Screening · September initialization · ONDJ 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 2017–2024 | Tercile RPSS (no blend) 1993–2016 | Tercile RPSS (no blend) 2017–2024 | Mean bias (mm) | MAE (mm) | Correlation | Spread–error | Reliability index | Members ≤ 1 mm |
|---|---|---|---|---|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.180 | -0.116 | -0.149 | -0.109 | -14.8 | 69.6 | 0.43 | 0.54 | 0.37 | 0.0% |
| Linear Scaling | +0.070 | +0.131 | +0.025 | +0.058 | -0.1 | 57.4 | 0.31 | 0.78 | 0.16 | 0.0% |
| Mean-Variance Scaling (operational) | +0.070 | +0.178 | +0.035 | +0.065 | -0.5 | 57.6 | 0.27 | 0.96 | 0.09 | 1.8% |
| Variance Scaling (unbounded) | +0.063 | +0.182 | +0.036 | +0.064 | -0.5 | 57.8 | 0.26 | 1.01 | 0.10 | 2.3% |
| Square-root-space Mean-Variance Scaling | +0.080 ✓ | +0.189 | +0.038 | +0.073 | -0.6 | 57.4 | 0.28 | 0.94 | 0.07 | 0.1% |
| Power Transformation | +0.071 | +0.188 | +0.036 | +0.065 | -0.9 | 57.9 | 0.26 | 1.01 | 0.05 | 0.0% |
| Delta Change | +0.093 | +0.114 | +0.028 | +0.011 | -0.1 | 57.4 | 0.31 | 1.16 | 0.05 | 0.0% |
| Local Intensity Scaling | +0.070 | +0.131 | +0.024 | +0.058 | -0.2 | 57.4 | 0.30 | 0.77 | 0.17 | 0.0% |
| Empirical Quantile Mapping | +0.053 | +0.168 | +0.025 | +0.049 | -1.1 | 57.8 | 0.25 | 0.97 | 0.10 | 0.0% |
| Gamma Quantile Mapping | +0.082 ✓ | +0.192 | +0.039 | +0.076 | -0.5 | 57.3 | 0.28 | 0.93 | 0.08 | 0.0% |
| Detrended Quantile Mapping | +0.072 | +0.115 | +0.010 | +0.024 | -1.7 | 57.0 | 0.32 | 0.98 | 0.08 | 0.0% |
| Quantile Delta Mapping | +0.075 | +0.118 | +0.009 | +0.020 | -0.1 | 57.4 | 0.31 | 1.04 | 0.09 | 0.0% |
| Scaled Distribution Mapping | +0.061 | +0.108 | -0.005 | +0.010 | -5.2 | 56.9 | 0.30 | 0.86 | 0.18 | 0.4% |
| CDF-transform | +0.074 | +0.118 | +0.011 | +0.029 | -3.8 | 56.8 | 0.32 | 0.83 | 0.12 | 0.0% |
| MVS with all-zero guard (variant) | +0.070 | +0.178 | +0.035 | +0.065 | -0.5 | 57.6 | 0.27 | 0.96 | 0.09 | 1.8% |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.203 | -0.033 | -0.118 | -0.551 | -0.180 |
| Linear Scaling | -0.016 | +0.073 | -0.008 | -0.132 | +0.070 |
| Mean-Variance Scaling (operational) | -0.002 | +0.084 | +0.028 | -0.048 | +0.070 |
| Variance Scaling (unbounded) | -0.004 | +0.082 | +0.031 | -0.007 ✓ | +0.063 |
| Square-root-space Mean-Variance Scaling | +0.006 | +0.089 | +0.037 ✓ | +0.034 ✓✓ | +0.080 ✓ |
| Power Transformation | +0.001 | +0.082 | +0.020 | -0.025 | +0.071 |
| Delta Change | +0.021 | +0.085 | +0.026 | -0.047 | +0.093 |
| Local Intensity Scaling | -0.016 | +0.079 | +0.010 | -0.104 | +0.070 |
| Empirical Quantile Mapping | -0.012 | +0.075 | +0.033 | +0.010 | +0.053 |
| Gamma Quantile Mapping | +0.007 | +0.088 | +0.030 | +0.015 ✓✓ | +0.082 ✓ |
| Detrended Quantile Mapping | +0.005 | +0.075 | -0.001 | -0.065 | +0.072 |
| Quantile Delta Mapping | +0.010 | +0.076 | +0.014 | -0.027 | +0.075 |
| Scaled Distribution Mapping | -0.002 | +0.068 | -0.021 | -0.216 | +0.061 |
| CDF-transform | +0.002 | +0.073 | -0.019 | -0.108 | +0.074 |
| MVS with all-zero guard (variant) | -0.002 | +0.084 | +0.028 | -0.048 | +0.070 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.165 | -0.043 | -0.175 | -0.516 | -0.149 |
| Linear Scaling | -0.033 | +0.035 | -0.080 | -0.144 | +0.025 |
| Mean-Variance Scaling (operational) | -0.009 | +0.044 | -0.068 | -0.213 | +0.035 |
| Variance Scaling (unbounded) | -0.009 | +0.045 | -0.060 | -0.176 ✓ | +0.036 |
| Square-root-space Mean-Variance Scaling | -0.005 | +0.060 ✓✓ | -0.030 ✓ | -0.017 ✓✓ | +0.038 |
| Power Transformation | -0.013 | +0.044 | -0.049 | -0.046 ✓✓ | +0.036 |
| Delta Change | -0.003 | +0.044 | -0.154 | -0.214 | +0.028 |
| Local Intensity Scaling | -0.028 | +0.047 | -0.109 | -0.153 | +0.024 |
| Empirical Quantile Mapping | -0.023 | +0.046 | -0.065 | -0.010 ✓ | +0.025 |
| Gamma Quantile Mapping | -0.006 | +0.052 | -0.111 | -0.038 ✓✓ | +0.039 |
| Detrended Quantile Mapping | -0.020 | +0.031 | -0.189 | -0.211 | +0.010 |
| Quantile Delta Mapping | -0.015 | +0.020 | -0.116 | -0.074 | +0.009 |
| Scaled Distribution Mapping | -0.025 | +0.018 | -0.192 | -0.321 | -0.005 |
| CDF-transform | -0.026 | +0.010 | -0.241 | -0.254 | +0.011 |
| MVS with all-zero guard (variant) | -0.009 | +0.044 | -0.068 | -0.213 | +0.035 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.120 | +0.031 | -0.183 | -0.573 | -0.116 |
| Linear Scaling | +0.054 | +0.125 | -0.114 | -0.182 | +0.131 |
| Mean-Variance Scaling (operational) | +0.059 | +0.158 | -0.033 | -0.078 | +0.178 |
| Variance Scaling (unbounded) | +0.056 | +0.159 | -0.032 | +0.007 | +0.182 |
| Square-root-space Mean-Variance Scaling | +0.060 | +0.162 | -0.026 | +0.093 | +0.189 |
| Power Transformation | +0.049 | +0.165 | -0.062 | +0.007 | +0.188 |
| Delta Change | +0.028 | +0.117 | -0.019 | -0.030 | +0.114 |
| Local Intensity Scaling | +0.052 | +0.134 | -0.079 | -0.115 | +0.131 |
| Empirical Quantile Mapping | +0.033 | +0.158 | -0.015 | +0.105 | +0.168 |
| Gamma Quantile Mapping | +0.059 | +0.165 | -0.037 | +0.053 | +0.192 |
| Detrended Quantile Mapping | +0.034 | +0.116 | -0.042 | -0.063 | +0.115 |
| Quantile Delta Mapping | +0.036 | +0.123 | -0.043 | +0.032 | +0.118 |
| Scaled Distribution Mapping | +0.025 | +0.103 | -0.055 | -0.184 | +0.108 |
| CDF-transform | +0.030 | +0.120 | -0.097 | -0.151 | +0.118 |
| MVS with all-zero guard (variant) | +0.059 | +0.158 | -0.033 | -0.078 | +0.178 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.226 | -0.048 | -0.136 | -0.599 | -0.205 |
| Linear Scaling | -0.031 | +0.068 | -0.007 | -0.119 | +0.060 |
| Mean-Variance Scaling (operational) | -0.009 | +0.082 | +0.023 | -0.066 | +0.066 |
| Variance Scaling (unbounded) | -0.011 | +0.080 | +0.026 | -0.019 ✓✓ | +0.060 |
| Square-root-space Mean-Variance Scaling | -0.002 | +0.085 | +0.032 ✓ | +0.030 ✓✓ | +0.075 ✓ |
| Power Transformation | -0.006 | +0.079 | +0.016 | -0.029 | +0.067 |
| Delta Change | +0.022 | +0.089 | +0.027 | -0.049 | +0.097 |
| Local Intensity Scaling | -0.031 | +0.075 | +0.009 | -0.099 | +0.059 |
| Empirical Quantile Mapping | -0.020 | +0.071 | +0.027 | +0.004 ✓ | +0.046 |
| Gamma Quantile Mapping | -0.001 | +0.083 | +0.024 | +0.008 ✓✓ | +0.076 |
| Detrended Quantile Mapping | -0.002 | +0.072 | -0.007 | -0.073 | +0.066 |
| Quantile Delta Mapping | +0.005 | +0.074 | +0.010 | -0.030 | +0.071 |
| Scaled Distribution Mapping | -0.013 | +0.059 | -0.035 | -0.240 | +0.052 |
| CDF-transform | -0.009 | +0.067 | -0.026 | -0.117 | +0.065 |
| MVS with all-zero guard (variant) | -0.009 | +0.082 | +0.023 | -0.066 | +0.066 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.058 | -0.054 | -0.084 | -0.257 | -0.109 |
| Linear Scaling | +0.062 | +0.006 | -0.028 | -0.011 | +0.058 |
| Mean-Variance Scaling (operational) | +0.012 | +0.041 | -0.049 | -0.300 | +0.065 |
| Variance Scaling (unbounded) | +0.008 | +0.044 | -0.042 | -0.220 | +0.064 |
| Square-root-space Mean-Variance Scaling | +0.018 | +0.058 | -0.033 | +0.052 | +0.073 |
| Power Transformation | +0.007 | +0.050 | -0.026 | +0.013 | +0.065 |
| Delta Change | -0.023 | -0.026 | -0.061 | -0.053 | +0.011 |
| Local Intensity Scaling | +0.037 | -0.001 | -0.036 | -0.018 | +0.058 |
| Empirical Quantile Mapping | -0.041 | +0.022 | -0.014 | +0.092 | +0.049 |
| Gamma Quantile Mapping | -0.002 | +0.050 | -0.136 | -0.012 | +0.076 |
| Detrended Quantile Mapping | -0.028 | -0.021 | -0.086 | -0.051 | +0.024 |
| Quantile Delta Mapping | -0.018 | -0.012 | -0.026 | +0.083 | +0.020 |
| Scaled Distribution Mapping | -0.033 | -0.068 | -0.088 | -0.127 | +0.010 |
| CDF-transform | -0.014 | -0.009 | -0.119 | -0.027 | +0.029 |
| MVS with all-zero guard (variant) | +0.012 | +0.041 | -0.049 | -0.300 | +0.065 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +4.4 | -5.4 | -4.8 | -9.0 | -14.8 |
| Linear Scaling | -0.0 | -0.1 | +0.0 | +0.1 | -0.1 |
| Mean-Variance Scaling (operational) | +0.4 | +0.2 | +0.1 | -0.0 | -0.5 |
| Variance Scaling (unbounded) | +0.4 | +0.3 | +0.1 | -0.0 | -0.5 |
| Square-root-space Mean-Variance Scaling | -0.1 | -0.1 | +0.0 | +0.0 | -0.6 |
| Power Transformation | -0.1 | -0.1 | +0.0 | -0.0 | -0.9 |
| Delta Change | -0.0 | -0.1 | +0.0 | +0.1 | -0.1 |
| Local Intensity Scaling | -0.0 | -0.1 | -0.3 | -0.9 | -0.2 |
| Empirical Quantile Mapping | -0.2 | -0.1 | -0.0 | -0.1 | -1.1 |
| Gamma Quantile Mapping | -0.1 | -0.1 | -0.1 | -0.1 | -0.5 |
| Detrended Quantile Mapping | -0.2 | -0.1 | +0.1 | +0.4 | -1.7 |
| Quantile Delta Mapping | +0.0 | +0.3 | +0.4 | +0.6 | -0.1 |
| Scaled Distribution Mapping | -4.5 | -3.9 | -3.4 | -5.3 | -5.2 |
| CDF-transform | -1.8 | -0.6 | +0.4 | +1.2 | -3.8 |
| MVS with all-zero guard (variant) | +0.4 | +0.2 | +0.1 | -0.0 | -0.5 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.23 | +0.38 | +0.16 | +0.18 | +0.43 |
