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Probabilistic Quantitative Precipitation Forecasts Based on Reforecast Analogs: Theory and Application

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  • 1 Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado
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Abstract

A general theory is proposed for the statistical correction of weather forecasts based on observed analogs. An estimate is sought for the probability density function (pdf) of the observed state, given today’s numerical forecast. Assume that an infinite set of reforecasts (hindcasts) and associated observations are available and that the climate is stable. Assume that it is possible to find a set of past model forecast states that are nearly identical to the current forecast state. With the dates of these past forecasts, the asymptotically correct probabilistic forecast can be formed from the distribution of observed states on those dates.

Unfortunately, this general theory of analogs is not useful for estimating the global pdf with a limited set of reforecasts, for the chance of finding even one effectively identical forecast analog in that limited set is vanishingly small, and the climate is not stable. Nonetheless, approximations can be made to this theory to make it useful for statistically correcting weather forecasts. For instance, when estimating the state in a local region, choose the dates of analogs based on a pattern match of the local weather forecast; with a few decades of reforecasts, there are usually many close analogs.

Several approximate analog techniques are then tested for their ability to skillfully calibrate probabilistic forecasts of 24-h precipitation amount. A 25-yr set of reforecasts from a reduced-resolution global forecast model is used. The analog techniques find past ensemble-mean forecasts in a local region that are similar to today’s ensemble-mean forecasts in that region. Probabilistic forecasts are formed from the analyzed weather on the dates of the past analogs. All of the analog techniques provide dramatic improvements in the Brier skill score relative to basing probabilities on the raw ensemble counts or the counts corrected for bias. However, the analog techniques did not produce guidance that was much more skillful than that produced by a logistic regression technique. Among the analog techniques tested, it was determined that small improvements to the baseline analog technique that matches ensemble-mean precipitation forecasts are possible. Forecast skill can be improved slightly by matching the ranks of the mean forecasts rather than the raw mean forecasts by using highly localized search regions for shorter-term forecasts and larger search regions for longer forecasts, by matching precipitable water in addition to precipitation amount, and by spatially smoothing the probabilities.

Corresponding author address: Dr. Thomas M. Hamill, NOAA/ESRL/PSD, R/PSD 1, 325 Broadway, Boulder, CO 80305-3328. Email: tom.hamill@noaa.gov

Abstract

A general theory is proposed for the statistical correction of weather forecasts based on observed analogs. An estimate is sought for the probability density function (pdf) of the observed state, given today’s numerical forecast. Assume that an infinite set of reforecasts (hindcasts) and associated observations are available and that the climate is stable. Assume that it is possible to find a set of past model forecast states that are nearly identical to the current forecast state. With the dates of these past forecasts, the asymptotically correct probabilistic forecast can be formed from the distribution of observed states on those dates.

Unfortunately, this general theory of analogs is not useful for estimating the global pdf with a limited set of reforecasts, for the chance of finding even one effectively identical forecast analog in that limited set is vanishingly small, and the climate is not stable. Nonetheless, approximations can be made to this theory to make it useful for statistically correcting weather forecasts. For instance, when estimating the state in a local region, choose the dates of analogs based on a pattern match of the local weather forecast; with a few decades of reforecasts, there are usually many close analogs.

Several approximate analog techniques are then tested for their ability to skillfully calibrate probabilistic forecasts of 24-h precipitation amount. A 25-yr set of reforecasts from a reduced-resolution global forecast model is used. The analog techniques find past ensemble-mean forecasts in a local region that are similar to today’s ensemble-mean forecasts in that region. Probabilistic forecasts are formed from the analyzed weather on the dates of the past analogs. All of the analog techniques provide dramatic improvements in the Brier skill score relative to basing probabilities on the raw ensemble counts or the counts corrected for bias. However, the analog techniques did not produce guidance that was much more skillful than that produced by a logistic regression technique. Among the analog techniques tested, it was determined that small improvements to the baseline analog technique that matches ensemble-mean precipitation forecasts are possible. Forecast skill can be improved slightly by matching the ranks of the mean forecasts rather than the raw mean forecasts by using highly localized search regions for shorter-term forecasts and larger search regions for longer forecasts, by matching precipitable water in addition to precipitation amount, and by spatially smoothing the probabilities.

Corresponding author address: Dr. Thomas M. Hamill, NOAA/ESRL/PSD, R/PSD 1, 325 Broadway, Boulder, CO 80305-3328. Email: tom.hamill@noaa.gov

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