An innovative method to estimate regional-scale hydraulic diffusivity using GRACE data

ABSTRACT

Estimation of hydraulic properties in the field is usually small-scale and not cost-effective. This paper proposes an innovative method for estimating hydraulic diffusivity at regional scale. Monthly groundwater storage change over the period from 2003 to 2013 is first estimated from GRACE-derived terrestrial water storage (TWS). Assuming that the aquifer system is unconfined and the hydraulic properties are uniform in a geographical cell, the water balance principle and Darcy’s law are used to establish a relation between groundwater storage and hydraulic diffusivity. The value of hydraulic diffusivity is then adjusted using the generalized least squares and linear correlation method. This GRACE-derived hydraulic diffusivity estimation method, or GHDE method for short, is first verified with a hypothetical case and then applied in the Beishan area with available field-measured hydraulic conductivity data. The hypothetical case study demonstrates that the method works perfectly if the TWS data are error free. The Beishan case study illustrates that the estimated hydraulic diffusivities using the GHDE method correlate reasonably well with field test results, suggesting that this method is applicable. The accuracy of this method is constrained by the resolution of the GRACE-derived TWS data and is most suitable for very large scale groundwater problems due to the current accuracy of the GRACE data.

EDITOR A. Castellarin ASSOCIATE EDITOR N. Verhoest     

Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system

Abstract

A numerical technique is presented whereby aquifer hydraulic diffusivities (D) and macrodispersivities (α) are calculated by linear equations rewritten from flow and solute transport differential equations. The approach requires a GIS to calculate spatial and temporal hydraulic head (h) and solute concentration gradients. The model is tested in Portugal, in a semi-confined aquifer periodically monitored for h and chloride/sulphate concentrations. Average D (0.46 m²/s) and α (1975 m) compare favourably with literature results. The relationship between α and scale (L) is also investigated. In this context, two aquifer groups could be identified: the first group is heterogeneous at the “macroscopic” scale (solute travelled distances <1 km), but homogeneous at the “megascopic” scale. The overall scale dependency in this case is given by an equation of logarithmic type. The second group is heterogeneous at the macroscopic and megascopic scales, with a scale dependency of linear type.

Citation Pacheco, F.A.L., 2013. Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system. Hydrological Sciences Journal, 58 (4), 930–944.     

REPORT ON THE ACTIVITIES OF THE INTERNATIONAL COMMISSION ON SNOW AND ICE FOR THE PERIOD 1971–1975

ABSTRACT

An infiltration model based on the Green-Ampt assumptions is developed for a class of non-uniform soils in which saturated hydraulic conductivity decreases as an exponential function of depth, and the storage-suction factor C = ΔθΔΨ is a constant. An analysis of measured hydraulic conductivity and porosity data suggests that the model may be useful in some soils where the changes of hydraulic characteristics with depth are of this form. A method for using the model with time variable rainfall rates is given. The model is applied to simulate the experimental results of Childs &; Bybordi (1969) who measured infiltration into layered sand profiles. Agreement was satisfactory even for this case.     

Research on the diffusion of pore fluid and in-situ hydraulic diffusivity in the epicentral region of Xinfengjiang reservoir earthquakes

According to the fact that the Xinfengjiang reservoir earthquakes are caused mainly by water seepage, this paper using the data ofM _s⩾2. 0 earthquakes, studies the hydraulic diffusivity of the mainshock zone by the expansion of the distribution area of epicenters. It is indicated thatin-situ hydraulic diffusivity during the preshock activity of the Xinfengjiang reservoir region was about 6. 2 m²/s. However, after the main shock, thein-situ hydraulic diffusivity in the main shock region increased by fifty percent, that is to say, to 9. 7 m²/s. During the long period after main shock occurrence thein-situ hydraulic diffusivity was affected by significant anisotropy of the medium and fluctuation of water level. No regularity can be found. In addition, we compare the diffusivity found by experiment with rock samples collected with thein-situ hydraulic diffusivity estimated. It is shown that the diffusivity of rock samples with fractures is about the same as the diffusivity estimatedin-situ. However, the diffusivity of whole rock samples is 3 orders of magnitudes smaller than that estimatedin-situ. Finally, we discuss the limits on the method by the expansion of distribution area of epicenters in the study of reservoir induced seismicity. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 364–371, 1991. This subject is sponsored by the Chinese Joint Seismological Science Foundation.     

