A dripper-TDR method for in situ determination of hydraulic conductivity and chemical transport properties of surface soils

Field determined hydraulic and chemical transport properties can be useful for the protection of groundwater resources from land-applied chemicals. Most field methods to determine flow and transport parameters are either time or energy consuming and/or they provide a single measurement for a given time period. In this study, we present a dripper-TDR field method that allows measurement of hydraulic conductivity and chemical transport parameters at multiple field locations within a short time period. Specifically, the dripper-TDR determines saturated hydraulic conductivity (K_s), macroscopic capillary length (λ_c), immobile water fraction (θ_im/θ), mass exchange coefficient (α) and dispersion coefficient (D_m). Multiple dripper lines were positioned over five crop rows in a field. Background and step solutions were applied through drippers to determine surface hydraulic conductivity parameters at 44 locations and surface transport properties at 38 locations. The hydraulic conductivity parameters (K_s, λ_c) were determined by application of three discharge rates from the drippers and measurements of the resultant steady-state flux densities at the soil surface beneath each dripper. Time domain reflectometry (TDR) was used to measure the bulk electrical conductivity of the soil during steady infiltration of a salt solution. Breakthrough curves (BTCs) for all sites were determined from the TDR measurements. The K_s and λ_c values were found to be lognormally distributed with average values of 31.4 cm h⁻¹ and 6.0 cm, respectively. BTC analysis produced chemical properties, θ_im/θ, α, and D_m with average values of 0.23, 0.0036 h⁻¹, and 1220 cm² h⁻¹, respectively. The estimated values of the flow and transport parameters were found to be within the ranges of values reported by previous studies conducted at nearby field locations. The dripper TDR method is a rapid and useful technique for in situ measurements of hydraulic conductivity and solute transport properties. The measurements reported in this study give clear evidence to the occurrence of non-equilibrium water and chemical movement in surface soil. The method allows for quantification of non-equilibrium model parameters and preferential flow. Quantifying the parameters is a necessary step toward determining the influences of surface properties on infiltration, runoff, and vadose zone transport.     

Transport of nonsorbing solutes in a streambed with periodic bedforms

Previous studies of hyporheic zone focused largely on the net mass transfer of solutes between stream and streambed. Solute transport within the bed has attracted less attention. In this study, we combined flume experiments and numerical simulations to examine solute transport processes in a streambed with periodic bedforms. Solute originating from the stream was subjected to advective transport driven by pore water circulation due to current–bedform interactions as well as hydrodynamic dispersion in the porous bed. The experimental and numerical results showed that advection played a dominant role at the early stage of solute transport, which took place in the hyporheic zone. Downward solute transfer to the deep ambient flow zone was controlled by transverse dispersion at the later stage when the elapsed time exceeded the advective transport characteristic time t_c (= L/u_c with L being the bedform length and u_c the characteristic pore water velocity). The advection-based pumping exchange model was found to predict reasonably well solute transfer between the overlying water and streambed at the early stage but its performance deteriorated at the later stage. With dispersion neglected, the pumping exchange model underestimated the long-term rate and total mass of solute transfer from the overlying water to the bed. Therefore both advective and dispersive transport components are essential for quantification of hyporheic exchange processes.     

Conditions when anisotropy is negligible for solute transfer in sediment beds of lakes or streams

To reduce the complexity and save computation time, an isotropic and a scalar dispersion model are explored and compared to the anisotropic advection/dispersion model to study the interstitial flow in a stream and lake sediment induced by a periodic pressure wave. In these systems, the solute transport is controlled by the ratio (R = a/(LS)) of the pressure wave steepness (a/L) to the stream slope (S), and the dispersivity ratio (λ = α_L/L) that measures the longitudinal dispersivity (α_L) relative to the pressure wave length (L). Through a series of numerical experiments, the conclusion is reached that a scalar dispersion model can be applied with satisfactory results for advection-dominated transport, i.e. when R ?  0.1 and λ ? 0.01, or λ ? 0.0001, i.e. Peclet number (Pe) ? 10000; an isotropic dispersion model can be applied when R ? 10 or λ ? 0.001, and the full anisotropic advection/dispersion model has to be applied when R > 10 and λ > 0.001.     

