Hydrogeology Journal

, Volume 19, Issue 8, pp 1515–1530 | Cite as

Quantifying the effects of subsurface heterogeneity on hillslope runoff using a stochastic approach

Paper

Abstract

The role of heterogeneity and uncertainty in hydraulic conductivity on hillslope runoff production was evaluated using the fully integrated hydrologic model ParFlow. Simulations were generated using idealized high-resolution hillslopes configured both with a deep water table and a water table equal to the outlet to isolate surface and subsurface flow, respectively. Heterogeneous, correlated random fields were used to create spatial variability in the hydraulic conductivity. Ensembles, generated by multiple realizations of hydraulic conductivity, were used to evaluate how this uncertainty propagates to runoff. Ensemble averages were used to determine the effective runoff for a given hillslope as a function of rainfall rate and degree of subsurface heterogeneity. Cases where the water table is initialized at the outlet show runoff behavior with little sensitivity to variance in hydraulic conductivity. A technique is presented that explicitly interrogates individual realizations at every simulation timestep to partition overland and subsurface flow contributions. This hydrograph separation technique shows that the degree of heterogeneity can play a role in determining proportions of surface and subsurface flow, even when effective hillslope outflow is seen. This method is also used to evaluate current hydrograph separation techniques and demonstrates that recursive filters can accurately proportion overland and base-flow for certain cases.

Keywords

Rainfall/runoff Heterogeneity Groundwater/surface-water relations Dunne Hortonian 

Quantification par une approche stochastique des effets de l’hétérogénéité de sub-surface sur le ruissellement de versant

Résumé

Le rôle de l’hétérogénéité de la perméabilité et de son incertitude dans la génération du ruissellement de versant a été évalué en utilisant le modèle hydrologique totalement intégré ParFlow. Des simulations ont été générées en utilisant des pentes idéalisées de haute résolution configurées aussi bien avec un niveau piézométrique de nappe libre profond qu’avec un niveau piézométrique égal à celui de l’exutoire, afin de distinguer respectivement écoulement de surface et écoulement de sub-surface. Des champs aléatoires corrélés hétérogènes ont été utilisés pour créer la variabilité spatiale de la perméabilité. Des ensembles, générés par de multiples réalisations du champ de perméabilité, ont été utilisés pour évaluer comment cette incertitude se propage au ruissellement. Des moyennes de ces ensembles ont été utilisées pour définir le ruissellement efficace pour un versant donné en fonction de l’intensité des précipitations et du degré d’hétérogénéité de la sub-surface. Les cas où la surface libre de la nappe est initialisée au niveau de l’exutoire montrent un comportement du ruissellement peu sensible vis-à-vis de la variance de la perméabilité. Une technique est présentée, qui analyse de manière explicite les réalisations individuelles à chaque pas de temps de calcul de la simulation, en vue de distinguer les contributions de l’écoulement de surface et de l’écoulement de sub-surface. Cette technique de décomposition de l’hydrogramme montre que le degré d’hétérogénéité peut jouer un rôle dans la détermination des proportions entre l’écoulement de surface et de sub-surface, même quand des venues d’eau sont constatées sur le versant. Cette méthode est aussi utilisée pour évaluer des techniques courantes de décomposition de l’hydrogramme et démontre que les filtres récursifs peuvent, dans certains cas, établir avec précision la proportion entre écoulement de surface et écoulement de base.

Cuantificación de los efectos de la heterogeneidad subsuperficial sobre el escurrimiento usando una aproximación estocástica

