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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Journal of the American Water Resources Association 18 (1982), S. 0 
    ISSN: 1752-1688
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: : Deep percolation rates are normally estimated from a water balance. Results are presented of a study undertaken to evaluate three alternative methods of estimating percolation below the root zone when knowledge about the history of applied water and evapotranspiration are not available. The alternative methods are: 1) use of Darcy's equation to calculate deep percolation rate; 2) measurement of the soil temperature prof and calculation of the deep percolation rate from the shape of the temperature depth curve; and 3) measurement of the tritium concentration in the soil water and its relationship to the history of the tritium concentration in rainfall.At the principal study site, the Darcy velocity of flow ranged from 9 cm per year determined by the temperature method, to 40 cm per year determined by the tritium method. Darcy's equation to calculate seepage rates resulted in an estimation of deep seepage of 18 cm per year. An average deep percolation rate at the principal study site of 22 cm per year was determined using the average of all three methods. Results for other sites based on the temperature method indicated a lower seepage rate.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 6 (1991), S. 739-744 
    ISSN: 1573-1634
    Keywords: Nonlinear solute transport ; perturbation method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A perturbation method is applied to the transport equation for a single reactive chemical with nonlinear rate loss relevant for a soil and water system. The results are compared with the linear rate loss case and the effect of different values of the perturbation parameter is shown. Exponential and step sinks modeling water withdrawn from the profile are illustrated.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 85-103 
    ISSN: 1573-8868
    Keywords: dispersion covariances ; Pearson correlation ; multivariate geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper extends the concept of dispersion variance to the multivariate case where the change of support affects dispersion covariances and the matrix of correlation between attributes. This leads to a concept of correlation between attributes as a function of sample supports and size of the physical domain. Decomposition of dispersion covariances into the spatial scales of variability provides a tool for computing the contribution to variability from different spatial components. Coregionalized dispersion covariances and elementary dispersion variances are defined for each multivariate spatial scale of variability. This allows the computation of dispersion covariances and correlation between attributes without integrating the cross-variograms. A correlation matrix, for a second-order stationary field with point support and infinite domain, converges toward constant correlation coefficients. The regionalized correlation coefficients for each spatial scale of variability, and the cases where the intrinsic correlation hypothesis holds are found independent of support and size of domain. This approach opens possibilities for multivariate geostatistics with data taken at different support. Two numerical examples from soil textural data demonstrate the change of correlation matrix with the size of the domain. In general, correlation between attributes is extended from the classic Pearson correlation coefficient based on independent samples to a most general approach for dependent samples taken with different support in a limited domain.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 701-722 
    ISSN: 1573-8868
    Keywords: dispersion covariances ; spatial support ; Pearson correlation ; spatial scales of variability ; PCA ; matrix variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Principal component analysis (PCA) is commonly applied without looking at the “spatial support” (size and shape, of the samples and the field), and the cross-covariance structure of the explored attributes. This paper shows that PCA can depend on such spatial features. If the spatial random functions for attributes correspond to largely dissimilar variograms and cross-variograms, the scale effect will increase as well. On the other hand, under conditions of proportional shape of the variograms and cross-variograms (i.e., intrinsic coregionalization), no scale effect may occur. The theoretical analysis leads to eigenvalue and eigenvector functions of the size of the domain and sample supports. We termed this analysis “growing scale PCA,” where spatial (or time) scale refers to the size and shape of the domain and samples. An example of silt, sand, and clay attributes for a second-order stationary vector random function shows the correlation matrix asymptotically approaches constants at two or three times the largest range of the spherical variogram used in the nested model. This is contrary to the common belief that the correlation structure between attributes become constant at the range value. Results of growing scale PCA illustrate the rotation of the orthogonal space of the eigenvectors as the size of the domain grows. PCA results are strongly controlled by the multivariate matrix variogram model. This approach is useful for exploratory data analysis of spatially autocorrelated vector random functions.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 22 (1990), S. 107-121 
