WATERRESOURCES RESEARCH, VOL. 27, NO. 7, PAGES 1623-1636, JULY 1991 Analysis of Soil WaterDynamics in Time andSpace by Use of PatternRecognition TIELIN ZHANG AND RONNY BERNDTSSON Department of Water Resources Engineering, University of Lund,Lurid,Sweden Thispaper presents a method to use pattern recognition in theanalysis of soil water dynamics in timeandspace simultaneously. Space-time correlation structures aregenerated by use of a numerical modelfor the one-dimensional unsaturated flow equation. By applying the method to various soil parameter combinations (unsaturated hydraulic conductivity and dispersion coefficient) and length of infiltration periods it is shown how space-time dependence of soil water changes. Themethod clearly visualizes effects of changes in infiltrated input andsoilheterogeneities which arenot noticeable in the original soilwatertimeseries. Application of themethod to field data reveals small-scale heteroge- neities andvertical andhorizontal variability in hydraulic properties. The method possesses special advantages when analyzing time- and space-dependent properties simultaneously. Sincethe method gives a statistical measure of the dependent property that varies withinthe space-time field, it canbe used to interpolate the fields to points where observations are not available, to estimate spatial or temporal averages from discrete observations, and to define regions (spatial or temporal) where observations are the most efficient. INTRODUCTION Soilwater and its spatial and temporal characteristics are the key factors which govern evaporation, infiltration, groundwater recharge, soil erosion, vegetation distribution, etc.Because of the inherent variability of soils and subse- quent difficultiesinvolved in treating this variability in hy- drological applications, soil scientists and hydrologists dur- ing recent decades have tended to handle the soil heterogeneity in a probablistic framework [e.g., Neuman, 1982; Gelhat, 1984; Shumway et al., 1989]. The spatial correlation structure and the correlation scale are fundamen- tal elements in the analysis of subsurface heterogeneities withina stochastic approach [e.g., Gelhar, 1986; Dagan, 1986]. Soil water dynamics and corresponding correlationstruc- tures extend, however, not only in space but also in time. Substantial research efforts have, e.g., tried to demonstrate the temporal persistence or time stability of spatial soilwater patterns[e.g., Vachaud et al., 1985; Kachanoski and de Jong, 1988]. These results are, however, not indisputable [e.g., Zhangand Berndtsson, 1988; Loagueand Gander, 1990]. It is doubtful that spatial infiltration properties will persist in time over a catchment area with substantial differences in soil type, vegetational pattern,agricultural practices, etc.Time stability may, however, be a function of spatial scale as shown by Kachanoski and de Jong [1988]. This implies, however, that variability patterns of soil water need to be analyzed simultaneously in bothtimeand space [e.g., Zhang etal., 1988], e.g., inorder tominimize sampling efforts. Numerous analytical and numerical models have been developed to simulate the soil watertransport andthe interaction between surface and groundwater [e.g., Nielsen et al.,1986]. However, it often appears that the parameters used in these models, such as the unsaturated hydraulic conductivity and the dispersion coefficient, arehighly non- Copyright 1991 by the American Geophysical Union. Paper number 9 !WR00436. 0043-1397/9 !/9!WR-00436505.00 linear and difficult to estimate. This becomes especially true when spatial heterogeneities are significant. In this sense there is a need to find new and better methods to determine the correlationstructure of soil water transport and govern- ing hydraulicparameters [Gelhat, 1986]. Similarly, there is a need to analyze simultaneous spatial and temporal proper- ties of soils to be used in probabilistic soil water transport models. Pattern recognitionor pattern analysis possesses special advantages when analyzing time-dependent properties in space [Fu, 1982]. Patterns usually imply a physical or mathematical two-dimensional field and a dependent prop- erty that varies within this field [Snyder and Thomas, 1987; Berndtsson, 1988]. Pattern analysis in hydrological investi- gations is a rather recent application [Panu and Unny, 1980a, b, c]. Pattern analysis of hydrological time series embraces both deterministic components and uncertainty together, thus characterizingthe hydrological phenomena as a whole rather than as individual parts [Macinnes and Unny, 1986; Snyder and Thomas, 1987]. The objective of this paper is to demonstrate a statistical method which involves pattern recognition and in which it is possible to analyzetemporaland spatial soilwater dynamics simultaneously.It is shown how effects of nonlinearly vary- ing soil properties and heterogeneous soil structures can be evaluated. By use of a numerical model for the one- dimensional unsaturated flow equation the scope of the method is illustrated in the opening sections of the paper. In the later sections,the method is applied to field data. METHODOLOGY Dynamic propertiesand space-timedependence of soil water transport may be investigated by use of space-time correlation analysis. By introducing both a time lag and a spatial lag depending on the depthin the calculation of the covariances between consecutive pairwise combined time seriesof soil water content, it is possible to trace a pulse of infiltrated water downward through the soil structure in the space-time correlation field. If evapotranspiration is disre- 1623