• Eckel, F. A., Allen M. S. , and Sittel M. C. , 2012: Estimation of ambiguity in ensemble forecasts. Wea. Forecasting, 27, 5069.

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    Reliability diagrams for (a) raw, (b) bulk-calibrated, and (c) conditionally calibrated JM forecasts using the dependent dataset, and similarly for (d),(e), and (f) but using the independent dataset. The observed relative frequency is the line with error bars while the number of forecasts in each probability bin is the line with square markers. The dashed line shows perfect reliability while the dashed–dotted line is the event sample climatology, which was nearly identical in both the dependent and independent datasets. Inset in each plot is the Brier skill score (BSS), reliability (rel), resolution (res), and uncertainty (unc).

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    Conditional calibration of JM for the (a) first and (b) second moments of the ensemble forecast PDF. The dashed line at 0.0 marks the break between positive–negative shift or stretch and also indicates the range of predictor values in the dependent dataset. The class interval width for ensemble mean or variance increases toward the extreme values to increase counts in the bins. Dots indicate the empirical correction values, and the solid line is the fitted (21st-order polynomial) correction curve, which is held constant past the last data point.

  • View in gallery

    Example comparison of a true (solid) and an ensemble forecast (dashed) (a) PDF and (b) cumulative distribution function (CDF) defined as N(2.2°C, 2.6°C) and N(2.8°C, 1.8°C), respectively. An error of −13.9% in pe for the chance of temperature ≤ 0°C is the difference in the PDFs' shaded areas, or the difference in the two CDFs (double arrow).

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    Scatterplots showing relationships between the ensemble PDF's variable statistics. Correlation coefficient (r) is shown in the inset in each plot.

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    Best-guess (bulk calibrated) pe, CES total ambiguity, and ensemble spread for the 5-day JM forecast valid 1200 UTC 17 Jan 2009.

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    Display of underdispersion by the L96M EPS, purposefully designed to mimic a real-world EPS. The average ensemble variance increases too slowly with forecast lead time, thereby not reflecting the actual error growth shown by the MSE of the ensemble mean. The period of maximum error growth is indicated to highlight when ensemble information is most useful.

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CORRIGENDUM

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  • 1 Naval Postgraduate School, Monterrey, California
  • | 2 University Corporation for Atmospheric Research, Boulder, Colorado
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Current affiliation: National Weather Service/Office of Science and Technology, Silver Spring, Maryland.

Current affiliation: Air Force Weather Agency, Offutt Air Force Base, Omaha, Nebraska.

Corresponding author address: F. Anthony Eckel, Dept. of Atmospheric Sciences, University of Washington, 408 ATG Bldg., Box 351640, Seattle, WA 98195. E-mail: tony.eckel@noaa.gov

Current affiliation: National Weather Service/Office of Science and Technology, Silver Spring, Maryland.

Current affiliation: Air Force Weather Agency, Offutt Air Force Base, Omaha, Nebraska.

Corresponding author address: F. Anthony Eckel, Dept. of Atmospheric Sciences, University of Washington, 408 ATG Bldg., Box 351640, Seattle, WA 98195. E-mail: tony.eckel@noaa.gov

A number of figures in Eckel et al. (2012) were not processed properly and resulted in a degraded quality in the final published version of the paper. Figures 2, 5, 6, 9, 14, and 20 are reproduced below in the proper high resolution as they were meant to be published.

Fig. 2.
Fig. 2.

Reliability diagrams for (a) raw, (b) bulk-calibrated, and (c) conditionally calibrated JM forecasts using the dependent dataset, and similarly for (d),(e), and (f) but using the independent dataset. The observed relative frequency is the line with error bars while the number of forecasts in each probability bin is the line with square markers. The dashed line shows perfect reliability while the dashed–dotted line is the event sample climatology, which was nearly identical in both the dependent and independent datasets. Inset in each plot is the Brier skill score (BSS), reliability (rel), resolution (res), and uncertainty (unc).

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

Fig. 5.
Fig. 5.

Conditional calibration of JM for the (a) first and (b) second moments of the ensemble forecast PDF. The dashed line at 0.0 marks the break between positive–negative shift or stretch and also indicates the range of predictor values in the dependent dataset. The class interval width for ensemble mean or variance increases toward the extreme values to increase counts in the bins. Dots indicate the empirical correction values, and the solid line is the fitted (21st-order polynomial) correction curve, which is held constant past the last data point.

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

Fig. 6.
Fig. 6.

Example comparison of a true (solid) and an ensemble forecast (dashed) (a) PDF and (b) cumulative distribution function (CDF) defined as N(2.2°C, 2.6°C) and N(2.8°C, 1.8°C), respectively. An error of −13.9% in pe for the chance of temperature ≤ 0°C is the difference in the PDFs' shaded areas, or the difference in the two CDFs (double arrow).

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

Fig. 9.
Fig. 9.

Scatterplots showing relationships between the ensemble PDF's variable statistics. Correlation coefficient (r) is shown in the inset in each plot.

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

Fig. 14.
Fig. 14.

Best-guess (bulk calibrated) pe, CES total ambiguity, and ensemble spread for the 5-day JM forecast valid 1200 UTC 17 Jan 2009.

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

Fig. 20.
Fig. 20.

Display of underdispersion by the L96M EPS, purposefully designed to mimic a real-world EPS. The average ensemble variance increases too slowly with forecast lead time, thereby not reflecting the actual error growth shown by the MSE of the ensemble mean. The period of maximum error growth is indicated to highlight when ensemble information is most useful.

Citation: Weather and Forecasting 27, 3; 10.1175/WAF-D-12-00025.1

The staff of Weather and Forecasting regrets any inconvenience this error may have caused.

REFERENCE

Eckel, F. A., Allen M. S. , and Sittel M. C. , 2012: Estimation of ambiguity in ensemble forecasts. Wea. Forecasting, 27, 5069.

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