| Linear Scaling | +0.07 | +0.24 | +0.03 | +0.11 | +0.31 |
| Mean-Variance Scaling (operational) | +0.08 | +0.23 | +0.02 | +0.01 | +0.27 |
| Variance Scaling (unbounded) | +0.08 | +0.23 | +0.01 | -0.03 | +0.26 |
| Square-root-space Mean-Variance Scaling | +0.09 | +0.23 | +0.01 | +0.05 | +0.28 |
| Power Transformation | +0.08 | +0.23 | +0.02 | +0.02 | +0.26 |
| Delta Change | +0.07 | +0.24 | +0.03 | +0.08 | +0.31 |
| Local Intensity Scaling | +0.07 | +0.24 | +0.03 | +0.08 | +0.30 |
| Empirical Quantile Mapping | +0.07 | +0.22 | +0.00 | -0.01 | +0.25 |
| Gamma Quantile Mapping | +0.09 | +0.22 | +0.00 | -0.04 | +0.28 |
| Detrended Quantile Mapping | +0.09 | +0.24 | +0.02 | +0.11 | +0.32 |
| Quantile Delta Mapping | +0.07 | +0.24 | +0.02 | +0.05 | +0.31 |
| Scaled Distribution Mapping | +0.06 | +0.25 | +0.06 | +0.11 | +0.30 |
| CDF-transform | +0.06 | +0.24 | +0.04 | +0.16 | +0.32 |
| MVS with all-zero guard (variant) | +0.08 | +0.23 | +0.02 | +0.01 | +0.27 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.61 | 0.68 | 0.63 | 0.39 | 0.54 |
| Linear Scaling | 0.72 | 0.94 | 1.15 | 1.81 | 0.78 |
| Mean-Variance Scaling (operational) | 0.90 | 1.01 | 0.96 | 0.83 | 0.96 |
| Variance Scaling (unbounded) | 0.93 | 1.02 | 1.00 | 1.00 | 1.01 |
| Square-root-space Mean-Variance Scaling | 0.90 | 0.97 | 0.95 | 1.07 | 0.94 |
| Power Transformation | 0.95 | 1.04 | 1.01 | 0.98 | 1.01 |
| Delta Change | 1.04 | 1.15 | 1.18 | 1.16 | 1.16 |
| Local Intensity Scaling | 0.72 | 0.95 | 1.10 | 1.59 | 0.77 |
| Empirical Quantile Mapping | 0.93 | 1.02 | 0.99 | 0.98 | 0.97 |
| Gamma Quantile Mapping | 0.90 | 0.96 | 0.94 | 0.98 | 0.93 |
| Detrended Quantile Mapping | 0.96 | 1.04 | 1.04 | 1.06 | 0.98 |
| Quantile Delta Mapping | 0.99 | 1.07 | 1.08 | 1.20 | 1.04 |
| Scaled Distribution Mapping | 0.81 | 0.87 | 0.81 | 0.75 | 0.86 |
| CDF-transform | 0.83 | 0.96 | 1.03 | 1.13 | 0.83 |
| MVS with all-zero guard (variant) | 0.90 | 1.01 | 0.96 | 0.83 | 0.96 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.45 | 0.14 | 0.38 | 1.02 | 0.37 |
| Linear Scaling | 0.38 | 0.13 | 0.38 | 0.66 | 0.16 |
| Mean-Variance Scaling (operational) | 0.10 | 0.11 | 0.22 | 0.68 | 0.09 |
| Variance Scaling (unbounded) | 0.10 | 0.11 | 0.21 | 0.69 | 0.10 |
| Square-root-space Mean-Variance Scaling | 0.15 | 0.15 | 0.26 | 0.11 | 0.07 |
| Power Transformation | 0.18 | 0.11 | 0.28 | 0.26 | 0.05 |
| Delta Change | 0.05 | 0.13 | 0.42 | 0.50 | 0.05 |
| Local Intensity Scaling | 0.33 | 0.13 | 0.40 | 0.65 | 0.17 |
| Empirical Quantile Mapping | 0.09 | 0.07 | 0.25 | 0.23 | 0.10 |
| Gamma Quantile Mapping | 0.13 | 0.13 | 0.23 | 0.42 | 0.08 |
| Detrended Quantile Mapping | 0.08 | 0.10 | 0.45 | 0.52 | 0.08 |
| Quantile Delta Mapping | 0.09 | 0.08 | 0.33 | 0.27 | 0.09 |
| Scaled Distribution Mapping | 0.17 | 0.15 | 0.53 | 0.78 | 0.18 |
| CDF-transform | 0.22 | 0.19 | 0.53 | 0.59 | 0.12 |
| MVS with all-zero guard (variant) | 0.10 | 0.11 | 0.22 | 0.68 | 0.09 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Oct | 1484 | 100% | 1479 | 100% |
| Nov | 1484 | 100% | 1479 | 100% |
| Dec | 1484 | 100% | 1378 | 93% |
| Jan | 1484 | 100% | 1149 | 77% |
| ONDJ | 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 | |
|---|---|---|
| Oct: CHIRPS | 0.4% | 2.3% |
| Raw ECMWF (no correction) | 0.0% | 0.8% |
| Linear Scaling | 0.0% | 0.9% |
| Mean-Variance Scaling (operational) | 4.3% | 5.0% |
| Variance Scaling (unbounded) | 4.4% | 5.2% |
| Square-root-space Mean-Variance Scaling | 0.9% | 2.7% |
| Power Transformation | 0.0% | 1.5% |
| Delta Change | 0.4% | 2.4% |
| Local Intensity Scaling | 2.3% | 2.3% |
| Empirical Quantile Mapping | 2.3% | 2.4% |
| Gamma Quantile Mapping | 2.5% | 3.2% |
| Detrended Quantile Mapping | 2.2% | 2.4% |
| Quantile Delta Mapping | 2.3% | 2.6% |
| Scaled Distribution Mapping | 3.6% | 3.7% |
| CDF-transform | 0.0% | 2.0% |
| MVS with all-zero guard (variant) | 4.3% | 5.0% |
| Nov: CHIRPS | 0.7% | 5.2% |
| Raw ECMWF (no correction) | 0.5% | 8.5% |
| Linear Scaling | 0.5% | 7.7% |
| Mean-Variance Scaling (operational) | 7.6% | 9.4% |
| Variance Scaling (unbounded) | 8.2% | 10.0% |
| Square-root-space Mean-Variance Scaling | 2.2% | 6.3% |
| Power Transformation | 0.5% | 6.5% |
| Delta Change | 0.7% | 5.7% |
| Local Intensity Scaling | 5.5% | 5.5% |
| Empirical Quantile Mapping | 5.2% | 5.3% |
| Gamma Quantile Mapping | 5.5% | 7.9% |
| Detrended Quantile Mapping | 4.9% | 5.6% |
| Quantile Delta Mapping | 5.2% | 6.1% |
| Scaled Distribution Mapping | 12.4% | 12.8% |
| CDF-transform | 0.3% | 4.9% |
| MVS with all-zero guard (variant) | 7.6% | 9.4% |
| Dec: CHIRPS | 0.6% | 18.9% |
| Raw ECMWF (no correction) | 6.5% | 32.5% |
| Linear Scaling | 6.5% | 32.2% |
| Mean-Variance Scaling (operational) | 12.0% | 22.2% |
| Variance Scaling (unbounded) | 8.9% | 21.3% |
| Square-root-space Mean-Variance Scaling | 2.7% | 19.6% |
| Power Transformation | 6.5% | 26.1% |
| Delta Change | 0.6% | 20.4% |
| Local Intensity Scaling | 21.5% | 21.5% |
| Empirical Quantile Mapping | 18.9% | 19.0% |
| Gamma Quantile Mapping | 18.2% | 23.4% |
| Detrended Quantile Mapping | 18.6% | 21.4% |
| Quantile Delta Mapping | 18.9% | 20.7% |
| Scaled Distribution Mapping | 36.0% | 39.8% |
| CDF-transform | 0.3% | 20.0% |
| MVS with all-zero guard (variant) | 12.0% | 22.2% |
| Jan: CHIRPS | 1.0% | 16.6% |
| Raw ECMWF (no correction) | 20.0% | 55.3% |
| Linear Scaling | 20.0% | 43.1% |
| Mean-Variance Scaling (operational) | 4.6% | 16.8% |
| Variance Scaling (unbounded) | 1.5% | 16.1% |
| Square-root-space Mean-Variance Scaling | 0.8% | 17.2% |
| Power Transformation | 20.0% | 27.2% |
| Delta Change | 1.0% | 20.6% |
| Local Intensity Scaling | 28.1% | 28.1% |
| Empirical Quantile Mapping | 16.6% | 16.7% |
| Gamma Quantile Mapping | 14.9% | 18.7% |
| Detrended Quantile Mapping | 16.5% | 21.6% |
| Quantile Delta Mapping | 16.6% | 17.2% |
| Scaled Distribution Mapping | 48.1% | 56.4% |
| CDF-transform | 0.2% | 19.3% |
| MVS with all-zero guard (variant) | 4.6% | 16.8% |
| ONDJ: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 1.5% | 1.6% |
| Variance Scaling (unbounded) | 2.0% | 2.1% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.1% |
| 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 | 0.7% | 0.7% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 1.5% | 1.6% |
Distribution of the corrected members (mean, spread, 10th and 90th percentiles)
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.98 | 0.79 | 0.82 | 0.34 | 0.86 |
| Linear Scaling | 1.00 | 1.00 | 1.00 | 1.01 | 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 | 0.97 | 0.90 | 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 | 1.02 | 0.99 |
| Quantile Delta Mapping | 1.00 | 1.01 | 1.03 | 1.04 | 1.00 |
| Scaled Distribution Mapping | 0.94 | 0.88 | 0.72 | 0.51 | 0.97 |
| CDF-transform | 0.99 | 0.99 | 1.04 | 1.11 | 0.98 |
| MVS with all-zero guard (variant) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.79 | 0.77 | 1.05 | 0.96 | 0.69 |
| Linear Scaling | 0.81 | 0.94 | 1.26 | 2.50 | 0.84 |
| Mean-Variance Scaling (operational) | 1.00 | 0.99 | 1.01 | 1.02 | 0.99 |
| Variance Scaling (unbounded) | 1.00 | 0.99 | 1.01 | 1.02 | 0.99 |
| Square-root-space Mean-Variance Scaling | 0.98 | 0.94 | 0.93 | 1.11 | 0.94 |
| Power Transformation | 1.00 | 1.00 | 1.01 | 1.00 | 1.00 |
| Delta Change | 1.06 | 1.09 | 1.17 | 1.34 | 1.07 |
| Local Intensity Scaling | 0.81 | 0.96 | 1.16 | 1.70 | 0.83 |
| Empirical Quantile Mapping | 1.00 | 0.99 | 1.00 | 1.00 | 0.98 |
| Gamma Quantile Mapping | 0.98 | 0.91 | 0.88 | 0.91 | 0.92 |
| Detrended Quantile Mapping | 0.99 | 1.00 | 1.09 | 1.29 | 0.96 |
| Quantile Delta Mapping | 1.01 | 1.03 | 1.16 | 1.37 | 0.99 |
| Scaled Distribution Mapping | 0.88 | 0.85 | 0.87 | 0.97 | 0.86 |
| CDF-transform | 0.93 | 0.98 | 1.13 | 1.53 | 0.89 |
| MVS with all-zero guard (variant) | 1.00 | 0.99 | 1.01 | 1.02 | 0.99 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.27 | 0.52 | 0.06 | 0.00 | 0.93 |
| Linear Scaling | 1.25 | 0.73 | 0.07 | 0.00 | 1.03 |
| Mean-Variance Scaling (operational) | 0.88 | 0.61 | 0.62 | 1.16 | 0.86 |
| Variance Scaling (unbounded) | 0.85 | 0.58 | 0.71 | 1.16 | 0.82 |
| Square-root-space Mean-Variance Scaling | 0.95 | 0.75 | 0.57 | 0.86 | 0.91 |
| Power Transformation | 1.00 | 0.64 | 0.24 | 0.00 | 0.89 |
| Delta Change | 0.92 | 0.86 | 0.71 | 0.62 | 0.91 |
| Local Intensity Scaling | 1.20 | 0.65 | 0.26 | 0.00 | 1.04 |
| Empirical Quantile Mapping | 0.96 | 0.97 | 0.98 | 0.99 | 0.97 |
| Gamma Quantile Mapping | 0.97 | 0.78 | 0.59 | 0.70 | 0.94 |
| Detrended Quantile Mapping | 0.95 | 0.87 | 0.69 | 0.61 | 0.96 |
