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Numerical models of weather and climate need to computegrid-box-averaged rates of physical processes such as microphysics.These averages are computed by integrating subgrid variability overa grid box.  For this reason, an important aspect of atmosphericmodeling is spatial integration over subgrid scales.  The needed integrals can be estimated by Monte Carlointegration.  Monte Carlo integration is simple and generalbut requires many evaluations of the physical process rate.To reduce the number of function evaluations, this paperdescribes a new, flexible method of importance sampling.  Itdivides the domain of integration into eight categories, suchas the portion that contains both precipitation and cloud, orthe portion that contains precipitation but no cloud.  It thenallows the modeler to prescribe the density of sample pointswithin each of the eight categories.  The new method is incorporated into the Subgrid ImportanceLatin Hypercube Sampler (SILHS).  The resulting method istested on drizzling cumulus and stratocumulus cases.  In thecumulus case, the sampling error can be considerably reducedby drawing more sample points from the region of rainevaporation

A flexible importance sampling method for integrating subgrid processes