Screening · May initialization · JJAS and its months
✓ = screening pass within the method (Holm across its targets); ✓✓ = also passes with Holm across all methods and targets (national aggregate only). A pass is screening evidence, not an adoption decision. Bold: the operational method. Skill is against the CHIRPS training climatology (0 = no better than climatology).
Region for the result tables
All Ethiopia (national aggregate)
| Method | Amount CRPSS 1993–2016 | Amount CRPSS 2017–2025 | Tercile RPSS (no blend) 1993–2016 | Tercile RPSS (no blend) 2017–2025 | Mean bias (mm) | MAE (mm) | Correlation | Spread–error | Reliability index | Members ≤ 1 mm |
|---|---|---|---|---|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -1.311 | -1.266 | -0.511 | -0.412 | +8.8 | 134.5 | 0.18 | 0.39 | 0.66 | 0.0% |
| Linear Scaling | -0.059 | -0.082 | -0.027 | -0.004 | +0.1 | 67.3 | 0.08 | 0.87 | 0.09 | 0.0% |
| Mean-Variance Scaling (operational) | -0.028 | -0.018 | -0.017 | +0.003 | -0.0 | 66.2 | 0.08 | 0.83 | 0.09 | 0.5% |
| Variance Scaling (unbounded) | -0.027 | -0.016 | -0.016 | +0.005 | -0.0 | 66.1 | 0.07 | 0.83 | 0.11 | 0.2% |
| Square-root-space Mean-Variance Scaling | -0.025 ✓ | -0.014 | -0.017 | +0.004 | -0.0 | 66.0 | 0.08 | 0.82 | 0.12 | 0.0% |
| Power Transformation | -0.027 | -0.016 | -0.017 | -0.000 | -0.0 | 66.1 | 0.07 | 0.83 | 0.12 | 0.0% |
| Delta Change | -0.030 | -0.058 | -0.015 | -0.034 | +0.1 | 67.3 | 0.08 | 0.98 | 0.05 | 0.0% |
| Local Intensity Scaling | -0.059 | -0.081 | -0.028 | -0.003 | +0.1 | 67.3 | 0.08 | 0.87 | 0.10 | 0.0% |
| Empirical Quantile Mapping | -0.040 | -0.032 | -0.024 | -0.008 | +0.1 | 65.8 | 0.06 | 0.83 | 0.14 | 0.0% |
| Gamma Quantile Mapping | -0.025 | -0.012 | -0.019 | +0.003 | -0.1 | 66.0 | 0.07 | 0.82 | 0.15 | 0.0% |
| Detrended Quantile Mapping | -0.056 | -0.078 | -0.044 | -0.055 | -0.7 | 67.3 | 0.08 | 0.83 | 0.17 | 0.0% |
| Quantile Delta Mapping | -0.062 | -0.097 | -0.062 | -0.062 | +1.2 | 67.6 | 0.08 | 0.84 | 0.21 | 0.0% |
| Scaled Distribution Mapping | -0.078 | -0.110 | -0.080 | -0.079 | -4.2 | 67.4 | 0.09 | 0.81 | 0.32 | 0.7% |
| CDF-transform | -0.061 | -0.081 | -0.061 | -0.059 | -0.1 | 67.4 | 0.08 | 0.78 | 0.21 | 0.0% |
| MVS with all-zero guard (variant) | -0.028 | -0.018 | -0.017 | +0.003 | -0.0 | 66.2 | 0.08 | 0.83 | 0.09 | 0.5% |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.788 | -0.613 | -0.764 | -0.816 | -1.311 |
| Linear Scaling | -0.121 | -0.029 | -0.064 | -0.090 | -0.059 |
| Mean-Variance Scaling (operational) | -0.096 | -0.007 | -0.028 | -0.060 | -0.028 |
| Variance Scaling (unbounded) | -0.093 | -0.000 ✓✓ | -0.021 ✓✓ | -0.058 ✓ | -0.027 |
| Square-root-space Mean-Variance Scaling | -0.088 ✓ | -0.003 ✓ | -0.023 ✓✓ | -0.057 ✓ | -0.025 ✓ |
| Power Transformation | -0.091 | -0.001 ✓ | -0.022 ✓✓ | -0.060 | -0.027 |
| Delta Change | -0.105 | +0.001 | -0.043 | -0.067 | -0.030 |
| Local Intensity Scaling | -0.118 | -0.028 | -0.061 | -0.087 | -0.059 |
| Empirical Quantile Mapping | -0.100 | -0.017 | -0.035 | -0.067 | -0.040 |
| Gamma Quantile Mapping | -0.088 ✓ | -0.006 | -0.021 ✓✓ | -0.056 ✓ | -0.025 |
| Detrended Quantile Mapping | -0.134 | -0.026 | -0.064 | -0.090 | -0.056 |
| Quantile Delta Mapping | -0.145 | -0.025 | -0.071 | -0.098 | -0.062 |
| Scaled Distribution Mapping | -0.162 | -0.037 | -0.084 | -0.107 | -0.078 |
| CDF-transform | -0.138 | -0.026 | -0.065 | -0.098 | -0.061 |
| MVS with all-zero guard (variant) | -0.096 | -0.007 | -0.028 | -0.060 | -0.028 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.450 | -0.394 | -0.405 | -0.383 | -0.511 |
| Linear Scaling | -0.118 | -0.046 | -0.040 | -0.072 | -0.027 |
| Mean-Variance Scaling (operational) | -0.113 | -0.029 | -0.031 | -0.064 | -0.017 |
| Variance Scaling (unbounded) | -0.109 | -0.024 | -0.026 | -0.058 | -0.016 |
| Square-root-space Mean-Variance Scaling | -0.101 ✓ | -0.026 | -0.027 | -0.058 | -0.017 |
| Power Transformation | -0.100 ✓ | -0.026 | -0.027 | -0.058 | -0.017 |
| Delta Change | -0.155 | -0.042 | -0.062 | -0.099 | -0.015 |
| Local Intensity Scaling | -0.127 | -0.045 | -0.039 | -0.072 | -0.028 |
| Empirical Quantile Mapping | -0.098 | -0.035 | -0.032 | -0.057 | -0.024 |
| Gamma Quantile Mapping | -0.108 | -0.027 | -0.026 | -0.057 | -0.019 |
| Detrended Quantile Mapping | -0.185 | -0.071 | -0.086 | -0.122 | -0.044 |
| Quantile Delta Mapping | -0.176 | -0.075 | -0.090 | -0.123 | -0.062 |
| Scaled Distribution Mapping | -0.213 | -0.091 | -0.114 | -0.144 | -0.080 |
| CDF-transform | -0.193 | -0.077 | -0.093 | -0.140 | -0.061 |
| MVS with all-zero guard (variant) | -0.113 | -0.029 | -0.031 | -0.064 | -0.017 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.550 | -0.566 | -0.610 | -0.641 | -1.266 |
| Linear Scaling | -0.065 | -0.035 | +0.019 | -0.086 | -0.082 |
| Mean-Variance Scaling (operational) | -0.030 | -0.000 | +0.055 | -0.034 | -0.018 |
| Variance Scaling (unbounded) | -0.026 | +0.006 | +0.059 | -0.031 | -0.016 |
| Square-root-space Mean-Variance Scaling | -0.021 | +0.003 | +0.058 | -0.031 | -0.014 |
| Power Transformation | -0.021 | +0.004 | +0.055 | -0.029 | -0.016 |
| Delta Change | -0.057 | -0.009 | +0.055 | -0.067 | -0.058 |
| Local Intensity Scaling | -0.063 | -0.034 | +0.020 | -0.083 | -0.081 |
| Empirical Quantile Mapping | -0.030 | -0.003 | +0.052 | -0.040 | -0.032 |
| Gamma Quantile Mapping | -0.021 | -0.001 | +0.057 | -0.029 | -0.012 |
| Detrended Quantile Mapping | -0.076 | -0.033 | +0.042 | -0.070 | -0.078 |
| Quantile Delta Mapping | -0.091 | -0.046 | +0.030 | -0.071 | -0.097 |
| Scaled Distribution Mapping | -0.102 | -0.057 | +0.021 | -0.079 | -0.110 |
| CDF-transform | -0.089 | -0.034 | +0.036 | -0.076 | -0.081 |
| MVS with all-zero guard (variant) | -0.030 | -0.000 | +0.055 | -0.034 | -0.018 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.831 | -0.650 | -0.802 | -0.855 | -1.379 |
| Linear Scaling | -0.131 | -0.040 | -0.070 | -0.096 | -0.070 |
| Mean-Variance Scaling (operational) | -0.109 | -0.014 | -0.035 | -0.069 | -0.039 |
| Variance Scaling (unbounded) | -0.106 | -0.008 ✓✓ | -0.029 ✓✓ | -0.068 ✓ | -0.038 |
| Square-root-space Mean-Variance Scaling | -0.101 ✓ | -0.010 ✓ | -0.030 ✓✓ | -0.066 ✓ | -0.037 ✓ |
| Power Transformation | -0.104 | -0.008 ✓ | -0.029 | -0.069 | -0.038 |
| Delta Change | -0.109 | +0.001 ✓ | -0.045 | -0.069 | -0.031 |
| Local Intensity Scaling | -0.129 | -0.040 | -0.068 | -0.094 | -0.070 |
| Empirical Quantile Mapping | -0.114 | -0.025 | -0.044 | -0.077 | -0.052 |
| Gamma Quantile Mapping | -0.101 ✓ | -0.012 | -0.029 ✓✓ | -0.066 ✓ | -0.037 |
| Detrended Quantile Mapping | -0.148 | -0.034 | -0.074 | -0.100 | -0.068 |
| Quantile Delta Mapping | -0.160 | -0.033 | -0.080 | -0.108 | -0.074 |
| Scaled Distribution Mapping | -0.183 | -0.048 | -0.098 | -0.122 | -0.095 |
| CDF-transform | -0.154 | -0.037 | -0.076 | -0.110 | -0.075 |
| MVS with all-zero guard (variant) | -0.109 | -0.014 | -0.035 | -0.069 | -0.039 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.327 | -0.305 | -0.345 | -0.326 | -0.412 |
| Linear Scaling | -0.025 | +0.007 | +0.060 | -0.065 | -0.004 |
| Mean-Variance Scaling (operational) | -0.056 | +0.022 | +0.066 | -0.041 | +0.003 |
| Variance Scaling (unbounded) | -0.049 | +0.026 | +0.071 | -0.036 | +0.005 |
| Square-root-space Mean-Variance Scaling | -0.032 | +0.022 | +0.065 | -0.034 | +0.004 |
| Power Transformation | -0.033 | +0.018 | +0.061 | -0.029 | -0.000 |
| Delta Change | -0.088 | +0.022 | +0.034 | -0.086 | -0.034 |
| Local Intensity Scaling | -0.032 | +0.005 | +0.060 | -0.063 | -0.003 |
| Empirical Quantile Mapping | -0.022 | +0.015 | +0.068 | -0.039 | -0.008 |
| Gamma Quantile Mapping | -0.042 | +0.017 | +0.064 | -0.030 | +0.003 |
| Detrended Quantile Mapping | -0.106 | -0.015 | +0.017 | -0.099 | -0.055 |
| Quantile Delta Mapping | -0.083 | -0.028 | +0.006 | -0.097 | -0.062 |
| Scaled Distribution Mapping | -0.095 | -0.042 | -0.005 | -0.118 | -0.079 |
| CDF-transform | -0.129 | -0.017 | +0.009 | -0.101 | -0.059 |
| MVS with all-zero guard (variant) | -0.056 | +0.022 | +0.066 | -0.041 | +0.003 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.4 | -0.3 | +1.1 | +8.4 | +8.8 |
| Linear Scaling | +0.1 | +0.1 | +0.1 | +0.1 | +0.1 |
| Mean-Variance Scaling (operational) | +0.1 | +0.3 | +0.1 | +0.1 | -0.0 |
| Variance Scaling (unbounded) | +0.1 | +0.1 | +0.0 | +0.0 | -0.0 |
| Square-root-space Mean-Variance Scaling | +0.0 | +0.1 | +0.1 | +0.1 | -0.0 |
| Power Transformation | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Delta Change | +0.1 | +0.1 | +0.1 | +0.1 | +0.1 |
| Local Intensity Scaling | +0.1 | +0.0 | +0.0 | +0.1 | +0.1 |
| Empirical Quantile Mapping | +0.1 | +0.0 | +0.0 | +0.0 | +0.1 |
| Gamma Quantile Mapping | +0.0 | +0.1 | +0.0 | +0.0 | -0.1 |
| Detrended Quantile Mapping | +0.0 | +0.2 | +0.0 | +0.1 | -0.7 |
| Quantile Delta Mapping | +0.8 | +0.4 | +0.6 | +0.7 | +1.2 |
| Scaled Distribution Mapping | -1.3 | -3.4 | -1.9 | -1.8 | -4.2 |
| CDF-transform | +0.2 | +0.3 | +0.2 | +0.2 | -0.1 |
| MVS with all-zero guard (variant) | +0.1 | +0.3 | +0.1 | +0.1 | -0.0 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.06 | +0.16 | +0.10 | +0.05 | +0.18 |
