Abstract—Rainfall-runoff (RR) models are integral components in any water resources management project. Conceptual, regression, or time series analysis are normally adopted for RR modeling. In the last decade or so, artificial neural network (ANN) technology has been proposed for efficient modeling of the complex natural systems. This paper presents the comparative results for one conceptual and five ANN models for daily RR modeling. The daily rainfall, streamflow, and evapotranspiration data from Jardine River catchment, Australia are used to demonstrate the methodologies proposed in this study. The results obtained here show that the ANN models are superior to the conventional conceptual models due to their ability to handle the non-linearity and dynamic nature of the natural physical processes in a more efficient manner.

Keywords—Hydrologic Modeling, Artificial Neural Networks, Water Resources Management, Conceptual Models.

I. INTRODUCTION

ATER is one of the most important natural resources available to mankind, which is primarily responsible for sustenance of life on the earth. Water continuously

evolves in various parts of the globe in what is called a hydrologic cycle. The nature provides various storage elements for the water to be stored: such as atmosphere, oceans, lakes, rivers, soils, glaciers, snowfields and ground water. The movement of water from one storage element to another takes place via the processes like evaporation, condensation, precipitation, deposition, runoff, infiltration, sub-surface flow, transpiration, and ground water flow. Hydrologic cycle is the system that describes this storage and movement of water. The cycle starts with the evaporation of water from oceans, lakes, rivers and streams, which forms clouds that drift over the land resulting in precipitation. The rainwater flows into rivers, lakes or aquifers which either evaporates back into atmosphere or reaches the ocean completing one cycle. As the components of the overall hydrologic cycle are highly dynamic, non-linear and complex in nature involving numerous interconnected variables, their modelling has been a difficult task [4].

1Jani Fathima. Jamal was post-graduate student, Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur-208016 (e-mail: jani.cet.05@gmail.com).

2Ashu. Jain, Professor, Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur-208016 (Phone: +91 512 259 7411; fax: +91 512 259 7395; e-mail: ashujain@iitk.ac.in).

A rainfall-runoff model is a mathematical model that simulates the process of transformation of rainfall into runoff over a catchment. To be more precise, it produces runoff hydrograph as a response to rainfall as input. Modeling of the RR process in a catchment is carried out using a variety of methods available. Broadly, there are two types of models, one that consider the laws of physics (called conceptual models) and second are those that do not consider the laws of physics but use the data analysis methods to derive the inter-relationships inherent in the inputs and outputs. The second category of models is known as systems theoretic models and the regression, time series, and artificial neural network (ANN) models fall in this category.

In this study, we use both conceptual and ANN techniques for modeling the daily RR-process. Specifically, one conceptual and five ANN models are developed. The daily rainfall, runoff, and evapotranspiration data derived from the Jardine River catchment in Australia are employed to develop various models in this study. The Australian Water Balance Model (AWBM) is used as the conceptual model and the feed-forward multi-layer perceptron is employed for ANN simulation in this study. A wide variety of standard error statistics are used to evaluate the model performance. The paper begins with a brief overview of the modeling techniques employed followed by the detailed description of the model development including the study area and data. The results obtained and their discussions are presented next before making concluding remarks.

II. MODELLING TECHNIQUES

A. AWBM Model

The Australian Water Balance Model (AWBM) is one of the most widely used RR model in Australia and since its inception in 1990s, it has undergone several revisions [1]. The AWBM is a catchment water balance model that can relate runoff to rainfall with daily or hourly time scales, and calculates losses from rainfall for flood hydrograph modelling. In addition to rainfall and runoff, AWBM also requires evapotranspiration (EVT) data as input. Fig. 1 shows the schematic diagram of the AWBM model. The model uses three surface storage elements to simulate partial areas of runoff. The water balance of each surface storage element is calculated independently of the others. The water balance equation can be described as follows:

Comparison of Conceptual and Neural Network Models for Daily Rainfall-Runoff Modelling

Jani Fathima Jamal1 and Ashu Jain2

W

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Storage (n) = Storage (n) + Rain – EVT (n = 1 to 3) (1)

The three parameters A1, A2 and A3 (which represent the proportions of the areas of the catchment) are constrained i.e. only A1 and A2 are set. The default pattern is A1= 0.134, A2= 0.433, and A3= 0.433.

