Screening · January initialization · FMAM 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) | -0.696 | -0.803 | -0.465 | -0.760 | -86.1 | 105.7 | 0.24 | 0.48 | 0.79 | 0.0% |
| Linear Scaling | +0.019 | +0.020 | +0.035 | +0.004 | +0.0 | 67.9 | 0.11 | 1.16 | 0.14 | 0.0% |
| Mean-Variance Scaling (operational) | +0.025 | +0.016 | +0.034 | +0.009 | -0.0 | 67.8 | 0.07 | 0.98 | 0.05 | 0.0% |
| Variance Scaling (unbounded) | +0.025 | +0.015 | +0.035 | +0.008 | -0.0 | 67.8 | 0.07 | 0.99 | 0.04 | 0.0% |
| Square-root-space Mean-Variance Scaling | +0.025 | +0.018 | +0.035 | +0.013 | -0.0 | 67.8 | 0.07 | 0.98 | 0.04 | 0.0% |
| Power Transformation | +0.024 | +0.017 | +0.034 | +0.014 | -0.0 | 67.8 | 0.07 | 0.99 | 0.05 | 0.0% |
| Delta Change | +0.029 | +0.010 | +0.031 | -0.010 | +0.0 | 67.9 | 0.11 | 1.04 | 0.04 | 0.0% |
| Local Intensity Scaling | +0.020 | +0.020 | +0.036 | +0.004 | +0.0 | 67.8 | 0.11 | 1.16 | 0.13 | 0.0% |
| Empirical Quantile Mapping | +0.011 | +0.005 | +0.023 | -0.004 | -0.0 | 68.0 | 0.06 | 0.98 | 0.05 | 0.0% |
| Gamma Quantile Mapping | +0.025 | +0.019 | +0.035 | +0.015 | +0.0 | 67.8 | 0.07 | 0.97 | 0.05 | 0.0% |
| Detrended Quantile Mapping | +0.013 | +0.004 | +0.024 | -0.009 | +0.2 | 68.1 | 0.10 | 0.99 | 0.05 | 0.0% |
| Quantile Delta Mapping | +0.013 | +0.001 | +0.023 | -0.013 | +1.2 | 67.9 | 0.11 | 1.02 | 0.07 | 0.0% |
| Scaled Distribution Mapping | +0.009 | -0.012 | +0.019 | -0.019 | -5.5 | 67.4 | 0.11 | 0.91 | 0.16 | 0.7% |
| CDF-transform | +0.013 | +0.003 | +0.023 | -0.013 | +0.4 | 68.0 | 0.11 | 1.00 | 0.04 | 0.0% |
| MVS with all-zero guard (variant) | +0.025 | +0.016 | +0.034 | +0.009 | -0.0 | 67.8 | 0.07 | 0.98 | 0.05 | 0.0% |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.370 | -0.372 | -0.287 | -0.238 | -0.696 |
| Linear Scaling | -0.084 | -0.083 | -0.030 | +0.004 | +0.019 |
| Mean-Variance Scaling (operational) | +0.070 | -0.044 | -0.016 | +0.007 | +0.025 |
| Variance Scaling (unbounded) | +0.076 ✓ | -0.040 ✓ | -0.016 | +0.007 | +0.025 |
| Square-root-space Mean-Variance Scaling | +0.110 ✓ | -0.019 ✓ | -0.014 | +0.011 | +0.025 |
| Power Transformation | +0.064 | -0.020 | -0.017 | +0.012 | +0.024 |
| Delta Change | +0.051 | -0.062 | -0.021 | +0.010 | +0.029 |
| Local Intensity Scaling | -0.049 | -0.076 | -0.029 | +0.004 | +0.020 |
| Empirical Quantile Mapping | +0.099 | -0.028 | -0.026 | +0.000 | +0.011 |
| Gamma Quantile Mapping | +0.084 | -0.021 ✓ | -0.014 | +0.011 | +0.025 |
| Detrended Quantile Mapping | +0.033 | -0.074 | -0.037 | -0.004 | +0.013 |
| Quantile Delta Mapping | +0.082 | -0.084 | -0.046 | -0.000 | +0.013 |
| Scaled Distribution Mapping | -0.111 | -0.101 | -0.050 | -0.007 | +0.009 |
| CDF-transform | -0.085 | -0.085 | -0.041 | -0.001 | +0.013 |
| MVS with all-zero guard (variant) | +0.070 | -0.044 | -0.016 | +0.007 | +0.025 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.298 | -0.325 | -0.248 | -0.208 | -0.465 |
| Linear Scaling | -0.050 | -0.055 | -0.026 | +0.028 | +0.035 |
| Mean-Variance Scaling (operational) | -0.093 | -0.111 | -0.027 | +0.026 | +0.034 |
| Variance Scaling (unbounded) | -0.083 | -0.104 ✓ | -0.022 | +0.026 | +0.035 |
| Square-root-space Mean-Variance Scaling | +0.077 ✓✓ | -0.012 ✓✓ | -0.021 | +0.034 | +0.035 |
| Power Transformation | +0.055 ✓✓ | -0.024 ✓✓ | -0.027 | +0.034 | +0.034 |
| Delta Change | +0.002 | -0.096 | -0.034 | +0.024 | +0.031 |
| Local Intensity Scaling | -0.057 | -0.054 | -0.026 | +0.028 | +0.036 |
| Empirical Quantile Mapping | +0.082 ✓✓ | -0.025 ✓ | -0.035 | +0.022 | +0.023 |
| Gamma Quantile Mapping | +0.036 ✓✓ | -0.035 ✓✓ | -0.022 | +0.034 | +0.035 |
| Detrended Quantile Mapping | -0.000 | -0.092 | -0.054 | +0.017 | +0.024 |
| Quantile Delta Mapping | +0.069 | -0.075 | -0.067 | +0.020 | +0.023 |
| Scaled Distribution Mapping | -0.122 | -0.150 | -0.070 | +0.011 | +0.019 |
| CDF-transform | -0.064 | -0.087 | -0.059 | +0.020 | +0.023 |
| MVS with all-zero guard (variant) | -0.093 | -0.111 | -0.027 | +0.026 | +0.034 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.628 | -0.414 | -0.356 | -0.391 | -0.803 |
| Linear Scaling | -0.259 | -0.028 | -0.022 | -0.019 | +0.020 |
| Mean-Variance Scaling (operational) | +0.000 | +0.005 | -0.006 | -0.007 | +0.016 |
| Variance Scaling (unbounded) | +0.003 | +0.009 | -0.005 | -0.009 | +0.015 |
| Square-root-space Mean-Variance Scaling | +0.015 | +0.030 | -0.000 | -0.012 | +0.018 |
| Power Transformation | -0.032 | +0.030 | +0.002 | -0.004 | +0.017 |
| Delta Change | -0.086 | +0.011 | -0.005 | -0.001 | +0.010 |
| Local Intensity Scaling | -0.218 | -0.024 | -0.021 | -0.019 | +0.020 |
| Empirical Quantile Mapping | +0.012 | +0.023 | -0.011 | -0.019 | +0.005 |
| Gamma Quantile Mapping | +0.010 | +0.029 | +0.002 | -0.015 | +0.019 |
| Detrended Quantile Mapping | -0.110 | +0.018 | -0.020 | -0.019 | +0.004 |
| Quantile Delta Mapping | -0.054 | +0.016 | -0.025 | -0.019 | +0.001 |
| Scaled Distribution Mapping | -0.265 | -0.037 | -0.039 | -0.023 | -0.012 |
| CDF-transform | -0.232 | +0.016 | -0.025 | -0.021 | +0.003 |
| MVS with all-zero guard (variant) | +0.000 | +0.005 | -0.006 | -0.007 | +0.016 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.404 | -0.406 | -0.311 | -0.261 | -0.740 |
| Linear Scaling | -0.070 | -0.075 | -0.029 | +0.002 | +0.022 |
| Mean-Variance Scaling (operational) | +0.063 | -0.055 | -0.023 | +0.001 | +0.020 |
| Variance Scaling (unbounded) | +0.069 ✓ | -0.050 ✓ | -0.022 | +0.002 | +0.021 |
| Square-root-space Mean-Variance Scaling | +0.109 ✓ | -0.025 ✓✓ | -0.019 | +0.008 | +0.021 |
| Power Transformation | +0.064 | -0.025 | -0.022 | +0.007 ✓ | +0.020 |
| Delta Change | +0.053 | -0.064 | -0.022 | +0.010 | +0.030 |
| Local Intensity Scaling | -0.040 | -0.069 | -0.028 | +0.002 | +0.022 |
| Empirical Quantile Mapping | +0.096 | -0.035 | -0.033 | -0.005 | +0.005 |
| Gamma Quantile Mapping | +0.079 | -0.027 ✓ | -0.019 | +0.007 | +0.020 |
| Detrended Quantile Mapping | +0.029 | -0.082 | -0.044 | -0.009 | +0.008 |
| Quantile Delta Mapping | +0.082 | -0.091 | -0.053 | -0.005 | +0.009 |
| Scaled Distribution Mapping | -0.129 | -0.117 | -0.061 | -0.017 | -0.000 |
| CDF-transform | -0.095 | -0.093 | -0.047 | -0.007 | +0.008 |
| MVS with all-zero guard (variant) | +0.063 | -0.055 | -0.023 | +0.001 | +0.020 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.889 | -0.417 | -0.361 | -0.414 | -0.760 |
| Linear Scaling | -0.467 | -0.063 | -0.043 | -0.055 | +0.004 |
| Mean-Variance Scaling (operational) | -0.116 | -0.067 | -0.029 | -0.025 | +0.009 |
| Variance Scaling (unbounded) | -0.099 | -0.058 | -0.028 | -0.027 | +0.008 |
| Square-root-space Mean-Variance Scaling | -0.031 | +0.017 | -0.018 | -0.038 | +0.013 |
| Power Transformation | -0.063 | +0.011 | -0.009 | -0.020 | +0.014 |
| Delta Change | -0.300 | -0.001 | -0.024 | -0.016 | -0.010 |
| Local Intensity Scaling | -0.471 | -0.056 | -0.044 | -0.056 | +0.004 |
| Empirical Quantile Mapping | -0.092 | +0.003 | -0.025 | -0.035 | -0.004 |
| Gamma Quantile Mapping | -0.039 | +0.017 | -0.013 | -0.031 | +0.015 |
| Detrended Quantile Mapping | -0.347 | -0.005 | -0.044 | -0.035 | -0.009 |
| Quantile Delta Mapping | -0.195 | -0.022 | -0.050 | -0.039 | -0.013 |
| Scaled Distribution Mapping | -0.599 | -0.100 | -0.067 | -0.052 | -0.019 |
| CDF-transform | -0.387 | -0.027 | -0.058 | -0.047 | -0.013 |
| MVS with all-zero guard (variant) | -0.116 | -0.067 | -0.029 | -0.025 | +0.009 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -8.7 | -25.9 | -28.8 | -22.6 | -86.1 |
| Linear Scaling | +0.1 | +0.2 | +0.1 | +0.0 | +0.0 |
| Mean-Variance Scaling (operational) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Variance Scaling (unbounded) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Square-root-space Mean-Variance Scaling | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Power Transformation | -0.0 | +0.0 | +0.0 | +0.0 | -0.0 |
| Delta Change | +0.1 | +0.2 | +0.1 | +0.0 | +0.0 |
| Local Intensity Scaling | -0.7 | -0.2 | -0.0 | +0.0 | +0.0 |
| Empirical Quantile Mapping | -0.1 | +0.0 | +0.0 | +0.0 | -0.0 |
| Gamma Quantile Mapping | -0.1 | -0.0 | +0.1 | -0.0 | +0.0 |
| Detrended Quantile Mapping | +0.5 | +0.9 | +0.3 | +0.3 | +0.2 |
| Quantile Delta Mapping | +1.1 | +2.1 | +1.1 | +0.6 | +1.2 |
| Scaled Distribution Mapping | -5.4 | -7.4 | -4.9 | -4.0 | -5.5 |
| CDF-transform | +2.3 | +2.0 | +0.8 | +0.5 | +0.4 |
| MVS with all-zero guard (variant) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.29 | +0.02 | +0.07 | +0.18 | +0.24 |
