Tuesday, September 8, 2015

Rainfall and Temperature Interpolation (for hydrologic purposes)

Spatial (hydrological) models require spatial hydrological inputs. Some measurements techniques, as radars and remote sensing, usually provide this spatial information. However, it is often not quantitatively reliable if not compared to ground measurements, because remoted sensed products are themselves the outcomes of some modelling. In any case, even if, remote measurements enter every day more and more in the practice of hydrologists, ground based, in station, measurements are today's standard. They provide localised information that has to be extrapolated to space. For accomplishing this task, several techniques were developed, moving from the Thiessen (1911) method to the use of inverse distance weighting (IDW), to splines (see for instance Hutchinson, 1995) to the use of Kringing (e.g. Goovaerts, 1997). 
When data are abundant, either splines, IDW, or kriging give acceptable results in interpolating temperatures and rainfall. The choice of one or another, more than on performances issues (either as computational resources needed or in reproducing known results), is actually related to the availability of tools to perform them. However, recently Kriging gained momentum, (because of the presence of good tools for doing it like gstat and) because it was generically found to perform better than the other methods, because it allows to include the effects of other explaining variables (as, for instance, elevation) in the method, and furnishes a built-in methodology to calculate estimations errors. 
In any case, please find below, a list of papers, certainly incomplete, where the general problem was analysed, and some more specific literature on rainfall and temperature interpolation.

The future will be certainly in mixed methods, where, for instance Kriging, will be mixed with machine learning techniques (see also here). However, in this direction I saw seeds,  not yet mature, mainstream work.


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Burrough PA, McDonnell RA. 1998. Principles of Geographical Information Systems. Oxford University Press: New York; 333. 

Carrea-Hernandez, J.J., Gaskin, S.J., 2007: Spatio temporal analysis of daily precipitation and temperature in the Basin of Mexico. J. Hydrol. 336, 231-249.

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Daley, R. 1991. Atmospheric Data Analysis. Cambridge University Press, Cambridge.

Daly, C. (2006). Guidelines for assessing the suitability of spatial climate data sets. International Journal of Climatology, 26(6), 707–721. http://doi.org/10.1002/joc.1322

Dubois, G., Malczewski, J. and De Cort, M. (2003). Mapping radioactivity in the environment. Spatial Interpolation Comparison 1997 (Eds.). EUR 20667 EN, EC. 268 p. 

Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation (pp. 1–488). New York : Oxford University Press. 

Goovaerts P., 1998. Ordinary cokriging revisited. Mathematical Geology, 30(1), 21–42

Hengl, T., Heuvelink, G.B.M., Rossiter, D.G., 2007. About regression-kriging: from equations to case studies. Comput. Geosci. 33, 1301e1315.

Hofstra, N., M. R. Haylock, M. New, P. D. Jones, and C. Frei (2008), Comparison of six methods for the interpolation of daily European cli- mate data, J. Geophys. Res., doi:10.1029/2008JD010100, in press.

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Mitasova, H., and Mitas, L., Interpolation by regularised spline with tension, I: theory and implementation, Mathematical Geology, 25:641-655

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Nalder I.A. & Wein R.W., 1998. Spatial interpolation of climatic normals: test of a new method in the Canadian boreal forest. Agric. For. Meteorol., 92(4), 211- 225. 

Shepard, D. 1968. A two dimensional interpolation function for irregularly spaced data, Proceedings of the 23rd National Conference, ACM, pp. 517-523.

Rivoirard, J.. On the structural link between variables in kriging with external drift [J]. Mathematical Geology, 2002, 34: 797–808

Thornton, P., Running, S. W., & White, M. A. (1997). Generating durfaces of daily meteorological variables over large regions of complex terrain. Journal of Hydrology, 190, 214–251.

Todini, E., 2001b. Influence of parameter estimation uncertainty  in Kriging. Part 1 – Theoretical Development, Hydrol. Earth. System Sci., 5, 215–223.

Todini, E., Pellegrini, F. and Mazzetti, C., 2001. Influence of  parameter estimation uncertainty in Kriging. Part 2 – Test and  case study applications, Hydrol. Earth. System Sci., 5, 225–232. 

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Weber, D. and Englund, E. 1992. ‘Evaluation and comparison of spatial interpolators’, Math. Geol., 24(4), 381-389.

Webster, R., Oliver, M., 2001. Geostatistics for Environmental Scientists. John Wiley
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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. 

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.

Buytaert, W., Celleri, R., Willems, P., Bie`vre, 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. 

Bussieres, N. and Hogg, W. 1989. The objective analysis of daily rainfall by distance weighting schemes on a mesoscale grid’, Atmos. Ocean, 27(3), 521-541.

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Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statistical–topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140–158. 
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Fiorucci, P., La Barbera, P., Lanza, L.G. and Minciardi, R., 2001. A geostatistical approach to multisensor rain field reconstruction and downscaling, Hydrol. Earth. System Sci., 5, 201–213. 

Guan, H., Wilson, J.L. and Makhnin, O.. Geostatistical mapping of mountain precipitation incorporating autosearched effects of terrain and climatic characteristics. Journal of Hydrometeorology, 2005, 6: 1018–1031

Hofierka, J., Parajka, J., Mitasova, H. and Mitas, L. (2002) Multivariate interpolation of precipitation using regularized spline with tension. Transactions in GIS, 6, 135-150. doi:10.1111/1467-9671.00101 

Hutchinson MF. 1995. Interpolating mean rainfall using thin plate smoothing splines. International Journal of Geographical Information Systems 9: 385–403.

Hutchinson, M. F., 1998: Interpolation of rainfall data with thin plate smoothing splines: II. Analysis of topographic dependence. J. Geogr. Inf. Decis. Anal., 2, 168–185. 

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Kyriakidis P.C., Kim J. & Miller N.L., 2001. Geostatistical mapping of precipitation from rain gauge data using atmospheric and terrain characteristics. J. Appl. Meteorol., 40(11), 1855-1877

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Todini, E., 2001a. A Bayesian technique for conditioning radar precipitation estimates to rain gauge measurements, Hydrol. Earth. System Sci., 5, 187–199.

Velasco-Forero C. A., Sempere-Torres, D., Cassiraga E. F., and Gomez-Hernandez, 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. 

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