Skip to main content

Advertisement

SpringerLink
Log in

Comparison of different wind data interpolation methods for a region with complex terrain in Central Asia

  • Published:
Climate Dynamics Aims and scope Submit manuscript

Abstract

While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \(\overrightarrow{u}\) and \(\overrightarrow{v}\) in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \(\overrightarrow{u}\) and \(\overrightarrow{v}\). In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and ordinary kriging. Overall, explanatory variables improve the interpolation results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Ali SM, Mahdi AS, Shaban AH (2012) Wind speed estimation for Iraq using several spatial interpolation methods. Br J Sci 7(2):48–55

    Google Scholar 

  • Apaydin H, Sonmez FK, Yildirim YE (2004) Spatial interpolation techniques for climate data in the GAP region in Turkey. Clim Res 28:31–40

    Article  Google Scholar 

  • Appelhans T, Mwangomo E, Hardy DR, Hemp A, Nauss T (2015) Evaluating machine learning approaches for the interpolation of monthly air temperature at Mt. Kilimanjaro, Tanzania. Spat Stat 14:91–113

    Article  Google Scholar 

  • Beek EG (1991) Spatial interpolation of daily meteorological data: theoretical evaluation of available techniques. Wageningen (The Netherlands), DLO The Winand Staring Centre. Report 53.1

  • Benestad RE, Hanssen-Bauer I, Chen D (2008) Empirical-statistical downscaling. World Scientific, New Jersey

    Book  Google Scholar 

  • Bivand RS, Pebesma E, Gómez-Rubio V (2013) Applied spatial data analysis with R, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Bivand R, Keitt T, Rowlingson B (2016) rgdal: bindings for the geospatial data abstraction library. R package version 1.1–10. https://CRAN.R-project.org/package=rgdal

  • Boser BE, Guyon IM, Vapnik VN (1992) A training algorithm for optimal margin classifiers. COLT ‘92. Proceedings of the fifth annual workshop on Computational learning theory. ACM Press, New York, pp 144–152

  • Brogniez D de, Ballabio C, Stevens A, Jones RJA, Montanarella L (2015) A map of the topsoil organic carbon content of Europe generated by a generalized additive model. Eur J Soil Sci 66:121–134

    Article  Google Scholar 

  • Brunsdon C, Comber L (2015) An introduction to R for spatial analysis and mapping. Sage, Los Angeles

    Google Scholar 

  • Cellura M, Cirrincione G, Marvuglia A, Miraoui A (2008) Wind speed spatial estimation for energy planning in Sicily: introduction and statistical analysis. Renew Energy 33:1237–1250

    Article  Google Scholar 

  • Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell SystTechnol 2:3 (Article 27)

    Google Scholar 

  • Chinta S (2014) A comparison of spatial interpolation methods in wind speed estimation across Anantapur District, Andhra Pradesh. J Earth Sci Res 2(2):48–54

    Article  Google Scholar 

  • Cook ER (1994) Spatial regression methods in dendroclimatology: a review and comparison of two techniques. Int J Climatol 14:379–402

    Article  Google Scholar 

  • Daly C, Halbleib M, Smith JI, Gibson WP, Doggett MK, Taylor GH, Curtis J, Pasteris PP (2008) Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States. Int J Climatol 28:2031–2064

    Article  Google Scholar 

  • Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Hólm EV, Isaksen L, Kållberg P, Köhler M, Matricardi M, McNally AP, Monge-Sanz BM, Morcrette J-J, Park B-K, Peubey C, de Rosnay P, Tavolato C, Thépaut J-N, Vitart F (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597

    Article  Google Scholar 

  • Denhard M, Walter A, Schönwiese C-D (1996) Simulation globaler Klimaänderungen mit Hilfe neuronaler Netze: Konzept, Anwendungsprinzipien und Ergebnisse. Nat Rdsch 49(8):295–301

    Google Scholar 

  • Everitt BS, Hothorn T (2010) A handbook of statistical analysis using R, 2nd ed. CRC Press, Boca Raton

    Google Scholar 

  • Gandin L (1965) Objective analysis of meteorological fields (Leningrad: Gidromet). 1963. English translation. Israel program for scientific translation), Jerusalem

