A Geostatistical Framework for Downscaling Spatial Data

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

In many scientific disciplines, spatially distributed models simulating physical or human-related processes require input parameter maps at a finer spatial resolution than what is often available. In hydrometeorology, for example, detailed modeling calls for transforming forecasts of climate-related variables produced by global circulation models to finer spatial resolutions for climate change impact assessment studies. Along the same lines, remotely sensed information must be often processed to obtain finer spatial resolution inputs for spatially explicit ecological, hydrological, or land use models. Such a transformation of coarse spatial resolution data to finer resolution predictions/maps (also termed downscaling) is a fundamental geographical research theme with wide implications for numerous and diverse scientific disciplines. Most existing methods for spatial data downscaling, however, tend to ignore one or more of the following critical issues: (i) the explicit account of scale differences between the available areal data and the sought-after predictions; for example, areal data are often treated as point values, (ii) the coherence (or mass preservation) of downscaled predictions, and (iii) the assessment of uncertainty regarding these predictions, and most importantly how such uncertainty is propagated to geographical analyses and model outputs. This project will employ geostatistics to develop and disseminate novel analytical tools for downscaling spatial data that satisfy the above critical requirements. In addition, prototype case studies will be conducted using remotely sensed imagery, regional climate model forecasts, and census data, to illustrate the application of such tools in practice. In particular, this project will address: (i) a wide class of areal data defined as convolutions of point values with appropriate sampling kernels, including summation and averaging as special cases, (ii) the estimation of spatial covariance models at fine resolutions from coarse spatial resolution areal data, accounting for physical knowledge at the fine resolution, and (iii) downscaling in a stochastic simulation mode; that is, the generation of alternative simulated realizations of downscaled attribute values conditioned to available areal data (possibly of different resolutions). In this latter case, the simulated values will reproduce (in addition to the areal data) a histogram and spatial correlation model at that fine resolution. The alternative simulated realizations will be consistent with all available pieces of information, and will be used in a Monte Carlo framework to assess the uncertainty in spatially distributed model outputs due to uncertain model inputs derived from coarse spatial resolution data. Project findings will be disseminated via: (i) presentations in relevant conferences, (ii) publications in peer reviewed journals, (iii) development of a public domain Matlab toolbox, and (iv) development of a set of prototype case studies and associated data products; items (iii) and (iv) will be made available for downloading from the project's Web site. The findings of this project will contribute to a deeper quantitative understanding of the nature and impact of scale issues in spatial analysis, and will offer novel solutions to fundamental data integration problems in Geography. In addition, this project will enhance the proper and cost-effective utilization of geospatial data in numerous and diverse scientific disciplines and user communities, such as geographers, developers of geographic information systems packages (commercial or public domain), urban planners, atmospheric scientists, hydrologists, environmental engineers, statisticians, geologists, and ecologists. Last, the bottom-up nature of the downscaling tools that will be developed in this project will offer a means for accounting for scientific knowledge regarding processes operating at the finest spatial resolution of interest. This characteristic will enable truly interdisciplinary collaborations between geographers and other domain-specific scientists that study spatial processes at precisely such fine resolutions.