Resumen

Se evaluó el rol de la heterogeneidad y la incertidumbre en la conductividad hidráulica sobre la producción del escurrimiento usando el modelo hidrológico completamente integrado ParFlow. Las simulaciones fueron generadas utilizando faldeos idealizados de alta resolución configurados tanto con el nivel freático profundo como con el nivel freático igual a la salida para aislar el flujo superficial y subsuperficial, respectivamente. Se utilizaron campos aleatorios correlacionados heterogéneos para crear la variabilidad espacial en la conductividad hidráulica. Se utilizaron conjuntos generados por realizaciones múltiples de la conductividad hidráulica para evaluar como esta incertidumbre se propaga al escurrimiento. Se usaron los promedios de conjuntos para determinar el escurrimiento efectivo para un faldeo dado como una función del ritmo de la precipitación y el grado de heterogeneidad subsuperficial. Los casos donde el nivel freático es inicializado a la salida muestran un comportamiento del escurrimiento con una baja sensibilidad a la varianza en la conductividad hidráulica. Se presenta una técnica que interroga explícitamente las realizaciones individuales en cada paso de tiempo de la simulación para particionar las contribuciones del flujo sobre la superficie y subsuperficial. Esta técnica de separación del hidrograma muestra que el grado de heterogeneidad puede jugar un rol en determinar las proporciones del flujo superficial y subsuperficial, aún cuando el flujo efectivo de salida del faldeo está a la vista. Este método también es usado para evaluar las técnicas corrientes de separación de hidrogramas y demuestra que los filtros recursivos pueden definir con exactitud la proporción de flujo de superficie y flujo de base para ciertos casos.

Quantificação dos efeitos da heterogeneidade subsuperficial na escorrência em vertentes, através de uma abordagem estocástica

Resumo

Foi avaliado o papel da heterogeneidade e da incerteza da condutividade hidráulica na escorrência produzida em vertentes, através da utilização do modelo hidrológico ParFlow. Foram geradas simulações utilizando vertentes ideais de alta resolução, incorporando um aquífero freático profundo, assim como uma superfície freática coincidente com a secção de medição no curso de água, de forma a permitir isolar, respectivamente, o escoamento superficial e subsuperficial. Campos aleatórios correlacionados heterogéneos foram utilizados para criar variabilidade espacial da condutividade hidráulica. Conjuntos gerados por múltiplas concepções da condutividade hidráulica foram utilizados para avaliar como esta incerteza se propaga na escorrência. Médias de conjunto foram usadas para determinar a escorrência eficaz para uma dada vertente, como uma função da taxa de precipitação e do grau de heterogeneidade do subsolo. Casos onde o aquífero freático é feito coincidir com a secção de medição no curso de água mostram um comportamento da escorrência pouco sensível à variação da condutividade hidráulica. É apresentada uma técnica que questiona explicitamente as realizações individuais em cada iteração da simulação, para separação das contribuições do escoamento superficial e subsuperficial. Esta técnica de separação do hidrograma mostra que o grau de heterogeneidade pode desempenhar um papel na determinação das proporções do escoamento superficial e do escoamento subsuperfícial, mesmo quando o escoamento eficaz da vertente é observado. Este método também é utilizado para avaliar técnicas de separação do hidrograma geral e demonstra que os filtros recursivos podem, para certos casos, relacionar com precisão o escoamento superficial e o escoamento de base.

