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Quantile-Regression-Ensemble: A Deep Learning Algorithm for Downscaling Extreme Precipitation
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Proposes Quantile-Regression-Ensemble (QRE), which trains Bernoulli-Gamma network members on intensity-quantile partitions of precipitation data and combines them with a softly assigning weight network to downscale extreme precipitation over New Zealand.
Problem
Regression-based deep learning statistical downscaling of precipitation regresses to the mean and underestimates extreme precipitation, which has the largest societal impact.
Approach
Split training data into disjoint quantile intervals of total daily precipitation, train one BGNet member per interval, and aggregate members with a Softmax weight network trained with an Earth Mover's Distance loss over interval classes, giving a boosting-inspired ensemble that improves extreme-event accuracy.
Key results
- QRE lowers New Zealand-wide MSE by 4.8% relative to BG-Net, with significant gains on high-intensity intervals (0.9-1.0 MSE 282.6 vs 297.4 for BG-Net).
- On the out-of-domain 0.0-0.2 interval, QRE achieves MSE 2.4 vs 2.8 for BG-Net.
- QRE is not significantly better than BG-Net on moderate-intensity precipitation regions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use QRE instead of BG-Net | precipitation downscaling · New Zealand | MSE: 63.6±2.0 -> 60.8±0.5 | Helped |
| use QRE instead of BG-Net | precipitation downscaling · 0.9-1.0 precipitation interval | MSE: 297.4±8.5 -> 282.6±4.9 | Helped |
| use QRE instead of BG-Net | precipitation downscaling · 0.0-0.2 precipitation interval | MSE: 2.8±0.4 -> 2.4±0.3 | Helped |
| use QRE instead of BG-Net | precipitation downscaling · moderate-intensity regions (Napier, Auckland, Wellington) | MSE: 23.7±1.6 -> 24.5±0.4; 31.6±0.9 -> 33.2±0.5; 26.9±0.9 -> 27.7±0.3 | Hurt |
| use QRE instead of BG-Net | precipitation downscaling · 0.392-0.61 precipitation interval | MSE: 30.9±1.9 -> 29.4±0.8 | Helped |
| remove elevation predictor (ablation) | BG-Net precipitation downscaling · New Zealand | MSE: 63.6±2.0 -> 65.2±1.4 | Hurt |
| use convolution and max pooling before elevation interpolation (ablation) | BG-Net precipitation downscaling · New Zealand | MSE: 63.6±2.0 -> 63.3±1.5 | No clear effect |
| bilinearly interpolate elevation data (ablation) | BG-Net precipitation downscaling · New Zealand | MSE: 63.6±2.0 -> 63.2±1.4 | No clear effect |
| reduce ensemble members from 6 to 4 (ablation) | QRE · New Zealand, 0.0-0.2 precipitation interval | MSE: 295 | Mixed |
| reduce ensemble members from 6 to 2 (ablation) | QRE · New Zealand, 0.0-0.2 precipitation interval | MSE: 270 | Mixed |
Surprising findings
- Increasing the number of members beyond 4 causes MSE over all intensities to rise, showing a trade-off between high and low intensity performance.
- Bagging and Probability fixed-weight ensembles perform much worse on high-intensity intervals (MSE above 640 at 0.923-1.0).
Limitations
- Weight network struggles to classify low-precipitation samples, so gains are insignificant over moderate precipitation regions.
- Sensitive to the number of members N; performance trades off between high and low intensity intervals.
- Only one hyperparameter studied on a single country-scale dataset (New Zealand).
Experimental setup
Datasets: ERA5 VCSN NZ elevation data
Benchmarks: VCSN precipitation over New Zealand
Metrics: MSE
Baselines: BGNet BG-Net(-) BG-Embed BG-Interp Bagging Probability Naive-Ensemble Perfect-Member
Builds on: Bernoulli-Gamma network (BGNet) gradient boosting channel attention
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