| Linear Scaling | -0.03 | +0.04 | -0.00 | -0.05 | +0.08 |
| Mean-Variance Scaling (operational) | -0.04 | +0.07 | +0.01 | -0.06 | +0.08 |
| Variance Scaling (unbounded) | -0.04 | +0.03 | -0.02 | -0.07 | +0.07 |
| Square-root-space Mean-Variance Scaling | -0.04 | +0.06 | +0.00 | -0.06 | +0.08 |
| Power Transformation | -0.04 | +0.04 | -0.02 | -0.06 | +0.07 |
| Delta Change | -0.03 | +0.04 | -0.00 | -0.05 | +0.08 |
| Local Intensity Scaling | -0.04 | +0.04 | -0.01 | -0.06 | +0.08 |
| Empirical Quantile Mapping | -0.05 | +0.04 | -0.02 | -0.07 | +0.06 |
| Gamma Quantile Mapping | -0.05 | +0.04 | -0.02 | -0.07 | +0.07 |
| Detrended Quantile Mapping | -0.03 | +0.04 | -0.00 | -0.06 | +0.08 |
| Quantile Delta Mapping | -0.03 | +0.03 | -0.01 | -0.05 | +0.08 |
| Scaled Distribution Mapping | -0.03 | +0.05 | -0.01 | -0.05 | +0.09 |
| CDF-transform | -0.02 | +0.04 | +0.00 | -0.05 | +0.08 |
| MVS with all-zero guard (variant) | -0.04 | +0.07 | +0.01 | -0.06 | +0.08 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.54 | 0.53 | 0.56 | 0.57 | 0.39 |
| Linear Scaling | 0.92 | 0.85 | 0.99 | 1.00 | 0.87 |
| Mean-Variance Scaling (operational) | 0.82 | 0.92 | 0.93 | 0.89 | 0.83 |
| Variance Scaling (unbounded) | 0.82 | 0.93 | 0.93 | 0.89 | 0.83 |
| Square-root-space Mean-Variance Scaling | 0.81 | 0.93 | 0.93 | 0.88 | 0.82 |
| Power Transformation | 0.82 | 0.94 | 0.93 | 0.89 | 0.83 |
| Delta Change | 0.93 | 1.02 | 0.98 | 0.95 | 0.98 |
| Local Intensity Scaling | 0.91 | 0.85 | 0.98 | 0.99 | 0.87 |
| Empirical Quantile Mapping | 0.82 | 0.93 | 0.92 | 0.89 | 0.83 |
| Gamma Quantile Mapping | 0.80 | 0.97 | 0.93 | 0.88 | 0.82 |
| Detrended Quantile Mapping | 0.81 | 0.92 | 0.91 | 0.88 | 0.83 |
| Quantile Delta Mapping | 0.81 | 0.96 | 0.92 | 0.90 | 0.84 |
| Scaled Distribution Mapping | 0.71 | 0.93 | 0.85 | 0.81 | 0.81 |
| CDF-transform | 0.79 | 0.83 | 0.87 | 0.86 | 0.78 |
| MVS with all-zero guard (variant) | 0.82 | 0.92 | 0.93 | 0.89 | 0.83 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.52 | 0.61 | 0.47 | 0.35 | 0.66 |
| Linear Scaling | 0.08 | 0.14 | 0.15 | 0.12 | 0.09 |
| Mean-Variance Scaling (operational) | 0.20 | 0.16 | 0.12 | 0.09 | 0.09 |
| Variance Scaling (unbounded) | 0.20 | 0.09 | 0.07 | 0.10 | 0.11 |
| Square-root-space Mean-Variance Scaling | 0.18 | 0.10 | 0.08 | 0.07 | 0.12 |
| Power Transformation | 0.14 | 0.07 | 0.09 | 0.08 | 0.12 |
| Delta Change | 0.18 | 0.20 | 0.21 | 0.12 | 0.05 |
| Local Intensity Scaling | 0.10 | 0.23 | 0.13 | 0.11 | 0.10 |
| Empirical Quantile Mapping | 0.18 | 0.23 | 0.16 | 0.11 | 0.14 |
| Gamma Quantile Mapping | 0.19 | 0.12 | 0.09 | 0.09 | 0.15 |
| Detrended Quantile Mapping | 0.28 | 0.32 | 0.30 | 0.19 | 0.17 |
| Quantile Delta Mapping | 0.24 | 0.30 | 0.25 | 0.17 | 0.21 |
| Scaled Distribution Mapping | 0.35 | 0.29 | 0.32 | 0.29 | 0.32 |
| CDF-transform | 0.31 | 0.32 | 0.32 | 0.21 | 0.21 |
| MVS with all-zero guard (variant) | 0.20 | 0.16 | 0.12 | 0.09 | 0.09 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Jun | 1484 | 100% | 1479 | 100% |
| Jul | 1484 | 100% | 1221 | 82% |
| Aug | 1484 | 100% | 1273 | 86% |
| Sep | 1484 | 100% | 1484 | 100% |
| JJAS | 1484 | 100% | 1484 | 100% |
Dry months: shares of totals at exactly 0 mm and at ≤ 1 mm, CHIRPS and corrected
| Exactly 0 mm | ≤ 1 mm | |
|---|---|---|
| Jun: CHIRPS | 0.1% | 1.4% |
| Raw ECMWF (no correction) | 0.0% | 4.7% |
| Linear Scaling | 0.0% | 3.2% |
| Mean-Variance Scaling (operational) | 1.7% | 3.2% |
| Variance Scaling (unbounded) | 1.3% | 2.5% |
| Square-root-space Mean-Variance Scaling | 0.0% | 1.8% |
| Power Transformation | 0.0% | 2.4% |
| Delta Change | 0.1% | 1.9% |
| Local Intensity Scaling | 1.5% | 1.5% |
| Empirical Quantile Mapping | 1.5% | 1.5% |
| Gamma Quantile Mapping | 1.5% | 2.5% |
| Detrended Quantile Mapping | 1.3% | 1.8% |
| Quantile Delta Mapping | 1.5% | 1.8% |
| Scaled Distribution Mapping | 6.4% | 6.6% |
| CDF-transform | 0.0% | 1.6% |
| MVS with all-zero guard (variant) | 1.7% | 3.2% |
| Jul: CHIRPS | 0.0% | 9.1% |
| Raw ECMWF (no correction) | 0.0% | 1.1% |
| Linear Scaling | 0.0% | 11.3% |
| Mean-Variance Scaling (operational) | 9.9% | 12.3% |
| Variance Scaling (unbounded) | 1.3% | 9.3% |
| Square-root-space Mean-Variance Scaling | 2.0% | 9.5% |
| Power Transformation | 0.0% | 9.5% |
| Delta Change | 0.0% | 9.6% |
| Local Intensity Scaling | 9.1% | 9.1% |
| Empirical Quantile Mapping | 9.1% | 9.1% |
| Gamma Quantile Mapping | 6.9% | 9.5% |
| Detrended Quantile Mapping | 9.1% | 10.1% |
| Quantile Delta Mapping | 9.1% | 10.2% |
| Scaled Distribution Mapping | 5.5% | 11.1% |
| CDF-transform | 0.0% | 9.5% |
| MVS with all-zero guard (variant) | 9.9% | 12.3% |
| Aug: CHIRPS | 0.0% | 4.4% |
| Raw ECMWF (no correction) | 0.0% | 1.6% |
| Linear Scaling | 0.0% | 7.4% |
| Mean-Variance Scaling (operational) | 5.9% | 8.5% |
| Variance Scaling (unbounded) | 0.4% | 4.9% |
| Square-root-space Mean-Variance Scaling | 0.4% | 5.4% |
| Power Transformation | 0.0% | 5.0% |
| Delta Change | 0.0% | 4.8% |
| Local Intensity Scaling | 4.4% | 4.4% |
| Empirical Quantile Mapping | 4.4% | 4.4% |
| Gamma Quantile Mapping | 1.7% | 4.7% |
| Detrended Quantile Mapping | 4.4% | 5.2% |
| Quantile Delta Mapping | 4.3% | 5.2% |
| Scaled Distribution Mapping | 3.0% | 6.3% |
| CDF-transform | 0.0% | 4.7% |
| MVS with all-zero guard (variant) | 5.9% | 8.5% |
| Sep: CHIRPS | 0.1% | 0.2% |
| Raw ECMWF (no correction) | 0.0% | 0.6% |
| Linear Scaling | 0.0% | 1.2% |
| Mean-Variance Scaling (operational) | 1.1% | 1.7% |
| Variance Scaling (unbounded) | 0.5% | 0.8% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.4% |
| Power Transformation | 0.0% | 0.8% |
| Delta Change | 0.1% | 0.3% |
| Local Intensity Scaling | 0.2% | 0.2% |
| Empirical Quantile Mapping | 0.2% | 0.2% |
| Gamma Quantile Mapping | 0.2% | 0.5% |
| Detrended Quantile Mapping | 0.2% | 0.3% |
| Quantile Delta Mapping | 0.3% | 0.3% |
| Scaled Distribution Mapping | 1.8% | 1.8% |
| CDF-transform | 0.0% | 0.1% |
| MVS with all-zero guard (variant) | 1.1% | 1.7% |
| JJAS: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 0.3% | 0.5% |
| Variance Scaling (unbounded) | 0.1% | 0.2% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.0% |
| Power Transformation | 0.0% | 0.0% |
| Delta Change | 0.0% | 0.0% |
| Local Intensity Scaling | 0.0% | 0.0% |
| Empirical Quantile Mapping | 0.0% | 0.0% |
| Gamma Quantile Mapping | 0.0% | 0.0% |
| Detrended Quantile Mapping | 0.0% | 0.0% |
| Quantile Delta Mapping | 0.0% | 0.0% |
| Scaled Distribution Mapping | 1.0% | 1.0% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 0.3% | 0.5% |
Distribution of the corrected members (mean, spread, 10th and 90th percentiles)
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.92 | 1.16 | 1.12 | 1.03 | 1.07 |
| Linear Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Mean-Variance Scaling (operational) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Variance Scaling (unbounded) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Square-root-space Mean-Variance Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Power Transformation | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Delta Change | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Local Intensity Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Detrended Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Quantile Delta Mapping | 1.01 | 1.00 | 1.00 | 1.01 | 1.00 |
| Scaled Distribution Mapping | 0.97 | 0.98 | 0.98 | 0.98 | 0.98 |
| CDF-transform | 1.00 | 1.00 | 1.00 | 1.01 | 1.00 |
| MVS with all-zero guard (variant) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.96 | 1.13 | 1.14 | 1.16 | 1.10 |
| Linear Scaling | 1.11 | 1.04 | 1.16 | 1.25 | 1.15 |
| Mean-Variance Scaling (operational) | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
| Variance Scaling (unbounded) | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Square-root-space Mean-Variance Scaling | 0.99 | 1.03 | 1.01 | 1.00 | 1.00 |
| Power Transformation | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Delta Change | 1.14 | 1.11 | 1.11 | 1.12 | 1.12 |
| Local Intensity Scaling | 1.09 | 1.00 | 1.08 | 1.23 | 1.13 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.98 | 1.01 | 0.99 | 0.98 | 1.00 |
| Detrended Quantile Mapping | 1.04 | 1.01 | 1.02 | 1.05 | 1.04 |
| Quantile Delta Mapping | 1.06 | 1.04 | 1.05 | 1.08 | 1.06 |
| Scaled Distribution Mapping | 0.94 | 1.01 | 1.01 | 0.97 | 1.02 |
| CDF-transform | 1.05 | 1.01 | 1.05 | 1.09 | 1.07 |
| MVS with all-zero guard (variant) | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.73 | 1.06 | 0.96 | 0.75 | 0.97 |
| Linear Scaling | 0.79 | 0.89 | 0.83 | 0.80 | 0.92 |
| Mean-Variance Scaling (operational) | 0.97 | 0.95 | 0.96 | 0.98 | 0.98 |
| Variance Scaling (unbounded) | 0.97 | 0.97 | 0.97 | 0.99 | 0.98 |
| Square-root-space Mean-Variance Scaling | 0.96 | 0.95 | 0.96 | 0.97 | 0.98 |
| Power Transformation | 0.93 | 0.95 | 0.95 | 0.96 | 0.98 |
| Delta Change | 0.86 | 0.91 | 0.91 | 0.91 | 0.94 |
| Local Intensity Scaling | 0.84 | 0.91 | 0.89 | 0.80 | 0.92 |
