Analysis and generation of groundwater concentration time series

Abstract

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.

Authors

M. Crăciun
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

C. Vamoș
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

N. Suciu
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Time series analysis; Monte Carlo simulations; Global random walk; Groundwater

Cite this paper as:

M. Crăciun, C. Vamos, N. Suciu, Analysis and generation of groundwater concentration time series, Advances in Water Resources, vol. 111 (2018), pp. 20-30
doi: 10.1016/j.advwatres.2017.10.039

[1] R. Andričević, Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers,Water Resour. Res., 34 (5) (1998), pp. 1115-1129
CrossRef (DOI)

[2] G. Bohm, G. Zech, Introduction to Statistics and Data Analysis for Physicists, Verlag Deutsches Elektronen-Synchrotron, Hamburg (2010)

[3] P.J. Brockwell, R. Davis, Time Series: Theory and Methods, Springer-Verlag, New York (1987)

[4] E. Caroni, V. Fiorotto, Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59 (1) (2005), pp. 19-45
CrossRef (DOI)

[5] G. Demmy, S. Berglund, W. Graham, Injection mode implications for solute transport in porous media: analysis in a stochastic Lagrangian framework, Water Resour. Res., 35 (7) (1999), pp. 1965-1973
CrossRef (DOI)

[6] M. Dentz, D. Tartakovsky, Probability density functions for passive scalars dispersed in random velocity fields, Geophys. Res. Lett., 37 (2010), p. L24406
CrossRef (DOI)

[7] A. Fiori, G. Dagan, Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications, J. Contam. Hydrol., 45 (1) (2000), pp. 139-163
CrossRef (DOI)

[8] F.C. Geer, B. Kronvang, H.P. Broers, High resolution monitoring of nutrients in groundwater and surface waters: process understanding. Quantification of loads and concentrations and management applications, Hydrol. Earth Syst. Sci., 20 (2016), pp. 3619-3629
CrossRef (DOI)

[9] J. Hamilton, Time Series Analysis, Princeton University Press, Princeton (1994)

[10] G. Kitagawa, W. Gersch, A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series, IEEE Trans. Autom. Control, 30 (1) (1985), pp. 48-56
CrossRef (DOI)

[11] R. Kraichnan, Diffusion by a random velocity field, Phys. Fluids, 13 (1) (1970), pp. 22-31
CrossRef (DOI)

[12] L.D. Landau, E. Lifshitz, Physique Statistique, Mir, Moscou (1984)

[13] G. Liu, J.J.J. Butler, G.C. Bohling, E. Reboulet, S.Knobbe, D. Hyndman, A new method for high-resolution characterization of hydraulic conductivity, Water Resour. Res (2009)
CrossRef (DOI)

[14] B. Mandelbrot, J.R. Wallis, Noah, Joseph, and operational hydrology, Water Resour. Res., 4 (5) (1968), pp. 909-918
CrossRef (DOI)

[15] B. Mandelbrot, J. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10 (4) (1968), pp. 422-437
CrossRef (DOI)

[16] B. Mandelbrot, J.R. Wallis, Some long-run properties of geophysical records, Water Resour. Res., 5 (2) (1969), pp. 321-340
CrossRef (DOI)

[17] M.M. Meerschaert, M. Dogan, R.L. Van Dam, D.W.Hyndman, D. Benson, Hydraulic conductivity fields: Gaussian or not?, Water Resour. Res., 49 (2013), pp. 4730-4737
CrossRef (DOI)

[18] D.D. Mehta, D. Rudoy, P. Wolfe, Kalman-based autoregressive moving average modeling and inference for formant and antiformant tracking a, J. Acoust. Soc. Am., 132 (3) (2012), pp. 1732-1746
CrossRef (DOI)

[19] D.W. Meyer, P. Jenny, H. Tchelepi, A joint velocity-concentration PDF method for tracer flow in heterogeneous porous media, Water Resour. Res., 46 (2010), p. W12522
CrossRef (DOI)