  • González-Longatt F, Medina H, González JS (2015) Spatial interpolation and orographic correction to estimate wind energy resource in Venezuela. Renew Sustain Energy Rev 48:1–16

    Article  Google Scholar 

  • Goodin WR, McRae GJ, Seinfeld JH (1979) A comparison of interpolation methods for sparse data: application to wind and concentration fields. J Appl Meteorol 18:761–771

    Article  Google Scholar 

  • Gunn SR (1998) Support vector machines for classification and regression. Technical Report. http://users.ecs.soton.ac.uk/srg/publications/pdf/SVM.pdf. Accessed 22 Nov 2016

  • Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182

    Google Scholar 

  • Hartmann AD, De Beurs K, Stein A, White JW (1999) Interpolation techniques for climate variables. NGG-GIS Series 99-01. CIMMYT, Mexico

    Google Scholar 

  • Hastie T, Tibshirani R (1986) Generalized additive models. Stat Sci 1(3):297–310

    Article  Google Scholar 

  • Haylock MR, Hofstra N, Klein Tank AMG, Klok EJ, Jones PD, New M (2008) A European daily high-resolution gridded data set of surface temperature and precipitation for 1950–2006. J Geophys Res 113:D20119

    Article  Google Scholar 

  • Heinert M, Riedel B (2010) Support vector machines. Teil 2: Praktische Beispiele und Anwendung. ZFV 135(5):308–313

    Google Scholar 

  • Hengl T (2009) A practical guide to geostatistical mapping. http://spatial-analyst.net/book/system/files/Hengl_2009_GEOSTATe2c1w.pdf. Accessed 6 Jun 2015

  • Hengl T, Heuvelink GBM, Rossiter DG (2007) About regression-kriging: form equations to case studies. Comput Geosci 33:1301–1315

    Article  Google Scholar 

  • Hernández-Escobedo Q, Saldaña-Flores R, Rodríguez-García ER, Manzano-Agugliaro F (2014) Wind energy resource in Northern Mexico. Renew Sustain Energy Rev 32:890–914

    Article  Google Scholar 

  • Hijmans RJ (2015) raster: geographic data analysis and modeling. R package version 2.5-2. https://CRAN.R-project.org/package=raster

  • Hijmans RJ, Cameron S, Parra JL, Jones PG, Jarvis A (2005) Very high resolution interpolated climate surfaces for global land areas. Int J Climatol 25:1965–1978

    Article  Google Scholar 

  • Hijmans RJ, Phillips S, Leathwick J, Elith J (2016) dismo: species distribution modeling. R package version 1.0–15. https://CRAN.R-project.org/package=dismo

  • Hohn ME (1999) Geostatistics and petroleum geology, 2nd edn. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Hsieh WW (2009) Machine learning methods in the environmental sciences. Neural networks and kernels. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Izenman AJ (2013) Modern multivariate statistical techniques: regression, classification, and manifold learning. Springer, New York

    Google Scholar 

  • James G, Witten D, Hastie T, Tibsgirani R (2013) An introduction to statistical learning: with applications in R. Springer, New York

    Book  Google Scholar 

  • Jarosch AH, Anslow FS, Clarke KC (2012) High-resolution precipitation and temperature downscaling for glacier models. Clim Dyn 38:391–409

    Article  Google Scholar 

  • Jia S, Zhu W, Lü A, Yan T (2011) A statistical spatial downscaling algorithm of TRIMM precipitation based on NDVI and DEM in the Qaidam Basin of China. Remote Sens Environ 115:3069–3079

    Article  Google Scholar 

  • Jiang D, Liu H, Wang W (2001) Test a modified surface wind interpolation scheme for complex terrain in a stable atmosphere. Atmos Environ 35:4877–4885

    Article  Google Scholar 

  • Joyner TA, Friedland CJ, Rohli RV, Treviño AM, Massarra C, Paulus G (2015) Cross-correlation modeling of European windstorms: a cokriging approach for optimizing surface wind estimates. Spat Stat 13:62–75

    Article  Google Scholar 

  • Kim G, Barros AP (2002) Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using constraction mapping and ancillary data. Remote Sens Environ 83:400–413

    Article  Google Scholar 

  • Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J Chem Metallurg Mining Soc S Afr 52 (6):119–139