| Empirical Quantile Mapping | 0.98 | 0.98 | 0.99 | 0.98 | 0.99 |
| Gamma Quantile Mapping | 0.95 | 0.95 | 0.96 | 0.96 | 0.98 |
| Detrended Quantile Mapping | 0.91 | 0.95 | 0.94 | 0.95 | 0.96 |
| Quantile Delta Mapping | 0.93 | 0.94 | 0.95 | 0.94 | 0.97 |
| Scaled Distribution Mapping | 0.91 | 0.94 | 0.95 | 0.94 | 0.97 |
| CDF-transform | 0.92 | 0.95 | 0.93 | 0.94 | 0.96 |
| MVS with all-zero guard (variant) | 0.97 | 0.95 | 0.96 | 0.98 | 0.98 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.99 | 1.16 | 1.13 | 1.11 | 1.09 |
| Linear Scaling | 1.08 | 1.05 | 1.06 | 1.10 | 1.04 |
| Mean-Variance Scaling (operational) | 1.01 | 1.03 | 1.02 | 1.02 | 1.01 |
| Variance Scaling (unbounded) | 1.01 | 1.02 | 1.02 | 1.01 | 1.01 |
| Square-root-space Mean-Variance Scaling | 1.02 | 1.03 | 1.02 | 1.02 | 1.01 |
| Power Transformation | 1.02 | 1.02 | 1.02 | 1.02 | 1.01 |
| Delta Change | 1.07 | 1.05 | 1.04 | 1.05 | 1.04 |
| Local Intensity Scaling | 1.07 | 1.01 | 1.03 | 1.10 | 1.04 |
| Empirical Quantile Mapping | 1.03 | 1.02 | 1.02 | 1.02 | 1.01 |
| Gamma Quantile Mapping | 1.01 | 1.02 | 1.02 | 1.02 | 1.01 |
| Detrended Quantile Mapping | 1.04 | 1.02 | 1.02 | 1.03 | 1.02 |
| Quantile Delta Mapping | 1.04 | 1.02 | 1.02 | 1.04 | 1.02 |
| Scaled Distribution Mapping | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 |
| CDF-transform | 1.04 | 1.02 | 1.03 | 1.04 | 1.02 |
| MVS with all-zero guard (variant) | 1.01 | 1.03 | 1.02 | 1.02 | 1.01 |
JJAS R1+R2 rainfall domain
| Method | Amount CRPSS 1993–2016 | Amount CRPSS 2017–2025 | Tercile RPSS (no blend) 1993–2016 | Tercile RPSS (no blend) 2017–2025 | Mean bias (mm) | MAE (mm) | Correlation | Spread–error | Reliability index | Members ≤ 1 mm |
|---|---|---|---|---|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -1.328 | -1.314 | -0.545 | -0.520 | +14.7 | 196.3 | 0.24 | 0.37 | 0.82 | 0.0% |
| Linear Scaling | -0.043 | -0.081 | +0.001 | -0.026 | +0.2 | 97.0 | 0.15 | 0.85 | 0.21 | 0.0% |
| Mean-Variance Scaling (operational) | -0.015 | -0.024 | +0.010 | -0.013 | -0.1 | 95.8 | 0.16 | 0.83 | 0.17 | 0.0% |
| Variance Scaling (unbounded) | -0.015 | -0.024 | +0.010 | -0.013 | -0.1 | 95.8 | 0.16 | 0.83 | 0.16 | 0.0% |
| Square-root-space Mean-Variance Scaling | -0.014 | -0.023 | +0.010 | -0.014 | -0.1 | 95.6 | 0.15 | 0.83 | 0.17 | 0.0% |
| Power Transformation | -0.015 | -0.025 | +0.010 | -0.016 | -0.0 | 95.8 | 0.16 | 0.83 | 0.16 | 0.0% |
| Delta Change | -0.017 | -0.056 | +0.019 | -0.004 | +0.2 | 97.0 | 0.15 | 0.98 | 0.05 | 0.0% |
| Local Intensity Scaling | -0.043 | -0.080 | +0.001 | -0.026 | +0.2 | 97.0 | 0.15 | 0.85 | 0.21 | 0.0% |
| Empirical Quantile Mapping | -0.030 | -0.039 | -0.008 | -0.027 | +0.1 | 95.4 | 0.15 | 0.84 | 0.16 | 0.0% |
| Gamma Quantile Mapping | -0.014 | -0.023 | +0.010 | -0.015 | -0.1 | 95.6 | 0.15 | 0.82 | 0.17 | 0.0% |
| Detrended Quantile Mapping | -0.040 | -0.074 | -0.012 | -0.033 | -1.2 | 97.1 | 0.14 | 0.84 | 0.16 | 0.0% |
| Quantile Delta Mapping | -0.042 | -0.086 | -0.017 | -0.039 | +1.1 | 97.3 | 0.15 | 0.85 | 0.18 | 0.0% |
| Scaled Distribution Mapping | -0.057 | -0.099 | -0.032 | -0.058 | -6.4 | 97.3 | 0.15 | 0.83 | 0.30 | 0.5% |
| CDF-transform | -0.042 | -0.073 | -0.009 | -0.028 | -0.3 | 97.0 | 0.15 | 0.79 | 0.19 | 0.0% |
| MVS with all-zero guard (variant) | -0.015 | -0.024 | +0.010 | -0.013 | -0.1 | 95.8 | 0.16 | 0.83 | 0.17 | 0.0% |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.799 | -0.522 | -0.729 | -0.889 | -1.328 |
| Linear Scaling | -0.112 | -0.015 | -0.052 | -0.063 | -0.043 |
| Mean-Variance Scaling (operational) | -0.089 | +0.010 | -0.016 | -0.051 | -0.015 |
| Variance Scaling (unbounded) | -0.086 | +0.009 | -0.016 | -0.051 | -0.015 |
| Square-root-space Mean-Variance Scaling | -0.083 | +0.008 | -0.016 | -0.051 | -0.014 |
| Power Transformation | -0.086 | +0.008 | -0.017 | -0.051 | -0.015 |
| Delta Change | -0.098 | +0.013 | -0.035 | -0.047 | -0.017 |
| Local Intensity Scaling | -0.111 | -0.015 | -0.051 | -0.062 | -0.043 |
| Empirical Quantile Mapping | -0.099 | -0.007 | -0.031 | -0.065 | -0.030 |
| Gamma Quantile Mapping | -0.083 | +0.003 | -0.017 | -0.051 | -0.014 |
| Detrended Quantile Mapping | -0.125 | -0.010 | -0.054 | -0.068 | -0.040 |
| Quantile Delta Mapping | -0.137 | -0.006 | -0.058 | -0.070 | -0.042 |
| Scaled Distribution Mapping | -0.152 | -0.018 | -0.073 | -0.081 | -0.057 |
| CDF-transform | -0.128 | -0.008 | -0.052 | -0.067 | -0.042 |
| MVS with all-zero guard (variant) | -0.089 | +0.010 | -0.016 | -0.051 | -0.015 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.442 | -0.364 | -0.430 | -0.450 | -0.545 |
| Linear Scaling | -0.103 | +0.000 | -0.032 | -0.052 | +0.001 |
| Mean-Variance Scaling (operational) | -0.101 | +0.018 | -0.022 | -0.049 | +0.010 |
| Variance Scaling (unbounded) | -0.098 | +0.018 | -0.023 | -0.049 | +0.010 |
| Square-root-space Mean-Variance Scaling | -0.095 | +0.017 | -0.023 | -0.050 | +0.010 |
| Power Transformation | -0.097 | +0.017 | -0.024 | -0.049 | +0.010 |
| Delta Change | -0.093 | +0.020 | -0.040 | -0.050 | +0.019 |
| Local Intensity Scaling | -0.102 | -0.000 | -0.032 | -0.053 | +0.001 |
| Empirical Quantile Mapping | -0.108 | +0.006 | -0.040 | -0.058 | -0.008 |
| Gamma Quantile Mapping | -0.096 | +0.016 | -0.023 | -0.050 | +0.010 |
| Detrended Quantile Mapping | -0.131 | -0.004 | -0.063 | -0.072 | -0.012 |
| Quantile Delta Mapping | -0.141 | -0.001 | -0.067 | -0.077 | -0.017 |
| Scaled Distribution Mapping | -0.161 | -0.013 | -0.086 | -0.092 | -0.032 |
| CDF-transform | -0.134 | -0.000 | -0.056 | -0.072 | -0.009 |
| MVS with all-zero guard (variant) | -0.101 | +0.018 | -0.022 | -0.049 | +0.010 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.598 | -0.487 | -0.590 | -0.637 | -1.314 |
| Linear Scaling | -0.066 | -0.043 | +0.012 | -0.057 | -0.081 |
| Mean-Variance Scaling (operational) | -0.026 | -0.002 | +0.046 | -0.023 | -0.024 |
| Variance Scaling (unbounded) | -0.024 | -0.003 | +0.046 | -0.024 | -0.024 |
| Square-root-space Mean-Variance Scaling | -0.022 | -0.006 | +0.046 | -0.024 | -0.023 |
| Power Transformation | -0.020 | -0.006 | +0.043 | -0.021 | -0.025 |
| Delta Change | -0.058 | -0.016 | +0.048 | -0.048 | -0.056 |
| Local Intensity Scaling | -0.065 | -0.043 | +0.013 | -0.057 | -0.080 |
| Empirical Quantile Mapping | -0.034 | -0.011 | +0.041 | -0.036 | -0.039 |
| Gamma Quantile Mapping | -0.022 | -0.012 | +0.045 | -0.024 | -0.023 |
| Detrended Quantile Mapping | -0.075 | -0.035 | +0.038 | -0.046 | -0.074 |
| Quantile Delta Mapping | -0.090 | -0.042 | +0.031 | -0.045 | -0.086 |
| Scaled Distribution Mapping | -0.102 | -0.052 | +0.020 | -0.055 | -0.099 |
| CDF-transform | -0.084 | -0.035 | +0.033 | -0.049 | -0.073 |
| MVS with all-zero guard (variant) | -0.026 | -0.002 | +0.046 | -0.023 | -0.024 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.841 | -0.560 | -0.769 | -0.933 | -1.398 |
| Linear Scaling | -0.123 | -0.027 | -0.059 | -0.072 | -0.056 |
| Mean-Variance Scaling (operational) | -0.102 | +0.003 | -0.023 | -0.060 | -0.026 |
| Variance Scaling (unbounded) | -0.099 | +0.002 | -0.023 | -0.061 | -0.026 |
| Square-root-space Mean-Variance Scaling | -0.096 | +0.002 | -0.023 | -0.060 | -0.025 |
| Power Transformation | -0.099 | +0.002 | -0.024 | -0.061 | -0.026 |
| Delta Change | -0.102 | +0.014 | -0.037 | -0.049 | -0.017 |
| Local Intensity Scaling | -0.122 | -0.027 | -0.059 | -0.072 | -0.056 |
| Empirical Quantile Mapping | -0.113 | -0.015 | -0.039 | -0.075 | -0.042 |
| Gamma Quantile Mapping | -0.096 | -0.002 | -0.024 | -0.060 | -0.025 |
| Detrended Quantile Mapping | -0.139 | -0.018 | -0.063 | -0.078 | -0.052 |
| Quantile Delta Mapping | -0.152 | -0.012 | -0.067 | -0.079 | -0.053 |
| Scaled Distribution Mapping | -0.172 | -0.028 | -0.086 | -0.095 | -0.073 |
| CDF-transform | -0.143 | -0.019 | -0.063 | -0.078 | -0.055 |
| MVS with all-zero guard (variant) | -0.102 | +0.003 | -0.023 | -0.060 | -0.026 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.414 | -0.319 | -0.404 | -0.338 | -0.520 |
| Linear Scaling | -0.020 | -0.023 | +0.044 | -0.046 | -0.026 |
| Mean-Variance Scaling (operational) | -0.011 | -0.004 | +0.053 | -0.032 | -0.013 |
| Variance Scaling (unbounded) | -0.006 | -0.004 | +0.053 | -0.032 | -0.013 |
| Square-root-space Mean-Variance Scaling | -0.002 | -0.007 | +0.052 | -0.030 | -0.014 |
| Power Transformation | +0.002 | -0.011 | +0.049 | -0.026 | -0.016 |
| Delta Change | -0.022 | +0.002 | +0.059 | -0.049 | -0.004 |
| Local Intensity Scaling | -0.019 | -0.023 | +0.043 | -0.047 | -0.026 |
| Empirical Quantile Mapping | -0.015 | -0.008 | +0.057 | -0.037 | -0.027 |
| Gamma Quantile Mapping | -0.003 | -0.010 | +0.051 | -0.028 | -0.015 |
| Detrended Quantile Mapping | -0.031 | -0.027 | +0.050 | -0.052 | -0.033 |
| Quantile Delta Mapping | -0.036 | -0.031 | +0.040 | -0.053 | -0.039 |
| Scaled Distribution Mapping | -0.052 | -0.047 | +0.033 | -0.069 | -0.058 |
| CDF-transform | -0.039 | -0.026 | +0.052 | -0.052 | -0.028 |
| MVS with all-zero guard (variant) | -0.011 | -0.004 | +0.053 | -0.032 | -0.013 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +4.1 | -8.2 | -2.5 | +21.3 | +14.7 |
