Keywords: Rainfall, runoff, RBF, ANN, model 5, watershed.

Transcription

1 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January 15 Assessing Runoff from Small Watershed with Data Driven Model A. D. Pundlik 1, S. M. Taley and M. U. Kale 3 * Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola Abstract: Radial Basis Function ANN models with Levenberg-Marquardt (L-M) and momentum algorithm were formulated to predict runoff from watershed. Best architecture of RBF ANN model to predict runoff from watershed was investigated on the basis of statistical performance. The model 5 (5-1-1) and model 5 (5-5-1) predicted runoff with accuracy, in terms of Nash-Sutcliffe coefficient of efficiency and persistence index for sowing along slope cultivation with opening of tide furrows (T1), contour cultivation with opening of alternate furrow (T) and contour cultivation with opening of ridge and furrow (T3), respectively. Therefore these models having inputs as current day rainfall, one day ahead rainfall, two day ahead rainfall, one day ahead runoff, two day ahead runoff should be used to predict simulated runoff from watershed for all three treatments. The study also confirmed that the number of processing elements in hidden layer and epochs did not have any consistent impact on the performance of RBF ANN models. Thus it is concluded that number of nodes in the hidden layer and epochs during training should be optimized by trial and error method. Keywords: Rainfall, runoff, RBF, ANN, model 5, watershed. I. INTRODUCTION Rainfall-runoff (R-R) relationship is one of the most complex hydrologic phenomena to comprehend due to the tremendous spatial and temporal variability of watershed characteristics and precipitation patterns, and the number of variables involved in the modelling of the physical processes. Various models were developed by the researchers to describe R-R relationship. Most of these models work best when data on the physical characteristics of the watershed are available at the model grid scale (Line et al., 1997; Colby, 1; Miller et al., ). This kind of data is rarely available, even in heavily instrumented research watersheds. One of the most widely used techniques for estimating direct runoff depths from storm rainfall is the United States Department of Agriculture (USDA) Soil Conservation Service s (SCS) curve number (CN) method. However, it requires a detailed knowledge of several important properties of the watershed which may not be readily available. The complexity and non-linearity involved in R-R process and routing of runoff downstream through a channel make it attractive to try data driven approach for R-R modeling. The artificial neural network (ANN), a data driven model, is inherently suited to the problems that are mathematically difficult to describe. Majority of studies in the past have proved that the ANNs are capable of performing quite satisfactorily in R-R modeling (Solaimani, 9; Bhola and Singh, 1; EI-shafie, 11). Due to acceptable performance in R-R modeling, ANN remains a topic of continuing interest. Artificial Neural Networks are a form of computing inspired by the functioning of the brain and nervous system and are discussed in detail in a number of hydrological papers (Minns and Hall, 1996; ASCE, a, b; Maier and Dandy, ; Sudheer et al., ; Senthil Kumar et al., 5; Vos and Rientjes, 8; Srinivasulu and Jain, 9). The basic structure of ANN usually consists of three layers: the input layer, where the data are introduced to the network; the hidden layer or layers, where data are processed; and the output layer, where the results of given outputs are produced. The neurons in the layers are interconnected by strength called weights. The incoming data are processed by nonlinear functions at hidden and output layers to get the output. The watershed of Agro-Ecology and Environment Center (AEEC) of Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola was selected for study. The daily rainfall and runoff values for the study area were obtained for three treatments viz. sowing along slope cultivation with opening of tide furrows (T1), contour cultivation with opening of alternate furrow (T) and contour cultivation with opening of ridge and furrow (T3) for the period from to 1. The area under T1, T and T3 is.4,.35 and.34 ha, respectively. The crop on the watershed is cotton. 1 M. Tech Student, Deptt. of SWCE, Dr. PDKV, Akola Head of Department, Deptt. of SWCE, Dr. PDKV, Akola 3 Assistant Professor, Deptt. of IDE, Dr. PDKV, Akola; kale91@gmail.com 195

