Skip to main content
SpringerLink
Log in

Stochastic analysis of the variability of groundwater flow fields in heterogeneous confined aquifers of variable thickness

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

The problem of flow through heterogeneous confined aquifers of variable thickness is analyzed from a stochastic point of view. The analysis is carried out on the basis of the integrated equations of the depth-averaged hydraulic head and integrated specific discharge, which are developed by integrating the continuity equation and equation for the specific discharge over the thickness, respectively. A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge. However, the closed-form expressions are obtained under the condition of steady unidirectional mean flow in the horizontal plane. In developing stochastic solutions, the input hydraulic conductivity parameter is viewed as a spatial random field characterized by the theoretical spatial covariance function. The evaluation of the closed-form solutions focuses on the influence of the controlling parameters, namely as a geometrical parameter defining the variation of the aquifer thickness and the correlation scale of log hydraulic conductivity, on the variability of the fluid fields. The application of the present stochastic theory to predict the total specific discharge under uncertainty using the field data is also provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Andreasen DC (2017) Effects of projected (2086) groundwater withdrawals on management water levels and domestic wells in Anne Arundel County, Maryland. Maryland Geological Survey Open-File Report 17-02-01.

  • Andreasen DC, Staley AW, Achmad G (2013) Maryland Coastal Plain aquifer information system-Hydrogeologic framework: Maryland Geological Survey Open-File Report 12–02–20.

  • Barthel R, Banzhaf S (2015) Groundwater and surface water interaction at the regional-scale—a review with focus on regional integrated models. Water Resour Manag 30(1):1–32

    Article  Google Scholar 

  • Bear J (1979) Hydraulics of groundwater. McGraw-Hill, New York

    Google Scholar 

  • Bear J, Cheng AH-D (2010) Modeling groundwater flow and contaminant transport. Springer, Dordrecht

    Book  Google Scholar 

  • Benekos ID, Shoemaker CA, Stedinger JR (2006) Probabilistic risk and uncertainty analysis for bioremediation of four chlorinated ethenes in groundwater. Stoch Environ Res Risk Assess 21(4):375–390

    Article  Google Scholar 

  • Christakos G (1992) Random field models in earth sciences. Academic, San Diego

    Google Scholar 

  • Christakos G (2003) Another look at the conceptual fundamentals of porous media upscaling. Stoch Environ Res Risk Assess 17(5):276–290

    Article  Google Scholar 

  • Cuello JE, Guarracino L, Monachesi LB (2017) Groundwater response to tidal fluctuations in wedge-shaped confined aquifers. Hydrogeol J 25(5):1509–1515

    Article  Google Scholar 

  • Cvetkovic VD, Dagan G, Shapiro AM (1991) An exact solution of solute transport by one-dimensional random velocity fields. Stoch Hydrol Hydraul 5(1):45–54

    Article  Google Scholar 

  • Dagan G (1989) Flow and transport in porous formations. Springer, New York

    Book  Google Scholar 

  • Dagan G (2001) Effective, equivalent and apparent properties of heterogeneous media. In: Aref H, Phillips JW (eds) Mechanics for a new millennium. Springer, New York, pp 473–485

    Google Scholar 

  • Dagan G, Neuman SP (eds) (1997) Subsurface flow and transport: a stochastic approach. Cambridge University Press, UK

    Google Scholar 

  • Darvini G (2013) An example of solute spreading in nonstationary, bounded geological formations. Stoch Environ Res Risk Assess 28(2):297–306

    Article  Google Scholar 

  • de Marsily G (1986) Quantitative hydrogeology: Groundwater hydrology for engineers. Academic Press, Orlando

    Google Scholar 

  • Fiori A, Jankovic I, Dagan G (2003) Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: numerical methodology and semi-analytical solutions. Stoch Environ Res Risk Assess 17(6):370–383

    Article  Google Scholar 

  • Gelhar LW (1977) Effects of hydraulic conductivity variations on groundwater flows. In: Proceedings second international symposium on stochastic hydraulics, Lund, Sweden, in hydraulic problems solved by stochastic methods, Water Resources Publications, Fort Collins, pp 409–431

  • Gelhar LW (1986) Stochastic subsurface hydrology from theory to applications. Water Resour Res 22(9S):135S-145S

