A review on missing hydrological data processing

Like almost all fields of science, hydrology has benefited to a large extent from the tremendous improvements in scientific instruments that are able to collect long-time data series and an increase in available computational power and storage capabilities over the last decades. Many model applications and statistical analyses (e.g., extreme value analysis) are based on these time series. Consequently, the quality and the completeness of these time series are essential. Preprocessing of raw data sets by filling data gaps is thus a necessary procedure. Several interpolation techniques with different complexity are available ranging from rather simple to extremely challenging approaches. In this paper, various imputation methods available to the hydrological researchers are reviewed with regard to their suitability for filling gaps in the context of solving hydrological questions. The methodological approaches include arithmetic mean imputation, principal component analysis, regression-based methods and multiple imputation methods. In particular, autoregressive conditional heteroscedasticity (ARCH) models which originate from finance and econometrics will be discussed regarding their applicability to data series characterized by non-constant volatility and heteroscedasticity in hydrological contexts. The review shows that methodological advances driven by other fields of research bear relevance for a more intensive use of these methods in hydrology. Up to now, the hydrological community has paid little attention to the imputation ability of time series models in general and ARCH models in particular.