Applicability of spectral analysis to determine hydraulic diffusivity

This study is to evaluate the applicability of estimating the one-dimensional horizontal hydraulic diffusivity of an unconfined aquifer with time-dependent fluctuation of lateral head and vertical recharge boundaries using observed water level spectra. Different models of boundary condition are imposed to evaluate the statistical significance between the calculated hydraulic diffusivity (ξ^′) with the given hydraulic diffusivity (ξ). The auto-spectra of the water level in observation wells tapping the same aquifer are closely related to those at the disturbed boundaries. For an aquifer with a constant hydraulic diffusivity, the water level fluctuation in the monitoring wells is linearly related to the water level spectra observed at the boundaries. The spectral density function of aquifer hydraulic head varies inversely with specific yield (S _y) and directly with recharge. Given small variation in water level spectra at the disturbed boundaries, the water level fluctuation in the aquifer is affected by the recharge condition and the aquifer spectral density function is sensitive to S _y. Using an iterative technique to estimate ξ from 1400 sets of given parameters, 99% of the ξ^′/ξ values deviated within only one order of magnitude with the model length (L) being equal to 1 km and 10 km. For L equal to 100 m, approximately 82% of the ξ^′/ξ population falls within two orders of magnitude. Therefore, spectral analysis of aquifer hydraulic head response can be used to estimate the hydraulic diffusivity of an unconfined aquifer which is affected by periodic variations in recharge and head at boundaries.     

Infiltration model in sloping layered soils and guidelines for model parameter estimation

A Green-Ampt type model for sloping layered soils (GASLS) was developed to investigate infiltration processes. We introduced a factor c, which is the same for all layers and represents the ratio of effective hydraulic conductivity over saturated hydraulic conductivity. Guidelines to estimate the factor c were established based on 234 scenarios under various conditions. The model with the estimated factor c can describe infiltration processes better than that with c = 1. For fine soils, or layered formations with finer soils on the top, c is smaller than 1. The factor c for coarse soils, or layer formations with coarse soils on the top is close to 1. Comparison with laboratory experiments on a sloping surface indicated that the GASLS model with a slope factor that is adjusted by the sine of the slope angle can represent the sloping surface effects. The GASLS model can incorporate any slope factor.     

Quantification of the hydraulic diffusivity of a bentonite-sand mixture using the water head decrease measured upon sudden flow interruption

This paper presents a new modelling approach to quantify the hydraulic diffusivity of low-permeability unconsolidated porous media under confined saturated-flow conditions in the laboratory. The derived analytical solution for the transient variation of the hydraulic head after flow interruption was applied to experimental data obtained from continuous measurements of the water pressure at two locations in the soil column. Three soil samples made of a mixture of natural bentonite (at different mass fractions) and medium sand were studied during a series of stepwise constant flow rates of water. The numerical results well fit the experimentally measured decrease of the dimensionless hydraulic head. The study shows that the increase of the mass fraction of bentonite in the soil sample from 10 to 30% is accompanied by a strong decrease of the hydraulic diffusivity from 2.4 × 10⁻² to 1.1 × 10⁻³ m² s⁻¹, which is clearly due to the decrease of the hydraulic conductivity of the soil sample. The specific storages obtained for each of the three samples are in the same order of magnitude and seem to decrease with the increase of mass fraction of bentonite. However, they clearly reflect the predominant portion of the compressibility of the porous medium compared with that of water. Compared with reported literature values for clayey soils, the specific storage values in this study are slightly higher, varying within the range of 2 × 10⁻³ to 8.1 × 10⁻³ m⁻¹._. The experimental results also give insight into the limitations of the modelling approach. In the case of low-permeability soils (K < 2 × 10⁻⁶ ms⁻¹) and steady-flow conditions with low Reynolds numbers, for example, Re < 0.003, it is recommended to choose a time duration for flow interruption between subsequent flow rate steps of longer than 5 s. For high-permeability porous media, to increase the precision of the quantified hydraulic diffusivity, it might be useful to select a measuring frequency significantly higher than 1 Hz.     

