Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties

Abstract. We consider the effect of measuring randomly varying soil hydraulic properties on one's ability to predict steady state unsaturated flow subject to random sources and/or initial and boundary conditions. Our aim is to allow optimum unbiased prediction of system states (pressure head, water content) and fluxes deterministically, without upscaling and without linearizing the constitutive characteristics of the soil. It has been shown by Neuman et al. [1999] that such prediction is possible by means of first ensemble moments of system states and fluxes, conditioned on measured values of soil properties, when the latter scale in a linearly separable fashion as proposed by Vogel et al. [1991]; the uncertainty associated with such predictions can be quantified by means of the corresponding conditional second moments. The derivation of moment equations for soils whose properties do not scale in the above manner requires linearizing the corresponding constitutive relations, which may lead to major inaccuracies when these relations are highly nonlinear, as is often the case in nature. When the scaling parameter of pressure head is a random variable independent of location, the steady state unsaturated flow equation can be linearized by means of the Kirchhoff transformation for gravity-free flow. Linearization is also possible in the presence of gravity when hydraulic conductivity varies exponentially with pressure head. For the latter case we develop exact conditional firstand second-moment equations which are nonlocal and therefore non-Darcian. We solve these equations analytically by perturbation for unconditional vertical infiltration and compare our solution with the results of numerical Monte Carlo simulations. Our analytical solution demonstrates in a rigorous manner that the concept of effective hydraulic conductivity does not apply to ensemble-averaged unsaturated flow except when gravity is the sole driving force.

Section: Introductionmentioning

confidence: 99%

Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff Transformation

Tartakovsky¹,

Neuman²,

Lü³

1999

“…The corresponding consistent moisture water content relationship developed by Russo [1988] was used:…”

Section: Equation For Variably Saturated Groundwater Flowmentioning

confidence: 99%

Joint interpretation of sequential pumping tests in unconfined aquifers

Mao

Yeh

Wan

et al. 2013

[1] In this study, we developed a stochastic estimator for characterizing the hydraulic heterogeneity in both unsaturated and saturated zones of unconfined aquifers using transient drawdown data from sequential pumping tests. This estimator was built upon the successive linear estimator by Yeh et al. (1996), the simultaneous successive linear estimator by Xiang et al. (2009), and the 3-D finite element program for flow and transport through heterogeneous media by Srivastava and Yeh (1992). The estimator was tested afterward using simulated data sets of sequential pumping tests in a synthetic unconfined aquifer where saturated conductivity, specific storage, saturated water content, and pore-size distribution parameter vary spatially in three dimensions. Test results show that the estimator is able to produce parameter fields that capture the overall 3-D pattern of the true heterogeneous parameter fields. We subsequently validated the estimated parameter fields by assessing their ability to predict drawdowns during an independent pumping test, which was not used during the estimation phase. Results of the validation show that the predicted drawdowns based on the estimated heterogeneous parameter fields are in close agreement with the true drawdowns. In addition, predicted drawdowns based on the parameter fields from the joint interpretation are superior to those based on the parameters estimated from the homogeneous conceptual model. Lastly, while many field experiments are necessary to fully assess the robustness of this estimator and sequential pumping tests, results of this study suggest they are a promising characterization technique for unconfined aquifers.

“…For the sake of completeness, we will review briefly the main results of this study. The following assumptions were employed by Russo [1998]: (1) the flow domain is variably saturated and unbounded; (2) the local steady state unsaturated flow obeys Darcy's law and continuity; (3) the flow is gravity-dominated, i.e., the mean pressure head gradient is zero so that the mean head-gradient, J i , is given by J i = d 1i (i = 1, 2, 3), where d 1i is the kronecker delta; (4) the local relationships between the hydraulic conductivity, K and the pressure head, {y} (considered as a positive quantity) and water saturation, Â and {y}, are nonhysteretic and are given by the Gardner-Russo model [Gardner, 1958;Russo, 1988]:…”

Section: Velocity Covariancesmentioning

confidence: 99%

Block‐effective macrodispersion in variably saturated heterogeneous formations

Russo

2003

Self Cite

[1] Numerical models are frequently used in order to quantify the effect of the spatial heterogeneity in the formation hydraulic properties on field-scale solute transport. Because of practical constraints it is common to discretize the flow domain into relatively large numerical cells, with characteristic length scales, ' 1 , ' 2 , ' 3 , comparable with those of the formation heterogeneity, I 1 , I 2 , I 3 , leading to a loss in the velocity variability, and, concurrently, in solute spreading. We analyzed block-effective dispersion coefficients, D 0 ij (i, j = 1, 2, 3), required to compensate for this loss in three-dimensional, variably saturated heterogeneous formations under conditions of steady state, gravity-dominated, unsaturated flow. The results that the principal components of D 0 ij are controlled by the ratio ' 0 = ' 2 /I 2 = ' 3 /I 3 , that they may reach their ergodic limits if ' 0 is sufficiently large, and that their tendency to their asymptotic limits with increasing scaled travel time, t 0 , is inversely related to ' 0 , are in agreement with previous results for saturated flow. New findings suggest that under unsaturated flow conditions, both the time required to reach the asymptotic limits of D 0 ij and the length scale needed to reach the ergodic limits of D 0 ij depend on soil stratification, soil texture, and mean soil water saturation and differ for the longitudinal and the transverse components of D 0 ij .