NAR–SPEI–NARX Hybrid Forecasting Model for Soil Moisture Index (SMI)

This paper introduces a new hybrid forecasting architecture that combines Nonlinear Autoregressive (NAR) models, the proxy Standardized Precipitation-Evapotranspiration Index (SPEI), and a Nonlinear Autoregressive with Exogenous Inputs (NARX) framework for Soil Moisture Index (SMI) prediction. The suggested methodology solves the crucial difficulty of combining future climatic knowledge into soil moisture forecasting by using a cascaded approach. Stage 1 uses univariate NAR models to create multi-step-ahead predictions of precipitation and temperature. Stage 2 converts these forecasts into proxy SPEI values using a physically based water balance computation, and Stage 3 employs a NARX model that uses observed historical SMI and forecast-derived proxy SPEI as exogenous inputs. The framework is assessed using high-frequency observations from 2014 to 2020, with training data through 2019 and validation covering the whole 2020 horizon. The study combining forecast-driven climatic indicators with autoregressive soil moisture dynamics resulted in prediction accuracy (R2 = 0.9888, RMSE = 0.0827, MAE = 0.0567). This study presents a new NAR–SPEI–NARX model for SMI prediction forecasting, based on three-stage modeling, where NAR models forecast precipitation and temperature and then turn them into SPEI-proxy as an exogenous input for NARX.