    Article  Google Scholar 

  • Gelhar LW (1993) Stochastic subsurface hydrology. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Gutjahr AL, Gelhar LW, Bakr AA, MacMillan JR (1978) Stochastic analysis of spatial variability in subsurface flows: 2. Eval Appl Water Resour Res 14(5):953–959

    Article  Google Scholar 

  • Hantush MS (1962a) Flow of ground water in sands of non-uniform thickness, part 2. Approximate theory. J Geophys Res 67(4):711–720

    Article  Google Scholar 

  • Hantush MS (1962b) Flow of ground water in sands of nonuniform thickness, part 3. Flow to wells. J Geophys Res 67(4):1527–1534

    Article  Google Scholar 

  • Henri CV, Harter T, Diamantopoulos E (2020) Stochastic assessment of the effect of land-use change on nonpoint source-driven groundwater quality using an efficient scaling approach. Stoch Environ Res Risk Assess 35(5):959–970

    Article  Google Scholar 

  • Kovitz JL, Christakos G (2004) Spatial statistics of clustered data. Stoch Environ Res Risk Assess 18(3):147–166

    Article  Google Scholar 

  • Leray S, de Dreuzy J-R, Bour O, Labasque T, Aquilina L (2012) Contribution of age data to the characterization of complex aquifers. J Hydrol 464–465:54–68

    Article  Google Scholar 

  • Lumley JL, Panofsky HA (1964) The structure of atmospheric turbulence. Wiley, New York

    Google Scholar 

  • Marino MA, Luthin JN (1982) Seepage and groundwater. Elsevier, New York

    Google Scholar 

  • Mathero G (1971) The theory of regionalized variables and its applications. Centre de Morphol Math de Fontainebleau, Fontainebleau, France

  • Mizell SA, Gutjahr AL, Gelhar LW (1982) Stochastic analysis of spatial variability in two-dimensional steady groundwater flow assuming stationary and nonstationary heads. Water Resour Res 18(4):1053–1067

    Article  Google Scholar 

  • Mumford KG, Mustafa N, Gerhard JI (2015) Probabilistic risk assessment of contaminant transport in groundwater and vapour intrusion following remediation of a contaminant source. Stoch Environ Res Risk Assess 30(3):1017–1031

    Article  Google Scholar 

  • Naff RL, Vecchia AV (1986) Stochastic analysis of three-dimensional flow in a bounded domain. Water Resour Res 22(5):695–704

    Article  Google Scholar 

  • Nastev M, Morin R, Godin R, Rouleau A (2008) Developing conceptual hydrogeological model for Potsdam sandstones in southwestern Quebec. Canada Hydrogeol J 16(2):373–388

    Article  CAS  Google Scholar 

  • Ni C-F, Li S-G (2005) Simple closed form formulas for predicting groundwater flow model uncertainty in complex, heterogeneous trending media. Water Resour Res 41(11):W11503

    Article  Google Scholar 

  • Ni C-F, Li S-G (2006) Modeling groundwater velocity uncertainty in nonstationary composite porous media. Adv Water Resour 29(12):1866–1875

    Article  Google Scholar 

  • Ni C-F, Li S-G, Liu C-J, Hsu SM (2010) Efficient conceptual framework to quantify flow uncertainty in large-scale, highly nonstationary groundwater systems. J Hydrol 381(3–4):297–307

    Article  Google Scholar 

  • Ni C-F, Lin C-P, Li S-G, Liu C-J (2011) Efficient approximate spectral method to delineate stochastic well capture zones in nonstationary groundwater flow systems. J Hydrol 407(1–4):184–195

    Article  Google Scholar 

  • Oliver LD, Christakos G (1995) Diagrammatic solutions for hydraulic head moments in 1-D and 2-D bounded domains. Stoch Hydrol Hydraul 9(4):269–296

    Article  Google Scholar 

  • Pétré M-A, Rivera A, Lefebvre R (2019) Numerical modeling of a regional groundwater flow system to assess groundwater storage loss, capture and sustainable exploitation of the transboundary Milk River Aquifer (Canada—USA). J Hydrol 575:656–670