Vertical heterogeneities of hydraulic aquitard parameters: preliminary results from laboratory and in situ monitoring

Abstract

A borehole is developed in a shallow multi-layered aquifer and used to derive the porosity, specific storage and hydraulic conductivity of the aquitard. Local values of hydrodynamical parameters are estimated from petrophysical analysis of core samples, and the empirical relationship between porosity and permeability. Vertical diffusivity is determined from the response of the aquitard to a loading cyclic signal using pressure records at different depths. Hydraulic conductivities deduced from the petrophysical analysis ranged from 10^?8 to 10^?10 m s^?1 and are comparable with those of facies of marine/lacustrine clay observed in samples. The permeability values calculated based on diffusivity are within the range 10^?9 to 10^?11 m s^?1 with a quasi-systematic bias of one order of magnitude. These values are average for a larger part of the aquitard and correspond to an integrated value. The methodology retained for the aquitard characterization is discussed with emphasis on the implications for the management of a complex aquifer system.

Citation Larroque, F., Cabaret, O., Atteia, O., Dupuy, A., and Franceschi, M., 2013. Vertical heterogeneities of hydraulic aquitard parameters: preliminary results from laboratory and in situ monitoring. Hydrological Sciences Journal, 58 (4), 912–929.     

Flood forecasting and infiltration modeling/Prévision de crue et modélisation de l’infiltration

Abstract

Abstract The role of accuracy in the representation of infiltration on the effectiveness of real-time flood forecasting models was investigated. A simple semi-distributed model of conceptual type with adaptive estimate of hydraulic characteristics included in the infiltration component was selected. Infiltration was described by a very accurate approach recently formulated for complex rainfall patterns, or alternatively through a simpler formulation known as an extension of the classical time compression approximation. The results indicated that, for situations involving a significant rainfall variability in space, the inaccuracy in the representation of infiltration cannot be corrected by the adaptive component of the rainfall–runoff model. A preliminary analysis of the role of an approximation of saturated hydraulic conductivity to be used in each homogeneous area of the semi-distributed model used both in non-adaptive version and in real-time is also presented.     

The onset of magnetoconvection at large Prandtl number in a rotating layer II. Small magnetic diffusion

Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection.     

Research on the diffusion of pore fluid andin-situ hydraulic diffusivity in the epicentral region of Xinfengjiang reservoir earthquakes

According to the fact that the Xinfengjiang reservoir earthquakes are caused mainly by water seepage, this paper using the data ofM _s?2. 0 earthquakes, studies the hydraulic diffusivity of the mainshock zone by the expansion of the distribution area of epicenters. It is indicated thatin-situ hydraulic diffusivity during the preshock activity of the Xinfengjiang reservoir region was about 6. 2 m²/s. However, after the main shock, thein-situ hydraulic diffusivity in the main shock region increased by fifty percent, that is to say, to 9. 7 m²/s. During the long period after main shock occurrence thein-situ hydraulic diffusivity was affected by significant anisotropy of the medium and fluctuation of water level. No regularity can be found. In addition, we compare the diffusivity found by experiment with rock samples collected with thein-situ hydraulic diffusivity estimated. It is shown that the diffusivity of rock samples with fractures is about the same as the diffusivity estimatedin-situ. However, the diffusivity of whole rock samples is 3 orders of magnitudes smaller than that estimatedin-situ. Finally, we discuss the limits on the method by the expansion of distribution area of epicenters in the study of reservoir induced seismicity.     

Performance of soil particle-size distribution models for describing deposited soils adjacent to constructed dams in the China Loess Plateau

Soil particle-size distributions (PSD) have been used to estimate soil hydraulic properties. Various parametric PSD models have been proposed to describe the soil PSD from sparse experimental data. It is important to determine which PSD model best represents specific soils. Fourteen PSD models were examined in order to determine the best model for representing the deposited soils adjacent to dams in the China Loess Plateau; these were: Skaggs (S-1, S-2, and S-3), fractal (FR), Jaky (J), Lima and Silva (LS), Morgan (M), Gompertz (G), logarithm (L), exponential (E), log-exponential (LE), Weibull (W), van Genuchten type (VG) as well as Fredlund (F) models. Four-hundred and eighty samples were obtained from soils deposited in the Liudaogou catchment. The coefficient of determination (R ²), the Akaike’s information criterion (AIC), and the modified AIC (mAIC) were used. Based upon R ² and AIC, the three- and four-parameter models were both good at describing the PSDs of deposited soils, and the LE, FR, and E models were the poorest. However, the mAIC in conjunction with R ² and AIC results indicated that the W model was optimum for describing PSD of the deposited soils for emphasizing the effect of parameter number. This analysis was also helpful for finding out which model is the best one. Our results are applicable to the China Loess Plateau.     