References

  1. Apostolopoulos TK, Georgakakos KP (1997) Parallel computation for streamflow prediction with distributed hydrologic models. J Hydrol 197:1–24CrossRefGoogle Scholar
  2. Ashby SF, Falgout RD (1996) A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations. Nucl Sci Eng 124(1):145–59Google Scholar
  3. Beven KJ (2001) Rainfall-runoff modeling: the primer. Wiley, Chichester, UKGoogle Scholar
  4. Binley A, Elgy J, Beven K (1989a) A physically based model of heterogeneous hillslopes. 1. Runoff production. Water Resour Res 25(6):1219–26CrossRefGoogle Scholar
  5. Binley A, Beven K, Elgy J (1989b) A physically based model of heterogeneous hillslopes. 2. Effective hydraulic conductivities. Water Resour Res 25(6):1227–33CrossRefGoogle Scholar
  6. Bloomfield JP, Allen DJ, Griffiths KJ (2009) Examining geological controls on baseflow index (BFI) using regression analysis: an illustration from the Thames Basin, UK. J Hydrol 373:164–176CrossRefGoogle Scholar
  7. Camporese M, Paniconi C, Putti M, Orlandini S (2010) Surface–subsurface flow modeling with path-based routing boundary condition-based coupling and assimilation of multisource observation data. Water Resour Res 42(2):W02512Google Scholar
  8. Carle SF, Fogg GE (1996) Transition probability-based indicator geostatistics. Math Geol 28(4):453–76CrossRefGoogle Scholar
  9. Carle SF, Fogg GE (1997) Modeling spatial variability with one and multidimensional continuous-lag Markov Chains. Math Geol 29(7):891–918CrossRefGoogle Scholar
  10. Christensen OF, Diggle PJ, Ribeiro PJ (2000) Analysis positive-valued spatial data: the transformed Gaussian model. GeoENVGoogle Scholar
  11. Dagan G (1989) Flow and transport in porous formations. Springer, New YorkGoogle Scholar
  12. Dunne T, Black RD (1970a) An experimental investigation of runoff production in permeable soils. Water Resour Res 6:478–490CrossRefGoogle Scholar
  13. Dunne T, Black RD (1970b) Partial area contributions to storm runoff in a small New England watershed. Water Resour Res 6:1296–1311CrossRefGoogle Scholar
  14. Dunne T, Moore TR, Taylor CH (1975) Recognition and prediction of runoff-producing zones in humid regions. Bull Int Assoc Sci Hydrol 20:305–327Google Scholar
  15. Eagleson PS (1978) Climate, soil, and vegetation 1: introduction to water balance dynamics. Water Resour Res 14:705–712CrossRefGoogle Scholar
  16. Eckhardt K (2005) How to construct recursive digital filters for baseflow separation. Hydrol Proc 19:507–515CrossRefGoogle Scholar
  17. Eckhardt K (2008) A comparison of baseflow indices, which were calculated with seven different baseflow separation methods. J Hydrol 352:168–173CrossRefGoogle Scholar
  18. Fielder FR, Ramirez JA (2000) A numerical method for simulating discontinuous shallow flow over an infiltrating surface. Int J Numer Methods Fluids 32:219–239CrossRefGoogle Scholar
  19. Fiori A, Russo D (2007) Numerical analyses of subsurface flow in a steep hillslope under rainfall: The role of the spatial heterogeneity of the formation hydraulic properties. Water Resour Res 43(7):W07445Google Scholar
  20. Fiori A, Russo D (2008) Travel time distributions in a hillslope: insight from numerical simulations. Water Resour Res 44, W12426Google Scholar
  21. Fiori A, Romanelli M, Cavalli DJ, Russo D (2007) Numerical experiments of streamflow generation in steep catchments. J Hydrol 339:183–192CrossRefGoogle Scholar
  22. Freeze RA (1972a) Role of subsurface flow in generating runoff: 1. base flow contributions to channel flow. Water Resour Res 8:609–624CrossRefGoogle Scholar
  23. Freeze RA (1972b) Role of subsurface flow in generating runoff: 2. upstream source areas. Water Resour Res 8:1272–1283CrossRefGoogle Scholar
  24. Freeze RA (1980) A stochastic-conceptual analysis of rainfall-runoff processes on a hillslope. Water Resour Res 16(2):391–408CrossRefGoogle Scholar
  25. Freeze RA, Harlan RL (1969) Blueprint for a physically-based digitally simulated, hydrologic response model. J Hydrol 9:237–258CrossRefGoogle Scholar
