o trabalho e permitindo alcançar o máximo de eficiência no processo, ... históricas de ET0 e series históricas de elementos do clima, como temperaturas máxima, .... 0,6763. 0,7217. 0,7470. Meteorological data. 15-3-3-1. 0,7637. 0,6871.
http://dx.doi.org/10.12702/ii.inovagri.2014-a577
FORECASTING REFERENCE EVAPOTRANSPIRATION WITH ARTIFICIAL NEURAL NETWORK Araújo, G. L.; Oliveira Jr, M. M.; Pinto, F. A. C.; Mantovani, E. C. Abstract: Planning of irrigation requires an adequate prediction of the reference evapotranspiration (ET0) in order to maximize the efficiency of the system. The availability of simple and accurate tool for the estimation of these values is of extreme interest for designers and managers of these systems. Artificial neural networks (ANN) have been widely used lately to model complex non-linear processes, as it does not require an extensive understanding of the processes involved. The objective of this work is to develop a tool to predict the values of ET0 with ANN. The ANNs were obtained through trainings using 10-year meteorological data, such as mean air temperature, maximum and minimum temperature, mean air speed, sunshine hours, and relative humidity and with the respective values of ET0. Several architectures of feed forward back propagation neural networks (BPNN) having either meteorological or ET0 values as input were evaluated. The models of ANN were trained so as to predict the cumulative ET0 for 1, 1, 3, 5 and 7 days with data of the 3, 5, 10, 10 and 12 previous days as input, respectively. The mean square error (MSE) and the coefficient of correlation (R) showed that the adopted method was able to predict well the cumulative values of ET 0 for the number of days studied. Keywords: Reference Evapotranspiration, Artificial Neural Networks, Forecast.
PREVISÃO DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA COM REDES NEURAIS ARTIFICIAIS RESUMO: Para o planejamento eficiente da irrigação é de extremo interesse por parte de irrigantes e gestores, ferramentas que possibilitem a previsão da evapotranspiração de referência (ET0), facilitando o trabalho e permitindo alcançar o máximo de eficiência no processo, entretanto estas ferramentas têm de fornecer estimativas de forma precisa e confiável, minimizando os possíveis erros associados ao processo. As redes neurais artificiais (RNA) têm sido amplamente utilizados para modelar processos não-lineares complexos, uma vez que não requererem uma compreensão ampla dos processos envolvidos. O objetivo deste trabalho foi obter ferramentas por meio da modelagem com redes neurais artificiais, para a previsão da evapotranspiração de referência, tendo como dados de entrada series históricas de ET0 e series históricas de elementos do clima, como temperaturas máxima, mínima e média do ar, velocidade média do ar, horas de brilho solar e umidade relativa do ar, sendo a abrangência das series de dez anos. Foram testadas diversas estruturas de rede, utilizando a metodologia de retro propagação, sendo que para as duas formas de entrada de dados, ET0 e elementos do clima, foram feitas previsões para intervalos de 1, 3, 5, e 7 dias, tomando como base de os intervalos de entrada 3, 5, 10 e 12 dias, anteriores aos dias de previsão. De acordo com os índices de erro médio quadrático (MSE) e coeficientes de correlação (R) metodologia proposta pode ser utilizada com boa precisão para prever a ET0 para os intervalos de dias estudados. Palavras Chave: Evapotranspiração de referência, Redes neurais artificiais, Previsão.
G. L. Araújo et al.
INTRODUCTION Evapotranspiration is defined as the amount of water that evaporates and is transpired by a vegetated surface during a determined amount of time, this includes the water evaporation from the soil, evaporation of the water deposited by irrigation, rain or dew on the leaf surface and vegetal transpiration. Reference evapotranspiration (ET0) is defined as the amount of water used by an extensive surface vegetated with grass, with high between 0.08 and 0.15 m, in active growth, covering completely the surface of the soil and without hydric restrictions. As a matter of standardization in the estimation of the phenomenon of ET0, the concept of reference surface has come into use, this being defined as a vegetated surface with an hypothetic culture with a height of 0.12 m, with an aerodynamic resistance to the transport of steam of 70 s m-1 and albedo of 0.23. The reference surface is similar to an extensive surface, covered with green grass, without restrictions of water and uniform height, growing actively and shadowing the ground completely (PEREIRA, 2013). The ET0 is used to determine the consumption of water by cultures, being fundamental in the management and planning of irrigation (ARAUJO et al., 2011). The Penman-Monteith FAO-56 method is currently considered as the standard method for the estimation of the ET 0 (ALLEN et al., 1998). The use of tools that allow the forecasting of ET0 is of great interest to irrigators and managers as it provides an improvement in the efficiency of irrigation planning and maximize the efficiency of the system. However, this tool must provide precise and trustworthy forecasts, minimizing the occurrence of possible errors. One of the possible tools to be used in the forecasting of ET0 are mathematical functions obtained through modelling and the use of Artificial Neural Networks (ANN). ANN have been used successfully to model relations, which involve complex temporal series in several areas of science (ZANETTI et al., 2008). ANN are systems composed of simple processing units that calculate determined mathematical functions. These units are disposed in one or more layers and linked by connections, which are associated to weights that, after a training process, store the knowledge acquired by the network. The working mechanism of the ANN is inspired in the way the brain works (BRAGA et al., 2000; HAYKIN, 2001; KOVÁCS, 2002). The objective of this work is to obtain tools using Artificial Neural Networks and evaluate their potential