Estimation of Reference Evapotranspiration Using Limited Climatic Data and Bayesian Model Averaging

Motivated by the increased number of sensors and sensor networks for environmental and weather monitoring, we propose a method to estimate reference evapotranspiration (ETo) from limited climate data. There are several modifications to the standard FAO Penman-Monteith equation (FAO PM) that enables us to use limited climatic data for estimating ETo, however these equations have to be adjusted locally depending of the different climatic conditions. In this paper, we use Bayesian model averaging in order to determine the uncertainty of different models that explain ETo. Using this approach, we tackle the multi-collinearity problem of climatic variables by combining multiple regression models. More specifically, we consider estimation of ETo as a non- stationary regression problem where the rules governing the mean and noise processes might change depending of the different climatic conditions. In order to build the candidate models, we use a divide and conquer approach known as Treed Gaussian Processes (TGP) and then demonstrate the method by using time series of ETo calculated by means of the FAO PM equation. The results are also compared with other regression techniques and simplified equations for calculating ETo.