Fast multi-output relevance vector regression for joint groundwater and lake water depth modeling

Abstract

Fast multi-output relevance vector regression (FMRVR) algorithm is developed for simultaneous estimation of groundwater and lake water depth for the first time in this study. The FMRVR is a multi-output regression analysis technique which can simultaneously predict multiple outputs for a multi-dimensional input. The data used in this study is collected from 34 stations located in the lake Urmia basin over a 40-year time period. The performance of the FMRVR model is examined in contrast to the support vector regression (SVR) and multi-linear regression (MLR) benchmarks. Results reveal that FMRVR is able to generate more accurate estimation for groundwater and lake water depth with coefficient of determination (R2) of 0.856 and 0.992 and root mean square error (RMSE) of 0.857 and 0.083, respectively. The outperformance of FMRVR can be linked to its capability for a joint estimation of multiple relevant outputs by taking into account possible correlations among the outputs.