Non-Linear Output Structure Learning: A Novel Multi-Target Technique for Multi-Station and Multi-Index Drought Modelling

Abstract

Exiting artificial intelligence-based drought models estimate a single drought index in a single station. This study advances drought modelling by proposing Non-linear Output Structure Learning (NOSL) for simultaneously estimating two drought indices at eight stations. A multi-target drought model provides insights for a better understanding of the meteorological and hydrological impacts of drought. Hydro-meteorological data including precipitation evaporation and streamflow are used for a joint estimation of Streamflow Drought Index (SDI) and Standardized Precipitation Evapotranspiration Index (SPEI). The efficacy of the NOSL algorithm is examined against single-target Kernel Ridge Regression (KRR) and Fast Multi-output Relevance Vector Regression (FMRVR) models. The data during October 1981 to September 2015 at a monthly scale (408 Months) from eight different stations in Buyuk Menderes Basin (BMB) located (BMB) in Western Türkiye are used in this study. The effects of 1- 3- and 6-month Moving Average (MA) are also considered for drought estimation. Results show that NOSL can effectively estimate the SPEI and SDI indices and outperforms KRR and FMRVR benchmarks. The effectiveness of the NOSL technique can be linked to a structural modelling mechanism based on vector-valued functions where the dependencies among output variables are captured utilising a non-linear function for enhanced performance. The developed multi-target drought model based on the NOSL technique not only helps in incorporating multiple variables in the model for a better estimation but it enhances our understanding of various aspects of droughts and building adaptive strategies and resilience map counter to drought hazard. © 2025 Elsevier B.V. All rights reserved.