The Impact of Improved Topographic Resolution on the Distribution of Terrain Spectra and Grid-Size Selection for Mesoscale Models

Spectral analysis of terrain height variance is conducive to quantitatively study the terrain characteristics and grid-size selection for mesoscale models. Improved topographic resolutions can lead to the variations of terrain characteristics and the appropriate grid size for a fixed analyzed area. Spectral methods of one-dimensional weighted average and arithmetic mean were used to investigate the specific impact on the distribution of terrain spectra and grid-size selection for mesoscale models of the landslide-prone areas in western Sichuan. The results indicate that the maximum spectral energy (the variance of the terrain height series) of 30″ resolution (R1) is larger than that of 90 m resolution (R2), indicating a gentler undulation of terrain for R2. The spectral curve of R2 almost overlaps with that of R1 because the difference in topographic resolution does not change the dominant distribution of the topography. Their differing spectral energies at longer wavelengths are related to the majority of grid points of R2 distributed at shorter wavelength bands. A least squares fit in the form of $S=a{\lambda }^b$ was used to estimate the decreasing trend of the spectral distribution. The difference in spectral slope between R1 and R2 is mainly caused by the spectral energy of R2 at shorter wavelengths. The exponent b is connected with grid-size selection for mesoscale models. A universal horizontal grid size of 2.5 km for R1 and 1.9 km for R2 are required to resolve 95% of the terrain height variance for a mesoscale model application without a subgrid-scale parameterization. The simulation tests show that the improved topographic resolution appears to perform better in reproducing precipitation, which is probably related to the finer details of the terrain recognized by the model.