| Linear Scaling | +0.2 | +0.1 | +0.1 | +0.1 | +0.2 |
| Mean-Variance Scaling (operational) | +0.1 | +0.1 | +0.0 | +0.0 | -0.1 |
| Variance Scaling (unbounded) | +0.1 | +0.1 | +0.0 | +0.0 | -0.1 |
| Square-root-space Mean-Variance Scaling | +0.1 | -0.0 | +0.0 | +0.0 | -0.1 |
| Power Transformation | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Delta Change | +0.2 | +0.1 | +0.1 | +0.1 | +0.2 |
| Local Intensity Scaling | +0.2 | +0.1 | +0.1 | +0.1 | +0.2 |
| Empirical Quantile Mapping | +0.1 | +0.1 | +0.0 | +0.0 | +0.1 |
| Gamma Quantile Mapping | +0.1 | +0.1 | +0.0 | +0.0 | -0.1 |
| Detrended Quantile Mapping | -0.1 | +0.2 | +0.0 | +0.1 | -1.2 |
| Quantile Delta Mapping | +1.0 | +0.4 | +0.6 | +0.5 | +1.1 |
| Scaled Distribution Mapping | -1.4 | -5.7 | -2.9 | -2.4 | -6.4 |
| CDF-transform | +0.1 | +0.4 | +0.1 | -0.1 | -0.3 |
| MVS with all-zero guard (variant) | +0.1 | +0.1 | +0.0 | +0.0 | -0.1 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.09 | +0.23 | +0.12 | +0.08 | +0.24 |
| Linear Scaling | +0.01 | +0.09 | -0.02 | -0.04 | +0.15 |
| Mean-Variance Scaling (operational) | +0.00 | +0.11 | -0.00 | -0.03 | +0.16 |
| Variance Scaling (unbounded) | +0.00 | +0.11 | -0.00 | -0.03 | +0.16 |
| Square-root-space Mean-Variance Scaling | -0.00 | +0.11 | -0.00 | -0.03 | +0.15 |
| Power Transformation | -0.00 | +0.11 | -0.00 | -0.03 | +0.16 |
| Delta Change | +0.01 | +0.09 | -0.02 | -0.04 | +0.15 |
| Local Intensity Scaling | +0.01 | +0.08 | -0.02 | -0.04 | +0.15 |
| Empirical Quantile Mapping | -0.01 | +0.10 | -0.01 | -0.04 | +0.15 |
| Gamma Quantile Mapping | -0.00 | +0.11 | -0.01 | -0.03 | +0.15 |
| Detrended Quantile Mapping | +0.00 | +0.08 | -0.02 | -0.04 | +0.14 |
| Quantile Delta Mapping | +0.01 | +0.08 | -0.02 | -0.04 | +0.15 |
| Scaled Distribution Mapping | +0.01 | +0.09 | -0.02 | -0.03 | +0.15 |
| CDF-transform | +0.01 | +0.10 | -0.00 | -0.03 | +0.15 |
| MVS with all-zero guard (variant) | +0.00 | +0.11 | -0.00 | -0.03 | +0.16 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.55 | 0.51 | 0.54 | 0.56 | 0.37 |
| Linear Scaling | 0.91 | 0.83 | 0.97 | 0.94 | 0.85 |
| Mean-Variance Scaling (operational) | 0.82 | 0.92 | 0.93 | 0.89 | 0.83 |
| Variance Scaling (unbounded) | 0.82 | 0.94 | 0.94 | 0.89 | 0.83 |
| Square-root-space Mean-Variance Scaling | 0.81 | 0.94 | 0.94 | 0.88 | 0.83 |
| Power Transformation | 0.82 | 0.94 | 0.93 | 0.89 | 0.83 |
| Delta Change | 0.93 | 1.03 | 0.98 | 0.96 | 0.98 |
| Local Intensity Scaling | 0.90 | 0.83 | 0.97 | 0.94 | 0.85 |
| Empirical Quantile Mapping | 0.82 | 0.93 | 0.93 | 0.89 | 0.84 |
| Gamma Quantile Mapping | 0.80 | 0.97 | 0.94 | 0.88 | 0.82 |
| Detrended Quantile Mapping | 0.81 | 0.93 | 0.92 | 0.89 | 0.84 |
| Quantile Delta Mapping | 0.81 | 0.97 | 0.93 | 0.90 | 0.85 |
| Scaled Distribution Mapping | 0.72 | 0.95 | 0.87 | 0.82 | 0.83 |
| CDF-transform | 0.79 | 0.84 | 0.87 | 0.86 | 0.79 |
| MVS with all-zero guard (variant) | 0.82 | 0.92 | 0.93 | 0.89 | 0.83 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.55 | 0.57 | 0.54 | 0.56 | 0.82 |
| Linear Scaling | 0.16 | 0.22 | 0.14 | 0.15 | 0.21 |
| Mean-Variance Scaling (operational) | 0.22 | 0.11 | 0.11 | 0.13 | 0.17 |
| Variance Scaling (unbounded) | 0.23 | 0.11 | 0.11 | 0.14 | 0.16 |
| Square-root-space Mean-Variance Scaling | 0.23 | 0.10 | 0.10 | 0.13 | 0.17 |
| Power Transformation | 0.22 | 0.10 | 0.10 | 0.13 | 0.16 |
| Delta Change | 0.09 | 0.03 | 0.04 | 0.05 | 0.05 |
| Local Intensity Scaling | 0.17 | 0.22 | 0.14 | 0.15 | 0.21 |
| Empirical Quantile Mapping | 0.20 | 0.10 | 0.11 | 0.13 | 0.16 |
| Gamma Quantile Mapping | 0.23 | 0.09 | 0.10 | 0.13 | 0.17 |
| Detrended Quantile Mapping | 0.20 | 0.10 | 0.12 | 0.13 | 0.16 |
| Quantile Delta Mapping | 0.22 | 0.09 | 0.14 | 0.12 | 0.18 |
| Scaled Distribution Mapping | 0.33 | 0.19 | 0.26 | 0.23 | 0.30 |
| CDF-transform | 0.22 | 0.15 | 0.15 | 0.13 | 0.19 |
| MVS with all-zero guard (variant) | 0.22 | 0.11 | 0.11 | 0.13 | 0.17 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Jun | 833 | 100% | 833 | 100% |
| Jul | 833 | 100% | 833 | 100% |
| Aug | 833 | 100% | 833 | 100% |
| Sep | 833 | 100% | 833 | 100% |
| JJAS | 833 | 100% | 833 | 100% |
Dry months: shares of totals at exactly 0 mm and at ≤ 1 mm, CHIRPS and corrected
| Exactly 0 mm | ≤ 1 mm | |
|---|---|---|
| Jun: CHIRPS | 0.0% | 0.7% |
| Raw ECMWF (no correction) | 0.0% | 1.2% |
| Linear Scaling | 0.0% | 1.1% |
| Mean-Variance Scaling (operational) | 0.7% | 1.0% |
| Variance Scaling (unbounded) | 0.3% | 0.4% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.5% |
| Power Transformation | 0.0% | 0.5% |
| Delta Change | 0.0% | 0.9% |
| Local Intensity Scaling | 0.7% | 0.7% |
| Empirical Quantile Mapping | 0.7% | 0.7% |
| Gamma Quantile Mapping | 0.7% | 1.0% |
| Detrended Quantile Mapping | 0.6% | 0.8% |
| Quantile Delta Mapping | 0.7% | 0.9% |
| Scaled Distribution Mapping | 2.3% | 2.3% |
| CDF-transform | 0.0% | 0.6% |
| MVS with all-zero guard (variant) | 0.7% | 1.0% |
| Jul: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 0.0% | 0.0% |
| Variance Scaling (unbounded) | 0.0% | 0.0% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.0% |
| Power Transformation | 0.0% | 0.0% |
| Delta Change | 0.0% | 0.0% |
| Local Intensity Scaling | 0.0% | 0.0% |
| Empirical Quantile Mapping | 0.0% | 0.0% |
| Gamma Quantile Mapping | 0.0% | 0.0% |
| Detrended Quantile Mapping | 0.0% | 0.0% |
| Quantile Delta Mapping | 0.0% | 0.0% |
| Scaled Distribution Mapping | 1.2% | 1.2% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 0.0% | 0.0% |
| Aug: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 0.0% | 0.0% |
| Variance Scaling (unbounded) | 0.0% | 0.0% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.0% |
| Power Transformation | 0.0% | 0.0% |
| Delta Change | 0.0% | 0.0% |
| Local Intensity Scaling | 0.0% | 0.0% |
| Empirical Quantile Mapping | 0.0% | 0.0% |
| Gamma Quantile Mapping | 0.0% | 0.0% |
| Detrended Quantile Mapping | 0.0% | 0.0% |
| Quantile Delta Mapping | 0.0% | 0.0% |
| Scaled Distribution Mapping | 0.9% | 0.9% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 0.0% | 0.0% |
| Sep: CHIRPS | 0.0% | 0.2% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 0.1% | 0.1% |
| Variance Scaling (unbounded) | 0.0% | 0.0% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.0% |
| Power Transformation | 0.0% | 0.0% |
| Delta Change | 0.0% | 0.2% |
| Local Intensity Scaling | 0.2% | 0.2% |
| Empirical Quantile Mapping | 0.2% | 0.2% |
| Gamma Quantile Mapping | 0.2% | 0.2% |
| Detrended Quantile Mapping | 0.1% | 0.1% |
| Quantile Delta Mapping | 0.2% | 0.2% |
| Scaled Distribution Mapping | 1.1% | 1.1% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 0.1% | 0.1% |
| JJAS: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 0.0% | 0.0% |
| Variance Scaling (unbounded) | 0.0% | 0.0% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.0% |
| Power Transformation | 0.0% | 0.0% |
| Delta Change | 0.0% | 0.0% |
| Local Intensity Scaling | 0.0% | 0.0% |
| Empirical Quantile Mapping | 0.0% | 0.0% |
| Gamma Quantile Mapping | 0.0% | 0.0% |
| Detrended Quantile Mapping | 0.0% | 0.0% |
| Quantile Delta Mapping | 0.0% | 0.0% |
| Scaled Distribution Mapping | 1.0% | 1.0% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 0.0% | 0.0% |
Distribution of the corrected members (mean, spread, 10th and 90th percentiles)
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.01 | 0.97 | 0.99 | 1.12 | 1.01 |
| Linear Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Mean-Variance Scaling (operational) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Variance Scaling (unbounded) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Square-root-space Mean-Variance Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Power Transformation | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Delta Change | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Local Intensity Scaling | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Detrended Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Quantile Delta Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Scaled Distribution Mapping | 0.99 | 0.98 | 0.99 | 0.98 | 0.99 |
| CDF-transform | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| MVS with all-zero guard (variant) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.01 | 0.80 | 0.89 | 1.05 | 0.93 |
| Linear Scaling | 1.02 | 0.84 | 0.94 | 0.99 | 0.94 |
| Mean-Variance Scaling (operational) | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Variance Scaling (unbounded) | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Square-root-space Mean-Variance Scaling | 1.00 | 1.01 | 1.00 | 1.00 | 1.00 |
| Power Transformation | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Delta Change | 1.13 | 1.05 | 1.06 | 1.07 | 1.12 |
| Local Intensity Scaling | 1.02 | 0.83 | 0.93 | 0.99 | 0.94 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.99 | 1.02 | 1.00 | 0.99 | 1.00 |
| Detrended Quantile Mapping | 1.01 | 0.99 | 1.00 | 1.01 | 1.01 |
| Quantile Delta Mapping | 1.03 | 1.01 | 1.02 | 1.03 | 1.02 |
