Hydrology and Earth System Sciences
www.hydrol-earth-syst-sci.net
1027-5606
1607-7938
10
5
2006
10.5194/hess-10-645-2006
http://www.hydrol-earth-syst-sci.net/10/645/2006/
http://www.hydrol-earth-syst-sci.net/10/645/2006/hess-10-645-2006.html
http://www.hydrol-earth-syst-sci.net/10/645/2006/hess-10-645-2006.pdf
645
662
2006-09-26
Catchments as space-time filters – a joint spatio-temporal geostatistical analysis of runoff and precipitation
J. O. Skøien
skoien@hydro.tuwien.ac.at
G. Blöschl
Institute for Hydraulic and Water Resources Engineering, Vienna Univ. of Technology, Karlsplatz 13, 1040 Vienna, Austria
In this paper catchments are conceptualised as linear space-time filters.
Catchment area <i>A</i> is interpreted as the spatial support and the catchment
response time <i>T</i> is interpreted as the temporal support of the runoff
measurements. These two supports are related by <i>T</i>~<i>A</i><sup>κ</sup> 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.
Anderson, M. G. and Burt, T. P.: Subsurface runoff, in: Process Studies in Hillslope Hydrology, edited by: Anderson, M. G. and Burt, T. P., Wiley, Chichester, 365–400, 1990.
Blöschl, G. and Sivapalan, M.: Process controls on regional flood frequency: Coefficient of variation and basin scale, Water Resour. Res., 33, 2967–2980, 1997.
Blöschl, G. and Sivapalan, M.: Scale issues in hydrological modelling – a review, Hydrol. Processes, 9, 251–290, 1995.
Bochner, S.: Harmonic Analysis and the Theory of Probability, University of California Press, Berkeley and Los Angeles, 176 pp., 1955.
Corradini, C., Melone, F., and Singh, V. P.: Some remarks on the use of GIUH in the hydrologic practice, Nordic Hydrol., 26, 297–312, 1995.
Cressie, N. and Huang, H. C.: Classes of nonseparable, spatio-temporal stationary covariance functions, J. Amer. Stat. Assoc., 94, 1330–1340, 1999.
Cressie, N.: Fitting variogram models by weighted least squares, Math. Geol., 17, 563–586, 1985.
Cressie, N.: Statistics for spatial data, Wiley, New York, NY, 1991.
De Cesare, L., Myers, D. E., and Posa, D.: Estimating and modeling space-time correlation structures, Statistics & Probability Letters, 51, 9–14, 2001.
De Iaco, S., Myers, D. E., and Posa, D.: Space-time analysis using a general product-sum model, Statistics & Probability Letters, 52, 21–28, 2001.
Duan, Q., Sorooshian, S., and Gupta, V. K.: Effective and Efficient Global Optimization for Conceptual Rainfall-runoff Models, Water Resour. Res., 28, 1015–1031, 1992.
Fuentes M.: Testing for separability of spatial-temporal covariance functions, J. Stat. Planning and Inference, 136, 447–466, 2006.
Gottschalk, L.: Correlation and covariance of runoff, Stochastic hydrology and hydraulics, 7, 85–101, 1993a.
Gottschalk, L.: Interpolation of runoff applying objective methods, Stochastic hydrology and hydraulics, 7, 269–281, 1993b.
James, B. R. and Freeze, R. A.: The worth of data in predicting aquitard continuity in hydrogeological design, Water Resour. Res., 29, 2049–2065, 1993.
Journel, A. G. and Huijbregts, C. J.: Mining geostatistics, Academic Press, London, UK, 600 pp., 1978.
Kyriakidis, P. C. and Journel A. G.: Geostatistical space-time models: a review, Math. Geology, 31, 651–684, 1999.
Merz, R. and Blöschl, G.: A process typology of regional floods, Water Resour. Res., 39(12), SWC51–SWC520, doi:10.1029/2002WR001952, 2003.
Merz, R., Blöschl, G., and Parajka, D.: Raum-zeitliche Variabilität von Ereignisabflussbeiwerten in Österreich (Spatial-temporal variability of event runoff coefficients in Austria), Hydrologie und Wasserbewirtschaftung, 50, 2–11, 2006.
Mitchell M. W., Genton, M. G., and Gumpertz M. L. Testing for separability of space-time covariances, Environmetrics, 16, 819–831, 2005.
Pilgrim, D. H. (Ed.): Australian Rainfall and Runoff, The Institution of Engineers, Barton, ACT, Australia, 374 pp., 1987.
Renard, P., Demougeot-Renard, H., and Froidevaux, R. (Eds.): Geostatistics for Environmental Applications, Springer, Berlin Heidelberg, New York, 480, 2005.
Rodríguez-Iturbe, I. and Mejía, J. M.: The Design of rainfall networks in time and space, Water Resour. Res., 10, 713–728, 1974.
Sauquet, E., Gottschalk, L., and Leblois, E.: Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme, Hydrol. Sci. J., 45, 799–815, 2000.
Sivapalan, M., Takeuchi, K., Franks, S. W., Gupta, V. K., Karambiri, H., Lakshmi, V., Liang, X., McDonnell, J. J., Mendiondo, E. M., O'Connell, P. E., Oki, T., Pomeroy, J. W., Schertzer, D., Uhlenbrook, S., and Zehe, E.: IAHS Decade on Predictions in Ungauged Basins (PUB), 2003–2012: Shaping an exciting future for the hydrological sciences, Hydrol. Sci. J., 48, 857–880, 2003.
Skøien, J. O. and Blöschl, G.: Sampling scale effects in two dimensional random fields and implications for environmental modelling, Environ. Monit. Assessment 114, 521–552 , 2006a.
Skøien, J. O. and Blöschl, G.: Scale effects in estimating the variogram and implications for soil hydrology, Vadose Zone J 5, 153–167, doi:10.2136/vzj2005.0069, 2006b.
Skøien, J. O., Blöschl, G., and Western, A. W.: Characteristic space-time scales in hydrology, Water Resour. Res., 39(10), SWC111–SWC1119, doi:10.1029/2002WR001736, 2003.
Skøien, J., Merz, R., and Blöschl, G.: Top-kriging – geostatistics on stream networks, Hydrol. Earth Syst. Sci., 10, 277–287, 2005.
Skøien, J. O. and Blöschl, G.: Geostatistical interpolation of runoff, EGU General Assembly 2005, Vienna, Austria, 24–29 April 2005, Geophysical Research Abstracts, 7, EGU05-A-06526, 2005.
Taylor, G. I.: The spectrum of turbulence, Proc. R. Soc. Lond. A., 164, 476–490, 1938.
Western, A. W. and Blöschl, G.: On the spatial scaling of soil moisture, J. Hydrol., 217, 203–224, 1999.
Western, A. W., Zhou, S.-L., Grayson, R. B., McMahon, T. A., Blöschl, G., and Wilson, D. J.: Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes, J. Hydrol., 286(1–4), 113–134, 2004.
Western, A., Grayson, R., and Blöschl, G.: Scaling of soil moisture: a hydrologic perspective, Ann. Rev. Earth Planet. Sci., 30, 149–180, 2002.
Woods, R. and Sivapalan, M.: A synthesis of space-time variability in storm response: Rainfall, runoff generation, and routing, Water Resour. Res., 35, 2469–2485, 1999.
Woods, R., Sivapalan, M., and Duncan, M.: Investigating the representative elementary area concept: An approach based on field data., Hydrol. Process., 9, 291–312, 1995.