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Hydrogeology Journal

, Volume 27, Issue 6, pp 2061–2075 | Cite as

Short-term variations in tracer-test responses in a highly karstified watershed

  • Vianney SivelleEmail author
  • David Labat
Paper
  • 62 Downloads

Abstract

Methods of modelling non-reactive solute transport based on artificial tracer tests have been widely developed in the past few decades. The dependence of solute transport parameters on boundary conditions has been investigated across different hydrological settings (low and high water level) but still not investigated at the short-term scale (i.e. hourly and daily scale). In this study, a campaign of several tracer tests was performed over a few days to investigate the short-term variations of tracer-test responses in a conduit-dominated karst system (Baget watershed, in the Pyrenees Mountains, France) during a recession without the influence of rainfall. Also, an improved method of interpreting artificial tracer test results, using a process engineering tool, is introduced, consisting of a Laplace-transform transfer function approach with respect to the residence-time distribution curve. Considering the karstic system as a chemical reactor, the introduction of a transfer function approach appears to be an efficient way to describe the solute transport. Moreover, the transfer function is parametrized depending on the spring discharge. The model is extended for testing source pollution scenarios.

Keywords

Tracer tests Karst Transfer function Groundwater pollution 

Variations à court terme de la réponse d’essais de traçage dans un bassin d’alimentation très karstifié

Résumé

Les méthodes de modélisation du transport de solutés non réactifs sur la base d’essais de traçage artificiels ont été largement développées ces quelques dernières dizaines d’années. La dépendance des paramètres de transport de solutés aux conditions aux limites a été étudiée pour différentes conditions hydrologiques (basses et hautes eaux) mais pas encore sur de courtes échelles de temps (horaire ou journalière). Dans cette étude, une campagne comprenant plusieurs essais de traçage a été réalisée sur quelques jours pour investiguer les variations à court-terme des réponses des essais de traçage dans un système karstique dominé par des écoulements de conduit (système du Baget, Pyrénées, France) pendant une récession non influencée par la pluie. En outre, une méthode améliorée d’interprétation des résultats d’essais de traçage, utilisant un outil d’ingénierie des procédés, a été introduite. Elle consiste en une approche par une fonction de transfert transformée de Laplace par rapport à la courbe de distribution des temps de séjour. En considérant le système karstique comme un réacteur chimique, l’introduction d’une approche par fonction de transfert apparaît comme un moyen efficace de décrire le transport de solutés. De plus, la fonction de transfert est paramétrée selon le débit de la source. Le modèle est étendu pour tester des scénarios de pollution ponctuelle.

Variaciones a corto plazo en las respuestas de las pruebas de trazadores en una cuenca kárstica

Resumen

En las últimas décadas se han desarrollado ampliamente los métodos de modelado del transporte de soluto no reactivo basado en pruebas de trazabilidad artificial. La dependencia de los parámetros de transporte de los solutos de las condiciones límite ha sido investigada a través de diferentes escenarios hidrológicos (nivel de agua alto y bajo), pero aún no ha sido investigada a una escala de corto plazo (es decir, a escala horaria y diaria). En este estudio, se realizó una campaña de varias pruebas de trazadores durante unos días para investigar las variaciones a corto plazo de las respuestas a dichas pruebas en un sistema kárstico dominado por conductos (cuenca de Baget, en los Pirineos, Francia) durante una recesión sin la influencia de las precipitaciones. Además, se introduce un método mejorado de interpretación de los resultados de las pruebas de trazador artificial, utilizando una herramienta de ingeniería de procesos. Consiste en un enfoque de función de transferencia de transformada de Laplace con respecto a la curva de distribución del tiempo de residencia. Considerando el sistema kárstico como un reactor químico, la introducción de un enfoque de función de transferencia parece ser una forma eficiente de describir el transporte de solutos. Además, la función de transferencia se parametriza en función de la descarga del manantial. El modelo se amplía para probar escenarios de contaminación de la fuente.