| Quantile Delta Mapping | 0.97 | 0.89 | 0.76 | 0.93 | 0.97 |
| Scaled Distribution Mapping | 0.97 | 0.69 | 0.00 | 0.00 | 0.98 |
| CDF-transform | 1.01 | 0.87 | 0.61 | 0.58 | 0.98 |
| MVS with all-zero guard (variant) | 0.88 | 0.61 | 0.62 | 1.16 | 0.86 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.92 | 0.81 | 1.10 | 0.47 | 0.81 |
| Linear Scaling | 0.96 | 1.01 | 1.31 | 1.42 | 0.98 |
| Mean-Variance Scaling (operational) | 1.03 | 1.01 | 1.11 | 0.92 | 1.04 |
| Variance Scaling (unbounded) | 1.03 | 1.01 | 1.07 | 0.92 | 1.05 |
| Square-root-space Mean-Variance Scaling | 1.03 | 0.99 | 1.09 | 1.06 | 1.02 |
| Power Transformation | 1.03 | 1.01 | 1.12 | 1.11 | 1.04 |
| Delta Change | 1.06 | 1.05 | 1.07 | 1.12 | 1.06 |
| Local Intensity Scaling | 0.96 | 1.01 | 1.16 | 1.08 | 0.98 |
| Empirical Quantile Mapping | 1.03 | 1.04 | 1.07 | 1.04 | 1.03 |
| Gamma Quantile Mapping | 1.03 | 0.98 | 1.00 | 0.97 | 1.02 |
| Detrended Quantile Mapping | 1.03 | 1.03 | 1.08 | 1.13 | 1.02 |
| Quantile Delta Mapping | 1.04 | 1.04 | 1.11 | 1.08 | 1.04 |
| Scaled Distribution Mapping | 0.96 | 0.89 | 0.83 | 0.71 | 0.97 |
| CDF-transform | 1.01 | 1.03 | 1.15 | 1.30 | 1.01 |
| MVS with all-zero guard (variant) | 1.03 | 1.01 | 1.11 | 0.92 | 1.04 |
ONDJ R3 (Deyr) domain
| Method | Amount CRPSS 1993–2016 | Amount CRPSS 2017–2024 | Tercile RPSS (no blend) 1993–2016 | Tercile RPSS (no blend) 2017–2024 | Mean bias (mm) | MAE (mm) | Correlation | Spread–error | Reliability index | Members ≤ 1 mm |
|---|---|---|---|---|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.039 | +0.004 | -0.018 | +0.043 | -43.7 | 78.5 | 0.61 | 0.44 | 0.49 | 0.0% |
| Linear Scaling | +0.122 | +0.284 | +0.121 | +0.282 | -0.3 | 71.1 | 0.50 | 0.72 | 0.29 | 0.0% |
| Mean-Variance Scaling (operational) | +0.141 | +0.375 | +0.150 | +0.314 | -0.6 | 70.4 | 0.49 | 0.96 | 0.18 | 2.8% |
| Variance Scaling (unbounded) | +0.130 | +0.383 | +0.150 | +0.313 | -0.4 | 71.0 | 0.47 | 1.03 | 0.22 | 4.1% |
| Square-root-space Mean-Variance Scaling | +0.151 | +0.386 | +0.154 | +0.320 | -0.9 | 70.3 | 0.49 | 0.97 | 0.13 | 0.2% |
| Power Transformation | +0.143 | +0.394 | +0.153 | +0.325 | -1.1 | 71.2 | 0.47 | 1.04 | 0.08 | 0.0% |
| Delta Change | +0.147 | +0.273 | +0.135 | +0.253 | -0.3 | 71.1 | 0.50 | 1.21 | 0.10 | 0.0% |
| Local Intensity Scaling | +0.120 | +0.282 | +0.119 | +0.281 | -0.3 | 71.2 | 0.50 | 0.71 | 0.29 | 0.0% |
| Empirical Quantile Mapping | +0.114 | +0.367 | +0.141 | +0.316 | -1.7 | 71.5 | 0.45 | 0.99 | 0.10 | 0.0% |
| Gamma Quantile Mapping | +0.154 | +0.389 | +0.153 | +0.321 | -0.7 | 70.2 | 0.50 | 0.97 | 0.10 | 0.0% |
| Detrended Quantile Mapping | +0.129 | +0.267 | +0.123 | +0.275 | -3.0 | 70.8 | 0.51 | 0.99 | 0.10 | 0.0% |
| Quantile Delta Mapping | +0.134 | +0.273 | +0.126 | +0.267 | -1.0 | 71.1 | 0.50 | 1.07 | 0.09 | 0.0% |
| Scaled Distribution Mapping | +0.122 | +0.267 | +0.116 | +0.269 | -9.5 | 70.1 | 0.49 | 0.85 | 0.13 | 0.5% |
| CDF-transform | +0.133 | +0.274 | +0.131 | +0.277 | -6.5 | 69.9 | 0.53 | 0.82 | 0.16 | 0.0% |
| MVS with all-zero guard (variant) | +0.141 | +0.375 | +0.150 | +0.314 | -0.6 | 70.4 | 0.49 | 0.96 | 0.18 | 2.8% |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.035 | +0.038 | -0.039 | -0.452 | -0.039 |
| Linear Scaling | +0.057 | +0.093 | +0.048 | -0.089 | +0.122 |
| Mean-Variance Scaling (operational) | +0.084 | +0.101 | +0.064 | -0.030 | +0.141 |
| Variance Scaling (unbounded) | +0.080 | +0.098 | +0.065 | +0.019 | +0.130 |
| Square-root-space Mean-Variance Scaling | +0.090 | +0.104 | +0.072 | +0.081 | +0.151 |
| Power Transformation | +0.083 | +0.100 | +0.058 | -0.025 | +0.143 |
| Delta Change | +0.074 | +0.099 | +0.065 | +0.013 | +0.147 |
| Local Intensity Scaling | +0.055 | +0.099 | +0.060 | -0.071 | +0.120 |
| Empirical Quantile Mapping | +0.068 | +0.089 | +0.062 | +0.043 | +0.114 |
| Gamma Quantile Mapping | +0.092 | +0.104 | +0.066 | +0.042 | +0.154 |
| Detrended Quantile Mapping | +0.065 | +0.090 | +0.039 | +0.011 | +0.129 |
| Quantile Delta Mapping | +0.066 | +0.090 | +0.056 | +0.056 | +0.134 |
| Scaled Distribution Mapping | +0.057 | +0.083 | +0.029 | -0.234 | +0.122 |
| CDF-transform | +0.062 | +0.089 | +0.035 | -0.027 | +0.133 |
| MVS with all-zero guard (variant) | +0.084 | +0.101 | +0.064 | -0.030 | +0.141 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.009 | +0.041 | -0.154 | -0.542 | -0.018 |
| Linear Scaling | +0.091 | +0.075 | -0.084 | -0.152 | +0.121 |
| Mean-Variance Scaling (operational) | +0.124 | +0.100 | -0.062 | -0.282 | +0.150 |
| Variance Scaling (unbounded) | +0.124 | +0.102 | -0.054 | -0.248 | +0.150 |
| Square-root-space Mean-Variance Scaling | +0.126 | +0.105 | -0.032 | +0.027 | +0.154 |
| Power Transformation | +0.122 | +0.086 | -0.051 | +0.008 | +0.153 |
| Delta Change | +0.081 | +0.078 | -0.190 | -0.165 | +0.135 |
| Local Intensity Scaling | +0.089 | +0.095 | -0.157 | -0.188 | +0.119 |
| Empirical Quantile Mapping | +0.107 | +0.089 | -0.132 | +0.039 | +0.141 |
| Gamma Quantile Mapping | +0.126 | +0.102 | -0.166 | -0.008 | +0.153 |
| Detrended Quantile Mapping | +0.087 | +0.073 | -0.255 | -0.121 | +0.123 |
| Quantile Delta Mapping | +0.083 | +0.068 | -0.194 | +0.002 | +0.126 |
| Scaled Distribution Mapping | +0.079 | +0.068 | -0.250 | -0.366 | +0.116 |
| CDF-transform | +0.090 | +0.067 | -0.318 | -0.175 | +0.131 |
| MVS with all-zero guard (variant) | +0.124 | +0.100 | -0.062 | -0.282 | +0.150 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.042 | +0.123 | -0.002 | -0.499 | +0.004 |
| Linear Scaling | +0.155 | +0.242 | -0.018 | -0.218 | +0.284 |
| Mean-Variance Scaling (operational) | +0.190 | +0.280 | +0.029 | -0.144 | +0.375 |
| Variance Scaling (unbounded) | +0.185 | +0.282 | +0.029 | -0.054 | +0.383 |
| Square-root-space Mean-Variance Scaling | +0.190 | +0.284 | +0.037 | +0.067 | +0.386 |
| Power Transformation | +0.190 | +0.292 | +0.002 | -0.063 | +0.394 |
| Delta Change | +0.145 | +0.225 | +0.047 | -0.102 | +0.273 |
| Local Intensity Scaling | +0.154 | +0.253 | +0.010 | -0.139 | +0.282 |
| Empirical Quantile Mapping | +0.173 | +0.286 | +0.035 | +0.074 | +0.367 |
| Gamma Quantile Mapping | +0.192 | +0.288 | +0.024 | +0.008 | +0.389 |
| Detrended Quantile Mapping | +0.137 | +0.222 | +0.014 | -0.165 | +0.267 |
| Quantile Delta Mapping | +0.143 | +0.227 | +0.008 | -0.005 | +0.273 |
| Scaled Distribution Mapping | +0.134 | +0.222 | +0.054 | -0.246 | +0.267 |
| CDF-transform | +0.140 | +0.228 | -0.045 | -0.323 | +0.274 |
| MVS with all-zero guard (variant) | +0.190 | +0.280 | +0.029 | -0.144 | +0.375 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.057 | +0.019 | -0.057 | -0.499 | -0.065 |
| Linear Scaling | +0.044 | +0.085 | +0.049 | -0.076 | +0.109 |
| Mean-Variance Scaling (operational) | +0.079 | +0.098 | +0.060 | -0.049 | +0.138 |
| Variance Scaling (unbounded) | +0.077 | +0.096 | +0.062 | +0.006 | +0.129 |
| Square-root-space Mean-Variance Scaling | +0.086 | +0.101 | +0.067 | +0.079 | +0.148 |
| Power Transformation | +0.078 | +0.097 | +0.056 | -0.028 | +0.140 |
| Delta Change | +0.077 | +0.103 | +0.068 | +0.013 | +0.154 |
| Local Intensity Scaling | +0.042 | +0.093 | +0.058 | -0.070 | +0.107 |
| Empirical Quantile Mapping | +0.063 | +0.085 | +0.057 | +0.038 | +0.108 |
| Gamma Quantile Mapping | +0.088 | +0.100 | +0.060 | +0.035 | +0.150 |
| Detrended Quantile Mapping | +0.060 | +0.087 | +0.034 | +0.006 | +0.125 |
| Quantile Delta Mapping | +0.063 | +0.088 | +0.053 | +0.058 | +0.132 |
| Scaled Distribution Mapping | +0.048 | +0.074 | +0.016 | -0.264 | +0.114 |
| CDF-transform | +0.053 | +0.084 | +0.029 | -0.031 | +0.124 |
| MVS with all-zero guard (variant) | +0.079 | +0.098 | +0.060 | -0.049 | +0.138 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.079 | +0.171 | +0.005 | -0.365 | +0.043 |
| Linear Scaling | +0.160 | +0.229 | +0.031 | -0.072 | +0.282 |
| Mean-Variance Scaling (operational) | +0.146 | +0.239 | +0.036 | -0.432 | +0.314 |
| Variance Scaling (unbounded) | +0.139 | +0.238 | +0.035 | -0.346 | +0.313 |
| Square-root-space Mean-Variance Scaling | +0.140 | +0.240 | +0.030 | +0.031 | +0.320 |
| Power Transformation | +0.139 | +0.246 | +0.038 | -0.015 | +0.325 |
| Delta Change | +0.118 | +0.175 | +0.028 | -0.161 | +0.253 |
| Local Intensity Scaling | +0.159 | +0.224 | +0.043 | -0.100 | +0.281 |
| Empirical Quantile Mapping | +0.131 | +0.228 | +0.034 | +0.079 | +0.316 |
| Gamma Quantile Mapping | +0.138 | +0.226 | -0.069 | -0.076 | +0.321 |
| Detrended Quantile Mapping | +0.111 | +0.204 | +0.005 | -0.125 | +0.275 |
| Quantile Delta Mapping | +0.115 | +0.193 | +0.060 | +0.119 | +0.267 |
| Scaled Distribution Mapping | +0.110 | +0.194 | +0.022 | -0.226 | +0.269 |
| CDF-transform | +0.114 | +0.213 | +0.020 | -0.021 | +0.277 |