| Scaled Distribution Mapping | 0.95 | 0.99 | 0.99 | 0.95 | 1.08 |
| CDF-transform | 1.02 | 0.96 | 1.00 | 1.01 | 0.99 |
| MVS with all-zero guard (variant) | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.96 | 1.00 | 0.98 | 1.11 | 1.00 |
| Linear Scaling | 0.95 | 1.04 | 1.00 | 0.99 | 1.00 |
| Mean-Variance Scaling (operational) | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 |
| Variance Scaling (unbounded) | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 |
| Square-root-space Mean-Variance Scaling | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 |
| Power Transformation | 0.97 | 0.99 | 0.99 | 0.99 | 0.99 |
| Delta Change | 0.91 | 0.96 | 0.97 | 0.95 | 0.97 |
| Local Intensity Scaling | 0.95 | 1.04 | 1.00 | 0.99 | 1.00 |
| Empirical Quantile Mapping | 0.97 | 0.98 | 0.99 | 0.98 | 0.99 |
| Gamma Quantile Mapping | 0.98 | 0.98 | 0.99 | 0.99 | 1.00 |
| Detrended Quantile Mapping | 0.96 | 0.99 | 0.98 | 0.97 | 0.99 |
| Quantile Delta Mapping | 0.96 | 0.98 | 0.98 | 0.98 | 0.99 |
| Scaled Distribution Mapping | 0.97 | 0.98 | 0.98 | 0.98 | 0.99 |
| CDF-transform | 0.97 | 1.00 | 0.99 | 0.98 | 0.99 |
| MVS with all-zero guard (variant) | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 |
| Method | Jun | Jul | Aug | Sep | JJAS |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.04 | 0.95 | 0.99 | 1.12 | 1.01 |
| Linear Scaling | 1.01 | 0.98 | 1.00 | 1.01 | 1.00 |
| Mean-Variance Scaling (operational) | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
| Variance Scaling (unbounded) | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
| Square-root-space Mean-Variance Scaling | 1.01 | 1.02 | 1.01 | 1.01 | 1.01 |
| Power Transformation | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
| Delta Change | 1.05 | 1.03 | 1.02 | 1.03 | 1.03 |
| Local Intensity Scaling | 1.01 | 0.97 | 0.99 | 1.01 | 1.00 |
| Empirical Quantile Mapping | 1.02 | 1.01 | 1.01 | 1.01 | 1.01 |
| Gamma Quantile Mapping | 1.00 | 1.02 | 1.01 | 1.01 | 1.01 |
| Detrended Quantile Mapping | 1.02 | 1.01 | 1.01 | 1.02 | 1.01 |
| Quantile Delta Mapping | 1.02 | 1.01 | 1.01 | 1.02 | 1.01 |
| Scaled Distribution Mapping | 0.98 | 0.98 | 0.99 | 0.98 | 0.99 |
| CDF-transform | 1.02 | 1.00 | 1.01 | 1.01 | 1.01 |
| MVS with all-zero guard (variant) | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 |
Screening statistics
Every method, target and score (within-method and family-wide Holm)
Screening rule (docs/36 rule applied as a screen): a method passes for a target and score if, on the leave-one-year-out 1993-2016 per-year scores, its mean improvement over mvs has a one-sided sign-flip p-value below 0.05 after Holm adjustment, and its mean score over 2017-2025 (fits on 1993-2016) is not worse. 'screen_pass': Holm across the 5 targets of one method. 'screen_pass_family': Holm across every method and target of the benchmark for that score. A screening pass is not an operational adoption decision (see the confirmation run).
| Method | Target | Δ CRPS 1993–2016 (mm) | 95% interval | Years better | p (one-sided) | Holm p (method) | Holm p (all 60) | Δ 2017–2025 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Jun | +0.42 | +0.20 to +0.65 | 5/24 | 0.9993 | 1.0000 | 1.0000 | +0.67 | — |
| Linear Scaling | Jul | +0.50 | +0.19 to +0.82 | 9/24 | 0.9965 | 1.0000 | 1.0000 | +0.77 | — |
| Linear Scaling | Aug | +0.71 | +0.44 to +1.02 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.80 | — |
| Linear Scaling | Sep | +0.55 | +0.38 to +0.71 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.04 | — |
| Linear Scaling | JJAS | +1.48 | +0.68 to +2.32 | 6/24 | 0.9993 | 1.0000 | 1.0000 | +2.90 | — |
| Variance Scaling (unbounded) | Jun | -0.04 | -0.08 to +0.00 | 12/24 | 0.0473 | 0.0946 | 1.0000 | -0.07 | — |
| Variance Scaling (unbounded) | Jul | -0.14 | -0.17 to -0.10 | 23/24 | 0.0000 | 0.0000 | 0.0000 | -0.14 | ✓✓ |
| Variance Scaling (unbounded) | Aug | -0.13 | -0.15 to -0.11 | 24/24 | 0.0000 | 0.0000 | 0.0000 | -0.08 | ✓✓ |
| Variance Scaling (unbounded) | Sep | -0.03 | -0.05 to -0.01 | 19/24 | 0.0030 | 0.0090 | 0.1557 | -0.05 | ✓ |
| Variance Scaling (unbounded) | JJAS | -0.04 | -0.08 to +0.01 | 19/24 | 0.0531 | 0.0946 | 1.0000 | -0.09 | — |
| Square-root-space Mean-Variance Scaling | Jun | -0.13 | -0.21 to -0.04 | 18/24 | 0.0030 | 0.0090 | 0.1557 | -0.16 | ✓ |
| Square-root-space Mean-Variance Scaling | Jul | -0.08 | -0.13 to -0.02 | 17/24 | 0.0070 | 0.0139 | 0.3478 | -0.08 | ✓ |
| Square-root-space Mean-Variance Scaling | Aug | -0.10 | -0.13 to -0.07 | 22/24 | 0.0000 | 0.0000 | 0.0000 | -0.06 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Sep | -0.06 | -0.09 to -0.03 | 18/24 | 0.0011 | 0.0045 | 0.0610 | -0.05 | ✓ |
| Square-root-space Mean-Variance Scaling | JJAS | -0.11 | -0.20 to -0.02 | 16/24 | 0.0111 | 0.0139 | 0.5330 | -0.18 | ✓ |
| Power Transformation | Jun | -0.07 | -0.14 to +0.01 | 17/24 | 0.0420 | 0.1261 | 1.0000 | -0.17 | — |
| Power Transformation | Jul | -0.12 | -0.19 to -0.06 | 20/24 | 0.0009 | 0.0038 | 0.0517 | -0.09 | ✓ |
| Power Transformation | Aug | -0.12 | -0.18 to -0.07 | 20/24 | 0.0000 | 0.0002 | 0.0017 | -0.01 | ✓✓ |
| Power Transformation | Sep | -0.01 | -0.07 to +0.04 | 12/24 | 0.3596 | 0.5845 | 1.0000 | -0.10 | — |
| Power Transformation | JJAS | -0.02 | -0.11 to +0.06 | 13/24 | 0.2923 | 0.5845 | 1.0000 | -0.07 | — |
| Delta Change | Jun | +0.15 | -0.18 to +0.52 | 13/24 | 0.7837 | 1.0000 | 1.0000 | +0.52 | — |
| Delta Change | Jul | -0.16 | -0.40 to +0.06 | 15/24 | 0.1076 | 0.5378 | 1.0000 | +0.19 | — |
| Delta Change | Aug | +0.31 | +0.04 to +0.60 | 9/24 | 0.9772 | 1.0000 | 1.0000 | +0.01 | — |
| Delta Change | Sep | +0.12 | -0.13 to +0.36 | 8/24 | 0.8097 | 1.0000 | 1.0000 | +0.66 | — |
| Delta Change | JJAS | +0.11 | -0.91 to +1.15 | 12/24 | 0.5781 | 1.0000 | 1.0000 | +1.82 | — |
| Local Intensity Scaling | Jun | +0.37 | +0.15 to +0.59 | 5/24 | 0.9982 | 1.0000 | 1.0000 | +0.63 | — |
| Local Intensity Scaling | Jul | +0.48 | +0.18 to +0.81 | 9/24 | 0.9960 | 1.0000 | 1.0000 | +0.76 | — |
| Local Intensity Scaling | Aug | +0.67 | +0.40 to +0.96 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.78 | — |
| Local Intensity Scaling | Sep | +0.49 | +0.34 to +0.65 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.97 | — |
| Local Intensity Scaling | JJAS | +1.45 | +0.66 to +2.28 | 6/24 | 0.9993 | 1.0000 | 1.0000 | +2.86 | — |
| Empirical Quantile Mapping | Jun | +0.08 | -0.01 to +0.18 | 9/24 | 0.9407 | 1.0000 | 1.0000 | +0.01 | — |
| Empirical Quantile Mapping | Jul | +0.23 | +0.12 to +0.34 | 5/24 | 0.9997 | 1.0000 | 1.0000 | +0.06 | — |
| Empirical Quantile Mapping | Aug | +0.15 | +0.08 to +0.23 | 4/24 | 0.9998 | 1.0000 | 1.0000 | +0.07 | — |
| Empirical Quantile Mapping | Sep | +0.12 | +0.06 to +0.18 | 5/24 | 0.9999 | 1.0000 | 1.0000 | +0.13 | — |
| Empirical Quantile Mapping | JJAS | +0.59 | +0.19 to +0.94 | 5/24 | 0.9969 | 1.0000 | 1.0000 | +0.64 | — |
| Gamma Quantile Mapping | Jun | -0.13 | -0.23 to -0.03 | 18/24 | 0.0098 | 0.0293 | 0.4787 | -0.16 | ✓ |
| Gamma Quantile Mapping | Jul | -0.01 | -0.11 to +0.09 | 11/24 | 0.4390 | 0.4390 | 1.0000 | +0.00 | — |
| Gamma Quantile Mapping | Aug | -0.13 | -0.17 to -0.09 | 22/24 | 0.0000 | 0.0000 | 0.0003 | -0.05 | ✓✓ |
| Gamma Quantile Mapping | Sep | -0.07 | -0.11 to -0.03 | 19/24 | 0.0018 | 0.0071 | 0.0941 | -0.09 | ✓ |
| Gamma Quantile Mapping | JJAS | -0.12 | -0.25 to +0.02 | 16/24 | 0.0518 | 0.1037 | 1.0000 | -0.25 | — |
| Detrended Quantile Mapping | Jun | +0.63 | +0.31 to +1.03 | 6/24 | 1.0000 | 1.0000 | 1.0000 | +0.89 | — |
| Detrended Quantile Mapping | Jul | +0.42 | +0.14 to +0.73 | 6/24 | 0.9967 | 1.0000 | 1.0000 | +0.73 | — |
| Detrended Quantile Mapping | Aug | +0.72 | +0.42 to +1.06 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.30 | — |
| Detrended Quantile Mapping | Sep | +0.54 | +0.34 to +0.78 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.71 | — |
| Detrended Quantile Mapping | JJAS | +1.33 | +0.39 to +2.37 | 6/24 | 0.9923 | 1.0000 | 1.0000 | +2.74 | — |
| Quantile Delta Mapping | Jun | +0.82 | +0.40 to +1.34 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.17 | — |
| Quantile Delta Mapping | Jul | +0.42 | +0.07 to +0.84 | 6/24 | 0.9856 | 1.0000 | 1.0000 | +1.03 | — |
| Quantile Delta Mapping | Aug | +0.86 | +0.48 to +1.32 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.57 | — |
| Quantile Delta Mapping | Sep | +0.68 | +0.43 to +0.98 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.73 | — |
| Quantile Delta Mapping | JJAS | +1.62 | +0.57 to +2.88 | 5/24 | 0.9976 | 1.0000 | 1.0000 | +3.61 | — |
| Scaled Distribution Mapping | Jun | +1.11 | +0.64 to +1.64 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +1.37 | — |
| Scaled Distribution Mapping | Jul | +0.67 | +0.30 to +1.10 | 5/24 | 0.9996 | 1.0000 | 1.0000 | +1.26 | — |
| Scaled Distribution Mapping | Aug | +1.13 | +0.69 to +1.62 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.76 | — |
| Scaled Distribution Mapping | Sep | +0.86 | +0.57 to +1.20 | 1/24 | 1.0000 | 1.0000 | 1.0000 | +0.89 | — |
| Scaled Distribution Mapping | JJAS | +2.39 | +1.35 to +3.61 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +4.19 | — |