  26. Frei S, Fleckenstein JH, Kollet SJ, Maxwell RM (2009) Patterns and dynamics of river-aquifer exchange with variably-saturated flow using a fully-coupled model. J Hydrol 375:383–393CrossRefGoogle Scholar
  27. Gonzales AL, Nonner J, Heijkers J, Uhlenbrook S (2009) Comparison of different base flow separation methods in a lowland catchment. Hydrol Earth System Sci Discuss 6:3483–3515CrossRefGoogle Scholar
  28. Graham W, McLaughlin D (1989) Stochastics analysis of nonstationary subsurface solute transport: 1. unconditional moments. Water Resour Res 25(2):215–232CrossRefGoogle Scholar
  29. Hall FR (1968) Base-flow recessions: a review. Water Resour Res 4(5):973–983CrossRefGoogle Scholar
  30. Harman C, Sivapalan M (2009) Effects of hydraulic conductivity variability on hillslope-scale shallow subsurface flow response and storage-discharge relations. Water Resour Res 45(1):W01421Google Scholar
  31. Herbst M, Diekkruger B, Vanderborght J (2006) Numerical experiments on the sensitivity of runoff generation to the spatial variation of soil hydraulic properties. J Hydrol 326:43–58CrossRefGoogle Scholar
  32. Hooper RP, Shoemaker CA (1986) A comparison of chemical and isotopic hydrograph separation. Water Resour Res 22(10):1444–1454CrossRefGoogle Scholar
  33. Horton RE (1931) The role of infiltration in the hydrologic cycle. Trans Am Geophys Union 12:189–202Google Scholar
  34. Horton RE (1933) The role of infiltration in the hydrologic cycle. Trans Am Geophys Union 14:446–460Google Scholar
  35. Jones JE, Woodward CS (2001) Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems. Adv Water Resour 24:763–74CrossRefGoogle Scholar
  36. Jones JP, Sudicky EA, Brookfield AE, Park YJ (2006) An assessment of the tracer-based approach to quantifying groundwater contributions to streamflow. Water Resour Res 42(2):W02407Google Scholar
  37. Kendall C, McDonnell JJ, Gu W (2001) A look inside ‘black box’ hydrograph separation models: a study at the hydrohill catchment. Hydrol Proc 15:1877–1902CrossRefGoogle Scholar
  38. Kitanidis PK (1986) Parameter uncertainty in estimation of spatial functions: Bayesian analysis. Water Resour Res 22(4):499–507CrossRefGoogle Scholar
  39. Kollet SJ, Maxwell RM (2006) Integrated surface-groundwater flow modeling: a free surface overland flow boundary condition in a parallel groundwater flow model. Adv Water Resour 29(7):945–958CrossRefGoogle Scholar
  40. Kollet SJ, Maxwell RM, Woodward CS, Smith S, Vanderborght J, Vereecken H, Simmer C (2010) Proof of concept of regional scale hydrologic simulations at hydrologic resolution utilizing massively parallel computer resources. Water Resour Res 46, W04201Google Scholar
  41. LeBlanc DR, Garabedian SP, Hess KM, Gelhar LW, Quadri RD, Stollenwerk KG, Wood WW (1991) Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 1. experimental design and observed tracer movement. Water Resour Res 27(5):895–910CrossRefGoogle Scholar
  42. Linsley RK, Kohler MA, Paulhus JLH (1975) Hydrology for engineers, McGraw-Hill, New YorkGoogle Scholar
  43. Loague K (1988) Impact of rainfall and soil hydraulic property information on runoff predictions at the hillslope scale. Water Resour Res 24(9):1501–1510CrossRefGoogle Scholar
  44. Loague K, Heppner CS, Ebel BA, VanderKwaak JE (2010) The quizotic search for a comprehensive understanding of hydrologic response at the surface: Horton, Dunne, Dunton, and the role of concept-development simulation. Hydrol Proc 24:2499–2505Google Scholar
  45. Maxwell RM, Kollet SJ (2008) Quantifying the effects of three-dimensional subsurface heterogeneity on Hortonian runoff processes using a coupled numerical stochastic approach. Adv Water Resour 31:807–817CrossRefGoogle Scholar
  46. Maxwell RM, Welty C, Harvey RW (2007) Revisiting the Cape Cod Bacteria Injection Experiment using a stochastic modeling approach. Env Sci Tech 41(15):5548–5558CrossRefGoogle Scholar
  47. Nahar N, Govindaraju RS, Corradini C, Morbidelli R (2004) Role of run-on for describing field-scale infiltration and overland flow over spatially variable soils. J Hydrol 286:36–51CrossRefGoogle Scholar
