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.
GENERAL
Attore, F., Alfo, M., De Sanctis, M., Francesconi, F., Bruno, F., 2007:
Comparison of interpolation methods for mapping climatic and bioclimatic variables at regional scale. Int. J. Climatol. 27, 1825-1843.
Burrough PA, McDonnell RA. 1998. Principles of Geographical Information Systems. Oxford University Press: New York; 333.
Moore, I.D., Terrain analysis programs for the environmental sciences, Agricultural System and information Technology, 2:37-39, 1992
Rivoirard, J.. On the structural link between variables in kriging with external drift [J]. Mathematical Geology, 2002, 34: 797–808
Vizi, L., Hlasny, T., Farda, A., stepanek, P., Skalak, P., & Sitkova, S. (2011).
Geostatistical modeling of high resolutionclimate change scenario data. Quartely Journal of the Hungarian Meteorological Service, 115(1-2), 1–16.
Webster, R., Oliver, M., 2001. Geostatistics for Environmental Scientists. John Wiley
& Sons, Ltd, Chichester.
RAINFALL
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.
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.
Morin E, Gabella M. 2007
Radar-based quantitative precipitation estimation over Mediterranean and dry climate regimes. Journal of Geophysical Research 112: D20108. DOI:10.1029/2006JD008206.
Obled C., Wendling J. & Beven K., 1994.
The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data. J. Hydrol., 159(1-4), 305-333.
Phillips, D.L., Dolph, J. and Marks, D., 1992.
A comparison of geostatistical procedures for spatial analysis of precipitation in mountainous terrain. Agric. For. Meteorol., 58: 119-141.
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., Bierkens, M. F. P., Pebesma, E. J., and Uijlen- hoet, R.:
Automatic prediction of high-resolution daily rainfall fields for multiple extents: The potential of operational radar, J. Hydrometeorol., 8, 1204–1224, 2007.
TEMPERATURE
Hudson, G., Wackernagel, H., 1994: Mapping temperature using kriging with external drift: Theory
and example from Scotland. Int. J. Climatol. 14, 77-91.
Ishida, T. and Kawashima, S. (1993) Use of cokriging to estimate surface air temperature from elevation. Theoretical and Applied Climatology, 47, 147-157. doi:10.1007/BF00867447
Jabot, E., Zin, I., Lebel, T., Gautheron, A., & Obled, C. (2012).
Spatial interpolation of sub-daily air temperatures for snow and hydrologic applications in mesoscale Alpine catchments. Hydrological Processes, 26(17), 2618–2630. http://doi.org/10.1002/hyp.942316/j.agrformet. 2009.06.006.
141−151.
Robeson, S. M. and Willmott, C. J. 1993. ‘Spherical spatial interpolation and terrestrial air temperature variability’, Proceedings. Second International Conference on Integrating GIS and Environmental Modeling, Breckenridge, CO, in press.