Propagation of hydropeaking waves in heterogeneous aquifers: effects on flow topology and uncertainty quantification. (English) Zbl 1495.76086
Summary: Topological flow properties are proxies for mixing processes in aquifers and allow us to better understand the mechanisms controlling transport of solutes in the subsurface. However, topological descriptors, such as the Okubo-Weiss metric, are affected by the uncertainty in the solution of the flow problem. While the uncertainty related to the heterogeneous properties of the aquifer has been widely investigated in the past, less attention has been given to the one related to highly transient boundary conditions. We study the effect of different transient boundary conditions associated with hydropeaking events (i.e., artificial river stage fluctuations due to hydropower production) on groundwater flow and the Okubo-Weiss metric. We define deterministic and stochastic modeling scenarios applying four typical settings to describe river stage fluctuations during hydropeaking events: a triangular wave, a sine wave, a complex wave that results of the superposition of two sine waves, and a trapezoidal wave. We use polynomial chaos expansions to quantify the spatiotemporal uncertainty that propagates into the hydraulic head in the aquifer and the Okubo-Weiss. The wave-shaped highly transient boundary conditions influence not only the magnitude of the deformation and rotational forces of the flow field but also the temporal dynamics of dominance between local strain and rotation properties. Larger uncertainties are found in the scenario where the trapezoidal wave was imposed due to sharp fluctuation in the stage. The statistical moments that describe the propagation of the uncertainty highly vary depending on the applied boundary condition.
Highlights
Highlights
- ●
- Deterministic and stochastic scenarios to describe the groundwater flow field under river stage fluctuations during hydropeaking.
- ●
- Propagation of uncertainty of highly transient boundary conditions in the Okubo-Weiss metric.
- ●
- Highly transient boundary conditions can significantly affect mixing potential.
MSC:
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 76R99 | Diffusion and convection |
| 76-10 | Mathematical modeling or simulation for problems pertaining to fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
Okubo-Weiss metric; uncertainty quantification; polynomial chaos expansion; transient boundary condition; groundwater flow; river stage fluctuation; stochastic modelingReferences:
| [1] | Anderson, MP; Woessner, WW; Hunt, RJ, Applied Groundwater Modeling: Simulation of Flow and Advective Transport (2015), London, San Diego: Academic Press, London, San Diego |
| [2] | Bakker, M.; Post, V.; Langevin, CD; Hughes, JD; White, JT; Starn, JJ; Fienen, MN, Scripting MODFLOW model development using Python and FloPy, Groundwater, 54, 733-739 (2016) · doi:10.1111/gwat.12413 |
| [3] | Basilio Hazas, M.; Ziliotto, F.; Rolle, M.; Chiogna, G., Linking mixing and flow topology in porous media: an experimental proof, Phys. Rev. E, 105, 035105 (2022) · doi:10.1103/PhysRevE.105.035105 |
| [4] | Bear, J., Hydraulics of Groundwater, McGraw-Hill Series in Water Resources and Environmental Engineering (1979), London, New York: McGraw-Hill International Book Co, London, New York |
| [5] | Bear, JJ; Cheng, H-DA; Bear, J.; Cheng, AHD, Modeling under uncertainty, Modeling Groundwater Flow and Contaminant Transport, 637-693 (2010), Dordrecht: Springer Netherlands, Dordrecht · Zbl 1195.76002 · doi:10.1007/978-1-4020-6682-5_10 |
| [6] | Boano, F.; Harvey, JW; Marion, A.; Packman, AI; Revelli, R.; Ridolfi, L.; Wörman, A., Hyporheic flow and transport processes: mechanisms, models, and biogeochemical implications, Rev. Geophys., 52, 603-679 (2014) · doi:10.1002/2012RG000417 |
| [7] | Boisson, A.; de Anna, P.; Bour, O.; Le Borgne, T.; Labasque, T.; Aquilina, L., Reaction chain modeling of denitrification reactions during a push-pull test, J. Contam. Hydrol., 148, 1-11 (2013) · doi:10.1016/j.jconhyd.2013.02.006 |