2 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January 15 Taking into account the spatial and temporal non availability of data on physical process of hydrologic cycle, this study was undertaken aimed to predict runoff using limited commonly available data. II. MATERIAL AND METHODS A. Study area and Data collection The common parameters require for formulation of ANN model are optimum number of hidden layers, number of processing elements in hidden layer, training algorithm, activation function, stop criteria and input parameters. Radial Basis Function (RBF) ANN is mostly used type of ANN in hydrological modeling (Harun et al., 3; Karem et al., 7; Fernando and Shamseldin, 1; Joshi and Patel, 11) and so is adopted in this research to predict runoff. A single hidden layer was used in this study considering the recommendations of Hornik et al. (1989) and Dawson and Wilby (1). As no specific guidelines exist in literature for choosing the optimum number of hidden nodes for a given problem, this network parameter was optimized using trial and error procedure. Among various algorithms reported in literature Levenberg-Marquardt (L-M) algorithm is much more robust and outperformed other algorithms (e.g. variable learning rate and momentum (BPvm), Resilient Back Propagation (RBP), Polak-Ribiere etc.) in terms of accuracy and convergence speed (Vos and Rientjes, 5b; Solaimani, 9). Levenberg-Marquardt (L-M) algorithm was, therefore, chosen for modeling application in this research. Also momentum algorithm was selected for judging its ability to predict runoff. In literature, most commonly used transfer functions for R-R modeling are sigmoidal type transfer functions in hidden layers and linear transfer functions in output layer due to its advantage in extrapolation beyond the range of training data (Zealand et al., 1999; Calvoa and Portelab, 7). Therefore, these transfer functions are used in this study. The use of early stopping (split sampling method) approach reduced training time four times and provides better and more reliable generalization performance than use of L-M algorithm alone (Coulibaly et al. ). Considering advantages of early stopping approach, it was used in this research work. A so-called batch training approach was used for training ANNs i.e. the whole training data set is presented once, after which the weights and biases are updated according to the average error. B. Brief information of model In ANN modeling, choice of input variables is an important issue. There is no general theory to choose input parameters to ANN model, rather it is problem dependent. Generally, trial and error procedure is used to finalize the input variables to ANN model. As hydrological state (i.e. amount and distribution of stored water in catchment) for a great part determines catchment s response to a rainfall event, it is critical as input to ANN model. Previous discharge values are therefore often used as ANN inputs, since these are indirectly indicative for hydrological state (ASCE, ). Based on this line of work, five models were formulated as follows using current and previous days rainfall as well as runoff as inputs and desirable output is one-day later runoff. Model 1 R t+1 = f((p t, )(R t )).. (1) Model R t+1 = f((p t, P t-1 )(R t )).. () Model 3 R t+1 = f((p t, P t-1 )(R t, R t-1 )).. (3) Model 4 R t+1 = f(( P t- )(R t, R t-1 )).. (4) Model 5 R t+1 = f(( P t- )(R t, R t-1, R t- )).. (5) Where, P t = Current day rainfall; P t-n = Rainfall of n th days before current day; R t = Current day runoff; R t-n = runoff n days before current day; R t+1 = One day later runoff; t = Current day; n = 1,, 3.. N th day; The performance of these formulated models was tested with Levenberg Marquardt algorithm at 1 epochs. The best ANN model, in terms of statistical parameters, among these formulated models, was tested with Momentum algorithm for 5, 1,, 5 and 3 epochs by varying nodes (1-1) in the hidden layer. The best ANN model found for treatment T1 was further tested for treatment T and T3 by varying 1-1 nodes in the hidden layer. 196