    ISSN: 1573-8868
    Keywords: Variogram ; geostatistics ; sample support ; variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The effect of sample support size on variance is examined and evaluated. Results based on variograms and geostatistics are compared to the classical relationship developed by H. F. Smith in 1938; that is, that the variance is reduced fromV 1 toV 1 /n b as the support area increases from I ton plots for uniformity trials. The exponentb is between zero and one. Theoretical results are based on use of auxiliary functions and account for the size and shape of the sample support and the overall field geometry. Results are given in terms of approximations by rational functions for ease of calculation. Experimental results for uniformity trials, infiltration measurements, and spectral data from satellites are compared to theoretical and empirical results. Applications include not only uniformity trials, but also measurement theory.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 32 (2000), S. 851-871 
    ISSN: 1573-8868
    Keywords: scales ; multiresolution ; moving windows ; regularized variograms ; spatial variances ; spatial covariances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical analysis of spatial random functions frequently uses sample variograms computed from increments of samples of a regionalized random variable. This paper addresses the theory of computing variograms not from increments but from spatial variances. The objective is to extract information about the point support space from the average or larger support data. The variance is understood as a parametric and second moment average feature of a population. However, it is well known that when the population is for a stationary random function, spatial variance within a region is a function of the size and geometry of the region and not a function of location. Spatial variance is conceptualized as an estimation variance between two physical regions or a region and itself. If such a spatial variance could be measured within several sizes of windows, such variances allow the computation of the sample variogram. The approach is extended to covariances between attributes that lead to the cross-variogram. The case of nonpoint sample support of the blocks or elements composing each window is also included. A numerical example illustrates the application of this conceptualization.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied climatology 38 (1987), S. 15-23 
    ISSN: 1434-4483
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Description / Table of Contents: Zusammenfassung Es werden mit Hilfe des ARSEB (Aerodynamisches Widerstands-Energiebilanz-Modell) von Monteith Schätzwerte der mittleren täglichen Evapotranspiration eines Luzernenfeldes für die Periode zwischen 3. September und 15. November 1983 gewonnen. Die Ergebnisse wurden mit denen der Penman-Methode, der Methode der Bodenwasserbilanz (SWB) und der Abschätzung über die langfristige Reduktion des Bodenwassers in Zentralarizona verglichen. Die SWB-Werte wurden aus Bodenfeuchtedaten in 1,5 m Tiefe von 60 Punkten und 1,8 m Tiefe von 16 Punkten berechnet. Während relativ feuchter Bedingungen im September waren die ARSEB-Schätzwerte durchschnittlich etwa 19 bis 23% niedriger als die der Penman- und SWB-Methode. Für feuchte Verhältnisse wurden allerdings nur Daten aus 1,5 m Tiefe gesammelt. Daher mag die SWB-Methode die Evapotranspiration überschätzt haben, weil der Abfluß unter dem Wurzelbereich nicht gemessen wurde. Unter trockeneren Bedingungen waren die ARSEB-Werte etwa 5% höher als die nach Penman. Gegenüber den SWB-Werten lagen die der ARSEB-Methode um etwa 24 bis 35% höher. Die Übereinstimmung zwischen ARSEB-Werten und den Abschätzungen der Luzernenevapotranspiration nach Erie et al. (1981) für Zentralarizona war gut.
    Notes: Summary Estimates of mean daily evapotranspiration using the aerodynamic resistance-surface energy balance (ARSEB) model of Monteith were obtained for three periods during 3 September (day of year 246) to 15 November (day 319) 1983 in an alfalfa (Medicago sativa L.) field in central Arizona near Coolidge. These estimates were compared with Penman method estimates, within situ soil water balance (SWB) method estimates, and with long-term soil water depletion-based estimates of evapotranspiration for central Arizona. The SWB method estimates were obtained from soil moisture data collected to 1.5 m depth at 60 field sites, and to 1.8 m depth at 16 of the 60 sites. During relatively wet field conditions in September, daily estimates from the ARSEB method were on average about 19% to 23% lower than estimates from the Penman and SWB methods, respectively. However, for these wetter conditions, soil moisture data were only collected to 1.5 m depth. Thus, the SWB method may have overestimated evapotranspiration because drainage below the crop root zone was not measured. During drier conditions later in the season, ARSEB estimates of daily evapotranspiration were on average about 5% greater than Penman estimates. Also, ARSEB estimates were on the average about 24% to 35% greater than SWB method estimates. Agreement was good between ARSEB method estimates and long-term alfalfa evapotranspiration estimates by Erie et al. (1981) for central Arizona.
    Type of Medium: Electronic Resource
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