[논문]기준 일증발산량 산정을 위한 인공신경망 모델과 경험모델의 적용 및 비교

최용훈; 김민영; 수잔 오샤네시; 전종길; 김영진; 송원정

doi:10.5389/ksae.2018.60.6.043

[국내논문] 기준 일증발산량 산정을 위한 인공신경망 모델과 경험모델의 적용 및 비교
Comparison of Artificial Neural Network and Empirical Models to Determine Daily Reference Evapotranspiration 원문보기

한국농공학회논문집 = Journal of the Korean Society of Agricultural Engineers, v.60 no.6, 2018년, pp.43 - 54

최용훈 (Department of Agricultural Engineering, National Institute of Agricultural Sciences(NAS), Rural Development Administration(RDA)) , 김민영 (Department of Agricultural Engineering, National Institute of Agricultural Sciences(NAS), Rural Development Administration(RDA)) , 수잔 오샤네시 (Conservation and Production Research Laboratory, USDA Agricultural Research Service (USDA-ARS)) , 전종길 (Department of Agricultural Engineering, National Institute of Agricultural Sciences(NAS), Rural Development Administration(RDA)) , 김영진 (Department of Agricultural Engineering, National Institute of Agricultural Sciences(NAS), Rural Development Administration(RDA)) , 송원정 (Sangju Agricultural Technology Center)

Abstract ▼ AI-Helper

The accurate estimation of reference crop evapotranspiration ($ET_o$) is essential in irrigation water management to assess the time-dependent status of crop water use and irrigation scheduling. The importance of $ET_o$ has resulted in many direct and indirect methods to approximate its value and include pan evaporation, meteorological-based estimations, lysimetry, soil moisture depletion, and soil water balance equations. Artificial neural networks (ANNs) have been intensively implemented for process-based hydrologic modeling due to their superior performance using nonlinear modeling, pattern recognition, and classification. This study adapted two well-known ANN algorithms, Backpropagation neural network (BPNN) and Generalized regression neural network (GRNN), to evaluate their capability to accurately predict $ET_o$ using daily meteorological data. All data were obtained from two automated weather stations (Chupungryeong and Jangsu) located in the Yeongdong-gun (2002-2017) and Jangsu-gun (1988-2017), respectively. Daily $ET_o$ was calculated using the Penman-Monteith equation as the benchmark method. These calculated values of $ET_o$ and corresponding meteorological data were separated into training, validation and test datasets. The performance of each ANN algorithm was evaluated against $ET_o$ calculated from the benchmark method and multiple linear regression (MLR) model. The overall results showed that the BPNN algorithm performed best followed by the MLR and GRNN in a statistical sense and this could contribute to provide valuable information to farmers, water managers and policy makers for effective agricultural water governance.

Keyword

표/그림 (8)

그림 Fig. 1 Multi-year daily climate characteristics of study area (a: Yeongdong, b: Jangsu)
그림 Fig. 2 Schematic structure of BPNN (left) and GRNN (right) architectures (modified from Kim et al. (2011))
그림 Fig. 3 Monthly variation in reference evapotranspiration (ET_o) of Yeongdong and Jangsu
표 Table 1 Correlation coefficient between meteorological data and ETo in the study regions
그림 Fig. 4 X:Y scattering plot between FAO56-PM estimated and BPNN simulated results of daily ET_o (Left: Yeongdong, Right: Jangsu)
그림 Fig. 5 Scattering plot between FAO56-PM estimated and GRNN simulated results of daily ET_o (Left: Yeongdong, Right: Jangsu)
그림 Fig. 6 X:Y scattering plot between FAO56-PM estimated and MLR simulated results of daily ET_o (Left: Yeongdong, Right: Jangsu)
표 Table 2 Statistical criteria for test data with ANN and MLR models

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제안 방법

However, the situations are not always in that way. Therefore, this study was initiated to develop ANN model to accurately predict ET_o and further utilize for irrigation scheduling even though there are limited and/or less available data. To cope with this, as the first step, this study assessed the performance of ANN using rich data accessible from automated weather stations operated by the Korea Meteorological Administration; investigated the accuracy of ANN algorithms compared with the empirical model (Multiple Linear Regression); and determined the benefit or disadvantage of ANN models with two different computational algorithms in estimating ET_o.
Therefore, this study was initiated to develop ANN model to accurately predict ET_o and further utilize for irrigation scheduling even though there are limited and/or less available data. To cope with this, as the first step, this study assessed the performance of ANN using rich data accessible from automated weather stations operated by the Korea Meteorological Administration; investigated the accuracy of ANN algorithms compared with the empirical model (Multiple Linear Regression); and determined the benefit or disadvantage of ANN models with two different computational algorithms in estimating ET_o.
Six daily meteorological data, average air temperature (Tavg, ℃), minimum and maximum air temperature (Tmin and Tmax, ℃), relative humidity (RH, %), wind speed (WS, m/s) and sunshine hour (SH, hr), were obtained from the Chupungryeong weather station, Yeongdong-gun, Gyeongbuk-province (Lat. 36 ˚25’N, Long. 128˚09’E, 96.2 m above sea level) and the Jangsu weather station, Jangsu-gun, Jeonbuk-province (Lat. 35˚39’N, Long. 127˚31’E, 406.5 m above sea level).
Artificial Neural Networks (ANNs) have universal approximation capabilities, which enable them to solve given differential equations possessing unsupervised error. Backpropagation and Generalized Regression Neural Network models, two well-known feed-forward neural network techniques, were evaluated in this study.
To achieve the best performance model, the governing factors in BPNN, such as the number of hidden layers, the number of hidden processing elements (PEs), the transfer function (e.g., sigmoid, tan-sigmoid), learning algorithms (e.g., Delta, extended DBD), and learning parameters (e.g., learning rate, momentum factor, initial weights), were evaluated. Depending on the problem being solved, the success of training varies with selected factors.
The performance of the BPNN, GRNN and MLR models were evaluated by comparing their predictive accuracies with the benchmark ET_o values. The performance was characterized based on the following statistical criteria; R (correlation coefficient), R² (coefficient of determination), RMSE (root mean square error), E (Nash-Sutcliffe efficiency) and MAE (mean absolute error).
High smoothing factors increase the network’s ability to generalize and degrade the error of prediction while low smoothing factors degrade the network’s ability to generalize and make predictions at all (Kişi, 2005). In this study, a range of smoothing factors and method for selecting the smoothing factors were tested to determine the optimum smoothing factor which could be calculated as a sigma exponent divided by the number of input units (NeuralWare, 1993a).
The present study also discussed the application and usefulness of the MLR and two different ANN modeling approaches in predicting ET_o. The results from the training and test datasets clearly demonstrated the ability of the BPNN model to predict daily values of ET_o accurately using the climatic parameters, which were introduced as inputs to the chosen ANN models. Simulation results showed that the BPNN model outperformed the MLR and GRNN models.

