Uncertainty Analysis of Rainfall Spatial Interpolation in Urban Small Area

  • Jie Huang
  • Changfeng JingEmail author
  • Jiayun Fu
  • Zejun Huang
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 270)


Uncertainty analysis have attracted increasing attention of both theory and application over the last decades. Owing to the complex of surrounding, uncertainty analysis of rainfall in urban area is very little. Existing literatures on uncertainty analysis paid less attention on gauge density and rainfall intensity. Therefore, this study focuses on urban area, which a good complement to uncertainty research. In this study, gauge density was investigated with carefully selecting of gauge to covering evenly. Rainfall intensity data were extracted from one rainfall event at begin, summit and ending phases of rainfall process. Three traditional methods (Ordinary Kriging, RBF and IDW) and three machine methods (RF, ANN and SVM) were investigated for the uncertainty analysis. The result shows that (1) gauge density has important influence on the interpolation accuracy, and the higher gauge density means the higher accuracy. (2) The uncertainty is progressively stable with the increasing of rainfall intensity. (3) Geostatistic methods has better result than the IDW and RBF owing to considering spatial variability. The selected machine learning methods have good performance than traditional methods. However, the complex training processing and without spatial variability may reduce its practicability in modern flood management. Therefore, the combining of traditional methods and machine learning will be the good paradigm for spatial interpolation and uncertainty analysis.


Rainfall Spatial interpolation Ordinary Kriging Random forest Machine learning 



The authors would like to thank the valuable comments from anonymous reviewers. This study is jointly supported by the National Natural Science Foundation of China (Grant No. 41771412), the Beijing Natural Science Foundation (Grant No. 8182015), Beijing Advanced innovation center for future urban design (Grant No. X18052, X18058, X18158) and the Zhejiang Province Research Program (Grant No. 2015C33064).


