Analysis and generation of groundwater concentration time series

• Published in: Advances in water resources Vol. 111; pp. 20 - 30
• Main Authors: Crăciun, Maria, Vamoş, Călin, Suciu, Nicolae
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.01.2018; Elsevier Science Ltd
• Subjects: Algorithms; Amplitude; Coefficients; Computer applications; Computer simulation; Concentration time; Fluctuations; Gaussian distribution; Global random walk; Groundwater; Mathematical models; Monte Carlo simulations; Normal distribution; Order parameters; Probability density function; Probability density functions; Probability theory; Regression analysis; Solutes; Statistical analysis; Statistical methods; Studies; Time dependence; Time series; Time series analysis; Global random walk; 37M10; Monte Carlo simulations; Groundwater; Time series analysis; 86A05; 60G50; 65C05
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2017.10.039

•Cross-section integrated numerical solutions result in concentration time series.•Time series are driven by a descending trend and amplitude modulated fluctuations.•Fluctuations are modeled by linear regression with the increments and AR(1) noise.•The analysis yields an algorithm able to generate series with the same statistics.•The time series generating algorithm generalizes mixing models used in PDF methods. Concentration time series are provided by simulated concentrations of a nonreactive solute transported in groundwater, integrated over the transverse direction of a two-dimensional computational domain and recorded at the plume center of mass. The analysis of a statistical ensemble of time series reveals subtle features that are not captured by the first two moments which characterize the approximate Gaussian distribution of the two-dimensional concentration fields. The concentration time series exhibit a complex preasymptotic behavior driven by a nonstationary trend and correlated fluctuations with time-variable amplitude. Time series with almost the same statistics are generated by successively adding to a time-dependent trend a sum of linear regression terms, accounting for correlations between fluctuations around the trend and their increments in time, and terms of an amplitude modulated autoregressive noise of order one with time-varying parameter. The algorithm generalizes mixing models used in probability density function approaches. The well-known interaction by exchange with the mean mixing model is a special case consisting of a linear regression with constant coefficients.