    Article  Google Scholar 

  • Priestley MB (1965) Evolutionary spectra and non-stationary processes. J R Stat Soc Ser B 27(2):204–237

    Google Scholar 

  • Refsgaard JC (1997) Parameterisation, calibration and validation of distributed hydrological models. J Hydrol 198(1–4):69–97

    Article  Google Scholar 

  • Rodriguez-Iturbe I, Mejia JM (1974) The design of rainfall networks in time and space. Water Resour Res 10(4):713–728

    Article  Google Scholar 

  • Rotiroti M, Bonomi T, Sacchi E, McArthur JM, Stefania GA, Zanotti C, Taviani S, Patelli M, Nava V, Soler M, Fumagalli L, Leoni B (2019) The effects of irrigation on groundwater quality and quantity in a human-modified hydro-system: the Oglio River basin, Po Plain, northern Italy. Sci Total Environ 672:342–356

    Article  CAS  Google Scholar 

  • Rotzoll K, Gingerich SB, Jenson JW, El-Kadi AI (2013) Estimating hydraulic properties from tidal attenuation in the Northern Guam Lens Aquifer, territory of Guam, USA. Hydrogeol J 21(3):643–654

    Article  Google Scholar 

  • Rubin Y (2003) Applied stochastic hydrogeology. Oxford University Press, New York

    Book  Google Scholar 

  • Rubin Y, Bellin A (1994) The effects of recharge on flow nonuniformity and macrodispersion. Water Resour Res 30(4):939–948

    Article  Google Scholar 

  • Sanchez-Vila X (1997) Radially convergent flow in heterogeneous porous media. Water Resour Res 33(7):1633–1641

    Article  Google Scholar 

  • Sishodia RP, Shukla S, Graham WD, Wani SP, Jones JW, Heaney J (2017) Current and future groundwater withdrawals: effects, management and energy policy options for a semi-arid Indian watershed. Adv Water Resour 110:459–475

    Article  Google Scholar 

  • Vanmarcke E (1983) Random fields: analysis and synthesis. MIT Press, Cambridge

    Google Scholar 

  • Vassena C, Rienzner M, Ponzini G, Giudici M, Gandolfi C, Durante C, Agostani D (2012) Modeling water resources of a highly irrigated alluvial plain (Italy): calibrating soil and groundwater models. Hydrogeol J 20(3):449–467

    Article  Google Scholar 

  • Whittle P (1954) On stationary processes in the plane. Biometrika 41:434–449

    Article  Google Scholar 

  • Zamrsky D, Oude Essink GH, Bierkens MF (2018) Estimating the thickness of unconsolidated coastal aquifers along the global coastline. Earth Syst Sci Data 10(3):1591–1603

    Article  Google Scholar 

  • Zhang D (2002) Stochastic methods for flow in porous media: coping with uncertainties. Academic Press, San Diego

    Google Scholar 

  • Zhou Y, Li W (2011) A review of regional groundwater flow modeling. Geosci Front 2(2):205–214

    Article  Google Scholar 

Download references

Acknowledgements

Research leading to this paper has been partially supported by the grant from the Taiwan Ministry of Science and Technology under the Grants MOST 108-2638-E-008-001-MY2, MOST 110-2621-M-008-003-, MOST 110-MOEA-M-008-001-, MOST 110-2123-M-008-001-, and MOST 108-2638-E-008-001-MY2. We are grateful to the associate editor and anonymous reviewers for constructive comments that improved the quality of the work.

Author information

Authors and Affiliations

  1. Graduate Institute of Applied Geology, National Central University, Taoyuan, Taiwan

    Ching-Min Chang, Chuen-Fa Ni & We-Ci Li

  2. Center for Environmental Studies, National Central University, Taoyuan, Taiwan

    Chi-Ping Lin & I-Hsian Lee

Authors
  1. Ching-Min Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuen-Fa Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. We-Ci Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chi-Ping Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I-Hsian Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuen-Fa Ni.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, CM., Ni, CF., Li, WC. et al. Stochastic analysis of the variability of groundwater flow fields in heterogeneous confined aquifers of variable thickness. Stoch Environ Res Risk Assess 36, 2503–2518 (2022). https://doi.org/10.1007/s00477-021-02125-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-021-02125-7

Keywords

Search

Navigation