高度岩溶流域示踪试验响应的短期变化

摘要

在过去的几十年,基于人工示踪试验的非反应性溶质运移的模拟方法已得到广泛应用。不同水文环境(低水位和高水位)溶质运移参数对边界条件的相关性已经开展过研究,但未开展短期尺度(即每小时和每日尺度)研究。本研究中,几天内开展了多次示踪试验,旨在调查无降雨影响的枯水期以管道为主的岩溶系统(法国Pyrenees山脉的Baget流域)中示踪试验响应的短期变化。此外,还介绍了使用过程工程工具解释人工示踪试验结果的改进方法。该方法包括关于停留时间分布曲线的拉普拉斯变换传递函数方法。考虑到岩溶系统是化学反应器,引入传递函数方法可有效描述溶质的运移。而且传递函数根据泉排泄量进行参数化。该模型可扩展应用于测试源污染方案。

Variações a curto prazo nas respostas de um traçador-teste em uma bacia hidrográfica altamente carsteificada

Resumo

Métodos de modelagem de transporte de solutos não reativos baseados em testes de traçadores artificiais têm sido amplamente desenvolvidos nas últimas décadas. A dependência dos parâmetros de transporte de solutos nas condições de contorno tem sido investigada sob diferentes condições hidrológicas (ex. nível de água baixo e alto), entretanto, para escalas de curto prazo (como escala horária e diária) ainda não foi analisada. Neste estudo, uma campanha de vários testes com traçadores foi realizada durante alguns dias, para investigar as variações em curto prazo nas respostas do traçador-teste em um sistema cárstico com canais (bacia hidrográfica Baget, nas montanhas dos Pirineus, França) durante um período com ausência de chuva. Além disso, um método aperfeiçoado para interpretação dos resultados dos testes do traçador artificial, utilizando uma ferramenta de engenharia, foi introduzido. Este método consiste em uma função de transferência obtida por meio da Transformada de Laplace da curva de distribuição do tempo de residência. Considerando o sistema cárstico como um reator químico, o uso da função de transferência se mostrou uma forma eficiente para descrever o transporte do soluto. Além disso, a função de transferência foi parametrizada de acordo com a nascente (descarga do aquífero). O modelo pode ser aplicado para testar a origem de cenários de poluição.

Notes

Acknowledgements

The authors would like to thank the KARST observatory network (SNO KARST) initiative at the INSU/CNRS, which aims to strengthen knowledge sharing and promote cross-disciplinary research on karst systems at the national scale. We also thank “Météo-France” for providing rainfall data and BRGM (French Geological Survey) for providing discharge data.

Funding information

This work has been funded by “l’Agence de l’eau Adour Garonne”.

