Statistical conditional simulation of a multiresolution numerical air quality model

This paper addresses subgrid variability, an issue that naturally arises in multiresolution numerical air quality models. Unlike previous approaches, which fit a parametric distribution over a spatial block and perform the fit from block to block independently over space and time, our approach to dealing with the subgrid variability is to describe the space-time conditional distribution of high-resolution output given its low-resolution counterpart. A novel conditional simulation approach is proposed to produce an ensemble of high-resolution runs based on the runs we have, and various criteria are used to assess whether our simulated high-resolution runs capture the overall space-time variability of the original high-resolution runs. The main idea of our algorithm is to apply a nonlinear filter to the high-resolution runs based on the low-resolution runs and then perform a time domain block bootstrap for the residuals simultaneously over space. The algorithm proposed in this paper can be readily used by practitioners to generate random high-resolution runs as a useful surrogate to the real high-resolution runs whe one has low-resolution runs for a long period and only a few days' high-resolution runs.