Mathematical Geosciences

, Volume 50, Issue 2, pp 169–186 | Cite as

Oscillatory Pumping Test to Estimate Aquifer Hydraulic Parameters in a Bayesian Geostatistical Framework

  • D’Oria MarcoEmail author
  • Zanini Andrea
  • Cupola Fausto
Special Issue


Comprehensive information about the spatial distribution of the subsurface hydraulic properties is crucial to model groundwater flow, to predict solute transport in aquifers and to design remediation actions. In this work, a Bayesian Geostatistical approach, as implemented in bgaPEST, was adopted to estimate the hydraulic properties of a well field located at the Campus of Science and Technology of the University of Parma (Northern Italy), in a contest of a highly parameterized inversion. Head data, collected by means of multi frequency oscillatory pumping tests, were used to both estimate the hydraulic parameters and validate the results. The groundwater flow processes were modelled by means of MODFLOW 2005 and an adjoint-state formulation of the same software was used to efficiently calculate the sensitivity matrix, required by the inverse procedure. The Bayesian Geostatistical approach estimated the hydraulic conductivity and specific storage fields, handling a large number of parameters. The results of the inversion are consistent with the alluvial nature of the investigated aquifer and the preliminary traditional pumping tests carried out at the site.


Oscillatory pumping test Bayes Geostatistical approach Hydraulic parameter estimation Groundwater 



The authors are grateful to the editor and the anonymous reviewers for their valuable comments and suggestions on this work.