3 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January 15 C. Calibration and validation of ANN model The available data was split into three separate data sets: (1) training set, () cross-validation set, and (3) validation set. These data sets were then used for respective operation. The size of training, cross validation and testing set was (6%), (%) and (%) exemplars, respectively. The ANN model implementation was carried out using Neuro Solutions for Excel version V. D. Model performance Nash-Sutcliffe coefficient was used as performance indicator along with Persistence Index, a dimensionless statistical performance criterion. While during training and cross validation the software uses mean squared error, a built in statistical performance criterion. These performance measures are described below. a) Nash-Sutcliffe coefficient of efficiency Nash-Sutcliffe coefficient of efficiency ( R ) is used to assess predictive power of hydrological models (Nash and Sutcliffe, 197). R NS = 1 - R NS is described by following relationship (Q -Q ) o s (Q -Q ) o av Where, Q o = observed runoff; Q s = simulated runoff; and Q av = mean of observed runoff. NS.. (6) b) Persistence index Persistence index (PI) was generally used to evaluate the performance of model (Kitanidis and Bras, 198). PI index is especially useful when previous discharge values are used as input to ANN model since it evaluates model in comparison to a persistence model, which is a model that presents the last observation as a prediction (Anctil et al., 4b; Vos and Rientjes, 5b). PI = 1- N k=1 N k=1 (Q - Q ) O P (Q - Q ) O O-1 where, Q = discharge at time k; O Q = discharge at time k-1; and Q O-1 P = predicted discharge.. (7) c) Mean Square Error MSE is measures the averages of squares of error. It is risk function, corresponding to the expected value of the squared error loss or quadratic loss.mse was calculated by using following equation MSE= where, N = number of observations, P i =simulated runoff, = observed runoff Qi.. (8) III. RESULTS AND DISCUSSION A. Performance of formulated ANN models For real time prediction of runoff, one day ahead forecast of runoff from watershed was chosen and accordingly five RBF ANN models were formulated with varying input parameters. Accurate forecast of runoff in monsoon season (June to September) is of particular interest. The best ANN architecture for each of all models were determined and presented in Table 1 197

4 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January 15 Table.1 Statistical evaluation of best neural network architecture of each ANN model on test data set for treatment T1 Model No. Particular ANN architecture 1/1/1 /5/1 3//1 4/4/1 5/1/1 5/5/1 5//1 5/5/1 5/8/1 5/9/1 Inputs P t P t, R t P t, P t-1, R t P t, P t-1, R t, R t-1 P t-, R t, R t- 1 P t-, R t, R t-1 P t-, R t, R t-1 P t-, R t, R t-1 P t-, R t, R t-1 Input layer Hidden layer Output layer Nodes in hidden layer Epochs P t-, R t, R t-1 Algorithm LM LM LM LM LM Moment Moment Moment Moment Moment Transfer function Hidden layer Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Sigmoid Output layer R NS PI Pt = current day rainfall, Rt = current day runoff; t = current day, t-n = n day before current day; n = 1,, 3 N From Table 1, it is cleared that the performance of five models i.e. with Levenberg- Marquardt (L-M) algorithm is comparable with each other though at varying number of nodes in hidden layer. Performance of models with momentum algorithm except for Model 7 is below the minimum criteria for statistical measures. The model 7 (5--1, for 1 epochs) performed better with R and PI values as.986 and.675, respectively. But the NS value of PI is below the minimum criteria i.e..7 and thus it is not considered for prediction of runoff from watershed. Therefore, it is cleared from the Table 4.1 that the RBF ANN models with momentum algorithm could not quantify the runoff from the watershed to the accuracy. Among formulated five ANN RBF models the performance of model 5 was found best for the architecture i.e. five inputs, ten processing elements in the hidden layer and one output at 1 epochs with Levenberg Marquadt (L-M) algorithm. It performed best in terms of statistical parameters such as Nash-Sutcliffe coefficient of efficiency as.86 and persistence index as.9. Therefore, performance of Model 5 is discussed in detail below. 198