| MVS with all-zero guard (variant) | +0.146 | +0.239 | +0.036 | -0.432 | +0.314 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -15.4 | -15.2 | -5.6 | -7.5 | -43.7 |
| Linear Scaling | -0.1 | -0.1 | +0.0 | +0.0 | -0.3 |
| Mean-Variance Scaling (operational) | +0.1 | +0.4 | +0.2 | -0.0 | -0.6 |
| Variance Scaling (unbounded) | +0.3 | +0.5 | +0.2 | -0.1 | -0.4 |
| Square-root-space Mean-Variance Scaling | -0.2 | -0.2 | -0.0 | -0.0 | -0.9 |
| Power Transformation | -0.1 | -0.1 | +0.0 | -0.1 | -1.1 |
| Delta Change | -0.1 | -0.1 | +0.0 | +0.0 | -0.3 |
| Local Intensity Scaling | -0.1 | -0.1 | -0.4 | -1.6 | -0.3 |
| Empirical Quantile Mapping | -0.3 | -0.2 | -0.1 | -0.2 | -1.7 |
| Gamma Quantile Mapping | -0.1 | -0.1 | -0.0 | -0.1 | -0.7 |
| Detrended Quantile Mapping | -0.3 | -0.4 | +0.0 | +0.4 | -3.0 |
| Quantile Delta Mapping | -0.1 | +0.1 | +0.3 | +0.5 | -1.0 |
| Scaled Distribution Mapping | -6.8 | -4.3 | -3.8 | -5.4 | -9.5 |
| CDF-transform | -2.1 | -1.6 | +0.4 | +1.4 | -6.5 |
| MVS with all-zero guard (variant) | +0.1 | +0.4 | +0.2 | -0.0 | -0.6 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.42 | +0.48 | +0.26 | +0.32 | +0.61 |
| Linear Scaling | +0.28 | +0.33 | +0.12 | +0.25 | +0.50 |
| Mean-Variance Scaling (operational) | +0.29 | +0.35 | +0.12 | +0.14 | +0.49 |
| Variance Scaling (unbounded) | +0.28 | +0.34 | +0.11 | +0.03 | +0.47 |
| Square-root-space Mean-Variance Scaling | +0.29 | +0.34 | +0.11 | +0.19 | +0.49 |
| Power Transformation | +0.28 | +0.34 | +0.12 | +0.13 | +0.47 |
| Delta Change | +0.28 | +0.33 | +0.12 | +0.25 | +0.50 |
| Local Intensity Scaling | +0.28 | +0.34 | +0.13 | +0.21 | +0.50 |
| Empirical Quantile Mapping | +0.28 | +0.33 | +0.10 | +0.07 | +0.45 |
| Gamma Quantile Mapping | +0.30 | +0.34 | +0.11 | +0.02 | +0.50 |
| Detrended Quantile Mapping | +0.28 | +0.34 | +0.08 | +0.25 | +0.51 |
| Quantile Delta Mapping | +0.27 | +0.33 | +0.09 | +0.17 | +0.50 |
| Scaled Distribution Mapping | +0.27 | +0.33 | +0.15 | +0.26 | +0.49 |
| CDF-transform | +0.28 | +0.32 | +0.13 | +0.32 | +0.53 |
| MVS with all-zero guard (variant) | +0.29 | +0.35 | +0.12 | +0.14 | +0.49 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.56 | 0.57 | 0.61 | 0.37 | 0.44 |
| Linear Scaling | 0.75 | 0.88 | 1.15 | 2.03 | 0.72 |
| Mean-Variance Scaling (operational) | 0.93 | 0.99 | 0.99 | 0.85 | 0.96 |
| Variance Scaling (unbounded) | 0.99 | 1.02 | 1.03 | 1.04 | 1.03 |
| Square-root-space Mean-Variance Scaling | 0.97 | 0.96 | 0.97 | 1.15 | 0.97 |
| Power Transformation | 1.01 | 1.03 | 1.04 | 1.02 | 1.04 |
| Delta Change | 1.10 | 1.16 | 1.25 | 1.28 | 1.21 |
| Local Intensity Scaling | 0.74 | 0.90 | 1.11 | 1.64 | 0.71 |
| Empirical Quantile Mapping | 0.98 | 1.02 | 1.01 | 1.01 | 0.99 |
| Gamma Quantile Mapping | 0.98 | 0.95 | 0.98 | 1.00 | 0.97 |
| Detrended Quantile Mapping | 1.00 | 1.04 | 1.08 | 1.19 | 0.99 |
| Quantile Delta Mapping | 1.04 | 1.06 | 1.12 | 1.37 | 1.07 |
| Scaled Distribution Mapping | 0.82 | 0.87 | 0.82 | 0.69 | 0.85 |
| CDF-transform | 0.85 | 0.94 | 1.06 | 1.32 | 0.82 |
| MVS with all-zero guard (variant) | 0.93 | 0.99 | 0.99 | 0.85 | 0.96 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.43 | 0.32 | 0.31 | 1.15 | 0.49 |
| Linear Scaling | 0.33 | 0.24 | 0.33 | 0.92 | 0.29 |
| Mean-Variance Scaling (operational) | 0.09 | 0.17 | 0.31 | 0.85 | 0.18 |
| Variance Scaling (unbounded) | 0.12 | 0.19 | 0.30 | 0.86 | 0.22 |
| Square-root-space Mean-Variance Scaling | 0.06 | 0.12 | 0.35 | 0.41 | 0.13 |
| Power Transformation | 0.09 | 0.10 | 0.34 | 0.49 | 0.08 |
| Delta Change | 0.08 | 0.12 | 0.48 | 0.71 | 0.10 |
| Local Intensity Scaling | 0.34 | 0.14 | 0.44 | 0.92 | 0.29 |
| Empirical Quantile Mapping | 0.11 | 0.08 | 0.38 | 0.36 | 0.10 |
| Gamma Quantile Mapping | 0.07 | 0.09 | 0.29 | 0.57 | 0.10 |
| Detrended Quantile Mapping | 0.09 | 0.10 | 0.52 | 0.70 | 0.10 |
| Quantile Delta Mapping | 0.08 | 0.11 | 0.47 | 0.40 | 0.09 |
| Scaled Distribution Mapping | 0.16 | 0.12 | 0.65 | 1.10 | 0.13 |
| CDF-transform | 0.18 | 0.19 | 0.63 | 0.76 | 0.16 |
| MVS with all-zero guard (variant) | 0.09 | 0.17 | 0.31 | 0.85 | 0.18 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Oct | 575 | 100% | 575 | 100% |
| Nov | 575 | 100% | 570 | 99% |
| Dec | 575 | 100% | 574 | 100% |
| Jan | 575 | 100% | 362 | 63% |
| ONDJ | 575 | 100% | 575 | 100% |
Dry months: shares of totals at exactly 0 mm and at ≤ 1 mm, CHIRPS and corrected
| Exactly 0 mm | ≤ 1 mm | |
|---|---|---|
| Oct: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 2.8% | 3.0% |
| Variance Scaling (unbounded) | 3.3% | 3.5% |
| Square-root-space Mean-Variance Scaling | 0.2% | 0.5% |
| 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% | 0.1% |
| Detrended Quantile Mapping | 0.0% | 0.0% |
| Quantile Delta Mapping | 0.0% | 0.0% |
| Scaled Distribution Mapping | 1.6% | 1.6% |
| CDF-transform | 0.0% | 0.0% |
| MVS with all-zero guard (variant) | 2.8% | 3.0% |
| Nov: CHIRPS | 1.6% | 7.2% |
| Raw ECMWF (no correction) | 0.3% | 3.4% |
| Linear Scaling | 0.3% | 2.8% |
| Mean-Variance Scaling (operational) | 12.0% | 13.3% |
| Variance Scaling (unbounded) | 13.7% | 15.0% |
| Square-root-space Mean-Variance Scaling | 4.2% | 8.3% |
| Power Transformation | 0.3% | 5.3% |
| Delta Change | 1.6% | 7.5% |
| Local Intensity Scaling | 7.3% | 7.3% |
| Empirical Quantile Mapping | 7.2% | 7.3% |
| Gamma Quantile Mapping | 7.7% | 9.7% |
| Detrended Quantile Mapping | 6.7% | 7.2% |
| Quantile Delta Mapping | 7.2% | 8.1% |
| Scaled Distribution Mapping | 8.8% | 9.1% |
| CDF-transform | 0.5% | 6.1% |
| MVS with all-zero guard (variant) | 12.0% | 13.3% |
| Dec: CHIRPS | 0.0% | 27.1% |
| Raw ECMWF (no correction) | 7.6% | 32.9% |
| Linear Scaling | 7.6% | 33.5% |
| Mean-Variance Scaling (operational) | 16.4% | 28.0% |
| Variance Scaling (unbounded) | 15.6% | 27.9% |
| Square-root-space Mean-Variance Scaling | 4.5% | 25.0% |
| Power Transformation | 7.6% | 32.6% |
| Delta Change | 0.0% | 28.4% |
| Local Intensity Scaling | 30.1% | 30.1% |
| Empirical Quantile Mapping | 27.1% | 27.2% |
| Gamma Quantile Mapping | 28.1% | 32.7% |
| Detrended Quantile Mapping | 26.6% | 30.3% |
| Quantile Delta Mapping | 27.1% | 29.5% |
| Scaled Distribution Mapping | 44.1% | 45.4% |
| CDF-transform | 0.3% | 26.8% |
| MVS with all-zero guard (variant) | 16.4% | 28.0% |
| Jan: CHIRPS | 0.0% | 25.2% |
| Raw ECMWF (no correction) | 32.7% | 71.5% |
| Linear Scaling | 32.7% | 61.0% |
| Mean-Variance Scaling (operational) | 5.6% | 25.9% |
| Variance Scaling (unbounded) | 0.0% | 24.9% |
| Square-root-space Mean-Variance Scaling | 0.3% | 26.1% |
| Power Transformation | 32.7% | 43.3% |
| Delta Change | 0.0% | 32.7% |
| Local Intensity Scaling | 45.9% | 45.9% |
| Empirical Quantile Mapping | 25.2% | 25.3% |
| Gamma Quantile Mapping | 22.0% | 28.5% |
| Detrended Quantile Mapping | 25.0% | 34.8% |
| Quantile Delta Mapping | 25.2% | 26.2% |
| Scaled Distribution Mapping | 58.1% | 72.2% |
| CDF-transform | 0.0% | 30.7% |
| MVS with all-zero guard (variant) | 5.6% | 25.9% |
| ONDJ: CHIRPS | 0.0% | 0.0% |
| Raw ECMWF (no correction) | 0.0% | 0.0% |
| Linear Scaling | 0.0% | 0.0% |
| Mean-Variance Scaling (operational) | 2.7% | 2.8% |
| Variance Scaling (unbounded) | 3.9% | 4.0% |
| Square-root-space Mean-Variance Scaling | 0.1% | 0.3% |
| 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) | 2.7% | 2.8% |
Distribution of the corrected members (mean, spread, 10th and 90th percentiles)
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.84 | 0.72 | 0.82 | 0.31 | 0.77 |
| Linear Scaling | 1.00 | 1.00 | 1.00 | 1.01 | 1.00 |
| Mean-Variance Scaling (operational) | 1.00 | 1.01 | 1.01 | 1.00 | 1.00 |
| Variance Scaling (unbounded) | 1.00 | 1.01 | 1.01 | 1.00 | 1.00 |
| Square-root-space Mean-Variance Scaling | 1.00 | 0.99 | 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 | 1.01 | 1.00 |
| Local Intensity Scaling | 1.00 | 0.99 | 0.95 | 0.62 | 1.00 |
| Empirical Quantile Mapping | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Detrended Quantile Mapping | 1.00 | 0.99 | 0.99 | 1.03 | 0.98 |
| Quantile Delta Mapping | 1.00 | 0.99 | 1.02 | 1.04 | 0.99 |
| Scaled Distribution Mapping | 0.92 | 0.91 | 0.72 | 0.44 | 0.92 |
| CDF-transform | 0.98 | 0.96 | 1.03 | 1.23 | 0.96 |
| MVS with all-zero guard (variant) | 1.00 | 1.01 | 1.01 | 1.00 | 1.00 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.62 | 0.57 | 0.88 | 1.10 | 0.50 |
| Linear Scaling | 0.73 | 0.77 | 1.07 | 3.21 | 0.65 |
| Mean-Variance Scaling (operational) | 0.99 | 0.96 | 1.01 | 1.04 | 0.95 |
| Variance Scaling (unbounded) | 0.99 | 0.97 | 1.01 | 1.03 | 0.98 |
| Square-root-space Mean-Variance Scaling | 0.98 | 0.90 | 0.88 | 1.18 | 0.93 |
