Selecting models for the estimation of reference evapotranspiration for irrigation scheduling purposes.

Alternative models for the estimation of reference evapotranspiration (ETo) are typically assessed using traditional error metrics, such as root mean square error (RMSE), which may not be sufficient to select the best model for irrigation scheduling purposes. Thus, this study analyzes the performance of the original and calibrated Hargreaves-Samani (HS), Romanenko (ROM) and Jensen-Haise (JH) equations, initially assessed using traditional error metrics, for use in irrigation scheduling, considering the simulation of different irrigation intervals/time scales. Irrigation scheduling was simulated using meteorological data collected in Viçosa-MG and Mocambinho-MG, Brazil. The Penman-Monteith FAO-56 equation was used as benchmark. In general, the original equations did not perform well to estimate ETo, except the ROM and HS equations used at Viçosa and Mocambinho, respectively. Calibration and the increase in the time scale provided performance gains. When applied in irrigation scheduling, the calibrated HS and JH equations showed the best performances. Even with greater errors in estimating ETo, the calibrated HS equation performed similarly or better than the calibrated JH equation, as it had errors with greater potential to be canceled during the soil water balance. Finally, in addition to using error metrics, the performance of the models throughout the year should be considered in their assessment. Furthermore, simulating the application of ETo models in irrigation scheduling can provide valuable information for choosing the most suitable model.

Machine learning models for streamflow regionalization in a tropical watershed.

This study aims to assess different machine learning approaches for streamflow regionalization in a tropical watershed, analyzing their advantages and limitations, and to point the benefits of using them for water resources management. The algorithms applied were: Random Forest, Earth and linear model. The response variables were the three types of minimum streamflow (Q7.10, Q95 and Q90), besides the long-term average streamflow (Qmld). The database involved 76 environmental covariates related to morphometry, topography, climate, land use and cover, and surface conditions. The elimination of covariates was performed using two processes: Pearson's correlation analysis and importance analysis by Recursive Feature Elimination (RFE). To validate the models, the following statistical metrics were used: Nash-Sutcliffe coefficient (NSE), percent bias (PBIAS), Willmott's index of agreement (d), coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE) and relative error (RE). The linear model was unsatisfactory for all response variables. The results show that nonlinear models performed well, and their covariate of greatest predictive importance was flow equivalent to the precipitated volume, considering the subtraction of an abstraction factor of 750 mm (Peq750). Generally, the Random Forest and Earth models showed similar performances and great ability to predict the minimum streamflow and long-term average streamflow assessed, constituting powerful and promising alternatives for the streamflow regionalization in support to the management and integrated planning of water resources at the level of river basins.

Reference evapotranspiration estimated from air temperature using the MARS regression technique / Evapotranspiração de referência estimada a partir da temperatura do ar usando a técnica de regressão MARS

The reference evapotranspiration (ETo) is an important component for determining the water requirements of the crops. In order to estimate this variable accurately, the Food and Agriculture Organization (FAO) proposed the Penman-Monteith equation, however, this demands a large number of meteorological data, which restricts its use. In this context, this study compares the performance of the Penman-Monteith equation using only measured air temperature (PMT) and the Hargreaves-Samani (HS) equation with the performance of the multivariate adaptive regression splines (MARS) technique for the daily ETo estimation with only air temperature data. For the study, daily meteorological data from 2002 to 2016 were used. The data were collected from weather stations located in Florianópolis- SC, Manaus-AM and Petrolina-PE, being these selected in order to capture different climatic conditions. MARS models were developed for each weather station and the PMT e HS equations were locally calibrated. The performances of the original and calibrated equations and MARS models were evaluated based on the statistical indices root mean square error, mean absolute error, mean bias error and coefficient of determination. The ETo estimated by the Penman-Monteith method with full data was used as reference for the development of the MARS models, calibration of the equations and for the performance evaluation of the models under study. The calibration of the HS and PMT equations promoted better performances in relation to the original equations, improving the methods accuracy. The MARS technique presented good performance, outperforming the original and calibrated PMT and HS equations, with lower error values and higher coefficient of determination, and can be considered as an alternative to empirical methods.

