Abstract
The objective of this paper is to evaluate four interpolation methods, concerning their suitability for spatial prediction of long-term mean daily reference evapotranspiration (calculated by Penman–Monteith equation) for each month in Greece. The methods studied were ordinary kriging (OK) and inverse distance squared (IDS) and their modifications in which elevation data was incorporated into the interpolation process. The modified methods were named residual kriging (RK), and gradient-plus-inverse distance squared (GIDS). Apart from interpolation methods, two different approaches were studied in order to define what the proper sequence of steps is in the case of the interpolation of reference evapotranspiration. More particularly the ‘calculate first, interpolate later’ (CI) procedure was compared to the reverse procedure, namely ‘interpolate first, calculate later’ (IC). The assessment criteria of the methods accuracy were: mean error (ME), mean absolute error (MAE) and root mean squared error (RMSE). The results revealed that the incorporation of elevation significantly improved the performance of interpolation methods. On the contrary, procedures CI and IC were very similar since they had no effect on the performance of the four interpolation methods studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allen, R. G., Pereira, L. S., Raes, D., and Smith, M., 1998, Crop evapotranspiration–-Guidelines for computing crop water requirements, FAO Irrigation and drainage paper 56, FAO, Rome, Italy.
Antonic, O., Krizan, J., Marki, A., and Bukovec, D., 2001, ‘Spatio-temporal interpolation of climatic variables over large region of complex terrain using neural networks’, Ecol. Model. 138, 255–263.
Ashraf, M., Loftis, J. C., and Hubbard, K. G., 1997, ‘Application of geostatistics to evaluate partial weather station networks’, Agric. Forest Meteorol. 84, 255–271.
Bechini, L., Ducco, G., Donatelli, M., and Stein, A., 2000, ‘Modelling, interpolation and stochastic simulation in space and time of global solar radiation’, Agric. Ecosyst. Environ. 81, 29–42.
Blaney, H. P. & Criddle, W. D., 1950, ‘Determining water requirements in irrigated areas from climatological and irrigation data’, USDA Soil of Conservation Service, Tech Paper 96.
Boer, E. P. J., deBeurs, K. M., and Hartkamp, A. D., 2001, ‘Kriging and thin plate splines for mapping climate variables’, Int. J. Appl. Earth Observation Geoinform. 3, 146–154.
Borga, M. and Vizzaccaro, A., 1997, ‘On the interpolation of the hydrologic variables: Formal equivalence of multiquadratic surface fitting and kriging’, J. Hydrol. 195, 160–171.
Bourennane, H., King, D., Chery, P., and Bruand, A., 1996, ‘Improving the kriging of a soil variable using slope gradient as external drift’, Eur. J. Soil Sci. 47, 473–483.
Burgess, T. M. & Webster, R., 1980, ‘Optimal interpolation and isarithmic mapping of soil properties. I. The semi-variogram and punctual kriging’, J. Soil Sci. 31, 315–331.
Burrough, P. A. and McDonnell, R. A., 1998, Principles of Geographical Information Systems, Oxford University Press, Oxford, UK.
Caprio, J. M., 1974, ‘The solar thermal unit concept in problems related to plant development and potential evapotranspiration’, in H. Lieth (ed.), Phenology and Seasonality Modeling. Ecological Studies, Springer Verlag, New York, pp. 353–364.
Caruso, C. and Quarta, F., 1998, ‘Interpolation methods comparison’, Comput. Math. Appl. 35, 109–126.
Dalezios, N. R., Loukas, A., and Bampzelis, D., 2002, ‘Spatial variability of reference evapotranspiration in Greece’, Phys. Chem. Earth 27, 1031–1038.
Dirks, K. N., Hay, J. E., Stow, C. D., and Harris, D., 1998, ‘High-resolution studies of rainfall on Norfolk Island. Part II: Interpolation of rainfall data’, J. Hydrol. 208, 187–193.
Goovaerts, P., 1999, ‘Geostatistics in soil science: State-of-the-art and perspectives’, Geoderma 89, 1–45.
Goovaerts, P., 2000, ‘Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall’, J. Hydrol. 228, 113–129.
Hargreaves, G. H., 1974, ‘Estimation of potential and crop evapotranspiration’, Trans. ASAE 17, 701–704.
Holawe, F. and Dutter, R., 1999, ‘Geostatistical study of precipitation series in Austria: Time and space’, J. Hydrol. 219, 70–82.
Hutchinson, M. F., 1995, ‘Stochastic space–time weather models from ground-based data’, Agric. Forest Meteorol. 73, 237–264.
Idso, S. B., Reginato, R. J., and Jackson, R. D., 1977, ‘An equation for potential evaporation from soil, water and crop surfaces adaptable to use by remote sensing’, Geophys. Res. Lett. 4, 187–188.
Jensen, M. E. and Haise, H. R., 1963, ‘Estimating evapotranspiration from solar radiation’, J. Irrig. Drain. Div., ASCE 89, 15–41.
