Academic journal article Geographical Analysis

Geostatistical Prediction and Simulation of Point Values from Areal Data

Academic journal article Geographical Analysis

Geostatistical Prediction and Simulation of Point Values from Areal Data

Article excerpt

The spatial prediction and simulation of point values from areal data are addressed within the general geostatistical framework of change of support (the term support referring to the domain informed by each measurement or unknown value). It is shown that the geostatistical framework (i) can explicitly and consistently account for the support differences between the available areal data and the sought-after point predictions, (ii) yields coherent (mass-preserving or pycnophylactic) predictions, and (iii) provides a measure of reliability (standard error) associated with each prediction. In the case of stochastic simulation, alternative point-support simulated realizations of a spatial attribute reproduce (i) a point-support histogram (Gaussian in this work), (ii) a point-support semivariogram model (possibly including anisotropic nested structures), and (iii) when upscaled, the available areal data. Such point-support-simulated realizations can be used in a Monte Carlo framework to assess the uncertainty in spatially distributed model outputs operating at a fine spatial resolution because of uncertain input parameters inferred from coarser spatial resolution data. Alternatively, such simulated realizations can be used in a model-based hypothesis-testing context to approximate the sampling distribution of, say, the correlation coefficient between two spatial data sets, when one is available at a point support and the other at an areal support. A case study using synthetic data illustrates the application of the proposed methodology in a remote sensing context, whereby areal data are available on a regular pixel support. It is demonstrated that point-support (sub-pixel scale) predictions and simulated realizations can be readily obtained, and that such predictions and realizations are consistent with the available information at the coarser (pixel-level) spatial resolution.

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Introduction

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 predictions of climate-related variables produced by global circulation models (GCMs) 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. In addition, it is often desirable to evaluate the sampling distribution, of, say, the correlation coefficient between two data sets of different spatial resolution for hypothesis testing purposes. In an exposure assessment setting, for example, one might be interested in the significance of the correlation between (point-support) air-quality observations and (areal-support) relative humidity predictions derived from a regional climate model. In such cases, the latter areal-support predictions must also be transformed to the point-support level, because any significance testing should be performed at that level. For a recent review of general scale issues in geography and some geostatistical solutions, the reader is referred to Atkinson and Tate (2000).

The transformation of coarse spatial resolution data to finer spatial resolution maps is often termed as downscaling, and it is a particular case of change of support (the term support referring to the domain informed by each measurement); see, for example, Gotway and Young (2002). In this article, we focus on a particular case of downscaling, that of predicting point-support values from areal data, a procedure also termed as area-to-point interpolation. Most existing methods for area-to-point interpolation in geography (e.g., Lam 1983), however, tend to ignore one or more of the following critical issues: (i) the explicit account of the different data supports, (ii) the coherence of predictions: for example, the areal-average of point predictions within any areal support should be equal to the corresponding areal datum (if the latter is defined as the average of point values within its support, and is assumed error-free), and (iii) the assessment of uncertainty regarding the resulting point predictions. …

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