Spatial Up-Scaling Correction for Leaf Area Index Based on the Fractal Theory

The scaling effect correction of retrieved parameters is an essential and difficult issue in analysis and application of remote sensing information. Based on fractal theory, this paper developed a scaling transfer model to correct the scaling effect of the leaf area index (LAI) estimated from coarse spatial resolution image. As the key parameter of the proposed model, the information fractal dimension (D) of the up-scaling pixel was calculated by establishing the double logarithmic linear relationship between D-2 and the normalized difference vegetation index (NDVI) standard deviation (sigma(NDVI)) of the up-scaling pixel. Based on the calculated D and the fractal relationship between the exact LAI and the approximated LAI estimated from the coarse resolution pixel, a LAI scaling transfer model was established. Finally, the model accuracy in correcting the scaling effect was discussed. Results indicated that the D increases with increasing sigma(NDVI), and the D-2 was highly linearly correlated with sigma(NDVI) on the double logarithmic coordinate axis. The scaling transfer model corrected the scaling effect of LAI with a maximum value of root-mean-square error (RMSE) of 0.011. The maximum absolute correction error (ACE) and relative correction error (RCE) were only 0.108% and 8.56%, respectively. The spatial heterogeneity was the primary cause resulting in the scaling effect and the key influencing factor of correction effect. The results indicated that the developed method based on fractal theory could effectively correct the scaling effect of LAI estimated from the heterogeneous pixels.