[en] Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably the interpolation with the Thiessen polygon, commonly used in various hydrological models. Integrating elevation into Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) did not improve the interpolation accuracy for daily rainfall. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases. Care should be taken in applying UNK and KED when interpolating daily rainfall with very few neighbourhood sample points. These recommendations complement the results reported in the literature. ORK, UNK and KED using only spherical model offered a slightly better result whereas OCK using seven variogram models achieved better result.
Research Center/Unit :
Gembloux Agro-Bio Tech, Hydrologie et hydraulique agricole
Andréassian, V., Perrain, C., Michel, C., Usart-Sanchez, I., and Lavabre, J.: Impact of imperfect rainfall knowledge on efficiency and the parameters of watershed models, J. Hydrol., 250, 206-223, 2001. (Pubitemid 32736199)
Angulo-Martínez, M., López-Vicente, M., Vicente-Serrano, S. M., and Beguería, S.: Mapping rainfall erosivity at a regional scale: A comparison of interpolation methods in the Ebro Basin (NE Spain), Hydrol. Earth Syst. Sci., 13, 1907-1920, doi:10.5194/hess-13-1907-2009, 2009.
Angulo-Martínez, M. and Beguería, S.: Estimating rainfall erosivity from daily precipitation records: A comparison among methods using data from the Ebro Basin (NE Spain), J. Hydrol., 379, 111-121, 2009.
Aronica, G. and Ferro, V.: Rainfall erosivity over the Calabrian region/ Erosivité des précipitations en Calabre, Hydrolog. Sci. J., 42(1), 35-48, 1997.
Attorre, F., Alfo, M., Sanctis, M. D., Francesconi, F., and Bruno, F.: Comparison of interpolation methods for mapping climatic and bioclimatic variables at regional scale, Int. J. Climatol., 27, 1825-1843, 2007. (Pubitemid 350120180)
Basistha, A., Arya, D. S., and Goel, N. K.: Spatial Distribution of Rainfall in Indian Himalayas - A case study of Uttarakhand Region, Water Resour. Manag., 22, 1325-1346, 2008.
Beek, E. G.: Spatial variability and interpolation of daily precipitation amount, Stochastic Hydrol. Hydraul., 6, 304-320, 1992.
Berne, A., Delrieu, G., Creutin, J.-D., and Obled, C.: Temporal and spatial resolution of rainfall measurements required for urban hydrology, J. Hydrol., 299, 166-179, 2004. (Pubitemid 39379475)
Boer, E. P. J., de Beurs, K. M., and Hartkamp, A. D.: Kriging and thin plate splines for mapping climate Variables, Int. J. Appl. Earth Obs. Geoinf., 3, 146-154, 2001.
Borga M. and Vizzaccaro, A.: On the interpolation of hydrologic variables: Formal equivalence of multiquadratic surface fitting and kriging, J. Hydrol., 195, 160-171, 1997. (Pubitemid 27324167)
Buytaert, W., Celleri, R., Willems, P., Bièvre, D. B., and Wyseure, G.: Spatial and temporal rainfall variability in mountainous areas: A case study from the south Ecuadorian Andes, J. Hydrol. 329, 413-421, 2006. (Pubitemid 44436232)
Campling, P., Gobin, A., and Feyen, J.: Temporal and spatial rainfall analysis across a humid tropical catchment, Hydrol. Process. 15, 359-375, 2001. (Pubitemid 32207932)
Carrera-Hernández, J. J. and Gaskin, S. J.: Spatio temporal analysis of daily precipitation and temperature in the Basin of Mexico, J. Hydrol., 336, 231-249, 2007. (Pubitemid 46399721)
Caruso, C. and Quarta, F.: Interpolation Methods Comparison, Comput. Math. Applic., 35, 109-126, 1998. (Pubitemid 128389641)
Chaubey, I., Haan, C. T., Grunwald, S., and Salisbury, J. M.: Uncertainty in the model parameters due to spatial variability of rainfall, J. Hydrol., 220, 48-61, 1999. (Pubitemid 29341834)
Chilès, J. P. and Delfiner, P.: Geostatistics: Modelling Spatial Uncertainty, John Wiley & Sons, New York, 1999.
Chow, V. T.: Handbook of applied hydrology: A compendium of water-resources technology, McGraw-Hill, Inc. 1964.
Cole, S. J. and Moore, R. J.: Hydrological modelling using raingage and radar-based estimators of areal rainfall, J. Hydrol., 358, 159-181, 2008.
Collischonn, B., Collischonn, W., and Tucci, C. E. M.: Daily hydrological modeling in the Amazon basin using TRMM rainfall estimates, J. Hydrol., 360, 207-216, 2008.
