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Hydrogeology Journal

, Volume 23, Issue 7, pp 1431–1448 | Cite as

Decomposing groundwater head variations into meteorological and pumping components: a synthetic study

  • V. ShapooriEmail author
  • T. J. Peterson
  • A. W. Western
  • J. F. Costelloe
Paper

Abstract

Time-series modeling is often used to decompose groundwater hydrographs into individual drivers such as pumping and meteorological factors. To date, there has been an assumption that a simulation fitting the total hydrograph produces reliable estimates of the impact from each driver. That is, assessment of the decomposition has not used an independent estimate of each decomposition result. To begin to address this, a synthetic study is undertaken so that the impact of each driver is known. In this study, 500 MODFLOW groundwater models of a one-layer unconfined aquifer were constructed. For each model, three hydrogeological properties (saturated hydraulic conductivity, storativity and depth to aquifer basement), the distance between observation and pumping bores, and extraction rate were set randomly and synthetic groundwater hydrographs were derived. For each hydrograph, the influence of individual drivers was estimated using six different time-series models. These estimates were then compared to the known meteorological and pumping influences derived from the MODFLOW models. The results demonstrate that hydrograph separations obtained from time-series models do not always result in reliable estimation of pumping and meteorological influences even when the overall hydrograph fit is good. However, when the time-series model represents the important processes (e.g. phreatic evaporation is included for shallow water tables) and the (head) variance of the pumping signal to the meteorological signal is between 0.1 and 10, the time-series model has the potential to adequately separate the influence of pumping and climate.

Keywords

Statistical modeling Groundwater pumping Time series modeling Australia 

Décomposition des variations de charge hydraulique des eaux souterraines en composantes météorologiques et de pompage: étude de synthèse

Résumé

La modélisation des séries chronologiques est souvent utilisée pour décomposer les hydrogrammes des eaux souterraines en leurs déterminants pris individuellement, par exemple le pompage et les facteurs météorologiques. Jusqu’à ce jour, il y avait une hypothèse selon laquelle une simulation qui concorde avec l’hydrogramme dans sa totalité fournit une estimation fiable de l’impact imputable à chaque déterminant. Autrement dit, l’évaluation de la décomposition n’utilisait pas une estimation indépendante de chaque résultat de décomposition. Pour avancer dans la résolution de ce problème, une étude de synthèse destinée à connaître l’impact de chaque déterminant a été entreprise. Dans cette étude, 500 modèles MODFLOW d’aquifère libre mono-couche ont été établis. Pour chaque modèle, trois propriétés hydrogéologiques (conductivité hydraulique de la zone saturée, coefficient d’emmagasinement et profondeur du mur de l’aquifère), la distance entre piézomètre et puits de pompage et le débit de pompage ont été fixés de manière aléatoire et des hydrogrammes synthétiques des eaux souterraines ont été déduits. Pour chaque hydrogramme, l’influence de chaque facteur a été estimée d’après la modélisation de six chroniques différentes. Ces évaluations ont été ensuite comparées aux influences connues de la météorologie et du pompage telles que déduites des modèles MODFLOW. Les résultats montrent que les séparations d’hydrogramme obtenues par la modélisation des séries temporelles ne se traduisent pas toujours par une estimation fiable des influences du pompage et de la météorologie, même quand la correspondance avec l’hydrogramme global est bonne. Cependant, quand le modèle des séries chronologiques représente les processus importants (par exemple l’évaporation phréatique est comptabilisée pour une surface de nappe libre peu profonde) et que la variance du signal de pompage par rapport au signal météorologique est comprise entre 0.1 et 10, le modèle de séries chronologiques est capable de séparer correctement l’influence du pompage de celle du climat.

Descomposición de las variaciones de la carga hidráulica de las aguas subterráneas en componentes meteorológicos y de bombeo: un estudio sintético