5 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January Performance of model 5 during training and cross validation The performance of Model 5 in terms of MSE during training and cross validation with respect to epochs as given by software is depicted in Fig.1. The Fig. 1 shows that the minimum MSE during training was.167 for 1 epochs, while during cross validation the MSE started increasing after 6 epochs. The minimum MSE during cross validation was while final MSE was Performance of model 5 during testing The temporal variation of rainfall, observed runoff and runoff simulated with Model 5 over test period is shown in Fig., while Fig 3 depicts the scatter plot. It is cleared from Fig. that the observed and simulated runoff is in good agreement with each other. Though, all runoff events small as well as large are well simulated by the model, the model 5 underestimated the moderate peak flows. The scatter plot clears that the simulated runoff lies on both sides of 1:1 line, which shows that there is no consistent over or under estimation. Nash-Sutcliffe coefficient of efficiency close to 1 indicates that the Model 5 predicts runoff from watershed with accuracy. Value of Persistence index as.9 also confirms satisfactory agreement between simulated and observed runoff. B. Performance of model 5 for treatment T The model 5 was tested for treatment T, as its performance of model 5 was found best. The performance of model 5 was assessed by varying 1-1 nodes in the hidden layer. From Table, it is cleared that model 5 performed best for the architecture i.e. five inputs, five processing elements in the hidden layer and one output at 1 epochs. Fig. 4 and 5 shows temporal variation of rainfall runoff and scatter plot for testing period, respectively. Table : Statistical performance of model for treatment T No. of nodes in hidden layer R PI NS From Fig.4, it is cleared that the observed and simulated runoff is in good agreement. The model 5 underestimated the moderate peak flow. All runoff events small as well as large are well simulated by the model. The scatter plot shows that there is no consistent over or under estimation. High values of statistical performance measures confirm good agreement between simulated and observed runoff. C. Performance of model for treatment T3 The model 5 was also tested for treatment T3 by varying nodes 1-1 in hidden layer and presented in Table 3. Fig. 6 and 7 shows temporal variation of runoff and scatter plot over testing period, respectively. Table 3: Statistical performance of model for treatment T3 No. of nodes in hidden layer R PI NS

6 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January From Fig.6, it is cleared that the observed and simulated runoff are in good agreement. It is also cleared from figure that the model 5 underestimated the moderate peak flow. There is no consistent over or under estimation as evidenced in Fig.7. The performance of Model 5 (5-5-1) in terms of statistical measures confirms good agreement between simulated and observed runoff. D. Prediction of runoff using simulated results The runoff was predicted using model 5 for treatments T1, T, T3 using validated architectures, for the period Fig. 8, 9 and 1 shows temporal variation of runoff for treatments T1, T and T3, respectively. The figures confirmed good agreement between observed and simulated runoff. High value of statistical measures confirmed the close agreement between observed and simulated runoff. It is also cleared from Fig.8, 9 and 1 that there was no significant difference in the runoff generated from various tillage treatments on the watershed. It might be due to small size of watershed. IV. CONCLUSIONS As model 5 (5-1-1) identified as five inputs (current day rainfall, one day ahead rainfall, two day ahead rainfall, one day ahead runoff, two day ahead runoff and current day runoff from the watershed); ten nodes in hidden layer and for single output with Levenberg Marquadt (L-M) algorithm, and model 5 with architecture i.e. (current day rainfall, one day ahead rainfall, two day ahead rainfall, one day ahead runoff, two day ahead runoff and current day runoff from the watershed); five processing elements in the hidden layer for single output with Levenberg Marquadt (L-M) algorithm predicts runoff with accuracy for sowing along slope cultivation with opening of tide furrows (T1); and contour cultivation with opening of alternate furrow (T) and contour cultivation with opening of ridge and furrow (T3), respectively. Thus these RBF ANN models should be used for assessment of effect of tillage treatments (T1, T and T3) on runoff from this small watershed. ANN model with Levenberg Marquadt (L-M) algorithm predicts runoff with more accuracy compared to that with momentum algorithm. REFERENCES [1] Anctil, F., C. Michel, C.Perrin, and V.Andrassian (4). A soil moisture index as an auxiliary ANN input for streamflow forecasting, J. Hydrol., 86, [] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (a). artificial neural networks in hydrology-i: Preliminary concepts. J. Hydrol. Eng., 5(), [3] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (b). artificial neural networks in hydrology-ii: Hydrologic applications. J. Hydrol. Eng., 5(), [4] Bhola P.K., and A. Singh (1). Rainfall-runoff modeling of river Kosi using SCS-CS method and ANN. Unpublished B. Tech. thesis, Department of Civil Engineering, National Institute of Technology Rourkela. < CN_method _and_ann.pdf.>. [5] Calvoa I., and M. Portelab (7). Application of neural approaches to one step daily flow forecasting in Portuguese watersheds. J. Hydrol., 33(1-): [6] Colby J.D. (1). Simulation of a Costa Rica watershed: resolution effects and fractals. J. Water Resour. Plng. Mgmt., ASCE, 17(4): [7] Coulibaly P, F.Anctil, and B. Bobee (). Daily reservoir inflow forecasting using artificial neural networks with stopped training approach. J. Hydrol., 3: [8] Dawson, C.W. and R.L.Wilby, (1). Hydrological modelling using artificial neural networks. Prog. Phys. Geog., 5:8-18. [9] El-shafie A, M.Mukhlisin, A.A. Najah, and M.R. Taha (11). Performance of artificial neural network and regression techniques for rainfall-runoff prediction. Int. J. Physical Sciences, 6(8):

