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Artificial Intelligence for the Earth Systems Bulletin of the American Meteorological Society Earth Interactions Journal of Applied Meteorology and Climatology Journal of Atmospheric and Oceanic Technology Journal of Climate Journal of Hydrometeorology Journal of Physical Oceanography Journal of the Atmospheric Sciences Monthly Weather Review Weather and Forecasting Weather, Climate, and Society Meteorological Monographs

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JOURNALS

Artificial Intelligence for the Earth Systems Bulletin of the American Meteorological Society Earth Interactions Journal of Applied Meteorology and Climatology Journal of Atmospheric and Oceanic Technology Journal of Climate Journal of Hydrometeorology Journal of Physical Oceanography Journal of the Atmospheric Sciences Monthly Weather Review Weather and Forecasting Weather, Climate, and Society Meteorological Monographs

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Weather and Forecasting

Volume 22: Issue 5

Early Online Release

Volume: 41 (2026)

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Volume: 40 (2025)

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Sections

Abstract

1. Introduction

2. Expected Brier scores
a. Definitions

b. The effects of ensemble size

c. c. Unbiased estimators

d. Exchangeability

e. Data example

3. Sampling variation
a. Standard errors

b. Confidence intervals

4. Simulation study
a. Serial independence

b. Serial dependence

c. Modified bootstrap intervals

5. Comparing Brier scores

6. Multiple comparisons

7. Discussion

Conditional Brier Scores
Unbiased estimators

Standard errors

Confidence intervals

Simulation study

Comparing Brier scores

Hypothesis Tests

References

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Crossref

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Brier, G. W., 1950: Verification of forecasts expressed in terms of probability.Mon. Wea. Rev., 78, 1–3.

Crossref

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Crossref

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Crossref

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Chatfield, C., 2004: The Analysis of Time Series: An Introduction.Chapman and Hall, 333 pp.

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Davison, A. C., and HinkleyD. V. , 1997: Bootstrap Methods and Their Application.Cambridge University Press, 592 pp.

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Hall, P., 1987: On the bootstrap and continuity correction.J. Roy. Stat. Soc., 49B, 82–89.

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Hamill, T. M.
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