Comparison of Interpolation Methods for Spatial Distribution of Monthly Precipitation in the State of Pernambuco, Brazil
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 3
Abstract
In the quest for a best approach to estimate the spatial distribution of monthly precipitation for the state of Pernambuco, Brazil, this work tests different versions (choices of parameters and functions) of seven interpolation methods, totaling 26 distinct interpolation schemes. The performance of each method in estimating monthly precipitation was evaluated through a set of seven measures of performance evaluation through a cross-validation procedure. It was found that the trend surface analysis yielded the best overall interpolation results, followed by natural neighbor method, inverse distance weighting, and kriging. Performance ranking of all 26 methods is provided. Moreover, in order to assess the regional performance quality of the best identified method (trend surface analysis) in estimating monthly precipitation, a spatially explicit error analysis was also performed for each of the evaluation measures. Finally, temporal evolution of the error evaluation measures of the best performing methods is presented in order to demonstrate the seasonal impact of interpolation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge the support from Brazilian agencies CAPES for the scholarships to students and financial aid from both Facepe (Grant No. APQ-0532-5.01/14) and CNPq (Grant Nos. 403129/2013-3, 465764/2014-2, 310441/2015-3, and 446137/2015-4).
References
Andriotti, J. 2003. Fundamentos de estatística e geoestatística. São Leopoldo, Brazil: UNISINOS.
Bakkali, S., and M. Amrani. 2008. “About the use of spatial interpolation methods to denoising Moroccan resistivity data phosphate ‘disturbances’ map.” Acta Montanistica Slovaca 13 (2): 216–222.
Black, T. L. 1994. “The new NMC mesoscale Eta model: Description and forecast examples.” Weather Forecasting 9 (2): 265–278. https://doi.org/10.1175/1520-0434(1994)009%3C0265:TNNMEM%3E2.0.CO;2.
Borges, P. A., J. Franke, Y. M. T. Anunciação, and H. WeissBernhofer 2016. “Comparison of spatial interpolation methods for the estimation of precipitation distribution in Distrito Federal, Brazil.” Theor. Appl. Climatol. 123 (1–2): 335–348. https://doi.org/10.1007/s00704-014-1359-9.
Burrough, P. A., and R. McDonnell. 1998. Vol. 333of Principles of geographical information systems. Oxford, UK: Oxford University Press.
Camargo, E. C. G., S. D. Fucks, and G. Câmara. 2004. “Análise espacial de superfícies.” In Análise espacial de dados geográficos, 79–122. Planaltina, Brazil: Embrapa Cerrados.
Cecílio, R. A., and F. F. Pruski. 2003. “Interpolação dos parâmetros da equaçãoo de chuvas intensas com uso do inverso de potências da distância.” Rev. Bras. Engenharia Agrícola e Ambiental 7 (3): 501–504. https://doi.org/10.1590/S1415-43662003000300016.
Chen, D., T. Ou, L. Gong, C. Y. Xu, W. Li, C. H. Ho, and W. Qian. 2010. “Spatial interpolation of daily precipitation in China: 1951–2005.” Adv. Atmos. Sci. 27 (6): 1221–1232. https://doi.org/10.1007/s00376-010-9151-y.
Cressie, N. 1991. Statistics for spatial data. New York: Wiley.
Cunha, A. M., J. L. Lani, G. R. Santos, E. I. FernandesFilho, F. S. Trindade, and E. Souza. 2013. “Espacialização da precipitação pluvial por meio de krigagem e cokrigagem.” Pesquisa Agropecuária Bras 48 (9): 1179–1191. https://doi.org/10.1590/S0100-204X2013000900001.
Delaunay, B. 1934. “Sur la sphere vide: Izv Akad Nauk SSSR.” Otdelenie Matematicheskii i Estestvennyka Nauk 7 (1–2): 793–800.
Foley, T. A. 1987. “Interpolation and approximation of 3-D and 4-D scattered data.” Comput. Math. Appl. 13 (8): 711–740. https://doi.org/10.1016/0898-1221(87)90043-5.
