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.

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.

Borga M. & Vizzaccaro A., 1997. On the interpolation of hydrologic variables: formal equivalence of multiquadratic surface fitting and kriging. J. Hydrol., 195(1-4), 160-171. 

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.

Caruso C. & Quarta F., 1998. Interpolation methods comparison. Comput. Math. Appl., 35(12), 109-126.

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.

Li, J., Heap, A., 2008. A Review of Spatial Interpolation Methods for Environmental Scientists. Geoscience Australia, p. 137. Record 2008/23.

Li, J., Heap, A., 2011. A review of comparative studies of spatial interpolation methods in environmental sciences: performance and impact factors. Ecol. Inform. 6, 228e241.

Li, J., & Heap, A. D. (2014). Spatial interpolation methods applied in the environmental sciences: A review, Environmental Modelling & Software, Volume 53, March 2014, Pages 173–189

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

Moore, I.D., Terrain analysis programs for the environmental sciences, Agricultural System and information Technology, 2:37-39, 1992

Myers DE (1994) Spatial Interpolation: an overview. Geoderma 62(1): 17-28

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.

TobinC. et al., 2011. Improved interpolation of meteorological forcings for hydrologic applications in a Swiss alpine region. J. Hydrol., 401(1-2), 77-89.

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. 

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.

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

& Sons, Ltd, Chichester.

WMO, 1994. Guide to Hydrological Practices. WMO N. 168, Geneva.

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. 

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.

Creutin, J.D., Obled, C., 1982. Objective analyses and mapping techniques for rainfall fields: an objective comparison. Water Resources Research, 18(2), 413-431

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. 

Diodato N., 2005. The influence of topographic co-variables on the spatial variability of precipitation over small regions of complex terrain. Int. J. Climatol., 25(3), 351- 363.

Dirks K.N., Hay J.E., Stow C.D. & Harris D., 1998. High- resolution studies of rainfall on Norfolk Island. Part 2: Interpolation of rainfall data. J. Hydrol., 208(3-4), 187- 193. 

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. 

Goovaerts, P.: Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall, J. Hydrol., 228, 113–129, 2000. 

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. 

Kurtzman, D., Navon, S., & Morin, E. (2009). Improving interpolation of daily precipitation for hydrologic modelling: spatial patterns of preferred interpolators. Hydrological Processes, 23(23), 3281–3291. http://doi.org/10.1002/hyp.7442

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

Lanza L.G., Ramirez J.A. & Todini E., 2001. Stochastic rainfall interpolation and downscaling. Hydrol. Earth  Syst. Sci., 5(2), 139-143.

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.

Ly, S., Charles, C., & Degré, A. (2011). Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium. Hydrology and Earth System Sciences, 15(7), 2259–2274. http://doi.org/10.5194/hess-15-2259-2011l., 2009) 

Ly, S, Charles, C., & Degree, A. (2013). Different methods for spatial interpolation of rainfall data for operational hydrology and hydrological modeling at watershed scale. A review.  Biotechnol. Agron. Soc. Environ., 17(2), 392–406.

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. 

Tabios,G.Q.and Salas, J.D.,1985. A comparative analysis of techniques for spatial interpolation of precipitation. Water Resour. Bull., 21: 365-380.

Tait A, Henderson R, Turner R, Zheng X. 2006. Thin plate smoothing spline interpolation of daily rainfall for New Zealand using a climatological rainfall surface. International Journal of Climatology 26: 2097–2115. 

Thiessen, A.H., 1911. Precipitation averages for large areas. Mon. Weather Rev., 39: 1082-1084.

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. 

Xie P, Yatagai A, Chen M, Hayasaka T, Fukushima Y, Liu C, Yang S. 2007. A gauge-based analysis of daily precipitation over east Asia. Journal of Hydrometeorology 8: 607–626. 

TEMPERATURE

Benavides, et al. 2007. Geostatistical modelling of air temperature in a mountainous region of Northern Spain. Agricultural and Forest Meteorology 146: 173−188. DOI:10.1016 /j.agrformet.2007.05.014.

Blandford TR, et al. 2008. Seasonal and synoptic variations in near-surface air temperature lapse rates in a mountainous basin. Journal of Applied Meteorology and Climatology 47: 249−261. DOI: 10.1175/2007JAMC1565.1. 

Courault, D., & Monestiez, P. (1999). Spatial interpolation of air temperature according to atmospheric circulation patterns in southeast France. International Journal of Climatology, 19(4), 365–378. http://doi.org/10.1002/(SICI)1097-0088(19990330)19:4<365::AID-JOC369>3.0.CO;2-E

Dobrowski SZ, et al. 2009. How much influence does landscape-scale physiography have on air temperature in a mountain environment? Agricultural and Forest Meteorology 149: 1751−1758. DOI:10.10

Dodson, R., & Marks, D. (1997). Daily air temperature interpolated at high spatial resolution over a large mountainous region. Climate Research, 8, 1–20.

Fury, R. and Joly, D. 1995. ‘Interpolation spatiale a` maille fine des temperatures journalieres’, Meteorol., 8(11), 36–43.

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., Lebel, T., Gautheron, A., & Obled, C. (2011). Spatial interpolation of sub-daily air temperatures for improving snow and hydrological forecasts on Alpine catchments (pp. 1–19). Presented at the th Eastern Snow Conference, Montreal. (But see Jabot on HP, 2012)

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. 

Lookingbill TR, and Urban DL. 2003. Spatial estimation of air temperature differences for 

landscape scale studies in montane environments. Agricultural and Forest Meteorology 114: 

141−151.

Robeson, S. M. 1993. ‘Spatial interpolation, network bias, and terrestrial air temperature variability’, Publ. Climatol.,*I), 1-51. 

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.

Stahl K, et al. 2006. Comparison of approaches for spatial interpolation of daily air temperature in a large region with complex topography and highly variable station density. Agricultural and Forest Meteorology 139: 224-236. DOI:10.1016/j.agrformet.2006.07.004.

Willmott, C. J., & Robeson, S. M. (1995). CLIMATOLOGICALLY AIDED INTERPOLATION (CAI) OF TERRESTRIAL AIR TEMPERATURE. International Journal of Climatology, 15, 221–229.