7 ISSN: ISO 91:8 Certified Volume 4, Issue 1, January 15 [1] Eldar Y. C., A. Nehorai, and P. S. La Rosa, (7). A competitive mean-squared error approach to beamforming. IEEE transactions on signal processing, vol. 55, no. 11. [11] Fernando, D. A. K., and A. Y. Shamseldin, (9). Investigation of internal functioning of the radial-basis-function neural network river flow forecasting models. J. Hydrol. Eng., 14(3), [1] Harun, S., I.A. Nor, and A.H. Kassim, (3). Rainfall-Runoff Modelling Using Artificial Neural Network. M. Sc. Thesis, Kolej Universiti Tenkologi Tun Hussein Onn.pp: [13] Hornik, K., M. Stinchcombe, and H.White, (1989). Multilayer feed forward networks are universal approximators. Neural Networks, : [14] Hsu, K. L., H. V. Gupta, and S. Sorooshian, (1995). Artificial neural network modeling of the rainfall-runoff process. Water Resour. Res., 31(1): [15] Jain, A., and S. Srinivasulu, (4). Development of effective and efficient rainfall-runoff models using integration of deterministic, real-coded genetic algorithms and artificial neural network techniques. Water Resour. Res., 4(4), W43, 1 1. [16] Joshi, J. (11). Rainfall-Runoff Modeling Using Artificial Neural Network (A Literature Review). Proceeding of National Conference on Recent Trends in Engineering & Technology.1(6): [17] Kerem, H.P., Ahmet and A. Omer, (7). Artificial neural network models in rainfall-runoff modelling of Turkish rivers. [18] Line D.E., S.W. Coffey, and D.L. Osmond (1997). Watersheds GRASS-AGNPS model tool. Trans. ASAE, 4(4): [19] Maier, H. R., and G. C. Dandy, (). Neural networks for the prediction and forecasting of water resources variables: A review of modeling issues and applications. Environ. Model. Software, 15(1), [] Miller S.N., W.G. Kepner, M.H. Mehaffey, M. Hernandez, R.C. Miller, D.C. Goodrich, K.K. Devonald, D.T. Heggem, and W.P. Miller (). Integrating landscape assessment and hydrologic modeling for land cover change analysis. J. Am. Water Resour. Assoc., 38(4): [1] Minns, A.W., and M. J. Hall, (1996). Artificial neural networks as rainfall runoff models. Hydrol. Sci. J., 41(3), [] Nash, J.E. and J.V. Sutcliffe, (197). River flow forecasting through conceptual models part 1 - a discussion of principles. J. Hydrol., 1: 8 9. [3] Rumelhart, D. E., E.Hinton, and J. Williams, (1986). Learning internal representation by error propagation, parallel distributed processing, Vol. 1, MIT, Cambridge, MA, [4] Senthil Kumar, A. R., K. P. Sudheer, S. K. Jain, and P. K. Agarwal, (5). Rainfall-runoff modelling using artificial neural networks: Comparison of network types. Hydrol. Process. 19(6), [5] Solaimani, K. (9). Rainfall-runoff Prediction Based on Artificial Neural Network (A Case Study: Jarahi Watershed), American-Eurasian J. Agric. & Environ. Sci., 5 (6): [6] Srinivasulu, S., and A. Jain, (9). River flow prediction using an integrated approach. J. Hydrol. Eng., 14(1), [7] Sudheer, K. P., A. K. Gosain, and K. S. Ramasastri, (). A data-driven algorithm for constructing artificial neural network rainfall-runoff models. Hydrol. Process. 16(6), [8] Thirumalaiah, K., and M. C. Deo, (1998). River stage forecasting using artificial neural networks. J. Hydrol. Eng., 3(1), 6 3. [9] Vos, N. J., and T. H. M. Rientjes, (8). Multiobjective training of artificial neural networks for rainfall-runoff modelling. Water Resour.Res, 44, W8434, [3] Zealand C.M., D.H. Burn, and S.P. Simonovic (1999). Short term streamflow forecasting using artificial neural networks. J. Hydrol., 14(1-4),