Correlation of Geoelectric Data with Aquifer Parameters to Delineate the Groundwater Potential of Hard rock Terrain in Central Uganda

Knowledge of aquifer parameters is essential for management of groundwater resources. Conventionally, these parameters are estimated through pumping tests carried out on water wells. This paper presents a study that was conducted in three villages (Tumba, Kabazi, and Ndaiga) of Nakasongola District, central Uganda to investigate the hydrogeological characteristics of the basement aquifers. Our objective was to correlate surface resistivity data with aquifer properties in order to reveal the groundwater potential in the district. Existing electrical resistivity and borehole data from 20 villages in Nakasongola District were used to correlate the aquifer apparent resistivity (ρ _e) with its hydraulic conductivity (K _e), and aquifer transverse resistance (TR) with its transmissivity (T _e). K _e was found to be related to ρ _e by; $ {\text{Log }}(K_{\text{e}} ) = - 0.002\rho_{\text{e}} + 2.692 $ . Similarly, TR was found to be related to T by; $ {\text{TR}} = - 0.07T_{\text{e}} + 2260 $ . Using these expressions, aquifer parameters (T _c and K _c) were extrapolated from measurements obtained from surface resistivity surveys. Our results show very low resistivities for the presumed water-bearing aquifer zones, possibly because of deteriorating quality of the groundwater and their packing and grain size. Drilling at the preferred VES spots was conducted before the pumping tests to reveal the aquifer characteristics. Aquifer parameters (T _o and K _o) as obtained from pumping tests gave values (29,424.7 m²/day, 374.3 m/day), (9,801.1 m²/day, 437.0 m/day), (31,852.4 m²/day, 392.9 m/day). The estimated aquifer parameter (T _c and K _c) when extrapolated from surface geoelectrical data gave (7,142.9 m²/day, 381.9 m/day), (28,200.0 m²/day, 463.4 m/day), (19,428.6 m²/day, 459.2 m/day) for Tumba, Kabazi, and Ndaiga villages, respectively. Interestingly, the similarity between the K _c and K _o pairs was not significantly different. We observed no significant relationships between the T _c and T _o pairs_. The root mean square errors were estimated to be 18,159 m²/day and 41.4 m/day.     

Aerosol microphysics over a tropical coastal station inferred from the spectral dependence of Angstrom wavelength exponent and inversion of spectral aerosol optical depths

Six years of spectral aerosol optical depth (AOD) measurements have been analyzed from a tropical coastal site, Trivandrum (8.55°N, 76.9°E, 3 m msl) to infer on the seasonal changes in the microphysical properties of columnar aerosols, by examining the derivatives of the Angstrom wavelength exponent (α) in the wavelength domain (α′_λ) as well as in AOD domain (α′_τ) and by retrieving the columnar size distribution by numerical inversion of the AODs. The inference of the changes in the aerosol microphysics drawn from the features of the derivatives α′_λ and α′_τ is consistent with the pattern revealed by the aerosol properties obtained from the columnar size distributions retrieved from the AOD spectra as well as from the surface measurements of mass-size distributions, which are supported by the back-trajectory cluster analysis and the results of chemical species analysis.     

Прерывистое освещение поля зрения при методе соответствуюших высот и относительные уклонения отвеса в высоких татрах

To determine the relative deflections of the vertical from geodetic data and from astronomical measurements we used the method of equal altitudes, determining the time of passage by means of interrupted illumination of the field of view. The field of view of the telescope used (Zeiss Theo 010 and an astrolabe having an angle of 60°) was therefore supplied with five groups of seven horizontal fibres and during the passage of the two images the field of view was illuminated by a neon tube for a period of about 0·15 s every three seconds. The neon tube was connected either directly to an OMA 50 time signal by means of a transistor receiver or to a chronometer. The calculation was performed by means of relations (1) and (2). Apart from the corrections usually introduced, the personal-instrumental error (containing also a correction from the decimal equation) of the longitudeo _λ and the correctiona _η of the component η were also determined from the measurements. The correctionso _λ=?0·069s ando _η=?0·66″ also contain a correction from the decimal equation. Its value iso _λ ^′ =?0·030s for the longitude. The lago _λ?o _λ ^′ in reading the interpolation was ?0·039 s. The valueo _η=?0·66″ was introduced into the calculation of the vertical components η obtained from measurements in the High Tatras. The values of the corrections are given in Tab. 1. The method permits measurement of the passages of stars through the almucantar in the meridian. No conclusive proof was found for the impersonality (Tab. 1). The method was verified practically when determining the relative deflections of the vertical in the High Tatras for refining altitude measurements. The results are given in Tab. 2 and Fig. 2. The course of the quasigeoid profile in the Kriváňmeridian was also found (Fig. 3).     

