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Clustering Data and Incorporating Topographical Variables for Improving Spatial Interpolation of Rainfall in Mountainous Region

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Abstract

This study was an attempt to quantify the improvement in the accuracy of rainfall interpolation in the mountainous terrain by clustering of rainfall data at the data preparation stage and incorporating topographical variables at interpolation stage. The univariate kriging techniques, ordinary kriging (OK), simple kriging and universal kriging (UK) were compared with multivariate kriging method of ordinary cokriging (OCK). The elevation, slope and terrain ruggedness index (TRI) computed from digital elevation model were incorporated as explanatory variable in OCK. These algorithms were applied to the normal annual and seasonal rainfall data points located in Central Himalayas of Uttarakhand region. The study area was divided into two different zones of lowland and upland based on the elevation variability. This zonation was then used as a basis for clustering the rainfall data. The performance of the interpolation techniques was assessed for subdivided regions and compared with the results obtained for complete region. The evaluation was based on absolute error metrics of root mean square error (RMSE) in combination with RMSE-observations standard deviation ratio. The absolute percentage error (APE) statistics was calculated for every observation points and then the percentage of data for with APE ≤ 30% (APE30) was analyzed. It was observed that performance efficiency of the interpolation methods improves by 5-20% if the rainfall data is clustered based on homogeneity of terrain elevation as against considering the complete set of data. In complex terrain, the inclusion of topographical variables improves the cokriging based rainfall prediction if it is correlated with rainfall.

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References

  • Anctil F, Lauzon N, Andréassian V (2006) Improvement of rainfall-runoff forecasts through mean areal rainfall optimization. J Hydrol 328:717–725. doi:10.1016/j.jhydrol.2006.01.016

    Article  Google Scholar 

  • Anders AM, Roe GH, Hallet B, et al (2006) Spatial patterns of precipitation and topography in the Himalaya. In: Special Paper 398: Tectonics, Climate, and Landscape Evolution. Geological Society of America, pp 39–53

  • Austin GL, Dirks KN (2006) Topographic Effects on Precipitation, Topographic Effects on Precipitation. In: Encyclopedia of Hydrological Sciences, Encyclopedia of Hydrological Sciences. John Wiley & Sons, Ltd

  • Barros AP, Lang TJ (2003) Monitoring the Monsoon in the Himalayas: Observations in Central Nepal, June 2001. Mon Weather Rev 131:1408–1427. doi:10.1175/1520-0493(2003)131<1408:MTMITH>2.0.CO;2

    Article  Google Scholar 

  • Basistha A, Arya DS, Goel NK (2008) Spatial Distribution of Rainfall in Indian Himalayas – A Case Study of Uttarakhand Region. Water Resour Manag 22:1325–1346. doi:10.1007/s11269-007-9228-2

    Article  Google Scholar 

  • Bisht RC (2008) International Encyclopaedia Of Himalayas (5 Vols. Set). Mittal Publications

  • Blöschl G, Sivapalan M (1995) Scale issues in hydrological modelling: A review. Hydrol Process 9:251–290. doi:10.1002/hyp.3360090305

    Article  Google Scholar 

  • Bookhagen B, Burbank DW (2006) Topography, relief, and TRMM-derived rainfall variations along the Himalaya. Geophys Res Lett 33:L08405. doi:10.1029/2006GL026037

    Google Scholar 

  • Buishand TA (1982) Some methods for testing the homogeneity of rainfall records. J Hydrol 58(1–2):11–27

    Article  Google Scholar 

  • Buytaert W, Celleri R, Willems P et al (2006) Spatial and temporal rainfall variability in mountainous areas: A case study from the south Ecuadorian Andes. J Hydrol 329:413–421. doi:10.1016/j.jhydrol.2006.02.031

    Article  Google Scholar 

  • Chakravarti JR, Laha R, Mohan I (1967) Handbook of Methods of Applied Statistics, 1967 edition/volume I, Only edn. John Wiley & Sons

  • Dahal V, Shakya NM, Bhattarai R (2016) Estimating the Impact of Climate Change on Water Availability in Bagmati Basin, Nepal. Environ Prog 3:1–17. doi:10.1007/s40710-016-0127-5

    Article  Google Scholar 

  • Daly C, Neilson RP, Phillips DL (1994) A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J Appl Meteorol 33:140–158

    Article  Google Scholar 

  • Dingman SL (2002) Physical Hydrology. Prentice Hall

  • Diodato N (2005) The influence of topographic co-variables on the spatial variability of precipitation over small regions of complex terrain. Int J Climatol 25:351–363. doi:10.1002/joc.1131

    Article  Google Scholar 

  • Diodato N, Tartari G, Bellocchi G (2010) Geospatial Rainfall Modelling at Eastern Nepalese Highland from Ground Environmental Data. Water Resour Manag 24:2703–2720. doi:10.1007/s11269-009-9575-2

    Article  Google Scholar 

  • Goovaerts P (2000) Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. J Hydrol 228:113–129. doi:10.1016/S0022-1694(00)00144-X

    Article  Google Scholar 

  • Grimes DI, Pardo-Igúzquiza E (2010) Geostatistical Analysis of Rainfall. Geogr Anal 42:136–160

    Article  Google Scholar 

  • Hengl T (2006) Finding the right pixel size. Comput Geosci 32:1283–1298. doi:10.1016/j.cageo.2005.11.008