Fig. 1 Structure of the AWBM model (Source: CRC, www.toolkit.net.au/rrl)

When runoff occurs from any storage element, part of the runoff becomes recharge of the base flow storage if there is base flow in the stream flow. The fraction of the runoff used to recharge the base flow storage is BFI*runoff, where BFI is the base flow index i.e. the ratio of base flow to total flow in the stream. The remainder of the runoff, i.e. (1.0 - BFI)*runoff, is surface runoff. The base flow storage is depleted at the rate of (1.0 - K)*BS where BS is the current moisture in the base flow storage and K is the base flow recession constant.

The surface runoff can be routed through a storage if required to simulate the delay of surface runoff reaching the outlet of a medium to large catchment. The surface storage acts in the same way as the base flow storage, and is depleted at the rate of (1.0 - KS)*SS, where SS is the current moisture in the surface runoff storage and KS is the surface runoff recession constant of the time step being used.

B. ANN Model

Artificial neural network is an information processing system that is composed of a number of processing elements called neurons analogous to biological neurons and

interconnections between the elements called weights, which imitate the synaptic strength in biological neural system. The commonly cited advantages of ANN are (a) They can be used even though the underlying problem is poorly defined or not understood clearly, (b) Their applications do not require prior knowledge of underlying process, (c) They are particularly useful when specific solutions do not exist to the problem posed, and (d) Owing to distributed processing nature, errors in the input do not produce significant change in the output.

In an ANN architecture, neurons are arranged in groups called layers or slabs. The basic structure of an ANN usually consists of three layers: the input layer, where the data is introduced to the network; the hidden layer or the layers where the data is processed; and the output layer, where the results for given inputs are produced. The architecture of ANN is designed by weights between neurons, a transfer function that controls the generation of output in a neuron and learning laws that define the relative importance of weights for input to a neuron. ANNs can be either feed forward or feedback networks. In a feed forward network, information passes from the input to the output layer. The neurons in each layer are connected only to the neurons in the next layer. This study uses a feed-forward type of ANN structure which is shown in Fig. 2.

An important step in ANN model development is its training to learn the relationship inherent in the data presented. There are two types of training methods, supervised and unsupervised. In supervised training method, the training is evolved using a certain rule specified by a guide or a teacher. The most commonly used supervised training method routinely employed in the training of feed-forward ANN models in engineering and sciences is the back-propagation method [3]. The back-propagation method is a gradient descent method, which is used in this study for the training of all the models developed and presented here.

Fig. 2 Structure of a feed-forward ANN model

C. Model Performance

The performance of all the models developed in this study was evaluated using four different standard statistical performance evaluation statistics. They are average absolute

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relative error (AARE), Pearson coefficient of correlation (R), Nash-Sutchcliff efficiency (E) and threshold statistics (TS): TS10, TS25, TS50, TS75 and TS100. Mean Square Error (MSE) was used as the objective function during calibration/training of various models. The AARE and TS statistics measure the efficiency of a model in terms of its ability to predict data accurately from a calibrated model. The other statistics, R and E quantify the effectiveness of a model in capturing the complex, dynamic and non-linear rainfall runoff process. The global error statistics such as R, E tend to give more weightage to high magnitude flow due to the involvement of square of difference between observed and predicted flows or equivalent expressions. Therefore, the errors in estimating low-magnitude flows are dominated by the errors in estimating high-magnitude flows in such global statistics. The error statistics based on percentage error in prediction with respect to observed value (such as TS and AARE) are better for performance evaluation as they give appropriate weightage to all magnitude flows. A more detailed description of these error statistics can be found in [2].

III. MODEL DEVELOPMENT

A. Study Area and Data The data employed to develop various models in this study were taken from Jardine River catchment, Australia. The Jardine River is the largest perennial river in the Queensland state of Australia. The daily stream flow data of Jardine River at Telegraph line (gauging station, 927001), the average of daily rainfall data from five rain gauges located at Bamaga, Cape York Post Office, Eliot Falls, Jardine Monument, and Peak point stations distributed all through the catchment and the daily evapotranspiration data of the catchment were taken for the study. The catchment has a drainage area of 2500 km2. The data for a period of 13 years (1974-1986), 4749 days, were considered for this study. The whole data set was divided into two subsets: a training subset and a testing subset. The first eight-year data (1974-1981), 2922 days, used for training or calibration comprise the training subset and the remaining five-year data (1982-1986), 1827 days, used for testing or validation comprise the testing subset. The catchment map of Jardine is shown in Fig. 3 and the graphical representation of rainfall-runoff data of the catchment for the entire duration is shown in Fig. 4.