| CDF-transform | Jun | +0.70 | +0.32 to +1.17 | 6/24 | 0.9998 | 1.0000 | 1.0000 | +1.14 | — |
| CDF-transform | Jul | +0.42 | +0.12 to +0.76 | 7/24 | 0.9933 | 1.0000 | 1.0000 | +0.76 | — |
| CDF-transform | Aug | +0.73 | +0.41 to +1.10 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.43 | — |
| CDF-transform | Sep | +0.69 | +0.45 to +0.99 | 1/24 | 1.0000 | 1.0000 | 1.0000 | +0.83 | — |
| CDF-transform | JJAS | +1.56 | +0.57 to +2.69 | 6/24 | 0.9979 | 1.0000 | 1.0000 | +2.86 | — |
| MVS with all-zero guard (variant) | Jun | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Jul | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Aug | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Sep | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | JJAS | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| Method | Target | Δ fair CRPS 1993–2016 (mm) | 95% interval | Years better | p (one-sided) | Holm p (method) | Holm p (all 60) | Δ 2017–2025 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Jun | +0.36 | +0.14 to +0.59 | 6/24 | 0.9971 | 1.0000 | 1.0000 | +0.63 | — |
| Linear Scaling | Jul | +0.57 | +0.26 to +0.90 | 7/24 | 0.9988 | 1.0000 | 1.0000 | +0.81 | — |
| Linear Scaling | Aug | +0.68 | +0.40 to +0.99 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.78 | — |
| Linear Scaling | Sep | +0.47 | +0.31 to +0.64 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.00 | — |
| Linear Scaling | JJAS | +1.43 | +0.62 to +2.27 | 6/24 | 0.9990 | 1.0000 | 1.0000 | +2.87 | — |
| Variance Scaling (unbounded) | Jun | -0.04 | -0.08 to -0.00 | 12/24 | 0.0314 | 0.0627 | 1.0000 | -0.08 | — |
| Variance Scaling (unbounded) | Jul | -0.13 | -0.17 to -0.09 | 22/24 | 0.0000 | 0.0000 | 0.0000 | -0.13 | ✓✓ |
| Variance Scaling (unbounded) | Aug | -0.12 | -0.14 to -0.09 | 24/24 | 0.0000 | 0.0000 | 0.0000 | -0.08 | ✓✓ |
| Variance Scaling (unbounded) | Sep | -0.03 | -0.04 to -0.00 | 18/24 | 0.0134 | 0.0403 | 0.6454 | -0.05 | ✓ |
| Variance Scaling (unbounded) | JJAS | -0.03 | -0.07 to +0.02 | 16/24 | 0.1340 | 0.1340 | 1.0000 | -0.08 | — |
| Square-root-space Mean-Variance Scaling | Jun | -0.13 | -0.21 to -0.04 | 18/24 | 0.0031 | 0.0094 | 0.1654 | -0.16 | ✓ |
| Square-root-space Mean-Variance Scaling | Jul | -0.08 | -0.14 to -0.03 | 18/24 | 0.0049 | 0.0099 | 0.2514 | -0.08 | ✓ |
| Square-root-space Mean-Variance Scaling | Aug | -0.09 | -0.12 to -0.06 | 22/24 | 0.0000 | 0.0000 | 0.0000 | -0.06 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Sep | -0.06 | -0.09 to -0.02 | 18/24 | 0.0014 | 0.0056 | 0.0756 | -0.05 | ✓ |
| Square-root-space Mean-Variance Scaling | JJAS | -0.09 | -0.17 to +0.00 | 16/24 | 0.0362 | 0.0362 | 1.0000 | -0.16 | ✓ |
| Power Transformation | Jun | -0.08 | -0.15 to +0.00 | 18/24 | 0.0264 | 0.0791 | 1.0000 | -0.18 | — |
| Power Transformation | Jul | -0.12 | -0.19 to -0.05 | 20/24 | 0.0014 | 0.0054 | 0.0748 | -0.08 | ✓ |
| Power Transformation | Aug | -0.11 | -0.17 to -0.06 | 20/24 | 0.0003 | 0.0013 | 0.0146 | +0.00 | — |
| Power Transformation | Sep | -0.01 | -0.07 to +0.04 | 12/24 | 0.3328 | 0.6657 | 1.0000 | -0.10 | — |
| Power Transformation | JJAS | -0.02 | -0.10 to +0.07 | 13/24 | 0.3681 | 0.6657 | 1.0000 | -0.06 | — |
| Delta Change | Jun | +0.00 | -0.34 to +0.38 | 13/24 | 0.5030 | 1.0000 | 1.0000 | +0.14 | — |
| Delta Change | Jul | -0.31 | -0.56 to -0.08 | 16/24 | 0.0077 | 0.0387 | 0.3875 | -0.35 | ✓ |
| Delta Change | Aug | +0.19 | -0.08 to +0.50 | 12/24 | 0.8678 | 1.0000 | 1.0000 | -0.47 | — |
| Delta Change | Sep | +0.00 | -0.26 to +0.26 | 13/24 | 0.5021 | 1.0000 | 1.0000 | +0.24 | — |
| Delta Change | JJAS | -0.33 | -1.36 to +0.75 | 15/24 | 0.2828 | 1.0000 | 1.0000 | +0.62 | — |
| Local Intensity Scaling | Jun | +0.31 | +0.10 to +0.54 | 6/24 | 0.9937 | 1.0000 | 1.0000 | +0.59 | — |
| Local Intensity Scaling | Jul | +0.56 | +0.26 to +0.88 | 7/24 | 0.9987 | 1.0000 | 1.0000 | +0.79 | — |
| Local Intensity Scaling | Aug | +0.64 | +0.37 to +0.94 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.76 | — |
| Local Intensity Scaling | Sep | +0.43 | +0.27 to +0.59 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.94 | — |
| Local Intensity Scaling | JJAS | +1.40 | +0.61 to +2.24 | 6/24 | 0.9989 | 1.0000 | 1.0000 | +2.83 | — |
| Empirical Quantile Mapping | Jun | +0.08 | -0.01 to +0.18 | 9/24 | 0.9433 | 1.0000 | 1.0000 | +0.02 | — |
| Empirical Quantile Mapping | Jul | +0.25 | +0.14 to +0.36 | 5/24 | 0.9999 | 1.0000 | 1.0000 | +0.08 | — |
| Empirical Quantile Mapping | Aug | +0.17 | +0.10 to +0.25 | 4/24 | 0.9999 | 1.0000 | 1.0000 | +0.08 | — |
| Empirical Quantile Mapping | Sep | +0.13 | +0.07 to +0.19 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +0.14 | — |
| Empirical Quantile Mapping | JJAS | +0.63 | +0.25 to +0.96 | 5/24 | 0.9986 | 1.0000 | 1.0000 | +0.66 | — |
| Gamma Quantile Mapping | Jun | -0.12 | -0.22 to -0.02 | 18/24 | 0.0131 | 0.0392 | 0.6397 | -0.16 | ✓ |
| Gamma Quantile Mapping | Jul | -0.03 | -0.13 to +0.07 | 12/24 | 0.3015 | 0.3015 | 1.0000 | -0.00 | — |
| Gamma Quantile Mapping | Aug | -0.12 | -0.16 to -0.07 | 22/24 | 0.0000 | 0.0000 | 0.0003 | -0.04 | ✓✓ |
| Gamma Quantile Mapping | Sep | -0.06 | -0.11 to -0.02 | 19/24 | 0.0045 | 0.0181 | 0.2353 | -0.09 | ✓ |
| Gamma Quantile Mapping | JJAS | -0.08 | -0.22 to +0.06 | 13/24 | 0.1318 | 0.2636 | 1.0000 | -0.22 | — |
| Detrended Quantile Mapping | Jun | +0.62 | +0.30 to +1.03 | 6/24 | 0.9999 | 1.0000 | 1.0000 | +0.89 | — |
| Detrended Quantile Mapping | Jul | +0.44 | +0.16 to +0.74 | 6/24 | 0.9975 | 1.0000 | 1.0000 | +0.73 | — |
| Detrended Quantile Mapping | Aug | +0.74 | +0.43 to +1.08 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.30 | — |
| Detrended Quantile Mapping | Sep | +0.55 | +0.34 to +0.78 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.72 | — |
| Detrended Quantile Mapping | JJAS | +1.33 | +0.38 to +2.37 | 6/24 | 0.9919 | 1.0000 | 1.0000 | +2.74 | — |
| Quantile Delta Mapping | Jun | +0.81 | +0.39 to +1.33 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.17 | — |
| Quantile Delta Mapping | Jul | +0.41 | +0.06 to +0.84 | 7/24 | 0.9830 | 1.0000 | 1.0000 | +1.04 | — |
| Quantile Delta Mapping | Aug | +0.86 | +0.48 to +1.33 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.58 | — |
| Quantile Delta Mapping | Sep | +0.68 | +0.42 to +0.97 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.74 | — |
| Quantile Delta Mapping | JJAS | +1.61 | +0.56 to +2.88 | 5/24 | 0.9974 | 1.0000 | 1.0000 | +3.63 | — |
| Scaled Distribution Mapping | Jun | +1.17 | +0.70 to +1.71 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +1.39 | — |
| Scaled Distribution Mapping | Jul | +0.73 | +0.35 to +1.16 | 5/24 | 0.9998 | 1.0000 | 1.0000 | +1.31 | — |
| Scaled Distribution Mapping | Aug | +1.21 | +0.77 to +1.71 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.81 | — |
| Scaled Distribution Mapping | Sep | +0.93 | +0.64 to +1.27 | 1/24 | 1.0000 | 1.0000 | 1.0000 | +0.92 | — |
| Scaled Distribution Mapping | JJAS | +2.54 | +1.51 to +3.76 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +4.28 | — |
| CDF-transform | Jun | +0.71 | +0.33 to +1.17 | 6/24 | 0.9998 | 1.0000 | 1.0000 | +1.14 | — |
| CDF-transform | Jul | +0.50 | +0.19 to +0.83 | 7/24 | 0.9979 | 1.0000 | 1.0000 | +0.79 | — |
| CDF-transform | Aug | +0.78 | +0.45 to +1.15 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +0.45 | — |
| CDF-transform | Sep | +0.71 | +0.46 to +1.01 | 0/24 | 1.0000 | 1.0000 | 1.0000 | +0.84 | — |
| CDF-transform | JJAS | +1.63 | +0.63 to +2.77 | 4/24 | 0.9985 | 1.0000 | 1.0000 | +2.89 | — |
| MVS with all-zero guard (variant) | Jun | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Jul | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Aug | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Sep | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | JJAS | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| Method | Target | Δ RPS (no blend) 1993–2016 | 95% interval | Years better | p (one-sided) | Holm p (method) | Holm p (all 60) | Δ 2017–2025 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Jun | +0.0023 | -0.0072 to +0.0114 | 10/24 | 0.6767 | 1.0000 | 1.0000 | -0.0146 | — |
| Linear Scaling | Jul | +0.0077 | +0.0031 to +0.0122 | 6/24 | 0.9979 | 1.0000 | 1.0000 | +0.0069 | — |
| Linear Scaling | Aug | +0.0039 | +0.0015 to +0.0063 | 7/24 | 0.9971 | 1.0000 | 1.0000 | +0.0028 | — |
| Linear Scaling | Sep | +0.0039 | -0.0017 to +0.0098 | 12/24 | 0.8953 | 1.0000 | 1.0000 | +0.0110 | — |
| Linear Scaling | JJAS | +0.0047 | +0.0013 to +0.0082 | 6/24 | 0.9938 | 1.0000 | 1.0000 | +0.0031 | — |
| Variance Scaling (unbounded) | Jun | -0.0016 | -0.0046 to +0.0014 | 16/24 | 0.1649 | 0.3333 | 1.0000 | -0.0032 | — |
| Variance Scaling (unbounded) | Jul | -0.0024 | -0.0059 to +0.0012 | 15/24 | 0.1111 | 0.3333 | 1.0000 | -0.0016 | — |
| Variance Scaling (unbounded) | Aug | -0.0022 | -0.0048 to +0.0003 | 15/24 | 0.0572 | 0.2345 | 1.0000 | -0.0023 | — |
| Variance Scaling (unbounded) | Sep | -0.0026 | -0.0056 to +0.0002 | 14/24 | 0.0469 | 0.2345 | 1.0000 | -0.0026 | — |
