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 when one has low‐resolution runs for a long period and only a few days' high‐resolution runs.