Abstract
The application of objective methods for interpolation of stochastic fields is based on the assumption of homogeneity with respect to the correlation function, i.e. only the relative distance between two points is of importance. This is not the case for runoff data which is demonstrated in this paper. Taking into consideration the structure of the river network and the related drainage basin supporting areas theoretical expressions are derived for the correlation function for flow along a river from its outlet and upstream. The results are exact for a rectangular drainage basin. For more complex basin geometry a grid approximation is suggested. The found relations are demonstrated on a real world example with a good agreement between the theoretically calculated correlation functions and empirical data.
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References
Arnell, N. 1992: Developing grid-based estimates of hydrological characteristics in Northern and Western Europe using the FRIEND data base. NATO Advanced Research Workshop on opportunities for Hydrological Data in Support of Climate Change Studies, Lahnstein, August 1991, Proceedings, in press
Baumgartner, A.; Reichel, E. 1975: World water balance. Amsterdam: Elsevier
Benjamin, J. R.; Cornell, C. A. 1970: Probability, statistics, and decision for civil engineers. New York: McGraw-Hill
Creutin, J. D.; Obled, C. 1982: Objective analysis and mapping techniques for rainfall fields: An objective comparison. Water Resour. Res. 18, 413–439
Delhomme, J.-P. 1978: Kriging in the hydrosciences. Advan. Water Resour. 1, 251–266.
Eastman, J. R. 1990: IDRISI: A grid-based geographic analysis system. Version 3.2.2. Clark University, Graduate School of Geography, Worcester, Massachusetts, USA
Forsman, A. 1976: Water balance maps of the Nordic countries. Vannet i Norden, No 4
Gandin, L. S. 1963: Objektivnyi analyz meteorologicheskikh polei. Gidrometeoizdat Leningrad
Gandin, L. S.; Kagan, P. L. 1976: Statisticheskie methody interpretatsii meteorologicheskikh dannykh. Gidrometeoizdat, Leningrad
Gelfand, I. M.; Vilenkin, N. Ya. 1964: Generalized functions, Vol 4, Applications of Harmonic Analysis. New York: Academic Press
Gosh, B. 1951: Random distances within a rectangle and between two rectangles. Bull. Calcutta Math. Soc. 43, 17–24
Gottschalk, L. 1977: Correlation structure and time scale of simple hydrologic systems. Nordic Hydrology 8, 129–140
Gottschalk, L.; Krasovskaia, I.; Kundzewicz, Z. 1992: Detecting outliers in flood data with geostatistical methods. International workshop on “New uncertainty concepts in hydrology”, Madralin, Poland. Unesco Reports in hydrology (in press)
Kendall, M.; Stuart, A. 1977: The advanced Theory of Statistics. Vol. 1., Distribution Theory, Fourth Edition, London: Charles Griffin
Korzun, V. I. 1978: World water balance and water resources of the Earth. UNESCO. Studies and Reports in Hydrology, 25
Matérn, B. 1960: Spatial variation. Meddelanden fran Statens Skogsforskningsinstitut, band 49, nr. 5
Monestiez, P.; Habib, R.; Audergon, J. M. 1989: Estimation de la covariance et du variogramme pour une fonction aléatoire à support arborescent: application à l'étude des arbres fruitiers. In Armstrong, M. (ed.) Geostatistics 1, 39–56, Kluwer Academic Publishers
NVE (Norwegian Water Resources and Energy Administration) 1987: Directorate of Water Resources, Hydrology Department. Runoff Map of Norway (1930–1960), Oslo
Russell, G. L.; Miller, J. R. 1990: Global river runoff calculated from a global atmosphere general circulation model. Journal of Hydrology 117, 241–254
Villeneuve, J. P.; Morin, G.; Bobee, B.; Deblanc, D.; Delhomme, J. P. 1979: Kriging in the design of streamflow sampling networks. Water Resour. Res. 15, 1833–1840
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Gottschalk, L. Correlation and covariance of runoff. Stochastic Hydrol Hydraul 7, 85–101 (1993). https://doi.org/10.1007/BF01581418
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DOI: https://doi.org/10.1007/BF01581418