Temporal Lags and Depth-Dependent Soil Moisture Responses to Drought and Wet Periods in Europe

Understanding how drought signals propagate vertically through the soil profile is critical to improving hydroclimatic monitoring and predictability. Despite the widespread use of drought indices, large-scale, depth-resolved evaluations of their temporal relationships to soil moisture remain limited across climatically diverse regions. Here, we quantify the scale- and layer-dependent coupling between two widely used drought indices, the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI), and model-derived multi-layer soil moisture across Europe. SPI and SPEI were computed from ECAD station-based meteorological observations at accumulation timescales of 1, 3, 6, and 9 months. Monthly soil moisture was obtained independently from the FLDAS Noah land surface model and extracted from the nearest 0.10° grid cell for four soil layers: 0–10, 10–40, 40–100, and 100–200 cm. The analysis covered 2,022 paired ECAD–FLDAS locations over 1990–2024. Cross-correlation analysis identified maximum correlation strength and optimal lag structure. Results reveal a systematic vertical organization of drought propagation. The upper soil layers (0–10 and 10–40 cm) exhibited near-synchronous responses to short accumulation timescales, whereas deeper soil layers (40–100 and 100–200 cm) showed broader optimal-lag distributions and stronger associations with intermediate- to longer-timescales, consistent with subsurface moisture memory. A direct comparison across 40,392 paired location–layer–timescale combinations showed that SPEI produced slightly higher maximum absolute correlations than SPI in 59.6% of cases, with a small mean difference (Δ|r| ≈ +0.003), mainly in the upper soil layers. Because the drought indices and FLDAS soil moisture differ in spatial support and meteorological forcing, this difference is interpreted as specific to the ECAD–FLDAS pairing framework rather than as a product-independent estimate of the benefit of including evaporative demand. Drought- and wet-conditioned analyses revealed spatially varying deep-minus-surface soil moisture contrasts. Overall, drought–soil moisture coupling is strongly depth- and scale-dependent, whereas SPI–SPEI differences are small and subject to station–grid representativeness uncertainty.