AM–GM Algorithm for Evaluating, Analyzing, and Correcting the Spatial Scaling Bias of the Leaf Area Index

Abstract

The leaf area index (LAI) is a crucial variable in climate, ecological, and land surface modeling. However, the estimation of the LAI from coarse-resolution remote sensing data can be affected by the spatial scaling bias, which arises from the nonlinearity of retrieval models and the heterogeneity of the land surface. This study provides an algorithm named Arithmetic Mean and Geometric Mean (AM–GM) to correct the spatial scaling bias. It is established based on negative logarithmic functions and avoids second-order stationarity. In this algorithm, relationships are derived between the scaling bias of LAI and the arithmetic and geometric means of directional gap probability for two commonly used remote sensing models, the Beer–Lambert law and a semi-empirical transfer function, respectively. According to the AM–GM algorithm, the expression representing the model nonlinearity is derived and utilized for the analysis of LAI scaling bias. Furthermore, the AM–GM algorithm is simplified by a linear relationship, which is constructed between two quantities related to the directional gap probability between two specific resolutions. Two scenes simulated by the LargE-Scale remote sensing data and image Simulation framework (LESS) model and three sites are used to evaluate the proposed algorithm and analyze the scaling bias of LAI. The validation results show that the AM–GM algorithm provides accurate correction of LAI scaling bias. The analyses based on the AM–GM algorithm demonstrate that the scaling bias of LAI increases with the increase in the LAI value, with stronger surface heterogeneity and coarser spatial resolution. The validation results of the simplified AM–GM algorithm demonstrate that at the Sud-Ouest site, the absolute value of the bias for the estimated LAI decreases from 0.10, 0.22, 0.29, and 0.31 to 0.04, 0.01, 0.04, and 0.05 at 200 m, 500 m, 1000 m, and 1500 m resolutions, respectively. In conclusion, the proposed algorithm is effective in the analysis and correction of the scaling bias for coarse-resolution LAI.

Keywords

• leaf area index (LAI)
• spatial scaling bias
• coarse resolution
• Arithmetic Mean and Geometric Mean (AM–GM)
• Taylor series expansion method (TSEM)