Fornberg, B., E. Larsson, and G. Wright. 2006. “A new class of oscillatory radial basis functions.” Comput. Math. Appl. 51 (8): 1209–1222. https://doi.org/10.1016/j.camwa.2006.04.004.
Fox, D. G. 1981. “Judging air quality model performance.” Bull. Am. Meteorol. Soc. 62 (5): 599–609. https://doi.org/10.1175/1520-0477(1981)062%3C0599:JAQMP%3E2.0.CO;2.
Franke, R. 1982. “Scattered data interpolation: Tests of some methods.” Math. Comput. 38 (157): 181–200. https://doi.org/10.2307/2007474.
Franke, R., and G. Nielson. 1980. “Smooth interpolation of large sets of scattered data.” Int. J. Numer. Methods Eng. 15 (11): 1691–1704. https://doi.org/10.1002/nme.1620151110.
Gebbers, R., and S. De Bruin. 2010. Application of geostatistical simulation in precision agriculture. New York: Springer.
Hallak, R., and A. J. Pereira Filho. 2011. “Metodologia para análise de desempenho de simulações de sistemas convectivos na região metropolitana de São Paulo com o modelo ARPS: sensibilidade a variações com os esquemas de adveção e assimilação de dados.” Rev. Bras. Meteorologia 26 (4): 591–608. https://doi.org/10.1590/S0102-77862011000400009.
Hardy, R. L. 1971. “Multiquadric equations of topography and other irregular surfaces.” J. Geophys. Res. 76 (8): 1905–1915. https://doi.org/10.1029/JB076i008p01905.
Hernandez-Stefanoni, J. L., and R. Ponce-Hernandez. 2006. “Mapping the spatial variability of plant diversity in a tropical forest: Comparison of spatial interpolation methods.” Environ. Monit. Assess. 117 (1–3): 307–334. https://doi.org/10.1007/s10661-006-0885-z.
Hingray, B., C. Picouet, and A. Musy. 2014. Vol. 137of Hydrology: A science for engineers. 1st ed. New York: CRC Press.
Hoogenboom, G. 2000. “Contribution of agrometeorology to the simulation of crop production and its applications.” Agric. For. Meteorol. 103 (1): 137–157. https://doi.org/10.1016/S0168-1923(00)00108-8.
INMET (Instituto Nacional de Meteorologia). 2016. “Instituto nacional de meteorologia.” Accessed July 17, 2016. http://www.inmet.gov.br/portal/index.php?r=bdmep/bdmep.
ITEP (Instituto de Tecnologia de Pernambuco). 2016. “Instituto de tecnologia de pernambuco.” Accessed October 17, 2016. http://www.itep.br/.
Kansa, E. J. 1990. “Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations.” Comput. Math. Appl. 19 (8): 147–161. https://doi.org/10.1016/0898-1221(90)90271-K.
Kitanidis, P. K. 1997. Introduction to geostatistics: Applications in hydrogeology. London: Cambridge University Press.
Krause, P., D. Boyle, and F. Bäse. 2005. “Comparison of different efficiency criteria for hydrological model assessment.” Adv. Geosci. 5: 89–97. https://doi.org/10.5194/adgeo-5-89-2005.
Kravchenko, A., and D. G. Bullock. 1999. “A comparative study of interpolation methods for mapping soil properties.” Agron. J. 91 (3): 393–400. https://doi.org/10.2134/agronj1999.00021962009100030007x.
Lam, N. S. N. 1983. “Spatial interpolation methods: A review.” Am. Cartographer 10 (2): 129–150. https://doi.org/10.1559/152304083783914958.
Lanza, L. G., J. A. Ramirez, and E. Todini. 2001. “Stochastic rainfall interpolation and downscaling.” Hydrol. Earth Syst. Sci. Discuss. 5 (2): 139–143. https://doi.org/10.5194/hess-5-139-2001.
Ledoux, H., and C. Gold. 2005. “An efficient natural neighbour interpolation algorithm for geoscientific modelling.” In Developments in spatial data handling, 97–108. Berlin: Springer.
Legates, D. R., and G. J. McCabe. 1999. “Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation.” Water Resour. Res. 35 (1): 233–241. https://doi.org/10.1029/1998WR900018.
