Spatial interpolation schemes of daily precipitation for hydrologic modeling

  • Yeonsang Hwang
  • Martyn Clark
  • Balaji Rajagopalan
  • George Leavesley
Original Paper


Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.


Interpolation Local polynomial Regression Hydrologic Modeling Daily precipitation 



Partial support of this work by NOAA GAPP program (Award NA16GP2806) and the NOAA RISA Program (Award NA17RJ1229) is thankfully acknowledged. The authors also wish to thank Lauren Hay and Steve Markstrom at USGS Denver office, and Subhrendu Gangopadhyay at Hydrosphere for providing valuable comments and data that greatly enhanced the quality of the entire analysis.


  1. Ajami NK, Gupta H, Wagener T, Sorooshian S (2004) Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. J Hydrol 298:112–135CrossRefGoogle Scholar
  2. Barancourt C, Creutin JD, Rivoirard J (1992) A method for delineating and estimating rainfall fields. Water Resour Res 28:1133–1144CrossRefGoogle Scholar
  3. Beek EG, Stein A, Janssen LLF (1992) Spatial variability and interpolation of daily precipitation amount. Stoch Hydrol Hydraul 6:209–221CrossRefGoogle Scholar
  4. Beven K, Freer J (2001) A dynamic TOPMODEL. Hydrol Process 15:1993–2011CrossRefGoogle Scholar
  5. Bishop GD, Church MR, Daly C (1998) Effects of improved precipitation estimates on automated runoff mapping: Eastern United States. J Am Water Resour As 34:159–166CrossRefGoogle Scholar
  6. Borga M, Vizzaccaro A (1997) On the interpolation of hydrologic variables; formal equivalance of multiquadratic surface fitting and kriging. J Hydrol 195:160–171CrossRefGoogle Scholar
  7. Borga M, Fattorelli S, Valentini P (1994) Precipitation estimation for flood forecasting in a mountainous basin. In: Tsakiris G, Santos MA, Balkema AA (eds) Advances in water resources technology and management; proceedings of the second European conference on advances in water resources technology and management. Lisbon, Portugal, 14–18 June 1994, pp 403–410Google Scholar
  8. Bussieres N, Hogg W (1989) The objective analysis of daily rainfall by distance weighting schemes on a mesoscale grid. Atmos Ocean 27:521–541CrossRefGoogle Scholar
  9. Carpenter TM, Georgakakos KP (2004) Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulation of a distributed hydrologic model. J Hydrol 298:202–221CrossRefGoogle Scholar
  10. Carpenter TM, Georgakakos KP, Sperfslagea JA (2001) On the parametric and NEXRAD-radar sensitivities of a distributed hydrologic model suitable for operational use. J Hydrol 253:169–193CrossRefGoogle Scholar
  11. Carrera-Hernandez JJ, Gaskin SJ (2007) Spatio temporal analysis of daily precipitation and temperature in the Basin of Mexico. J Hydrol 336(3–4):231–249. doi: 10.1016/j.jhydrol.2006.12.021 CrossRefGoogle Scholar
  12. Chua SH, Bras R (1982) Optimal estimators of mean areal precipitation in regions of orographic influences. J Hydrol 57:23–48CrossRefGoogle Scholar
  13. Church MR, Bishop GD, Cassell DL (1995) Maps of regional evapotranspiration and runoff precipitation ratios in the northeast united-states. J Hydrol 168:283–298CrossRefGoogle Scholar
  14. Clark MP, Hay LE (2004) Use of medium-range numerical weather prediction model output to produce forecasts of streamflow. J Hydrometeorol 5:15–32CrossRefGoogle Scholar
  15. Clark M, Gangopadhyay S, Hay L, Rajagopalan B, Wilby R (2004) The Schaake shuffle: a method for reconstructing space-time variability in forecasted precipitation and temperature fields. J Hydrometeorol 5:243–262CrossRefGoogle Scholar
  16. Creutin JD, Obled C (1982) Objective analysis and mapping techniques for rainfall fields: an objective comparison. Water Resour Res 18:413–431CrossRefGoogle Scholar
  17. Daly C, Neilson RP, Phillips DL (1994) A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J Appl Meteorol 33:140–158CrossRefGoogle Scholar
  18. Dingman SL (1994) Physical hydrology, 1st ed. edn. Prentice Hall, New Jersey, p 575Google Scholar
  19. Dirks KN, Hay JE, Stow CE, Harris D (1998) High-resolution studies of rainfall on Norfolk Island Part II: interpolation of rainfall data. J Hydrol 208:187–193CrossRefGoogle Scholar