Jones, P. G. and Thornton, P. K., 1999, ‘Fitting a third-order Markov rainfall model to interpolated climate surfaces’, Agric. Forest Meteorol. 97, 213–231.
Journel, A. G. and Huijbregts, C. J., 1978, Mining Geostatistics, Academic Press, London.
Kollias, V. J., Kalivas, D. P., and Yassoglou, N. J., 1999, ‘Mapping the soil resources of a recent alluvial plain in Greece using fuzzy sets in a GIS environment’, Eur. J. Soil Sci. 50, 261–273.
Linacre, E. T., 1977, ‘A simple formula for estimating evaporation rates in various climates using temperature data alone’, Agric. Meteorol. 18, 409–424.
Makkink, G. F., 1957, ‘Ekzameno de la formula de Penman’, Netherlands J. Agric. Sci. 5, 290–305.
Martinez-Cob, A., 1996, ‘Multivariate geostatistical analysis of evapotranspiration and precipitation in mountain terrain’, J. Hydrol. 174, 19–35.
Matheron, G., 1965, Les Variables Regionalisees et leur Estimation, Masson, Paris.
Matheron, G., 1971, The Theory of Regionalized Variables and Its Application, Cahiers du Centre de Morphologie Mathematique, Fontenebleau, Paris.
Monteith, J. L., 1965, ‘Evaporation and environment’, Proceedings of the 19th Symposium of the Society of Experimental Biology, Vol. 19, University Press, Cambridge, pp. 205–233.
Nalder, I. A. and Wein, R. W., 1998, ‘Spatial interpolation of climatic normals: Test of a new method in the Canadian boreal forest’, Agric. Forest Meteorol. 92, 211–225.
Pannatier, Y., 1996, VARIOWIN: Software for spatial data analysis in 2D, Springer Verlag, New York.
Papazafiriou, G. Z., 1984, Principles and Practice on Irrigation (in Greek), Ziti Publications, Thessaloniki.
Penman, H. L., 1948, ‘Natural evaporation from open water, bare soil and grass’, Proceedings of the Royal Society of London (Ser. A), Vol. 193, London, pp. 120–145.
Penman, H. L., 1963, ‘Vegetation and hydrology’, Tech. Commun. 53, 125, Commonwealth Bureau of Soils, Harpenden, England.
Phillips, D. L. and Marks, D., 1996, ‘Spatial uncertainty analysis: Propagation of interpolation errors in spatially distributed models’, Ecol. Model. 91, 213–229.
Price, D. T., McKenney, D. W., Nalder, I. A., Hutchinson, M. F., and Kesteven, J. L., 2000, ‘A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data’, Agric. Forest Meteorol. 101, 81–94.
Priestley, C. H. B. and Taylor, R. J., 1972, ‘On the assessment of surface heat flux and evaporation using large scale parameters’, Monthly Weather Rev. 100, 81–92.
Rana, G. and Katerji, N., 2000, ‘Measurement and estimation of actual evapotranspiration in the field under Mediterranean climate: A review’, Eur. J. Agron. 13, 125–153.
Stanhill, G. A., 1961, ‘Comparison of methods of calculating potential evapotranspiration from climatic data’, Israel J. Agric. Res., Bet-Dagan, 11, 159–171.
Slatyer, R. O. and McIlroy, I. G., 1961, ‘Practical micro-climatology with special reference to water in soil–plant–atmospheric relationships’, GSIRO Austr. 1–296.
Tanner, C. B., 1967, ‘Measurement of evapotranspiration’, in Irrigation of Agricultural Lands. Agronomy II, American Society of Agronomy, Madison, WI, Chapter 29, pp. 534–574.
Thornthwaite, C. W., 1948, ‘An approach towards a rational classification of climates’, Geograph. Rev. 38, 55–94.
Thornton, P. E., Running, S. W., and White, M. A., 1997, ‘Generating surfaces of daily meteorological variables over large regions of complex terrain’, J. Hydrol. 190, 214–251.
Turc, L., 1961, ‘Evaluation des besoins en eau d’irrigation, évapotranspiration potentielle, formule climatique simplifiée et mise a jour’, Annals Agron. 12, 13–49.
Van Bavel, C. H. M., 1966, ‘Potential evaporation: The combination concept and its experimental verification’, Water Resour. Res. 2, 455–467.
Voltz, M. and Webster, R., 1990, ‘A comparison of kriging, cubic splines and classification for predicting soil properties from sample information’, J. Soil Sci. 41, 473–490.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mardikis, M.G., Kalivas, D.P. & Kollias, V.J. Comparison of Interpolation Methods for the Prediction of Reference Evapotranspiration—An Application in Greece. Water Resour Manage 19, 251–278 (2005). https://doi.org/10.1007/s11269-005-3179-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11269-005-3179-2