References

  1. Ali M, Fiori A, Russo D (2014) A comparison of travel-time based catchment transport models, with application to numerical experiments. J Hydrol 511:605–618.  https://doi.org/10.1016/j.jhydrol.2014.02.010 CrossRefGoogle Scholar
  2. Amin IE, Campana ME (1996) A general lumped parameter model for the interpretation of tracer data and transit time calculation in hydrologic systems. J Hydrol 179(1):1–21.  https://doi.org/10.1016/0022-1694(95)02880-3 CrossRefGoogle Scholar
  3. Becker M, Bellin A (2013) A reservoir model of tracer transport for karstic flow systems. Hydrogeol J 21:1011–1019.  https://doi.org/10.1007/s10040-013-0991-2 CrossRefGoogle Scholar
  4. Birk S, Geyer T, Liedl R, Sauter M (2005) Process-based interpretation of tracer tests in carbonate aquifers. Ground Water 43:381–388.  https://doi.org/10.1111/j.1745-6584.2005.0033.x CrossRefGoogle Scholar
  5. Bolin B, Rodhe H (1973) A note on the concepts of age distribution and transit time in natural reservoirs. Tellus 25(1):58–62.  https://doi.org/10.1111/j.2153-3490.1973.tb01594.x CrossRefGoogle Scholar
  6. Bovolin V, Cuomo A, Guida D (2017) Hydraulic modeling of flood pulses in the middle Bussento karst system (MBSKS), UNESCO Cilento global Geopark, southern Italy. Hydrol Process 31:639–653.  https://doi.org/10.1002/hyp.11056 CrossRefGoogle Scholar
  7. Cholet C (2017) Fonctionnement hydrogéologique et processus de transport dans les aquifères karstiques du massif du Jura [Hydrogeological functioning and transport processes in the karstic aquifers of the Jura massif]. PhD Thesis, Université de Bourgogne Franche-Comté, FranceGoogle Scholar
  8. Cornaton F, Perrochet P (2006) Groundwater age, life expectancy and transit time distributions in advective–dispersive systems: 1. Generalized reservoir theory. Adv Water Resour 29(9):1267–1291.  https://doi.org/10.1016/j.advwatres.2005.10.009 CrossRefGoogle Scholar
  9. Cvetkovic V (2012) A general memory function for modeling mass transfer in groundwater transport. Water Resour Res 48(4).  https://doi.org/10.1029/2011WR011657
  10. De Hoog FR, Knight JH, Stokes AN (1982) An improved method for numerical inversion of Laplace transforms. SIAM J Sci Stat Comput 3:357–366CrossRefGoogle Scholar
  11. Debroas E-J (2009) Géologie du bassin versant du Baget (zone Nord-pyrénéenne, Ariège, France): nouvelles observations et conséquences [Geology of the Baget watershed (north-Pyrenean zone, Ariège, France): new observations and consequences]. Strata 2:1–93Google Scholar
  12. Delannoy J-J (1997) Recherches géomorphologiques sur les massifs karstiques du Vercors et de la transversale de Ronda (Andalousie) : les apports morphogéniques du karst [Geomorphological research on the Vercors karst massif and the Ronda transversal (Andalusia): the morphogenic contributions of karst]. PhD Thesis, Université Joseph-Fourier - Grenoble I, FranceGoogle Scholar
  13. Dewaide L, Bonniver I, Rochez G, Hallet V (2016) Solute transport in heterogeneous karst systems: dimensioning and estimation of the transport parameters via multi-sampling tracer-tests modelling using the OTIS (one-dimensional transport with inflow and storage) program. J Hydrol 534:567–578.  https://doi.org/10.1016/j.jhydrol.2016.01.049 CrossRefGoogle Scholar
  14. Dewaide L, Collon P, Poulain A, Rochez G, Hallet V (2017) Double-peaked breakthrough curves as a consequence of solute transport through underground lakes: a case study of the Furfooz karst system, Belgium. Hydrogeol J.  https://doi.org/10.1007/s10040-017-1671-4
  15. Doerfliger N, Jeannin P-Y, Zwahlen F (1999) Water vulnerability assessment in karst environments: a new method of defining protection areas using a multi-attribute approach and GIS tools (EPIK method). Environ Geol 39:165–176CrossRefGoogle Scholar
  16. Doummar J, Margane A, Geyer T, Sauter M (2018) Assessment of key transport parameters in a karst system under different dynamic conditions based on tracer experiments: the Jeita karst system, Lebanon. Hydrogeol J.  https://doi.org/10.1007/s10040-018-1754-x
  17. Dreybrodt W (1988) Processes in karst systems: physics, chemistry, and geology. Springer Series in Physical Environment, Springer, Heidelberg, GermanyCrossRefGoogle Scholar