[20] F.J. Molz, H.H. Liu, J. Szulga, Fractional Brownian motion and fractional gaussian noise in subsurface hydrology: a review, presentation of fundamental properties, and extensions, Water Resour. Res., 33 (10) (1997), pp. 2273-2286
CrossRef (DOI)

[21] E. Moulines, P. Priouret, F. Roueff, On recursive estimation for time varying autoregressive processes, Ann. Stat., 33 (6) (2005), pp. 2610-2654
CrossRef (DOI)

[22] S. Pope, PDF Methods for turbulent reactive flows, Prog. Energy Combust. Sci., 11 (2) (1985), pp. 119-192
CrossRef (DOI)

[23] S. Pope, Turbulent Flows, Cambridge University Press, Cambridge (2000)

[24] M. Riva, S.P. Neuman, A. Guadagnini, New scaling model for variables and increments with heavy-tailed distributions, Water Resour. Res., 51 (2015), pp. 4623-4634
CrossRef (DOI)

[25] X. Sanchez-Vila, A. Guadagnini, D. Fernàndez-Garcia, Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers, Math. Geosci., 41 (2009), pp. 323-351
CrossRef (DOI)

[26] L. Schüler, N. Suciu, P. Knabner, S. Attinger, A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers, Adv. Water Resour., 96 (2016), pp. 55-67
CrossRef (DOI)

[27] N. Suciu, Diffusion in random velocity fields with applications to contaminant transport in groundwater, Adv. Water Resour., 69 (2014), pp. 114-133
CrossRef (DOI)

[28] N. Suciu, F.A. Radu, S. Attinger, L. Schüler, P. Knabner, A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous mediaJ. Comput. Appl. Math., 289 (2015), pp. 241-252
CrossRef (DOI)

[29] N. Suciu, L. Schüler, S. Attinger, P. Knabner, Towards a filtered density function approach for reactive transport in groundwater, Adv. Water Resour., 90 (2016), pp. 83-98
CrossRef (DOI)

[30] N. Suciu, C. Vamoş, J. Vanderborght, H. Hardelauf, H.Vereecken, Numerical investigations on ergodicity of solute transport in heterogeneous aquifersWater Resour. Res., 42 (2006), p. W04409
CrossRef (DOI)

[31] N. Suciu, C. Vamoş, F.A. Radu, H. Vereecken, P. Knabner, Persistent memory of diffusing particles, Phys. Rev. E, 80 (2009), p. 061134
CrossRef (DOI)

[32] N. Suciu, C. Vamos, H. Vereecken, P. Knabner, Global random walk simulations for sensitivity and uncertainty analysis of passive transport models, Ann. Acad. Rom. Sci. Ser. Math. Appl., 3 (1) (2011), pp. 218-234
(article on the journal website)

[33] S. Taylor, Modelling Financial Time Series (2nd ed.), World Scientific Publishing, Singapore (2007)

[34] T. Turkeltaub, D. Kurtzman, O. Dahan, Real-time monitoring of nitrate transport in the deep vadose zone under a crop field – implications for groundwater protection, Hydrol. Earth Syst. Sci., 20 (8) (2016), pp. 3099-3108
CrossRef (DOI)

[35] C. Vamoş, M. Crăciun, Automatic Trend Estimation, Springer, Dordrecht (2012)
CrossRef (DOI)

[36] C. Vamoş, M. Crăciun, N. Suciu, Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components, Eur. Phys. J. B, 88 (2015), p. 250
CrossRef (DOI)

[37] C. Vamoş, N. Suciu, H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processesJ. Comput. Phys., 186 (2) (2003), pp. 527-544
CrossRef  (DOI)

PDF

About this paper

Print ISSN

0169-3913

Online ISSN

1573-1634

MR

?

ZBL

?

Google Scholar

?

soon

2018

Related Posts