A. The AWBM Model The AWBM model was developed using the toolkit named Rainfall Runoff Library (RRL) (CRC, Cooperative Research Centre for Catchment Hydrology, www.toolkit.net.au/rrl). The RRL toolkit has eight built-in optimizers. It was found that AWBM model calibrated using genetic algorithm (GA) performed better than the other optimization techniques. Therefore, this study adopted GA optimizer for model development. Trial and error methods were employed to fix the best GA optimizer parameters. The calibrated AWBM

model was then used to calculate various error statistics during both training and testing data sets, which are presented and discussed in section IV.

B. The ANN Model Development The ANN model developed in this study consists of three layers: an input layer consisting of neurons depending on the inputs selected, a hidden layer, and an output layer consisting of neurons depending on the output being modeled. The input variables were determined by the correlation analysis of the data.

Fig. 3 Jardine River Catchment

Fig. 4 Rainfall-runoff data from Jardine River

The auto-correlation, partial-auto correlation and cross-correlation analysis of the daily rainfall-runoff data were carried out. Based on these correlation analyses, the most appropriate inputs were found as follows: one day lagged stream flow (Q(t-1)) and one to four day lagged rainfall (P(t-1), P(t-2), P(t-3), P(t-4)). Thus, the input layer consisted of five neurons and output layer had only one neuron representing runoff to be modeled.

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The data were normalized in the range (0.1, 0.9) in this study. After the selection and normalization of input and output variables, ANN models were developed to simulate the stream flow for Jardine River. Five different ANN models were developed with hidden neurons ranging from one to five. Each of the ANN models was trained and the error statistics was computed. The architecture was trained with MSE as the objective function. The acceptable limit of objective function and the maximum iteration were used as the criteria for termination of the training process. This study used back propagation algorithm with momentum factor [3]. After a series of trials on each of the models, the best values of learning constant and momentum constant for each model was determined. Once the training of each of the five models was complete, the trained ANN models were used to calculate the various error statistics considered in this study.

IV. RESULTS AND DISCUSSIONS

The results obtained during training and testing data sets in terms of various standard error statistics considered in this study are presented in Table I. The best error statistic from a particular model is highlighted in bold font. Analyzing the results during training, it can be observed that the error statistics of all the five ANN models are comparable with high R (all above 0.96) and E (all above 0.86) values, signifying models with good predictive power. When compared with other ANN architectures, the ANN model 5_1_1 obtained the best R (0.9762), E (0.9513), TS50 (98.9), TS75 (99.8) and TS100 (99.9) statistics; the 5_2_1 model obtained the best TS25 (88.9) statistic; the models 5_2_1 and 5_3_1 obtained the best AARE statistic (22.8). The models 5_2_1, 5_3_1 and 5_4_1 showed the least MSE values of 0.003. The results of AWBM model during training, R (0.8683), E (0.4782), MSE (0.0056), TS10 (24.8), TS25 (56.4), TS50 (84.4), are found to be quite inferior to those from all the ANN models. The statistics reveal that the AWBM model is limited by its much lower E values and low R values, indicating the model is far behind the ANN models in predictive power.

The results from the ANN models during testing when analyzed were also observed to be in comparable ranges, with high R values (all above 0.975) and E values (all above 0.92). The ANN model 5_1_1 obtained the best R (0.9824), E (0.9553), TS75 (100.0) statistics; the 5_3_1 model obtained the best AARE (13.1), TS10 (17.9), TS50 (95.7) statistics; the 5_2_1 model obtained best TS25 (48.4) and MSE (0.0054) statistics. TS100 (100) was found to be same for both 5_1_1 and 5_5_1 ANN models. The results of AWBM model, AARE (27.0), R (0.8369), E (0.5925), TS75 (95.7), TS100 (98.7) are found to be inferior to those from the ANN models. Though some TS and MSE values from the AWBM model were found comparable to those from some of the ANN models, a much lower E value from AWBM model indicate that the model is far behind in predictive power when compared to ANN models. In addition, the AWBM model is limited by its low R value and high AARE values. Thus, the results obtained in this study demonstrate that all the five

ANN models outperformed the conceptual AWBM model. Also, the ANN model (5_1_1) was found to the best among the ANN models developed in this study due to its compact nature. The graphical results in terms of scatter and time series plots during testing are shown in Fig. 5 and Fig. 6, respectively.