  18. Duran L, Fournier M, Massei N, Dupont J-P (2015) Use of tracing tests to study the impact of boundary conditions on the transfer function of karstic aquifers. In: Hydrogeological and environmental investigations in karst systems. Springer, Berlin, pp 113–122.  https://doi.org/10.1007/978-3-642-17435-3_13 Google Scholar
  19. Duran L, Fournier M, Massei N, Dupont J-P (2016) Assessing the nonlinearity of karst response function under variable boundary conditions. Ground Water 54:46–54.  https://doi.org/10.1111/gwat.12337 CrossRefGoogle Scholar
  20. Ender A, Goeppert N, Goldscheider N (2018) Spatial resolution of transport parameters in a subtropical karst conduit system during dry and wet seasons. Hydrogeol J.  https://doi.org/10.1007/s10040-018-1746-x
  21. Field MS (2002) The QTRACER2 program for tracer-breakthrough curve analysis for tracer tests in karstic aquifers and other hydrologic systems. National Center for Environmental Assessment, Office of Research and Development, US EPA, Washington, DCGoogle Scholar
  22. Field MS, Leij FJ (2012) Solute transport in solution conduits exhibiting multi-peaked breakthrough curves. J Hydrol 440–441:26–35.  https://doi.org/10.1016/j.jhydrol.2012.03.018 CrossRefGoogle Scholar
  23. Field MS, Pinsky PF (2000) A two-region nonequilibrium model for solute transport in solution conduits in karstic aquifers. J Contamin Hydrol 44:329–351CrossRefGoogle Scholar
  24. Filippini M, Squarzoni G, De Waele J, Fiorucci A, Vigna B, Grillo B, Riva A, Rossetti S, Zini L, Casagrande G, Stumpp C, Gargini A (2018) Differentiated spring behavior under changing hydrological conditions in an alpine karst aquifer. J Hydrol 556:572–584.  https://doi.org/10.1016/j.jhydrol.2017.11.040 CrossRefGoogle Scholar
  25. Ford D, Williams PD (2007) Karst hydrogeology and geomorphology. Wiley, Chichester, UKGoogle Scholar
  26. Goldscheider N (2004) The concept of groundwater vulnerability. In: Vulnerability and risk mapping for the protection of carbonate (karst) aquifers. Final report (COST Action 620) Report EUR 20912Google Scholar
  27. Goldscheider N (2008) A new quantitative interpretation of the long-tail and plateau-like breakthrough curves from tracer tests in the artesian karst aquifer of Stuttgart, Germany. Hydrogeol J 16:1311–1317.  https://doi.org/10.1007/s10040-008-0307-0 CrossRefGoogle Scholar
  28. Goldscheider N, Hötzl H, Fries W, Jordan P (2001) Validation of a vulnerability map (EPIK) with tracer tests. Presented at the Proc. 7th conference on limestone hydrology and fissured media, Besançon, France, September 2001, pp 167–170Google Scholar
  29. Goldscheider N, Meiman J, Pronk M, Smart C (2008) Tracer tests in karst hydrogeology and speleology. Int J Speleol 37:3CrossRefGoogle Scholar
  30. Göppert N, Goldscheider N (2007) Solute and colloid transport in karst conduits under low- and high-flow conditions. Ground Water.  https://doi.org/10.1111/j.1745-6584.2007.00373.x
  31. Hauns M, Jeannin P-Y, Atteia O (2001) Dispersion, retardation and scale effect in tracer breakthrough curves in karst conduits. J Hydrol 241:177–193CrossRefGoogle Scholar
  32. Hollenbeck KJ (1998) INVLAP.M: a MATLAB function for numerical inversion of Laplace transforms by de Hoog algorithm. https://www.mathworks.com/matlabcentral/answers/uploaded_files/1034/invlap.m. Accessed July 16
  33. Iván V, Mádl-Szőnyi J (2017) State of the art of karst vulnerability assessment: overview, evaluation and outlook. Environ Earth Sci 76.  https://doi.org/10.1007/s12665-017-6422-2
  34. Jeannin P-Y (1998) Structure et comportement hydraulique des aquifères karstiques [Structure and hydraulic behaviour of karst aquifers]. PhD Thesis, Université de Neuchâtel, Neuchâtel, FranceGoogle Scholar
  35. Jeannin P-Y, Cornaton F, Zwahlen F, Perrochet P (2001) VULK: a tool for intrinsic vulnerability assessment and validation. Presented at the Proc. 7th conference on limestone hydrology and fissured media. Besançon, France, September 2001 pp 185–190Google Scholar
  36. Jury WA, Roth K (1990) Transfer functions and solute movement through soil: theory and applications. Birkhauser, Basel, SwitzerlandGoogle Scholar
  37. Käss WA (1994) Hydrological tracing practice on underground contaminations. Environ Geol 23:23–29CrossRefGoogle Scholar
  38. Kavouri K, Plagnes V, Dörfliger N, Faycal R, Pierre M (2011) PaPRIKa: a method for estimating karst resource and source vulnerability: application to the Ouysse karst system (Southwest France). Hydrogeol J 19:339–353.  https://doi.org/10.1007/s10040-010-0688-8 CrossRefGoogle Scholar
  39. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE International Conference on Neural Networks Proceedings of IEEE International Conference on Neural Networks, vol 4. pp 1942–1948.  https://doi.org/10.1109/ICNN.1995.488968
  40. Kirchner JW, Feng X, Neal C (2000) Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 403(6769):524–527.  https://doi.org/10.1038/35000537 CrossRefGoogle Scholar
  41. Kovács A, Perrochet P (2008) A quantitative approach to spring hydrograph decomposition. J Hydrol 352:16–29.  https://doi.org/10.1016/j.jhydrol.2007.12.009 CrossRefGoogle Scholar
  42. Labat D, Mangin A (2015) Transfer function approach for artificial tracer test interpretation in karstic systems. J Hydrol 529:866–871.  https://doi.org/10.1016/j.jhydrol.2015.09.011 CrossRefGoogle Scholar
  43. Lauber U, Ufrecht W, Goldscheider N (2014) Spatially resolved information on karst conduit flow from in-cave dye tracing. Hydrol Earth Syst Sci 18:435–445.  https://doi.org/10.5194/hess-18-435-2014 CrossRefGoogle Scholar
  44. Leclerc JP, Claudel S, Lintz HG, Potier O, Antoine B (2000) Theoretical interpretation of residence-time distribution measurements in industrial processes. Oil Gas Sci Technol 55(2):159–169CrossRefGoogle Scholar
  45. Leibundgut C (1998) Vulnerability of karst aquifers. IAHS Publ. 247, IAHS, Wallingford, UK, pp 45–60Google Scholar
  46. Levenspiel O (1999) Chemical reaction engineering, 3rd edn. Wiley, Hoboken, NJGoogle Scholar
  47. Levenspiel O (2012) Tracer technology, fluid mechanics and its applications. Springer, New York.  https://doi.org/10.1007/978-1-4419-8074-8 Google Scholar
  48. Luhmann AJ, Covington MD, Alexander SC, Chai SY, Schwartz BF, Groten JT, Alexander EC Jr (2012) Comparing conservative and nonconservative tracers in karst and using them to estimate flow path geometry. J Hydrol 448–449:201–211.  https://doi.org/10.1016/j.jhydrol.2012.04.044 CrossRefGoogle Scholar
  49. Małoszewski P, Zuber A (1982) Determining the turnover time of groundwater systems with the aid of environmental tracers: 1. Models and their applicability. J Hydrol 57(3):207–231.  https://doi.org/10.1016/0022-1694(82)90147-0 CrossRefGoogle Scholar
  50. Mangin A (1975) Contribution à l’étude hydrodynamique des aquifères karstiques [Contribution to the hydrodynamic study of karst aquifers]. Université de Bourgogne, FranceGoogle Scholar
  51. Mangin A (1984) Pour une meilleure connaissance des systèmes hydrologiques à partir des analyses corrélatoire et spectrale [The use of autocorrelation and spectral analyses to obtain a better understanding of hydrological systems]. J Hydrol 67:25–43.  https://doi.org/10.1016/0022-1694(84)90230-0 CrossRefGoogle Scholar
  52. Mangin A (1994) Karst Hydrogeology. In: Danielopol DL, Stanford JA (eds) Groundwater ecology. Academic, San Diego, CA, pp 43–67CrossRefGoogle Scholar
  53. Marín AI, Andreo B, Mudarra M (2015) Vulnerability mapping and protection zoning of karst springs: validation by multitracer tests. Sci Total Environ 532:435–446.  https://doi.org/10.1016/j.scitotenv.2015.05.029 CrossRefGoogle Scholar
  54. Marsaud B (1997) Structure et fonctionnement de la zone noyée des karsts à partir des résultats expérimentaux [Structure and behaviour of the saturated zone of karst aquifers from experiential results]. Université de Paris XI Orsay, ParisGoogle Scholar
  55. Massei N, Wang HQ, Field MS, Dupont JP, Bakalowicz M, Rodet J (2006) Interpreting tracer breakthrough tailing in a conduit-dominated karstic aquifer. Hydrogeol J 14:849–858.  https://doi.org/10.1007/s10040-005-0010-3 CrossRefGoogle Scholar
  56. Massoudieh A (2013) Inference of long-term groundwater flow transience using environmental tracers: A theoretical approach. Water Resour Res 49(12):8039–8052.  https://doi.org/10.1002/2013WR014548 CrossRefGoogle Scholar
  57. Matsubayashi U, Velasquez GT, Takagi F (1993) Hydrograph separation and flow analysis by specific electrical conductance of water. J Hydrol 152:179–199CrossRefGoogle Scholar
  58. Milanović P (2014) Hydraulic properties of karst groundwater and its impacts on large structures. In: Mudry J, Zwahlen F, Bertrand C, LaMoreaux JW (eds) H2Karst research in limestone hydrogeology. Springer, Cham, Switzerland, pp 19–48.  https://doi.org/10.1007/978-3-319-06139-9_2 CrossRefGoogle Scholar
