تجزیه و تحلیل حساسیت از خروجی های مصنوعی شبکه های عصبی در شبیه سازی فرآیند تبخیر در رژیم های آب و هوایی مختلف

This study follows three aims; firstly to develop and examine three different Artificial Neural Networks (ANNs) viz.: Multi-Layer Perceptron (MLP), Radial Basis Neural Network (RBNN) and Elman network for estimating daily evaporation rate of Tabriz and Urmia cities using measured hydro-meteorological data; second to compare the results of ANN models with three physically-based models include, Energy balance, Aerodynamic, and Penman models and also black-box Multiple Linear Regression (MLR) model; and finally to perform a sensitivity analysis to investigate the effect of each input parameter on the output in terms of magnitude and direction. The used meteorological data set to develop the models for estimation of daily evaporation includes daily air temperature, evaporation, solar radiation, air pressure, relative humidity, and wind speed measured at synoptic stations of Tabriz and Urmia cities which have almost distinct climatologic conditions. The obtained results denote to the superiority of the ANN models on the classic models. Also based on the comparisons, the MLP network performs better than the RBNN and Elman network so that in the next step, sensitivity analysis is performed by the Partial Derivation (PaD) and Weights methods on the MLP outputs. Sensitivity analysis results show although air temperature, solar radiation and the amount of evaporation at previous time step are the effective parameters in estimation of daily evaporation at both regions, due to the climatologic condition wind speed and relative humidity are other predominant parameters in Tabriz and Urmia, respectively.

Evaporation as a major meteorological component of the hydrologic cycle plays a key role in climate change and water resources studies in arid and semi-arid climatic regions. Although there are empirical methods available for estimating evaporation, their performances are not satisfactory because evaporation is an incidental, non-linear, complex and unsteady process, so it is difficult to derive an accurate physical-based formula to represent all the physical meaning involved. As a result, there is a new trend in using data mining techniques such as Artificial Neural Network (ANN) to estimate evaporation. Chauhan and Shrivastava [1] used ANN approach to identify the best model in estimating evapotranspiration against climatic based methods for the Mahanadi reservoir area located in India, Moghaddamnia et al. [2] utilized ANN and adaptive neuro-fuzzy inference system (ANFIS) techniques to estimate evaporation in semi-arid regions and to tackle the problem of the best input data combination and how many data points should be used in the model calibration via the Gamma test. Deswal and Pal [3] used ANN method to study the influence of different combinations of meteorological parameters on evaporation losses from reservoirs. Jain et al. [4] investigated ANN accuracy in predicting evaporation with limited climatic data and used a procedure to evaluate the effects of input variables on the output variable using the weight connections of ANN models. Rahimikhoob [5] compared ANN technique with some empirical methods of evaporation estimation in Khuzestan plain in the southwest of Iran. Tan et al. [6] evaluated the applicability of the radiation-based, mass transfer, temperature-based and ANN models in estimating hourly and daily evaporation rates for an area with an equatorial climate. Among the empirical models, only the radiation-based model was found to be applicable for modeling the hourly and daily evaporations. ANN models are generally more accurate than the empirical models if appropriate network architecture is selected and a sufficient number of data points are used for training the network. Shirsath and Singh [7] utilized ANN, Multiple Linear Regression (MLR) and climate based (e.g., Penman, Priestley–Taylor and Stephens and Stewart) models for estimation of daily pan evaporation; results showed that there is slightly better agreement between the ANN estimations and measurements of daily pan evaporation than other models. Kisi [8] investigated the abilities of three different ANN techniques i.e., Multi-Layer Perceptron (MLP), Radial Basis Neural Network (RBNN) and Generalized Regression Neural Network (GRNN) to estimate pan evaporation rate and the results showed that the MLP and RBNN techniques could be successfully employed to model the evaporation process using the available climatic data. As well as evaporation, the study of ANN has recently aroused great interest at different fields of hydro-meteorology. As a few examples of many such studies, a GRNN was used for river suspended sediment estimation by Cigizoglu and Alp [9]; Nourani et al. [10] and [11] investigated the wavelet analysis linked to the ANN concept for hydrologic simulations of the Ligvanchai watershed. Nourani [12] utilized the ANN technique for modeling suspended sediment load of a delta mouth. In order to perform spatiotemporal prediction of the groundwater levels at different piezometers placed in an aquifer, a hybrid artificial neural network-geostatistics methodology was presented by Nourani et al. [13] and [14]. Demirel et al. [15] used the soil and water assessment tool (SWAT) and ANN models to analyze the issue of flow forecast. ANN, neuro-fuzzy, MLR and conventional sediment rating curve models were considered for time series modeling of suspended sediment concentration in the rivers by Rajaee et al. [16]. A Back-Propagation Neural Network (BPNN) model, based upon information at stations upstream of a river, was employed to forecast flood discharge at station downstream of a river by Kerh and Lee [17]. Dawson and Wilby [18] utilized ANN technique to rainfall-runoff modeling and flood forecasting. Lange [19] described the rainfall-runoff process of catchments using an ANN. Maier and Dandy [20] pointed out the steps that should be followed in the development of ANN models for predicting and forecasting of water resources variables so that disregarding these steps may result in non-optimal performance of ANN. Toth et al. [21] compared the accuracy of the short-term rainfall forecasts obtained with the linear stochastic techniques (i.e., auto-regressive moving-average), ANN and the non-parametric nearest-neighbors method using past rainfall depths as the sole input information. An ANN model was evaluated for precipitation forecasting by Bodri and Cermak [22] and most recently, Demirel et al. [23] proposed an ANN model for river flow prediction and applied a spatial cluster analysis to test the validation level of the predictions as well as recognizing the regional patterns of the water levels. The reason behind the mentioned interest is that ANNs are universal function estimators capable of mapping any linear or non-linear function [24]. Because of the flexibility in function approximation, ANNs are powerful methods in tasks involving pattern classification, estimating continuous variables and forecasting [25]. But the major shortcoming of ANNs is the difficulty of interpreting the knowledge gained by model. In short, an ANN model functions like a ‘black-box’ package, giving no clue on (1) how the answers or model outputs are obtained, and (2) how the input parameters affect the output [26]. Since the credibility of an artificial intelligence program frequently depends on its ability to explain its conclusions [27], therefore for verification of such models, as well as accuracy measuring of ANN-based models with available data, a methodology should be adopted to extract the meaningful rule from the trained network, which is comparable with trends inferred from experiments. Several methods, commonly called sensitivity analysis, have been proposed to overcome this disadvantage. Sensitivity analysis is used to determine how much “sensitive” a model is to the changes in the value of the parameters of the model and to the changes in the structure of the model. The sensitivity analysis as a simple and powerful tool to evaluate a system’s behavior and with wide application in the science and engineering is a critical step in the mathematical modeling of the hydro-meteorological processes. The sensitivity coefficients describe the change in the system’s outputs due to variations in the parameters that affect the system. A large sensitivity to a parameter suggests that the system’s performance can drastically change with small variation in the parameter. Vice versa, a small sensitivity suggests little change in the performance. There are a few methods to investigate the sensitivity of the ANN model. Lu et al. [26] reviewed these methods to acquire the knowledge contained in a trained ANN and stated that these methods could not determine the effect of each input parameter on the output variable, in terms of both magnitude and direction for sensitivity analysis of spool fabrication productivity problem. Therefore, they defined input sensitivity based on the first order Partial Derivation (PaD) method between the ANN output variable and the input parameters. The research presented in this paper investigates the abilities of ANNs to improve the accuracy of daily evaporation estimation in Tabriz and Urmia cities in comparison with three well-known physically-based models (i.e., Aerodynamic, Energy balance and combined Aerodynamic and Energy balance methods) [28] and also classic MLR method. Thereafter, as the original hydro-meteorological and water resources application, the PaD method which is able to perform sensitivity analysis in both terms of magnitude and direction is examined and compared to another scheme (i.e., Weights method). The most important drawback of black-box models (e.g., ANN) is their ignorance of the physics of the study process and therefore, their blindly application to a problem without attention to the physical conditions may lead to unreliable results. In this study by application of the proposed sensitivity analysis methods on two distinct sites, we tried to show how for a unique problem (evaporation), the model’s outputs and the inputs’ contributions may be different at different climatologic conditions. Therefore, the model and inputs should carefully be selected according to the physical characteristics of not only the process but also the study case. The rest of the paper has been organized as follows. Section 2 describes the study area and meteorological data. Sections 3 and 4 nominate the classic methods and ANN models used in this study, respectively. Section 5 summarizes the obtained results and compares the model’s performances. Section 6 presents sensitivity analysis formulation and its results. Finally, Section 7 concludes the study.