| Power Transformation | 1.00 | 1.00 | 1.02 | 1.01 | 0.99 |
| Delta Change | 1.05 | 1.08 | 1.20 | 1.50 | 1.06 |
| Local Intensity Scaling | 0.73 | 0.82 | 1.10 | 1.59 | 0.65 |
| Empirical Quantile Mapping | 0.99 | 0.99 | 1.00 | 0.98 | 0.98 |
| Gamma Quantile Mapping | 0.99 | 0.89 | 0.90 | 0.83 | 0.92 |
| Detrended Quantile Mapping | 0.99 | 0.97 | 1.09 | 1.44 | 0.92 |
| Quantile Delta Mapping | 1.01 | 0.99 | 1.15 | 1.48 | 0.97 |
| Scaled Distribution Mapping | 0.86 | 0.82 | 0.84 | 0.96 | 0.81 |
| CDF-transform | 0.89 | 0.88 | 1.06 | 2.02 | 0.78 |
| MVS with all-zero guard (variant) | 0.99 | 0.96 | 1.01 | 1.04 | 0.95 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.15 | 0.88 | 0.04 | 0.00 | 1.02 |
| Linear Scaling | 1.47 | 1.20 | 0.05 | 0.00 | 1.36 |
| Mean-Variance Scaling (operational) | 0.91 | 0.00 | 0.37 | 1.14 | 0.81 |
| Variance Scaling (unbounded) | 0.86 | 0.00 | 0.37 | 1.17 | 0.66 |
| Square-root-space Mean-Variance Scaling | 0.98 | 0.68 | 0.38 | 0.82 | 0.89 |
| Power Transformation | 1.07 | 0.73 | 0.04 | 0.00 | 0.91 |
| Delta Change | 0.92 | 0.88 | 0.67 | 0.44 | 0.91 |
| Local Intensity Scaling | 1.50 | 0.93 | 0.00 | 0.00 | 1.37 |
| Empirical Quantile Mapping | 0.96 | 0.94 | 0.97 | 0.99 | 0.97 |
| Gamma Quantile Mapping | 1.02 | 0.79 | 0.40 | 0.57 | 0.93 |
| Detrended Quantile Mapping | 0.98 | 0.89 | 0.60 | 0.43 | 0.97 |
| Quantile Delta Mapping | 1.00 | 0.90 | 0.72 | 0.96 | 0.98 |
| Scaled Distribution Mapping | 0.99 | 0.93 | 0.00 | 0.00 | 0.97 |
| CDF-transform | 1.09 | 0.95 | 0.48 | 0.42 | 1.07 |
| MVS with all-zero guard (variant) | 0.91 | 0.00 | 0.37 | 1.14 | 0.81 |
| Method | Oct | Nov | Dec | Jan | ONDJ |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.76 | 0.66 | 1.13 | 0.42 | 0.68 |
| Linear Scaling | 0.93 | 0.92 | 1.27 | 1.51 | 0.89 |
| Mean-Variance Scaling (operational) | 1.02 | 1.02 | 1.17 | 0.98 | 1.01 |
| Variance Scaling (unbounded) | 1.03 | 1.03 | 1.17 | 0.93 | 1.03 |
| Square-root-space Mean-Variance Scaling | 1.03 | 0.98 | 1.10 | 1.22 | 1.01 |
| Power Transformation | 1.02 | 1.00 | 1.16 | 1.54 | 1.02 |
| Delta Change | 1.06 | 1.05 | 1.06 | 1.33 | 1.06 |
| Local Intensity Scaling | 0.92 | 0.95 | 1.15 | 0.89 | 0.89 |
| Empirical Quantile Mapping | 1.03 | 1.04 | 1.11 | 1.03 | 1.04 |
| Gamma Quantile Mapping | 1.03 | 0.98 | 1.02 | 1.02 | 1.00 |
| Detrended Quantile Mapping | 1.02 | 1.02 | 1.09 | 1.19 | 0.99 |
| Quantile Delta Mapping | 1.03 | 1.03 | 1.13 | 0.99 | 1.02 |
| Scaled Distribution Mapping | 0.93 | 0.90 | 0.83 | 0.66 | 0.92 |
| CDF-transform | 0.99 | 0.99 | 1.14 | 1.77 | 0.94 |
| MVS with all-zero guard (variant) | 1.02 | 1.02 | 1.17 | 0.98 | 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 2017-2024 (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 2017–2024 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Oct | +0.41 | -0.38 to +1.28 | 11/24 | 0.8177 | 1.0000 | 1.0000 | +0.16 | — |
| Linear Scaling | Nov | +0.22 | +0.02 to +0.40 | 6/24 | 0.9805 | 1.0000 | 1.0000 | +0.77 | — |
| Linear Scaling | Dec | +0.27 | +0.12 to +0.41 | 7/24 | 0.9984 | 1.0000 | 1.0000 | +0.38 | — |
| Linear Scaling | Jan | +0.49 | -0.08 to +1.00 | 9/24 | 0.9439 | 1.0000 | 1.0000 | +0.42 | — |
| Linear Scaling | ONDJ | -0.01 | -1.28 to +1.23 | 14/24 | 0.4918 | 1.0000 | 1.0000 | +2.36 | — |
| Variance Scaling (unbounded) | Oct | +0.07 | -0.04 to +0.17 | 8/24 | 0.8931 | 1.0000 | 1.0000 | +0.08 | — |
| Variance Scaling (unbounded) | Nov | +0.05 | +0.02 to +0.08 | 7/24 | 0.9973 | 1.0000 | 1.0000 | -0.02 | — |
| Variance Scaling (unbounded) | Dec | -0.02 | -0.06 to +0.01 | 15/24 | 0.1110 | 0.4440 | 1.0000 | -0.00 | — |
| Variance Scaling (unbounded) | Jan | -0.24 | -0.37 to -0.11 | 16/24 | 0.0012 | 0.0062 | 0.0722 | -0.34 | ✓ |
| Variance Scaling (unbounded) | ONDJ | +0.34 | +0.04 to +0.67 | 7/24 | 0.9789 | 1.0000 | 1.0000 | -0.19 | — |
| Square-root-space Mean-Variance Scaling | Oct | -0.23 | -0.48 to +0.03 | 15/24 | 0.0488 | 0.0976 | 1.0000 | -0.01 | — |
| Square-root-space Mean-Variance Scaling | Nov | -0.09 | -0.22 to +0.05 | 16/24 | 0.0955 | 0.0976 | 1.0000 | -0.10 | — |
| Square-root-space Mean-Variance Scaling | Dec | -0.07 | -0.11 to -0.02 | 20/24 | 0.0048 | 0.0191 | 0.2722 | -0.03 | ✓ |
| Square-root-space Mean-Variance Scaling | Jan | -0.48 | -0.72 to -0.25 | 18/24 | 0.0004 | 0.0018 | 0.0209 | -0.69 | ✓✓ |
| Square-root-space Mean-Variance Scaling | ONDJ | -0.43 | -0.75 to -0.13 | 18/24 | 0.0065 | 0.0194 | 0.3615 | -0.57 | ✓ |
| Power Transformation | Oct | -0.09 | -0.51 to +0.35 | 15/24 | 0.3469 | 1.0000 | 1.0000 | +0.30 | — |
| Power Transformation | Nov | +0.05 | -0.13 to +0.24 | 14/24 | 0.6841 | 1.0000 | 1.0000 | -0.16 | — |
| Power Transformation | Dec | +0.06 | -0.03 to +0.14 | 6/24 | 0.9187 | 1.0000 | 1.0000 | +0.14 | — |
| Power Transformation | Jan | -0.13 | -0.36 to +0.10 | 12/24 | 0.1317 | 0.6587 | 1.0000 | -0.34 | — |
| Power Transformation | ONDJ | -0.03 | -0.67 to +0.65 | 15/24 | 0.4663 | 1.0000 | 1.0000 | -0.50 | — |
| Delta Change | Oct | -0.68 | -1.60 to +0.18 | 14/24 | 0.0811 | 0.3792 | 1.0000 | +0.94 | — |
| Delta Change | Nov | -0.02 | -0.57 to +0.50 | 11/24 | 0.4777 | 1.0000 | 1.0000 | +0.95 | — |
| Delta Change | Dec | +0.02 | -0.17 to +0.23 | 11/24 | 0.5728 | 1.0000 | 1.0000 | -0.07 | — |
| Delta Change | Jan | -0.01 | -0.47 to +0.41 | 10/24 | 0.4892 | 1.0000 | 1.0000 | -0.19 | — |
| Delta Change | ONDJ | -1.04 | -2.38 to +0.34 | 16/24 | 0.0758 | 0.3792 | 1.0000 | +3.22 | — |
| Local Intensity Scaling | Oct | +0.42 | -0.39 to +1.29 | 11/24 | 0.8166 | 1.0000 | 1.0000 | +0.23 | — |
| Local Intensity Scaling | Nov | +0.10 | -0.07 to +0.26 | 9/24 | 0.8616 | 1.0000 | 1.0000 | +0.57 | — |
| Local Intensity Scaling | Dec | +0.14 | -0.00 to +0.27 | 6/24 | 0.9646 | 1.0000 | 1.0000 | +0.22 | — |
| Local Intensity Scaling | Jan | +0.32 | -0.20 to +0.82 | 9/24 | 0.8749 | 1.0000 | 1.0000 | +0.15 | — |
| Local Intensity Scaling | ONDJ | +0.01 | -1.30 to +1.29 | 14/24 | 0.5070 | 1.0000 | 1.0000 | +2.39 | — |
| Empirical Quantile Mapping | Oct | +0.32 | -0.20 to +0.83 | 11/24 | 0.8782 | 1.0000 | 1.0000 | +0.81 | — |
| Empirical Quantile Mapping | Nov | +0.19 | -0.17 to +0.57 | 13/24 | 0.8269 | 1.0000 | 1.0000 | -0.01 | — |
| Empirical Quantile Mapping | Dec | -0.03 | -0.18 to +0.12 | 11/24 | 0.3358 | 1.0000 | 1.0000 | -0.09 | — |
| Empirical Quantile Mapping | Jan | -0.34 | -0.61 to -0.08 | 13/24 | 0.0117 | 0.0583 | 0.6294 | -0.74 | — |
| Empirical Quantile Mapping | ONDJ | +0.78 | -0.35 to +2.06 | 14/24 | 0.8665 | 1.0000 | 1.0000 | +0.49 | — |
| Gamma Quantile Mapping | Oct | -0.26 | -0.59 to +0.06 | 15/24 | 0.0654 | 0.1961 | 1.0000 | -0.01 | — |
| Gamma Quantile Mapping | Nov | -0.06 | -0.23 to +0.11 | 13/24 | 0.2370 | 0.4741 | 1.0000 | -0.16 | — |
| Gamma Quantile Mapping | Dec | -0.02 | -0.06 to +0.03 | 15/24 | 0.2769 | 0.4741 | 1.0000 | +0.02 | — |
| Gamma Quantile Mapping | Jan | -0.36 | -0.54 to -0.20 | 19/24 | 0.0001 | 0.0007 | 0.0084 | -0.53 | ✓✓ |
| Gamma Quantile Mapping | ONDJ | -0.52 | -0.92 to -0.14 | 18/24 | 0.0074 | 0.0297 | 0.4087 | -0.71 | ✓ |
| Detrended Quantile Mapping | Oct | -0.20 | -0.89 to +0.46 | 15/24 | 0.2844 | 1.0000 | 1.0000 | +0.75 | — |
| Detrended Quantile Mapping | Nov | +0.18 | -0.16 to +0.54 | 12/24 | 0.8360 | 1.0000 | 1.0000 | +0.98 | — |
| Detrended Quantile Mapping | Dec | +0.22 | +0.04 to +0.41 | 8/24 | 0.9855 | 1.0000 | 1.0000 | +0.04 | — |
| Detrended Quantile Mapping | Jan | +0.10 | -0.52 to +0.64 | 9/24 | 0.6134 | 1.0000 | 1.0000 | -0.06 | — |
| Detrended Quantile Mapping | ONDJ | -0.09 | -1.12 to +1.02 | 15/24 | 0.4402 | 1.0000 | 1.0000 | +3.18 | — |
| Quantile Delta Mapping | Oct | -0.36 | -1.09 to +0.35 | 15/24 | 0.1796 | 0.8980 | 1.0000 | +0.70 | — |
| Quantile Delta Mapping | Nov | +0.15 | -0.14 to +0.46 | 11/24 | 0.8314 | 1.0000 | 1.0000 | +0.81 | — |
| Quantile Delta Mapping | Dec | +0.11 | -0.08 to +0.32 | 9/24 | 0.8063 | 1.0000 | 1.0000 | +0.05 | — |
| Quantile Delta Mapping | Jan | -0.12 | -0.63 to +0.35 | 10/24 | 0.3274 | 1.0000 | 1.0000 | -0.44 | — |
| Quantile Delta Mapping | ONDJ | -0.22 | -1.08 to +0.74 | 16/24 | 0.3346 | 1.0000 | 1.0000 | +3.06 | — |
| Scaled Distribution Mapping | Oct | +0.00 | -1.17 to +1.28 | 14/24 | 0.4989 | 1.0000 | 1.0000 | +1.03 | — |
| Scaled Distribution Mapping | Nov | +0.32 | -0.34 to +1.07 | 14/24 | 0.7986 | 1.0000 | 1.0000 | +1.29 | — |
| Scaled Distribution Mapping | Dec | +0.36 | -0.12 to +0.84 | 10/24 | 0.9165 | 1.0000 | 1.0000 | +0.10 | — |
| Scaled Distribution Mapping | Jan | +0.98 | +0.21 to +1.73 | 11/24 | 0.9887 | 1.0000 | 1.0000 | +0.43 | — |
| Scaled Distribution Mapping | ONDJ | +0.40 | -1.01 to +2.02 | 15/24 | 0.6768 | 1.0000 | 1.0000 | +3.53 | — |
