Hydrology and Water Resources

Volume 5- Additional Volume International Conference on Water Resources Management in Arid Regions, 23-27 March 2002, Kuwait

M.M. Sherif, V.P. Singh, M. Al-Rashed

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781000151282
• Topic: Physical Sciences
• Subtopic: Hydrology

This is the fifth and last volume representing the proceedings of the International Conference on Water Resources Management in Arid Regions held March 23rd-27th 2002 in Kuwait. This book discusses major aspects of hydrology and water resources. It presents papers on important aspects of surface water and groundwater hydrology, including drought tendencies, regional flood frequency analysis, urban storm drainage with curb-opening inlets, isotopic investigations for lakes, hydrologic and sediment transport modeling, groundwater exploration using remote sensing and GIS, origin and recharge rates of alluvial ground waters, stormwater and groundwater management, and considerations for stochastic finite element in geostatistics and modeling. Papers on water quality supplement the discussion.

Section 1: Surface water hydrology

An ANN model for estimation of potential evaporation

Avinash Agarwal and R.P. Pandey
National Institute of Hydrology
Roorkee 247 667, Uttaranchal, India
e-mail: [email protected]

V.P. Singh
Department of Civil and Environmental Engineering
Louisiana State University
Baton Rouge, La 70803-6405
e-mail: [email protected]

Abstract

A back propagation artificial neural network (ANN) Model is introduced for estimation of potential evaporation from free water surface of a lake in Hoshangabad district located in a semi-arid region of India, and the results are compared with the conceptual Penman, Kohler, and Van-Bavel-Businger models and a multiregression model. This has a three-layered network with the number of nodes in the hidden layer approximately twice the input nodes and one node in the output layer. For application, the available data were normalized by the maximum value of the variable. The learning parameters (learning rate, and momentum term) were found to exhibit a decreasing trend with increasing number of iterations. In the estimation of the potential evaporation, the Kohler method performed better than both the Penman and Van-Bavel methods for all values of pan coefficients taken as 0.6, 0.7, and 0.8, the Kohler method performed the best for a pan coefficient value equal to 0.7, and the multi-input regression model was superior to the Kohler method. Based on the criteria (Nash and Sutcliffe, 1970) of mean absolute deviation (MAD), mean square error (MSE), correlation coefficient (CC), coefficient of efficiency (CE), and volumetric efficiency (EV), the ANN model performed better than the Kohler and regression methods.

Introduction

There exists an ample amount of literature on estimation of potential evaporation. The studies of Antal et. al. (1973), Keijman and Koopmans (1973), Ficke (1972), Harbeck (1962), Winter (1981), etc. reported in WMO (1973) are a few among many others. Using the data of lake Balaton in Hungary, Antal et. al. (1973) compared five evaporation methods and found the monthly evaporation values to differ by 10–15 percent from the computed average values, whereas annual values showed a deviation of 5 percent from the mean value. While comparing energy budget, mass transfer, and pan coefficient methods using data of lakes in the Netherlands, Keijman et. al. (1973) reported a 6–8 percent standard error for all the methods, except for the Pan coefficient method for which the error was about 20 percent. According to Ficke (1972), the energy budget estimate yields lower evaporation rates than those due to other methods during spring and autumn seasons, and higher during the summer season because of less reliable short-term energy budget data compared to mass transfer data.

It is of common experience that the rate of potential evaporation from a pan is greater than that from a large water body, leading to the use of a suitable pan coefficient for computation of the actual pan evaporation. For further detail, the works of Kohler (1955) and Blaney (1962) are worth citing. The studies conducted in India also indicate a considerable variation of pan to lake coefficients with space and time, approximately in the range of 0.6–0.9 (Ramdas, 1957; Sarma, 1973; Ramasastri, 1987; and others).

The reliable estimation of potential evaporation requires a detailed instrumentation along with a judicious selection of a model that suits climatic and physical data. The annual evaporation losses from Indian reservoirs in arid and semi-arid areas vary from 1.5 m to 3.0 m (CWC, 1988). The energy budget methods that may provide better estimates require extensive instrumentation and frequent surveys of the water body, which is an expensive undertaking. The pan evaporation does not represent the potential evaporation due to the phase difference in storage of heat due to solar radiation in pans and lakes and uses a pan- and site-specific pan coefficient. Thus, there exists a great deal of uncertainty in estimation of potential evaporation. Therefore, the objective of present study is to (a) introduce an ANN model requiring less amount of data; (b) compare its performance with the popular, conceptual Penman (1963), Kohler (Kohler et al., 1955), and Van-Bavel-Businger (1966) and multi-input regression models; and (c) investigate the ANN model performance for varying data lengths.

ANN Model

The multi-layer feed forward ANN is a layered parallel processing system consisting of input, output, and hidden layer(s). There are many processing elements in each layer called nodes and these are connected by links of different weights. The number of nodes in input and output layers corresponds to the number of input and output variables of the model. Though there exists no specific guidelines for fixing the number of nodes in hidden layer(s), the optimum number depends on the complexity of the modeling problem (Vemuri, 1992). A three-layer ANN consisting of layers j, i, and k with number of nodes in j as: j=1 to jj, in i as: i =1 to ii, and in k as: k=1 to kk along with the interconnecting weights W_ij and W _ki are shown in Figure 1. Here, ii, jj, and kk are integer values.

Computations in the back propagation scheme are based on gradient descent optimization technique and consists of feed forward and error back calculations (Rumelhart et al., 1986). In feed forward computations, nodes in the input layer j receive the data (input vector), and each neuron in layer i and k receives the weighted sum of output from the previous layer as input through an activation function. Expressed mathematically, the feed forward computation for layer i can be given as:

Figure 1. Structure and notations in a multi-layer artificial neural network model.

where net_(i) is the net input to the i^th node, W_(ij) is the interconnecting weight, O_(j) is the output of the j^th node, O_(i) is the output of the i^th node, and f[.] is a differentiable non-linear activation function.

Using the back gradient descent method, the error calculated in the output is propagated in the negative direction of the error function to hidden layer(s) and finally to the input layer to update weights of interconnection. At the outset of training, weights are randomly assigned and these are updated by moving in the direction of negative gradient along the multi dimensional surface of error/energy function (E):

where d_(k) is the observed output of the k^th node of the output layer and O_(k) is the estimated output at the k^th node of the output layer. The change in weights (ΔW_(ij)) with learning rate α in the direction of negative gradient is given as:

The weights at each iteration ‘it’ are updated as (Rumelhart et al., 1986):

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Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• Section 1: Surface water hydrology
• Section 2: Groundwater hydrology
• Section 3: Groundwater quality
• Section 4: Ecological modeling
• Section 5: Water resources development and management
• Author index