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 tech nique, then statistics of the errors produced by that scheme are required. These are the errors produced by the scheme's formulation itself, not count ing any errors in the scheme's input, Such errors are extremely difficult t o estimate, but examination of differences produced by various suitable sch emes can yield qualitative descriptions of such errors. Here, hourly accumu lated convective precipitation fields produced from six different versions of a short-term forecast model are compared. The versions have identical in itial and boundary conditions, but vary in the schemes used for either the convection or the planetary boundary layer, or both. The distribution of di fferences, or differences in logarithms of accumulations, between correspon ding precipitating grid points for pairs of forecasts are examined using a simple binning technique. When the convection schemes differ, results revea l that if either a log-normal or normal distribution is a better characteri zation of the distributions, it is the log-normal one. The standard deviati ons of these logarithmic distributions correspond to different schemes at i dentical grid points producing values differing by factors of 2 or more. A large proportion of grid points that have non-zero hourly accumulations usi ng one model version may have no accumulation using another version, For mo st pairs of forecasts examined, however, grid points having larger values o f accumulation for one scheme tend to have a smaller fraction of values hav ing no accumulation in the other scheme. These results suggest that the fin ite probability that the model produces no precipitation when the correspon ding, true atmospheric state does, should be considered in the statistical description of the model errors and that, because of the large standard dev iation of model errors as well as large possible errors of hourly precipita tion observations, the quantitative usefulness of assimilating such observa tions may be very limited.