DAILY RAINFALL-RUNOFF MODELING USING ARTIFICIAL NEURAL NETWORK

Abstract

The models developed to simulate the rainfall-runoff process can be broadly grouped under three categories, with increasing order of complexities involved as: i) empirical; ii) conceptual; and iii) physically based distributed models. The first category of models, namely the empirical models treat the hydrologic system (e.g. a catchment) as a black box and try to find relationship between historical inputs and the outputs without considering the physical laws operating Within it. The conceptual models, on the other hand, attempt to represent the known physical process occurring in the rainfall-runoff transformation in a simplified manner by way of linear/nonlinear mathematical formulations. The third category of models i.e. the physically based models, are too complex, data intensive and cumbersome to use. Typically, they involve solution of partial differential equations that represent the flow processes within the catchment. The kind of data required for use of the physically based distributed models is rarely available, even in the heavily instrumented research catchments. The physically based models and the conceptual models generally involve use of a number of parameters many of which are difficult to ascertain for catchments from different geographical and climatic regions. Even though many types of models are presently available for representing rainfall-runoff process, the problem still remains unresolved and it is perhaps for this reason that the alternative modeling approaches are still being sought. The system theoretic modeling approach has been added with a new dimension through adoption of the Artificial Neural Network (ANN) technique in rainfall-runoff modeling. Many studies utilizing ANNs are reported in literature because they possess desirable attributes of universal approximation and have the ability to learn from examples without the need for explicit physics. An ANN is a massively parallel distributed information processing system, capable of learning any nonlinear relationship and because of which it has emerged as a viable tool for the simulation and control of complicated, nonlinear dynamic systems. Different types of ANN structures are developed for solving various types of problems. The rainfall-runoff modeling using. ANNs would have to be classified as the empirical modeling. The application of the ANN for rainfall-runoff modeling on various time scales has been carried out by many researchers. In most of these studies, the ANN was used as an independent model and results obtained through its application were compared with those produced by the conventional models. In these studies the inputs to the ANN consisted of combinations of variable like current and antecedent rainfall and runoff values, temperature, snowmelt etc. It is very well established from these studies that, the rainfall information alone is not sufficient to estimate the runoff accurately from a catchment, as the state of the catchment i. e. the antecedent soil moisture condition in a catchment plays an important role in determining the amount of runoff generated from the given rainfall. While, it is well established that the inclusion of the recently observed discharges with the current and antecedent rainfalls as inputs to the ANN greatly enhances the forecasting ability of the neural networks in the updating case, the present study investigates whether good estimates of observed discharges enhance the flow simulation efficiency in the non-updating case. The inclusion of discharges observed in the past as input to the ANN based rainfall-runoff models makes it difficult to treat these models as cause-and-effect models. Such models are useful in forecasting problems but are not so useful in conceptualizing the catchment. The objective of the present study is to propose a modeling approach, which combines the linear/nonlinear models with the ANN so as to overcome the difficulties cited above, and explore the application of the neural networks for the non-updating flow simulation. The ANN model is therefore coupled with the system theoretic linear/nonlinear models such that output from these models forms an input to the ANN. The present study presents the ANN as a flexible nonlinear rainfall-runoff black box model, which is useful in sparse data scenario for the non-updating simulation of discharge from rainfall, using daily data for the case of isolated runoff events. An attempt is made to incorporate, as far as possible; the understanding of the physical process of runoff generation over a catchment in the ANN based rainfall-runoff modeling. The study also provides a viable alternative for the discharges observed in the past time periods, being used as one of the inputs to the ANN in most of the existing studies. A methodology is developed using the ANN for rainfall-runoff modeling over a catchment when the hydrologic applications require that the runoff be predicted with the help of rainfall information alone and without much understanding of the hydrologic dynamics of the catchment being investigated. The capability and effectiveness of the proposed methodology in sparse data scenarios is demonstrated. The daily rainfall and ii runoff data from seven catchments located in different parts of the world, two of which are relatively large in size, are used in the present study. These catchments are i) Bird Creek (USA), ii) Brosna (Ireland), iii) Garrapatas (Colombia), iv) Kizu (Japan), v) Pampanga (Philippines), vi) Krishna (India), and vi) Narmada (India). Daily runoff and the corresponding rainfall data of the runoff events that occurred during the flood period only are modeled in the study as during flood period (monsoon season) high flows are experienced and modeling of which is important for flood forecasting, design and operation of water resources structures etc. The consideration of losses due to evaporation and evapotranspiration is important as the rainfall-runoff