Modelos de espaço de estados e análise em Wavelets no estudo do relacionamento entre atributos físico-hídricos do solo e atributos topográficos em escala de bacia hidrográfica

Abstract

The statistical tools that consider the position and the possible dependence between the observations of variables in the field have been applied at small scales and not at watershed scales. Thus, this study aimed to evaluate the potential of statistical tools from the Time Series Analysis to characterize and identify the spatial variability structure of soil hydro-physical and topographic attributes as well as to study the relationship between them in the Fragata River Watershed (FRW), Pelotas, Southern Brazil. From the Passo dos Carros control section (FRW - PPC) a 15 km-spatial transect was established in which 100 points, 150 m equidistantly spaced, were demarcated. Undisturbed and disturbed soil samples were collected in the 0-0.20 m soil layer to determine textural fractions, soil bulk density, total porosity, macroporosity, saturated soil hydraulic conductivity and soil organic carbon. Using the hydrologically consistent digital elevation model (MDEHC), topographic attributes were obtained at each sampling point, namely: elevation, slope, and aspect. Classical statistics were applied to all data sets to calculate position, dispersion, and shape measures of each data set. The Kolmogorov-Smirnov test was applied to verify the normality of each data set. To characterize and identify the spatial variability structure of each attribute along the spatial transect, the autocorrelation function was calculated. The spatial correlation between two variables was calculated using the cross-correlation function. The spatial relationship among variables was studied by state-space models and classical multiple regression models. The characterization and quantification of the possible multi-spatial correlations among all attributes were evaluated through Wavelet analysis. It was possible to conclude that the state-space approach proved to be an effective tool to describe the spatial relationships among all attributes as compared to multiple regression models at watershed scale. Further, Wavelet analysis showed to be a promising tool to characterize and quantify the multispatial correlations among all soil hydro-physical and topographic attributes along the 15 km-FRW spatial transect. The substitution of the soil macroporosity by the land-use system as a potential explanatory variable to represent the soil structure in the state-space models should be better assessed in future studies at watershed scale.