  48. Nathan RJ, McMahon TA (1990) Evaluation of automated techniques for base flow and recession analyses. Water Resour Res 26(7):1465–1473CrossRefGoogle Scholar
  49. Panday S, Huyakorn PS (2004) A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow. Adv Water Resour 27:361–382CrossRefGoogle Scholar
  50. Qu, Y, Duffy CJ (2007) A semidiscrete finite volume formulation for multiprocess watershed simulation. Water Resour Res 43(8):W08419Google Scholar
  51. Rihani, JF, Maxwell RM, Chow FK (2010) Coupling groundwater and land surface processes: idealized simulations to identify effects of terrain and subsurface heterogeneity on land surface energy fluxes. Water Resour Res 46, W12523, 14 ppGoogle Scholar
  52. Rubin Y (2003) Applied stochastic hydrogeology, Oxford University Press, OxfordGoogle Scholar
  53. Rubin Y, Dagan G (1992) Conditional estimation of solute travel time in heterogeneous formations: impact of transmissivity measurements. Water Resour Res 28(4):1033–1040CrossRefGoogle Scholar
  54. Salandin P, Fiorotto V (1998) Solute transport in highly heterogeneous aquifers. Water Resour Res 34(5):949−961Google Scholar
  55. Sklash MG, Farvolden RN (1979) The role of groundwater in storm runoff. J Hydrol 48:45–65CrossRefGoogle Scholar
  56. Sloto RA, Crouse MY (1996) HYSEP: A computer program for streamflow hydrograph separation and analysis. US Geol Surv Invest Rep 96–4040Google Scholar
  57. Smith L, Schwartz FW (1980) Mass transport: 1. a stochastic analysis of macroscopic dispersion. Water Resour Res 16(2):303–313CrossRefGoogle Scholar
  58. Smith L, Schwartz FW (1981) Mass transport: 2. a stochastic analysis of uncertainty in prediction. Water Resour Res 17(2):351–369CrossRefGoogle Scholar
  59. Smith RE, Woolhiser DA (1971) Overland flow on an infiltrating surface. Water Resour Res 7:899–913CrossRefGoogle Scholar
  60. Tompson AFB, Gelhar LW (1990) Numerical simulation of solute trans-port in three-dimensional randomly heterogeneous porous media. Water Resour Res 26(10):2541–2562CrossRefGoogle Scholar
  61. Tompson AFB, Ababou R, Gelhar LW (1989) Implementation of the three-dimensional turning bands random field generator. Water Resour Res 25(10):2227–2243CrossRefGoogle Scholar
  62. Tompson AFB, Falgout RD, Smith SG, Bosl WJ, Ashby SF (1998) Analysis of subsurface contaminant migration and remediation using high performance computing. Adv Water Resour 22(3):203–221CrossRefGoogle Scholar
  63. Ulhenbrook S, Frey M, Leibundgut C, Maloszewski P (2002) Hydrograph separations in a mesoscale mountainous basin at event and seasonal timescales. Water Resour Res 38:1096, 14 ppGoogle Scholar
  64. van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRefGoogle Scholar
  65. VanderKwaak JE, Loague K (2001) Hydrologic-response simulations for the R-5 catchment with a comprehensive physics-based model. Water Resour Res 37:999–1013CrossRefGoogle Scholar
  66. Weill S, Mouche E, Patin J (2008) A generalized Richards’s equation for surface/subsurface flow modeling. J Hydrol 366:9–20CrossRefGoogle Scholar
  67. Wittenberg H, Sivapalan M (1999) Watershed groundwater balance estimation using streamflow recession analysis and baseflow separation. J Hydrol 21:20–33Google Scholar
  68. Wood EF (1976) An analysis of the effects of parameter uncertainty in deterministic hydrologic models. Water Resour Res 12:925–932CrossRefGoogle Scholar
  69. Wood EF, Sivapalan M, Beven K, Band L (1988) Effects of spatial variability and scale with implications to hydrologic modeling. J Hydrol 102:29–47CrossRefGoogle Scholar
  70. Woolhiser DA, Smith RE, Giraldez JV (1996) Effects of spatial variability of saturated hydraulic conductivity on Hortonian overland flow. Water Resour Res 32(3):671–678CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Geology and Geologic Engineering, Hydrologic Science and Engineering Program, Integrated Ground Water Modeling Center, Colorado School of MinesGoldenUSA

Personalised recommendations