  20. Dodson R, Marks D (1997) Daily air temperature interpolated at high spatial resolution over a large mountainous region. Clim Res 8:1–20CrossRefGoogle Scholar
  21. Duan Q, Gupta VK, Sorooshian S (1993) A shuffled complex evolution approach for effective and efficient global minimization. J Optim Theory Appl 76:501–521CrossRefGoogle Scholar
  22. Erxleben J, Elder K, Davis R (2002) Comparison of spatial interpolation methods for estimating snow distribution in the Colorado Rocky Mountains. Hydrol Process 16:3627–3649CrossRefGoogle Scholar
  23. Fassnacht SR, Dressler KS, Bales RC (2003) Snow water equivalent interpolation for the Colorado River Basin from snow telemetry (SNOTEL) data. Water Resour Res 39:1208. doi: 10.1029/2002WR001512 CrossRefGoogle Scholar
  24. Franke R, Nielson G (1980) Smooth interpolation of large sets of scattered data. Int J Numer Methods Eng 15:1691–1704CrossRefGoogle Scholar
  25. Gan TY, Burges SJ (2006) Assessment of soil-based and calibrated parameters of the Sacramento model and parameter transferability. J Hydrol 320:117–131CrossRefGoogle Scholar
  26. Goodale CL, Aber JD, Ollinger SV (1998) Mapping monthly precipitation, temperature, and solar radiation for Ireland with polynomial regression and a digital elevation model. Clim Res 10:35–49CrossRefGoogle Scholar
  27. Goovaerts P (2000) Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. J Hydrol 228:113–129CrossRefGoogle Scholar
  28. Groisman PV, Legates DR (1994) The accuracy of United-States precipitation data. Bull Am Meteorol Soc 75:215–227CrossRefGoogle Scholar
  29. Gupta VK, Waymire EC (1993) A statistical-analysis of mesoscale rainfall as a random cascade. J Appl Meteorol 32:251–267CrossRefGoogle Scholar
  30. Haberlandt U (2007) Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event. J Hydrol 332(1–2):144–157CrossRefGoogle Scholar
  31. Hartkamp AD, De Beurs K, Stein A, White JW (1999) Interpolation techniques for climate variables, NRG-GIS series 99-01. Mexico, D.F, CIMMYTGoogle Scholar
  32. Hay LE, McCabe GJ (2002) Spatial variability in water-balance model performance in the conterminous United States. J Am Water Resour As 38:847–860CrossRefGoogle Scholar
  33. Hay LE, Clark MP, Wilby RL, Gutowski WJ Jr, Leavesley GH, Pan Z, Arritt RW, Takle ES (2002) Use of regional climate model output for hydrologic simulations. J Hydrometeorol 3:571–590CrossRefGoogle Scholar
  34. Hay LE, Leavesley GH, Clark MP, Markstrom SL, Viger RJ, Umemoto M (2006) Step wise, multiple objective calibration of a hydrologic model for a snowmelt dominated basin. J Am Water Resour As 42:877–890CrossRefGoogle Scholar
  35. Helsel DR, Hirsch RM (1992) Statistical methods in water resources. Elsevier, Amsterdam, p 552Google Scholar
  36. Henry AJ (1919) Increase of precipitation with altitude. Mon Weather Rev 47:33–41CrossRefGoogle Scholar
  37. Hevesi JA, Istok JD, Flint AL (1992) Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis. J Appl Meteorol 31:661–676CrossRefGoogle Scholar
  38. Huber WC, Dickinson RE (1988) Storm water management model user’s manual, version 4, EPA/600/3-88/001a (NTIS PB88-236641/AS). Environmental Protection Agency, Athens, GA, p 595Google Scholar
  39. Jeffrey SJ, Carter JO, Moodie KB, Beswick AR (2001) Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environ Model Softw 16:309–330CrossRefGoogle Scholar
  40. Jothityangkoon C, Sivapalan M, Viney NR (2000) Tests of a space-time model of daily rainfall in southwestern Australia based on nonhomogeneous random cascades. Water Resour Res 36:267–284CrossRefGoogle Scholar
  41. Kastelec D, Košmelj K (2002) Spatial interpolation of mean yearly precipitation using universal kriging. Develop Stat 17:149–162Google Scholar
  42. Kitanidis PK (1986) Parameter uncertainty in estimation of spatial functions: bayesian analysis. Water Resour Res 22:499–507CrossRefGoogle Scholar
  43. Kruizinga S, Yperlaan GJ (1978) Spatial interpolation of daily totals of rainfall. J Hydrol 36:65–73CrossRefGoogle Scholar
