Gap Filling of Monthly Temperature Data and Its Effect on Climatic Variability and Trends

Observational datasets of climatic variables are frequently composed of fragmentary time series covering different time spans and plagued with data gaps. Most statistical methods and environmental models, however, require serially complete data, so gap filling is a routine procedure. However, very often this preliminary stage is undertaken with no consideration of the potentially adverse effects that it can have on further analyses. In addition to numerical effects and trade-offs that are inherent to any imputation method, observational climatic datasets often exhibit temporal changes in the number of available records, which result in further spurious effects if the gap-filling process is sensitive to it. We examined the effect of data reconstruction in a large dataset of monthly temperature records spanning over several decades, during which substantial changes occurred in terms of data availability. We made a thorough analysis in terms of goodness of fit (mean error) and bias in the first two moments (mean and variance), in the extreme quantiles, and in long-term trend magnitude and significance. We show that gap filling may result in biases in the mean and the variance of the reconstructed series, and also in the magnitude and significance of temporal trends. Introduction of a two-step bias correction in the gap-filling process solved some of these problems, although it did not allow us to produce completely unbiased trend estimates. Using only one (the best) neighbor and performing a one-step bias correction, being a simpler approach, closely rivaled this method, although it had similar problems with trend estimates. A trade-off must be assumed between goodness of fit (error minimization) and variance bias.