A Hybrid Prophet–LSTM–BPNN Framework for Seasonal Drought Prediction

Drought is among the most destructive hydroclimatic hazards, particularly in arid and semi-arid regions, where water scarcity directly threatens agricultural production and socioeconomic stability. Reliable seasonal drought prediction is therefore essential for effective early warning and water resources management. This study proposes a sequential hybrid prediction framework, termed Prophet–LSTM–BPNN, that integrates the Prophet model, a long short-term memory (LSTM) network, and a backpropagation neural network (BPNN) for seasonal drought prediction in Iran. The framework is applied separately to monthly basin-averaged values of the three-month Standardized Precipitation Evapotranspiration Index (SPEI-3) for 30 major hydrological basins across Iran during 1990–2021, relying exclusively on univariate time-series data to ensure applicability in data-limited contexts. The modeling strategy hierarchically decomposes drought dynamics: Prophet captures dominant trends and seasonality, LSTM models the remaining nonlinear temporal structures, and the BPNN combines these intermediate outputs. Prediction skill is assessed using a five-fold rolling-origin expanding-window validation scheme, in which each model forecasts 12 monthly SPEI-3 values for five predefined target years: 2011, 2013, 2015, 2017, and 2019. Model performance is evaluated using the Nash-Sutcliffe efficiency (NSE), coefficient of determination (R 2 ), and root mean square error (RMSE). Performance is benchmarked against standalone and hybrid baselines, including Prophet, LSTM, Prophet–LSTM–Add, and Prophet–LSTM–Lin models. The results demonstrate that Prophet–LSTM–BPNN outperforms all baseline models, achieving a mean RMSE of 0.329 and a mean NSE of 0.833 across the 30 basins. Notably, it surpasses the linearly weighted hybrid model, Prophet–LSTM–Lin (RMSE = 0.359, NSE = 0.800), confirming that nonlinear fusion is essential for capturing complex interactions between trend and residual components. This study provides methodological guidance for seasonal drought prediction in data-limited and water-scarce regions and highlights the suitability of the Prophet–LSTM–BPNN framework as a predictive tool for basin-scale drought early warning.