    Google Scholar 

  • Kubat M (2015) An introduction to machine learning. Springer, Cham

    Book  Google Scholar 

  • Kuhn M, Johnson K (2013) Applied predictive modeling. Springer, New York

    Book  Google Scholar 

  • Legates DR, McCabe GJ Jr (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241

    Article  Google Scholar 

  • Legates DR, McCabe GJ (2013) A refined index of model performance: a rejoinder. Int J Climatol 33(4):1053–1056

    Article  Google Scholar 

  • Li J (2017) Assessing the accuracy of predictive models for numerical data: not r or r2, why not? Then what? PLoS One 12(8):e0183250

    Article  Google Scholar 

  • Li J, Heap AD (2008) A review of spatial interpolation methods for environmental scientists. Geoscience Australia, Record 2008/23

  • Li J, Heap AD (2011) A review of comparative studies of spatial interpolation methods in environmental sciences: performance and impact factors. Ecol Inform 6:228–241

    Article  Google Scholar 

  • Li J, Heap AD, Potter A, Daniell JJ (2011) Application of machine learning methods to spatial interpolation of environmental variables. Environ Model Softw 26:1647–1659

    Article  Google Scholar 

  • Li J, Heap AD (2014) Spatial interpolation methods applied in the environmental sciences: A review. Environ Model Softw 53:173–189

    Article  Google Scholar 

  • Li T, Zheng X, Dai Y, Yang C, Chen Z, Zhang S, Wu G, Wang Z, Huang C, Shen Y, Liao R (2014) Mapping near-surface air temperature, pressure, relative humidity and wind speed over mainland China with high spatiotemporal resolution. Adv Atmos Sci 31:1127–1135

    Article  Google Scholar 

  • Luo W, Taylor MC, Parker SR (2008) A comparison of spatial interpolation methods to estimate continuous wind speed surfaces using irregularly distributed data from England and Wales. Int J Climatol 28:947–959

    Article  Google Scholar 

  • Marra G, Wood SN (2011) Practical variable selection for generalized additive models. Comput Stat Data Anal 55:2372–2387

    Article  Google Scholar 

  • Masseran N, Razali AM, Ibrahim K, Zin WZW, Zaharim A (2012) On spatial analysis of wind energy potential in Malaysia. WSEAS Trans Math 11(6):451–461

    Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266

    Article  Google Scholar 

  • Meyer D, Dimitriadou E, Hornik K, Weingessel A, Leisch F (2015) e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien. R package version 1.6-7. https://CRAN.R-project.org/package=e1071

  • Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2017) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900

    Article  Google Scholar 

  • Naimi B (2015) rts: raster time series analysis. R package version 1.0-10. https://CRAN.R-project.org/package=rts

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models. Part I—A discussion of principles. J Hydrol 10:282–290

    Article  Google Scholar 

  • Öztopal A (2006) Artificial neural network approach to spatial estimation of wind velocity data. Energy Convers Manag 47:395–406

    Article  Google Scholar 

  • Palomino I, Martin F (1995) A simple method for spatial interpolation of the wind in complex terrain. J Appl Meteorol 34:1678–1693

    Article  Google Scholar 

  • Pebesma EJ (2004) Multivariable geostatistics in S: the gstat package. Comput Geosci 30:683–691

    Article  Google Scholar 

  • Philippopoulos K, Deligiorgi D (2012) Application of artificial neural networks for the spatial estimation of wind speed in a coastal region with complex topography. Renew Energy 38:75–82

    Article  Google Scholar 

  • R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://ww.R-project.org/

  • Rossiter DG (2012) Technical note: cokriging with the gstat package of the R environment for statistical computing. http://www.css.cornell.edu/faculty/dgr2/teach/R/R_ck.pdf. Accessed 11 Nov 2016

  • Şahin AD (2001) Spatio-temporal modeling winds of Turkey, Unpublished PhD Thesis; Istanbul Technical University, p 286

  • Şahin AD, Şen Z (2004) A new spatial prediction model and its applications to wind records. Theor Appl Climatol 79:45–54

    Article  Google Scholar 

  • Schnur R, Lettermaier DP (1998) A case study of statistical downscaling in Australia using weather classification by recursive partitioning. J Hydrol 212–213:362–379