    Article  Google Scholar 

  • Isaaks EH, Srivastava MR (1989) An Introduction to Applied Geostatistics. Oxford University Press

  • Joshi SC (2004) Uttaranchal, Environment & Development. A Geo-ecological Overview, Gyanodaya Prakashan

    Google Scholar 

  • Joshi V, Negi GCS (1995) Analysis of Long-term Weather data from Garhwal Himalaya. ENVIS Bulletin on Himalayan Ecology 3:63

    Google Scholar 

  • Kumari M, Basistha A, Bakimchandra O, Singh CK (2016a) Comparison of Spatial Interpolation Methods for Mapping Rainfall in Indian Himalayas of Uttarakhand Region. In: Raju JN (ed) Geostatistical and Geospatial Approaches for the Characterization of Natural Resources in the Environment: Challenges. Processes and Strategies. Springer International Publishing, Cham, pp. 159–168

    Chapter  Google Scholar 

  • Kumari M, Singh CK, Bakimchandra O, Basistha A (2016b) DEM-based delineation for improving geostatistical interpolation of rainfall in mountainous region of Central Himalayas, India. Theor Appl Climatol:1–8. doi:10.1007/s00704-016-1866-y

  • Kumari M, Singh CK, Bakimchandra O, Basistha A (2016c) Geographically weighted regression based quantification of rainfall–topography relationship and rainfall gradient in central Himalayas. Int J Climatol. doi:10.1002/joc.4777

    Google Scholar 

  • Lang TJ, Barros AP (2002) An investigation of the onsets of the 1999 and 2000 monsoons in Central Nepal. Mon Weather Rev 130:1299–1316. doi:10.1175/1520-0493(2002)130<1299:AIOTOO>2.0.CO;2

    Article  Google Scholar 

  • Li H, Xu C-Y, Beldring S et al (2016) Water resources under climate change in Himalayan basins. Water Resour Manag 30:843–859. doi:10.1007/s11269-015-1194-5

    Article  Google Scholar 

  • Lloyd CD (2005) Assessing the effect of integrating elevation data into the estimation of monthly precipitation in great Britain. J Hydrol 308:128–150. doi:10.1016/j.jhydrol.2004.10.026

    Article  Google Scholar 

  • Mair A, Fares A (2011) Comparison of rainfall interpolation methods in a mountainous region of a Tropical Island. J Hydrol Eng 16:371–383. doi:10.1061/(ASCE)HE.1943-5584.0000330

    Article  Google Scholar 

  • Moral FJ (2010) Comparison of different geostatistical approaches to map climate variables: application to precipitation. Int J Climatol 30:620–631. doi:10.1002/joc.1913

    Google Scholar 

  • Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50:885–900

    Article  Google Scholar 

  • Price MF, Byers AC, Friend DA, et al (2013) Mountain Geography: Physical and Human Dimensions. Univ of California Press

  • Prudhomme C, Reed DW (1999) Mapping extreme rainfall in a mountainous region using geostatistical techniques: a case study in Scotland. Int J Climatol 19:1337–1356. doi:10.1002/(SICI)1097-0088(199910)19:12<1337::AID-JOC421>3.0.CO;2-G

    Article  Google Scholar 

  • Riley SJ, DeGloria SD, Elliot R (1999) A terrain ruggedness index that quantifies topographic heterogeneity. Int J Therm Sci 5:1–4

    Google Scholar 

  • Singh J, Knapp HV, Arnold JG, Demissie M (2005) Hydrological modeling of the Iroquois River watershed using HSPF and SWAT. J Am Water Resour Assoc 41:343–360. doi:10.1111/j.1752-1688.2005.tb03740.x

    Article  Google Scholar 

  • Wackernagel H (2003) Multivariate Geostatistics. Springer, Berlin Heidelberg

    Book  Google Scholar 

  • Walpole RE, Myers RH, Myers SL, Ye KE (2011) Probability and statistics for engineers and scientists, 9 edn. Pearson, Boston

    Google Scholar 

  • Wang JF, Stein A, Gao BB, Ge Y (2012) A review of spatial sampling. Spat Stat 2:1–14. doi:10.1016/j.spasta.2012.08.001

    Article  Google Scholar 

  • Xu H, Xu CY, Chen H et al (2013) Assessing the influence of rain gauge density and distribution on hydrological model performance in a humid region of China. J Hydrol 505:1–12. doi:10.1016/j.jhydrol.2013.09.004

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Natural Resources, TERI University, New Delhi, India

    Madhuri Kumari

  2. Department of Civil Engg., Amity School of Engineering & Technology, Amity University Uttar Pradesh, Noida, U.P, India

    Madhuri Kumari

  3. Department of Regional Water Studies, TERI University, New Delhi, India

    Chander Kumar Singh

  4. Egis India Consulting Engineers Pvt. Ltd. New Delhi, New Delhi, India

    Ashoke Basistha

Authors
  1. Madhuri Kumari
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  2. Chander Kumar Singh
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  3. Ashoke Basistha
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Correspondence to Chander Kumar Singh.

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Kumari, M., Singh, C.K. & Basistha, A. Clustering Data and Incorporating Topographical Variables for Improving Spatial Interpolation of Rainfall in Mountainous Region. Water Resour Manage 31, 425–442 (2017). https://doi.org/10.1007/s11269-016-1534-0

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