to forecast the accumulated reference evapotranspiration over a period of time. Two types of historical series will be used as input, values of ET 0 and values of climatological data (maximum and minimum air temperatures, mean air speed, number of sunshine hours and dew point temperature). METHODOLOGY The evaluation of the capacity of forecasting of ET 0 by ANN was made using meteorological data from the city of Viçosa, MG (latitude 20o45’ S longitude 42o52’ W). The meteorological data was measured by the station ID 83642 from the National Institute of Meteorology (INMET) from the year 2000 to 2010. The values of ET0 were calculated using this meteorological data and the software RefET (ALLEN, 2002), which uses the Penman-Monteith FAO-56 method in its calculations. The forecast of climatic values usually involves nonlinear problems with considerable complexity. The use of ANN allows the solution of this sort of problem without the requirement of a deep knowledge of the problem in question, which can be very useful when the problem to be solved is rather complex or not all of the required parameters are easily obtainable. A ANN have a number of parameters to be defined such as the number of layers, number of neurons in each layer and the type of activation function in each layer. There is no standard methodology for the selection of these parameters and they are usually selected by trial-and-error based on the experience of the user with ANN and with the problem. The number of neurons in the input and output layers are defined by the problem itself and are obtained directly. The activation function of the output layer for the forecast of ET0 was chosen to be the purelin function, as the output of the problem is not restricted to a interval from -1 to +1. Due to the nonlinearity of the problem, the activation function of the hidden layers was chosen to be a tansig function. The database was then randomly divided in three parts, one for training (70% of the data), 4288
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one for validation (15%) and the last one for test (15%) for each training. ANN were obtained using as input either the calculated values of ET0 of the n previous days or meteorological data for the same n days to forecast the accumulated reference evapotranspiration of the next m days. The potential use of ANN to forecast values of ET0 was evaluated for various configurations. At first, different combinations of n and m were studied and for each n-m pair several ANN structures were tested for each kind of input, ET0 and meteorological data. A structure was selected for each of this n-m pairs and for each input type. The results for each kind of input were then compared. The Mean Squared Error (MSE) and the coefficient of correlation (R) were used as criteria of performance. The n-m pairs chosen for this study are presented in the following table. Table 1 – Table with the number of days used n to forecast and the number of days m to be forecasted n m
3 1
5 1
10 3
10 5
12 7
RESULTS AND DISCUSSION At first, the values of ET0 were calculated using the meteorological data measured by the INMET station. The data was organized in a database which was used for training and selection of the ANNs with best performance. Table 2 shows the results and configurations of the best networks found for each pair n-m and type of input. Table 2 - Performance of the artificial neural networks for different n-m pairs n
m
Structure
MSE
R(training)
R(test)
ET0 Meteorological data
3
1
3-3-3-1 15-3-3-1
0,6763 0,7637
0,7217 0,6871
0,7470 0,6814
ET0 Meteorological data
5
1
5-4-4-1 25-3-3-1
0,6703 0,7393
0,7207 0,7015
0,7460 0,6821
10
3
10
5
12
7
10-3-3-1 50-1-1-1 10-4-3-1 50-3-2-1 12-10-10-1 60-1-1-1
46,167 51,833 110,000 107,667 171,333 221,667
0,7300 0,6896 0,7370 0,7599 0,7600 0,7103
0,7380 0,6741 0,7333 0,7331 0,7520 0,6959
ET0 Meteorological data ET0 Meteorological data ET0 Meteorological data
It can be observer in table 2 shows that the correlation coefficient suffers little variation for the various ANN structures shown. It can also be seen that for most of the tests the correlation coefficient was greater for networks using ET0 values as input then when meteorological data was used. As the number of days to be predicted became higher, the MSE raised considerably. This happened because of the bigger variability of the input values just as the elevation in complexity of the forecast. However, as it is an accumulated squared error for the forecasted days, as the daily values of error were calculated it was obtained, for all of the studied cases, an error smaller than one millimeter. Figure 1 compares the values of accumulated ET0 for 7 days as calculated with the PenmanMonteith equation with the values predicted using two different ANN, one trained using ET0 values and the other with meteorological data from the 12 previous days. The forecasts were made for a period of 11 years, from the year 2000 to 2010.
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Figure 1. Forecast of ET values for a period of 11 years using two ANN, the first using ET 0 values as inputs and the second using meteorological data. The ANN forecasts a period of 7 days having as base the 12 previous days. Figure 1 shows that the forecasted values of ET0 as obtained by the ANN trained with ET0 as input follows the trend of the series and estimating values closer to the maximums and minimums. Whereas the second ANN, which uses meteorological data as input, overestimates minimums and underestimates maximums several times in the whole series. Due to the complex nature of the evaporation phenomenon, the forecasting of evapotranspiration values can be a rather complex and laborious assignment. The use of ANNs as a tool in this process allows the improvement of both, the reliability and the easiness of this work as it is capable of retaining large amounts of information for processing. Figure 2 shows the dispersion graphs of some of the networks analyzed for each pair n-m and for each type of input.
