Multidimensional Analysis of Snow Cover Data in South Dakota Diversity of Landscapes

Abstract

Snow distribution in SD was studied with Factor Analysis (FA) of monthly total snowfall [in]. The long-term data obtained from the High Plains Regional Climate Center were used for the territory of South Dakota. The perspective for creating an Atlas of Climate and Water Resources for SD directed this study of total monthly snowfall with connection to landscape diversity.The initial matrix {Xn*p} where n is number of stations and p is number of variables of monthly average for period of observations. The maximum number of stations n with mutual interval of observations for SD is equal 93 (n=93). These stations have mutual time interval of 18 years observations (1952-53 – 1969-70). Total monthly snowfall has data for p=10 is number of months with observation and p=11 is number of months with observations with total snowfall for the winter season. The second matrix contains proportions of total monthly snowfall to total annual (proportion is the monthly total snowfall divided on total seasonal snowfall); the number of rows n and the number of variable are the same as in the first case: n=93 and p=10, 11.The average annual sum of total monthly snowfall (September-June) for SD 34.64 in obtained on 93 stations for 1952-1970, the median is 31.84 from the same data; ranged from 10.21 to 152.27 from the same data. The most variable month is April with average4.89 [in], median 3.67, min 0.75 and max 33.18; the average proportion for April is 0.13, min 0.03 and max 0.24. The averages for November to April grow as sequence: 3.60, 5.70, 4.88, 7.25, 7.46 and 4.89 the variability of those months has sequence: 2.49 2.52 2.25 3.33 3.53 and 4.87. The Pearson coefficient of correlation for the monthly snowfall averages from September to June with annual sum has sequence: 0.83, 0.92, 0.96, 0.92, 0.93, 0.93, 0.94, 0.92, 0.90, and 0.82; the correlation for the monthly proportions from September to June with annual sum has sequence: 0.38, 0.45, -0.01, -0.32, -0.33, -0.21, -0.15, 0.27, 0.36, and 0.35.The FA of both initial matrixes had extracted two factors for monthly observations with incorporation of 93 % of total variability of the data in the model; and three factors model with 70% variability of data for monthly proportions. The two factor groups in model of observed snowfall contain winter months (Dec – Mar) and all other. The model of monthly proportions with tree factor groups include winter months in two group and combination of spring and fall months in third. The factor scores presented as maps for SD allow trace distribution of factor groups of monthly snowfall patterns for two models through the territory of SD. The combination of factor scores distribution for two models is in a good agreement with main landscape regions and subregions of SD.