ANNs are powerful tools for forecasting hydro-meteorological time series. But the major shortcoming of ANNs is the difficulty of interpreting the knowledge gained by such a black-box type model. Because the credibility of an artificial intelligence program frequently depends on its ability to explain, it may be an essential and instructive matter to perform sensitivity analysis in the ANN modeling. In this paper, ANN models have been established in order to predict daily evaporation of Tabriz and Urmia cities. Results of the ANN models were compared to the classic models include: Energy balance, Aerodynamic, Penman and MLR models. The ANN models predicted daily evaporation with the highest and the lowest RMSE values rather than other models. But the BPNN is better than other ANN models in terms of structure simplicity and training time. Therefore, sensitivity analysis based on the first-order partial derivative between the BPNN output variable and the input parameters and based on the network connection weights was performed via the three-layer BPNN models. The results indicated that the PaD method is better than Weights method for sensitivity analysis of ANNs because of two reasons: (a) While the PaD method provides two elements of information on the contribution of inputs (order of contribution and mode of action), the Weights method is just able to classify the variables by order of importance of their contribution in the output (b) The PaD method gives the most stable results than the Weights method at different performances of the networks. Sensitivity analysis results showed that air temperature, solar radiation and previous day evaporation have maximum effect on daily evaporation in both cities. Wind speed and relative humidity are other important parameters in Tabriz and Urmia cities, respectively. Also, the graphs of sensitivity analysis of the BPNNs showed that scattering of some variables around the baseline (zero sensitivity) are both positive and negative due to the interaction of the input variables on each other. Hence, the interactions between each input variable with respect to other variables affecting the output levels can be investigated in subsequent studies using second-order partial derivative (PaD2) so that insights into the interactions can be useful for selecting optimum space of input variables. If the data are available, the sensitivity analysis can also be conducted for other effective parameters including in the evaporation process such as amount of rainfall, sunshine hours and water compounds. Furthermore to highlight the seasonality signature of the process, seasonality detectors such as wavelet transform may be linked to the proposed methodology in the form of a hybrid model [47].