  1. 1.
    Bárdossy, A., Pegram, G.: Interpolation of precipitation under topographic influence at different time scales. Water Resour. Res. 49(8), 4545–4565 (2013)CrossRefGoogle Scholar
  2. 2.
    Goovaerts, P.: Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. J. Hydrol. 228(1–2), 113–129 (2000)CrossRefGoogle Scholar
  3. 3.
    Jeffrey, S.J., Carter, J.O., Moodie, K.B., Beswick, A.R.: Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environ. Model Softw. 16(4), 309–330 (2001)CrossRefGoogle Scholar
  4. 4.
    Li, J., Heap, A.D.: Spatial interpolation methods applied in the environmental sciences: a review. Environ. Model Softw. 53, 173–189 (2014)CrossRefGoogle Scholar
  5. 5.
    Muthusamy, M., Schellart, A., Tait, S., Heuvelink, G.B.M.: Geostatistical upscaling of rain gauge data to support uncertainty analysis of lumped urban hydrological models. Hydrol. Earth Syst. Sci. 21(2), 1077–1091 (2017)CrossRefGoogle Scholar
  6. 6.
    Wagner, P.D., Fiener, P., Wilken, F., Kumar, S., Schneider, K.: Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions. J. Hydrol. 464–465, 388–400 (2012)CrossRefGoogle Scholar
  7. 7.
    Courty, L., Rico-Ramirez, M., Pedrozo-Acuña, A.: The significance of the spatial variability of rainfall on the numerical simulation of urban floods. Water 10(2), 207 (2018)CrossRefGoogle Scholar
  8. 8.
    Hall, J., Solomatine, D.: A framework for uncertainty analysis in flood risk management decisions. Int. J. River Basin Manag. 6(2), 85–98 (2008)CrossRefGoogle Scholar
  9. 9.
    Hutter, G., Schanze, J.: Learning how to deal with uncertainty of flood risk in long-term planning. Int. J. River Basin Manag. 6(2), 175–184 (2008)CrossRefGoogle Scholar
  10. 10.
    Hrachowitz, M., Weiler, M.: Uncertainty of precipitation estimates caused by sparse gauging networks in a small. Mountainous Watershed. J. Hydrol. Eng. 16(5), 460–471 (2011)CrossRefGoogle Scholar
  11. 11.
    Tsintikidis, D., Georgakakos, K.R., Sperfslage, J.A., Smith, D.E., Carpenter, T.M.: Precipitation uncertainty and raingauge network design within Folsom Lake watershed. J. Hydrol. Eng. 7(2), 175–184 (2002)CrossRefGoogle Scholar
  12. 12.
    Cheng, M., et al.: Performance assessment of spatial interpolation of precipitation for hydrological process simulation in the Three Gorges Basin. Water 9(11), 838 (2017)CrossRefGoogle Scholar
  13. 13.
    Rupa, C., Mujumdar, P.P.: Quantification of uncertainty in spatial return levels of urban precipitation extremes. J. Hydrol. Eng. 23(1), 04017053(2018)CrossRefGoogle Scholar
  14. 14.
    Yang, L., Tian, F., Niyogi, D.: A need to revisit hydrologic responses to urbanization by incorporating the feedback on spatial rainfall patterns. Urban Clim. 12, 128–140 (2015)CrossRefGoogle Scholar
  15. 15.
    Liu, M., Bárdossy, A., Zehe, E.: Interaction of valleys and circulation patterns (CPs) on spatial precipitation patterns in southern Germany. Hydrol. Earth Syst. Sci. 17(11), 4685–4699 (2013)CrossRefGoogle Scholar
  16. 16.
    Otieno, H., Yang, J., Liu, W., Han, D.: Influence of rain gauge density on interpolation method selection. J. Hydrol. Eng. 19(11), 04014024(2014)CrossRefGoogle Scholar
  17. 17.
    Jing, C., Yu, J., Dai, P., Wei, H., Du, M.: Rule-based rain gauge network design in urban areas aided by spatial kernel density. Water Pract. Technol. 11(1), 166–175 (2016)CrossRefGoogle Scholar
  18. 18.
    Moulin, L., Gaume, E., Obled, C.: Uncertainties on mean areal precipitation: assessment and impact on streamflow simulations. Hydrol. Earth Syst. Sci. 13(2), 99–114 (2009)CrossRefGoogle Scholar
  19. 19.
    Kobold, M., Sušelj, K.: Precipitation forecasts and their uncertainty as input into hydrological models. Hydrol. Earth Syst. Sci. 9(4), 322–332 (2005)CrossRefGoogle Scholar
  20. 20.
    Ly, S., Charles, C., Degré, A.: Different methods for spatial interpolation of rainfall data for operational hydrology and hydrological modeling at watershed scale: a review. Base 17(2), 392–406 (2013)Google Scholar
  21. 21.
    Li, J., Heap, A.D.: A review of comparative studies of spatial interpolation methods in environmental sciences: performance and impact factors. Ecol. Inform. 6(3–4), 228–241 (2011)CrossRefGoogle Scholar
  22. 22.
    de Amorim Borges, P., Franke, J., da Anunciação, Y.M.T., Weiss, H., Bernhofer, C.: Comparison of spatial interpolation methods for the estimation of precipitation distribution in Distrito Federal, Brazil. Theor. Appl. Climatol. 123(1–2), 335–348 (2016)CrossRefGoogle Scholar
  23. 23.
    Appelhans, T., Mwangomo, E., Hardy, D.R., Hemp, A., Nauss, T.: Evaluating machine learning approaches for the interpolation of monthly air temperature at Mt. Kilimanjaro, Tanzania. Spat. Stat. 14, 91–113 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gilardi, S., Begio, N.: Local machine learning models for spatial data analysis. J. Geogr. Inf. Decis. Anal. 4(EPFL-ARTICLE-82651), 11–28 (2000)Google Scholar
