Feature-preserving interpolation and filtering of environmental time series

Abstract

a b s t r a c tWe propose a method for filling gaps and removing interferences in time series for applications involving continuous monitoring of environmental variables. The approach is non-parametric and based on an iterative pattern-matching between the affected and the valid parts of the time series. It considers several variables jointly in the pattern matching process and allows preserving linear or non-linear dependences between variables. The uncertainty in the reconstructed time series is quantified through multiple realizations. The method is tested on self-potential data that are affected by strong interferences as well as data gaps, and the results show that our approach allows reproducing the spectral features of the original signal. Even in the presence of intense signal perturbations, it significantly improves the signal and corrects bias introduced by asymmetrical interferences. Potential applications are wide-ranging, including geophysics, meteorology and hydrology.

Missing data simulation inside flow rate time-series using multiple-point statistics

“…In this paper, we propose a non-parametric method to simulate missing data 20 inside flow rate time-series based on the Direct Sampling (DS) technique Ma-riethoz et al (2010) belonging to multiple-point statistics (MPS). Already tested on gap filling in multivariate data sets representing natural heterogeneities Mariethoz et al (2012Mariethoz et al ( , 2015 and on rainfall time-series simulation Oriani et al (2014), DS can simulate the outcome of a complex natural pro-25 cess by reproducing similar patterns to the ones found in the available data without imposing a specific statistical model. More particularly, missing data are simulated by sampling the available data set where a sufficiently similar pattern is found.…”

Tidal influence on self‐potential measurements

“…The Lomb‐Scargle PSD offers an alternative approach to dealing with data gaps to that proposed by Mariethoz et al . []. It also allowed determination of the probability of a certain frequency peak being related to a real periodic signal and not the result of random fluctuations; i.e., the probability of detection [ Trauth , ].…”

“…The Lomb-Scargle PSD, a least squares spectral analysis technique, was chosen because it can be used with time series data that have gaps or that are not evenly spaced in time [Lomb, 1976;Trauth, 2010]. The Lomb-Scargle PSD offers an alternative approach to dealing with data gaps to that proposed by Mariethoz et al [2015]. It also allowed determination of the probability of a certain frequency peak being related to a real periodic signal and not the result of random fluctuations; i.e., the probability of detection [Trauth, 2010].…”

Advancing quantitative understanding of self-potential signatures in the critical zone through long-term monitoring

“…Finally, we median filter the resulting time-series using a 1-hour window corresponding to the time-interval used to represent the SP data in this paper. See Mariethoz et al (2015) for an alternative data processing approach that has been demonstrated for a sub-set of the presented data.…”