대상 데이터

In ANN computation, careful consideration should be given to choose suitable data that adequately represent the characteristics critical to the physical processes because networks trained with such data achieve higher generalization capability. To accomplish this, the total of 5,830 and 10,944 data points for Yeongdong and Jangsu were divided into three subsets: a training set (62%), a validation set (8%) and a test set (30%).

데이터처리

In the multiple linear regression analysis, the values of ET_o were used as the dependent variable and T_min, T_max, T_avg, RH, WS and SH were used as independent variables to derive the coefficients in the multiple linear regression model.
Statistically, the GRNN models performed relatively well and the network structure which provided the best training and test results was selected based on the highest coefficient of correlation. The network structures of GRNN were with 5 inputs and 1 output for both regions, but different smoothing factors were empirically determined to be 0.

이론/모형

In this study, ET_o calculated with the FAO56-PM (equation 1) was used as the benchmark output value. The characteristics of a hypothetical reference crop (height = 0.
Sunshine hour, which is generally provided from two automated weather stations in the Korea Meteorological Administration, was converted to net solar radiation (SR) using the Angstrom-Prescott equation (2) (de Medeiros et al., 2017) in order to use the Penman-Monteith equation. The coefficients a (0.
In this study, daily values of T_avg, T_max, T_min, RH, WS and SR were used to compute ET_o using the FAO56-PM equation which was coded into an Excel Spreadsheet. Daily results from the ANN and MLR models were compared against these approximated ET_o values.
5 for Jangsu, respectively. In addition, this study adopted the Delta learning rule with the Tanh transfer function, which adjusts the weight of neurons by calculating the gradient of the loss function (i.e., gradient descent optimization algorithm).
Much time was spent determining the best values for several network parameters, such as the number of layers and neurons, choosing the type of activation functions and training algorithms, learning rates, and momentum values. The effective way of obtaining a good BPNN model was to use trial-and-error methods and thoroughly understand the theory of backpropagation. Conversely, for the GRNN models, there was only one parameter, the smoothing factor, that was adjusted experimentally.

성능/효과

Seven ANNs with different input combinations were used and compared with ten empirical and semi-empirical ET_o calculations. This study showed that ANNs performed better than the locally calibrated ET_o equations, so ANNs could be recommended in most situations if there is a deficiency in some of the meteorological sensors typically used in the FAO56-PM equation, such as solar radiation, vapor pressure, wind speed and relative humidity data (FAO, 1998). Antonopoulos et al.
However, the Hargreaves method over-estimated higher values of ET_o. The RMSE from their investigations compared with the historical ET_o calculations were rather larger and demonstrated that the model estimated ET_o with the RMSE ranging from 0.574 to 1.33 mm/day. Importantly, Landeras et al.
The statistical analysis of data showed a close relationship between ET_o calculated using the FAO56-PM equation and ET_o simulated using the BPNN model; R² and E were 0.947 and 0.964, respectively, for Yeongdong and 0.962 and 0.962, respectively, for Jangsu, which indicated a high goodness-of-fit for both models for both locations. The RMSE and MAE were 0.
In the case of the MLR model, its negative estimates are a major drawback to estimating ET_o accurately. This study also indicated that even though the BPNN model required more time and effort to predict ET_o compared with the GRNN and MLR models, it resulted in predicting the most accurate values of ET_o. Although the predictions of the GRNN model were simpler and faster to obtain, they may not suit the needs of farmers or policy makers at critical crop growth stages and therefore, the modeler should take this into account before choosing the neural network algorithm to determine evapotranspiration.
This study showed that six weather parameters, T_avg, T_min, T_max, WS, RH and SH, measured in Yeongdong and Jangsu were significantly correlated with ET_o calculated for the areas using the FAO56-PM equation. All of these parameters were positively correlated with ET_o with the exception of RH.
The results from the training and test datasets clearly demonstrated the ability of the BPNN model to predict daily values of ET_o accurately using the climatic parameters, which were introduced as inputs to the chosen ANN models. Simulation results showed that the BPNN model outperformed the MLR and GRNN models.

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