Estimation of the error distributions of precipitation produced by convective parametrization schemes

If a parametrization scheme for convective precipitation is to be used for assimilating observations of precipitation using a statistically based technique, then statistics of the errors produced by that scheme are required. These are the errors produced by the scheme's formulation itself, not counting any errors in the scheme's input. Such errors are extremely difficult to estimate, but examination of differences produced by various suitable schemes can yield qualitative descriptions of such errors. Here, hourly accumulated convective precipitation fields produced from six different versions of a short-term forecast model are compared. The versions have identical initial and boundary conditions, but vary in the schemes used for either the convection of the planetary boundary layer, or both. The distribution of differences, or differences in logarithms of accumulations, between corresponding precipitating grid points for pairs of forecasts are examined using a simple binning technique. When the convection schemes differ, results reveal that if either a log-normal or normal distribution is a better characterization of the distributions, it is the log-normal one. The standard deviations of these logarithmic distributions correspond to different schemes at identical grid points producing values differing by factors of 2 or more. A large proportion of grid points that have non-zero hourly accumulations using one model version may have no accumulation using another version. For most pairs of forecasts examined, however, grid points having larger values of accumulation for one scheme tend to have a smaller fraction of values having no accumulation in the other scheme. These results suggest that the finite probability that the model produces no precipitation when the corresponding, true atmospheric state does, should be considered in the statistical description of the model errors and that, because of the large standard deviation of model errors as well as large possible errors of hourly precipitation observations. The quantitative usefulness of assimilating such observations may be very limited.