| Variance Scaling (unbounded) | JJAS | -0.0002 | -0.0020 to +0.0016 | 13/24 | 0.4003 | 0.4003 | 1.0000 | -0.0012 | — |
| Square-root-space Mean-Variance Scaling | Jun | -0.0051 | -0.0084 to -0.0021 | 17/24 | 0.0020 | 0.0102 | 0.1218 | -0.0112 | ✓ |
| Square-root-space Mean-Variance Scaling | Jul | -0.0013 | -0.0054 to +0.0031 | 14/24 | 0.2854 | 0.5848 | 1.0000 | +0.0002 | — |
| Square-root-space Mean-Variance Scaling | Aug | -0.0021 | -0.0060 to +0.0015 | 12/24 | 0.1462 | 0.5848 | 1.0000 | +0.0006 | — |
| Square-root-space Mean-Variance Scaling | Sep | -0.0024 | -0.0076 to +0.0024 | 10/24 | 0.1782 | 0.5848 | 1.0000 | -0.0034 | — |
| Square-root-space Mean-Variance Scaling | JJAS | +0.0003 | -0.0030 to +0.0038 | 12/24 | 0.5698 | 0.5848 | 1.0000 | -0.0004 | — |
| Power Transformation | Jun | -0.0056 | -0.0094 to -0.0018 | 17/24 | 0.0043 | 0.0213 | 0.2510 | -0.0110 | ✓ |
| Power Transformation | Jul | -0.0012 | -0.0072 to +0.0050 | 15/24 | 0.3508 | 0.7953 | 1.0000 | +0.0020 | — |
| Power Transformation | Aug | -0.0019 | -0.0074 to +0.0030 | 10/24 | 0.2441 | 0.7953 | 1.0000 | +0.0023 | — |
| Power Transformation | Sep | -0.0026 | -0.0087 to +0.0031 | 12/24 | 0.1988 | 0.7953 | 1.0000 | -0.0057 | — |
| Power Transformation | JJAS | +0.0004 | -0.0030 to +0.0037 | 11/24 | 0.5788 | 0.7953 | 1.0000 | +0.0014 | — |
| Delta Change | Jun | +0.0192 | -0.0046 to +0.0429 | 10/24 | 0.9310 | 1.0000 | 1.0000 | +0.0146 | — |
| Delta Change | Jul | +0.0060 | -0.0013 to +0.0132 | 10/24 | 0.9339 | 1.0000 | 1.0000 | -0.0000 | — |
| Delta Change | Aug | +0.0140 | +0.0051 to +0.0238 | 8/24 | 0.9965 | 1.0000 | 1.0000 | +0.0149 | — |
| Delta Change | Sep | +0.0160 | +0.0031 to +0.0299 | 8/24 | 0.9829 | 1.0000 | 1.0000 | +0.0205 | — |
| Delta Change | JJAS | -0.0009 | -0.0133 to +0.0109 | 11/24 | 0.4426 | 1.0000 | 1.0000 | +0.0170 | — |
| Local Intensity Scaling | Jun | +0.0067 | -0.0008 to +0.0141 | 10/24 | 0.9506 | 1.0000 | 1.0000 | -0.0112 | — |
| Local Intensity Scaling | Jul | +0.0072 | +0.0032 to +0.0115 | 7/24 | 0.9986 | 1.0000 | 1.0000 | +0.0082 | — |
| Local Intensity Scaling | Aug | +0.0035 | +0.0005 to +0.0065 | 9/24 | 0.9822 | 1.0000 | 1.0000 | +0.0028 | — |
| Local Intensity Scaling | Sep | +0.0037 | -0.0008 to +0.0085 | 10/24 | 0.9302 | 1.0000 | 1.0000 | +0.0102 | — |
| Local Intensity Scaling | JJAS | +0.0052 | +0.0019 to +0.0087 | 4/24 | 0.9974 | 1.0000 | 1.0000 | +0.0028 | — |
| Empirical Quantile Mapping | Jun | -0.0067 | -0.0136 to +0.0008 | 16/24 | 0.0481 | 0.2407 | 1.0000 | -0.0160 | — |
| Empirical Quantile Mapping | Jul | +0.0028 | -0.0010 to +0.0069 | 13/24 | 0.9063 | 1.0000 | 1.0000 | +0.0031 | — |
| Empirical Quantile Mapping | Aug | +0.0004 | -0.0029 to +0.0040 | 13/24 | 0.5957 | 1.0000 | 1.0000 | -0.0009 | — |
| Empirical Quantile Mapping | Sep | -0.0032 | -0.0071 to +0.0005 | 16/24 | 0.0582 | 0.2407 | 1.0000 | -0.0010 | — |
| Empirical Quantile Mapping | JJAS | +0.0034 | -0.0019 to +0.0086 | 10/24 | 0.8873 | 1.0000 | 1.0000 | +0.0048 | — |
| Gamma Quantile Mapping | Jun | -0.0019 | -0.0073 to +0.0035 | 13/24 | 0.2512 | 1.0000 | 1.0000 | -0.0065 | — |
| Gamma Quantile Mapping | Jul | -0.0007 | -0.0065 to +0.0052 | 15/24 | 0.4031 | 1.0000 | 1.0000 | +0.0025 | — |
| Gamma Quantile Mapping | Aug | -0.0026 | -0.0088 to +0.0033 | 11/24 | 0.2103 | 1.0000 | 1.0000 | +0.0012 | — |
| Gamma Quantile Mapping | Sep | -0.0031 | -0.0119 to +0.0050 | 10/24 | 0.2454 | 1.0000 | 1.0000 | -0.0049 | — |
| Gamma Quantile Mapping | JJAS | +0.0010 | -0.0037 to +0.0059 | 11/24 | 0.6492 | 1.0000 | 1.0000 | -0.0003 | — |
| Detrended Quantile Mapping | Jun | +0.0328 | +0.0148 to +0.0525 | 6/24 | 0.9992 | 1.0000 | 1.0000 | +0.0231 | — |
| Detrended Quantile Mapping | Jul | +0.0189 | +0.0095 to +0.0297 | 7/24 | 0.9998 | 1.0000 | 1.0000 | +0.0175 | — |
| Detrended Quantile Mapping | Aug | +0.0248 | +0.0140 to +0.0358 | 5/24 | 0.9999 | 1.0000 | 1.0000 | +0.0226 | — |
| Detrended Quantile Mapping | Sep | +0.0262 | +0.0141 to +0.0400 | 7/24 | 0.9998 | 1.0000 | 1.0000 | +0.0265 | — |
| Detrended Quantile Mapping | JJAS | +0.0124 | +0.0030 to +0.0217 | 7/24 | 0.9910 | 1.0000 | 1.0000 | +0.0263 | — |
| Quantile Delta Mapping | Jun | +0.0288 | +0.0174 to +0.0411 | 5/24 | 1.0000 | 1.0000 | 1.0000 | +0.0122 | — |
| Quantile Delta Mapping | Jul | +0.0207 | +0.0095 to +0.0336 | 6/24 | 0.9994 | 1.0000 | 1.0000 | +0.0235 | — |
| Quantile Delta Mapping | Aug | +0.0266 | +0.0161 to +0.0383 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.0277 | — |
| Quantile Delta Mapping | Sep | +0.0270 | +0.0118 to +0.0429 | 5/24 | 0.9986 | 1.0000 | 1.0000 | +0.0260 | — |
| Quantile Delta Mapping | JJAS | +0.0207 | +0.0101 to +0.0311 | 6/24 | 0.9996 | 1.0000 | 1.0000 | +0.0298 | — |
| Scaled Distribution Mapping | Jun | +0.0456 | +0.0278 to +0.0651 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.0179 | — |
| Scaled Distribution Mapping | Jul | +0.0282 | +0.0170 to +0.0406 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +0.0301 | — |
| Scaled Distribution Mapping | Aug | +0.0374 | +0.0246 to +0.0514 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +0.0328 | — |
| Scaled Distribution Mapping | Sep | +0.0361 | +0.0207 to +0.0533 | 3/24 | 1.0000 | 1.0000 | 1.0000 | +0.0357 | — |
| Scaled Distribution Mapping | JJAS | +0.0290 | +0.0171 to +0.0407 | 3/24 | 0.9999 | 1.0000 | 1.0000 | +0.0377 | — |
| CDF-transform | Jun | +0.0366 | +0.0222 to +0.0523 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.0337 | — |
| CDF-transform | Jul | +0.0218 | +0.0112 to +0.0339 | 4/24 | 0.9998 | 1.0000 | 1.0000 | +0.0180 | — |
| CDF-transform | Aug | +0.0279 | +0.0172 to +0.0389 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +0.0263 | — |
| CDF-transform | Sep | +0.0346 | +0.0190 to +0.0517 | 5/24 | 0.9998 | 1.0000 | 1.0000 | +0.0275 | — |
| CDF-transform | JJAS | +0.0200 | +0.0105 to +0.0295 | 5/24 | 0.9997 | 1.0000 | 1.0000 | +0.0283 | — |
| MVS with all-zero guard (variant) | Jun | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Jul | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Aug | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Sep | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | JJAS | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
Diagnostics
How often limits, caps and fallbacks act
| Method | Target | Activated (share of the corrected area, or of members / cells for events) |
|---|---|---|
| Mean-Variance Scaling (operational) | Jun | ratio lower limit: 7.0% of the area; ratio upper limit: 7.9% of the area; clipped at zero: 1.9% |
| Mean-Variance Scaling (operational) | Jul | ratio lower limit: 31.8% of the area; ratio upper limit: 4.5% of the area; clipped at zero: 9.8% |
| Mean-Variance Scaling (operational) | Aug | ratio lower limit: 27.9% of the area; ratio upper limit: 1.5% of the area; clipped at zero: 6.0% |
| Mean-Variance Scaling (operational) | Sep | ratio lower limit: 14.4% of the area; ratio upper limit: 0.8% of the area; clipped at zero: 1.3% |
| Mean-Variance Scaling (operational) | JJAS | ratio lower limit: 14.0% of the area; ratio upper limit: 0.8% of the area; clipped at zero: 0.3% |
| Variance Scaling (unbounded) | Jun | clipped at zero: 1.4% |
| Variance Scaling (unbounded) | Jul | clipped at zero: 1.2% |
| Variance Scaling (unbounded) | Aug | clipped at zero: 0.2% |
| Variance Scaling (unbounded) | Sep | clipped at zero: 0.6% |
| Variance Scaling (unbounded) | JJAS | clipped at zero: 0.2% |
| Square-root-space Mean-Variance Scaling | Jun | ratio lower limit: 2.3% of the area; ratio upper limit: 0.4% of the area; clipped at zero: 0.1% |
| Square-root-space Mean-Variance Scaling | Jul | ratio lower limit: 27.0% of the area; ratio upper limit: 5.2% of the area; clipped at zero: 2.0% |
| Square-root-space Mean-Variance Scaling | Aug | ratio lower limit: 24.3% of the area; ratio upper limit: 0.9% of the area; clipped at zero: 0.4% |
| Square-root-space Mean-Variance Scaling | Sep | ratio lower limit: 9.5% of the area; clipped at zero: 0.0% |
| Square-root-space Mean-Variance Scaling | JJAS | ratio lower limit: 8.7% of the area; ratio upper limit: 0.3% of the area; clipped at zero: 0.0% |
| Power Transformation | Jun | b at bound: 0.2% of the area |
| Power Transformation | Jul | b at bound: 0.9% of the area |
| Power Transformation | Aug | b at bound: 2.8% of the area |
| Delta Change | Jun | ratio capped: 0.1% |
| Delta Change | Jul | ratio capped: 0.0% |
| Delta Change | Aug | ratio capped: 0.0% |
| Delta Change | Sep | ratio capped: 0.0% |
| Delta Change | JJAS | ratio capped: 0.0% |
| Local Intensity Scaling | Jun | always wet: 93.6% of the area |
| Local Intensity Scaling | Jul | always wet: 87.5% of the area; never wet: 3.7% of the area |
| Local Intensity Scaling | Aug | always wet: 94.7% of the area; never wet: 2.2% of the area |
| Local Intensity Scaling | Sep | always wet: 96.7% of the area |
| Local Intensity Scaling | JJAS | always wet: 100.0% of the area |