    Article  Google Scholar 

  • Schölkopf B, Smola A (2002) Learning with kernels. Support vector machines, regularization, optimization and beyond. The MIT Press, Cambridge

    Google Scholar 

  • Schoof JT (2013) Statistical Downscaling in Climatology. Geogr Compass 7(4):249–265

    Article  Google Scholar 

  • Sinha SK, Talwalkar DR, Narkhedkar SG, Rajamani S (1989) A scheme for objective analysis of wind field incorporating multi-weighting functions in the optimum interpolation method. Adv Atmos Sci 6(4):435–446

    Article  Google Scholar 

  • Sinha SK, Narkhedkar SG, Talwalkar DR, Rajamani S (1992) Some experiments with multivariate objective analysis scheme of heights and winds using optimum interpolation. Adv Atmos Sci 9(4):431–440

    Article  Google Scholar 

  • Sliz-Szkliniarz B, Vogt J (2011) GIS-based approach for the evaluation of wind energy potential: a case study for the Kujawsko–Pomorskie Voivodeship. Renew Sustain Energy Rev 15:1696–1707

    Article  Google Scholar 

  • Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222

    Article  Google Scholar 

  • Stoyan D, Stoyan H, Jansen U (1997) Umweltstatistik: statistische verarbeitung und analyse von umweltdaten. Teubner, Stuttgart

    Book  Google Scholar 

  • Vapnik V (1995) The nature of statistical learning theory. Springer, New York

    Book  Google Scholar 

  • Venables WN, Ripley BD (2002) Modern applied statistics with S. 4th ed. Springer, New York (ISBN 0-387-95457-0)

    Book  Google Scholar 

  • Wackernagel H (2010) Multivariate geostatistics: an introduction with applications, 3rd edn. Springer, Berlin

    Google Scholar 

  • Walter A (2001) Zur Anwendung neuronaler Netze in der Klimatologie. Berichte des Deutschen Wetterdienstes. Heft 218. Selbstverlag des Deutschen Wetterdienstes, Offenbach am Main

    Google Scholar 

  • Webster R, Oliver MA (2007) Geostatistics for environmental scientists, 2nd edn. Wiley, Chichester

    Book  Google Scholar 

  • Wilks DS (2011) Statistical methods in the atmospheric sciences, 3rd edn. Academic Press, Oxford

    Google Scholar 

  • Wood SN (2006) Generalized additive models: an introduction with R. Chapman & Hall, Boca Raton

    Book  Google Scholar 

  • Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J R Stat Soc 73(1):3–36

    Article  Google Scholar 

  • Ye W, Hong HP, Wang JF (2015) Comparison of spatial interpolation methods for extreme wind speeds over Canada. J Comput Civ Eng 29(6):401 4095

    Article  Google Scholar 

  • Zeileis A, Grothendieck G (2005) zoo: S3 infrastructure for regular and irregular time series. J Stat Softw 14(6):1–27

  • Zlatev Z, Middleton SE, Veres G (2010) Benchmarking knowledge-assisted kriging for automated spatial interpolation of wind measurements. In: Proceedings of the 2010 13th conference on information Fusion (FUSION), Edinburgh, UK

Download references

Acknowledgements

By the financial support of the University of Bayreuth, the University of Bayreuth Graduate school and DAAD it was possible to organize and finance field work in Central Asia. Thanks for grammar and spelling correction to Thomas Kolb and Daniela Kretz. The authors also would like to thank the two anonymous reviewers for their helpful comments and suggestions that significantly improved the quality of this paper.

Author information

Authors and Affiliations

  1. Department of Geography, University of Bayreuth, Universitätsstr. 30, 95447, Bayreuth, Germany

    Katja Reinhardt & Cyrus Samimi

  2. Bayreuth Center of Ecology and Environmental Research (BAYCEER), University of Bayreuth, 95447, Bayreuth, Germany

    Cyrus Samimi

Authors
  1. Katja Reinhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cyrus Samimi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Katja Reinhardt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reinhardt, K., Samimi, C. Comparison of different wind data interpolation methods for a region with complex terrain in Central Asia. Clim Dyn 51, 3635–3652 (2018). https://doi.org/10.1007/s00382-018-4101-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00382-018-4101-y

Keywords

Search

Navigation