State-space approach to evaluate spatial variability of field measured soil water status along a line transect in a volcanic-vesuvian soil

Abstract. Unsaturated hydraulic properties and their spatial variability today are analyzed in order to use properly mathematical models developed to simulate flow of the water and solute movement at the field-scale soils. Many studies have shown that observations of soil hydraulic properties should not be considered purely random, given that they possess a structure which may be described by means of stochastic processes. The techniques used for analyzing such a structure have essentially been based either on the theory of regionalized variables or to a lesser extent, on the analysis of time series. This work attempts to use the time-series approach mentioned above by means of a study of pressure head h and water content θ which characterize soil water status, in the space-time domain. The data of the analyses were recorded in the open field during a controlled drainage process, evaporation being prevented, along a 50 m transect in a volcanic Vesuvian soil. The isotropic hypothesis is empirical proved and then the autocorrelation ACF and the partial autocorrelation functions PACF were used to identify and estimate the ARMA(1,1) statistical model for the analyzed series and the AR(1) for the extracted signal. Relations with a state-space model are investigated, and a bivariate AR(1) model fitted. The simultaneous relations between θ and h are considered and estimated. The results are of value for sampling strategies and they should incite to a larger use of time and space series analysis.