Exploring machine learning and multi-task learning to estimate meteorological data and reference evapotranspiration across Brazil

Abstract

Reference evapotranspiration (ETo) can be estimated using the FAO56-Penman-Monteith (FAO56-PM) equation but it requires commonly unavailable meteorological data. Therefore, this study assessed different approaches to estimate ETo based on temperature and relative humidity, and temperature only across Brazil, as follows: (i) using the FAO56-PM equation with missing data estimated based on FAO56 methodologies; (ii) using the FAO56-PM equation with missing data estimated based on machine learning; and (iii) estimating ETo directly using machine learning. The FAO56-PM equation was also calibrated through linear regression and by calibrating the methodologies used to estimate missing data. The potential benefits of using multi-task learning (MTL) and clustering were also investigated. Data from 437 weather stations were used. Artificial neural network (ANN), random forest (RF), extreme gradient boosting (XGBoost) and multivariate adaptive regression splines (MARS) were employed. In both general and clustering scenarios, calibrating the FAO56-PM equation using linear regression provided slightly better results than calibrating the methodologies used to estimate missing data. In contrast to temperature- and relative humidity-based FAO56-PM equation, its temperature-based version performed better before both calibration types assessed. The machine learning models performed the best to estimate ETo and missing data. Combining the machine learning models with the FAO56-PM equation to estimate ETo performed similarly to using them individually. MTL and single-task learning (STL) provided similar results. In the general scenario, for the temperature-based models, using PM-ANN-STL increased mean NSE from 0.49 to 0.53 in relation to the non-calibrated FAO56-PM equation. For the temperature- and relative humidity-based models, using ANN and RF developed with STL or MTL increased NSE from 0.56 to 0.67 in relation to the FAO56-PM equation calibrated using linear regression. When using the clustering strategy, performance gains were obtained in estimating ETo with the temperature-based models, increasing mean NSE up to 0.58.