TABLE I

MODEL PERFORMANCE STATISTICS FROM VARIOUS MODELS

MODEL AARE R E MSE TS10 TS25 TS50 TS75 TS100 5_1_1 24.0 0.9762 0.9513 0.0040 53.0 81.5 98.9 99.8 99.9 5_2_1 23.1 0.9608 0.9050 0.0030 53.1 88.9 96.0 97.8 98.5 5_3_1 22.8 0.9662 0.8677 0.0030 54.9 83.3 92.5 95.9 97.2 5_4_1 22.8 0.9632 0.8992 0.0030 63.3 84.9 91.9 94.7 96.9 5_5_1 26.0 0.9751 0.9114 0.0040 56.8 85.5 94.2 96.8 98.1 T

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5_2_1 14.2 0.9752 0.9391 0.0054 17.7 48.4 94.6 99.8 99.9

5_3_1 13.1 0.9767 0.9211 0.0062 17.9 47.2 95.7 99.8 99.9

5_4_1 13.6 0.9761 0.9372 0.0062 17.3 46.6 94.3 99.7 99.9

5_5_1 15.3 0.9815 0.9408 0.0080 15.6 39.8 84.0 99.8 100.0

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AWBM 27.0 0.8369 0.5925 0.0070 29.7 54.7 85.9 95.7 98.7

It is clear from the scatter plots that all the five ANN models were able to predict the flow values very well as seen from the narrow scatter around the ideal line. Similarly, the ANN models were able to capture the peak flows and timing to peak flows very well as compared to the AWBM model. The graphical results confirm the superiority of all ANN models in general and the compact 5_5_1 model in particular.

V. CONCLUSIONS

This paper presents the results of a study aimed at the comparison of the performance of conceptual and ANN methodologies in forecasting one-day ahead daily runoff in a catchment. The Australian Water Balance Model (AWBM) was considered as the conceptual model while a feed-forward ANN architecture trained using the popular back-propagation training algorithm with momentum correction factor was employed in this study. The daily rainfall, flow, and evapotranspiration data were employed for the model development of the conceptual model but the ANN models developed considered only the rainfall and flow data. The daily data derived from Jardine River catchment in Australia were used to demonstrate the application of the proposed methodologies. Correlation analyses were used for the selection of inputs for the ANN models. A wide range of error statistics available in literature were adopted for model performance evaluation purposes in addition to using the graphical aides of scatter and time series plots for the observed and predicted outputs from various models. The results obtained in this study clearly demonstrate the superiority of the ANN methodology over the conceptual models in modeling the complex, non-linear, and dynamic natural physical processes such as a rainfall-runoff process in a catchment. All the five ANN models (containing hidden neurons ranging from one to five) outperformed the AWBM

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model on the data considered here. The ANN model consisting of only one hidden neuron with a very compact structure and minimum number of weight parameters to be estimated was deemed to be the best model in this study highlighting the importance of the principle of parsimony. ANNs are powerful tools for the modeling and forecasting of complex engineering systems and need to be employed in the operation and maintenance of existing engineering systems, which is somehow lacking.

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The ANNs are not being employed for operational purposes currently due to their black-box nature in spite of many studies demonstrating their superiority over the conventional modeling approaches of regression, time series, and conceptual models. The studies such as the one presented here can go a long way in the ANNs being accepted as potential tools for the implementation in the efficient water resources management.

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REFERENCES

[1] Boughton, W.C. (2004), The Australian Water Balance Model, Environmental Modelling and Software, 19(10): 943-956.

[2] Jain, A. and Srinivasulu, S. (2006), Integrated approach to model decomposed flow hydrograph using artificial neural network and conceptual techniques. Journal of Hydrology, 317(3-4): 291-306.

[3] Rumelhart, D.E., Hintont, G.E. and Williams, R.J. (1986), Learning representations by back-propagating errors. Nature, 323, 6088: 533-536.

[4] Zhang, B. and Govindaraju, S. (2000), Prediction of watershed runoff using Bayesian concepts and modular neural networks, Water Resources Research, 36 (3): 753-762.

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