Physics-Guided Neural Networks for Physically Consistent SPEI: A Bias Correction Framework for Drought Monitoring over Southern Africa

Abstract

The Standardised Precipitation-Evapotranspiration Index (SPEI) is widely used for drought monitoring, but reanalysis datasets like ERA5-Land contain biases that affect its reliability. Conventional bias correction, which adjusts variables independently, can violate the physical relationship between precipitation and PET. We introduce a Physics-Guided Neural Network (PGNN) that corrects both variables simultaneously while enforcing a water-balance constraint within the loss function. Using a rigorous temporal split (training 1950–2010, validation 2011–2018, testing 2019–2025), the PGNN framework shows improved performance compared with quantile distribution mapping (QDM). On the validation period (2011–2018), the correction reduces precipitation RMSE by 32% (from 40.4 to 27.6 mm month−1) and increases PET R2 from −2.820 to 0.890, compared with QDM’s 0.326. For the 3-month agricultural drought index, PGNN reduces RMSE by 27% (from 0.440 to 0.320), increases R2 from 0.737 to 0.857, and improves correlation from 0.890 to 0.943, whereas QDM shows only marginal improvement (R2 = 0.715). Consistent gains are observed across all timescales, with PGNN-corrected SPEI achieving R2 exceeding 0.78 for the 1-, 3-, and 6-month agricultural indices. At longer timescales, PGNN shows improved skill, achieving R2 = 0.101 and 0.113 for 12- and 24-month SPEI, respectively—outperforming QDM (R2 = 0.043 and 0.032). The period-specific analysis reveals two distinct degradation mechanisms: error accumulation in the water balance explains the decline from short to long timescales, while climate non-stationarity explains the degradation from the validation period to the test period. In the independent test period (2019–2025), both methods show substantial degradation: PGNN precipitation RMSE increases from 27.6 to 32.0 mm month−1 (+16%), PET R2 drops from 0.890 to 0.458 (−49%), and longer timescales (9–24 months) yield negative R2 values. Categorical metrics for extreme drought detection show mixed results on the validation period: the Critical Success Index (CSI) for Extreme Dry conditions (3-month SPEI) decreases from 0.269 (raw) to 0.164 for PGNN, while QDM achieves 0.277. This unexpected behaviour is attributed to the differing event distribution in the validation period. However, PGNN improves detection for severe and moderate dry classes, and Cohen’s Kappa increases from 0.552 (raw) to 0.646 (PGNN) compared with QDM’s 0.493. The water-balance constraint ensures climatic consistency and preserves the annual cycle (PET peaks in October at 148.1 mm month−1, close to the CRU reference of 152.2 mm month−1), while QDM introduces a two-month phase shift. The framework offers a potential scalable pathway for operational drought monitoring, but the test-period degradation suggests a need for adaptive correction methods that can track evolving climate baselines.