Further validation for the scaling rule of the spatial independent variables on the basis of the image assimilation and the simultaneous experiment

In the article, one universal formula presented by RH Zhang (2004) is validated based on the TM image assimilation and the surface simultaneous experiment data which was measured in remote sensing experimental field of Xiaotangshan of Beijing. Several scales was used to study: the first is the experimental field (2 m × 2 m), another is a 30 m × 30 m TM image validated by the experiment data, the others are images degraded using the Landsat TM image. The scaling rule of independent variables defined as those surface parameters whose values are not affected by its neighboring pixels but depend on the characteristics of the pixel itself, such as NDVI, albedo, LAI, surface emissivity and apparent thermal inertia (ATI). They are investigated using the areas composed by farmland, the areas of the same size but different water area fractions, within which the difference of the surface characteristics are obvious. Generally, the independent variables can be expressed as the form of x/y. Therefore, when degrading these parameters, the scaling rule have close relationship with the numerator x and the denominator y. In terms of our analysis, when the denominator y_i is the same for the aggregated pixels, there is no scaling difference. However, when y_i is variable, the scaling difference is affected by the magnitude of x and y, and the variance of x_i (varx) and y_i (vary) divided by the average x_i (meanx) and y_i (meany) can reduce this effect; for a moderate heterogeneous surface, the scaling difference of NDVI, LAI, emissivity and ATI can be ignored, however, for obvious contrasting surface, the scaling difference can lead to large errors; when the meanx, meany, varx and vary are in the same magnitude, it can be considered that there is the same scaling difference regardless of resolution.