| Linear Scaling | +0.21 | -0.09 | -0.11 | +0.01 | +0.11 |
| Mean-Variance Scaling (operational) | +0.14 | -0.15 | -0.14 | -0.00 | +0.07 |
| Variance Scaling (unbounded) | +0.12 | -0.15 | -0.14 | -0.00 | +0.07 |
| Square-root-space Mean-Variance Scaling | +0.17 | -0.12 | -0.13 | +0.01 | +0.07 |
| Power Transformation | +0.20 | -0.11 | -0.14 | +0.01 | +0.07 |
| Delta Change | +0.20 | -0.09 | -0.11 | +0.01 | +0.11 |
| Local Intensity Scaling | +0.20 | -0.09 | -0.11 | +0.01 | +0.11 |
| Empirical Quantile Mapping | +0.16 | -0.12 | -0.14 | -0.00 | +0.06 |
| Gamma Quantile Mapping | +0.13 | -0.13 | -0.14 | +0.01 | +0.07 |
| Detrended Quantile Mapping | +0.22 | -0.07 | -0.10 | +0.02 | +0.10 |
| Quantile Delta Mapping | +0.19 | -0.07 | -0.10 | +0.02 | +0.11 |
| Scaled Distribution Mapping | +0.22 | -0.06 | -0.11 | +0.01 | +0.11 |
| CDF-transform | +0.25 | -0.06 | -0.09 | +0.03 | +0.11 |
| MVS with all-zero guard (variant) | +0.14 | -0.15 | -0.14 | -0.00 | +0.07 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.61 | 0.55 | 0.64 | 0.66 | 0.48 |
| Linear Scaling | 1.91 | 1.44 | 1.17 | 1.05 | 1.16 |
| Mean-Variance Scaling (operational) | 1.02 | 0.93 | 0.95 | 0.96 | 0.98 |
| Variance Scaling (unbounded) | 1.05 | 0.95 | 0.96 | 0.97 | 0.99 |
| Square-root-space Mean-Variance Scaling | 1.06 | 1.00 | 0.99 | 1.01 | 0.98 |
| Power Transformation | 1.04 | 0.96 | 0.96 | 0.97 | 0.99 |
| Delta Change | 1.26 | 0.99 | 0.99 | 1.01 | 1.04 |
| Local Intensity Scaling | 1.74 | 1.41 | 1.16 | 1.05 | 1.16 |
| Empirical Quantile Mapping | 1.03 | 0.95 | 0.96 | 0.97 | 0.98 |
| Gamma Quantile Mapping | 0.95 | 0.98 | 0.98 | 1.02 | 0.97 |
| Detrended Quantile Mapping | 1.12 | 0.95 | 0.96 | 0.97 | 0.99 |
| Quantile Delta Mapping | 1.22 | 0.98 | 0.99 | 1.00 | 1.02 |
| Scaled Distribution Mapping | 0.87 | 0.81 | 0.86 | 0.87 | 0.91 |
| CDF-transform | 1.07 | 0.99 | 0.98 | 0.96 | 1.00 |
| MVS with all-zero guard (variant) | 1.02 | 0.93 | 0.95 | 0.96 | 0.98 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.96 | 0.63 | 0.46 | 0.44 | 0.79 |
| Linear Scaling | 0.74 | 0.33 | 0.14 | 0.09 | 0.14 |
| Mean-Variance Scaling (operational) | 0.52 | 0.45 | 0.18 | 0.16 | 0.05 |
| Variance Scaling (unbounded) | 0.57 | 0.44 | 0.17 | 0.15 | 0.04 |
| Square-root-space Mean-Variance Scaling | 0.14 | 0.10 | 0.09 | 0.11 | 0.04 |
| Power Transformation | 0.32 | 0.14 | 0.06 | 0.08 | 0.05 |
| Delta Change | 0.45 | 0.12 | 0.05 | 0.03 | 0.04 |
| Local Intensity Scaling | 0.71 | 0.32 | 0.14 | 0.08 | 0.13 |
| Empirical Quantile Mapping | 0.15 | 0.07 | 0.06 | 0.04 | 0.05 |
| Gamma Quantile Mapping | 0.35 | 0.15 | 0.07 | 0.07 | 0.05 |
| Detrended Quantile Mapping | 0.45 | 0.11 | 0.07 | 0.03 | 0.05 |
| Quantile Delta Mapping | 0.26 | 0.09 | 0.08 | 0.04 | 0.07 |
| Scaled Distribution Mapping | 0.78 | 0.28 | 0.13 | 0.12 | 0.16 |
| CDF-transform | 0.60 | 0.16 | 0.08 | 0.05 | 0.04 |
| MVS with all-zero guard (variant) | 0.52 | 0.45 | 0.18 | 0.16 | 0.05 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Feb | 1484 | 100% | 1263 | 85% |
| Mar | 1484 | 100% | 1463 | 99% |
| Apr | 1484 | 100% | 1484 | 100% |
| May | 1484 | 100% | 1484 | 100% |
| FMAM | 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 | |
|---|---|---|
| Feb: CHIRPS | 0.2% | 12.9% |
| Raw ECMWF (no correction) | 12.2% | 50.0% |
| Linear Scaling | 12.2% | 40.7% |
| Mean-Variance Scaling (operational) | 2.7% | 13.4% |
| Variance Scaling (unbounded) | 1.5% | 12.6% |
| Square-root-space Mean-Variance Scaling | 0.5% | 13.4% |
| Power Transformation | 12.2% | 21.1% |
| Delta Change | 0.2% | 16.1% |
| Local Intensity Scaling | 19.8% | 19.8% |
| Empirical Quantile Mapping | 12.9% | 13.0% |
| Gamma Quantile Mapping | 11.3% | 14.9% |
| Detrended Quantile Mapping | 12.7% | 17.1% |
| Quantile Delta Mapping | 12.9% | 13.9% |
| Scaled Distribution Mapping | 43.3% | 50.7% |
| CDF-transform | 0.2% | 16.0% |
| MVS with all-zero guard (variant) | 2.7% | 13.4% |
| Mar: CHIRPS | 0.7% | 5.1% |
| Raw ECMWF (no correction) | 2.2% | 20.1% |
| Linear Scaling | 2.2% | 14.5% |
| Mean-Variance Scaling (operational) | 1.3% | 3.0% |
| Variance Scaling (unbounded) | 0.6% | 3.0% |
| Square-root-space Mean-Variance Scaling | 0.4% | 5.1% |
| Power Transformation | 2.2% | 7.3% |
| Delta Change | 0.7% | 6.1% |
| Local Intensity Scaling | 6.5% | 6.5% |
| Empirical Quantile Mapping | 5.1% | 5.1% |
| Gamma Quantile Mapping | 5.1% | 7.4% |
| Detrended Quantile Mapping | 4.8% | 6.2% |
| Quantile Delta Mapping | 5.1% | 5.5% |
| Scaled Distribution Mapping | 21.9% | 22.3% |
| CDF-transform | 0.4% | 5.9% |
| MVS with all-zero guard (variant) | 1.3% | 3.0% |
| Apr: CHIRPS | 0.2% | 1.3% |
| Raw ECMWF (no correction) | 0.3% | 3.6% |
| Linear Scaling | 0.3% | 2.4% |
| Mean-Variance Scaling (operational) | 0.2% | 0.3% |
| Variance Scaling (unbounded) | 0.2% | 0.3% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.5% |
| Power Transformation | 0.3% | 0.7% |
| Delta Change | 0.2% | 1.4% |
| Local Intensity Scaling | 1.4% | 1.4% |
| Empirical Quantile Mapping | 1.3% | 1.4% |
| Gamma Quantile Mapping | 1.3% | 1.5% |
| Detrended Quantile Mapping | 1.3% | 1.4% |
| Quantile Delta Mapping | 1.4% | 1.6% |
| Scaled Distribution Mapping | 4.9% | 4.9% |
| CDF-transform | 0.1% | 1.2% |
| MVS with all-zero guard (variant) | 0.2% | 0.3% |
| May: CHIRPS | 0.5% | 1.3% |
| Raw ECMWF (no correction) | 0.2% | 2.4% |
| Linear Scaling | 0.2% | 1.5% |
| Mean-Variance Scaling (operational) | 0.2% | 0.2% |
| Variance Scaling (unbounded) | 0.2% | 0.3% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.3% |
| Power Transformation | 0.2% | 0.3% |
| Delta Change | 0.5% | 1.3% |
| Local Intensity Scaling | 1.3% | 1.3% |
| Empirical Quantile Mapping | 1.3% | 1.3% |
| Gamma Quantile Mapping | 1.2% | 1.4% |
| Detrended Quantile Mapping | 1.2% | 1.3% |
| Quantile Delta Mapping | 1.3% | 1.3% |
| Scaled Distribution Mapping | 3.6% | 3.7% |
| CDF-transform | 0.2% | 1.1% |
| MVS with all-zero guard (variant) | 0.2% | 0.2% |
| FMAM: 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 | 0.7% | 0.7% |
| 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 | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.43 | 0.47 | 0.67 | 0.70 | 0.63 |
| 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 | 0.96 | 1.00 | 1.00 | 1.00 | 1.00 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 |
| Detrended Quantile Mapping | 1.02 | 1.01 | 1.00 | 1.00 | 1.00 |
| Quantile Delta Mapping | 1.06 | 1.03 | 1.01 | 1.01 | 1.00 |
| Scaled Distribution Mapping | 0.59 | 0.82 | 0.95 | 0.96 | 0.98 |
| CDF-transform | 1.13 | 1.03 | 1.01 | 1.01 | 1.00 |
| MVS with all-zero guard (variant) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.92 | 0.69 | 0.82 | 0.79 | 0.70 |
| Linear Scaling | 2.01 | 1.54 | 1.22 | 1.16 | 1.12 |
| Mean-Variance Scaling (operational) | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 |
| Variance Scaling (unbounded) | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 |
| Square-root-space Mean-Variance Scaling | 1.05 | 1.06 | 1.02 | 1.03 | 0.99 |
| Power Transformation | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Delta Change | 1.33 | 1.12 | 1.05 | 1.04 | 1.05 |
| Local Intensity Scaling | 1.73 | 1.47 | 1.22 | 1.16 | 1.12 |
| Empirical Quantile Mapping | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.90 | 1.02 | 1.01 | 1.03 | 0.98 |
| Detrended Quantile Mapping | 1.27 | 1.09 | 1.02 | 1.02 | 1.01 |
| Quantile Delta Mapping | 1.34 | 1.13 | 1.04 | 1.04 | 1.03 |
| Scaled Distribution Mapping | 0.95 | 0.92 | 0.92 | 0.92 | 0.92 |
| CDF-transform | 1.41 | 1.14 | 1.05 | 1.04 | 1.04 |
| MVS with all-zero guard (variant) | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.01 | 0.09 | 0.47 | 0.63 | 0.54 |
| Linear Scaling | 0.03 | 0.21 | 0.69 | 0.90 | 0.87 |
| Mean-Variance Scaling (operational) | 1.18 | 1.54 | 1.06 | 1.06 | 0.97 |
| Variance Scaling (unbounded) | 1.21 | 1.49 | 1.05 | 1.05 | 0.96 |
| Square-root-space Mean-Variance Scaling | 0.89 | 0.98 | 0.97 | 1.00 | 0.96 |
| Power Transformation | 0.36 | 0.73 | 0.92 | 1.00 | 0.94 |
| Delta Change | 0.53 | 0.85 | 0.92 | 0.93 | 0.95 |
| Local Intensity Scaling | 0.16 | 0.30 | 0.68 | 0.88 | 0.87 |
| Empirical Quantile Mapping | 0.99 | 0.96 | 0.94 | 0.95 | 0.98 |
| Gamma Quantile Mapping | 0.68 | 0.90 | 0.95 | 0.98 | 0.96 |
| Detrended Quantile Mapping | 0.52 | 0.86 | 0.92 | 0.94 | 0.96 |
| Quantile Delta Mapping | 0.88 | 0.86 | 0.91 | 0.94 | 0.97 |
| Scaled Distribution Mapping | 0.00 | 0.00 | 0.91 | 0.96 | 0.98 |
| CDF-transform | 0.48 | 0.83 | 0.92 | 0.96 | 0.96 |
