A Directional Gradient-Curvature Method for Gap Filling of Gridded Environmental Spatial Data with Potentially Anisotropic Correlations

TL;DR

The paper presents the Directional Gradient-Curvature (DGC) method, a new gap-filling approach for gridded environmental data that captures anisotropic correlations efficiently using data-conditioned simulations.

Contribution

The DGC method introduces a novel objective function and simulation approach for gap filling, effectively handling anisotropy and non-stationarity in large spatial datasets.

Findings

DGC performs competitively with established methods in cross-validation tests.

DGC effectively captures anisotropic and non-stationary spatial correlations.

The method is computationally efficient and suitable for large remote sensing datasets.

Abstract

We introduce the Directional Gradient-Curvature (DGC) method, a novel approach for filling gaps in gridded environmental data. DGC is based on an objective function that measures the distance between the directionally segregated normalized squared gradient and curvature energies of the sample and entire domain data. DGC employs data-conditioned simulations, which sample the local minima configuration space of the objective function instead of the full conditional probability density function. Anisotropy and non-stationarity can be captured by the local constraints and the direction-dependent global constraints. DGC is computationally efficient and requires minimal user input, making it suitable for automated processing of large (e.g., remotely sensed) spatial data sets. Various effects are investigated on synthetic data. The gap-filling performance of DGC is assessed in comparison with established classification and interpolation methods using synthetic and real satellite data, including a skewed distribution of daily column ozone values. It is shown that DGC is competitive in terms of cross validation performance.