  44. Kurtzman D, Kadmon R (1999) Mapping of temperature variables in Israel: a comparison of different interpolation methods. Clim Res 13:33–43CrossRefGoogle Scholar
  45. Kurtzman D, Navon S, Morin E (2009) Improving interpolation of daily precipitation for hydrologic modelling: spatial pattern of preferred interpolators. Hydrol Process 23:3281–3291CrossRefGoogle Scholar
  46. Kyriakidis PG, Kim J, Miller NR (2001) Geostatistical mapping of precipitation from rain gauge data using atmospheric and terrain characteristics. J Appl Meteorol 40:1855–1877CrossRefGoogle Scholar
  47. Lanza LG, Ramirez JA, Todini E (2001) Stochastic rainfall interpolation and downscaling. Hydrol Earth Syst Sci 5:139–143CrossRefGoogle Scholar
  48. Leavesley GH, Lichty RW, Troutman BM, Saindon LG (1983) Precipitation-runoff modeling system: user’s manual. U.S. Geological Survey Water-Resources Investigations 83-4238, p 207Google Scholar
  49. Leavesley GH, Restrepo PJ, Markstrom SL, Dixon M, Stannard LG (1996) The modular modeling system—MMS: user’s manual. Open file report 96-151, U.S. Geological Survey, p 182Google Scholar
  50. Leavesley GH, Markstrom SL, Restrepo PJ, Viger RJ (2002) A modular approach to addressing model design, scale, and parameter estimation issues in distributed hydrological modeling. Hydrol Process 16:173–187CrossRefGoogle Scholar
  51. Li M, Shao Q (2010) An improved statistical approach to merge satellite rainfall estimates and raingauge data. J Hydrol 385:51–64. doi: 10.1016/j.jhydrol.2010.01.023 CrossRefGoogle Scholar
  52. Loader C (1997) LOCFIT: an introduction. Stat Comput Graph Newsl 8:11–17Google Scholar
  53. Loader C (1999) Local regression and likelihood. Springer, New York, p 308Google Scholar
  54. Mackay NG, Chandler RE, Onof C, Wheater HS (2001) Disaggregation of spatial rainfall fields for hydrological modelling. Hydrol Earth Syst Sci 5:165–173CrossRefGoogle Scholar
  55. Marqunez J, Lastra J, Garcia P (2003) Estimation models for precipitation in mountainous regions: the use of GIS and multivariate analysis. J Hydrol 270:1–11CrossRefGoogle Scholar
  56. 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
  57. Myers DE (1994) Spatial interpolation: an overview. Geoderma 62:17–28CrossRefGoogle Scholar
  58. Ninyerola M, Pons X, Roure JM (2000) A methodological approach of climatological modeling of air temperature and precipitation through GIS techniques. Int J Climatol 20:1823–1841CrossRefGoogle Scholar
  59. Ollinger SV, Aber JD, Lovett GM, Millham SE, Lathrop RG, Ellis JM (1993) A spatial model of atmospheric deposition for the northeastern US. Ecol Appl 3:459–472CrossRefGoogle Scholar
  60. Owosina A (1992) Methods for assessing the space and time variability of ground water data. M.S. Thesis, Utah, Utah State UniversityGoogle Scholar
  61. Pardo-Iguzquiza E (1998) Comparison of geostatistical methods for estimating the areal average climatological rainfall mean using data on precipitation and topography. Int J Climatol 18:1031–1047CrossRefGoogle Scholar
  62. Prudhomme C, Reed DW (1999) Mapping extreme rainfall in a mountainous region using geostatistical techniques: a case study in Scotland. Int J Climatol 19:1337–1356CrossRefGoogle Scholar
  63. Rajagopalan B, Lall U (1998) Locally weighted polynomial estimation of spatial precipitation. J Geograph Inf Decis Anal 2:44–51Google Scholar
  64. Reek T, Doty SR, Owen TW (1992) A deterministic approach to the validation of historical daily temperature and precipitation data from the cooperative network. Bull Am Meteorol Soc 73:753–762CrossRefGoogle Scholar
  65. Refsgaard JC, Storm B (1995) MIKE SHE. In: Singh VP (ed) Computer models of watershed hydrology. Water Resources Publications, Colorado, pp 809–782Google Scholar
  66. Salvetti A, Ruf W, Burlando P, Lehmann C, Juon U (2002) Hydrotope-based river flow simulation in a Swiss Alpine catchment accounting for topographic, micro-climatic and landuse controls. In: Rizzoli AE, Jakeman AJ (eds) Proceedings of the 1st biennial meeting of the Int Env Modell and Softw Soc (iEMSs). Lugano, Switzerland, 24–27, June 2002, vol 1, pp 340–345Google Scholar