| [8] | Bresciani, E.; Kang, PK; Lee, S., Theoretical analysis of groundwater flow patterns near stagnation points, Water Resour. Res., 55, 1624-1650 (2019) · doi:10.1029/2018WR023508 |
| [9] | Cameron, RH; Martin, WT, The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals, Ann. Math., 48, 385 (1947) · Zbl 0029.14302 · doi:10.2307/1969178 |
| [10] | Casella, E.; Molcard, A.; Provenzale, A., Mesoscale vortices in the Ligurian Sea and their effect on coastal upwelling processes, J. Mar. Syst., 88, 12-19 (2011) · doi:10.1016/j.jmarsys.2011.02.019 |
| [11] | Cheng, AH-D; Cheng, DT, Heritage and early history of the boundary element method, Eng. Anal. Bound. Elem., 29, 268-302 (2005) · Zbl 1182.65005 · doi:10.1016/j.enganabound.2004.12.001 |
| [12] | Chiogna, G.; Marcolini, G.; Liu, W.; Pérez Ciria, T.; Tuo, Y., Coupling hydrological modeling and support vector regression to model hydropeaking in alpine catchments, Sci. Total Environ., 633, 220-229 (2018) · doi:10.1016/j.scitotenv.2018.03.162 |
| [13] | Cho, MS; Solano, F.; Thomson, NR; Trefry, MG; Lester, DR; Metcalfe, G., Field trials of chaotic advection to enhance reagent delivery, Groundw. Monit. Remediat., 39, 23-39 (2019) · doi:10.1111/gwmr.12339 |
| [14] | Coduto, DP, Geotechnical Engineering: Principles and Practices (1999), Upper Saddle River, NJ: Prentice Hall, Upper Saddle River, NJ |
| [15] | de Anna, P.; Dentz, M.; Tartakovsky, A.; Le Borgne, T., The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows, Geophys. Res. Lett., 41, 4586-4593 (2014) · doi:10.1002/2014GL060068 |
| [16] | de Anna, P.; Jimenez-Martinez, J.; Tabuteau, H.; Turuban, R.; Le Borgne, T.; Derrien, M.; Méheust, Y., Mixing and reaction kinetics in porous media: an experimental pore scale quantification, Environ. Sci. Technol., 48, 508-516 (2014) · doi:10.1021/es403105b |
| [17] | de Barros, FPJ; Dentz, M.; Koch, J.; Nowak, W., Flow topology and scalar mixing in spatially heterogeneous flow fields, Geophys. Res. Lett. (2012) · doi:10.1029/2012GL051302 |
| [18] | Dentz, M.; Carrera, J., Effective solute transport in temporally fluctuating flow through heterogeneous media, Water Resour. Res., 41, 1-20 (2005) · doi:10.1029/2004WR003571 |
| [19] | Dudley-Southern, M.; Binley, A., Temporal responses of groundwater-surface water exchange to successive storm events, Water Resour. Res., 51, 1112-1126 (2015) · doi:10.1002/2014WR016623 |
| [20] | Engdahl, NB; Benson, DA; Bolster, D., Predicting the enhancement of mixing-driven reactions in nonuniform flows using measures of flow topology, Phys. Rev. E, 90 (2014) · doi:10.1103/PhysRevE.90.051001 |
| [21] | Feinberg, J.: ChaosPy—Uncertainty Quantification Library [WWW Document]. ChaosPy—Uncertainty Quantification Library. https://chaospy.readthedocs.io/en/master/ (2019) |
| [22] | Ferencz, SB; Cardenas, MB; Neilson, BT, Analysis of the effects of dam release properties and ambient groundwater flow on surface water-groundwater exchange over a 100-km-long reach, Water Resour. Res., 55, 8526-8546 (2019) · doi:10.1029/2019WR025210 |
| [23] | Formaggia, L.; Guadagnini, A.; Imperiali, I.; Lever, V.; Porta, G.; Riva, M.; Scotti, A.; Tamellini, L., Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model, Comput. Geosci., 17, 25-42 (2013) · Zbl 1356.86021 · doi:10.1007/s10596-012-9311-5 |
| [24] | Francis, BA; Francis, LK; Cardenas, MB, Water table dynamics and groundwater-surface water interaction during filling and draining of a large fluvial island due to dam-induced river stage fluctuations, Water Resour. Res., 46, 7513 (2010) · doi:10.1029/2009WR008694 |
| [25] | Geng, X.; Michael, HA; Boufadel, MC; Molz, FJ; Gerges, F.; Lee, K., Heterogeneity affects intertidal flow topology in coastal beach aquifers, Geophys. Res. Lett., 47, 7513 (2020) · doi:10.1029/2020GL089612 |
| [26] | Golub, GH; Welsch, JH, Calculation of Gauss quadrature rules, Math. Comp., 23, 221-221 (1968) · Zbl 0179.21901 · doi:10.1090/S0025-5718-69-99647-1 |
| [27] | Halton, JH, Algorithm 247: radical-inverse quasi-random point sequence, Commun. ACM, 7, 701-702 (1964) · doi:10.1145/355588.365104 |
