Impact of nonlinearity and discontinuity on the spatial scaling effects of the leaf area index retrieved from remotely sensed data

Abstract

This article addresses the major scaling problems in leaf area index (LAI) retrieval for a heterogeneous surface associated with (1) the nonlinearity in the relationships between remotely sensed reflectances and LAI products, (2) the discontinuity caused by the mixture of contrasting cover types that is categorized as the dominating type within a large-scale pixel, and (3) the algorithm for the dominant cover type being used for the retrieval of the LAI in that large-scale mixed pixel. Through mathematical analysis, two scaling models (a component-based model and a pixel-based model) are proposed on the basis of the Taylor series expansion with the corresponding textural and contextural parameters (i.e. variance–covariance matrices and component fractions) to correct for the scaling effects among LAI products at different scales. These models express the magnitude of the scaling effects for the nonlinear and discontinuous situations as a function of (1) the degree of nonlinearity quantified by the second derivative of the retrieval function, (2) the spatial heterogeneity quantified by variance–covariance matrices, and (3) the component fractions in the large-scale mixed pixel. To evaluate the proposed scaling models, a scaling correction test is performed and analysed on a SPOT (Système Pour l'Observation de la Terre) image for two vegetation types. The component fractions have proven to be the main reason for the scaling effects in a mixed pixel. Compared to the results before scaling, using either of the two proposed models greatly reduces the retrieval errors that the scaling effects cause. The relative scaling effects of the LAI may be up to 55% in an uncorrected, large-scale mixed pixel. However, the relative scaling errors can be as low as 2% with the intra-component textural parameters and about 13% with the intra-pixel textural parameters. Because the scaling effects can be corrected for the spatial heterogeneity caused either by density changes within the same cover or by cover type changes, our work indicates that the proposed scaling models are promising and feasible.