Scale variance analysis coupled with Moran's I scalogram to identify hierarchy and characteristic scale

Scale variance is highly sensitive to multi-scale patterns of variables, which is advantageous in identifying spatial hierarchy and characteristic scale(s). However, the significance of peak(s) in scale variance cannot be statistically tested, and different spatial patterns may be obtained when different zoning systems are used to calculate scale variance. To address these two problems, this study compared the scale levels with peaks in scale variance and the scale levels at which there were breaks in the nature of spatial autocorrelation as identified by shifts in Moran's I scalogram. The estimates for three simulated landscapes showed that accordance between scale levels identified employing the two methods can be used to evaluate the significance of peaks in scale variance and choose a more reasonable zoning system. The approach of scale variance analysis coupled with Moran's I scalogram was also applied to the Xilin River Basin of Inner Mongolia, China. The most vital characteristic scale (64 x 32 km) identified for the growing-season net ecosystem productivity (NEP) of the basin was validated by other spatial pattern analysis methods such as semi-variogram, Moran's I correlogram, and wavelet variance analyses, and the directionality of the chosen zoning systems was found to be similar to the orientation of actual dominant vegetation type patches. The results demonstrate that Moran's I scalogram can be used to improve the interpretation of the results of scale variance analysis and increase the reliability of scale variance analysis for landscapes having a repetitive patch pattern or gradient variation and that the proposed approach is suitable for identifying the hierarchy and the characteristic scales of patterns or processes. In summary, this study used a simple approach to solve two problems in scale variance analysis, thereby improving the methodology and enhancing the theoretical basis of multi-scale analysis.