cs.LGOct 5, 2026
SaveSkillful Data-Driven Subseasonal Soil Moisture Forecasting: Prospects and Limits for Flash Drought Prediction
Organizations: Applied Machine Learning Group, Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Berlin, Germany · Department of Signal Theory and Communications, Universidad Carlos III de Madrid (UC3M), Madrid, Spain
Abstract
Despite substantial progress in short-to-medium-range weather forecasting, predicting high-impact events such as flash droughts remains a key challenge for both early warning operations and physically-based subseasonal-to-seasonal (S2S) prediction systems. Here we demonstrate that, for S2S soil-moisture forecasting over Europe, forecast skill depends as much on how the prediction problem is formulated as on the forecasting model itself. Using a Vision Transformer-based architecture with dual-pathway temporal and spatial attention, we show that residual learning is essential to outperform persistence. This advantage is realized only when forecasting root-zone soil moisture in physical units rather than standardized anomalies, revealing that the target representation itself constrains predictability. A probabilistic extension via quantile-head fine-tuning further provides well-calibrated predictive distributions. Benchmarked against deep-learning and operational ECMWF S2S baselines over 2021-2022, our model achieves the highest deterministic and probabilistic skill at all lead times and reliably detects anomalously dry root-zone states (below the 20th percentile). Yet flash drought onset, defined by multi-pentad intensification criteria, remains a fundamental challenge shared across all current S2S systems. These findings advance data-driven S2S soil-moisture forecasting while highlighting the remaining challenge of predicting rapid drought development.
Figures & tables
Figure 1: Schematic overview of the proposed SMCast framework. (1) The end-to-end processing pipeline maps a historical sequence of daily ERA5 atmospheric and land-surface fields to future subseasonal soil moisture trajectories. (2) Input frames are converted into structured sequences via non-overlapping patch embedding with spatial positional encodings. The spatiotemporal encoder features a stack of factorized (divided) space–time attention blocks, where relative temporal distances are dynamically handled using Rotary Position Embeddings (RoPE). Within each block, parallel temporal and spatial self-attention pathways isolate local land-surface memory and regional hydroclimatic co-variability, respectively, before being integrated via a learnable fusion gate. (3) The lead-time conditioned decoder utilizes a shared projection head combined with horizon-specific learnable embeddings to directly generate multi-horizon target forecasts for all future pentad lead times simultaneously. Absolute target values are reconstructed using a residual learning formulation ( ) relative to the most recent observed soil moisture state ( ). (4) Flash drought events and standardized anomalies are subsequently diagnosed post-hoc by transforming the forecasted SM100 fields into percentile space.
| Lead | SMCast | U-Net | CrossFormer | E3D-LSTM | Persistence | Climatology |
|---|---|---|---|---|---|---|
| 1 (d 1–5) | 0.1035 | 0.1108 | 0.1130 | 0.1791 | 0.1081 | 0.3251 |
| 2 (d 6–10) | 0.1291 | 0.1359 | 0.1366 | 0.1930 | 0.1375 | 0.3237 |
| 3 (d 11–15) | 0.1473 | 0.1545 | 0.1539 | 0.2072 | 0.1602 | 0.3240 |
| 4 (d 16–20) | 0.1582 | 0.1673 | 0.1638 | 0.2194 | 0.1760 | 0.3241 |
| 5 (d 21–25) | 0.1686 | 0.1774 | 0.1744 | 0.2325 | 0.1932 | 0.3241 |
| 6 (d 26–30) | 0.1825 | 0.1897 | 0.1888 | 0.2495 | 0.2128 | 0.3240 |
Table 1: Per-lead MAE on the full 2021–2022 test set, reported as the mean across five random seeds and in normalized units (standardized over the training period). All DL models use the residual formulation, 90-day SM100 inputs, and a comparable parameter budget ( 65 M, except E3D-LSTM at 81 M; see Supplementary Text 3); persistence and climatology (seed-independent) are shown for reference. The Mean row is the average over leads, with the across-seed standard deviation; the best value at each lead time is in bold. Verification is against ERA5.
Figure 2: Forecast error and skill against climatology across pentad lead times. a) MAE (lower is better). b) Skill score vs. climatology (%; higher is better). Different colors lines and shapes correspond to the different models and baselines considered in this study. All scores are verified against ERA5 over the 2021–2022 test period and reported in physical units (m 3 m -3 ).
| Model | MAE (m 3 /m 3 ) | RMSE (m 3 /m 3 ) |
|---|---|---|
| Climatology | 0.0358 | 0.0498 |
| Persistence | 0.0172 | 0.0266 |
| ECMWF S2S (raw) | 0.0843 | 0.1234 |
| ECMWF S2S (BC) | 0.0197 | 0.0304 |
| SMCast (direct) | 0.0183 | 0.0263 |
| SMCast (residual) | 0.0134 | 0.0209 |
Table 2: Overall forecast performance averaged over the first nine pentad lead times (days 1–45). The comparison is restricted to leads 1–9 because the ECMWF S2S forecasts extend only to day 46, so the days 46–50 pentad is not available for S2S. Lower MAE/RMSE indicates better performance. All scores are verified against ERA5 over the 2021–2022 test period and reported in physical units (m 3 m -3 ).