| CDF-transform | Oct | -0.10 | -0.87 to +0.68 | 14/24 | 0.4051 | 1.0000 | 1.0000 | +0.87 | — |
| CDF-transform | Nov | +0.23 | -0.06 to +0.54 | 11/24 | 0.9163 | 1.0000 | 1.0000 | +0.89 | — |
| CDF-transform | Dec | +0.35 | +0.13 to +0.59 | 6/24 | 0.9984 | 1.0000 | 1.0000 | +0.30 | — |
| CDF-transform | Jan | +0.35 | -0.35 to +0.96 | 6/24 | 0.8347 | 1.0000 | 1.0000 | +0.30 | — |
| CDF-transform | ONDJ | -0.18 | -1.16 to +0.87 | 16/24 | 0.3736 | 1.0000 | 1.0000 | +3.04 | — |
| MVS with all-zero guard (variant) | Oct | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Nov | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Dec | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Jan | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | ONDJ | +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 2017–2024 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Oct | +0.63 | -0.16 to +1.48 | 9/24 | 0.9187 | 1.0000 | 1.0000 | +0.26 | — |
| Linear Scaling | Nov | +0.25 | +0.06 to +0.43 | 5/24 | 0.9906 | 1.0000 | 1.0000 | +0.79 | — |
| Linear Scaling | Dec | +0.21 | +0.06 to +0.35 | 7/24 | 0.9912 | 1.0000 | 1.0000 | +0.36 | — |
| Linear Scaling | Jan | +0.30 | -0.28 to +0.82 | 9/24 | 0.8356 | 1.0000 | 1.0000 | +0.34 | — |
| Linear Scaling | ONDJ | +0.27 | -0.98 to +1.49 | 13/24 | 0.6583 | 1.0000 | 1.0000 | +2.51 | — |
| Variance Scaling (unbounded) | Oct | +0.04 | -0.06 to +0.14 | 9/24 | 0.7881 | 1.0000 | 1.0000 | +0.07 | — |
| Variance Scaling (unbounded) | Nov | +0.04 | +0.01 to +0.07 | 9/24 | 0.9911 | 1.0000 | 1.0000 | -0.02 | — |
| Variance Scaling (unbounded) | Dec | -0.03 | -0.06 to +0.01 | 15/24 | 0.0766 | 0.3064 | 1.0000 | -0.01 | — |
| Variance Scaling (unbounded) | Jan | -0.26 | -0.39 to -0.14 | 18/24 | 0.0006 | 0.0029 | 0.0339 | -0.35 | ✓✓ |
| Variance Scaling (unbounded) | ONDJ | +0.27 | -0.02 to +0.60 | 7/24 | 0.9504 | 1.0000 | 1.0000 | -0.22 | — |
| Square-root-space Mean-Variance Scaling | Oct | -0.21 | -0.46 to +0.05 | 15/24 | 0.0689 | 0.1378 | 1.0000 | -0.00 | — |
| Square-root-space Mean-Variance Scaling | Nov | -0.07 | -0.20 to +0.07 | 16/24 | 0.1659 | 0.1659 | 1.0000 | -0.09 | — |
| Square-root-space Mean-Variance Scaling | Dec | -0.07 | -0.11 to -0.02 | 20/24 | 0.0055 | 0.0219 | 0.3063 | -0.03 | ✓ |
| Square-root-space Mean-Variance Scaling | Jan | -0.54 | -0.78 to -0.31 | 20/24 | 0.0001 | 0.0003 | 0.0029 | -0.72 | ✓✓ |
| Square-root-space Mean-Variance Scaling | ONDJ | -0.37 | -0.69 to -0.06 | 18/24 | 0.0163 | 0.0489 | 0.8962 | -0.54 | ✓ |
| Power Transformation | Oct | -0.09 | -0.51 to +0.35 | 15/24 | 0.3515 | 1.0000 | 1.0000 | +0.30 | — |
| Power Transformation | Nov | +0.04 | -0.13 to +0.23 | 14/24 | 0.6662 | 1.0000 | 1.0000 | -0.17 | — |
| Power Transformation | Dec | +0.04 | -0.04 to +0.12 | 7/24 | 0.8435 | 1.0000 | 1.0000 | +0.13 | — |
| Power Transformation | Jan | -0.20 | -0.43 to +0.02 | 14/24 | 0.0468 | 0.2342 | 1.0000 | -0.38 | — |
| Power Transformation | ONDJ | -0.04 | -0.67 to +0.61 | 15/24 | 0.4455 | 1.0000 | 1.0000 | -0.51 | — |
| Delta Change | Oct | -0.88 | -1.82 to -0.02 | 14/24 | 0.0363 | 0.1807 | 1.0000 | +0.31 | — |
| Delta Change | Nov | -0.13 | -0.69 to +0.39 | 12/24 | 0.3266 | 0.9797 | 1.0000 | +0.52 | — |
| Delta Change | Dec | -0.03 | -0.21 to +0.17 | 13/24 | 0.3855 | 0.9797 | 1.0000 | -0.22 | — |
| Delta Change | Jan | -0.09 | -0.56 to +0.33 | 11/24 | 0.3514 | 0.9797 | 1.0000 | -0.33 | — |
| Delta Change | ONDJ | -1.34 | -2.71 to +0.06 | 16/24 | 0.0361 | 0.1807 | 1.0000 | +2.26 | — |
| Local Intensity Scaling | Oct | +0.63 | -0.17 to +1.50 | 11/24 | 0.9186 | 1.0000 | 1.0000 | +0.33 | — |
| Local Intensity Scaling | Nov | +0.13 | -0.04 to +0.29 | 9/24 | 0.9266 | 1.0000 | 1.0000 | +0.58 | — |
| Local Intensity Scaling | Dec | +0.10 | -0.04 to +0.23 | 7/24 | 0.9037 | 1.0000 | 1.0000 | +0.20 | — |
| Local Intensity Scaling | Jan | +0.18 | -0.35 to +0.68 | 11/24 | 0.7412 | 1.0000 | 1.0000 | +0.09 | — |
| Local Intensity Scaling | ONDJ | +0.31 | -0.99 to +1.56 | 13/24 | 0.6724 | 1.0000 | 1.0000 | +2.54 | — |
| Empirical Quantile Mapping | Oct | +0.33 | -0.20 to +0.84 | 11/24 | 0.8836 | 1.0000 | 1.0000 | +0.82 | — |
| Empirical Quantile Mapping | Nov | +0.20 | -0.16 to +0.58 | 13/24 | 0.8435 | 1.0000 | 1.0000 | -0.00 | — |
| Empirical Quantile Mapping | Dec | -0.03 | -0.17 to +0.12 | 12/24 | 0.3440 | 1.0000 | 1.0000 | -0.09 | — |
| Empirical Quantile Mapping | Jan | -0.39 | -0.66 to -0.13 | 14/24 | 0.0047 | 0.0237 | 0.2702 | -0.76 | ✓ |
| Empirical Quantile Mapping | ONDJ | +0.87 | -0.25 to +2.16 | 12/24 | 0.8950 | 1.0000 | 1.0000 | +0.53 | — |
| Gamma Quantile Mapping | Oct | -0.24 | -0.57 to +0.09 | 14/24 | 0.0911 | 0.2733 | 1.0000 | +0.01 | — |
| Gamma Quantile Mapping | Nov | -0.03 | -0.20 to +0.14 | 12/24 | 0.3567 | 0.7133 | 1.0000 | -0.14 | — |
| Gamma Quantile Mapping | Dec | -0.01 | -0.05 to +0.04 | 14/24 | 0.3842 | 0.7133 | 1.0000 | +0.02 | — |
| Gamma Quantile Mapping | Jan | -0.41 | -0.58 to -0.25 | 21/24 | 0.0000 | 0.0001 | 0.0009 | -0.55 | ✓✓ |
| Gamma Quantile Mapping | ONDJ | -0.44 | -0.85 to -0.05 | 18/24 | 0.0222 | 0.0889 | 1.0000 | -0.67 | — |
| Detrended Quantile Mapping | Oct | -0.21 | -0.90 to +0.45 | 15/24 | 0.2742 | 1.0000 | 1.0000 | +0.75 | — |
| Detrended Quantile Mapping | Nov | +0.18 | -0.16 to +0.54 | 12/24 | 0.8378 | 1.0000 | 1.0000 | +0.98 | — |
| Detrended Quantile Mapping | Dec | +0.21 | +0.04 to +0.40 | 8/24 | 0.9834 | 1.0000 | 1.0000 | +0.04 | — |
| Detrended Quantile Mapping | Jan | +0.04 | -0.59 to +0.58 | 9/24 | 0.5430 | 1.0000 | 1.0000 | -0.08 | — |
| Detrended Quantile Mapping | ONDJ | -0.01 | -1.05 to +1.11 | 15/24 | 0.4933 | 1.0000 | 1.0000 | +3.22 | — |
| Quantile Delta Mapping | Oct | -0.40 | -1.14 to +0.32 | 15/24 | 0.1534 | 0.7671 | 1.0000 | +0.70 | — |
| Quantile Delta Mapping | Nov | +0.14 | -0.15 to +0.45 | 11/24 | 0.8109 | 1.0000 | 1.0000 | +0.81 | — |
| Quantile Delta Mapping | Dec | +0.09 | -0.10 to +0.31 | 11/24 | 0.7625 | 1.0000 | 1.0000 | +0.05 | — |
| Quantile Delta Mapping | Jan | -0.20 | -0.72 to +0.27 | 11/24 | 0.2326 | 0.9305 | 1.0000 | -0.47 | — |
| Quantile Delta Mapping | ONDJ | -0.22 | -1.09 to +0.74 | 16/24 | 0.3323 | 0.9969 | 1.0000 | +3.08 | — |
| Scaled Distribution Mapping | Oct | +0.11 | -1.06 to +1.39 | 13/24 | 0.5643 | 1.0000 | 1.0000 | +1.08 | — |
| Scaled Distribution Mapping | Nov | +0.43 | -0.24 to +1.17 | 12/24 | 0.8633 | 1.0000 | 1.0000 | +1.33 | — |
| Scaled Distribution Mapping | Dec | +0.41 | -0.07 to +0.89 | 9/24 | 0.9405 | 1.0000 | 1.0000 | +0.12 | — |
| Scaled Distribution Mapping | Jan | +0.97 | +0.20 to +1.72 | 11/24 | 0.9881 | 1.0000 | 1.0000 | +0.42 | — |
| Scaled Distribution Mapping | ONDJ | +0.62 | -0.78 to +2.23 | 15/24 | 0.7620 | 1.0000 | 1.0000 | +3.62 | — |
| CDF-transform | Oct | -0.01 | -0.78 to +0.76 | 14/24 | 0.4878 | 1.0000 | 1.0000 | +0.90 | — |
| CDF-transform | Nov | +0.27 | -0.03 to +0.59 | 11/24 | 0.9433 | 1.0000 | 1.0000 | +0.90 | — |
| CDF-transform | Dec | +0.34 | +0.13 to +0.59 | 7/24 | 0.9984 | 1.0000 | 1.0000 | +0.30 | — |
| CDF-transform | Jan | +0.28 | -0.42 to +0.89 | 7/24 | 0.7809 | 1.0000 | 1.0000 | +0.27 | — |
| CDF-transform | ONDJ | +0.04 | -0.93 to +1.10 | 15/24 | 0.5277 | 1.0000 | 1.0000 | +3.13 | — |
| MVS with all-zero guard (variant) | Oct | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Nov | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Dec | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Jan | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | ONDJ | +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 2017–2024 | Screening |
|---|---|---|---|---|---|---|---|---|---|
| Linear Scaling | Oct | +0.0109 | -0.0080 to +0.0289 | 9/24 | 0.8667 | 1.0000 | 1.0000 | -0.0219 | — |
| Linear Scaling | Nov | +0.0043 | -0.0098 to +0.0183 | 10/24 | 0.7164 | 1.0000 | 1.0000 | +0.0150 | — |
| Linear Scaling | Dec | +0.0056 | -0.0219 to +0.0318 | 9/24 | 0.6546 | 1.0000 | 1.0000 | -0.0096 | — |
| Linear Scaling | Jan | -0.0315 | -0.1398 to +0.0731 | 10/24 | 0.2926 | 1.0000 | 1.0000 | -0.1296 | — |
| Linear Scaling | ONDJ | +0.0048 | -0.0056 to +0.0156 | 12/24 | 0.8009 | 1.0000 | 1.0000 | +0.0033 | — |
| Variance Scaling (unbounded) | Oct | +0.0001 | -0.0013 to +0.0013 | 9/24 | 0.5294 | 0.9337 | 1.0000 | +0.0014 | — |
| Variance Scaling (unbounded) | Nov | -0.0006 | -0.0015 to +0.0003 | 13/24 | 0.1050 | 0.4199 | 1.0000 | -0.0013 | — |
| Variance Scaling (unbounded) | Dec | -0.0035 | -0.0087 to +0.0018 | 15/24 | 0.1094 | 0.4199 | 1.0000 | -0.0030 | — |
| Variance Scaling (unbounded) | Jan | -0.0168 | -0.0268 to -0.0066 | 16/24 | 0.0029 | 0.0143 | 0.1568 | -0.0356 | ✓ |
| Variance Scaling (unbounded) | ONDJ | -0.0001 | -0.0022 to +0.0019 | 8/24 | 0.4668 | 0.9337 | 1.0000 | +0.0005 | — |
