Spatial Statistical Downscaling for Constructing High-Resolution Nature Runs in Global Observing System Simulation Experiments

ABSTRACT

Observing system simulation experiments (OSSEs) have been widely used as a rigorous and cost-effective way to guide development of new observing systems, and to evaluate the performance of new data assimilation algorithms. Nature runs (NRs), which are output from deterministic models, play an essential role in building OSSE systems for global atmospheric processes because they are used both to create synthetic observations at high spatial resolution, and to represent the “true” atmosphere against which the forecasts are verified. However, most NRs are generated at resolutions coarser than actual observations from satellite instruments or predictions from data assimilation algorithms. Our goal is to develop a principled statistical downscaling framework to construct high-resolution NRs via conditional simulation from coarse-resolution numerical model output. We use nonstationary spatial covariance function models that have basis function representations to capture spatial variability. This approach not only explicitly addresses the change-of-support problem, but also allows fast computation with large volumes of numerical model output. We also propose a data-driven algorithm to select the required basis functions adaptively, in order to increase the flexibility of our nonstationary covariance function models. In this article we demonstrate these techniques by downscaling a coarse-resolution physical numerical model output at a native resolution of $1^{°} \text{latitude}\times {1.25}^{°} \text{longitude}$ of global surface ${\text{CO}}_2$ concentrations to 655,362 equal-area hexagons.

KEYWORDS:

• Basis functions
• Change of support
• Conditional simulation
• Nonstationary covariance function
• Observing system simulation experiment
• Statistical downscaling

Acknowledgment

We thank the Editor, Associate Editor, and two anonymous referees for constructive comments and suggestions. We would like to thank Noel Cressie, Anna M. Michalak, and Tim Stough for their helpful suggestions.

Additional information

Funding

The research was partially carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This material was based upon work partially supported by the National Science Foundation under Grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material do not necessarily reflect the views of the National Science Foundation. This research was part of Ma’s Ph.D. dissertation supported by the Charles Phelps Taft Dissertation Fellowship at the University of Cincinnati. Kang’s research was partially supported by the Simons Foundation’s Collaboration Award (#317298) and the Taft Research Center at the University of Cincinnati.