🌧 CASA — Indonesian Rainfall Forecasting

Climate-Adaptive Spatial Attention (傘 = umbrella) for LSTM-GSTARX. Headline result: a GSTAR-consistent LSTM-GSTARX(K;1) (spatial lag kept inside the recurrence) reaches RMSE 71.4 mm at K=12 (71.99±0.57 mm over three seeds) — about 10% below the best single-step deep model and 17% below the linear GSTAR baseline (Diebold-Mariano p < 0.001). 40 regions (38 IDN provinces + PNG + Borneo non-IDN), 484 months 1985–2025, 5-fold walk-forward CV.

1 — Overview

Best model
LSTM-GSTARX(24;1)
Best RMSE (mm)
71.10
± Std
6.55
Models × Folds
8 × 5
Full summary table
model rmse_mean rmse_std mae_mean mae_std n_folds
LSTM-GSTARX(24;1) 71.10 6.55 54.03 3.73 5
LSTM-GSTARX(18;1) 71.20 6.69 54.08 3.90 5
LSTM-GSTARX(12;1) 71.37 6.82 54.34 3.90 5
LSTM-GSTARX(6;1) 72.33 7.18 54.82 4.38 5
CASA LSTM-GSTARX(1;1) 80.34 7.62 60.63 4.11 5
LSTM-static (1;1) 80.36 7.64 60.64 4.13 5
GSTARX(1;1) 88.23 4.27 68.08 2.63 5
GSTAR(1;1) 88.79 4.21 68.37 2.18 5

2 — Per-Province Rainfall Forecast

Type to search (province name or ISO code), then pick from the box below. Black line = observed rainfall; dashed orange line = model forecast (CASA, LSTM-GSTARX) over the walk-forward test period. The RMSE in the title is the root-mean-square error over all displayed test months (the five walk-forward folds concatenated into one series) for that province — not the average of per-fold RMSEs.

3 — Model Comparison

4 — Diebold-Mariano Test (HLN-corrected)

|−log₁₀(p)| > 1.30 ≈ p < 0.05; > 2.0 ≈ p < 0.01; > 3.0 ≈ p < 0.001. Negative-signed (blue) cells: row outperforms column.

Significant pairs (p < 0.05)
model_A model_B dm_hln p_value A_better sig_001
LSTM-GSTARX(6;1) GSTAR(1;1) -6.924 4.46e-10 True True
LSTM-GSTARX(24;1) GSTAR(1;1) -6.800 7.99e-10 True True
LSTM-GSTARX(18;1) GSTAR(1;1) -6.779 8.83e-10 True True
LSTM-GSTARX(12;1) GSTAR(1;1) -6.688 1.36e-09 True True
LSTM-GSTARX(6;1) GSTARX(1;1) -6.674 1.45e-09 True True
LSTM-GSTARX(24;1) GSTARX(1;1) -6.580 2.26e-09 True True
LSTM-GSTARX(18;1) GSTARX(1;1) -6.565 2.41e-09 True True
LSTM-GSTARX(12;1) GSTARX(1;1) -6.456 4.02e-09 True True
CASA LSTM-GSTARX(1;1) GSTAR(1;1) -5.312 6.69e-07 True True
GSTAR(1;1) LSTM-static (1;1) 5.288 7.41e-07 False True
LSTM-GSTARX(6;1) LSTM-static (1;1) -5.256 8.50e-07 True True
CASA LSTM-GSTARX(1;1) LSTM-GSTARX(6;1) 5.238 9.17e-07 False True
LSTM-GSTARX(24;1) LSTM-static (1;1) -5.017 2.31e-06 True True
LSTM-GSTARX(18;1) LSTM-static (1;1) -5.011 2.37e-06 True True
CASA LSTM-GSTARX(1;1) LSTM-GSTARX(24;1) 5.004 2.44e-06 False True
CASA LSTM-GSTARX(1;1) LSTM-GSTARX(18;1) 4.997 2.51e-06 False True
LSTM-GSTARX(12;1) LSTM-static (1;1) -4.921 3.44e-06 True True
CASA LSTM-GSTARX(1;1) LSTM-GSTARX(12;1) 4.907 3.64e-06 False True
CASA LSTM-GSTARX(1;1) GSTARX(1;1) -4.670 9.50e-06 True True
GSTARX(1;1) LSTM-static (1;1) 4.646 1.05e-05 False True

5 — Regime-Stratified RMSE

CASA leans on learned spatial structure during El Niño / La Niña, while the geographic prior dominates in neutral periods (gate α tracks the signed Niño 3.4 index).

6 — α_t Timeline (CASA blending gate)

The CASA blending gate α_t over the test period (left axis) against the Niño 3.4 index (right axis). Lower α_t means more learned spatial structure relative to the geographic prior.

7 — Geographic Network & Per-province RMSE

KNN edges (k=5) overlaid. Marker colour = per-province RMSE from best CASA ablation; orange squares = boundary nodes (PNG, Borneo non-IDN), not forecast targets.