Comparison of continuum and pore-scale models of nutrient biodegradation under transverse mixing conditions

Recent studies indicate that during in situ bioremediation of contaminated groundwater, degradation occurs primarily along transverse mixing zones. Classical reactive-transport models overpredict the amount of degradation because solute spreading and mixing are not distinguished. Efforts to correct this have focused on modifying both dispersion and reaction terms, but no consensus on the best approach has emerged. In this work, a pore-scale model was used to simulate degradation along a transverse mixing zone between two required nutrients, and a continuum model with fitted parameters was used to match degradation rates from the pore-scale model. The pore-scale model solves for the flow field, concentration field, and biomass development within pore spaces of porous medium. For the continuum model, the flow field and biomass distributions are assumed to be homogeneous, and the fitting parameters are the transverse dispersion coefficient (D_T) and maximum substrate utilization rate (k_S,c). Results from the pore-scale model show that degradation rates near the system inlet are limited by the reaction rate, while degradation rates downgradient are limited by transverse mixing. For the continuum model, the value of D_T may be adjusted so that the degradation rate with distance matches that from the pore-scale model in the mixing-limited region. However, adjusting the value of k_S only improves the fit to pore-scale results within the reaction-limited region. Comparison with field and laboratory experiments suggests that the length of the reaction rate-limited region is small compared to the length scale over which degradation occurs. This indicates that along transverse mixing zones in the field, values of k_S are unimportant and only the value of D_T must be accurately fit.     

Use of a harpacticoid copepod in toxicity tests

The harpacticoid copepod Nitocra spinipes has been tested for acute toxicity of 12 metal chlorides in brackish water. Their order of toxicity, expressed as 96 h LC₅₀, was in good agreement with other investigations performed in freshwater and seawater. The 96 h LC₅₀-values were of intermediate levels compared to these two environments. The organochlorines p,p′-DDE and p,p′-DDE methyl sulphone were tested for effects on reproduction and mortality during two weeks, and it was found that p,p′-DDE was the most toxic. It is concluded from the investigation that N. spinipes is a suitable toxicity test organism in brackish water.     

Quantification of longitudinal dispersion by upscaling Brownian motion of tracer displacement in a 3D pore-scale network model

We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented. Within the bonds, two different velocity profiles are used. At the network scale the longitudinal dispersion of the particles is quantified through the coefficient D_L, for which we evaluate a number of methods already known in the literature. Additionally, we introduce a new method for derivation of D_L based on the first-arrival times distribution (FTD). To validate our particle tracking method, we simulate Taylor’s classical experiments in a single tube. Subsequently, we carry out network simulations for a wide range of the characteristic Péclet number Pe_? to assess the various methods for obtaining D_L. Using the new method, additional simulations have been carried out to evaluate the choice of nodal jump conditions and velocity profile, in combination with varying network heterogeneity. In general, we conclude that the presented network model with particle tracking is a robust tool to obtain the macroscopic longitudinal dispersion coefficient. The new method to determine D_L from the FTD statistics works for the full range of Pe_?, provided that for large Pe_? a sufficiently large number of particles is used. Nodal jump conditions should include molecular diffusion and allow jumps in the upstream direction, and a parabolic velocity profile in the tubes must be implemented. Then, good agreement with experimental evidence is found for the full range of Pe_?, including increased D_L for increased porous medium heterogeneity.     

A scaling law for K′0 for silicates with constant mean atomic mass

It is shown that Birch's formula for the isothermal pressure derivative of the isothermal bulk modulus, K′, can be used to generate reasonable values of K′₀ for a sequence of silicates with various ambient densities and constant mean atomic mass, m¯. The theory predicts values in fairly good agreement with experimental results, although there is a regrettable spread of experimental values of K′₀ for each solid. This first-order approximation theory for scaling between K′₀ and ?₀ is analogous to the law of corresponding states which scales K₀ and ?₀.     

A way of estimating the characteristic slip displacement

During the ruptures of an earthquake,the strain energy.△E,.will be transferred into,at least,three parts,i.e..the seismic radiation energy(E_s),fracture energy(E_g),and frictional energy(E_f),that is,△E = E_s + E_g + E_f.Friction,which is represented by a velocity- and state-dependent friction law by some researchers,controls the three parts.One of the main parameters of the law is the characteristic slip displacement.D_c.It is significant and necessary to evaluate the reliable value of D_c from observed and inverted seismic data.Since D_c controls the radiation efficiency.η_R = E_s/(E_s+ E_g),the value of η_r is a good constraint of estimating D_c.Integrating observed data and inverted results of source parameters from recorded seismograms.the values of E_s and E_g of an earthquake can be measured,thus leading to the value of η_R.The constraint used to estimate the reliable value of D_c will be described in this work.An example of estimates of D_c.based on the observed and inverted values of source parameters of the September 20,1999 M_S 7.6 Chi-Chi(Ji-Ji).Taiwan region,earthquake will be presented.     

