Multivariate geostatistical approach to space-time data analysis (original) (raw)
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Spatio-temporal geostatistical analyses of runoff and precipitation
… of the fifth European conference on …, 2005
In this paper catchments are conceptualised as linear space-time filters. Catchment area A is interpreted as the spatial support and the catchment response time T is interpreted as the temporal support of the runoff measurements. These two supports are related by T~Aκ which embodies the space-time connections of the rainfall-runoff process from a geostatistical perspective. To test the framework, spatio-temporal variograms are estimated from about 30 years of quarter hourly precipitation and runoff data from about 500 catchments in Austria. In a first step, spatio-temporal variogram models are fitted to the sample variograms for three catchment size classes independently. In a second step, variograms are fitted to all three catchment size classes jointly by estimating the parameters of a point/instantaneous spatio-temporal variogram model and aggregating (regularising) it to the spatial and temporal scales of the catchments. The exponential, Cressie-Huang and product-sum variogram models give good fits to the sample variograms of runoff with dimensionless errors ranging from 0.02 to 0.03, and the model parameters are plausible. This indicates that the first order effects of the spatio-temporal variability of runoff are indeed captured by conceptualising catchments as linear space-time filters. The scaling exponent κ is found to vary between 0.3 and 0.4 for different variogram models.
Water Resources Research, 2002
The objective of this paper is to implement an original method for spatial and multivariate data, combining a method of three-way array analysis (STATIS) with geostatistical tools. The variables of interest are the monthly amounts of rainfall in the Nordeste region of Brazil, recorded from 1937 to 1975. The principle of the technique is the calculation of a linear combination of the initial variables, containing a large part of the initial variability and taking into account the spatial dependencies. It is a promising method that is able to analyze triple variability: spatial, seasonal, and interannual. In our case, the first component obtained discriminates a group of rain gauges, corresponding approximately to the Agreste, from all the others. The monthly variables of July and August strongly influence this separation. Furthermore, an annual study brings out the stability of the spatial structure of components calculated for each year.
On the physical geometry concept at the basis of space/time geostatistical hydrology
Advances in Water Resources, 2000
The objective of this paper is to show that the structure of the spatiotemporal continuum has important implications in practical stochastic hydrology (e.g., geostatistical analysis of hydrologic sites) and is not merely an abstract mathematical concept. We propose that the concept of physical geometry as a spatiotemporal continuum with properties that are empirically de®ned is important in hydrologic analyses, and that the elements of the spatiotemporal geometry (e.g., coordinate system and space/time metric) should be selected based on the physical properties of the hydrologic processes. We investigate the concept of space/time distance (metric) in various physical spaces, and its implications for hydrologic modeling. More speci®cally, we demonstrate that physical geometry plays a crucial role in the determination of appropriate spatiotemporal covariance models, and it can aect the results of geostatistical operations involved in spatiotemporal hydrologic mapping.
Studying the spatial structure evolution of soil water content using multivariate geostatistics
Journal of Hydrology, 2005
Soil water content varies widely in space and time as the soil is wetted by rain, drained by gravity and dried by evaporation and root extraction. Consequently there has been increased interest in modelling and measuring soil water content evolution at varying spatial scale.The objective of this study was to examine the utility of multivariate geostatistical models for characterising the spatio-temporal variability of soil water content. This approach uses the set of t sampled times as a realisation of t correlated random functions. Estimation of soil water content involved fitting an anisotropic linear model of coregionalization to the t(t+1)/2 simple and cross variograms consisting of four spatial structures: a nugget effect, an isotropic structure and two anisotropic structures in E–W and N–S directions.Variography revealed a high temporal correlation between the soil water contents measured at different times, declining as the interval between the observations increases. The autumn rain events on dry soil produced an erratic distribution pattern of water in the soil. Inspection of the cokriged maps of soil water revealed the dynamics of soil water redistribution owing to evapotranspiration or rainfall.
Geostatistical Analysis of Spatial and Temporal Variations of Groundwater Level
Environmental Monitoring and Assessment, 2006
Groundwater and water resources management plays a key role in conserving the sustainable conditions in arid and semi-arid regions. Applying management tools which can reveal the critical and hot conditions seems necessary due to some limitations such as labor and funding. In this study, spatial and temporal analysis of monthly groundwater level fluctuations of 39 piezometric wells monitored during 12 years was carried out. Geostatistics which has been introduced as a management and decision tool by many researchers has been applied to reveal the spatial and temporal structure of groundwater level fluctuation. Results showed that a strong spatial and temporal structure existed for groundwater level fluctuations due to very low nugget effects. Spatial analysis showed a strong structure of groundwater level drop across the study area and temporal analysis showed that groundwater level fluctuations have temporal structure. On average, the range of variograms for spatial and temporal analysis was about 9.7 km and 7.2 months, respectively. Ordinary and universal kriging methods Keywords water resources management. groundwater level fluctuations. geostatistics. kriging. spatial analysis. temporal analysis
Problems in space-time kriging of geohydrological data
Mathematical Geology, 1990
Spatiotemporal variables constitute a large class of geohydrological phenomena. Estimation of these variables requires the extension of geostatistical tools into the space-time domain. Before applying these techniques to space-time data, a number of important problems must be addressed. These problems can be grouped into four general categories: (1) fundamental differences with respect to spatial problems, (2) data characteristics, (3) structural analysis including valid models, and (4) space-time kriging. Adequate consideration of these problems leads to more appropriate estimation techniques for spatiotemporal data.
Progress in Physical Geography, 2002
Based on a review of research, the linkages between distributed hydrological modelling (DHM) remote sensing (RS) and geographical information system (GIS) techniques, coupled with geomorphological knowledge are discussed. While presenting characteristics of the models, techniques, and supporting analytical tools of geographical hydrology, the emphasis is on the estimation of hydrological variables. The first is limited to the spatialization and integration of low resolution meteorological data with hydrological models in a GIS environment. The second includes research in the calculation of precipitation, evapotranspiration, radiation, etc., from the digital analyses of remote sensing data, to feed either lumped or spatially distributed models. The third links the tools of GIS and RS with hydrological modelling; usually it makes intensive use of the tools of GIS for several scales of spatial modelling. The last group integrates GIS, RS and hydrological modelling supported by the delimitation and characterization of environmental units, generally to detailed and semidetailed scales.
Space–time modeling of rainfall data
Environmetrics, 2004
Climate variables assume non-negative values and are often measured as zero. This is just the case when the rainfall level, in the dry season, is measured in a specified place. Then, the stochastic modeling demands the inclusion of a probability mass point at the zero level, and the resulting model is a mixture of a continuous and a Bernoulli distribution.