  1. Alberti L, Lombi S, Zanini A (2011) Identifying sources of chlorinated aliphatic hydrocarbons in a residential area in Italy using the integral pumping test method. Hydrogeol J 19(6):1253–1267. CrossRefGoogle Scholar
  2. Butera I, Tanda MG, Zanini A (2013) Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach. Stoch Environ Res Risk Assess 27(5):1269–1280. CrossRefGoogle Scholar
  3. Cardiff M, Bakhos T, Kitanidis PK, Barrash W (2013) Aquifer heterogeneity characterization with oscillatory pumping: sensitivity analysis and imaging potential. Water Resour Res 49:5395–5410. CrossRefGoogle Scholar
  4. Cardiff M, Barrash W (2011) 3-D transient hydraulic tomography in unconfined aquifers with fast drainage response. Water Resour Res 47:W12518. CrossRefGoogle Scholar
  5. Cardiff M, Barrash W, Kitanidis PK (2012) A field proof-of-concept of aquifer imaging using 3-D transient hydraulic tomography with modular, temporarily emplaced equipment. Water Resour Res 48:W05531. CrossRefGoogle Scholar
  6. Carrera J, Alcolea A, Medina A, Hidalgo J, Slootenet LJ (2005) Inverse problem in hydrogeology. Hydrogeol J 13:206. CrossRefGoogle Scholar
  7. Chen Y, Oliver DS (2012) Ensemble randomized maximum likelihood method as an iterative ensemble smoother. Math Geosci 44:1–26. CrossRefGoogle Scholar
  8. Clemo T (2007) MODFLOW-2005 ground water model—user guide to the adjoint state based sensitivity process (ADJ). Center for the Geophysical Investigation of the Shallow Subsurface, Boise State University, BoiseGoogle Scholar
  9. Cupola F, Tanda MG, Zanini A (2015) Contaminant release history identification in 2-D heterogeneous aquifers through a minimum relative entropy approach. SpringerPlus 4:656. CrossRefGoogle Scholar
  10. Doherty JE (2010) PEST, model-independent parameter estimation—user manual, 5th edn. Watermark Numerical Computing, Brisbane (with slight additions)Google Scholar
  11. Doherty JE, Hunt RJ (2010) Approaches to highly parameterized inversion—a guide to using PEST for groundwater-model calibration: U.S. Geological Survey Scientific Investigations Report 5169.
  12. D’Oria M, Fienen MN (2012) MODFLOW-style parameters in underdetermined parameter estimation. Ground Water 50:149–153. CrossRefGoogle Scholar
  13. D’Oria M, Mignosa P, Tanda MG (2014) Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems. Adv Water Resour 63:143–151. CrossRefGoogle Scholar
  14. D’Oria M, Mignosa P, Tanda MG (2015) An inverse method to estimate the flow through a levee breach. Adv Water Resour 82:166–175. CrossRefGoogle Scholar
  15. D’Oria M, Tanda MG (2012) Reverse flow routing in open channels: a Bayesian geostatistical approach. J Hydrol 460:130–135. CrossRefGoogle Scholar
  16. Emerick AA, Reynolds AC (2013) Ensemble smoother with multiple data assimilation. Comput Geosci 55:3–15. CrossRefGoogle Scholar
  17. Evensen G (2009) Data assimilation: the ensemble Kalman filter, 2nd edn. Springer, Berlin. CrossRefGoogle Scholar
  18. Fienen MN, Clemo TM, Kitanidis PK (2008) An interactive Bayesian geostatistical inverse protocol for hydraulic tomography. Water Resour Res 44:W00B01. CrossRefGoogle Scholar
  19. Fienen M, Hunt R, Krabbenhoft D, Clemo T (2009) Obtaining parsimonious hydraulic conductivity fields using head and transport observations: a Bayesian geostatistical parameter estimation approach. Water Resour Res 45:W08405. CrossRefGoogle Scholar
  20. Fienen MN, D’Oria M, Doherty JE, Hunt RJ (2013) Approaches in highly parameterized inversion: bgaPEST, a Bayesian geostatistical approach implementation with PEST-Documentation and instructions. In: U.S. Geological Survey Techniques and Methods 7-C9.
  21. Grana D, Fjeldstad T, Omre H (2017) Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Math Geosci 49:493. CrossRefGoogle Scholar
  22. Hansen TM, Journel AG, Tarantola A, Mosegaard K (2006) Linear inverse Gaussian theory and geostatistics. Geophysics 71(6):R101–R111. CrossRefGoogle Scholar
  23. Hantush MS (1956) Analysis of data from pumping tests in leaky aquifers. Trans Am Geophys Union 37(6):702–714CrossRefGoogle Scholar
  24. Harbaugh AW (2005) MODFLOW-2005, The U.S. Geological Survey modular ground-water model—the Ground-Water Flow Process. In: U.S. Geological Survey Techniques and Methods 6-A16.
  25. Hendricks Franssen HJ, Alcolea A, Riva M, Bakr M, van der Wiel N, Stauffer F, Guadagnini A (2009) A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments. Adv Water Resour 32(6):851–872. CrossRefGoogle Scholar
  26. Hill MC (2006) Using models to manage systems subject to sustainability indicators. In: Webb B, Hirata R, Kruse E, Vrba J (eds) Sustainability of groundwater resources and its indicators, IAHS publication 302. IAHS Press, WallingfordGoogle Scholar
  27. Hoeksema RJ, Kitanidis PK (1984) An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling. Water Resour Res 20(7):1003–1020. CrossRefGoogle Scholar
  28. Kitanidis PK, Vomvoris EG (1983) A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations. Water Resour Res 19(3):677–690. CrossRefGoogle Scholar
  29. Kitanidis PK (1993) Generalized covariance functions in estimation. Math Geol 25(5):525–540. CrossRefGoogle Scholar
