Development of a Model Combining Covariance Matrices Derived from Spatial and Temporal Data to Estimate Missing Rainfall Data

공간 데이터와 시계열 데이터로부터 유도된 공분산행렬을 결합한 강수량 결측값 추정 모형

Sung, Chan Yong

  • Received : 2012.10.27
  • Accepted : 2013.02.12
  • Published : 2013.03.29


This paper proposed a new method for estimating missing values in time series rainfall data. The proposed method integrated the two most widely used estimation methods, general linear model(GLM) and ordinary kriging(OK), by taking a weighted average of covariance matrices derived from each of the two methods. The proposed method was cross-validated using daily rainfall data at thirteen rain gauges in the Hyeong-san River basin. The goodness-of-fit of the proposed method was higher than those of GLM and OK, which can be attributed to the weighting algorithm that was designed to minimize errors caused by violations of assumptions of the two existing methods. This result suggests that the proposed method is more accurate in missing values in time series rainfall data, especially in a region where the assumptions of existing methods are not met, i.e., rainfall varies by season and topography is heterogeneous.


Missing rainfall data;Geostatistics;General linear model;Ordinary kriging


  1. ASCE Task Committee on Definition of Criteria for Evaluation of Watershed Models of the Watershed Management Committee, Irrigation and Drainage Division, 1993, Criteria for evaluation of watershed models, J. Irrig. Drain. E.-ASCE, 119, 429-442.
  2. Bacchi, B., Kottegoda, N. T., 1995, Identification and calibration of spatial correlation patterns of rainfall, J. Hydrol., 165, 311-348.
  3. Beek, E. G., Stein, A., Janssen, L. L. F., 1992, Spatial variability and interpolation of daily precipitation amount, Stoch. Hydrol. Hydraul., 6, 304-320.
  4. Choi, Y. J., Kim, Y. S., Lee, G. H., Kim, J. C., 2010, The verification of application of distributed runoff model according to estimation methods for the missing rainfall data, J. Environ. Sci., 19, 1375-1384.
  5. Jeffrey, S. J., Carter, J. O., Moodie, K. B., Beswick, A. R., 2001, Using Spatial interpolation to construct a comprehensive archive of Australian climate data, Environ. Modell. softw., 16, 309-330.
  6. Michaud, J. D., Sorooshian, S., 1994, Effect of rainfallsampling errors on simulations of desert flash floods, Water Resour. Res., 30, 2765-2775.
  7. Ribeiro, P. J., Diggle, P. J., 2001, geoR: a package for geostatistical analysis, R-NEWS 1, 15-18.
  8. Schabenberger, O., Gotway, C. A., 2005, Statistical methods for spatial data analysis, Chapman & Hall, Boca Raton, FL.
  9. Sung, C. Y., 2012, Estimating missing rainfall data in urban areas using hybrid approach of geostatistics and generalized least square estimation, J. Nakdong River Environ. Res. Inst., 16, 301-320.
  10. Sung, C. Y., Li, M. H., 2010, The effect of urbanization on stream hydrology in hillslope watersheds in central Texas, Hydrol. Process., 24, 3706-2717.
  11. Tabios, G., Salas, J. D., 1985, A comparative analysis of techniques for spatial interpolation of precipitation, Water Resour. Bull., 21, 365-380.