Cressie, N.: Fitting Variogram Models by Weighted Least Squares, Math. Geol. 17, 563-586, 1985.
Cressie, N.: Statistics for spatial data, Wiley, New York, 900 pp., 1991.
Demarcin, P., Degre, A., Smoos, A., and Dautrebande, S.: Projet ERRUISSOL. Cartographie numérique des zones à risque de ruissellement et d'érosion des sols en Région wallonne (Belgique), Rapport final de convention DGO3, Unité d'hydrologie et hydraulique agricole, Faculté Universitaire des Sciences Agronomiques de Gembloux, 55 pp., 2009.
Deutsch, C. V.: Correcting for negative weights in ordinary kriging, Comput Geosci, 22, 765-773, 1996.
Diggle, P. J. and Ribeiro Jr., P. J.: Model-based Geostatistics, Springer Series in Statistics, Springer Science, Business Media, LLC, 228 pp., 2007.
Dirks, K. N., Hay, J. E., Stow, C. D., and Harris, D.: High-resolution of rainfall on Norfolk Island, Part II: Interpolation of rainfall data, J. Hydrol. 208, 187-193, 1998. (Pubitemid 28428481)
Faurès, J. M., Goodrich, D. C., Woolhiser, D. A, and Sorooshian, S.: Impact of small-scale spatial variability on runoff modeling, J. Hydrol., 173, 309-326, 1995. (Pubitemid 26472232)
Gabellani, S., Boni, G., Ferraris, L., Hardenberg, J. V., and Provenzale, A.: Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator, Adv. Water Resour., 30, 2061-2071, 2007. (Pubitemid 47194388)
Goovaerts, P.: Geostatistics for Natural Resources Evaluation, Oxford University Press, New York, 483 pp., 1997.
Goovaerts, P.: Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties, Biol. Fert. Soils., 27, 315-334, 1998. (Pubitemid 28456441)
Goovaerts, P.: Using elevation to aid the geostatistical mapping of rainfall erosivity, Catena, 34, 227-242, 1999. (Pubitemid 29101011)
Goovaerts, P.: Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall, J. Hydrol., 228, 113-129, 2000. (Pubitemid 30156971)
Haberlandt, U.: Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event, J. Hydrol. 332, 144-157, 2007. (Pubitemid 44937318)
Hevesi, J., Istok, J., and Flint, A.: Precipitation Estimation in Mountainous Terrain Using Multivariate Geostatistics. Part I: Structural Analysis, J. Appl. Meteorol. 31, 661-676, 1992. (Pubitemid 23376310)
Hoyos, N., Waylena, P. R., and Jaramillo, A.: Seasonal and spatial patterns of erosivity in a tropical watershed of the Colombian Andes, J. Hydrol., 314, 177-191, 2005. (Pubitemid 41727779)
Isaaks, E. H. and Srivastava, R. M.: An Introduction to Applied Geostatistics, Oxford University Press, New York, 561 pp., 1989.
Johnson, G. L. and Hanson, C. L.: Topographic and atmospheric influences on precipitation variability over a mountains watershed, J. Appl. Meteor., 34, 68-87, 1995.
Kobold, M. and Sušelj, K.: Precipitation forecasts and their uncertainty as input into hydrological models, Hydrol. Earth Syst. Sci., 9, 322-332, doi:10.5194/hess-9-322-2005, 2005. (Pubitemid 41555691)
Lanza, L. G., Ramírez, J. A., and Todini, E.: Stochastic rainfall interpolation and downscaling, Hydrol. Earth Syst. Sci., 5, 139-143, doi:10.5194/hess-5-139-2001, 2001.
Leander, R., Buishand, T. A., van den Hurk, B. J. J. M, and de Wit, M. J. M: Estimated changes in flood quantiles of the river Meuse from resampling of regional climate model output, J. Hydrol., 351, 331-343, 2008.
Lloyd, C. D.: Assessing the effect of integrating elevation data into the estimation of monthly precipitation in Great Britain, J. Hydrol., 308, 128-150, 2005. (Pubitemid 40772196)
Lu, G. Y. and Wong, D. W.: An adaptive inverse-distance weighting spatial interpolation technique, Comput. Geosci., 34, 1044-1055, 2008.
Matheron, G.: The Theory of Regionalised Variables and its Applications: Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau N°5, The Ecole Nationale Supérieure des Mines de Paris, Paris, France, 1971.
