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.

The terrain of Changbai Mountain has great influence on the distribution of atmospheric flows and the occurrence and development of precipitation. This study quantitatively analyzes the regional characteristic of topographic perturbations and the relationship between terrain, wind and precipitation in Changbai Mountain region, by using a spectral analysis of the two-dimensional discrete cosine transform. Three domains with relatively heavy summer precipitation are selected as the study region. The results indicate that the overall terrain of Changbai Mountain region exhibits anisotropic characteristics. The terrain spectra of domain B are less than those of domain A and C across the whole wavelength (λ) bands, indicating that the large-scale topographic perturbations of domain B are relatively weak. The largest topographic spectral peak of domain C shows the most pronounced undulation of terrain among the three domains. The dominant wavelengths of terrain height variance for domain A and C, both close to the respective maximum wavelengths, indicate more prominent large-scale topographic perturbations. For domain A, the variation of the precipitation spectra is consistent with that of the wind spectra at the wavelength bands of λ < 390 km, showing a high correlation between wind field and the occurrence of rainfall. The inverse relationship at larger wavelengths indicates that multiple factors contribute to the occurrence of rainfall. For domain B, there is consistency in the fluctuations of terrain spectra, precipitation spectra, and wind spectra at the wavelength bands of λ < 278.3 km, implying that the smaller-scale terrain has an important effect on the occurrence of summer precipitation. For domain C, the variations of terrain spectra, precipitation spectra, and wind spectra are almost consistent across the whole wavelength bands, indicating that the large-scale terrain and minor terrain both play a crucial role in atmospheric uplift and the occurrence and development of summer rainfall.

The terrain of Changbai Mountain has great influence on the distribution of atmospheric flows and the occurrence and development of precipitation. However, quantitative studies on the real terrain characteristics and the terrain effect on precipitation distribution in this region are scant at present. This study quantitatively analyzes the regional characteristic of topographic perturbations and the relationship between terrain, wind, and precipitation in Changbai Mountain region by using a spectral analysis of the two-dimensional discrete cosine transform. Three domains with relatively heavy summer precipitation are selected as the study region. The results indicate that the overall terrain of the Changbai Mountain region exhibits anisotropic characteristics. The terrain spectra of domain B are less than those of domains A and C across the whole wavelength (λ) bands, indicating that the large-scale topographic perturbations of domain B are relatively weak. The largest topographic spectral peak of domain C shows the most pronounced undulation of terrain among the three domains. The dominant wavelengths of terrain height variance for domains A and C, both close to the respective maximum wavelengths, indicate more prominent large-scale topographic perturbations. For domain A, the variation of the precipitation spectra is consistent with that of the wind spectra at the wavelength bands of λ < 390 km, showing a high correlation between wind field and the occurrence of rainfall. The inverse relationship at larger wavelengths indicates that multiple factors contribute to the occurrence of rainfall. For domain B, there is consistency in the fluctuations of terrain spectra, precipitation spectra, and wind spectra at the wavelength bands of λ < 278.3 km, implying that the smaller-scale terrain has an important effect on the occurrence of summer precipitation. For domain C, the variations of terrain spectra, precipitation spectra, and wind spectra are almost consistent across the whole wavelength bands, indicating that the large-scale terrain and minor terrain both play a crucial role in atmospheric uplift and the occurrence and development of summer rainfall.