Rationale: The QPFs rarely predict the rain pattern in exactly the same place. When combining multiple rain fields to produce a deterministic rain forecast, the ensemble mean is likely to predict the best location of the rain center, but the averaging process "smears" the rain rates so that the maximum rainfall is reduced and area of light rain is artificially enhanced (see plot below). However, the rain rate frequency distribution in the original ensemble (collating all the rain rates from all the individual members) is usually closer to the observed rain rate frequency distribution. Probability matching transforms the rain rate distribution in the ensemble mean rain field to look like that from the complete ensemble:
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------------------- How to do probability matching: --------------------- 1. Rank the gridded rainfall from all n QPFs from largest to smallest, the keep every nth value starting with the n/2-th value. 2. Rank the gridded rainfall from the ensemble mean from largest to smallest. 3. Match the two histograms, mapping rain rates from (1) onto locations from (2). ------------------------------------------------------------------------- |
The example below shows the impact of the probability matching in the Bureau of Meteorology's Poor Man's Ensemble. Notice that the maximum rainfall is significantly heavier (132 mm in the PM, as opposed to 89 mm in the AVG product; the maximum value from the daily gauge analysis on that day was 125 mm) and the region of light rainfall does not extend as far to the west. For run-of-the-mill rainfall the impact is usually pretty small and the probability-matched mean looks very similar to the simple ensemble mean. For heavy rain situations the probability matching usually gives a more realistic maximum rain rate.