| MVS with all-zero guard (variant) | 1.18 | 1.54 | 1.06 | 1.06 | 0.97 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.59 | 0.56 | 0.75 | 0.75 | 0.66 |
| Linear Scaling | 1.34 | 1.23 | 1.11 | 1.09 | 1.05 |
| Mean-Variance Scaling (operational) | 0.94 | 0.98 | 1.01 | 1.02 | 1.00 |
| Variance Scaling (unbounded) | 0.93 | 0.98 | 1.02 | 1.02 | 1.01 |
| Square-root-space Mean-Variance Scaling | 1.05 | 1.02 | 1.03 | 1.04 | 1.00 |
| Power Transformation | 1.11 | 1.02 | 1.02 | 1.02 | 1.00 |
| Delta Change | 1.13 | 1.06 | 1.04 | 1.03 | 1.03 |
| Local Intensity Scaling | 1.20 | 1.20 | 1.11 | 1.09 | 1.05 |
| Empirical Quantile Mapping | 1.04 | 1.05 | 1.03 | 1.02 | 1.02 |
| Gamma Quantile Mapping | 0.97 | 1.00 | 1.03 | 1.04 | 1.00 |
| Detrended Quantile Mapping | 1.14 | 1.07 | 1.03 | 1.03 | 1.02 |
| Quantile Delta Mapping | 1.14 | 1.08 | 1.04 | 1.03 | 1.02 |
| Scaled Distribution Mapping | 0.71 | 0.88 | 0.96 | 0.96 | 0.97 |
| CDF-transform | 1.30 | 1.09 | 1.04 | 1.03 | 1.02 |
| MVS with all-zero guard (variant) | 0.94 | 0.98 | 1.01 | 1.02 | 1.00 |
FMAM rainfall contribution 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) | -0.831 | -0.906 | -0.564 | -0.918 | -104.5 | 118.3 | 0.26 | 0.43 | 0.94 | 0.0% |
| Linear Scaling | +0.023 | +0.021 | +0.040 | +0.000 | +0.0 | 70.8 | 0.13 | 1.17 | 0.14 | 0.0% |
| Mean-Variance Scaling (operational) | +0.028 | +0.016 | +0.037 | +0.006 | -0.0 | 70.8 | 0.10 | 0.98 | 0.05 | 0.0% |
| Variance Scaling (unbounded) | +0.028 | +0.015 | +0.039 | +0.005 | -0.0 | 70.8 | 0.10 | 0.99 | 0.04 | 0.0% |
| Square-root-space Mean-Variance Scaling | +0.028 | +0.018 | +0.039 | +0.011 | -0.0 | 70.7 | 0.10 | 0.98 | 0.05 | 0.0% |
| Power Transformation | +0.027 | +0.017 | +0.038 | +0.013 | -0.0 | 70.8 | 0.10 | 0.99 | 0.07 | 0.0% |
| Delta Change | +0.032 | +0.012 | +0.037 | -0.008 | +0.0 | 70.8 | 0.13 | 1.04 | 0.03 | 0.0% |
| Local Intensity Scaling | +0.023 | +0.021 | +0.041 | +0.000 | +0.0 | 70.8 | 0.13 | 1.17 | 0.13 | 0.0% |
| Empirical Quantile Mapping | +0.014 | +0.006 | +0.028 | -0.007 | -0.0 | 71.0 | 0.09 | 0.98 | 0.05 | 0.0% |
| Gamma Quantile Mapping | +0.028 | +0.019 | +0.039 | +0.013 | +0.0 | 70.7 | 0.10 | 0.97 | 0.06 | 0.0% |
| Detrended Quantile Mapping | +0.017 | +0.005 | +0.031 | -0.010 | +0.2 | 71.0 | 0.13 | 0.99 | 0.04 | 0.0% |
| Quantile Delta Mapping | +0.018 | +0.002 | +0.031 | -0.014 | +1.3 | 70.8 | 0.14 | 1.03 | 0.06 | 0.0% |
| Scaled Distribution Mapping | +0.014 | -0.014 | +0.026 | -0.023 | -6.0 | 70.3 | 0.14 | 0.92 | 0.15 | 0.7% |
| CDF-transform | +0.018 | +0.003 | +0.031 | -0.017 | +0.4 | 70.9 | 0.14 | 1.00 | 0.04 | 0.0% |
| MVS with all-zero guard (variant) | +0.028 | +0.016 | +0.037 | +0.006 | -0.0 | 70.8 | 0.10 | 0.98 | 0.05 | 0.0% |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.364 | -0.398 | -0.331 | -0.271 | -0.831 |
| Linear Scaling | -0.068 | -0.087 | -0.035 | +0.019 | +0.023 |
| Mean-Variance Scaling (operational) | +0.074 | -0.045 | -0.021 | +0.019 | +0.028 |
| Variance Scaling (unbounded) | +0.079 | -0.041 | -0.020 | +0.019 | +0.028 |
| Square-root-space Mean-Variance Scaling | +0.115 | -0.020 | -0.019 | +0.024 | +0.028 |
| Power Transformation | +0.069 | -0.020 | -0.022 | +0.026 | +0.027 |
| Delta Change | +0.062 | -0.062 | -0.025 | +0.023 | +0.032 |
| Local Intensity Scaling | -0.040 | -0.080 | -0.034 | +0.019 | +0.023 |
| Empirical Quantile Mapping | +0.103 | -0.028 | -0.032 | +0.013 | +0.014 |
| Gamma Quantile Mapping | +0.088 | -0.022 | -0.020 | +0.024 | +0.028 |
| Detrended Quantile Mapping | +0.045 | -0.075 | -0.043 | +0.013 | +0.017 |
| Quantile Delta Mapping | +0.088 | -0.086 | -0.051 | +0.016 | +0.018 |
| Scaled Distribution Mapping | -0.096 | -0.103 | -0.056 | +0.009 | +0.014 |
| CDF-transform | -0.073 | -0.088 | -0.045 | +0.013 | +0.018 |
| MVS with all-zero guard (variant) | +0.074 | -0.045 | -0.021 | +0.019 | +0.028 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.327 | -0.361 | -0.309 | -0.238 | -0.564 |
| Linear Scaling | -0.053 | -0.058 | -0.033 | +0.042 | +0.040 |
| Mean-Variance Scaling (operational) | -0.113 | -0.117 | -0.033 | +0.038 | +0.037 |
| Variance Scaling (unbounded) | -0.097 | -0.108 | -0.028 | +0.038 | +0.039 |
| Square-root-space Mean-Variance Scaling | +0.078 | -0.012 | -0.029 | +0.048 | +0.039 |
| Power Transformation | +0.058 | -0.024 | -0.034 | +0.048 | +0.038 |
| Delta Change | +0.004 | -0.099 | -0.040 | +0.041 | +0.037 |
| Local Intensity Scaling | -0.065 | -0.057 | -0.032 | +0.041 | +0.041 |
| Empirical Quantile Mapping | +0.083 | -0.021 | -0.044 | +0.037 | +0.028 |
| Gamma Quantile Mapping | +0.036 | -0.036 | -0.030 | +0.047 | +0.039 |
| Detrended Quantile Mapping | +0.001 | -0.096 | -0.065 | +0.036 | +0.031 |
| Quantile Delta Mapping | +0.071 | -0.080 | -0.077 | +0.040 | +0.031 |
| Scaled Distribution Mapping | -0.125 | -0.151 | -0.081 | +0.031 | +0.026 |
| CDF-transform | -0.060 | -0.094 | -0.067 | +0.037 | +0.031 |
| MVS with all-zero guard (variant) | -0.113 | -0.117 | -0.033 | +0.038 | +0.037 |
More scores by target: test years, fair CRPS, bias, correlation, spread, reliability, coverage
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.672 | -0.427 | -0.383 | -0.486 | -0.906 |
| Linear Scaling | -0.273 | -0.017 | -0.017 | -0.040 | +0.021 |
| Mean-Variance Scaling (operational) | -0.009 | +0.011 | -0.005 | -0.027 | +0.016 |
| Variance Scaling (unbounded) | -0.007 | +0.015 | -0.005 | -0.028 | +0.015 |
| Square-root-space Mean-Variance Scaling | +0.005 | +0.036 | +0.001 | -0.030 | +0.018 |
| Power Transformation | -0.046 | +0.036 | +0.003 | -0.022 | +0.017 |
| Delta Change | -0.103 | +0.020 | -0.001 | -0.024 | +0.012 |
| Local Intensity Scaling | -0.235 | -0.015 | -0.017 | -0.039 | +0.021 |
| Empirical Quantile Mapping | +0.005 | +0.030 | -0.011 | -0.035 | +0.006 |
| Gamma Quantile Mapping | -0.000 | +0.035 | +0.003 | -0.031 | +0.019 |
| Detrended Quantile Mapping | -0.130 | +0.029 | -0.017 | -0.040 | +0.005 |
| Quantile Delta Mapping | -0.071 | +0.027 | -0.023 | -0.038 | +0.002 |
| Scaled Distribution Mapping | -0.268 | -0.031 | -0.038 | -0.045 | -0.014 |
| CDF-transform | -0.265 | +0.029 | -0.023 | -0.041 | +0.003 |
| MVS with all-zero guard (variant) | -0.009 | +0.011 | -0.005 | -0.027 | +0.016 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.400 | -0.434 | -0.359 | -0.298 | -0.883 |
| Linear Scaling | -0.054 | -0.079 | -0.034 | +0.016 | +0.026 |
| Mean-Variance Scaling (operational) | +0.065 | -0.056 | -0.028 | +0.014 | +0.023 |
| Variance Scaling (unbounded) | +0.071 | -0.051 | -0.027 | +0.014 | +0.024 |
| Square-root-space Mean-Variance Scaling | +0.113 | -0.026 | -0.024 | +0.021 | +0.024 |
| Power Transformation | +0.069 | -0.026 | -0.027 | +0.021 | +0.023 |
| Delta Change | +0.065 | -0.064 | -0.026 | +0.024 | +0.034 |
| Local Intensity Scaling | -0.031 | -0.073 | -0.033 | +0.016 | +0.026 |
| Empirical Quantile Mapping | +0.100 | -0.035 | -0.039 | +0.008 | +0.009 |
| Gamma Quantile Mapping | +0.083 | -0.028 | -0.025 | +0.021 | +0.023 |
| Detrended Quantile Mapping | +0.041 | -0.083 | -0.050 | +0.008 | +0.012 |
| Quantile Delta Mapping | +0.089 | -0.094 | -0.058 | +0.013 | +0.014 |
| Scaled Distribution Mapping | -0.114 | -0.119 | -0.068 | +0.000 | +0.005 |
| CDF-transform | -0.081 | -0.096 | -0.052 | +0.008 | +0.013 |
| MVS with all-zero guard (variant) | +0.065 | -0.056 | -0.028 | +0.014 | +0.023 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -0.957 | -0.474 | -0.427 | -0.499 | -0.918 |
| Linear Scaling | -0.476 | -0.053 | -0.043 | -0.073 | +0.000 |
| Mean-Variance Scaling (operational) | -0.124 | -0.039 | -0.029 | -0.044 | +0.006 |
| Variance Scaling (unbounded) | -0.123 | -0.027 | -0.027 | -0.045 | +0.005 |
| Square-root-space Mean-Variance Scaling | -0.043 | +0.044 | -0.020 | -0.055 | +0.011 |
| Power Transformation | -0.102 | +0.038 | -0.013 | -0.035 | +0.013 |
| Delta Change | -0.358 | +0.034 | -0.021 | -0.041 | -0.008 |
| Local Intensity Scaling | -0.495 | -0.045 | -0.043 | -0.074 | +0.000 |
| Empirical Quantile Mapping | -0.109 | +0.026 | -0.028 | -0.051 | -0.007 |
| Gamma Quantile Mapping | -0.084 | +0.043 | -0.016 | -0.047 | +0.013 |
| Detrended Quantile Mapping | -0.411 | +0.030 | -0.044 | -0.056 | -0.010 |
| Quantile Delta Mapping | -0.205 | +0.004 | -0.054 | -0.057 | -0.014 |
| Scaled Distribution Mapping | -0.609 | -0.090 | -0.071 | -0.075 | -0.023 |
| CDF-transform | -0.439 | +0.004 | -0.059 | -0.067 | -0.017 |
| MVS with all-zero guard (variant) | -0.124 | -0.039 | -0.029 | -0.044 | +0.006 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | -11.2 | -31.5 | -36.4 | -25.4 | -104.5 |
| Linear Scaling | +0.1 | +0.2 | +0.1 | +0.0 | +0.0 |
| Mean-Variance Scaling (operational) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Variance Scaling (unbounded) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Square-root-space Mean-Variance Scaling | -0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Power Transformation | -0.0 | +0.0 | +0.0 | +0.0 | -0.0 |
| Delta Change | +0.1 | +0.2 | +0.1 | +0.0 | +0.0 |
| Local Intensity Scaling | -0.8 | -0.2 | -0.0 | -0.0 | +0.0 |
| Empirical Quantile Mapping | -0.1 | +0.0 | +0.0 | +0.0 | -0.0 |
| Gamma Quantile Mapping | -0.2 | -0.0 | +0.1 | -0.0 | +0.0 |
| Detrended Quantile Mapping | +0.6 | +1.0 | +0.2 | +0.2 | +0.2 |
| Quantile Delta Mapping | +1.4 | +2.4 | +1.2 | +0.6 | +1.3 |
| Scaled Distribution Mapping | -6.5 | -8.3 | -5.5 | -4.2 | -6.0 |
| CDF-transform | +2.8 | +2.4 | +0.8 | +0.3 | +0.4 |
| MVS with all-zero guard (variant) | +0.0 | +0.1 | +0.0 | +0.0 | -0.0 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | +0.32 | +0.04 | +0.04 | +0.24 | +0.26 |
| Linear Scaling | +0.23 | -0.08 | -0.14 | +0.07 | +0.13 |
| Mean-Variance Scaling (operational) | +0.15 | -0.13 | -0.17 | +0.05 | +0.10 |
| Variance Scaling (unbounded) | +0.14 | -0.13 | -0.17 | +0.05 | +0.10 |
| Square-root-space Mean-Variance Scaling | +0.19 | -0.11 | -0.17 | +0.07 | +0.10 |
| Power Transformation | +0.23 | -0.10 | -0.17 | +0.07 | +0.10 |
| Delta Change | +0.23 | -0.08 | -0.14 | +0.07 | +0.13 |
| Local Intensity Scaling | +0.22 | -0.08 | -0.14 | +0.07 | +0.13 |
| Empirical Quantile Mapping | +0.18 | -0.11 | -0.17 | +0.06 | +0.09 |
| Gamma Quantile Mapping | +0.15 | -0.11 | -0.17 | +0.07 | +0.10 |
| Detrended Quantile Mapping | +0.24 | -0.06 | -0.13 | +0.08 | +0.13 |
| Quantile Delta Mapping | +0.21 | -0.06 | -0.14 | +0.08 | +0.14 |
| Scaled Distribution Mapping | +0.24 | -0.05 | -0.15 | +0.07 | +0.14 |
| CDF-transform | +0.28 | -0.04 | -0.12 | +0.07 | +0.14 |
| MVS with all-zero guard (variant) | +0.15 | -0.13 | -0.17 | +0.05 | +0.10 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.57 | 0.53 | 0.60 | 0.60 | 0.43 |
| Linear Scaling | 1.91 | 1.45 | 1.16 | 1.04 | 1.17 |
| Mean-Variance Scaling (operational) | 1.02 | 0.93 | 0.95 | 0.97 | 0.98 |
| Variance Scaling (unbounded) | 1.05 | 0.95 | 0.96 | 0.98 | 0.99 |
| Square-root-space Mean-Variance Scaling | 1.06 | 1.00 | 0.98 | 1.01 | 0.98 |
| Power Transformation | 1.04 | 0.96 | 0.96 | 0.98 | 0.99 |
| Delta Change | 1.26 | 0.99 | 0.99 | 1.02 | 1.04 |
| Local Intensity Scaling | 1.74 | 1.42 | 1.15 | 1.03 | 1.17 |
| Empirical Quantile Mapping | 1.03 | 0.95 | 0.96 | 0.98 | 0.98 |
| Gamma Quantile Mapping | 0.96 | 0.98 | 0.98 | 1.01 | 0.97 |
| Detrended Quantile Mapping | 1.12 | 0.95 | 0.95 | 0.98 | 0.99 |
| Quantile Delta Mapping | 1.22 | 0.98 | 0.98 | 1.01 | 1.03 |
| Scaled Distribution Mapping | 0.87 | 0.81 | 0.86 | 0.88 | 0.92 |
| CDF-transform | 1.07 | 0.99 | 0.97 | 0.96 | 1.00 |
| MVS with all-zero guard (variant) | 1.02 | 0.93 | 0.95 | 0.97 | 0.98 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 1.05 | 0.70 | 0.55 | 0.51 | 0.94 |
| Linear Scaling | 0.72 | 0.37 | 0.13 | 0.07 | 0.14 |
| Mean-Variance Scaling (operational) | 0.58 | 0.44 | 0.15 | 0.13 | 0.05 |
| Variance Scaling (unbounded) | 0.59 | 0.42 | 0.14 | 0.12 | 0.04 |
| Square-root-space Mean-Variance Scaling | 0.10 | 0.07 | 0.08 | 0.09 | 0.05 |
| Power Transformation | 0.32 | 0.14 | 0.06 | 0.06 | 0.07 |
| Delta Change | 0.44 | 0.13 | 0.05 | 0.04 | 0.03 |
| Local Intensity Scaling | 0.71 | 0.35 | 0.12 | 0.06 | 0.13 |
| Empirical Quantile Mapping | 0.15 | 0.08 | 0.07 | 0.05 | 0.05 |
| Gamma Quantile Mapping | 0.32 | 0.16 | 0.08 | 0.05 | 0.06 |
| Detrended Quantile Mapping | 0.45 | 0.13 | 0.09 | 0.03 | 0.04 |
| Quantile Delta Mapping | 0.26 | 0.10 | 0.09 | 0.04 | 0.06 |
| Scaled Distribution Mapping | 0.80 | 0.28 | 0.15 | 0.11 | 0.15 |
| CDF-transform | 0.60 | 0.17 | 0.10 | 0.04 | 0.04 |
| MVS with all-zero guard (variant) | 0.58 | 0.44 | 0.15 | 0.13 | 0.05 |
| Target | Amount cells | Amount area | Probability cells | Probability area |
|---|---|---|---|---|
| Feb | 1120 | 100% | 1018 | 91% |
| Mar | 1120 | 100% | 1117 | 100% |
| Apr | 1120 | 100% | 1120 | 100% |
| May | 1120 | 100% | 1120 | 100% |
| FMAM | 1120 | 100% | 1120 | 100% |
Dry months: shares of totals at exactly 0 mm and at ≤ 1 mm, CHIRPS and corrected
| Exactly 0 mm | ≤ 1 mm | |
|---|---|---|
| Feb: CHIRPS | 0.2% | 11.6% |
| Raw ECMWF (no correction) | 12.2% | 48.8% |
| Linear Scaling | 12.2% | 38.4% |
| Mean-Variance Scaling (operational) | 1.8% | 11.7% |
| Variance Scaling (unbounded) | 1.1% | 11.1% |
| Square-root-space Mean-Variance Scaling | 0.2% | 11.7% |
| Power Transformation | 12.2% | 20.3% |
| Delta Change | 0.2% | 14.1% |
| Local Intensity Scaling | 19.4% | 19.4% |
| Empirical Quantile Mapping | 11.6% | 11.7% |
| Gamma Quantile Mapping | 10.1% | 13.5% |
| Detrended Quantile Mapping | 11.3% | 15.2% |
| Quantile Delta Mapping | 11.6% | 12.5% |
| Scaled Distribution Mapping | 42.6% | 49.2% |
| CDF-transform | 0.1% | 14.4% |
| MVS with all-zero guard (variant) | 1.8% | 11.7% |
| Mar: CHIRPS | 0.1% | 2.5% |
| Raw ECMWF (no correction) | 1.8% | 18.3% |
| Linear Scaling | 1.8% | 12.0% |
| Mean-Variance Scaling (operational) | 0.6% | 1.1% |
| Variance Scaling (unbounded) | 0.6% | 1.1% |
| Square-root-space Mean-Variance Scaling | 0.2% | 2.8% |
| Power Transformation | 1.8% | 5.3% |
| Delta Change | 0.1% | 3.5% |
| Local Intensity Scaling | 4.1% | 4.1% |
| Empirical Quantile Mapping | 2.5% | 2.5% |
| Gamma Quantile Mapping | 2.5% | 4.8% |
| Detrended Quantile Mapping | 2.3% | 3.5% |
| Quantile Delta Mapping | 2.5% | 2.7% |
| Scaled Distribution Mapping | 19.7% | 20.0% |
| CDF-transform | 0.1% | 3.3% |
| MVS with all-zero guard (variant) | 0.6% | 1.1% |
| Apr: CHIRPS | 0.1% | 0.5% |
| Raw ECMWF (no correction) | 0.2% | 2.6% |
| Linear Scaling | 0.2% | 1.4% |
| Mean-Variance Scaling (operational) | 0.2% | 0.3% |
| Variance Scaling (unbounded) | 0.2% | 0.3% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.1% |
| Power Transformation | 0.2% | 0.3% |
| Delta Change | 0.1% | 0.5% |
| Local Intensity Scaling | 0.6% | 0.6% |
| Empirical Quantile Mapping | 0.5% | 0.5% |
| Gamma Quantile Mapping | 0.5% | 0.5% |
| Detrended Quantile Mapping | 0.5% | 0.5% |
| Quantile Delta Mapping | 0.5% | 0.6% |
| Scaled Distribution Mapping | 3.5% | 3.5% |
| CDF-transform | 0.0% | 0.3% |
| MVS with all-zero guard (variant) | 0.2% | 0.3% |
| May: CHIRPS | 0.4% | 1.2% |
| Raw ECMWF (no correction) | 0.2% | 2.3% |
| Linear Scaling | 0.2% | 1.4% |
| Mean-Variance Scaling (operational) | 0.2% | 0.3% |
| Variance Scaling (unbounded) | 0.2% | 0.3% |
| Square-root-space Mean-Variance Scaling | 0.0% | 0.2% |
| Power Transformation | 0.2% | 0.3% |
| Delta Change | 0.4% | 1.2% |
| Local Intensity Scaling | 1.3% | 1.3% |
| Empirical Quantile Mapping | 1.2% | 1.2% |
| Gamma Quantile Mapping | 1.2% | 1.3% |
| Detrended Quantile Mapping | 1.1% | 1.2% |
| Quantile Delta Mapping | 1.2% | 1.3% |
| Scaled Distribution Mapping | 3.7% | 3.7% |
| CDF-transform | 0.2% | 1.1% |
| MVS with all-zero guard (variant) | 0.2% | 0.3% |
| FMAM: 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 | 0.8% | 0.8% |
| 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 | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.40 | 0.44 | 0.63 | 0.65 | 0.60 |
| 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 | 0.96 | 1.00 | 1.00 | 1.00 | 1.00 |
| Empirical Quantile Mapping | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 |
| Detrended Quantile Mapping | 1.03 | 1.01 | 1.00 | 1.00 | 1.00 |
| Quantile Delta Mapping | 1.07 | 1.03 | 1.01 | 1.00 | 1.00 |
| Scaled Distribution Mapping | 0.59 | 0.84 | 0.96 | 0.96 | 0.98 |
| CDF-transform | 1.14 | 1.03 | 1.01 | 1.01 | 1.00 |
| MVS with all-zero guard (variant) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.79 | 0.64 | 0.73 | 0.75 | 0.65 |
| Linear Scaling | 1.96 | 1.52 | 1.18 | 1.12 | 1.09 |
| Mean-Variance Scaling (operational) | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 |
| Variance Scaling (unbounded) | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 |
| Square-root-space Mean-Variance Scaling | 1.05 | 1.05 | 1.01 | 1.03 | 0.99 |
| Power Transformation | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Delta Change | 1.32 | 1.11 | 1.04 | 1.04 | 1.04 |
| Local Intensity Scaling | 1.72 | 1.46 | 1.18 | 1.12 | 1.09 |
| Empirical Quantile Mapping | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 |
| Gamma Quantile Mapping | 0.90 | 1.02 | 1.00 | 1.03 | 0.98 |
| Detrended Quantile Mapping | 1.27 | 1.09 | 1.01 | 1.02 | 1.01 |
| Quantile Delta Mapping | 1.34 | 1.12 | 1.04 | 1.04 | 1.03 |
| Scaled Distribution Mapping | 0.94 | 0.92 | 0.92 | 0.92 | 0.92 |
| CDF-transform | 1.39 | 1.13 | 1.04 | 1.04 | 1.03 |
| MVS with all-zero guard (variant) | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.01 | 0.08 | 0.48 | 0.64 | 0.53 |
| Linear Scaling | 0.02 | 0.20 | 0.73 | 0.92 | 0.89 |
| Mean-Variance Scaling (operational) | 1.23 | 1.56 | 1.02 | 1.03 | 0.97 |
| Variance Scaling (unbounded) | 1.24 | 1.49 | 1.01 | 1.03 | 0.96 |
| Square-root-space Mean-Variance Scaling | 0.91 | 0.97 | 0.96 | 0.99 | 0.96 |
| Power Transformation | 0.36 | 0.74 | 0.92 | 1.00 | 0.94 |
| Delta Change | 0.50 | 0.86 | 0.93 | 0.94 | 0.96 |
| Local Intensity Scaling | 0.14 | 0.30 | 0.74 | 0.91 | 0.89 |
| Empirical Quantile Mapping | 0.99 | 0.96 | 0.95 | 0.96 | 0.98 |
| Gamma Quantile Mapping | 0.67 | 0.92 | 0.95 | 0.97 | 0.96 |
| Detrended Quantile Mapping | 0.50 | 0.87 | 0.93 | 0.95 | 0.96 |
| Quantile Delta Mapping | 0.87 | 0.86 | 0.93 | 0.95 | 0.97 |
| Scaled Distribution Mapping | 0.00 | 0.23 | 0.94 | 0.96 | 0.98 |
| CDF-transform | 0.46 | 0.84 | 0.93 | 0.97 | 0.96 |
| MVS with all-zero guard (variant) | 1.23 | 1.56 | 1.02 | 1.03 | 0.97 |
| Method | Feb | Mar | Apr | May | FMAM |
|---|---|---|---|---|---|
| Raw ECMWF (no correction) | 0.52 | 0.52 | 0.69 | 0.71 | 0.62 |
| Linear Scaling | 1.31 | 1.23 | 1.10 | 1.07 | 1.04 |
| Mean-Variance Scaling (operational) | 0.93 | 0.98 | 1.01 | 1.01 | 1.00 |
| Variance Scaling (unbounded) | 0.93 | 0.98 | 1.02 | 1.02 | 1.01 |
| Square-root-space Mean-Variance Scaling | 1.04 | 1.02 | 1.03 | 1.03 | 1.00 |
| Power Transformation | 1.13 | 1.01 | 1.02 | 1.02 | 1.00 |
| Delta Change | 1.11 | 1.06 | 1.04 | 1.03 | 1.03 |
| Local Intensity Scaling | 1.21 | 1.20 | 1.09 | 1.06 | 1.03 |
| Empirical Quantile Mapping | 1.04 | 1.04 | 1.02 | 1.02 | 1.02 |
| Gamma Quantile Mapping | 0.98 | 1.00 | 1.02 | 1.03 | 1.00 |
| Detrended Quantile Mapping | 1.14 | 1.06 | 1.03 | 1.03 | 1.02 |
| Quantile Delta Mapping | 1.15 | 1.07 | 1.03 | 1.03 | 1.02 |
| Scaled Distribution Mapping | 0.71 | 0.89 | 0.96 | 0.96 | 0.97 |
| CDF-transform | 1.27 | 1.09 | 1.04 | 1.03 | 1.02 |
| MVS with all-zero guard (variant) | 0.93 | 0.98 | 1.01 | 1.01 | 1.00 |
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 | Feb | +1.06 | +0.48 to +1.57 | 6/24 | 0.9992 | 1.0000 | 1.0000 | +1.87 | — |
| Linear Scaling | Mar | +0.78 | -0.38 to +1.77 | 8/24 | 0.9097 | 1.0000 | 1.0000 | +0.77 | — |
| Linear Scaling | Apr | +0.38 | -0.21 to +0.92 | 7/24 | 0.8955 | 1.0000 | 1.0000 | +0.49 | — |
| Linear Scaling | May | +0.09 | -0.38 to +0.51 | 7/24 | 0.6468 | 1.0000 | 1.0000 | +0.31 | — |
| Linear Scaling | FMAM | +0.27 | -0.58 to +1.08 | 7/24 | 0.7281 | 1.0000 | 1.0000 | -0.23 | — |
| Variance Scaling (unbounded) | Feb | -0.04 | -0.06 to -0.02 | 19/24 | 0.0028 | 0.0139 | 0.1637 | -0.02 | ✓ |
| Variance Scaling (unbounded) | Mar | -0.07 | -0.12 to -0.02 | 19/24 | 0.0037 | 0.0149 | 0.2158 | -0.10 | ✓ |
| Variance Scaling (unbounded) | Apr | -0.02 | -0.07 to +0.03 | 13/24 | 0.2331 | 0.6992 | 1.0000 | -0.01 | — |
| Variance Scaling (unbounded) | May | +0.00 | -0.03 to +0.03 | 10/24 | 0.5319 | 0.8480 | 1.0000 | +0.04 | — |
| Variance Scaling (unbounded) | FMAM | -0.01 | -0.07 to +0.05 | 11/24 | 0.4240 | 0.8480 | 1.0000 | +0.05 | — |
| Square-root-space Mean-Variance Scaling | Feb | -0.28 | -0.46 to -0.09 | 17/24 | 0.0045 | 0.0179 | 0.2545 | -0.11 | ✓ |
| Square-root-space Mean-Variance Scaling | Mar | -0.49 | -0.82 to -0.19 | 15/24 | 0.0015 | 0.0076 | 0.0918 | -0.58 | ✓ |
| Square-root-space Mean-Variance Scaling | Apr | -0.08 | -0.23 to +0.06 | 17/24 | 0.1440 | 0.3055 | 1.0000 | -0.17 | — |
| Square-root-space Mean-Variance Scaling | May | -0.13 | -0.32 to +0.05 | 13/24 | 0.1018 | 0.3055 | 1.0000 | +0.14 | — |
| Square-root-space Mean-Variance Scaling | FMAM | -0.04 | -0.12 to +0.05 | 11/24 | 0.2197 | 0.3055 | 1.0000 | -0.14 | — |
| Power Transformation | Feb | +0.04 | -0.29 to +0.38 | 10/24 | 0.5978 | 1.0000 | 1.0000 | +0.23 | — |
| Power Transformation | Mar | -0.48 | -0.94 to -0.03 | 13/24 | 0.0261 | 0.1042 | 1.0000 | -0.58 | — |
| Power Transformation | Apr | +0.00 | -0.20 to +0.22 | 14/24 | 0.5065 | 1.0000 | 1.0000 | -0.25 | — |
| Power Transformation | May | -0.15 | -0.28 to -0.02 | 16/24 | 0.0179 | 0.0895 | 0.9850 | -0.09 | — |
| Power Transformation | FMAM | +0.03 | -0.17 to +0.22 | 8/24 | 0.6242 | 1.0000 | 1.0000 | -0.04 | — |
| Delta Change | Feb | +0.14 | -0.33 to +0.63 | 11/24 | 0.7023 | 1.0000 | 1.0000 | +0.63 | — |
| Delta Change | Mar | +0.36 | -0.47 to +1.19 | 9/24 | 0.7894 | 1.0000 | 1.0000 | -0.14 | — |
| Delta Change | Apr | +0.12 | -0.29 to +0.54 | 10/24 | 0.7086 | 1.0000 | 1.0000 | -0.01 | — |
| Delta Change | May | -0.08 | -0.42 to +0.25 | 11/24 | 0.3229 | 1.0000 | 1.0000 | -0.15 | — |
| Delta Change | FMAM | -0.21 | -0.98 to +0.57 | 12/24 | 0.3090 | 1.0000 | 1.0000 | +0.34 | — |
| Local Intensity Scaling | Feb | +0.82 | +0.33 to +1.27 | 6/24 | 0.9983 | 1.0000 | 1.0000 | +1.58 | — |
| Local Intensity Scaling | Mar | +0.64 | -0.49 to +1.61 | 7/24 | 0.8699 | 1.0000 | 1.0000 | +0.68 | — |
| Local Intensity Scaling | Apr | +0.35 | -0.23 to +0.86 | 7/24 | 0.8778 | 1.0000 | 1.0000 | +0.47 | — |
| Local Intensity Scaling | May | +0.09 | -0.37 to +0.50 | 7/24 | 0.6445 | 1.0000 | 1.0000 | +0.30 | — |
| Local Intensity Scaling | FMAM | +0.24 | -0.59 to +1.05 | 7/24 | 0.7117 | 1.0000 | 1.0000 | -0.24 | — |
| Empirical Quantile Mapping | Feb | -0.20 | -0.41 to +0.01 | 14/24 | 0.0421 | 0.2105 | 1.0000 | -0.08 | — |
| Empirical Quantile Mapping | Mar | -0.33 | -0.73 to +0.06 | 13/24 | 0.0632 | 0.2529 | 1.0000 | -0.43 | — |
| Empirical Quantile Mapping | Apr | +0.28 | +0.05 to +0.51 | 7/24 | 0.9868 | 1.0000 | 1.0000 | +0.17 | — |
| Empirical Quantile Mapping | May | +0.20 | -0.05 to +0.46 | 10/24 | 0.9287 | 1.0000 | 1.0000 | +0.30 | — |
| Empirical Quantile Mapping | FMAM | +0.71 | +0.50 to +0.91 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.64 | — |
| Gamma Quantile Mapping | Feb | -0.09 | -0.26 to +0.08 | 13/24 | 0.1507 | 0.6029 | 1.0000 | -0.07 | — |
| Gamma Quantile Mapping | Mar | -0.45 | -0.78 to -0.14 | 15/24 | 0.0045 | 0.0225 | 0.2545 | -0.56 | ✓ |
| Gamma Quantile Mapping | Apr | -0.08 | -0.23 to +0.08 | 16/24 | 0.1814 | 0.6029 | 1.0000 | -0.23 | — |
| Gamma Quantile Mapping | May | -0.10 | -0.32 to +0.10 | 10/24 | 0.1706 | 0.6029 | 1.0000 | +0.20 | — |
| Gamma Quantile Mapping | FMAM | -0.01 | -0.13 to +0.12 | 10/24 | 0.4681 | 0.6029 | 1.0000 | -0.16 | — |
| Detrended Quantile Mapping | Feb | +0.26 | -0.46 to +1.02 | 10/24 | 0.7370 | 1.0000 | 1.0000 | +0.80 | — |
| Detrended Quantile Mapping | Mar | +0.61 | -0.45 to +1.83 | 8/24 | 0.8265 | 1.0000 | 1.0000 | -0.32 | — |
| Detrended Quantile Mapping | Apr | +0.59 | +0.18 to +1.09 | 11/24 | 0.9932 | 1.0000 | 1.0000 | +0.43 | — |
| Detrended Quantile Mapping | May | +0.32 | -0.09 to +0.71 | 7/24 | 0.9249 | 1.0000 | 1.0000 | +0.31 | — |
| Detrended Quantile Mapping | FMAM | +0.60 | +0.02 to +1.17 | 6/24 | 0.9706 | 1.0000 | 1.0000 | +0.73 | — |
| Quantile Delta Mapping | Feb | -0.08 | -0.92 to +0.81 | 12/24 | 0.4320 | 1.0000 | 1.0000 | +0.39 | — |
| Quantile Delta Mapping | Mar | +0.80 | -0.53 to +2.29 | 8/24 | 0.8377 | 1.0000 | 1.0000 | -0.25 | — |
| Quantile Delta Mapping | Apr | +0.85 | +0.19 to +1.67 | 9/24 | 0.9883 | 1.0000 | 1.0000 | +0.58 | — |
| Quantile Delta Mapping | May | +0.22 | -0.22 to +0.66 | 7/24 | 0.8164 | 1.0000 | 1.0000 | +0.29 | — |
| Quantile Delta Mapping | FMAM | +0.57 | -0.09 to +1.19 | 5/24 | 0.9438 | 1.0000 | 1.0000 | +0.90 | — |
| Scaled Distribution Mapping | Feb | +1.24 | +0.77 to +1.73 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.92 | — |
| Scaled Distribution Mapping | Mar | +1.14 | -0.15 to +2.28 | 6/24 | 0.9568 | 1.0000 | 1.0000 | +0.98 | — |
| Scaled Distribution Mapping | Apr | +0.96 | +0.33 to +1.56 | 3/24 | 0.9975 | 1.0000 | 1.0000 | +1.01 | — |
| Scaled Distribution Mapping | May | +0.41 | -0.02 to +0.81 | 7/24 | 0.9649 | 1.0000 | 1.0000 | +0.41 | — |
| Scaled Distribution Mapping | FMAM | +0.80 | +0.13 to +1.49 | 6/24 | 0.9811 | 1.0000 | 1.0000 | +1.67 | — |
| CDF-transform | Feb | +1.07 | -0.32 to +2.56 | 8/24 | 0.9114 | 1.0000 | 1.0000 | +1.68 | — |
| CDF-transform | Mar | +0.83 | -0.44 to +2.38 | 7/24 | 0.8465 | 1.0000 | 1.0000 | -0.27 | — |
| CDF-transform | Apr | +0.69 | +0.16 to +1.34 | 9/24 | 0.9905 | 1.0000 | 1.0000 | +0.59 | — |
| CDF-transform | May | +0.24 | -0.18 to +0.65 | 7/24 | 0.8575 | 1.0000 | 1.0000 | +0.35 | — |
| CDF-transform | FMAM | +0.58 | -0.09 to +1.21 | 6/24 | 0.9461 | 1.0000 | 1.0000 | +0.77 | — |
| MVS with all-zero guard (variant) | Feb | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Mar | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Apr | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | May | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | FMAM | +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 | Feb | +0.87 | +0.28 to +1.38 | 6/24 | 0.9968 | 1.0000 | 1.0000 | +1.78 | — |
| Linear Scaling | Mar | +0.40 | -0.76 to +1.39 | 8/24 | 0.7518 | 1.0000 | 1.0000 | +0.58 | — |
| Linear Scaling | Apr | +0.15 | -0.45 to +0.68 | 9/24 | 0.6837 | 1.0000 | 1.0000 | +0.38 | — |
| Linear Scaling | May | -0.01 | -0.49 to +0.42 | 7/24 | 0.4797 | 1.0000 | 1.0000 | +0.27 | — |
| Linear Scaling | FMAM | -0.08 | -0.94 to +0.74 | 8/24 | 0.4309 | 1.0000 | 1.0000 | -0.39 | — |
| Variance Scaling (unbounded) | Feb | -0.04 | -0.07 to -0.02 | 19/24 | 0.0015 | 0.0061 | 0.0864 | -0.02 | ✓ |
| Variance Scaling (unbounded) | Mar | -0.08 | -0.13 to -0.04 | 19/24 | 0.0011 | 0.0057 | 0.0676 | -0.10 | ✓ |
| Variance Scaling (unbounded) | Apr | -0.03 | -0.08 to +0.02 | 13/24 | 0.1139 | 0.3417 | 1.0000 | -0.02 | — |
| Variance Scaling (unbounded) | May | -0.01 | -0.04 to +0.02 | 12/24 | 0.2705 | 0.4002 | 1.0000 | +0.03 | — |
| Variance Scaling (unbounded) | FMAM | -0.03 | -0.09 to +0.03 | 13/24 | 0.2001 | 0.4002 | 1.0000 | +0.04 | — |
| Square-root-space Mean-Variance Scaling | Feb | -0.30 | -0.49 to -0.12 | 19/24 | 0.0020 | 0.0080 | 0.1123 | -0.12 | ✓ |
| Square-root-space Mean-Variance Scaling | Mar | -0.57 | -0.90 to -0.27 | 17/24 | 0.0003 | 0.0015 | 0.0186 | -0.62 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Apr | -0.13 | -0.28 to +0.01 | 18/24 | 0.0454 | 0.1035 | 1.0000 | -0.20 | — |
| Square-root-space Mean-Variance Scaling | May | -0.18 | -0.38 to -0.01 | 14/24 | 0.0345 | 0.1035 | 1.0000 | +0.11 | — |
| Square-root-space Mean-Variance Scaling | FMAM | -0.05 | -0.13 to +0.04 | 11/24 | 0.1500 | 0.1500 | 1.0000 | -0.14 | — |
| Power Transformation | Feb | -0.01 | -0.34 to +0.32 | 10/24 | 0.4783 | 1.0000 | 1.0000 | +0.20 | — |
| Power Transformation | Mar | -0.56 | -1.02 to -0.10 | 14/24 | 0.0140 | 0.0562 | 0.7582 | -0.62 | — |
| Power Transformation | Apr | -0.03 | -0.23 to +0.19 | 14/24 | 0.3856 | 1.0000 | 1.0000 | -0.26 | — |
| Power Transformation | May | -0.17 | -0.30 to -0.04 | 18/24 | 0.0079 | 0.0396 | 0.4356 | -0.10 | ✓ |
| Power Transformation | FMAM | -0.00 | -0.20 to +0.18 | 9/24 | 0.4980 | 1.0000 | 1.0000 | -0.06 | — |
| Delta Change | Feb | +0.06 | -0.40 to +0.54 | 13/24 | 0.5990 | 1.0000 | 1.0000 | +0.47 | — |
| Delta Change | Mar | +0.19 | -0.64 to +1.00 | 11/24 | 0.6617 | 1.0000 | 1.0000 | -0.61 | — |
| Delta Change | Apr | -0.05 | -0.45 to +0.37 | 11/24 | 0.4122 | 1.0000 | 1.0000 | -0.66 | — |
| Delta Change | May | -0.25 | -0.60 to +0.08 | 14/24 | 0.0772 | 0.3859 | 1.0000 | -0.77 | — |
| Delta Change | FMAM | -0.48 | -1.26 to +0.31 | 14/24 | 0.1279 | 0.5117 | 1.0000 | -0.74 | — |
| Local Intensity Scaling | Feb | +0.67 | +0.19 to +1.12 | 6/24 | 0.9940 | 1.0000 | 1.0000 | +1.51 | — |
| Local Intensity Scaling | Mar | +0.28 | -0.86 to +1.26 | 8/24 | 0.6903 | 1.0000 | 1.0000 | +0.50 | — |
| Local Intensity Scaling | Apr | +0.12 | -0.46 to +0.64 | 9/24 | 0.6538 | 1.0000 | 1.0000 | +0.36 | — |
| Local Intensity Scaling | May | -0.01 | -0.48 to +0.41 | 7/24 | 0.4851 | 1.0000 | 1.0000 | +0.26 | — |
| Local Intensity Scaling | FMAM | -0.09 | -0.94 to +0.71 | 8/24 | 0.4151 | 1.0000 | 1.0000 | -0.40 | — |
| Empirical Quantile Mapping | Feb | -0.22 | -0.43 to -0.01 | 15/24 | 0.0293 | 0.1464 | 1.0000 | -0.09 | — |
| Empirical Quantile Mapping | Mar | -0.39 | -0.80 to +0.01 | 13/24 | 0.0390 | 0.1559 | 1.0000 | -0.47 | — |
| Empirical Quantile Mapping | Apr | +0.26 | +0.03 to +0.49 | 7/24 | 0.9799 | 1.0000 | 1.0000 | +0.17 | — |
| Empirical Quantile Mapping | May | +0.18 | -0.08 to +0.45 | 10/24 | 0.9042 | 1.0000 | 1.0000 | +0.29 | — |
| Empirical Quantile Mapping | FMAM | +0.71 | +0.51 to +0.92 | 2/24 | 1.0000 | 1.0000 | 1.0000 | +0.65 | — |
| Gamma Quantile Mapping | Feb | -0.11 | -0.28 to +0.07 | 13/24 | 0.1137 | 0.2491 | 1.0000 | -0.08 | — |
| Gamma Quantile Mapping | Mar | -0.53 | -0.85 to -0.21 | 16/24 | 0.0013 | 0.0067 | 0.0774 | -0.60 | ✓ |
| Gamma Quantile Mapping | Apr | -0.12 | -0.27 to +0.04 | 18/24 | 0.0769 | 0.2491 | 1.0000 | -0.25 | — |
| Gamma Quantile Mapping | May | -0.17 | -0.38 to +0.03 | 13/24 | 0.0623 | 0.2491 | 1.0000 | +0.17 | — |
| Gamma Quantile Mapping | FMAM | -0.00 | -0.13 to +0.12 | 10/24 | 0.4808 | 0.4808 | 1.0000 | -0.16 | — |
| Detrended Quantile Mapping | Feb | +0.22 | -0.49 to +0.98 | 11/24 | 0.7098 | 1.0000 | 1.0000 | +0.79 | — |
| Detrended Quantile Mapping | Mar | +0.53 | -0.53 to +1.74 | 8/24 | 0.7935 | 1.0000 | 1.0000 | -0.35 | — |
| Detrended Quantile Mapping | Apr | +0.57 | +0.15 to +1.06 | 11/24 | 0.9907 | 1.0000 | 1.0000 | +0.42 | — |
| Detrended Quantile Mapping | May | +0.29 | -0.12 to +0.68 | 7/24 | 0.9085 | 1.0000 | 1.0000 | +0.30 | — |
| Detrended Quantile Mapping | FMAM | +0.60 | +0.02 to +1.16 | 7/24 | 0.9696 | 1.0000 | 1.0000 | +0.73 | — |
| Quantile Delta Mapping | Feb | -0.13 | -0.97 to +0.75 | 13/24 | 0.3860 | 1.0000 | 1.0000 | +0.37 | — |
| Quantile Delta Mapping | Mar | +0.70 | -0.62 to +2.19 | 8/24 | 0.8065 | 1.0000 | 1.0000 | -0.30 | — |
| Quantile Delta Mapping | Apr | +0.80 | +0.14 to +1.63 | 9/24 | 0.9826 | 1.0000 | 1.0000 | +0.57 | — |
| Quantile Delta Mapping | May | +0.17 | -0.27 to +0.61 | 7/24 | 0.7622 | 1.0000 | 1.0000 | +0.28 | — |
| Quantile Delta Mapping | FMAM | +0.53 | -0.13 to +1.16 | 6/24 | 0.9335 | 1.0000 | 1.0000 | +0.89 | — |
| Scaled Distribution Mapping | Feb | +1.26 | +0.78 to +1.75 | 4/24 | 1.0000 | 1.0000 | 1.0000 | +1.93 | — |
| Scaled Distribution Mapping | Mar | +1.19 | -0.10 to +2.33 | 6/24 | 0.9625 | 1.0000 | 1.0000 | +0.98 | — |
| Scaled Distribution Mapping | Apr | +1.04 | +0.41 to +1.65 | 3/24 | 0.9987 | 1.0000 | 1.0000 | +1.04 | — |
| Scaled Distribution Mapping | May | +0.50 | +0.07 to +0.91 | 7/24 | 0.9848 | 1.0000 | 1.0000 | +0.44 | — |
| Scaled Distribution Mapping | FMAM | +0.98 | +0.30 to +1.67 | 6/24 | 0.9945 | 1.0000 | 1.0000 | +1.74 | — |
| CDF-transform | Feb | +1.03 | -0.34 to +2.52 | 8/24 | 0.9052 | 1.0000 | 1.0000 | +1.66 | — |
| CDF-transform | Mar | +0.73 | -0.54 to +2.27 | 7/24 | 0.8116 | 1.0000 | 1.0000 | -0.31 | — |
| CDF-transform | Apr | +0.65 | +0.12 to +1.30 | 9/24 | 0.9851 | 1.0000 | 1.0000 | +0.58 | — |
| CDF-transform | May | +0.22 | -0.19 to +0.63 | 7/24 | 0.8436 | 1.0000 | 1.0000 | +0.34 | — |
| CDF-transform | FMAM | +0.56 | -0.11 to +1.19 | 6/24 | 0.9398 | 1.0000 | 1.0000 | +0.76 | — |
| MVS with all-zero guard (variant) | Feb | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Mar | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | Apr | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | May | +0.00 | +0.00 to +0.00 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.00 | — |
| MVS with all-zero guard (variant) | FMAM | +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 | Feb | -0.0198 | -0.1116 to +0.0684 | 13/24 | 0.3361 | 1.0000 | 1.0000 | +0.1508 | — |
| Linear Scaling | Mar | -0.0257 | -0.0693 to +0.0147 | 12/24 | 0.1290 | 0.6450 | 1.0000 | -0.0022 | — |
| Linear Scaling | Apr | -0.0005 | -0.0104 to +0.0081 | 11/24 | 0.4579 | 1.0000 | 1.0000 | +0.0064 | — |
| Linear Scaling | May | -0.0010 | -0.0114 to +0.0087 | 11/24 | 0.4220 | 1.0000 | 1.0000 | +0.0129 | — |
| Linear Scaling | FMAM | -0.0009 | -0.0060 to +0.0038 | 10/24 | 0.3737 | 1.0000 | 1.0000 | +0.0023 | — |
| Variance Scaling (unbounded) | Feb | -0.0045 | -0.0090 to +0.0000 | 16/24 | 0.0325 | 0.1300 | 1.0000 | -0.0074 | — |
| Variance Scaling (unbounded) | Mar | -0.0034 | -0.0056 to -0.0014 | 17/24 | 0.0017 | 0.0085 | 0.0898 | -0.0045 | ✓ |
| Variance Scaling (unbounded) | Apr | -0.0020 | -0.0043 to +0.0002 | 12/24 | 0.0562 | 0.1685 | 1.0000 | -0.0005 | — |
| Variance Scaling (unbounded) | May | -0.0002 | -0.0007 to +0.0003 | 11/24 | 0.2748 | 0.2828 | 1.0000 | +0.0005 | — |
| Variance Scaling (unbounded) | FMAM | -0.0006 | -0.0015 to +0.0003 | 12/24 | 0.1414 | 0.2828 | 1.0000 | +0.0005 | — |
| Square-root-space Mean-Variance Scaling | Feb | -0.0771 | -0.1090 to -0.0471 | 20/24 | 0.0000 | 0.0001 | 0.0009 | -0.0362 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Mar | -0.0448 | -0.0642 to -0.0267 | 19/24 | 0.0001 | 0.0002 | 0.0035 | -0.0379 | ✓✓ |
| Square-root-space Mean-Variance Scaling | Apr | -0.0026 | -0.0050 to -0.0000 | 18/24 | 0.0294 | 0.0882 | 1.0000 | -0.0049 | — |
| Square-root-space Mean-Variance Scaling | May | -0.0037 | -0.0091 to +0.0012 | 10/24 | 0.0921 | 0.1841 | 1.0000 | +0.0054 | — |
| Square-root-space Mean-Variance Scaling | FMAM | -0.0008 | -0.0027 to +0.0010 | 13/24 | 0.1967 | 0.1967 | 1.0000 | -0.0018 | — |
| Power Transformation | Feb | -0.0674 | -0.1032 to -0.0332 | 18/24 | 0.0003 | 0.0013 | 0.0185 | -0.0226 | ✓✓ |
| Power Transformation | Mar | -0.0393 | -0.0577 to -0.0208 | 19/24 | 0.0002 | 0.0012 | 0.0137 | -0.0352 | ✓✓ |
| Power Transformation | Apr | -0.0001 | -0.0066 to +0.0067 | 14/24 | 0.4870 | 0.8274 | 1.0000 | -0.0088 | — |
| Power Transformation | May | -0.0037 | -0.0071 to -0.0005 | 16/24 | 0.0199 | 0.0598 | 0.9965 | -0.0022 | — |
| Power Transformation | FMAM | -0.0004 | -0.0037 to +0.0030 | 11/24 | 0.4137 | 0.8274 | 1.0000 | -0.0024 | — |
| Delta Change | Feb | -0.0431 | -0.1080 to +0.0226 | 15/24 | 0.1116 | 0.5580 | 1.0000 | +0.0791 | — |
| Delta Change | Mar | -0.0068 | -0.0413 to +0.0268 | 13/24 | 0.3507 | 1.0000 | 1.0000 | -0.0298 | — |
| Delta Change | Apr | +0.0031 | -0.0076 to +0.0137 | 9/24 | 0.7117 | 1.0000 | 1.0000 | -0.0022 | — |
| Delta Change | May | +0.0010 | -0.0061 to +0.0081 | 14/24 | 0.6077 | 1.0000 | 1.0000 | -0.0040 | — |
| Delta Change | FMAM | +0.0010 | -0.0076 to +0.0105 | 13/24 | 0.5824 | 1.0000 | 1.0000 | +0.0086 | — |
| Local Intensity Scaling | Feb | -0.0166 | -0.1094 to +0.0724 | 13/24 | 0.3619 | 1.0000 | 1.0000 | +0.1529 | — |
| Local Intensity Scaling | Mar | -0.0257 | -0.0716 to +0.0165 | 12/24 | 0.1400 | 0.6998 | 1.0000 | -0.0050 | — |
| Local Intensity Scaling | Apr | -0.0006 | -0.0105 to +0.0080 | 11/24 | 0.4522 | 1.0000 | 1.0000 | +0.0066 | — |
| Local Intensity Scaling | May | -0.0007 | -0.0112 to +0.0091 | 11/24 | 0.4476 | 1.0000 | 1.0000 | +0.0131 | — |
| Local Intensity Scaling | FMAM | -0.0009 | -0.0060 to +0.0036 | 10/24 | 0.3624 | 1.0000 | 1.0000 | +0.0021 | — |
| Empirical Quantile Mapping | Feb | -0.0795 | -0.1227 to -0.0379 | 17/24 | 0.0007 | 0.0036 | 0.0386 | -0.0101 | ✓✓ |
| Empirical Quantile Mapping | Mar | -0.0391 | -0.0659 to -0.0135 | 17/24 | 0.0047 | 0.0189 | 0.2452 | -0.0316 | ✓ |
| Empirical Quantile Mapping | Apr | +0.0037 | -0.0023 to +0.0097 | 9/24 | 0.8770 | 1.0000 | 1.0000 | -0.0015 | — |
| Empirical Quantile Mapping | May | +0.0017 | -0.0047 to +0.0080 | 9/24 | 0.6966 | 1.0000 | 1.0000 | +0.0041 | — |
| Empirical Quantile Mapping | FMAM | +0.0049 | +0.0014 to +0.0083 | 6/24 | 0.9924 | 1.0000 | 1.0000 | +0.0061 | — |
| Gamma Quantile Mapping | Feb | -0.0587 | -0.0783 to -0.0395 | 21/24 | 0.0000 | 0.0000 | 0.0003 | -0.0331 | ✓✓ |
| Gamma Quantile Mapping | Mar | -0.0344 | -0.0532 to -0.0164 | 16/24 | 0.0007 | 0.0026 | 0.0363 | -0.0378 | ✓✓ |
| Gamma Quantile Mapping | Apr | -0.0021 | -0.0060 to +0.0022 | 17/24 | 0.1618 | 0.3236 | 1.0000 | -0.0072 | — |
| Gamma Quantile Mapping | May | -0.0034 | -0.0071 to -0.0001 | 12/24 | 0.0389 | 0.1167 | 1.0000 | +0.0024 | — |
| Gamma Quantile Mapping | FMAM | -0.0007 | -0.0036 to +0.0024 | 13/24 | 0.3359 | 0.3359 | 1.0000 | -0.0027 | — |
| Detrended Quantile Mapping | Feb | -0.0422 | -0.1112 to +0.0264 | 15/24 | 0.1266 | 0.6331 | 1.0000 | +0.0994 | — |
| Detrended Quantile Mapping | Mar | -0.0086 | -0.0436 to +0.0253 | 10/24 | 0.3186 | 1.0000 | 1.0000 | -0.0283 | — |
| Detrended Quantile Mapping | Apr | +0.0125 | +0.0025 to +0.0237 | 9/24 | 0.9834 | 1.0000 | 1.0000 | +0.0070 | — |
| Detrended Quantile Mapping | May | +0.0043 | -0.0055 to +0.0133 | 10/24 | 0.8024 | 1.0000 | 1.0000 | +0.0042 | — |
| Detrended Quantile Mapping | FMAM | +0.0042 | -0.0038 to +0.0122 | 9/24 | 0.8285 | 1.0000 | 1.0000 | +0.0083 | — |
| Quantile Delta Mapping | Feb | -0.0736 | -0.1341 to -0.0160 | 16/24 | 0.0121 | 0.0604 | 0.6163 | +0.0341 | — |
| Quantile Delta Mapping | Mar | -0.0165 | -0.0529 to +0.0172 | 11/24 | 0.1901 | 0.7604 | 1.0000 | -0.0204 | — |
| Quantile Delta Mapping | Apr | +0.0184 | +0.0040 to +0.0349 | 9/24 | 0.9850 | 1.0000 | 1.0000 | +0.0095 | — |
| Quantile Delta Mapping | May | +0.0029 | -0.0074 to +0.0123 | 8/24 | 0.7060 | 1.0000 | 1.0000 | +0.0057 | — |
| Quantile Delta Mapping | FMAM | +0.0048 | -0.0045 to +0.0138 | 8/24 | 0.8395 | 1.0000 | 1.0000 | +0.0100 | — |
| Scaled Distribution Mapping | Feb | +0.0130 | -0.0902 to +0.1144 | 11/24 | 0.5964 | 1.0000 | 1.0000 | +0.2076 | — |
| Scaled Distribution Mapping | Mar | +0.0174 | -0.0435 to +0.0728 | 10/24 | 0.7158 | 1.0000 | 1.0000 | +0.0145 | — |
| Scaled Distribution Mapping | Apr | +0.0198 | +0.0085 to +0.0315 | 4/24 | 0.9990 | 1.0000 | 1.0000 | +0.0171 | — |
| Scaled Distribution Mapping | May | +0.0071 | -0.0027 to +0.0167 | 10/24 | 0.9139 | 1.0000 | 1.0000 | +0.0116 | — |
| Scaled Distribution Mapping | FMAM | +0.0065 | -0.0032 to +0.0166 | 10/24 | 0.8849 | 1.0000 | 1.0000 | +0.0128 | — |
| CDF-transform | Feb | -0.0134 | -0.0921 to +0.0641 | 13/24 | 0.3701 | 1.0000 | 1.0000 | +0.1167 | — |
| CDF-transform | Mar | -0.0108 | -0.0431 to +0.0239 | 13/24 | 0.2763 | 1.0000 | 1.0000 | -0.0184 | — |
| CDF-transform | Apr | +0.0145 | +0.0036 to +0.0274 | 8/24 | 0.9898 | 1.0000 | 1.0000 | +0.0133 | — |
| CDF-transform | May | +0.0030 | -0.0062 to +0.0117 | 9/24 | 0.7323 | 1.0000 | 1.0000 | +0.0093 | — |
| CDF-transform | FMAM | +0.0048 | -0.0031 to +0.0125 | 7/24 | 0.8694 | 1.0000 | 1.0000 | +0.0100 | — |
| MVS with all-zero guard (variant) | Feb | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Mar | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | Apr | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | May | +0.0000 | +0.0000 to +0.0000 | 0/24 | 1.0000 | 1.0000 | — (variant) | +0.0000 | — |
| MVS with all-zero guard (variant) | FMAM | +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 | Feb | mean fallback: 0.6% of the area |
| Mean-Variance Scaling (operational) | Feb | sd fallback: 3.9% of the area; ratio lower limit: 20.2% of the area; ratio upper limit: 9.1% of the area; clipped at zero: 2.7% |
| Mean-Variance Scaling (operational) | Mar | ratio lower limit: 2.5% of the area; ratio upper limit: 9.1% of the area; clipped at zero: 1.3% |
| Mean-Variance Scaling (operational) | Apr | ratio lower limit: 0.2% of the area; ratio upper limit: 6.1% of the area; clipped at zero: 0.2% |
| Mean-Variance Scaling (operational) | May | ratio lower limit: 0.1% of the area; ratio upper limit: 6.2% of the area; clipped at zero: 0.4% |
| Mean-Variance Scaling (operational) | FMAM | ratio lower limit: 0.0% of the area; ratio upper limit: 6.6% of the area; clipped at zero: 0.0% |
| Variance Scaling (unbounded) | Feb | sd fallback: 3.9% of the area; clipped at zero: 1.8% |
| Variance Scaling (unbounded) | Mar | clipped at zero: 0.8% |
| Variance Scaling (unbounded) | Apr | clipped at zero: 0.2% |
| Variance Scaling (unbounded) | May | clipped at zero: 0.5% |
| Variance Scaling (unbounded) | FMAM | clipped at zero: 0.0% |
| Square-root-space Mean-Variance Scaling | Feb | ratio lower limit: 23.9% of the area; clipped at zero: 0.5% |
| Square-root-space Mean-Variance Scaling | Mar | ratio lower limit: 0.3% of the area; ratio upper limit: 0.2% of the area; clipped at zero: 0.4% |
| Square-root-space Mean-Variance Scaling | Apr | ratio lower limit: 0.1% of the area; ratio upper limit: 0.1% of the area; clipped at zero: 0.1% |
| Square-root-space Mean-Variance Scaling | May | ratio lower limit: 0.0% of the area; ratio upper limit: 0.1% of the area; clipped at zero: 0.0% |
| Square-root-space Mean-Variance Scaling | FMAM | ratio upper limit: 0.1% of the area |
| Power Transformation | Feb | b at bound: 16.6% of the area |
| Delta Change | Feb | mean fallback: 0.6% of the area; ratio capped: 3.3% |
| Delta Change | Mar | ratio capped: 0.1% |
| Local Intensity Scaling | Feb | always wet: 83.0% of the area; never wet: 2.8% of the area |
| Local Intensity Scaling | Mar | always wet: 88.6% of the area |
| Local Intensity Scaling | Apr | always wet: 85.7% of the area |
| Local Intensity Scaling | May | always wet: 90.6% of the area |
| Local Intensity Scaling | FMAM | always wet: 100.0% of the area |
| Empirical Quantile Mapping | Feb | model has dry: 100.0% of the area; obs has dry: 17.0% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | Mar | model has dry: 97.8% of the area; obs has dry: 11.4% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | Apr | model has dry: 60.2% of the area; obs has dry: 14.3% of the area; extrapolated: 0.2% |
| Empirical Quantile Mapping | May | model has dry: 23.4% of the area; obs has dry: 9.4% of the area; extrapolated: 0.3% |
| Empirical Quantile Mapping | FMAM | model has dry: 5.8% of the area; extrapolated: 0.3% |
| Gamma Quantile Mapping | Feb | gamma fallback: 3.6% of the area; model has dry: 100.0% of the area; obs has dry: 17.0% of the area |
| Gamma Quantile Mapping | Mar | gamma fallback: 0.1% of the area; model has dry: 97.8% of the area; obs has dry: 11.4% of the area |
| Gamma Quantile Mapping | Apr | model has dry: 60.2% of the area; obs has dry: 14.3% of the area |
| Gamma Quantile Mapping | May | model has dry: 23.4% of the area; obs has dry: 9.4% of the area |
| Gamma Quantile Mapping | FMAM | model has dry: 5.8% of the area |
| Detrended Quantile Mapping | Feb | model has dry: 100.0% of the area; obs has dry: 17.0% of the area; ratio capped: 3.3%; extrapolated: 0.1% |
| Detrended Quantile Mapping | Mar | model has dry: 97.8% of the area; obs has dry: 11.4% of the area; ratio capped: 0.1%; extrapolated: 0.1% |
| Detrended Quantile Mapping | Apr | model has dry: 60.2% of the area; obs has dry: 14.3% of the area; extrapolated: 0.2% |
| Detrended Quantile Mapping | May | model has dry: 23.4% of the area; obs has dry: 9.4% of the area; extrapolated: 0.3% |
| Detrended Quantile Mapping | FMAM | model has dry: 5.8% of the area; extrapolated: 0.3% |
| Quantile Delta Mapping | Feb | model has dry: 100.0% of the area; obs has dry: 17.0% of the area; low denominator: 49.4%; ratio capped: 0.7% |
| Quantile Delta Mapping | Mar | model has dry: 97.8% of the area; obs has dry: 11.4% of the area; low denominator: 19.9%; ratio capped: 0.2% |
| Quantile Delta Mapping | Apr | model has dry: 60.2% of the area; obs has dry: 14.3% of the area; low denominator: 3.5%; ratio capped: 0.1% |
| Quantile Delta Mapping | May | model has dry: 23.4% of the area; obs has dry: 9.4% of the area; low denominator: 2.3%; ratio capped: 0.0% |
| Quantile Delta Mapping | FMAM | model has dry: 5.8% of the area |
| Scaled Distribution Mapping | Feb | gamma fallback: 6.3% of the area; linear scaling fallback: 17.0% |
| Scaled Distribution Mapping | Mar | gamma fallback: 0.1% of the area; linear scaling fallback: 0.2% |
| CDF-transform | Feb | mean fallback: 0.6% of the area; at forecast range edge: 0.5% |
| CDF-transform | Mar | at forecast range edge: 1.0% |
| CDF-transform | Apr | at forecast range edge: 2.3% |
| CDF-transform | May | at forecast range edge: 4.9% |
| CDF-transform | FMAM | at forecast range edge: 2.3% |
| MVS with all-zero guard (variant) | Feb | sd fallback: 3.9% of the area; ratio lower limit: 20.2% of the area; ratio upper limit: 9.1% of the area; clipped at zero: 2.7% |
| MVS with all-zero guard (variant) | Mar | ratio lower limit: 2.5% of the area; ratio upper limit: 9.1% of the area; clipped at zero: 1.3% |
| MVS with all-zero guard (variant) | Apr | ratio lower limit: 0.2% of the area; ratio upper limit: 6.1% of the area; clipped at zero: 0.2% |
| MVS with all-zero guard (variant) | May | ratio lower limit: 0.1% of the area; ratio upper limit: 6.2% of the area; clipped at zero: 0.4% |
| MVS with all-zero guard (variant) | FMAM | ratio lower limit: 0.0% of the area; ratio upper limit: 6.6% of the area; clipped at zero: 0.0% |
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 2.8% of area | mixed 14.2% of area | always wet 83.0% of area |
|---|---|---|---|---|---|
| Linear Scaling | +1.060 | +0.000 | +0.001 | +0.019 | +1.041 |
| Variance Scaling (unbounded) | -0.039 | +0.000 | -0.001 | +0.000 | -0.039 |
| Square-root-space Mean-Variance Scaling | -0.275 | +0.000 | -0.001 | -0.009 | -0.265 |
| Power Transformation | +0.044 | +0.000 | +0.000 | +0.004 | +0.040 |
| Delta Change | +0.136 | +0.000 | +0.000 | +0.007 | +0.129 |
| Local Intensity Scaling | +0.821 | +0.000 | +0.003 | +0.021 | +0.797 |
| Empirical Quantile Mapping | -0.196 | +0.000 | +0.003 | +0.020 | -0.219 |
| Gamma Quantile Mapping | -0.092 | +0.000 | +0.003 | +0.018 | -0.113 |
| Detrended Quantile Mapping | +0.256 | +0.000 | +0.003 | +0.021 | +0.232 |
| Quantile Delta Mapping | -0.077 | +0.000 | +0.003 | +0.019 | -0.099 |
| Scaled Distribution Mapping | +1.245 | +0.000 | +0.001 | +0.027 | +1.217 |
| CDF-transform | +1.069 | +0.000 | +0.002 | +0.040 | +1.027 |
| 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 11.4% of area | always wet 88.6% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.784 | +0.000 | +0.000 | -0.021 | +0.805 |
| Variance Scaling (unbounded) | -0.070 | +0.000 | +0.000 | +0.002 | -0.072 |
| Square-root-space Mean-Variance Scaling | -0.490 | +0.000 | +0.000 | -0.025 | -0.465 |
| Power Transformation | -0.485 | +0.000 | +0.000 | -0.023 | -0.462 |
| Delta Change | +0.360 | +0.000 | +0.000 | -0.012 | +0.372 |
| Local Intensity Scaling | +0.643 | +0.000 | +0.000 | -0.017 | +0.660 |
| Empirical Quantile Mapping | -0.326 | +0.000 | +0.000 | -0.015 | -0.311 |
| Gamma Quantile Mapping | -0.452 | +0.000 | +0.000 | -0.015 | -0.437 |
| Detrended Quantile Mapping | +0.611 | +0.000 | +0.000 | -0.003 | +0.614 |
| Quantile Delta Mapping | +0.797 | +0.000 | +0.000 | -0.007 | +0.804 |
| Scaled Distribution Mapping | +1.142 | +0.000 | +0.000 | +0.000 | +1.142 |
| CDF-transform | +0.828 | +0.000 | +0.000 | -0.004 | +0.832 |
| 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 14.3% of area | always wet 85.7% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.383 | +0.000 | +0.000 | +0.061 | +0.322 |
| Variance Scaling (unbounded) | -0.018 | +0.000 | +0.000 | -0.008 | -0.010 |
| Square-root-space Mean-Variance Scaling | -0.081 | +0.000 | +0.000 | -0.026 | -0.055 |
| Power Transformation | +0.002 | +0.000 | +0.000 | -0.032 | +0.034 |
| Delta Change | +0.120 | +0.000 | +0.000 | -0.017 | +0.137 |
| Local Intensity Scaling | +0.345 | +0.000 | +0.000 | +0.062 | +0.284 |
| Empirical Quantile Mapping | +0.282 | +0.000 | +0.000 | -0.019 | +0.301 |
| Gamma Quantile Mapping | -0.076 | +0.000 | +0.000 | -0.041 | -0.035 |
| Detrended Quantile Mapping | +0.595 | +0.000 | +0.000 | +0.033 | +0.562 |
| Quantile Delta Mapping | +0.851 | +0.000 | +0.000 | +0.074 | +0.777 |
| Scaled Distribution Mapping | +0.958 | +0.000 | +0.000 | +0.100 | +0.858 |
| CDF-transform | +0.694 | +0.000 | +0.000 | +0.061 | +0.632 |
| 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 9.4% of area | always wet 90.6% of area |
|---|---|---|---|---|---|
| Linear Scaling | +0.091 | +0.000 | +0.000 | -0.032 | +0.123 |
| Variance Scaling (unbounded) | +0.001 | +0.000 | +0.000 | -0.001 | +0.002 |
| Square-root-space Mean-Variance Scaling | -0.127 | +0.000 | +0.000 | -0.039 | -0.088 |
| Power Transformation | -0.146 | +0.000 | +0.000 | -0.055 | -0.091 |
| Delta Change | -0.076 | +0.000 | +0.000 | -0.040 | -0.036 |
| Local Intensity Scaling | +0.088 | +0.000 | +0.000 | -0.024 | +0.112 |
| Empirical Quantile Mapping | +0.202 | +0.000 | +0.000 | -0.046 | +0.248 |
| Gamma Quantile Mapping | -0.103 | +0.000 | +0.000 | -0.050 | -0.053 |
| Detrended Quantile Mapping | +0.316 | +0.000 | +0.000 | -0.035 | +0.352 |
| Quantile Delta Mapping | +0.215 | +0.000 | +0.000 | -0.039 | +0.254 |
| Scaled Distribution Mapping | +0.410 | +0.000 | +0.000 | -0.019 | +0.429 |
| CDF-transform | +0.239 | +0.000 | +0.000 | -0.037 | +0.276 |
| 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 | +0.270 | +0.000 | +0.000 | +0.000 | +0.270 |
| Variance Scaling (unbounded) | -0.006 | +0.000 | +0.000 | +0.000 | -0.006 |
| Square-root-space Mean-Variance Scaling | -0.036 | +0.000 | +0.000 | +0.000 | -0.036 |
| Power Transformation | +0.033 | +0.000 | +0.000 | +0.000 | +0.033 |
| Delta Change | -0.205 | +0.000 | +0.000 | +0.000 | -0.205 |
| Local Intensity Scaling | +0.245 | +0.000 | +0.000 | +0.000 | +0.245 |
| Empirical Quantile Mapping | +0.708 | +0.000 | +0.000 | +0.000 | +0.708 |
| Gamma Quantile Mapping | -0.005 | +0.000 | +0.000 | +0.000 | -0.005 |
| Detrended Quantile Mapping | +0.600 | +0.000 | +0.000 | +0.000 | +0.600 |
| Quantile Delta Mapping | +0.567 | +0.000 | +0.000 | +0.000 | +0.567 |
| Scaled Distribution Mapping | +0.796 | +0.000 | +0.000 | +0.000 | +0.796 |
| CDF-transform | +0.582 | +0.000 | +0.000 | +0.000 | +0.582 |
| MVS with all-zero guard (variant) | +0.000 | +0.000 | +0.000 | +0.000 | +0.000 |