A probabilistic framework for floodplain mapping using hydrological modeling and unsteady hydraulic modeling

ABSTRACT

Prediction of design hydrographs is key in floodplain mapping using hydraulic models, which are either steady state or unsteady. The former, which require only an input peak, substantially overestimate the volume of water entering the floodplain compared to the more realistic dynamic case simulated by the unsteady models that require the full hydrograph. Past efforts to account for the uncertainty of boundary conditions using unsteady hydraulic modeling have been based largely on a joint flood frequency–shape analysis, with only a very limited number of studies using hydrological modeling to produce the design hydrographs. This study therefore presents a generic probabilistic framework that couples a hydrological model with an unsteady hydraulic model to estimate the uncertainty of flood characteristics. The framework is demonstrated on the Swannanoa River watershed in North Carolina, USA. Given its flexibility, the framework can be applied to study other sources of uncertainty in other hydrological models and watersheds.     

Magnetic field structure in differentially rotating discs

Abstract

In order to gain a better understanding of the processes that may give rise to non-axisymmetric magnetic fields in galaxies, we have calculated field decay rates for models with a realistic galactic rotation curve and including the effects of a locally enhanced turbulent magnetic diffusivity within the disc. In all cases we have studied, the differential rotation increases the decay rate of non-axisymmetric modes, whereas axisymmetric ones are unaffected. A stronger magnetic diffusivity inside the disc does not lead to a significant preference for non-axisymmetric modes. Although Elsasser's antidynamo theorem has not yet been proved for the present case of a non-spherical distribution of the magnetic diffusivity, we do not find any evidence for the theorem not to be valid in general.     

Application of spectral analysis to determine hydraulic diffusivity of a sandy aquifer (Pingtung County,Taiwan)

The study demonstrates spectral relationships in the time–frequency domain for one‐dimensional groundwater flow in aquifers bounded by fluctuating boundaries. By nature, the solutions of spectral equations are non‐linear complex functions. To determine hydraulic diffusivity in the governing equations, it is required that the data are collected from the spectra of water levels at the fluctuating boundaries and observation wells. Hydraulic diffusivity thus can be obtained by an iterative inverse approach. This paper presents an application in Pingtung County of Taiwan to determine the hydraulic diffusivity of a sandy aquifer under confined conditions. Spectral density function of water level obtained from tidal boundaries and observation wells are used to approximate hydraulic diffusivity, which yields an averaged value of 1·26 × 10⁶ m²/h. Copyright © 2004 John Wiley & Sons, Ltd.     

Impact of fractal characteristics on evaporation and infiltration in unsaturated heterogeneous soils

ABSTRACT

In this study, an approach is developed to investigate the impact of fractal characteristics of unsaturated soil between the water table and land surface on the steady-state evaporation and infiltration across a heterogeneous landscape. The soil domain is conceptualized as a collection of stream tubes of soils and the particle diameters in various stream tubes follow a fractal distribution. The saturated hydraulic conductivity of each stream tube is related to the representative particle diameter in the tube. The effective specific discharge is then integrated from the specific discharge for each stream tube and the fractal distribution. The effective evaporation and infiltration in unsaturated soils increase with the fractal dimension. The ratio of minimum over maximum diameters does not significantly affect the specific discharge in the fractal soil. The specific discharge in unsaturated fractal soils calculated by using the simple average particle diameter mostly over-predicts the actual effective specific discharge.     

Soil hydraulic properties for moisture redistribution in a large-scale heterogeneous landscape

Abstract

Guidelines of effective soil hydraulic parameters were developed to be applicable in simulating average infiltration and subsequent moisture redistribution over a large-scale heterogeneous field. Average large-scale infiltration and redistribution in heterogeneous soils were quantified through multiple simulations of local-scale processes. The effective hydraulic parameters were derived to simulate the average amount of infiltrating water, and to capture the subsequent surface soil moisture redistribution averaged over the large heterogeneous landscape. The results demonstrated that the effective hydraulic parameters typically exhibited a step change from infiltration to redistribution, with the size of the step change being related to the degree of hydraulic parameter heterogeneity and the correlations among the hydraulic parameters. However, the effective hydraulic parameters did not change significantly over time for the moisture redistribution. It was further demonstrated that the size of the step change was smallest for effective saturated hydraulic conductivity.