Figure 3: Spatial anomaly correlation coefficient (ACC) for SMCast and ECMWF S2S (BC) at selected lead times. a) SMCast (residual) at pentad leads 1, 2, 4, 7 and 9; b) ECMWF S2S (BC) at the same leads. Higher values (darker blue) indicate better agreement with ERA5 anomalies. Anomalies are computed relative to the 1980–2015 training-period pentad-of-year climatology.
Figure 4: Spatial skill score vs. climatology (%) for SMCast and ECMWF S2S (BC) at selected pentad lead times (leads 1, 2, 4, 7, and 9; days 1–45). a) SMCast (residual); b) ECMWF S2S (BC), in the same lead order. Blue indicates regions where the model outperforms climatology; red indicates lower skill. Verification is against ERA5 over the 2021–2022 test period, with the reference climatology computed over the 1980–2015 training period.
| SM100 (residual) | SMA (residual) | |||
| Lead | MAE | Pers MAE | MAE | Pers MAE |
| 1 (d 1–5) | 0.1035 | 0.1081 | 0.3112 | 0.3090 |
| 2 (d 6–10) | 0.1289 | 0.1375 | 0.4427 | 0.4411 |
| 3 (d 11–15) | 0.1470 | 0.1602 | 0.5293 | 0.5280 |
| 4 (d 16–20) | 0.1575 | 0.1760 | 0.5836 | 0.5826 |
| 5 (d 21–25) | 0.1676 | 0.1932 | 0.6295 | 0.6284 |
Table 3: Per-lead MAE (normalized units) for SM100 vs. SMA as target variable, both using the residual formulation with 90-day inputs. Persistence MAE is shown for reference. Mean MAE and SS relative to the Persistence baseline are reported on the bottom row. Verification is against ERA5 over the 2021–2022 test period; values are in normalized units (standardized with training-period statistics). Both configurations are single training runs (seed 42), so the values are not directly comparable with the five-seed means of Table 1 .
Figure 5: Probabilistic forecast performance across pentad lead times. a) CRPS per lead time in physical units (m 3 /m 3 ) for SMCast QH, ECMWF S2S (raw), ECMWF S2S (BC), and climatology. b) CRPSS vs climatology (%). Verification is against ERA5 over the 2021–2022 test period, and the reference climatology is computed over the 1980–2015 training period.
Figure 6: Low-soil-moisture detection skill per lead time for the simple percentile threshold (SM percentile 20th), SMCast vs. ECMWF S2S (BC). a) CSI and POD (higher is better): SMCast outperforms S2S BC at all leads, with the largest advantage at short-to-medium leads. b) FAR (lower is better): SMCast is consistently more precise than S2S BC. The more demanding event-based definitions (Yuan onset, FDII) are reported in Table 4 . Verification is against ERA5 percentiles derived from the 1980–2015 pentad-of-year climatology over the 2021–2022 test period.
Figure 7: Spatial low-soil-moisture detection over the 2021–2022 test period. a) Top row: observed frequency of low-soil-moisture conditions (fraction of forecast dates with SM percentile 20th). b) Bottom row: SMCast CSI at leads 1, 5, and 9. Verification is against ERA5 percentiles derived from the 1980–2015 pentad-of-year climatology, over the 2021–2022 test period.
| Yuan onset | FDII ( 0) | FDII MAE | |||
|---|---|---|---|---|---|
| Lead | CSI | FAR | CSI | FAR | |
| 5 (d 21–25) | 0.04 / 0.02 | 0.84 / 0.95 | 0.02 / 0.02 | 0.88 / 0.95 | 0.24 / 0.35 |
| 7 (d 31–35) | 0.05 / 0.03 | 0.80 / 0.93 | 0.04 / 0.04 | 0.85 / 0.92 | 0.42 / 0.66 |
| 9 (d 41–45) | 0.05 / 0.04 | 0.81 / 0.92 | 0.04 / 0.05 | 0.85 / 0.90 | 0.33 / 0.46 |
Table 4: Event-based flash drought skill at selected lead times, for both SMCast (left) and ECMWF S2S (BC) (right). Both the Yuan onset criterion [ 5 ] and the FDII binary detection (FDII 0) yield near-zero CSI, reflecting the difficulty of resolving rapid intensification within a bounded forecast window. SMCast nonetheless shows higher precision (lower FAR) and lower continuous FDII error (FDII MAE) than ECMWF S2S (BC). Verification is against ERA5 percentiles derived from the 1980–2015 pentad-of-year climatology, over the 2021–2022 test period.
Figure 8: Reliability diagram for the probabilistic detection of low-soil-moisture conditions (SM percentile 20th). SMCast QH (red) closely follows the diagonal, indicating well-calibrated low-soil-moisture probabilities. The ECMWF S2S (BC) ensemble (orange) is systematically overconfident. Verification is against ERA5 percentiles derived from the 1980–2015 pentad-of-year climatology, over the 2021–2022 test period.
| Type | Short name | Description | Resolution |
| Inputs | d2m | 2m dewpoint temperature | 0.25 ∘ , daily |
| t2m_max | Daily maximum 2m temperature | ||
| msl | Mean sea level pressure | ||
| ws10 | 10m wind speed | ||
| e | Evaporation | ||
| pev | Potential evaporation |
Table 5: Summary of input and target variables.