  30. Kitanidis PK (1995) Quasi-linear geostatistical theory for inversing. Water Resour Res 31(10):2411–2419. CrossRefGoogle Scholar
  31. Kitanidis PK (1997) Introduction to geostatistics, applications in hydrogeology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  32. Kitanidis PK, Lee J (2014) Principal component geostatistical approach for large-dimensional inverse problems. Water Resour Res 50:5428–5443. CrossRefGoogle Scholar
  33. Leonhardt G, D’Oria M, Kleidorfer M, Rauch W (2014) Estimating inflow to a combined sewer overflow structure with storage tank in real time: evaluation of different approaches. Water Sci Technol 70(7):1143–1151. CrossRefGoogle Scholar
  34. Li L, Srinivasan S, Zhou H, Gomez-Hernandez JJ (2015) Two-point or multiple point statistics? A comparison between the ensemble Kalman filtering and the ensemble pattern matching inverse methods. Adv Water Resour 86(B):297–310. CrossRefGoogle Scholar
  35. Liu X, Lee J, Kitanidis PK, Parker J, Kim U (2012) Value of information as a context-specific measure of uncertainty in groundwater remediation. Water Resour Manage 26(6):1513–1535. CrossRefGoogle Scholar
  36. McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. Water Resour Res 32(5):1131–1161. CrossRefGoogle Scholar
  37. Michalak AM, Bruhwiler L, Tans PP (2004) A geostatistical approach to surface flux estimation of atmospheric trace gases. J Geophys Res 109:D14. CrossRefGoogle Scholar
  38. Nowak W, Cirpka OA (2004) A modified Levenberg–Marquardt algorithm for quasi-linear geostatistical inversing. Adv Water Resour 27(7):737–750. CrossRefGoogle Scholar
  39. Rabinovich A, Barrash W, Cardiff M, Hochstetler DL, Bakhos T, Dagan G, Kitanidis PK (2015) Frequency dependent hydraulic properties estimated from oscillatory pumping tests in an unconfined aquifer. J Hydrol 531(1):2–16. CrossRefGoogle Scholar
  40. Regione Emilia-Romagna, Servizio Geologico Sismico e dei Suoli, ENI-AGIP (1998) Riserve idriche sotterranee della Regione Emilia-Romagna, p 119 (in Italian) Google Scholar
  41. Rimstad K, Avseth P, Omre H (2012) Hierarchical Bayesian lithology/fluid prediction: a North Sea case study. Geophysics 77(2):B69–B85CrossRefGoogle Scholar
  42. Rubin Y, Chen X, Murakami H, Hahn M (2010) A Bayesian approach for inverse modeling, data assimilation, and conditional simulation of spatial random fields. Water Resour Res 46:W10523. CrossRefGoogle Scholar
  43. Snodgrass MF, Kitanidis PK (1997) A geostatistical approach to contaminant source identification. Water Resour Res 33(4):537–546. CrossRefGoogle Scholar
  44. Soares A, Nunes R, Azevedo L (2017) Integration of uncertain data in geostatistical modelling. Math Geosci 49:253. CrossRefGoogle Scholar
  45. Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, PhiladelphiaCrossRefGoogle Scholar
  46. Theis CV (1935) The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans Am Geophys Union 2:519–524CrossRefGoogle Scholar
  47. Yeh WWG (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22(2):95–108. CrossRefGoogle Scholar
  48. Yeh TCJ, Liu S (2000) Hydraulic tomography: development of a new aquifer test method. Water Resour Res 36(8):2095–2105. CrossRefGoogle Scholar
  49. Veling EJM, Maas C (2010) Hantush well function revisited. J Hydrol 393(3):381–388. CrossRefGoogle Scholar
  50. Xu T, Gomez-Hernandez JJ (2016) Joint identification of contaminant source location, initial release time, and initial solute concentration in an aquifer via ensemble Kalman filtering. Water Resour Res 52:6587–6595. CrossRefGoogle Scholar
  51. Zanini A, Kitanidis PK (2009) Geostatistical inversing for large-contrast transmissivity fields. Stoch Environ Res Risk Assess 23:565. CrossRefGoogle Scholar
  52. Zanini A, Woodbury AD (2016) Contaminant source reconstruction by empirical Bayes and Akaike’s Bayesian information criterion. J Contam Hydrol 185–186:74–86. CrossRefGoogle Scholar
  53. Zanini A, Tanda MG, Woodbury AD (2017) Identification of transmissivity fields using a Bayesian strategy and perturbative approach. Adv Water Resour 108:69–82. CrossRefGoogle Scholar
  54. Zhou H, Gómez-Hernández JJ, Liangping L (2014) Inverse methods in hydrogeology: evolution and recent trends. Adv Water Resour 63:22–37. CrossRefGoogle Scholar
  55. Zhou H, Li L, Hendricks Franssen HJ, Gómez-Hernández JJ (2012) Pattern recognition in a bimodal aquifer using the normal-score ensemble Kalman filter. Math Geosci 44:169. CrossRefGoogle Scholar
  56. Zhou YQ, Lim D, Cupola F, Cardiff M (2016) Aquifer imaging with pressure waves—evaluation of low-impact characterization through sandbox experiments. Water Resour Res 52:2141–2156. CrossRefGoogle Scholar
  57. Zimmerman DA, de Marsily G, Gotway CA, Marietta MG, Axness CL, Beauheim RL, Bras RL, Carrera J, Dagan G, Davies PB, Gallegos DP, Galli A, Gómez-Hernández J, Grindrod P, Gutjahr AL, Kitanidis PK, Lavenue AM, McLaughlin D, Neuman SP, RamaRao BS, Ravenne C, Rubin Y (1998) A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow. Water Resour Res 34(6):1373–1413. CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2017

Authors and Affiliations

  1. 1.Department of Engineering and ArchitectureUniversity of ParmaParmaItaly

Personalised recommendations