Methodological approaches for imputing missing data into monthly flows series

Abstract

Missing data is one of the main difficulties in working with fluviometric records. Database gaps may result from fluviometric stations components problems, monitoring interruptions and lack of observers. Incomplete series analysis generates uncertain results, negatively impacting water resources management. Thus, proper missing data consideration is very important to ensure better information quality. This work aims to analyze, comparatively, missing data imputation methodologies in monthly river-flow time series, considering, as a case study, the Doce River, located in Southeast Brazil. Missing data were simulated in 5%, 10%, 15%, 25% and 40% proportions following a random distribution pattern, ignoring the missing data generation mechanisms. Ten missing data imputation methodologies were used: arithmetic mean, median, simple and multiple linear regression, regional weighting, spline and Stineman interpolation, Kalman smoothing, multiple imputation and maximum likelihood. Their performances were compared through bias, root mean square error, absolute mean percentage error, determination coefficient and concordance index. Results indicate that for 5% missing data, any methodology for imputing can be considered, recommending caution for arithmetic mean method application. However, as the missing data proportion increases, it is recommended to use multiple imputation and maximum likelihood methodologies when there are support stations for imputation, and the Stineman interpolation and Kalman Smoothing methods when only the studied series is available.
 Keywords: Doce river, imputation, missing data.

Gap-filling meteorological data series using the GapMET software in the state of Mato Grosso, Brazil

“…However, these authors did not consider the impact of the increase in the number of missing data, which were being tested in time series with a percentage of gaps below 30% of the datasets. Bleidorn et al (2022), for example, compared the MAS, RLS, and RLM methods with a percentage of missing data ranging from 5 to 40% and observed better performances with the RLS method. In this case, these results were justified by the algorithm used, which, similarly to GapMET, selects the reference AWS by the highest correlation coefficient, allowing the change of the reference AWS when finding missing data in it, which does not occur with the RLM method, which requires at least three reference AWS.…”

“…In the literature, there is a range of methods for gap-filling, e.g., the simple arithmetic means (MAS) (Bier & Ferraz, 2017), UK traditional method (MUK) (Tabony, 1983), inverse distance method (MID) (Hubbard, 1994), regional weighting method (MPR) (Paulhus & Kohler, 1952), simple linear regression (RLS) (Bleidorn et al, 2022), and multiple linear regression (RLM) (Coutinho et al, 2018), whose basic requirement is a reference time series, that can be extracted from nearby AWS or remote sensing datasets.…”

Hydrological methodologies analysis to obtaining ecological and grantable flows, considering annual and monthly criteria for Doce river, Brazil

“…Complete time series are important for quality assurance in information obtaining , and it is often necessary resort to missing data treatment (Bleidorn et al, 2022). According to Tucci (1997), missing flow data imputation can be performed through linear regression, expressed as Equation 1.…”

Rainfall Projections for the Brazilian Legal Amazon using Recurrent Neural Networks

“…Rainfall data from Brazilian meteorological stations net are known to be prone to failure, particularly in the BLA. However, such issues did not prevent the BLA from conducting rainfall research, some of which included gap filling approaches such as simple linear regression (RLS), data imputation, and outlier treatment (Alves and Gomes, 2020;Bleidorn et al, 2022). RLS is the gap-filling method used by the World Meteorological Organization (WMO) - (Pacheco et al, 2012;WMO, 2023).…”