Numerical Sensitivities in Convective/Nonconvective Cloud Interactions in MM5

During our experiences optimizing the MM5 meteorological model for microprocessor based shared memory parallel computer systems, we observed substantial difficulty with model-validation, in getting the results to agree with our base-case benchmark. Finally, we did multiple successive days of forecast runs where the only numeric difference was an optimization of the EXMOISS simple-ice explicit moisture routine. We used an algebraic identity that both speeds up the code noticeably and reduces the amount of roundoff error within an innermost ("miter") loop. We observe that the resulting small differences in model state variables lead eventually to different convective-triggering behavior (a process that is already ill-conditioned in nature itself); which leads to an interaction between subgrid-scale convective cloud parameterization and grid-scale explicit cloud submodel that quickly causes substantial differences in the MM5 state variables. The resulting differences in forecast precipitation can be locally quite large, but seem to be unbiased: for a twenty-four hour forecast at 15 kilometers resolution in which the grid maximum rainfall was about 4.5 centimeters, we observed grid-maximum forecast rainfall differences between control-EXMOISS and optimized-EXMOISS as large as 0.9 centimeter! On the other hand, the grid arithmetic-mean difference (where cancellation can take place) was on the order of 0.001 centimeter, while the grid root mean square difference (where all terms are positive, and cancellation does not take place) was on the order of 0.1 centimeter, an indication of lack of bias. Systematically over the 7-day period studied, we find that the grid arithmetic-mean control-vs.-optimized-EXMOISS difference is two orders of magnitude smaller than the grid root mean square difference. We examine the implications for the formulation of meteorological models, and for forecast operating procedures generally.