| Square-root-space Mean-Variance Scaling | Oct | -0.0015 | -0.0046 to +0.0015 | 12/24 | 0.1727 | 0.2718 | 1.0000 | -0.0028 | — |
| Square-root-space Mean-Variance Scaling | Nov | -0.0071 | -0.0106 to -0.0039 | 19/24 | 0.0002 | 0.0009 | 0.0128 | -0.0077 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Dec | -0.0170 | -0.0313 to -0.0039 | 15/24 | 0.0121 | 0.0363 | 0.6531 | -0.0070 | ✓ |
| Square-root-space Mean-Variance Scaling | Jan | -0.0890 | -0.1345 to -0.0459 | 18/24 | 0.0002 | 0.0008 | 0.0097 | -0.1581 | ✓✓ |
| Square-root-space Mean-Variance Scaling | ONDJ | -0.0014 | -0.0037 to +0.0010 | 13/24 | 0.1359 | 0.2718 | 1.0000 | -0.0036 | — |
| Power Transformation | Oct | +0.0022 | -0.0045 to +0.0086 | 9/24 | 0.7383 | 1.0000 | 1.0000 | +0.0020 | — |
| Power Transformation | Nov | -0.0002 | -0.0047 to +0.0044 | 11/24 | 0.4697 | 1.0000 | 1.0000 | -0.0043 | — |
| Power Transformation | Dec | -0.0086 | -0.0192 to +0.0013 | 14/24 | 0.0637 | 0.2546 | 1.0000 | -0.0106 | — |
| Power Transformation | Jan | -0.0756 | -0.1179 to -0.0359 | 17/24 | 0.0004 | 0.0022 | 0.0254 | -0.1404 | ✓✓ |
| Power Transformation | ONDJ | -0.0001 | -0.0080 to +0.0080 | 13/24 | 0.4871 | 1.0000 | 1.0000 | +0.0000 | — |
| Delta Change | Oct | -0.0027 | -0.0215 to +0.0154 | 12/24 | 0.3906 | 1.0000 | 1.0000 | +0.0149 | — |
| Delta Change | Nov | -0.0000 | -0.0222 to +0.0210 | 10/24 | 0.4979 | 1.0000 | 1.0000 | +0.0294 | — |
| Delta Change | Dec | +0.0389 | +0.0008 to +0.0791 | 8/24 | 0.9661 | 1.0000 | 1.0000 | +0.0056 | — |
| Delta Change | Jan | +0.0006 | -0.0759 to +0.0710 | 8/24 | 0.5058 | 1.0000 | 1.0000 | -0.1111 | — |
| Delta Change | ONDJ | +0.0032 | -0.0143 to +0.0200 | 10/24 | 0.6366 | 1.0000 | 1.0000 | +0.0245 | — |
| Local Intensity Scaling | Oct | +0.0088 | -0.0045 to +0.0215 | 9/24 | 0.8941 | 1.0000 | 1.0000 | -0.0110 | — |
| Local Intensity Scaling | Nov | -0.0015 | -0.0125 to +0.0092 | 10/24 | 0.3979 | 1.0000 | 1.0000 | +0.0185 | — |
| Local Intensity Scaling | Dec | +0.0185 | -0.0221 to +0.0569 | 9/24 | 0.8074 | 1.0000 | 1.0000 | -0.0057 | — |
| Local Intensity Scaling | Jan | -0.0273 | -0.1362 to +0.0798 | 10/24 | 0.3191 | 1.0000 | 1.0000 | -0.1266 | — |
| Local Intensity Scaling | ONDJ | +0.0050 | -0.0058 to +0.0162 | 12/24 | 0.8044 | 1.0000 | 1.0000 | +0.0033 | — |
| Empirical Quantile Mapping | Oct | +0.0065 | -0.0061 to +0.0192 | 12/24 | 0.8336 | 1.0000 | 1.0000 | +0.0226 | — |
| Empirical Quantile Mapping | Nov | -0.0007 | -0.0126 to +0.0106 | 11/24 | 0.4502 | 1.0000 | 1.0000 | +0.0080 | — |
| Empirical Quantile Mapping | Dec | -0.0011 | -0.0290 to +0.0265 | 10/24 | 0.4704 | 1.0000 | 1.0000 | -0.0160 | — |
| Empirical Quantile Mapping | Jan | -0.0920 | -0.1479 to -0.0393 | 16/24 | 0.0022 | 0.0109 | 0.1215 | -0.1762 | ✓ |
| Empirical Quantile Mapping | ONDJ | +0.0047 | -0.0048 to +0.0146 | 12/24 | 0.8196 | 1.0000 | 1.0000 | +0.0072 | — |
| Gamma Quantile Mapping | Oct | -0.0010 | -0.0071 to +0.0049 | 13/24 | 0.3697 | 0.7395 | 1.0000 | +0.0057 | — |
| Gamma Quantile Mapping | Nov | -0.0035 | -0.0107 to +0.0030 | 11/24 | 0.1715 | 0.6859 | 1.0000 | -0.0041 | — |
| Gamma Quantile Mapping | Dec | +0.0195 | +0.0047 to +0.0351 | 8/24 | 0.9894 | 0.9894 | 1.0000 | +0.0402 | — |
| Gamma Quantile Mapping | Jan | -0.0794 | -0.1078 to -0.0523 | 22/24 | 0.0000 | 0.0000 | 0.0000 | -0.1294 | ✓✓ |
| Gamma Quantile Mapping | ONDJ | -0.0014 | -0.0045 to +0.0017 | 13/24 | 0.1926 | 0.6859 | 1.0000 | -0.0049 | — |
| Detrended Quantile Mapping | Oct | +0.0050 | -0.0072 to +0.0169 | 12/24 | 0.7830 | 1.0000 | 1.0000 | +0.0171 | — |
| Detrended Quantile Mapping | Nov | +0.0060 | -0.0094 to +0.0214 | 9/24 | 0.7698 | 1.0000 | 1.0000 | +0.0271 | — |
| Detrended Quantile Mapping | Dec | +0.0548 | +0.0168 to +0.0917 | 6/24 | 0.9949 | 1.0000 | 1.0000 | +0.0172 | — |
| Detrended Quantile Mapping | Jan | -0.0011 | -0.0787 to +0.0705 | 8/24 | 0.4885 | 1.0000 | 1.0000 | -0.1118 | — |
| Detrended Quantile Mapping | ONDJ | +0.0113 | +0.0026 to +0.0204 | 9/24 | 0.9874 | 1.0000 | 1.0000 | +0.0187 | — |
| Quantile Delta Mapping | Oct | +0.0027 | -0.0099 to +0.0151 | 12/24 | 0.6596 | 1.0000 | 1.0000 | +0.0129 | — |
| Quantile Delta Mapping | Nov | +0.0109 | -0.0027 to +0.0242 | 7/24 | 0.9320 | 1.0000 | 1.0000 | +0.0231 | — |
| Quantile Delta Mapping | Dec | +0.0218 | -0.0128 to +0.0559 | 9/24 | 0.8812 | 1.0000 | 1.0000 | -0.0104 | — |
| Quantile Delta Mapping | Jan | -0.0632 | -0.1330 to +0.0038 | 12/24 | 0.0487 | 0.2434 | 1.0000 | -0.1719 | — |
| Quantile Delta Mapping | ONDJ | +0.0121 | +0.0034 to +0.0209 | 7/24 | 0.9931 | 1.0000 | 1.0000 | +0.0208 | — |
| Scaled Distribution Mapping | Oct | +0.0075 | -0.0090 to +0.0241 | 13/24 | 0.8035 | 1.0000 | 1.0000 | +0.0193 | — |
| Scaled Distribution Mapping | Nov | +0.0116 | -0.0137 to +0.0371 | 9/24 | 0.8078 | 1.0000 | 1.0000 | +0.0481 | — |
| Scaled Distribution Mapping | Dec | +0.0563 | -0.0121 to +0.1223 | 8/24 | 0.9386 | 1.0000 | 1.0000 | +0.0181 | — |
| Scaled Distribution Mapping | Jan | +0.0489 | -0.0850 to +0.1802 | 9/24 | 0.7543 | 1.0000 | 1.0000 | -0.0774 | — |
| Scaled Distribution Mapping | ONDJ | +0.0185 | +0.0070 to +0.0301 | 8/24 | 0.9973 | 1.0000 | 1.0000 | +0.0250 | — |
| CDF-transform | Oct | +0.0078 | -0.0023 to +0.0179 | 8/24 | 0.9235 | 1.0000 | 1.0000 | +0.0110 | — |
| CDF-transform | Nov | +0.0155 | +0.0032 to +0.0279 | 6/24 | 0.9883 | 1.0000 | 1.0000 | +0.0220 | — |
| CDF-transform | Dec | +0.0786 | +0.0382 to +0.1216 | 7/24 | 0.9995 | 1.0000 | 1.0000 | +0.0325 | — |
| CDF-transform | Jan | +0.0188 | -0.0635 to +0.0931 | 8/24 | 0.6745 | 1.0000 | 1.0000 | -0.1226 | — |
| CDF-transform | ONDJ | +0.0110 | +0.0038 to +0.0183 | 6/24 | 0.9959 | 1.0000 | 1.0000 | +0.0165 | — |
| MVS with all-zero guard (variant) | Oct | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Nov | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Dec | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Jan | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | ONDJ | +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) |
|---|---|---|
| Linear Scaling | Dec | mean fallback: 0.4% of the area |
| Linear Scaling | Jan | mean fallback: 2.8% of the area |
| Mean-Variance Scaling (operational) | Oct | ratio lower limit: 0.9% of the area; ratio upper limit: 11.8% of the area; clipped at zero: 6.5% |
| Mean-Variance Scaling (operational) | Nov | ratio lower limit: 5.2% of the area; ratio upper limit: 9.4% of the area; clipped at zero: 8.0% |
| Mean-Variance Scaling (operational) | Dec | sd fallback: 1.3% of the area; ratio lower limit: 17.3% of the area; ratio upper limit: 5.8% of the area; clipped at zero: 12.2% |
| Mean-Variance Scaling (operational) | Jan | sd fallback: 3.9% of the area; ratio lower limit: 25.8% of the area; ratio upper limit: 28.2% of the area; clipped at zero: 4.5% |
| Mean-Variance Scaling (operational) | ONDJ | ratio lower limit: 2.2% of the area; ratio upper limit: 22.3% of the area; clipped at zero: 1.7% |
| Variance Scaling (unbounded) | Oct | clipped at zero: 6.8% |
| Variance Scaling (unbounded) | Nov | clipped at zero: 8.2% |
| Variance Scaling (unbounded) | Dec | sd fallback: 1.3% of the area; clipped at zero: 8.9% |
| Variance Scaling (unbounded) | Jan | sd fallback: 3.9% of the area; clipped at zero: 1.8% |
| Variance Scaling (unbounded) | ONDJ | clipped at zero: 2.2% |
| Square-root-space Mean-Variance Scaling | Oct | ratio upper limit: 0.4% of the area; clipped at zero: 1.5% |
| Square-root-space Mean-Variance Scaling | Nov | ratio lower limit: 0.3% of the area; clipped at zero: 2.3% |
| Square-root-space Mean-Variance Scaling | Dec | ratio lower limit: 14.0% of the area; clipped at zero: 2.9% |
| Square-root-space Mean-Variance Scaling | Jan | ratio lower limit: 30.9% of the area; ratio upper limit: 0.3% of the area; clipped at zero: 1.0% |
| Square-root-space Mean-Variance Scaling | ONDJ | ratio lower limit: 0.0% of the area; ratio upper limit: 1.8% of the area; clipped at zero: 0.0% |
| Power Transformation | Dec | b at bound: 1.7% of the area |
| Power Transformation | Jan | b at bound: 23.3% of the area |
| Delta Change | Dec | mean fallback: 0.4% of the area; ratio capped: 0.1% |
| Delta Change | Jan | mean fallback: 2.8% of the area; ratio capped: 1.1% |
| Local Intensity Scaling | Oct | always wet: 91.6% of the area |
| Local Intensity Scaling | Nov | always wet: 78.9% of the area |
| Local Intensity Scaling | Dec | always wet: 73.6% of the area; never wet: 2.9% of the area |
| Local Intensity Scaling | Jan | always wet: 80.2% of the area; never wet: 9.2% of the area |
| Local Intensity Scaling | ONDJ | always wet: 100.0% of the area |
