A Missing Value Replacement Method for Agricultural Meteorological Data Using Bayesian Spatio-Temporal Model

농업기상 결측치 보정을 위한 통계적 시공간모형

  • Park, Dain (Department of Statistics, Daegu University) ;
  • Yoon, Sanghoo (Division of Mathematics and big data science, Daegu University)
  • 박다인 (대구대학교 통계학과) ;
  • 윤상후 (대구대학교 수리빅데이터 학부 통계.빅데이터 전공)
  • Received : 2018.02.07
  • Accepted : 2018.04.26
  • Published : 2018.07.31


Agricultural meteorological information is an important resource that affects farmers' income, food security, and agricultural conditions. Thus, such data are used in various fields that are responsible for planning, enforcing, and evaluating agricultural policies. The meteorological information obtained from automatic weather observation systems operated by rural development agencies contains missing values owing to temporary mechanical or communication deficiencies. It is known that missing values lead to reduction in the reliability and validity of the model. In this study, the hierarchical Bayesian spatio-temporal model suggests replacements for missing values because the meteorological information includes spatio-temporal correlation. The prior distribution is very important in the Bayesian approach. However, we found a problem where the spatial decay parameter was not converged through the trace plot. A suitable spatial decay parameter, estimated on the bias of root-mean-square error (RMSE), which was determined to be the difference between the predicted and observed values. The latitude, longitude, and altitude were considered as covariates. The estimated spatial decay parameters were 0.041 and 0.039, for the spatio-temporal model with latitude and longitude and for latitude, longitude, and altitude, respectively. The posterior distributions were stable after the spatial decay parameter was fixed. root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and bias were calculated for model validation. Finally, the missing values were generated using the independent Gaussian process model.


  1. Bakar, K. S., Sahu, S. K., 2015, spTimer: Spatio-temporal Bayesian modelling using R, J. Stat. Softw, 63, 1-32.
  2. Banerjee, S., Carlin, B. P., Gelfand, A. E., 2014, Hierarchical modeling and analysis for spatial data, Crc Press.
  3. Baraldi, A. N., Enders, C. K., 2010, An Introduction to modern missing data analyses, J. Sch. Psychol., 48(1): 5-37.
  4. Cressie, N., 1994, An Approach to statistical spatial-temporal modeling of meteorological elds: Comment, J. Am. Stat. Assoc, 89, 379-382.
  5. Gelfand, A. E., Banerjee, S., Gamerman, D., 2005, Spatial process modeling for univariate and multivariate dynamic spatial data, Environmetrics, 16, 465-479.
  6. Gelfand, A. E., Smith, A. F. M., 1990, Sampling-based approaches to calculating marginal densities, J. Am. Stat. Assoc, 85, 398-409.
  7. Jang, H. I., Seo, H. H., Park, S. J., 2002, Strategy for fruit cultivation research under the changing climate, Korean J. Hort. Sci. Technol, 20, 270-275.
  8. Ko, K., Tak, H., 2016, The treatment of missing values using the integrated multiple imputation and callback method, Korean Journal of Pol. Stud., 54(4), 291-319.
  9. Lee, B. L., 2000, Prospects on agrometeorological information for agricultural applications. Korean J. Agric. For. Meteorol., 2(1), 24-30.
  10. Lee, H. J., Han, H. S., Chon, S. U., Kim, D. K., Kwon, H., Lee, K., 2014, Physiological characteristics and yield of onion affected by rapid temperature changes, Korean J. Environ Agric, 33(4), 364-371.
  11. Lee, J., Lee, Y., 1995, Determinant Factors of Planted Area and Crop Situation of Red Pepper, Garlic, and Onions, Korea Rural Econ. INST.
  12. Lee, K. K., Ko, K. K., Lee, J. W., 2012, Correlation analysis between meteorological factors and crop products, J. Environ. Sci. Int., 21(4), 461-470.
  13. Lee, S., Kim, D., 2010, The comparison of imputation methods in space time series data with missing values, Commun Stat Appl Methods, 17, 263-273.
  14. Min, J. S., Lee, M. H., Jee, J. B., Jang, M., 2016, A Study of the method for estimating the missing data from weather measurement instruments. J. Digital Convergence, 14, 245-252.
  15. Yoon, D. K., Oh, S. Y., Nam, K. W., Eom, K. C., Jung, P. K., 2014, Changes of cultivation areas and major disease for spicy vegetables by the change of meteorological factors, J. Climate Change Res, 5(1), 47-59.
  16. Yoon, S., Kim, M., 2016, Spatio-temporal models for generating a map of high resolution $NO_2$ level, J. Korea Data Info. Sci, 27(3), 803-814.