| [28] | Harbaugh, A., MODFLOW-2005, The U.S. Geological Survey Modular Ground-Water Model—The Ground-Water Flow Process, U.S. Geological Survey Techniques and Methods 6-A16 (2005), Reston: U.S. Geological Survey, Reston |
| [29] | Hauer, C.; Siviglia, A.; Zolezzi, G., Hydropeaking in regulated rivers—from process understanding to design of mitigation measures, Sci. Total Environ., 579, 22-26 (2017) · doi:10.1016/j.scitotenv.2016.11.028 |
| [30] | Hester, ET; Santizo, KY; Nida, AA; Widdowson, MA, Hyporheic transverse mixing zones and dispersivity: laboratory and numerical experiments of hydraulic controls, J. Contam. Hydrol., 243, 103885 (2021) · doi:10.1016/j.jconhyd.2021.103885 |
| [31] | Kang, PK; Bresciani, E.; An, S.; Lee, S., Potential impact of pore-scale incomplete mixing on biodegradation in aquifers: from batch experiment to field-scale modeling, Adv. Water Resour., 123, 1-11 (2019) · doi:10.1016/j.advwatres.2018.10.026 |
| [32] | Le Maitre, OP; Knio, OM, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, Scientific Computation (2010), Dordrecht: Springer, Dordrecht · Zbl 1193.76003 · doi:10.1007/978-90-481-3520-2 |
| [33] | Li, T.; Pasternack, GB, Revealing the diversity of hydropeaking flow regimes, J. Hydrol., 598, 126392 (2021) · doi:10.1016/j.jhydrol.2021.126392 |
| [34] | Liu, Z., Multiphysics in Porous Materials (2018), Cham: Springer International Publishing, Cham · doi:10.1007/978-3-319-93028-2 |
| [35] | Lykkegaard, MB; Dodwell, TJ; Moxey, D., Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy, Comput. Methods Appl. Mech. Eng., 383, 113895 (2021) · Zbl 1506.76170 · doi:10.1016/j.cma.2021.113895 |
| [36] | Mays, DC; Neupauer, RM, Plume spreading in groundwater by stretching and folding, Water Resour. Res., 48, 7501 (2012) · doi:10.1029/2011WR011567 |
| [37] | McCarty, PL; Criddle, CS; Kitanidis, PK; McCarty, PL, Chemical and biological processes: the need for mixing, Delivery and Mixing in the Subsurface, SERDP/ESTCP Environmental Remediation Technology, 7-52 (2012), New York: Springer, New York · doi:10.1007/978-1-4614-2239-6_2 |
| [38] | Meile, T.; Boillat, J-L; Schleiss, AJ, Hydropeaking indicators for characterization of the Upper-Rhone River in Switzerland, Aquat. Sci., 73, 171-182 (2011) · doi:10.1007/s00027-010-0154-7 |
| [39] | Merchán-Rivera, P.; Wohlmuth, B.; Chiogna, G., Identifying stagnation zones and reverse flow caused by river-aquifer interaction: an approach based on polynomial chaos expansions, Water Res. (2021) · doi:10.1029/2021WR029824 |
| [40] | Merchán-Rivera, P.; Basilio Hazas, M.; Marcolini, G.; Chiogna, G., Dataset for the research “Propagation of hydropeaking waves in heterogeneous aquifers: effects on flow topology and uncertainty quantification”, Mendeley Data, V1 (2022) · Zbl 1495.76086 · doi:10.17632/sk3my3mtd8.1 |
| [41] | Moslehi, M.; de Barros, FPJ, Uncertainty quantification of environmental performance metrics in heterogeneous aquifers with long-range correlations, J. Contam. Hydrol., 196, 21-29 (2017) · doi:10.1016/j.jconhyd.2016.12.002 |
| [42] | Neupauer, RM; Meiss, JD; Mays, DC, Chaotic advection and reaction during engineered injection and extraction in heterogeneous porous media, Water Resour. Res., 50, 1433-1447 (2014) · doi:10.1002/2013WR014057 |
| [43] | Nowak, W.; de Barros, FPJ; Rubin, Y., Bayesian geostatistical design: task-driven optimal site investigation when the geostatistical model is uncertain, Water Resour. Res., 46, W03535 (2010) · doi:10.1029/2009WR008312 |
| [44] | Okubo, A., Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences, Deep Sea Res. Oceanogr. Abstr., 17, 445-454 (1970) · doi:10.1016/0011-7471(70)90059-8 |
| [45] | Pérez Ciria, T.; Labat, D.; Chiogna, G., Detection and interpretation of recent and historical streamflow alterations caused by river damming and hydropower production in the Adige and Inn river basins using continuous, discrete and multiresolution wavelet analysis, J. Hydrol., 578, 124021 (2019) · doi:10.1016/j.jhydrol.2019.124021 |