  25. 25.
    Li, J., Heap, A.D., Potter, A., Daniell, J.J.: Application of machine learning methods to spatial interpolation of environmental variables. Environ. Model Softw. 26(12), 1647–1659 (2011)CrossRefGoogle Scholar
  26. 26.
    Hengl, T., Heuvelink, G.B.M., Rossiter, D.G.: About regression-Kriging: from equations to case studies. Comput. Geosci. 33(10), 1301–1315 (2007)CrossRefGoogle Scholar
  27. 27.
    Bhargava, N., Bhargava, R., Tanwar, P.S., Narooka, P.C.: Comparative study of inverse power of IDW interpolation method in inherent error analysis of aspect variable. In: Mishra, D., Nayak, M., Joshi, A. (eds.) Information and Communication Technology for Sustainable Development, pp. 521–529. Springer, Singapore (2018). Scholar
  28. 28.
    Maciej, T.: 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 (1998)Google Scholar
  29. 29.
    Adhikary, S.K., Muttil, N., Yilmaz, A.G.: Genetic programming-based Ordinary Kriging for spatial interpolation of rainfall. J. Hydrol. Eng. 21(2), 1–14 (2016)CrossRefGoogle Scholar
  30. 30.
    Berndt, C., Rabiei, E., Haberlandt, U.: Geostatistical merging of rain gauge and radar data for high temporal resolutions and various station density scenarios. J. Hydrol. 508, 88–101 (2014)CrossRefGoogle Scholar
  31. 31.
    ESRI: How radial basis functions work (2013)Google Scholar
  32. 32.
    Xie, Y., et al.: Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: accuracy and uncertainty analysis. Chemosphere 82(3), 468–476 (2011)CrossRefGoogle Scholar
  33. 33.
    Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)zbMATHCrossRefGoogle Scholar
  34. 34.
    Genuer, R., Poggi, J.M., Tuleau-Malot, C., Villa-Vialaneix, N.: Random forests for big data. Big Data Res. 9, 28–46 (2017)CrossRefGoogle Scholar
  35. 35.
    Kühnlein, M., Appelhans, T., Thies, B., Nauss, T.: Improving the accuracy of rainfall rates from optical satellite sensors with machine learning - a random forests-based approach applied to MSG SEVIRI. Remote Sens. Environ. 141, 129–143 (2014)CrossRefGoogle Scholar
  36. 36.
    Basheer, I.A., Hajmeer, M.: Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Methods 43(1), 3–31 (2000)CrossRefGoogle Scholar
  37. 37.
    Prasad, R., Deo, R.C., Li, Y., Maraseni, T.: Input selection and performance optimization of ANN-based streamflow forecasts in the drought-prone Murray Darling Basin region using IIS and MODWT algorithm. Atmos. Res. 197, 42–63 (2017)CrossRefGoogle Scholar
  38. 38.
    Cortes, C., Cortes, C., Vapnik, V., Vapnik, V.: Support vector networks. Mach. Learn. 20(3), 273–297 (1995)zbMATHGoogle Scholar
  39. 39.
    Kavzoglu, T., Colkesen, I.: A kernel functions analysis for support vector machines for land cover classification. Int. J. Appl. Earth Obs. Geoinf. 11(5), 352–359 (2009)CrossRefGoogle Scholar
  40. 40.
    Sadler, J.M., Goodall, J.L., Morsy, M.M.: Effect of rain gauge proximity on rainfall estimation for problematic urban coastal watersheds in Virginia Beach, Virginia. J. Hydrol. Eng. 22(9), 04017036(2017)CrossRefGoogle Scholar
  41. 41.
    Cox, J.C., Sadiraj, V.: On the coefficient of variation as a measure of risk sensitivity. SSRN 3(3), (2011)Google Scholar
  42. 42.
    Reed, G.F., Lynn, F., Meade, B.D.: Quantitative assays. Clin. Diagn. Lab. Immunol. 9(6), 1235–1239 (2002)Google Scholar
  43. 43.
    Cristiano, E., Veldhuis, M.-C., Van De Giesen, N.: Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas-a review. Hydrol. Earth Syst. Sci. 21, 3859–3878 (2017)CrossRefGoogle Scholar
  44. 44.
    WMO: Guide to Meteorological Instruments and Methods of observation (WMO-No.8), Seven edit. Geneva, Switzerland (2008)Google Scholar
  45. 45.
    Goovaerts, P.: Geostatistics in soil science: state-of-the-art and perspectives. Geoderma 89(1–2), 1–45 (1999)CrossRefGoogle Scholar
  46. 46.
    Ma, L., Chi, X., Zuo, C.: Evaluation of interpolation models for rainfall erosivity on a large scale. In: First International Conference on Agro-Geoinformatics (Agro-Geoinformatics), pp. 1–5. IEEE, Shanghai (2012)Google Scholar
  47. 47.
    Zhang, P., Liu, R., Bao, Y., Wang, J., Yu, W., Shen, Z.: Uncertainty of SWAT model at different DEM resolutions in a large mountainous watershed. Water Res. 53, 132–144 (2014)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  • Jie Huang
    • 1
  • Changfeng Jing
    • 2
    Email author
  • Jiayun Fu
    • 2
  • Zejun Huang
    • 1
  1. 1.School of Computer Science and TechnologyHangzhou Dianzi UniversityHangzhouChina
  2. 2.School of Geomatics and Urban Spatial InformaticsBeijing University of Civil, Engineering and ArchitectureBeijingChina

Personalised recommendations