  67. Seo DJ (1996) Nonlinear estimation of spatial distribution of rainfall–An Indicator cokriging approach. Stoch Hydrol Hydraul 10:127–150CrossRefGoogle Scholar
  68. Sevruk B, Matokova-Sadlonova K, Toskano L (1998) Topography effects on small-scale precipitation variability in the Swiss pre-Alps, hydrology, water resources and ecology in headwaters. In: Proceedings of the HeadWater’98 conference, Meran/Merano, Italy, pp 51–58Google Scholar
  69. Singh VP (1995) Computer models of watershed hydrology. Water Resources Publications, Colorado, p 1144Google Scholar
  70. Smith MB, Seo DJ, Koren VI, Reed SM, Zhang Z, Duan Q, Moreda F, Cong S (2004) The distributed model intercomparison project (DMIP): motivation and experiment design. J Hydrol 298:4–26CrossRefGoogle Scholar
  71. Sorooshian S, Duan QY, Gupta VK (1993) Calibration of rainfall-runoff models—application of global optimization to the sacramento soil-moisture accounting model. Water Resour Res 29:1185–1194CrossRefGoogle Scholar
  72. Sun H, Cornish PS, Daniell TM (2002) Spatial variability in hydrologic modeling using rainfall-runoff model and digital elevation model. J Hydrol Eng 7:404–412CrossRefGoogle Scholar
  73. Syed KH, Goodrich DC, Myers DE, Sorooshian S (2003) Spatial characteristics of thunderstorm rainfall fields and their relation to runoff. J Hydrol 271:1–21CrossRefGoogle Scholar
  74. Tabios GQ III, Salas JD (1985) A comparative analysis of techniques for spatial interpolation of precipitation. Water Resour Bull 21:356–379Google Scholar
  75. Thiessen AH (1911) Precipitation averages for large areas. A subsection in the climatology data for July 1911, District No. 10, Great Basin. Mon Weather Rev July:1082–1084Google Scholar
  76. Thornton PE, Running SW, White MA (1997) Generating surfaces of daily meteorological variables over large regions of complex terrain. J Hydrol 190:214–251CrossRefGoogle Scholar
  77. Tobin C, Nicotina L, Parlange MB, Berne A, Rinaldo A (2011) Improved interpolation of meteorological forcings for hydrologic applications in a Swiss alpine region. J Hydrol 401:77–89. doi: /10.1016/J.Jhydrol.2011.02.010 CrossRefGoogle Scholar
  78. Todini E, Pellegrini F, Mazzetti C (2001) Influence of parameter estimation uncertainty in Kriging. Part 2-test and case study applications. Hydrol Earth Syst Sci 5:225–232CrossRefGoogle Scholar
  79. Troutman BM (1985) Errors and parameter estimation in precipitation-runoff modeling: 2. Case study. Water Resour Res 21:1214–1222CrossRefGoogle Scholar
  80. USDA Soil Conservation Service (1986) Urban hydrology for small watersheds, technical release 55. NTIS PB87-101580, 2nd edn. Springfield, Virginia, p 164Google Scholar
  81. Walpole RE, Myers RH, Myers SL (1998) Probability and statistics for engineers and scientists, 6th ed. edn. Prentice Hall, New York, p 665Google Scholar
  82. Wilby RL, Hay LH, Leavesley GH (1999) A comparison of downscaled and raw GCM output: implications for climate change scenarios in the San Juan River basin, Colorado. J Hydrol 225:67–91CrossRefGoogle Scholar
  83. Xie P, Yatagai A, Chen M, Hayasaka T, Fukushima Y, Liu C, Yang S (2007) A gauge-based analysis of daily precipitation over East Asia. J Hydrometeorol 8(3):607–626CrossRefGoogle Scholar
  84. Young KC (1992) A three-model for interpolating for monthly precipitation values. Mon Weather Rev 120:2561–2569CrossRefGoogle Scholar
  85. Zhang X, Srinivasan R (2009) GIS-based spatial precipitation estimation: a comparison of geostatistical approaches. J Am Water Resour As 45:894–906CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Yeonsang Hwang
    • 1
  • Martyn Clark
    • 2
  • Balaji Rajagopalan
    • 3
  • George Leavesley
    • 4
  1. 1.College of Engineering, Arkansas State UniversityState UniversityUSA
  2. 2.Research Applications LaboratoryNational Center for Atmospheric ResearchBoulderUSA
  3. 3.Department of Civil, Environmental and Architectural EngineeringUniversity of ColoradoBoulderUSA
  4. 4.U.S. Geological SurveyDenverUSA

Personalised recommendations