8 Simulated runoff, mm MSE ISSN: ISO 91:8 Certified Volume 4, Issue 1, January Training MSE Cross Validation MSE Epoch Fig. 1 Performance of model 5 during training and cross validation Fig. Performance of model 5 during testing R NS =.86 PI = Obsrved Runoff, mm Fig. 3 Scatter diagram of simulated and observed runoff

9 Simulated runoff, mm Rainfall, mm Runoff, mm Simulated runoff, mm Rainfall, mm Runoff, mm ISSN: ISO 91:8 Certified Volume 4, Issue 1, January Rainfall Observed Runoff Simulated Runoff 15-Aug-6 15-Jan-7 15-Jun-7 15-Nov-7 15-Apr-8 Period Fig.4 Performance of model for treatment T during testing Sept R NS =.93 PI = Observed Runoff, mm Fig.5 Scatter diagram of simulated and observed runoff from watershed for treatment T Rainfall Observed Runoff Simulated Runoff 15-Aug-6 15-Jan-7 15-Jun-7 15-Nov-7 15-Apr-8 Period Fig. 6 Performance of model for treatment T3 during testing Sept R NS =.89 PI = Observed Runoff, mm Fig. 7 Scatter diagram of simulated and observed runoff from watershed for treatment T3 3

10 Rainfall,mm Runoff, mm Rainfall,mm Runoff, mm Rainfall,mm Runoff, mm ISSN: ISO 91:8 Certified Volume 4, Issue 1, January Rainfall Observed Runoff Simulated Runoff Jun-1 7-Jul-1 17-Jul-1 7-Jul-1 6-Aug-1 14-Aug-1 Period Fig. 8 Performance of model for prediction for treatment T1 during testing Jun-1 7-Jul-1 17-Jul-1 7-Jul-1 6-Aug-1 Period Rainfall Observed Runoff Simulated Runoff Aug-1 Fig.9 Performance of model for prediction for treatment T during testing Rainfall Observed Runoff Simulated Runoff 6-Jun-1 7-Jul-1 17-Jul-1 7-Jul-1 6-Aug-1 14-Aug-1 Period Fig.1 Performance of model for prediction for treatment T3 during testing