © 2006). Discussions are open until June 1, 2007. 2Respectively, Assistant Professor, Department of Environmental Studies, ECS 339, Florida International University, 11200 SW 8th Street, Miami, Florida 33199 (formerly at Upper Midwest Aerospace Consortium, University of North Dakota, Grand Forks, North Dakota); and Research Scientist, Environmental and Energy Research Center, University of North Dakota 15 North 23rd Street, Grand Forks, North Dakota 58202-9018 (E-Mail/Melesse: [email protected]). JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1647 JAWRA JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION DECEMBER AMERICAN WATER RESOURCES ASSOCIATION 2006 MULTITEMPORAL SCALE HYDROGRAPH PREDICTION USING ARTIFICIAL NEURAL NETWORKS1 Assefa M. Melesse and Xixi Wang2 A typical ANN architecture is shown in Figure 1. The artificial neuron receives a set of inputs or signals (x), calculates a weighted average of them (z) using the summation function and weights (w) and then uses some activation function (f) to produce an output (y), where The connections between the input layer and the middle or hidden layer contain weights, which are usually determined through training the system. The hidden layer sums the weighted inputs and uses the transfer function to create an output value. The transfer function (local memory) is a relationship between the internal activation level of the neuron (activation function) and the outputs. A commonly used typical transfer function is the sigmoid function, Equation (2), which varies from 0 to 1 for a range of inputs (Caudill and Butler, 1992). A function f(x) will be a sigmoid function if it is bounded and if its value always increases as x increases (Smith, 1993). A number of different functions have these characteristics and thus qualify as sigmoid functions. The sigmoid logistic nonlinear function is described in Equation (2) and illustrated in Figure 2. In time series prediction, supervised training is used in which the ANN is trained to minimize the difference between the network output and the target (observed). The most common training algorithm used in the ANN literature is called back propagation (BP). One of the basic requirements of the BP training is that the transfer function be continuous and differentiable. The sigmoid logistic nonlinear function explained above fulfills the requirement, making the implementation of BP easier.