| Empirical Quantile Mapping | Oct | model has dry: 25.2% of the area; obs has dry: 8.4% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | Nov | model has dry: 86.0% of the area; obs has dry: 21.1% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | Dec | model has dry: 98.9% of the area; obs has dry: 26.4% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | Jan | model has dry: 100.0% of the area; obs has dry: 19.8% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | ONDJ | model has dry: 1.6% of the area; extrapolated: 0.4% |
| Gamma Quantile Mapping | Oct | model has dry: 25.2% of the area; obs has dry: 8.4% of the area |
| Gamma Quantile Mapping | Nov | model has dry: 86.0% of the area; obs has dry: 21.1% of the area |
| Gamma Quantile Mapping | Dec | gamma fallback: 2.7% of the area; model has dry: 98.9% of the area; obs has dry: 26.4% of the area |
| Gamma Quantile Mapping | Jan | gamma fallback: 4.5% of the area; model has dry: 100.0% of the area; obs has dry: 19.8% of the area |
| Gamma Quantile Mapping | ONDJ | model has dry: 1.6% of the area |
| Detrended Quantile Mapping | Oct | model has dry: 25.2% of the area; obs has dry: 8.4% of the area; extrapolated: 0.2% |
| Detrended Quantile Mapping | Nov | model has dry: 86.0% of the area; obs has dry: 21.1% of the area; extrapolated: 0.1% |
| Detrended Quantile Mapping | Dec | model has dry: 98.9% of the area; obs has dry: 26.4% of the area; ratio capped: 0.1%; extrapolated: 0.1% |
| Detrended Quantile Mapping | Jan | model has dry: 100.0% of the area; obs has dry: 19.8% of the area; ratio capped: 1.1%; extrapolated: 0.1% |
| Detrended Quantile Mapping | ONDJ | model has dry: 1.6% of the area; extrapolated: 0.2% |
| Quantile Delta Mapping | Oct | model has dry: 25.2% of the area; obs has dry: 8.4% of the area; low denominator: 0.6%; ratio capped: 0.0% |
| Quantile Delta Mapping | Nov | model has dry: 86.0% of the area; obs has dry: 21.1% of the area; low denominator: 7.9%; ratio capped: 0.3% |
| Quantile Delta Mapping | Dec | model has dry: 98.9% of the area; obs has dry: 26.4% of the area; low denominator: 31.5%; ratio capped: 0.4% |
| Quantile Delta Mapping | Jan | model has dry: 100.0% of the area; obs has dry: 19.8% of the area; low denominator: 54.4%; ratio capped: 0.2% |
| Quantile Delta Mapping | ONDJ | model has dry: 1.6% of the area; ratio capped: 0.0% |
| Scaled Distribution Mapping | Dec | gamma fallback: 5.5% of the area; linear scaling fallback: 5.9% |
| Scaled Distribution Mapping | Jan | gamma fallback: 13.7% of the area; linear scaling fallback: 23.4% |
| CDF-transform | Oct | at forecast range edge: 13.9% |
| CDF-transform | Nov | at forecast range edge: 7.1% |
| CDF-transform | Dec | mean fallback: 0.4% of the area; at forecast range edge: 2.2% |
| CDF-transform | Jan | mean fallback: 2.8% of the area; at forecast range edge: 0.6% |
| CDF-transform | ONDJ | at forecast range edge: 9.5% |
| MVS with all-zero guard (variant) | Oct | ratio lower limit: 0.9% of the area; ratio upper limit: 11.8% of the area; clipped at zero: 6.5% |
| MVS with all-zero guard (variant) | Nov | ratio lower limit: 5.2% of the area; ratio upper limit: 9.4% of the area; clipped at zero: 8.0% |
| MVS with all-zero guard (variant) | Dec | sd fallback: 1.3% of the area; ratio lower limit: 17.3% of the area; ratio upper limit: 5.8% of the area; clipped at zero: 12.2% |
| MVS with all-zero guard (variant) | Jan | sd fallback: 3.9% of the area; ratio lower limit: 25.8% of the area; ratio upper limit: 28.2% of the area; clipped at zero: 4.5% |
| MVS with all-zero guard (variant) | ONDJ | ratio lower limit: 2.2% of the area; ratio upper limit: 22.3% of the area; clipped at zero: 1.7% |
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 8.4% of area | always wet 91.6% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.415 | +0.000 | +0.000 | +0.034 | +0.381 |
| Variance Scaling (unbounded) | +0.067 | +0.000 | +0.000 | +0.000 | +0.067 |
| Square-root-space Mean-Variance Scaling | -0.227 | +0.000 | +0.000 | -0.014 | -0.213 |
| Power Transformation | -0.087 | +0.000 | +0.000 | +0.005 | -0.092 |
| Delta Change | -0.677 | +0.000 | +0.000 | -0.044 | -0.634 |
| Local Intensity Scaling | +0.417 | +0.000 | +0.000 | -0.010 | +0.427 |
| Empirical Quantile Mapping | +0.318 | +0.000 | +0.000 | +0.021 | +0.298 |
| Gamma Quantile Mapping | -0.263 | +0.000 | +0.000 | -0.010 | -0.253 |
| Detrended Quantile Mapping | -0.204 | +0.000 | +0.000 | -0.022 | -0.182 |
| Quantile Delta Mapping | -0.357 | +0.000 | +0.000 | -0.037 | -0.320 |
| Scaled Distribution Mapping | +0.001 | +0.000 | +0.000 | -0.023 | +0.024 |
| CDF-transform | -0.099 | +0.000 | +0.000 | -0.016 | -0.083 |
| 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 21.1% of area | always wet 78.9% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.221 | +0.000 | +0.000 | +0.088 | +0.133 |
| Variance Scaling (unbounded) | +0.046 | +0.000 | +0.000 | +0.002 | +0.044 |
| Square-root-space Mean-Variance Scaling | -0.093 | +0.000 | +0.000 | -0.020 | -0.073 |
| Power Transformation | +0.047 | +0.000 | +0.000 | +0.026 | +0.021 |
| Delta Change | -0.016 | +0.000 | +0.000 | +0.061 | -0.077 |
| Local Intensity Scaling | +0.095 | +0.000 | +0.000 | -0.012 | +0.107 |
| Empirical Quantile Mapping | +0.186 | +0.000 | +0.000 | +0.039 | +0.146 |
| Gamma Quantile Mapping | -0.065 | +0.000 | +0.000 | -0.009 | -0.055 |
| Detrended Quantile Mapping | +0.182 | +0.000 | +0.000 | +0.069 | +0.113 |
| Quantile Delta Mapping | +0.154 | +0.000 | +0.000 | +0.062 | +0.091 |
| Scaled Distribution Mapping | +0.323 | +0.000 | +0.000 | +0.068 | +0.254 |
| CDF-transform | +0.228 | +0.000 | +0.000 | +0.069 | +0.159 |
| 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 2.9% of area | mixed 23.6% of area | always wet 73.6% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.266 | +0.000 | -0.001 | +0.002 | +0.264 |
| Variance Scaling (unbounded) | -0.022 | +0.000 | -0.001 | -0.004 | -0.017 |
| Square-root-space Mean-Variance Scaling | -0.065 | +0.000 | -0.001 | -0.014 | -0.051 |
| Power Transformation | +0.063 | +0.000 | -0.001 | -0.013 | +0.077 |
| Delta Change | +0.019 | +0.000 | -0.001 | -0.028 | +0.048 |
| Local Intensity Scaling | +0.136 | +0.000 | +0.001 | +0.005 | +0.130 |
| Empirical Quantile Mapping | -0.033 | +0.000 | +0.001 | +0.011 | -0.044 |
| Gamma Quantile Mapping | -0.015 | +0.000 | +0.001 | +0.010 | -0.026 |
| Detrended Quantile Mapping | +0.218 | +0.000 | +0.001 | +0.018 | +0.199 |
| Quantile Delta Mapping | +0.105 | +0.000 | +0.001 | +0.007 | +0.097 |
| Scaled Distribution Mapping | +0.360 | +0.000 | -0.001 | +0.006 | +0.354 |
| CDF-transform | +0.346 | +0.000 | -0.001 | -0.006 | +0.353 |
| 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 9.2% of area | mixed 10.6% of area | always wet 80.2% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.487 | +0.000 | +0.003 | +0.003 | +0.480 |
| Variance Scaling (unbounded) | -0.240 | +0.000 | -0.005 | -0.006 | -0.229 |
| Square-root-space Mean-Variance Scaling | -0.479 | +0.000 | -0.003 | -0.018 | -0.458 |
| Power Transformation | -0.134 | +0.000 | +0.001 | -0.004 | -0.131 |
| Delta Change | -0.005 | +0.000 | +0.001 | -0.006 | -0.001 |
| Local Intensity Scaling | +0.325 | +0.000 | +0.010 | +0.011 | +0.303 |
| Empirical Quantile Mapping | -0.337 | +0.000 | +0.010 | +0.011 | -0.359 |
| Gamma Quantile Mapping | -0.365 | +0.000 | +0.010 | +0.003 | -0.378 |
| Detrended Quantile Mapping | +0.100 | +0.000 | +0.010 | +0.011 | +0.079 |
| Quantile Delta Mapping | -0.121 | +0.000 | +0.010 | +0.012 | -0.144 |
| Scaled Distribution Mapping | +0.977 | +0.000 | +0.003 | +0.027 | +0.947 |
| CDF-transform | +0.350 | +0.000 | +0.004 | +0.003 | +0.343 |
| 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 | -0.012 | +0.000 | +0.000 | +0.000 | -0.012 |
| Variance Scaling (unbounded) | +0.336 | +0.000 | +0.000 | +0.000 | +0.336 |
| Square-root-space Mean-Variance Scaling | -0.432 | +0.000 | +0.000 | +0.000 | -0.432 |
| Power Transformation | -0.028 | +0.000 | +0.000 | +0.000 | -0.028 |
| Delta Change | -1.044 | +0.000 | +0.000 | +0.000 | -1.044 |
| Local Intensity Scaling | +0.014 | +0.000 | +0.000 | +0.000 | +0.014 |
| Empirical Quantile Mapping | +0.779 | +0.000 | +0.000 | +0.000 | +0.779 |
| Gamma Quantile Mapping | -0.524 | +0.000 | +0.000 | +0.000 | -0.524 |
| Detrended Quantile Mapping | -0.086 | +0.000 | +0.000 | +0.000 | -0.086 |
| Quantile Delta Mapping | -0.218 | +0.000 | +0.000 | +0.000 | -0.218 |
| Scaled Distribution Mapping | +0.402 | +0.000 | +0.000 | +0.000 | +0.402 |
| CDF-transform | -0.179 | +0.000 | +0.000 | +0.000 | -0.179 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |