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Directional gap probability or gap fraction is a basic parameter in the optical remote sensing modeling. Although some approaches have been proposed to estimate this gap probability from remotely sensed measurements, few efforts have been made to investigate the scaling effects of this parameter. This paper analyzes the scaling effect through aggregating the high-resolution directional gap probability (pixel size of 20 meters) estimated from leaf area index (LAI) images of VALERI database by means of Beer's law and introduces an extension of clumping index, Ĉ, to compensate the scaling bias. The results show that the scaling effect depends on both the surface heterogeneity and the nonlinearity degree of the retrieved function. Analytical expressions for the scaling bias of gap probability and Ĉ are established in function of the variance of LAI and the mean value of LAI in a coarse pixel. With the VALERI dataset, the study in this paper shows that relative scaling bias of gap probability increases with decreasing spatial resolution for most of land cover types. Large relative biases are found for most of crops sites and a mixed forest site due to their relative large variance of LAI, while very small biases occur over grassland and shrubs sites. As for Ĉ, it varies slowly in the pure forest, grassland and shrubs sites, while more significantly in crops and mixed forest.

Directional gap probability or gap fraction is a basic parameter in the optical remote sensing modeling. Although some approaches have been proposed to estimate this gap probability from remotely sensed measurements, few efforts have been made to investigate the scaling effects of this parameter. This paper analyzes the scaling effect through aggregating the high-resolution directional gap probability (pixel size of 20 meters) estimated from leaf area index (LAI) images of VALERI database by means of Beer's law and introduces an extension of clumping index, Ĉ, to compensate the scaling bias. The results show that the scaling effect depends on both the surface heterogeneity and the nonlinearity degree of the retrieved function. Analytical expressions for the scaling bias of gap probability and Ĉ are established in function of the variance of LAI and the mean value of LAI in a coarse pixel. With the VALERI dataset, the study in this paper shows that relative scaling bias of gap probability increases with decreasing spatial resolution for most of land cover types. Large relative biases are found for most of crops sites and a mixed forest site due to their relative large variance of LAI, while very small biases occur over grassland and shrubs sites. As for Ĉ, it varies slowly in the pure forest, grassland and shrubs sites, while more significantly in crops and mixed forest.