  59. Morales T, Uriarte JA, Olazar M, Antigüedad I, Angulo B (2010) Solute transport modelling in karst conduits with slow zones during different hydrologic conditions. J Hydrol 390:182–189.  https://doi.org/10.1016/j.jhydrol.2010.06.041 CrossRefGoogle Scholar
  60. Moser H (1995) Groundwater tracing. In: Tracer technologies for hydrological systems. Presented at the Proceedings of a Boulder Symposium, IAHS, Wallingford, UKGoogle Scholar
  61. Nash JE (1957) The form of the instantaneous unit hydrograph. IAHS Publ. 3, IAHS, Wallingford, UK, pp 114–121Google Scholar
  62. Niemi AJ (1977) Residence time distributions of variable flow processes. Int J Appl Radiat Isot 28(10):855–860.  https://doi.org/10.1016/0020-708X(77)90026-6 CrossRefGoogle Scholar
  63. Ozyurt NN, Bayari CS (2005) Steady- and unsteady-state lumped parameter modelling of tritium and chlorofluorocarbons transport: hypothetical analyses and application to an alpine karst aquifer. Hydrol Process 19(17):3269–3284.  https://doi.org/10.1002/hyp.5969 CrossRefGoogle Scholar
  64. Padilla A, Pulido-Bosch A (1995) Study of hydrographs of karstic aquifers by means of correlation and cross-spectral analysis. J Hydrol 168:73–89CrossRefGoogle Scholar
  65. Perrin J, Pochon A, Jeannin P-Y, Zwahlen F (2004) Vulnerability assessment in karstic areas: validation by field experiments. Environ Geol 46.  https://doi.org/10.1007/s00254-004-0986-3
  66. Quinif Y (1999) Karst et évolution des rivières: le cas de l’Ardenne [Karst and river evolution: the Ardenne case]. Geodin Acta 12:267–277CrossRefGoogle Scholar
  67. Ravbar N, Goldscheider N (2009) Comparative application of four methods of groundwater vulnerability mapping in a Slovene karst catchment. Hydrogeol J 17(3):725–733.  https://doi.org/10.1007/s10040-008-0368-0 CrossRefGoogle Scholar
  68. Schnegg P-A (2002) An fextensive field fluorometer for hydrogeological tracer tests with three tracers and turbidity measurement. In: Bocanegra E, Martinez D, Massone H (eds) Groundwater and human development. Presented at the XXXII IAH and ALHSUD Congress. Mar del Plata, Argentina, 2002, Balkema, Rotterdam, The Netherlands, pp 1484–1488Google Scholar
  69. Sivelle V, Labat D, Duran L, Massei N, Fournier M (2018) Artificial tracer tests interpretation using transfer function approach to study the Norville Karst system. In: Bertrand C, Renard P, Denimal S, Steinmann M (eds) Advances in the hydrogeology of karst and carbonate reservoirs, chap 22. Eurokarst 2018, Besançon, FranceGoogle Scholar
  70. Toride N, Leu FJ, Van Genuchten MT (1993) A comprehensive set of analytical solutions for nonequilibrium solute transport with first-order decay and zero-order production. Water Resour Res 29:2167–2182CrossRefGoogle Scholar
  71. Toride N, Leij FJ, Van Genuchten MT et al (1995) The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. US Salinity Laboratory, Riverside, CAGoogle Scholar
  72. Van Genuchten MT, Simunek J, Leij FJ, Toride N, Sejna M (2012) STANMOD: model use, calibration, and validation. Trans ASABE 55:1353–1366Google Scholar
  73. Vincenzi V, Riva A, Rossetti S (2011) Towards a better knowledge of Cansiglio karst system (Italy): results of the first successful groundwater tracer test. Acta Carsol 40(1)Google Scholar
  74. Walas SM (2005) Chemical reaction engineering handbook of solved problems. Gordon and Breach, AustraliaGoogle Scholar
  75. Wang HQ, Crampon N, Huberson S, Garnier JM (1987) A linear graphical method for determining hydrodispersive characteristics in tracer experiments with instantaneous injection. J Hydrol 95:143–154.  https://doi.org/10.1016/0022-1694(87)90121-1 CrossRefGoogle Scholar
  76. Worthington SR (2003) A comprehensive strategy for understanding flow in carbonate aquifer. Speleogenesis Evol Karst Aquifers 1:1–8Google Scholar
  77. Worthington SRH, Ford DC (2009) Self-organized permeability in carbonate aquifers. Ground Water 47:326–336.  https://doi.org/10.1111/j.1745-6584.2009.00551.x CrossRefGoogle Scholar
  78. Zhao X, Chang Y, Wu J, Peng F (2017) Laboratory investigation and simulation of breakthrough curves in karst conduits with pools. Hydrogeol J 25:2235–2250.  https://doi.org/10.1007/s10040-017-1626-9 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Géosciences Environnement Toulouse (UMR 5563 CNRS UPS IRD)Université de ToulouseToulouseFrance

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