Lennon, J. J., and J. R. Turner. 1995. “Predicting the spatial distribution of climate: Temperature in Great Britain.” J. Anim. Ecol. 64 (3): 370–392. https://doi.org/10.2307/5898.
Li, J., and A. D. Heap. 2008. Vol. 137 of A review of spatial interpolation methods for environmental scientists. Symonston, Australia: Geoscience Australia.
Li, J., and A. D. Heap. 2011. “A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors.” Ecol. Inf. 6 (3): 228–241. https://doi.org/10.1016/j.ecoinf.2010.12.003.
Longley, P. A., M. F. Goodchild, D. J. Maguire, and D. W. Rhind. 2013. Sistemas e Ciência da Informação Geográfica. Porto Algegre, Brazil: Bookman.
Luo, W., M. Taylor, and S. Parker. 2008. “A comparison of spatial interpolation methods to estimate continuous wind speed surfaces using irregularly distributed data from England and Wales.” Int. J. Climatol. 28 (7): 947–959. https://doi.org/10.1002/joc.1583.
Mazzini, P. L. F., and C. A. F. Schettini. 2009. “Avaliação de metodologias de interpolação espacial aplicadas a dados hidrográficos costeiros quase-sinóticos.” Braz. J. Aquat. Sci. Technol. 13 (1): 53–64. https://doi.org/10.14210/bjast.v13n1.p53-64.
Mesinger, F., Z. I. Janjic, S. Nickovic, D. Gavrilov, and D. G. Deaven. 1988. “The step-mountain coordinate: Model description and performance for cases of alpine lee cyclogenesis and for a case of an Appalachian redevelopment.” Mon. Weather Rev. 116 (7): 1493–1518. https://doi.org/10.1175/1520-0493(1988)116%3C1493:TSMCMD%3E2.0.CO;2.
Mueller, T. G., N. B. Pusuluri, K. K. Mathias, P. L. Cornelius, R. I. Barnhisel, and S. A. Shearer. 2004. “Map quality for ordinary kriging and inverse distance weighted interpolation.” Soil Sci. Soc. Am. J. 68 (6): 2042–2047. https://doi.org/10.2136/sssaj2004.2042.
Nalder, I. A., and R. W. Wein. 1998. “Spatial interpolation of climatic normals: Test of a new method in the Canadian boreal forest.” Agric. For. Meteorol. 92 (4): 211–225. https://doi.org/10.1016/S0168-1923(98)00102-6.
Nash, J., and J. V. Sutcliffe. 1970. “River flow forecasting through conceptual models. Part i—A discussion of principles.” J. Hydrol. 10 (3): 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Olea, R. A. 2000. “Geostatistics for engineers and earth scientists.” Technometrics 42 (4): 444–445. https://doi.org/10.1080/00401706.2000.10485748.
Oliver, M. A. 2010. “An overview of geostatistics and precision agriculture.” In Geostatistical applications for precision agriculture, 1–34. Dordrecht, Netherlands: Springer.
Paninatier, Y. 1996. Variowin: Software for spatial data analysis in 2-D. New York: Springer.
Parton, W. J., D. S. Schimel, C. V. Cole, and D. S. Ojima. 1987. “Analysis of factors controlling soil organic matter levels in Great Plains grasslands.” Soil Sci. Soc. Am. J. 51 (5): 1173–1179. https://doi.org/10.2136/sssaj1987.03615995005100050015x.
Renka, R. J. 1988. “Multivariate interpolation of large sets of scattered data.” ACM Trans. Math. Software 14 (2): 139–148. https://doi.org/10.1145/45054.45055.
Shepard, D. 1968. “A two-dimensional interpolation function for irregularly-spaced data.” In Proc., 1968 23rd ACM National Conf., 517–524. New York: ACM.
Sibson, R. 1980. “A vector identity for the Dirichlet tessellation.” Vol. 87 of Mathematical Proc., Cambridge Philosophical Society, 151–155. Cambridge, UK: Cambridge University Press.