An accuracy analysis of selected finite difference methods for shelf waves

This paper compares the relative accuracy of five finite difference schemes for modeling barotropic shelf waves. One scheme assumes an Arakawa B lattice for the discrete variables while the other four assume an Arakawa C. Accuracy is measured by comparing numerical and analytic dispersion curves and cross-shelf amplitude profiles. The analysis is illustrated for typical depth profiles from the Australian, and Beaufort Sea shelves. Relative accuracy is found to vary with the particular shelf profile and both the cross-shelf and long-shelf resolution. The Arakawa-Lamb and Sadourny schemes are found to be slightly more accurate than the other C lattice schemes. For the Beaufort Sea profile and specific long-shelf wave-numbers, all schemes are shown to have a strong 2Δy signal in their cross-shelf amplitudes. The B lattice scheme is also shown to have problems with numerical instabilities and dispersion curves that merge for different modes.     

An overview of surface wave methods and a reliability study of a simplified inversion technique

Following a brief overview of the history and the development of the Surface Wave Method—with a focus on techniques for processing and inverting field data—a Simplified Inversion Method (SIM) is described, which constitutes an improvement of the Satoh et al. (1991) [1] method. The SIM is a direct inversion method of surface wave dispersion data, making use of a penetration depth coefficient, a_R, whose value is a function of Poisson's ratio and the overall shape of the dispersion curve. In the present study the coefficient a_R has been evaluated using data from (a) an extensive database compiled from the technical literature and containing results of inverted surface wave measurements and nearby cross-hole/down-hole measurements, (b) results of side by side surface wave and cross-hole measurements, performed at five sites in the course of this study, (c) finite element analyses simulating the performance of surface wave measurements and thus providing “virtual” data, and (d) applying a current advanced inversion code, available on the Web. Based on all the above data, optimum values of a_R (and of the corresponding uncertainty of the derived V_so vs. depth profile) have been estimated. These values were found to be independent of depth from ground surface. The results of all analyses and comparisons indicate that for the majority of realistic soil profiles (including cases of normal and inverse dispersion conditions) the proposed SIM provides very reliable V_so vs. depth profiles when a value of a_R=0.63–0.67 is used in the inversion process. It is concluded that the SIM can be used with confidence as a direct inversion method of surface wave dispersion data.     

Determination of the thermal conductivity of opalinus clay via simulations of experiments performed at the Mont Terri underground laboratory

Storage in deep geological formations is a potential solution for the management of high-level radioactive wastes. In this context, different types of rocks such as argillite are extensively studied. In the Mont Terri underground laboratory (Switzerland), several experiments have been performed in order to characterize the properties of the opalinus clay. One of these experiments, called HE-C, has consisted in measuring in situ the time evolution of the rock temperature submitted to a heating source. Experimental measurements have shown that the thermal behaviour of the clay was not homogeneous around the borehole where the heater was installed. Furthermore, 3D direct numerical simulations of this experiment performed with the code Cast3M have proved that it was necessary to introduce a new parameter α to model the amount of electric power lost in cables and by air convection inside the metallic tube containing the heater. A numerical simulation–optimization technique has been used to estimate the thermal longitudinal and transverse conductivities (λ_// and λ_⊥) of the host rock. It consists in minimizing an objective function that is the sum of the squared differences between measured and calculated temperatures. But this method induced a lot of Cast3M simulations. In order to drastically reduce the CPU time, we used a neural network approximation built from a sample training of 1100 Cast3M simulations. It allowed us to calculate the objective function for 500 000 different values of the triplet (λ_//,λ_⊥,α).Finally, we obtained the following values for the thermal conductivities

• –on one side of the borehole, λ_// = 1.84 ± 0.04 W m^− 1 K^− 1 and λ_⊥ = 0.55 ± 0.03 W m^− 1 K^− 1;
• –on the other side, λ_// = 1.90 ± 0.07 W m^− 1 K^− 1 and λ_⊥ = 1.07 ± 0.09 W m^− 1 K^− 1.

The estimated thermal conductivities λ_⊥ perpendicular to the bedding plane are quite different. It is perhaps caused by the presence of an intensive fractured zone on one side of the borehole, due to bentonite swelling. It can also be due to the presence of a bed of carbonated rock.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Thermal effects of chemical reactions in the undifferentiated earth

Calculations of thermal effects of oxidation-reduction reactions in the open systems for the undifferentiated earth have been carried out up to 2000 kbar. It is shown that a change in the sign of the thermal effect occurs with increase of pressure in these open systems: endothermal reactions which occur at pressures P_s < P_c become exothermal at pressures P_s > P_c and vice versa. At a certain critical pressure P_s = P_c the enthalpy of reaction is equal to zero.The results of calculations show that the central part of the earth and the deep interior could become warm due to reduction processes (for example reduction of ferromagnesian silicates and oxides, and stishovite) during core formation. Reducing conditions in the undifferentiated earth during core formation imply that a large fraction of the total heat of chemical reactions was released in the deep interior and was absorbed in the upper parts of the planet.     