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Figure 2. Dispersion graphs of the best networks
It is possible to observe that all the dispersion graphs have a similar trend. However, the networks based on ET0 values as input have smaller dispersion. This results bring to light the potential of the practical use of the forecasting of ET0 trough use of ANN for irrigation planning. 4291
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The ANNs have shown to be an adequate mathematical model to recognize patterns (HAYKIN, 2000) in agrometeorological forecasting. The artificial neural networks have the capacity of perceiving implicit dependencies amongst data, even when there is no deep knowledge of the nature fo this dependencies (NEVES & CORTEZ, 1997). Silva et al. (2006) also used ANN to forecast ET 0 using ET0 values from the previous days as input. They obtained better results using data from the last 10 days to forecast the next day with a MSE of 0,79 mm². The authors observed that, as the number of forecasted days heightened, the smaller the precision of the ANN, which was also observed in this work. Trajkovic et al. (2003), working in Nis, Servia and Montenegro, used meteorological data (air temperature, relative humidity, air speed and sunshine) in networks for the forecast of the monthly accumulated ET0 based on the previous 11 months and also based on the previous 23 months. They concluded that ANN can be used to forecast evapotranspiration with high accuracy. Landeras et al. (2009) used ANN to forecast weekly-accumulated values of evapotranspiration having as input ET0 values as calculated by the Hargreaves-Samani method as calibrated with Penman-Monteith FAO 56 for a region in the north of Spain. The authors also concluded that the use of ANN can be effective in forecasting evapotranspiration, although they also suggest the use of ANN associated with some other tool in order to improve the reliability of the output. CONCLUSIONS It can be concluded the ANN can be used to forecast the accumulated reference evapotranspiration one, three, five and seven subsequent days based on the previous days. It was also observed that ANNs that used ET0 values as input showed better results when compared to the use of a set of meteorological data. Both input types showed a daily absolute error smaller than 1.0 mm. REFERENCES ALLEN, R. G. REF-ET: Reference evapotranspiration calculation software for FAO and ASCE Standardized Equations. Version 2.0 for Windows. Utah State University, Logan, USA, 2000. ALLEN, R. G.; PEREIRA, L. S.; RAES, D.; SMITH, M. Guidelines for computing crop water requirements. Irrigation and Drainage Paper, 56. Rome: FAO, 1998. 310 p. ARAUJO, G. L.; REIS, E. F. dos; MARTINS, C. A. da S.; BARBOSA, V. S.; RODRIGUES, R. R. DESEMPENHO COMPARATIVO DE MÉTODOS PARA A ESTIMATIVA DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA (ET0). Revista Brasileira de Agricultura Irrigada, v. 5, nº. 2, p. 84-95, 2011. http://dx.doi.org/10.7127/rbai.v5n200045 BRAGA, A. P.; LUDEMIR, T. B.; CARVALHO, A. C. P. L. F. Redes neurais artificiais: Teoria e aplicações. Rio de Janeiro: LTC, 2000. 262 p. HAYKIN, S. Redes Neurais - Princípios e Prática. Tradução: Paulo Martins Engel, Porto Alegre: Editora Bookman, 2a Edição, 2000. 900p. LANDERAS, G.; ORTIZ-BARREDO, A.; LÓPEZ, J. J. Forecasting Weekly Evapotranspiration with ARIMA and Artificial Neural Network Models. JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING, v.135, p.323-334, 2009. http://dx.doi.org/10.1061/(ASCE)IR.19434774.0000008 NEVES, J., CORTEZ, P. An Artificial Neural Network – Genetic Based Approach for Time Series Forecasting. In: Brazilian Symposium on Neural Networks, 4, 1997. Proceedings... Sociedade Brasileira de Computação, Belo Horizonte - MG, 1997. p.9-13. PEREIRA, A. R; SEDIYAMA, G. C; VILA NOVA, N. A. Evapotranspiração. Campinas: FUNDAG, 2013. 323 p. SILVA, A. F. da; COSTA, L. C.; SEDIYAMA, G. C. Previsão da evapotranspiração de referência utilizando redes neurais. Engenharia na Agricultura, v.14, n.2, p.93-99, 2006. TRAJKOVIC, S.; TODOROVIC, B.; STANKOVIC, M. Forecasting of Reference Evapotranspiration by Artificial Neural Networks. JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING, v.129, p.454-457, 2003. http://dx.doi.org/10.1061/(ASCE)0733-9437(2003)129:6(454) ZANETTI, S. S.; SOUSA, E. F. CARVALHO, D. F.; BERNARDO, S. Estimação da evapotranspiração de referência no Estado do Rio de Janeiro usando redes neurais artificiais. 4292
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Revista Brasileira de Engenharia Agrícola e Ambiental, v.12, n.2, p.174-180, 2008. http://dx.doi.org/10.1590/S1415-43662008000200010
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