| [46] | Pérez Ciria, T.; Puspitarini, HD; Chiogna, G.; François, B.; Borga, M., Multi-temporal scale analysis of complementarity between hydro and solar power along an alpine transect, Sci. Total Environ., 741, 140179 (2020) · doi:10.1016/j.scitotenv.2020.140179 |
| [47] | Pinay, G.; Peiffer, S.; De Dreuzy, J-R; Krause, S.; Hannah, DM; Fleckenstein, JH; Sebilo, M.; Bishop, K.; Hubert-Moy, L., Upscaling nitrogen removal capacity from local hotspots to low stream orders’ drainage basins, Ecosystems, 18, 1101-1120 (2015) · doi:10.1007/s10021-015-9878-5 |
| [48] | Rolle, M.; Le Borgne, T., Mixing and reactive fronts in the subsurface, Rev. Mineral. Geochem., 85, 111-142 (2019) · doi:10.2138/rmg.2018.85.5 |
| [49] | Roullet, G.; Klein, P., Cyclone-anticyclone asymmetry in geophysical turbulence, Phys. Rev. Lett., 104, 218501 (2010) · doi:10.1103/PhysRevLett.104.218501 |
| [50] | Santizo, KY; Widdowson, MA; Hester, ET, Abiotic mixing-dependent reaction in a laboratory simulated hyporheic zone, Water Resour. Res., 56, e2020WR027090 (2020) · doi:10.1029/2020WR027090 |
| [51] | Sawyer, A.; Bayani Cardenas, M.; Bomar, A.; Mackey, M., Impact of dam operations on hyporheic exchange in the riparian zone of a regulated river, Hydrol. Process., 23, 2129-2137 (2009) · doi:10.1002/hyp.7324 |
| [52] | Singh, SK, Aquifer response to sinusoidal or arbitrary stage of semipervious stream, J. Hydraul. Eng., 130, 1108-1118 (2004) · doi:10.1061/(ASCE)0733-9429(2004)130:11(1108) |
| [53] | Singh, T.; Wu, L.; Gomez-Velez, JD; Lewandowski, J.; Hannah, DM; Krause, S., Dynamic hyporheic zones: exploring the role of peak flow events on bedform-induced hyporheic exchange, Water Resour. Res., 55, 218-235 (2019) · doi:10.1029/2018WR022993 |
| [54] | Singh, T.; Gomez-Velez, JD; Wu, L.; Wörman, A.; Hannah, DM; Krause, S., Effects of successive peak flow events on hyporheic exchange and residence times, Water Resour. Res., 56, e2020WR027113 (2020) · doi:10.1029/2020WR027113 |
| [55] | Smith, RC, Uncertainty Quantification: Theory, Implementation, and Applications, Computational Science and Engineering (2013), Philadelphia: SIAM, Philadelphia |
| [56] | Song, X.; Chen, X.; Zachara, JM; Gomez-Velez, JD; Shuai, P.; Ren, H.; Hammond, GE, River dynamics control transit time distributions and biogeochemical reactions in a dam-regulated river corridor, Water Resour. Res., 56, e2019WR026470 (2020) · doi:10.1029/2019WR026470 |
| [57] | Sudret, B., Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Saf., 93, 964-979 (2008) · doi:10.1016/j.ress.2007.04.002 |
| [58] | Valocchi, AJ; Bolster, D.; Werth, CJ, Mixing-limited reactions in porous media, Transp. Porous Med., 130, 157-182 (2019) · doi:10.1007/s11242-018-1204-1 |
| [59] | Wagner, B.; Hauer, C.; Schoder, A.; Habersack, H., A review of hydropower in Austria: past, present and future development, Renew. Sustain. Energy Rev., 50, 304-314 (2015) · doi:10.1016/j.rser.2015.04.169 |
| [60] | Wallace, CD; Tonina, D.; McGarr, JT; Barros, FPJ; Soltanian, MR, Spatiotemporal dynamics of nitrous oxide emission hotspots in heterogeneous riparian sediments, Water Resour. Res., 57, e2021WR030496 (2021) · doi:10.1029/2021WR030496 |
| [61] | Weiss, J., The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D, 48, 273-294 (1991) · Zbl 0716.76025 · doi:10.1016/0167-2789(91)90088-Q |
| [62] | Wright, EE; Richter, DH; Bolster, D., Effects of incomplete mixing on reactive transport in flows through heterogeneous porous media, Phys. Rev. Fluids, 2, 114501 (2017) · doi:10.1103/PhysRevFluids.2.114501 |
| [63] | Xiu, D., Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010), Princeton: Princeton University Press, Princeton · Zbl 1210.65002 · doi:10.1515/9781400835348 |
| [64] | Xiu, D.; Karniadakis, GE, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24, 619-644 (2002) · Zbl 1014.65004 · doi:10.1137/S1064827501387826 |
| [65] | Ziliotto, F.; Basilio Hazas, M.; Rolle, M.; Chiogna, G., Mixing enhancement mechanisms in aquifers affected by hydropeaking: insights from flow-through laboratory experiments, Geophys. Res. Lett., 48, e2021GL095336 (2021) · doi:10.1029/2021GL095336 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