Editor Z.W. Kundzewicz; Associate editor Y. Guttman

Citation Zhu, J.T. and Sun, D.M., 2012. Soil hydraulic properties for moisture redistribution in a large-scale heterogeneous landscape. Hydrological Sciences Journal, 57 (6), 1196–1206.     

Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited

Abstract

A tension-saturated water slug descends through a homogenous soil after a rainfall (irrigation) event and shrinks due to transpiration by a distributed root-sink and evaporation. The upper (drainage) and lower (imbibition) sharp fronts of the slug separate it from the superjacent and subjacent vadose zones, where water is immobile. In the slug, the hydraulic conductivity is constant according to the Green-Ampt model. The capillary pressures as well as effective porosities on the fronts are given (generally, different) constants that can be viewed as a kind of hysteresis. A volumetric sink models mild (no desaturation of the slug) soil water withdrawal by the plant roots. The sink intensity varies with the depth from the soil surface and with time. Mathematically, the hydraulic head is immediately expressed by double integration of a governing 1-D flow equation. The pressure and kinematic conditions on the fronts result in a Cauchy problem for a system of two ODEs, which is solved by computer algebra routines.

Editor D. Koutsoyiannis

Citation Kacimov, A. and Obnosov, U., 2013. Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited. Hydrological Sciences Journal, 58 (1), 1–12.     

Bulk density effects on soil hydrologic and thermal characteristics: A numerical investigation

Soil bulk density (ρ_b) is commonly treated as static in studies of land surface dynamics. Magnitudes of errors associated with this assumption are largely unknown. Our objectives were to (a) quantify ρ_b effects on soil hydrologic and thermal properties and (b) evaluate effects of ρ_b on surface energy balance and heat and water transfer. We evaluated 6 soil properties, volumetric heat capacity, thermal conductivity, soil thermal diffusivity, water retention characteristics, hydraulic conductivity, and vapour diffusivity, over a range of ρ_b, using a combination of 6 models. Thermal conductivity, water retention, hydraulic conductivity, and vapour diffusivity were most sensitive to ρ_b, each changing by fractions greater than the associated fractional changes in ρ_b. A 10% change in ρ_b led to 10–11% change in thermal conductivity, 6–11% change in saturated and residual water content, 49–54% change in saturated hydraulic conductivity, and 80% change in vapour diffusivity. Subsequently, 3 field seasons were simulated with a numerical model (HYDRUS‐1D) for a range of ρ_b values. When ρ_b increased 25% (from 1.2 to 1.5 Mg m^?3), soil temperature variation decreased by 2.1 °C in shallow layers and increased by 1 °C in subsurface layers. Surface water content differed by 0.02 m³ m^?3 for various ρ_b values during drying events but differences mostly disappeared in the subsurface. Matric potential varied by >100 m of water. Surface energy balance showed clear trends with ρ_b. Latent heat flux decreased 6%, sensible heat flux increased 9%, and magnitude of ground heat flux varied by 18% (with a 25% ρ_b increase). Transient ρ_b impacted surface conditions and fluxes, and clearly, it warrants consideration in field and modelling investigations.     

Hydrodynamic characterization of a Sahelian coastal aquifer using the ocean tide effect (Dridrate Aquifer,Morocco)

Abstract

In wells tapping coastal aquifers, piezometric fluctuations can be observed in response to the ocean tide. Simultaneous recordings of the ocean tide and of the piezometric variations may provide a basis for characterizing the hydrodynamics of the aquifer. This approach was attempted to characterize the Dridrate aquifer, located on the Atlantic coast of Morocco. This aquifer accounts for most of the regional drinking water resources. However, its hydrodynamic characteristics are very poorly known. The study compares observed and simulated piezometric fluctuations, under various assumptions (confined, semi-confined aquifer). The model, which best explains the hydrodynamic behaviour of this aquifer is a semi-confined and strongly heterogeneous aquifer model (calculated hydraulic diffusivity values vary over several orders of magnitude). This result is new and rather surprising, since to date this aquifer was considered confined in view of its geological setting. Consequently, new questions are raised regarding the protection and management of the groundwater resources of this aquifer.