Silva, B. M., S. M. G. L. Montenegro, F. D. Silva, and P. F. Araújofilho. 2012. “Chuvas intensas em localidades do estado de Pernambuco.” Rev. Bras. Recursos Hídricos 17 (3): 135–147. https://doi.org/10.21168/rbrh.v17n3.p135-147.
Sironvalle, M. A. 1980. “The random coin method: Solution of the problem of the simulation of a random function in the plane.” Math. Geol. 12 (1): 25–32. https://doi.org/10.1007/BF01039901.
Smith, M. J., M. F. Goodchild, and P. Longley. 2007. Geospatial analysis: A comprehensive guide to principles, techniques and software tools. Leicester, UK: Troubador.
Tabios, G. Q., and J. D. Salas. 1985. “A comparative analysis of techniques for spatial interpolation of precipitation.” J. Am. Water Resour. Assoc. 21 (3): 365–380. https://doi.org/10.1111/j.1752-1688.1985.tb00147.x.
Thiessen, A. H. 1911. “Precipitation averages for large areas.” Mon. Weather Rev. 39 (7): 1082–1089. https://doi.org/10.1175/1520-0493(1911)39%3C1082b:PAFLA%3E2.0.CO;2.
Tomczak, M. 1998. “Spatial interpolation and its uncertainty using automated anisotropic inverse distance weighting (IDW)-cross-validation/jackknife approach.” J. Geogr. Inf. Decis. Anal. 2 (2): 18–30.
Tveito, O. E., M. Wegehenkel, F. van der Wel, and H. Dobesch. 2008. COST action 719: The use of geographic information systems in climatology and meteorology. Luxembourg: EUR-OP.
Vicente-Serrano, S. M., S. Saz-Sanchez, and J. M. Cuadrat. 2003. “Comparative analysis of interpolation methods in the middle Ebro Valley (Spain): Application to annual precipitation and temperature.” Clim. Res. 24 (2): 161–180. https://doi.org/10.3354/cr024161.
Voronoi, G. 1908. “Nouvelles applications des parametres continus àla theorie des formes quadratiques. deuxième mémoire: Recherches sur les parallélloèdres primitifs.” J. fur die reine undangewandte Mathematik 134: 198–287.
Wagner, P. D., P. Fiener, F. Wilken, S. Kumar, and K. Schneider. 2012. “Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions.” J. Hydrol. 464: 388–400. https://doi.org/10.1016/j.jhydrol.2012.07.026.
Wang, S., G. H. Huang, Q. G. Lin, Z. Li, H. Zhang, and Y. R. Fan. 2014. “Comparison of interpolation methods for estimating spatial distribution of precipitation in Ontario, Canada.” Int. J. Climatol. 34 (14): 3745–3751. https://doi.org/10.1002/joc.3941.
Webster, R., and M. A. Oliver. 2007. Geostatistics for environmental scientists. Chichester, UK: Wiley.
Willmott, C. J. 1981. “On the validation of models.” Phys. Geogr. 2 (2): 184–194. https://doi.org/10.1080/02723646.1981.10642213.
Willmott, C. J. 1982. “Some comments on the evaluation of model performance.” Bull. Am. Meteorol. Soc. 63 (11): 1309–1313. https://doi.org/10.1175/1520-0477(1982)063%3C1309:SCOTEO%3E2.0.CO;2.
Wong, S., Y. Hon, and M. Golberg. 2002. “Compactly supported radial basis functions for shallow water equations.” Appl. Math. Comput. 127 (1): 79–101. https://doi.org/10.1016/S0096-3003(01)00006-6.
Xie, Y., T. B. Chen, M. Lei, J. Yang, Q. J. Guo, B. Song, and X. Y. Zhou. 2011. “Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis.” Chemosphere 82 (3): 468–476. https://doi.org/10.1016/j.chemosphere.2010.09.053.
Yamamoto, J. 1998. “A review of numerical methods for the interpolation of geological data.” Anais da Academia Brasileira de Ciências 70 (1): 91–116.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 24 • Issue 3 • March 2019
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 11, 2018
Accepted: Aug 20, 2018
Published online: Dec 18, 2018
Published in print: Mar 1, 2019
Discussion open until: May 18, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.