Nyquist–Shannon Guidance for Linking Sampling Adequacy and Predictive Uncertainty in Geospatial Mapping

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Lu, Meng ; Wang, Jiong:
Nyquist–Shannon Guidance for Linking Sampling Adequacy and Predictive Uncertainty in Geospatial Mapping.
In: Mathematical Geosciences. (15 Juni 2026) .
ISSN 1874-8953
DOI: https://doi.org/10.1007/s11004-026-10307-8

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Abstract

Modeling geospatial patterns of environmental variables at increasingly fine resolutions and broader scales highlights the reliability of map products built from sparse samples as a critical issue in scientific research and practical applications. It is desirable to attribute predictive uncertainty to identifiable sources, namely, sampling density, data noise, and model limitations. To approach this, we examine whether a spatial process imposes a minimum achievable predictive variance as a function of sampling density. We first present a transition from the geometric/spatial domain to the spectral domain, linking spatial autocorrelation to bandwidth frequency through the spectrum of the Gaussian radial basis function (RBF) kernel. We then apply the Nyquist–Shannon sampling theorem to link sampling rate and predictive uncertainty. The Gaussian RBF kernel is used as a demonstration vehicle instead of a restrictive assumption. We derive the effective bandwidth as a function of the kernel length scale and subsequently generalize this to a tolerance-based prediction error floor that quantifies unresolved high-frequency variance captured by the kernel for a given sampling rate. A practical implication is that sampling density induces fundamental, model-independent limits on achievable accuracy and resolution. Furthermore, this work provides a quantitative interpretation of kernel length scale, linking predictive variance to resolvable spectral energy, and provides guidance on sampling sufficiency, resolution limits, and uncertainty interpretation. Using both simulated fields and remote sensing imagery as real-world data, one- and two-dimensional experiments with and without covariates show that the Nyquist-based limits provide practical guidance for assessing sampling adequacy and quantifying predictive uncertainty in geospatial modeling.