C. Pappas, Optimal infilling of missing hydrometeorological data using time-adjacent observations, Diploma thesis, 226 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, October 2010.
The understanding of hydrometeorological phenomena is based on the study of existing observations (time series). Often, the infilling e time series have gaps, in other words, there are some periods with no measurements. Filling the missing values is necessary for further investigation of natural phenomena. In literature, there are many methodologies for infilling those gaps, but most of them, can expressed in a simple linear relationship. The interpolation can be based either on measurements of neighboring gauges or on measurements of neighboring time steps. In this diploma thesis, we study the problem of interpolation in time series with sporadic gaps and we examine the interpolation by using neighboring observation in time (local average). Depending on the autocorrelation structure of time-series, we investigated whether the use of a weighted local average is appropriate for the infilling. Assuming that the underlying hydrometeorological process behaves like either a Markovian or a Hurst-Kolmogorov process we estimate the missing values using different techniques based on a weighted local average. In each of the cases we determine the unknown quantities so as to minimize the estimation mean square error. The results are very satisfactory and the proposed methodology is appropriate for quick and immediate filling of a small number of missing measurements.