Multivariate missing data in hydrology – Review and applications

Abstract

Water resources planning and management require complete data sets of a number of hydrological variables, such as flood peaks and volumes. However, hydrologists are often faced with the problem of missing data (MD) in hydrological databases. Several methods are used to deal with the imputation of MD. During the last decade, multivariate approaches have gained popularity in the field of hydrology, especially in hydrological frequency analysis (HFA). However, treating the MD remains neglected in the multivariate HFA literature whereas the focus has been mainly on the modeling component. For a complete analysis and in order to optimize the use of data, MD should also be treated in the multivariate setting prior to modeling and inference. Imputation of MD in the multivariate hydrological framework can have direct implications on the quality of the estimation. Indeed, the dependence between the series represents important additional information that can be included in the imputation process. The objective of the present paper is to highlight the importance of treating MD in multivariate hydrological frequency analysis by reviewing and applying multivariate imputation methods and by comparing univariate and multivariate imputation methods. An application is carried out for multiple flood attributes on three sites in order to evaluate the performance of the different methods based on the leave-one-out procedure. The results indicate that, the performance of imputation methods can be improved by adopting the multivariate setting, compared to mean substitution and interpolation methods, especially when using the copula-based approach.

Copula Theory as a Generalized Framework for Flow‐Duration Curve Based Streamflow Estimates in Ungaged and Partially Gaged Catchments

“…For gap filling of missing data or record extension in partially gaged catchments, the copula models show substantial promise, especially if there are sufficient data at the partially gaged site to estimate FDCs and correlations with reasonable accuracy. This result is consistent with recent work on this topic (Aissia et al, 2017). However, if the record at the partially gaged site is too short, direct empirical estimates of both FDCs and correlations to donors can suffer from a substantial amount of sampling uncertainty.…”

Analyzing the duration frequency and severity of drought using copula function in the Yazd city

“…It should be noted that p i andp i are the observable i values and the i values could be calculated from the cumulative distribution function. n is the number of data (Ben Aissia et al 2017;Aguayo et al 2021).…”

Complete multivariate flood frequency analysis, applied to northern Algeria

“…To overcome some these limitations, reconstruction of the historical data can be considered for future studies, which may allow extending the FFA to other stations (Grimaldi, Petroselli, Salvadori, & De Michele, 2016). In addition, filling the data gaps in a multivariate context using copula is also a promising option (Chebana, Ben Aissia & Ouarda, 2017).…”