| Empirical Quantile Mapping | Jun | model has dry: 41.8% of the area; obs has dry: 6.4% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | Jul | model has dry: 23.2% of the area; obs has dry: 12.5% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | Aug | model has dry: 23.1% of the area; obs has dry: 5.3% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | Sep | model has dry: 25.4% of the area; obs has dry: 3.3% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | JJAS | extrapolated: 0.4% |
| Gamma Quantile Mapping | Jun | model has dry: 41.8% of the area; obs has dry: 6.4% of the area |
| Gamma Quantile Mapping | Jul | gamma fallback: 3.4% of the area; model has dry: 23.2% of the area; obs has dry: 12.5% of the area |
| Gamma Quantile Mapping | Aug | gamma fallback: 1.7% of the area; model has dry: 23.1% of the area; obs has dry: 5.3% of the area |
| Gamma Quantile Mapping | Sep | model has dry: 25.4% of the area; obs has dry: 3.3% of the area |
| Detrended Quantile Mapping | Jun | model has dry: 41.8% of the area; obs has dry: 6.4% of the area; ratio capped: 0.1%; extrapolated: 0.1% |
| Detrended Quantile Mapping | Jul | model has dry: 23.2% of the area; obs has dry: 12.5% of the area; ratio capped: 0.0%; extrapolated: 0.2% |
| Detrended Quantile Mapping | Aug | model has dry: 23.1% of the area; obs has dry: 5.3% of the area; ratio capped: 0.0%; extrapolated: 0.2% |
| Detrended Quantile Mapping | Sep | model has dry: 25.4% of the area; obs has dry: 3.3% of the area; ratio capped: 0.0%; extrapolated: 0.2% |
| Detrended Quantile Mapping | JJAS | ratio capped: 0.0%; extrapolated: 0.2% |
| Quantile Delta Mapping | Jun | model has dry: 41.8% of the area; obs has dry: 6.4% of the area; low denominator: 4.3%; ratio capped: 0.1% |
| Quantile Delta Mapping | Jul | model has dry: 23.2% of the area; obs has dry: 12.5% of the area; low denominator: 1.0%; ratio capped: 0.1% |
| Quantile Delta Mapping | Aug | model has dry: 23.1% of the area; obs has dry: 5.3% of the area; low denominator: 1.7%; ratio capped: 0.0% |
| Quantile Delta Mapping | Sep | model has dry: 25.4% of the area; obs has dry: 3.3% of the area; low denominator: 0.5%; ratio capped: 0.0% |
| Quantile Delta Mapping | JJAS | ratio capped: 0.0% |
| Scaled Distribution Mapping | Jul | gamma fallback: 7.1% of the area; linear scaling fallback: 7.1% |
| Scaled Distribution Mapping | Aug | gamma fallback: 4.0% of the area; linear scaling fallback: 3.9% |
| CDF-transform | Jun | at forecast range edge: 4.1% |
| CDF-transform | Jul | at forecast range edge: 7.7% |
| CDF-transform | Aug | at forecast range edge: 5.2% |
| CDF-transform | Sep | at forecast range edge: 4.7% |
| CDF-transform | JJAS | at forecast range edge: 6.0% |
| MVS with all-zero guard (variant) | Jun | ratio lower limit: 7.0% of the area; ratio upper limit: 7.9% of the area; clipped at zero: 1.9% |
| MVS with all-zero guard (variant) | Jul | ratio lower limit: 31.8% of the area; ratio upper limit: 4.5% of the area; clipped at zero: 9.8% |
| MVS with all-zero guard (variant) | Aug | ratio lower limit: 27.9% of the area; ratio upper limit: 1.5% of the area; clipped at zero: 6.0% |
| MVS with all-zero guard (variant) | Sep | ratio lower limit: 14.4% of the area; ratio upper limit: 0.8% of the area; clipped at zero: 1.3% |
| MVS with all-zero guard (variant) | JJAS | ratio lower limit: 14.0% of the area; ratio upper limit: 0.8% of the area; clipped at zero: 0.3% |
Where the amount differences come from: cells grouped by their training-year climate
Each cell is grouped by its CHIRPS totals in the fold’s training years only: every year exactly 0 mm; every year ≤ 1 mm (not all 0); some years dry and some wet; never dry. Contributions are area-weighted CRPS differences from Mean-Variance Scaling (mm; negative favours the method) and add up to the national difference. Leave-one-year-out 1993–2016, All Ethiopia.
| Method | Total Δ CRPS | all 0 mm 0.0% of area | all ≤ 1 mm 0.0% of area | mixed 6.4% of area | always wet 93.6% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.423 | +0.000 | +0.000 | -0.003 | +0.427 |
| Variance Scaling (unbounded) | -0.038 | +0.000 | +0.000 | -0.000 | -0.038 |
| Square-root-space Mean-Variance Scaling | -0.127 | +0.000 | +0.000 | -0.002 | -0.125 |
| Power Transformation | -0.068 | +0.000 | +0.000 | -0.005 | -0.063 |
| Delta Change | +0.151 | +0.000 | +0.000 | -0.011 | +0.162 |
| Local Intensity Scaling | +0.369 | +0.000 | +0.000 | +0.003 | +0.366 |
| Empirical Quantile Mapping | +0.081 | +0.000 | +0.000 | -0.001 | +0.082 |
| Gamma Quantile Mapping | -0.131 | +0.000 | +0.000 | -0.001 | -0.130 |
| Detrended Quantile Mapping | +0.632 | +0.000 | +0.000 | +0.005 | +0.627 |
| Quantile Delta Mapping | +0.815 | +0.000 | +0.000 | +0.004 | +0.811 |
| Scaled Distribution Mapping | +1.105 | +0.000 | +0.000 | +0.001 | +1.104 |
| CDF-transform | +0.703 | +0.000 | +0.000 | +0.003 | +0.701 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |
| Method | Total Δ CRPS | all 0 mm 0.0% of area | all ≤ 1 mm 3.7% of area | mixed 8.8% of area | always wet 87.5% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.497 | +0.000 | -0.013 | -0.037 | +0.546 |
| Variance Scaling (unbounded) | -0.139 | +0.000 | -0.014 | -0.042 | -0.083 |
| Square-root-space Mean-Variance Scaling | -0.075 | +0.000 | -0.010 | -0.030 | -0.036 |
| Power Transformation | -0.125 | +0.000 | -0.014 | -0.042 | -0.069 |
| Delta Change | -0.159 | +0.000 | -0.013 | -0.043 | -0.104 |
| Local Intensity Scaling | +0.482 | +0.000 | -0.009 | -0.014 | +0.506 |
| Empirical Quantile Mapping | +0.228 | +0.000 | -0.009 | -0.020 | +0.257 |
| Gamma Quantile Mapping | -0.008 | +0.000 | -0.009 | -0.032 | +0.033 |
| Detrended Quantile Mapping | +0.425 | +0.000 | -0.009 | -0.019 | +0.453 |
| Quantile Delta Mapping | +0.417 | +0.000 | -0.009 | -0.019 | +0.445 |
| Scaled Distribution Mapping | +0.673 | +0.000 | -0.013 | -0.028 | +0.714 |
| CDF-transform | +0.424 | +0.000 | -0.013 | -0.035 | +0.472 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |
| Method | Total Δ CRPS | all 0 mm 0.0% of area | all ≤ 1 mm 2.2% of area | mixed 3.1% of area | always wet 94.7% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.713 | +0.000 | -0.006 | -0.014 | +0.733 |
| Variance Scaling (unbounded) | -0.129 | +0.000 | -0.008 | -0.018 | -0.103 |
| Square-root-space Mean-Variance Scaling | -0.096 | +0.000 | -0.004 | -0.012 | -0.079 |
| Power Transformation | -0.124 | +0.000 | -0.008 | -0.017 | -0.099 |
| Delta Change | +0.305 | +0.000 | -0.006 | -0.015 | +0.327 |
| Local Intensity Scaling | +0.665 | +0.000 | +0.000 | -0.006 | +0.672 |
| Empirical Quantile Mapping | +0.151 | +0.000 | +0.000 | -0.006 | +0.157 |
| Gamma Quantile Mapping | -0.128 | +0.000 | +0.000 | -0.012 | -0.116 |
| Detrended Quantile Mapping | +0.722 | +0.000 | +0.000 | -0.005 | +0.727 |
| Quantile Delta Mapping | +0.858 | +0.000 | +0.000 | -0.005 | +0.864 |
| Scaled Distribution Mapping | +1.128 | +0.000 | -0.006 | -0.011 | +1.146 |
| CDF-transform | +0.735 | +0.000 | -0.006 | -0.013 | +0.754 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |
| Method | Total Δ CRPS | all 0 mm 0.0% of area | all ≤ 1 mm 0.0% of area | mixed 3.3% of area | always wet 96.7% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.546 | +0.000 | +0.000 | -0.002 | +0.548 |
| Variance Scaling (unbounded) | -0.032 | +0.000 | +0.000 | -0.007 | -0.025 |
| Square-root-space Mean-Variance Scaling | -0.058 | +0.000 | +0.000 | +0.000 | -0.058 |
| Power Transformation | -0.011 | +0.000 | +0.000 | -0.009 | -0.002 |
| Delta Change | +0.115 | +0.000 | +0.000 | -0.004 | +0.120 |
| Local Intensity Scaling | +0.495 | +0.000 | +0.000 | +0.012 | +0.483 |
| Empirical Quantile Mapping | +0.118 | +0.000 | +0.000 | -0.008 | +0.125 |
| Gamma Quantile Mapping | -0.072 | +0.000 | +0.000 | -0.005 | -0.067 |
| Detrended Quantile Mapping | +0.540 | +0.000 | +0.000 | -0.000 | +0.541 |
| Quantile Delta Mapping | +0.682 | +0.000 | +0.000 | -0.000 | +0.682 |
| Scaled Distribution Mapping | +0.857 | +0.000 | +0.000 | +0.002 | +0.856 |
| CDF-transform | +0.694 | +0.000 | +0.000 | -0.002 | +0.696 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |
| Method | Total Δ CRPS | all 0 mm 0.0% of area | all ≤ 1 mm 0.0% of area | mixed 0.0% of area | always wet 100.0% of area |
|---|---|---|---|---|---|
| Linear Scaling | +1.482 | +0.000 | +0.000 | +0.000 | +1.482 |
| Variance Scaling (unbounded) | -0.040 | +0.000 | +0.000 | +0.000 | -0.040 |
| Square-root-space Mean-Variance Scaling | -0.111 | +0.000 | +0.000 | +0.000 | -0.111 |
| Power Transformation | -0.024 | +0.000 | +0.000 | +0.000 | -0.024 |
| Delta Change | +0.108 | +0.000 | +0.000 | +0.000 | +0.108 |
| Local Intensity Scaling | +1.452 | +0.000 | +0.000 | +0.000 | +1.452 |
| Empirical Quantile Mapping | +0.588 | +0.000 | +0.000 | +0.000 | +0.588 |
| Gamma Quantile Mapping | -0.117 | +0.000 | +0.000 | +0.000 | -0.117 |
| Detrended Quantile Mapping | +1.334 | +0.000 | +0.000 | +0.000 | +1.334 |
| Quantile Delta Mapping | +1.620 | +0.000 | +0.000 | +0.000 | +1.620 |
| Scaled Distribution Mapping | +2.389 | +0.000 | +0.000 | +0.000 | +2.389 |
| CDF-transform | +1.555 | +0.000 | +0.000 | +0.000 | +1.555 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |