Report created: 2026-09-16 15:38:30.586922

Metric Descriptions

  • NSE - Nash-Sutcliffe Efficiency, a metric that measures performance relative to the mean of the data, values range from [-∞ , 1], with values greater than 0 indicating better performance than the mean, and a perfect forecast will have a value of 1.
  • KGE - Kling-Gupta Efficiency, a metric that is often used similarly to NSE, but addresses several shortcomings by explicitly incorporating variability and correlation between simulations and observations. Values can range from [-∞ , 1] with negative values generally considered to indicate poor performance.
  • PBIAS - Percent Bias, Bias of the simulation relative to the observations, represented as a percent. Negative values indicate a low bias and positive values indicate a high bias, values closer to 0 are preferable.
  • nRMSE - Normalized root mean square error, expressed as a percent, lower values are better.
  • r - Pearson’s correlation, a measure of how well the forecast and observations are correlated, values closer to 1 indicate better correlation.
  • rSD - Ratio of standard deviations of forecast and observed. Values close to 1 are preferable as they indicate that the forecast has the same variability as the observations.

Day Ahead Forecast Statistics

Overall

source location NSE KGE PBIAS nRMSE r rSD
A wilder 0.725 0.834 -8.0 52.4 0.884 1.087
B wilder 0.832 0.876 0.1 40.9 0.929 1.102
GRH wilder 0.882 0.885 -9.9 34.4 0.951 0.970
perfect wilder 1.000 1.000 0.0 0.0 1.000 1.000
persistence wilder -0.811 0.016 -75.9 134.5 0.750 0.426
A bellows 0.545 0.773 0.4 67.4 0.773 1.002
B bellows 0.911 0.951 0.6 29.8 0.955 0.982
GRH bellows 0.850 0.877 -10.4 38.7 0.933 0.995
perfect bellows 1.000 1.000 0.0 0.0 1.000 1.000
persistence bellows 0.394 0.349 -39.2 77.8 0.870 0.496
A vernon 0.806 0.835 -11.3 44.1 0.907 0.924
B vernon 0.888 0.940 1.7 33.4 0.944 0.990
GRH vernon 0.888 0.876 -11.0 33.5 0.951 0.970
perfect vernon 1.000 1.000 0.0 0.0 1.000 1.000
persistence vernon 0.801 0.691 -18.1 44.6 0.934 0.758

Winter

source location season NSE KGE PBIAS nRMSE r rSD
A wilder winter 0.628 0.812 -0.3 60.7 0.832 1.083
B wilder winter 0.746 0.738 -1.4 50.2 0.924 1.250
GRH wilder winter 0.876 0.852 -11.6 34.9 0.958 0.919
perfect wilder winter 1.000 1.000 0.0 0.0 1.000 1.000
persistence wilder winter -0.749 0.025 -74.5 131.9 0.839 0.392
A bellows winter -0.088 0.450 31.9 103.7 0.553 0.963
B bellows winter 0.915 0.922 -0.3 29.1 0.962 1.068
GRH bellows winter 0.871 0.887 -9.9 35.7 0.946 1.001
perfect bellows winter 1.000 1.000 0.0 0.0 1.000 1.000
persistence bellows winter 0.343 0.344 -40.3 80.8 0.851 0.505
A vernon winter 0.741 0.843 1.5 50.7 0.863 0.925
B vernon winter 0.911 0.905 -0.1 29.8 0.962 1.087
GRH vernon winter 0.921 0.896 -9.9 28.0 0.970 0.984
perfect vernon winter 1.000 1.000 0.0 0.0 1.000 1.000
persistence vernon winter 0.770 0.702 -17.6 47.8 0.912 0.776

Spring

source location season NSE KGE PBIAS nRMSE r rSD
A wilder spring 0.490 0.755 -5.5 71.0 0.782 1.097
B wilder spring 0.726 0.749 4.7 52.1 0.916 1.231
GRH wilder spring 0.767 0.881 -5.6 48.0 0.897 1.021
perfect wilder spring 1.000 1.000 0.0 0.0 1.000 1.000
persistence wilder spring -2.822 0.089 -73.5 194.7 0.825 0.491
A bellows spring 0.494 0.717 -4.2 70.7 0.732 0.918
B bellows spring 0.880 0.936 2.2 34.5 0.942 1.012
GRH bellows spring 0.786 0.855 -5.1 46.0 0.912 1.104
perfect bellows spring 1.000 1.000 0.0 0.0 1.000 1.000
persistence bellows spring -0.081 0.269 -43.2 103.5 0.868 0.425
A vernon spring 0.769 0.877 -5.2 47.8 0.889 0.997
B vernon spring 0.820 0.900 3.6 42.2 0.917 1.042
GRH vernon spring 0.859 0.910 -6.1 37.3 0.937 1.022
perfect vernon spring 1.000 1.000 0.0 0.0 1.000 1.000
persistence vernon spring 0.676 0.666 -20.4 56.6 0.909 0.752

Summer

source location season NSE KGE PBIAS nRMSE r rSD
A wilder summer 0.655 0.756 -9.4 58.6 0.880 1.190
B wilder summer 0.787 0.855 -3.8 46.0 0.890 0.914
GRH wilder summer 0.845 0.867 -11.8 39.3 0.940 0.983
perfect wilder summer 1.000 1.000 0.0 0.0 1.000 1.000
persistence wilder summer -1.226 0.002 -77.0 148.8 0.572 0.531
A bellows summer 0.569 0.754 -6.7 65.5 0.774 0.928
B bellows summer 0.863 0.828 -4.7 36.9 0.935 0.848
GRH bellows summer 0.764 0.817 -12.9 48.5 0.892 0.928
perfect bellows summer 1.000 1.000 0.0 0.0 1.000 1.000
persistence bellows summer 0.312 0.340 -37.0 82.7 0.784 0.498
A vernon summer 0.762 0.703 -18.5 48.7 0.905 0.789
B vernon summer 0.852 0.815 -4.1 38.4 0.929 0.834
GRH vernon summer 0.822 0.823 -13.5 42.1 0.921 0.917
perfect vernon summer 1.000 1.000 0.0 0.0 1.000 1.000
persistence vernon summer 0.777 0.673 -17.8 47.1 0.923 0.737

Fall

source location season NSE KGE PBIAS nRMSE r rSD
A wilder fall 0.627 0.640 -17.0 60.9 0.864 0.714
B wilder fall 0.913 0.901 1.3 29.4 0.964 1.092
GRH wilder fall 0.814 0.867 -10.9 42.9 0.926 0.985
perfect wilder fall 1.000 1.000 0.0 0.0 1.000 1.000
persistence wilder fall -1.865 -0.108 -80.8 168.8 0.779 0.274
A bellows fall 0.552 0.635 -16.9 66.8 0.797 0.749
B bellows fall 0.873 0.849 9.5 35.5 0.960 1.110
GRH bellows fall 0.786 0.833 -14.9 46.1 0.925 1.005
perfect bellows fall 1.000 1.000 0.0 0.0 1.000 1.000
persistence bellows fall 0.414 0.491 -32.5 76.3 0.891 0.625
A vernon fall 0.519 0.645 -24.4 69.2 0.809 0.826
B vernon fall 0.788 0.798 13.2 45.9 0.933 1.136
GRH vernon fall 0.760 0.812 -16.4 48.8 0.914 1.030
perfect vernon fall 1.000 1.000 0.0 0.0 1.000 1.000
persistence vernon fall 0.744 0.712 -14.0 50.5 0.898 0.770

Error Distributions (Forecast - Observed)

Overall

Winter

Spring

Summer

Fall

Day Ahead Observed vs. Forecast Scatterplot

Overall

Winter

Spring

Summer

Fall

Day Ahead Performance by Month

Paper Figure 4 is this plot for the four metrics below.

Kling-Gupta Efficiency (KGE)

Nash-Suttecliffe Efficiency (NSE)

Pearson’s Correlation (r)

Percent Bias

Daily forecast performance vs lead time

Paper Figure 3 is the “Overall” tab of each metric below.

Kling-Gupta Efficiency (KGE)

Overall

Winter

Spring

Summer

Fall

Nash-Suttecliffe Efficiency (NSE)

Overall

Winter

Spring

Summer

Fall

Pearson’s Correlation (r)

Overall

Winter

Spring

Summer

Fall

Percent Bias

Overall

Winter

Spring

Summer

Fall

Hourly forecast performance vs lead time

Kling-Gupta Efficiency (KGE)

Overall

Winter

Spring

Summer

Fall

### Nash-Suttecliffe Efficiency (NSE) {.tabset}

Overall

Winter

Spring

Summer

Fall

Pearson’s Correlation (r)

Overall

Winter

Spring

Summer

Fall

Percent Bias

Overall

Winter

Spring

Summer

Fall

Cumulative Error

Cumulative inflow error is what moves the forebay, so it is accumulated over each issue’s own delivered horizon rather than over absolute lead time. Forecast A is issued at 04:00 but for most of its issues the delivered series does not start until lead hour 25, so an absolute-lead axis compares 8 accumulated hours of A against 32 of B and produces a non-monotonic A curve driven purely by sample composition. Indexing by position in the horizon keeps every row and makes each point a like-for-like N-hour accumulation. This is the same construction as paper Figures 5 and 6 (make-revision-figures.R).

Only the three forecast products appear here. perfect accumulates exactly zero by construction and persistence is a day-ahead benchmark, so neither is informative on an hourly accumulation.

2.5th to 97.5th percentile (Middle 95%)

Paper Figure 5 is the “Overall” tab.

Overall

Winter

Spring

Summer

Fall

25th to 75th percentile (Middle 50%)

The same plot over the interquartile range instead of the middle 95%.

Overall

Winter

Spring

Summer

Fall

Probability of exceeding 0.5 ft cumulative error

Paper Figure 6 is the “Overall” tab, restricted to the marked hours.

Overall

Winter

Spring

Summer

Fall