Resumen

El modelado de series de tiempo se usa a menudo para descomponer hidrogramas de agua subterránea en componentes, tales como el bombeo y los factores meteorológicos. Hasta la fecha, ha existido el supuesto que una simulación adecuada del hidrograma total produce estimaciones fiables de los efectos de cada componente. Es decir, la evaluación de la descomposición no ha utilizado una estimación independiente de cada resultado de la descomposición. Para comenzar a abordar esto, se llevó a cabo un estudio sintético de modo de conocer el impacto de cada componente. En este estudio, se construyeron 500 modelos MODFLOW de aguas subterráneas de un acuífero no confinado de una sola capa. Para cada modelo, se fijaron al azar las propiedades hidrogeológicas (conductividad hidráulica saturada, almacenamiento y profundidad al basamento acuífero), la distancia entre pozos de observación y de bombeo y la tasa de extracción y a partir de ello fueron derivados los hidrogramas sintéticos de agua subterránea. Para cada hidrograma, se estimó la influencia de los componentes individuales usando seis diferentes modelos de series de tiempo. Estas estimaciones se compararon con las influencias meteorológicas y de bombeos conocidas, derivadas a partir de los modelos MODFLOW. Los resultados demuestran que las separaciones de hidrogramas obtenidas a partir de los modelos de series de tiempo no siempre resultan en estimaciones seguras de las influencias meteorológicas y del bombeo aún cuando el ajuste general del hidrograma es bueno. Sin embargo, cuando el modelo de series de tiempo representa los procesos importantes (por ejemplo, la evaporación desde la freática es incluida para niveles freáticos someros) y la (carga hidráulica) la varianza entre la señal de bombeo y la señal meteorológica es entre 0.1 y 10, el modelo de series de tiempo tiene el potencial para separar adecuadamente la influencia de bombeo y el clima.

把地下水头变化分解到气象和抽水成分中:综合研究

摘要

时间序列模拟常常用于分解地下水水位曲线到单个的驱动因素中,如抽水和气象因素。迄今为止,有一个假定就是,拟合整个水文曲线的模拟从每个驱动因素中可得出可靠的影响估算结果。这就是说,分解评价没有使用每个分解结果的独立估算值。为了首先强调这点,进行了综合研究,以便获知每个驱动因素的影响。在本项研究中,建立了一个单层非承压含水层500个MODFLOW地下水模型。每个模型,随机设定了三个水文地质特性(饱和水力传导系数、储存系数和含水层底部的深度)、观测井和抽水井的距离及抽水速度,得到了综合地下水水位曲线图。针对每个水位曲线图,利用六个不同的时间序列模型估算了每个驱动因素的影响。然后,把这些估算值与由MODFLOW模型得到的已知气象和抽水影响进行了对比。结果显示,即使是整体水位曲线图拟合非常好,时间序列模型得到的水位曲线图也并不总能得出抽水和气象影响的可靠估算结果。然而,当时间序列模型展示重要过程(例如,浅层水位中包括潜水蒸发)时及抽水信号对气象信号的(水头)变化在0.1和10之间时,时间序列模型具有充分分离抽水和气候影响的潜力。

Decompondo variações de carga hidráulica em componentes meteorológicas e de bombeamento: um estudo sintético

Resumo

Modelagem de séries temporais é comumente usada para decompor hidrogramas de água subterrânea em componentes forçantes individuais, como bombeamento e fatores meteorológicos. Até o momento, tem existido uma hipótese de que uma simulação que ajusta o hidrograma total produz uma estimativa confiável do impacto de cada componente. Isto é, uma avaliação de decomposição não utiliza uma estimativa independente de cada resultado da decomposição. Para começar a lidar com o problema, um estudo sintético foi feito de forma que o impacto de cada componente seja conhecido. Neste estudo, foram construídos 500 modelos de água subterrânea MODFLOW de um aquífero não confinado de uma camada. Para cada modelo, três propriedades hidrológicas (condutividade hidráulica saturada, coeficiente de armazenamento e profundidade da base do aquífero), a distância entre os poços de observação e de bombeamento e a taxa de extração foram definidas de forma aleatória, tendo seus hidrogramas de água subterrânea derivados. Para cada hidrograma, a influência das componentes forçantes individuais foi estimada usando seis modelos de séries temporais distintos. Estas estimativas foram então comparadas com influências meteorológicas e de bombeamento conhecidas, derivadas dos modelos MODFLOW. Os resultados demonstram que a separação dos hidrogramas obtidos através dos modelos de séries temporais nem sempre resultam em estimativas confiáveis da influência de bombeamento e de condições meteorológicas, mesmo quando o ajuste do hidrograma é bom. Entretanto, quando um modelo de séries temporais representa o processo importante (p. ex. evaporação freática é incluída em aquíferos rasos) e a variância (de carga) entre o sinal de bombeamento com o sinal meteorológico está entre 0.1 e 10, o modelo de séries temporais tem o potencial de separar adequadamente a influencia de bombeamento e clima.

Notes

Acknowledgements

The authors are grateful for the financial support received from the Australian Research Council (grant numbers: LP0991280 and LP130100958), the Department of Environment and Primary Industries (Victoria, Australia), and the Bureau of Meteorology (Australia). The authors thank the editors and anonymous reviewers for their constructive comments.

