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Volume 9, issue 1 | Copyright
Geosci. Model Dev., 9, 413-429, 2016
https://doi.org/10.5194/gmd-9-413-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Development and technical paper 29 Jan 2016

Development and technical paper | 29 Jan 2016

A flexible importance sampling method for integrating subgrid processes

E. K. Raut and V. E. Larson E. K. Raut and V. E. Larson
  • University of Wisconsin – Milwaukee, Department of Mathematical Sciences, Milwaukee, WI, USA

Abstract. Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales.

The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that contains both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories.

The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). The resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.

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Numerical models of weather and climate can estimate grid-box-averaged rates of physical processes such as microphysics using Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain into categories, and allows the modeler to prescribe the sampling density in each category.
Numerical models of weather and climate can estimate grid-box-averaged rates of physical...
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