Marquínez, J., Lastra, J., and García, P.: Estimation models for precipitation in mountainous regions: The use of GIS and multivariate analysis, J. Hydrol. 270, 1-11, 2003. (Pubitemid 36093341)
Moulin, L., Gaume, E., and Obled, C.: Uncertainties on mean areal precipitation: Assessment and impact on streamflow simulations, Hydrol. Earth Syst. Sci., 13, 99-114, doi:10.5194/hess-13-99- 2009, 2009.
Nalder, I. A. andWein, R.W.: Spatial interpolation of climatic Normals: Test of a new method in the Canadian boreal forest, Agric. For. Meteorol. 92, 211-225, 1998. (Pubitemid 28564754)
Nyssen, J., Vandenreyken, H., Poesen, J., Moeyersons, J., and Deckersd, J.: Rainfall erosivity and variability in the Northern Ethiopian Highlands, J. Hydrol., 311, 172-187, 2005. (Pubitemid 41261606)
Pardo-Igúzquiza, E.: MLREML4: A Program for the inference of the power variogram model by maximum likelihood and restricted maximum likelihood, Comput. Geosci., 24, 537-543, 1998. (Pubitemid 28556026)
Ruelland, D., Ardoin-Bardin, S., Billen, G., and Servat, E.: Sensitivity of a lumped and semi-distributed hydrological model to several methods of rainfall interpolation on a large basin in West Africa, J. Hydrol., 361, 96-117, 2008.
Schiemann, R., Erdin, R., Willi, M., Frei, C., Berenguer, M., and Sempere-Torres, D.: Geostatistical radar-raingauge combination with nonparametric correlograms: Methodological considerations and application in Switzerland, Hydrol. Earth Syst. Sci., 15, 1515-1536, doi:10.5194/hess-15-1515- 2011, 2011.
Schuurmans, J. M. and Bierkens, M. F. P.: Effect of spatial distribution of daily rainfall on interior catchment response of a distributed hydrological model, Hydrol. Earth Syst. Sci., 11, 677-693, doi:10.5194/hess-11-677-2007, 2007. (Pubitemid 46134827)
Schuurmans, J. M., Bierkens, M. F. P., Pebesma, E. J., and Uijlenhoet, R.: Automatic prediction of high-resolution daily rainfall fields for multiple extents: The potential of operational radar, J. Hydrometeorol., 8, 1204-1224, 2007.
Singh, V. P.: Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph, Hydrol. Process., 11, 1649-1669, 1997.
Spadavecchia, L. and Williams, M.: Can spatio-temporal geostatistical methods improve high resolution regionalisation of meteorological variables?, Agr. Forest Meteorol., 149, 1105-1117, 2009.
Syed, K. H., Goodrich, D. C., Myers, D. E., and Sorooshian, S.: Spatial characteristics of thunderstorm rainfall fields and their relation to runoff, J. Hydrol., 271, 1-21, 2003. (Pubitemid 36141142)
Teegavarapu, R. and Chandramouli, V.: Improved weighting methods, deterministic and stochastic data-driven models for estimation of missing precipitation records, J. Hydrol., 312, 191-206, 2005. (Pubitemid 41392959)
Todini, E., Pellegrini, F., and Mazzetti, C.: Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications, Hydrol. Earth Syst. Sci., 5, 225-232, doi:10.5194/hess-5-225-2001, 2001. (Pubitemid 32804659)
van de Beek, C. Z., Leijnse, H., Torfs, P. J. J. F., and Uijlenhoet, R.: Climatology of daily rainfall semi-variance in The Netherlands, Hydrol. Earth Syst. Sci., 15, 171-183, doi:10.5194/hess-15-171- 2011, 2011.
Velasco-Forero C. A., Sempere-Torres, D., Cassiraga E. F., and Gómez-Hernández, J. J.: A non-parametric automatic blending methodology to estimate rainfall fields from rain gauge and radar data, Adv. Water Resour., 32, 986-1002, 2009.
Verworn, A. and Haberlandt, U.: Spatial interpolation of hourly rainfall effect of additional information, variogram inference and storm properties, Hydrol. Earth Syst. Sci., 15, 569-584, doi:10.5194/hess-15-569-2011, 2011.
Vicent-Serrano, S. M., Saz-Sanchez, M. A., and Cuadrat, J. M.: Comparative analysis of interpolation methods in the middle Ebro Valley (Spain): Application to annual precipitation and temperature, Clim. Res., 24, 161-180, 2003. (Pubitemid 37124331)
Webster, R. and Oliver, M. A.: Geostatistics for Environmental Scientists, Statistics in Practice Series, John Wiley & Son Ltd., 315 pp., 2007.