References

  1. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration-guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56, FAO, RomeGoogle Scholar
  2. Andreu JM, Alcala FJ, Vallejos A, Pulido-Bosch A (2011) Recharge to mountainous carbonated aquifers in SE Spain: different approaches and new challenges. J Arid Environ 75:1262–1270. doi: 10.1016/j.jaridenv.2011.01.011 CrossRefGoogle Scholar
  3. Bakker M, Maas K, Von Asmuth JR (2008) Calibration of transient groundwater models using time series analysis and moment matching. Water Resour Res 44:W04420. doi: 10.1029/2007wr006239 Google Scholar
  4. Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Hydrology Papers, Colorado State University, Fort Collins, CO, 24 ppGoogle Scholar
  5. Butler JJ, Kluitenberg GJ, Whittemore DO, Loheide SP, Jin W, Billinger MA, Zhan XY (2007) A field investigation of phreatophyte-induced fluctuations in the water table. Water Resour Res 43:W02404. doi: 10.1029/2005WR004627 Google Scholar
  6. Crosbie RS, Binning P, Kalma JD (2005) A time series approach to inferring groundwater recharge using the water table fluctuation method. Water Resour Res 41:W01008. doi: 10.1029/2004WR003077 Google Scholar
  7. Cuthbert MO (2010) An improved time series approach for estimating groundwater recharge from groundwater level fluctuations. Water Resour Res 46:W09515. doi: 10.1029/2009WR008572 Google Scholar
  8. Doll P (2009) Vulnerability to the impact of climate change on renewable groundwater resources: a global-scale assessment. Environ Res Lett 4:035006. doi: 10.1088/1748-9326/4/3/035006 CrossRefGoogle Scholar
  9. Fan J, Pan J (2006) Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition. Comput Opt Appl 34:47–62CrossRefGoogle Scholar
  10. Ferdowsian R, George A, Bee G, Smart R (2002) Groundwater level reductions under Lucerne depend on the landform and groundwater flow systems (local and intermediate). Aust J Soil Res 40:381–396CrossRefGoogle Scholar
  11. Ferket BVA, Samain B, Pauwels VRN (2010) Internal validation of conceptual rainfall–runoff models using baseflow separation. J Hydrol 381:158–175. doi: 10.1016/j.jhydrol.2009.11.038 CrossRefGoogle Scholar
  12. Ferris JG, Knowles DB (1963) The slug-injection test for estimating the coefficient of transmissibility of an aquifer. In: Bentall R (ed) Methods of determining permeability, transmissibility, and drawdown. US Geol Surv Water Suppl Pap 1536-IGoogle Scholar
  13. Freeze RA, Cherry JA (1979) Groundwater. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  14. Gerla PJ (1992) The relationship of water-table changes to the capillary-fringe, evapotranspiration, and precipitation in intermittent wetlands. Wetlands 12:91–98CrossRefGoogle Scholar
  15. Hantush MS (1956) Analysis of data from pumping tests in leaky aquifers. Trans Am Geophys Union 37:702–714CrossRefGoogle Scholar
  16. Hill MC, Tiedeman CR (2006) Effective groundwater model calibration: with analysis of data, sensitivities, predictions, and uncertainty. Wiley, Hoboken, NJGoogle Scholar
  17. Jakeman AJJ, Hornberger GM (1993) How much complexity is warranted in a rainfall-runoff model? Water Resour Res 29:2637–2649CrossRefGoogle Scholar
  18. Kavetski D, Kuczera G, Franks S (2006) Bayesian analysis of input uncertainty in hydrological modeling, 1. Theor Water Resour Res 42:W03407. doi: 10.1029/2005WR004368 Google Scholar
  19. Konikow LF, Kendy E (2005) Groundwater depletion: a global problem. Hydrogeol J 13:317–320. doi: 10.1007/s10040-004-0411-8 CrossRefGoogle Scholar
  20. Kruseman GP, De Ridder NA (1994) Analysis and evaluation of pumping test data. International Institute for Land Reclamation and Improvement, Wageningen, The NetherlandsGoogle Scholar
  21. Kundzewicz ZW, Doll P (2009) Will groundwater ease freshwater stress under climate change? Hydrol Sci J 54:665–675. doi: 10.1623/hysj.54.4.665 CrossRefGoogle Scholar
  22. Lehsten D, Von Asmuth JR, Kleyer M (2011) Simulation of water level fluctuations in kettle holes using a time series model. Wetlands 31:511–520. doi: 10.1007/s13157-011-0174-7 CrossRefGoogle Scholar
  23. Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Quart Appl Math 2:164–168Google Scholar
  24. Li L, Maier HR, Lambert MF, Simmons CT, Partington D (2013) Framework for assessing and improving the performance of recursive digital filters for baseflow estimation with application to the Lyne and Hollick filter. Environ Model Softw 41:163–175. doi: 10.1016/j.envsoft.2012.11.009 CrossRefGoogle Scholar
  25. Li L, Maier HR, Partington D, Lambert MF, Simmons CT (2014) Performance assessment and improvement of recursive digital baseflow filters for catchments with different physical characteristics and hydrological inputs. Environ Model Softw 54:39–52. doi: 10.1016/j.envsoft.2013.12.011 CrossRefGoogle Scholar
  26. Loheide SP, Butler JJ, Gorelick SM (2005) Estimation of groundwater consumption by phreatophytes using diurnal water table fluctuations: a saturated–unsaturated flow assessment. Water Resour Res 41:W07030. doi: 10.1029/2005WR003942 Google Scholar
  27. Manzione RL, Knotters M, Heuvelink GBM, Von Asmuth JR, Camara G (2010) Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados. Hydrogeol J 18:1927–1937. doi: 10.1007/s10040-010-0654-5 CrossRefGoogle Scholar
  28. Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431–441CrossRefGoogle Scholar
  29. McMillan H, Jackson B, Clark M, Kavetski D, Woods R (2011) Rainfall uncertainty in hydrological modeling: an evaluation of multiplicative error models. J Hydrol 400:83–94. doi: 10.1016/j.jhydrol.2011.01.026 CrossRefGoogle Scholar
  30. Morton FI (1983) Operational estimates of areal evapotranspiration and their significance to the science and practice of hydrology. J Hydrol 66:1–76CrossRefGoogle Scholar
  31. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I: a discussion of principles. J Hydrol 10:282–290. doi: 10.1016/0022-1694(70)90255-6 CrossRefGoogle Scholar
  32. Niswonger RG, Prudic DE, Regan RS (2006) Documentation of the Unsaturated-Zone Flow (UZF1) Package for modeling unsaturated flow between the land surface and the water table with MODFLOW-2005. US Geological Survey, Reston, VAGoogle Scholar
  33. Obergfell C, Bakker M, Zaadnoordijk WJ, Maas K (2013) Deriving hydrogeological parameters through time series analysis of groundwater head fluctuations around well fields. Hydrogeol J 21:987–999. doi: 10.1007/s10040-013-0973-4 CrossRefGoogle Scholar
  34. Partington D, Brunner P, Simmons CT, Therrien R, Werner AD, Dandy GC, Maier HR (2011) A hydraulic mixing-cell method to quantify the groundwater component of streamflow within spatially distributed fully integrated surface water–groundwater flow models. Environ Model Softw 26:886–898CrossRefGoogle Scholar
  35. Partington D, Brunner P, Simmons C, Werner A, Therrien R, Maier H, Dandy G (2012) Evaluation of outputs from automated baseflow separation methods against simulated baseflow from a physically based, surface water-groundwater flow model. J Hydrol 458:28–39CrossRefGoogle Scholar
  36. Peel MC, Finlayson BL, McMahon TA (2007) Updated world map of the Köppen-Geiger climate classification. Hydrol Earth Syst Sci Discuss 4:439–473CrossRefGoogle Scholar
  37. Peterson TJ, Western AW (2011) Time-series modeling of groundwater head and its de-composition to historic climate periods. Paper presented at the 34th IAHR World Congress, Brisbane, Australia, 26 June–1 July 2011Google Scholar
  38. Peterson TJ, Western AW (2014) Nonlinear time series modeling of unconfined groundwater head. Water Resour Res 50:8330–8355. doi: 10.1002/2013WR014800 CrossRefGoogle Scholar
  39. Renard B, Kavetski D, Kuczera G, Thyer M, Franks SW (2010) Understanding predictive uncertainty in hydrologic modeling: the challenge of identifying input and structural errors. Water Resour Res 46:W05521. doi: 10.1029/2009wr008328 Google Scholar
  40. Rosenberry DO, Winter TC (1997) Dynamics of water-table fluctuations in an upland between two prairie-pothole wetlands in North Dakota. J Hydrol 191:266–289. doi: 10.1016/S0022-1694(96)03050-8 CrossRefGoogle Scholar
  41. Scanlon BR, Healy RW, Cook PG (2002) Choosing appropriate techniques for quantifying groundwater recharge. Hydrogeol J 10:19–39Google Scholar
  42. Shamsudduha M, Taylor R, Ahmed K, Zahid A (2011) The impact of intensive groundwater abstraction on recharge to a shallow regional aquifer system: evidence from Bangladesh. Hydrogeol J 19:901–916. doi: 10.1007/s10040-011-0723-4 CrossRefGoogle Scholar
  43. Shapoori V, Peterson TJ, Western AW, Costelloe JF (2015) Top-down groundwater hydrograph time series modeling for climate-pumping decomposition. Hydorgeol J. doi: 10.1007/s10040-014-1223-0 (Published online) Google Scholar
  44. Siriwardena L, Peterson TJ, Western AW (2011) A state-wide assessment of optimal groundwater hydrograph time series models. Paper presented at the International Congress on Modeling and Simulation, Perth, Australia, 12–16 December 2011Google Scholar
  45. Sivapalan M, Young PC (2005) Downward approach to hydrological model development. Encycl Hydrol Sci 3:2081–2098Google Scholar
  46. Sophocleous M (2003) Environmental implications of intensive groundwater use with special regard to streams and wetlands. In: Llamas MR, Custodio E (eds) Groundwater intensive use: challenges and opportunities. Balkema, Dordrecht, The NetherlandsGoogle Scholar
  47. Szilagyi J (2004) Heuristic continuous base flow separation. J Hydrol Eng 9:311–318. doi: 10.1061/(asce)1084-0699(2004)9:4(311) CrossRefGoogle Scholar
  48. Tularam GA, Krishna M (2009) Long term consequences of groundwater pumping in Australia a review of impacts around the globe. J Appl Sci Environ Sanit 4:151–166Google Scholar
  49. Viswanathan MN (1984) Recharge characteristics of an unconfined aquifer from the rainfall–water table relationship mathematical models, Newcastle, Australia, depends upon the intensity. J Hydrol 70:233–250. doi: 10.1016/0022-1694(84)90124-0 CrossRefGoogle Scholar
  50. Von Asmuth JR, Bierkens MFP, Maas K (2002) Transfer function-noise modeling in continuous time using predefined impulse response functions. Water Resour Res 38:23. doi: 10.1029/2001 WR001136 Google Scholar
  51. Von Asmuth JR, Maas K, Bakker M, Petersen J (2008) Modeling time series of ground water head fluctuations subjected to multiple stresses. Groundwater 46:30–40. doi: 10.1111/j.1745-6584.2007.00382.x Google Scholar
  52. Vrugt JA, Braak CFJ, Clark MP, Hyman JM, Robinson BA (2008) Treatment of input uncertainty in hydrologic modeling: doing hydrology backward with Markov chain Monte Carlo simulation. Water Resour Res 44:W00B09. doi: 10.1029/2007WR006720 Google Scholar
  53. Vrugt JA, Ter Braak CJF, Diks CGH, Robinson BA, Hyman JM, Higdon D (2009) Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. Int J Nonlinear Sci Numeric Simul 10:273–290Google Scholar
  54. White WN (1932) A method of estimating ground-water supplies based on discharge by plants and evaporation from soil: results of investigations in Escalante Valley. US Geol Surv Water Suppl Pap 659-AGoogle Scholar
  55. Yi MJ, Lee KK (2004) Transfer function-noise modeling of irregularly observed groundwater heads using precipitation data. J Hydrol 288:272–287. doi: 10.1016/j.jhydrol.2003.10.020 CrossRefGoogle Scholar
  56. Yihdego Y, Webb JA (2011) Modeling of bore hydrographs to determine the impact of climate and land-use change in a temperate subhumid region of southeastern Australia. Hydrogeol J 19:877–887. doi: 10.1007/s10040-011-0726-1 CrossRefGoogle Scholar
  57. Young PC (1978) A general theory of modeling for badly defined dynamic systems. In: Vansteenkiste GC (ed) Modeling, identification and control in environmental systems. North Holland, Amsterdam, pp 103–135Google Scholar
  58. Zektser S, Loaiciga HA, Wolf JT (2005) Environmental impacts of groundwater overdraft: selected case studies in the southwestern United States. Environ Geol 47:396–404. doi: 10.1007/s00254-004-1164-3 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • V. Shapoori
    • 1
    Email author
  • T. J. Peterson
    • 1
  • A. W. Western
    • 1
  • J. F. Costelloe
    • 1
  1. 1.Department of Infrastructure EngineeringThe University of MelbourneParkvilleAustralia

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