A evapotranspiração de referência (ETo) é um componente importante para determinar o requerimento de água das culturas. Para estimar esta variável com acurácia, a Food and Agriculture Organization (FAO) propôs a equação de Penman-Monteith, no entanto, esta demanda um grande número de dados meteorológicos, o que restringe seu uso. Neste contexto, este estudo compara o desempenho da equação de Penman-Monteith usando apenas temperatura do ar medida (PMT) e a equação Hargreaves-Samani (HS) com o desempenho da técnica multivariate adaptive regression splines (MARS) para a estimativa da ETo diária com apenas dados de temperatura do ar. Para o estudo, foram utilizados dados meteorológicos diários de 2002 a 2016. Os dados foram coletados de estações meteorológicas localizadas em Florianópolis-SC, Manaus-AM e Petrolina-PE, sendo estas selecionadas a fim de capturar diferentes condições climáticas. Modelos MARS foram desenvolvidos para cada estação meteorológica e as equações de PMT e HS foram calibradas localmente. Os desempenhos das equações originais e calibradas e modelos MARS foram avaliados com base nos indicadores estatísticos raiz do erro quadrático médio, erro absoluto médio, viés médio e coeficiente de determinação. A ETo estimada pelo método de Penman-Monteith com dados completos foi utilizada como referência para o desenvolvimento dos modelos MARS, calibração das equações e para a avaliação da performance dos modelos em estudo. A calibração das equações HS e PMT promoveu melhores desempenhos em relação às equações originais, melhorando a acurácia dos métodos. A técnica MARS apresentou bom desempenho, superando as equações de PMT e HS originais e calibradas, com menores valores de erro e maiores coeficientes de determinação, e pode ser considerada como uma alternativa aos métodos empíricos.

Calibration methods for the Hargreaves-Samani equation / Métodos de calibração para a equação de Hargreaves-Samani

ABSTRACT The estimation of the reference evapotranspiration is an important factor for hydrological studies, design and management of irrigation systems, among others. The Penman Monteith equation presents high precision and accuracy in the estimation of this variable. However, its use becomes limited due to the large number of required meteorological data. In this context, the Hargreaves-Samani equation could be used as alternative, although, for a better performance a local calibration is required. Thus, the aim was to compare the calibration process of the Hargreaves-Samani equation by linear regression, by adjustment of the coefficients (A and B) and exponent (C) of the equation and by combinations of the two previous alternatives. Daily data from 6 weather stations, located in the state of Minas Gerais, from the period 1997 to 2016 were used. The calibration of the Hargreaves-Samani equation was performed in five ways: calibration by linear regression, adjustment of parameter "A", adjustment of parameters "A" and "C", adjustment of parameters "A", "B" and "C" and adjustment of parameters "A", "B" and "C" followed by calibration by linear regression. The performances of the models were evaluated based on the statistical indicators mean absolute error, mean bias error, Willmott's index of agreement, correlation coefficient and performance index. All the studied methodologies promoted better estimations of reference evapotranspiration. The simultaneous adjustment of the empirical parameters "A", "B" and "C" was the best alternative for calibration of the Hargreaves-Samani equation.

RESUMO A estimativa da evapotranspiração de referência é um importante fator para estudos hidrológicos, projeto e manejo de sistemas de irrigação, dentre outros. A equação de Penman Monteith apresenta elevada precisão e acurácia na estimativa desta variável. No entanto, o uso desta se torna limitado devido ao grande número de dados meteorológicos requeridos. Neste contexto, a equação de Hargreaves-Samani pode ser utilizada como alternativa, contudo, requer uma calibração local para a obtenção de melhores performances. Assim, objetivou-se comparar o processo de calibração da equação de Hargreaves-Samani via regressão linear, via ajuste dos coeficientes (A e B) e expoente (C) da equação e via combinações das duas alternativas anteriores. Foram utilizados dados diários de 6 estações meteorológicas, situadas no estado de Minas Gerais, do período de 1997 a 2016. A calibração da equação de Hargreaves-Samani foi realizada de cinco formas: calibração via regressão linear, ajuste do parâmetro "A", ajuste dos parâmetros "A" e "C", ajuste dos parâmetros "A", "B" e "C" e ajuste dos parâmetros "A", "B" e "C" seguido de calibração por regressão linear. As performances dos modelos foram avaliadas com base nos indicadores estatísticos erro absoluto médio, erro de viés médio, índice de concordância de Willmott, coeficiente de correlação e índice de desempenho. Todas as metodologias estudadas promoveram melhores estimativas da evapotranspiração de referência. O ajuste simultâneo dos parâmetros empíricos "A", "B" e "C" foi a melhor alternativa para calibração da equação de Hargreaves-Samani.