Timescales of seawater intrusion and retreat

Quantifying the timescales associated with moving freshwater–seawater interfaces is critical for effective management of coastal groundwater resources. In this study, timescales of interface movement in response to both inland and coastal water level variations are investigated. We first assume that seawater intrusion (SWI) and retreat (SWR) are driven by an instantaneous freshwater-level variation at the inland boundary. Numerical modelling results reveal that logarithmic timescales of SWI (lnT_i) and SWR (lnT_r) can be described respectively by various simple linear equations. For example, SWI timescales are described by lnT_i = a + blnh′_f–s, where a and b are linear regression coefficients and h′_f–s is the boundary head difference after an instantaneous drop of inland freshwater head. For SWR cases with the same initial conditions, but with different increases in freshwater head, lnT_r = c + dΔX_T, where c and d are regression coefficients and ΔX_T is the distance of toe response that can be estimated by a steady-state, sharp-interface analytical solution. For SWR cases with the same freshwater head increase, but with different initial conditions, in contrast, lnT_r = e + flnΔX_T, where e and f are regression coefficients. The timescale of toe response caused by an instantaneous variation of sea level is almost equivalent to that induced by an instantaneous inland head variation with the same magnitude of water level change, but opposite in direction. Accordingly, the empirical equations of this study are also applicable for sea-level variations in head-controlled systems or for simultaneous variations of both inland and coastal water levels. Despite the idealised conceptual models adopted in this study, the results imply that for a particular coastal aquifer, SWI timescales are controlled by the boundary water levels after variations, whereas SWR timescales are dominated by the distance of toe response.     

On conditions for the unique inversion of seismic travel-time curves

It is shown that when the travel-time curve of a refracted wave from a surface source is known and at least one of the following conditions is satisfied, i.e. when

1. the travel-time curve of a wave reflected from a horizontal interface lying below the deepest low velocity layer is known, or
2. the travel-time curve of a wave from a deep source situated below the deepest low velocity layer is known, or
3. the measureH(u)=mes {z∶z≥0,v ^?1 (z)≥u} is analytical in some segment [c, d], where \(0< c< d< \infty , c< a_n , H(a_n ) = \bar z_n ,\bar z_n\) is the depth of the lower end of the deepest low velocity layer and in the interval [c, ∞) an analytical functionH(u)) exists which providesH(u)≡H(u)) ifu∈[c, d], then (1) velocityv(z) outside the low velocity layers and (2) the measureH _k (u)=mes {z∶z∈L _k,v ^?1 (z)≥u} for each low velocity layerL _k,k=1, 2, ..., n, are defined unambiguously.

     

G: Fracture energy,friction and dissipation in earthquakes

Recent estimates of fracture energy G ^′ in earthquakes show a power-law dependence with slip u which can be summarized as G ^′ ∝ u ^a where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to G _f : the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G ^′ and G _f should be comparable and show a similar scaling with slip. We test this hypothesis by analyzing experiments performed on various cohesive and non-cohesive rock types, under wet and dry conditions, with imposed deformation typical of seismic slip (normal stress of tens of MPa, target slip velocity > 1 m/s and fast accelerations ≈ 6.5 m/s²). The resulting fracture energy G _f is similar to the seismological estimates, with G _f and G ^′ being comparable over most of the slip range. However, G _f appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G ^′ appears to increase further and surpasses G _f at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.     

The destabilising nature of differential rotation

Abstract

In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts number q = 0) with differential rotation, U = sΩ(z)1 _?, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values of q) we found that differential rotations U = sΩ(s)1 _? which include a substantial proportion of negative gradient (dΩ/ds ≤ 0) give a destabilising effect which is largest when the magnetic Reynolds number R _m = O(10); the critical Rayleigh number, Ra _c, is about 7% smaller at minimum than at R_m = 0 for q = 10⁶. We also find that as q is reduced, the destabilising effect is diminished and at q = 10^?6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of the q = 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in the Ra_c vs. R_m curve similar to the A = 1 case. However, it has Ra_c ≤ 0 at its minimum and unlike the results for high A, larger values of R_m result in a restabilisation.