modeling carried out is on daily scale and the runoff events are spread over several days. The observed rainfall subtracted with the losses due to evaporation and evapotranspiration is called here as the Effective Rainfall, which is the actual rainfall that is contributing into the process of runoff generation over any catchment. Determination of the catchment memory length is the critical part of the system based rainfall-runoff modeling in which current and antecedent rainfall values are used as input. The memory of a catchment is determined adopting the two-step procedure consisting of i) correlation analysis, and ii) determination of ordinates of response function of the catchment. Appropriate linear/nonlinear model depending upon the size of the catchment is employed for determining the response function ordinates. The method of least squares and the smoothed least squares method are used in deriving the response functions for the different catchments. Two of the catchments being relatively large in size involve sub-divisions into smaller hydrologically homogeneous areas to account for the heterogeneity in the spatial distribution of rainfall. The application of the neural networks in case of large size catchments in the context of incorporating the distributed nature of input, i.e. the areal disaggregation of the rainfall is also demonstrated in the present study. An ANN model based on a feedforward neural network; with the logistic sigmoid function as the transfer function, and single hidden layer is used for modeling the daily rainfall-runoff relationship. The application of the three layer feedforward ANN is specifically made to account for the non-linearity present in the rainfall-runoff process. The non-linearity of the runoff distribution over all the catchment is verified by using the measure of non-linearity introduced by Rogers, known as the Standardized Peak iii Discharge Distribution (SPDD). The ANN application involves two different input combinations: Case-I: Only the output of the linear/nonlinear model computed through the convolution of the derived response functions with the current and antecedent rainfalls is given as input to the ANN. Case-II: The current and antecedent rainfall values for the length equal to memory of the catchment are also supplied as input to the ANN in addition to the input used in Case-I. The output of the system based linear model is denoted by RIL and that of a nonlinear model by RIN. The total number of runoff events identified in a catchment are divided into two sets. About 70% of the data is used in training and the remaining values of the data (approximately 30% of data) are used as the testing set. A data normalization procedure is adopted before presenting the data to the ANN because, the logistic sigmoid used as the transfer function for neurons in the hidden and the output layers has bounded output range in the interval [0, 1]. The backpropagation algorithm involving a forward and the backward pass is used for training the network. The TRAINGDX function in M_ATLAB routines, which works on gradient descent method and uses the adaptive learning and momentum parameter, is used for training. The various input combinations to the ANN consisted of (i) Only rainfall (P); (ii) Output of linear model (RIL); (iii) Output of the nonlinear model (RN); (iv) P in combination with RIL; (v) P in combination with RIN; and (vi) P in combination with runoff observed in the previous time period (Q/./). The ANN with these different inputs is applied to each of the catchment. It was ensured that the trial and error process of training the ANN leads to an optimal network configuration having the best possible performance without the network getting overtrained. The performance of the models applied in the present study (the linear/nonlinear and the ANN models) is evaluated based on the various statistical and graphical criteria, which are indicative of the model performance. The results obtained demonstrate that the proposed alternative for discharges observed in the past in the form of the output of the linear/nonlinear models provides better system theoretical representation of the rainfall-runoff relationship on catchments from different parts of the world investigated in the study. The results of the ANN model application in case of large size catchments prove that it is worthwhile to consider separate iv inputs into the sub-catchments (to a point) in order to improve the model efficiency. The input scenarios of P in combination with RIL or RIN are clearly superior to the RIL alone or RIN alone input scenario. Replacing the linear model with a nonlinear model did not result in any substantial improvement in the final results of the ANN, thus validating the claim that ANN completely takes care of the non-linearity existing in the rainfall-runoff relationship. The coupled SLM - ANN model with input scenario involving P in combination with RI is capable of producing reasonably satisfactory non-updated estimates of the outflows on most of the catchments. The response functions obtained for different catchments studied have physically realistic shapes. Parameterization of these response functions by using the discrete gamma function leads to the establishment of relations, albeit qualitatively, between these parameters and the catchment characteristics. So the proposed approach can possibly be extended to the catchments for which the gauge and discharge records are nonexistent. The ANNs trained on similar catchments can possibly be used for predicting the runoff over an ungauged catchment as the response function derived as above when convoluted with current and antecedent rainfalls in an ungauged catchment results in the estimates of runoff from a system based model which forms the input to a trained ANN as both are coupled. However, application of the proposed approach for runoff estimation could not . be tested in an ungauged catchment in the present study because of non-availability of elaborate da