Evaluation of groundwater recharge in semi-arid region of India using environmental tritium

Depth variations of environmental tritium and of soil moisture in the unsaturated zone of the semi-arid alluvial tracts of northern Gujarat (India) are measured and utilised to evaluate vertical groundwater recharge. Results obtained from the two different experiments carried out at an interval of two years are found to be in fair agreement. An average of recharge amounting to about 5 per cent is indicated. The observed depth variation of tritium gives support to the view that the movement of soil moisture in this region is layered.     

Ground water recharge in Western Uttar Pradesh

The downward movement of water in the soil due to 1971 monsoon precipitation and supplemental surface irrigation has been traced at about forty-five sites in Western Uttar Pradesh, using a thin layer of moisture tagged with tritiated water. The tritiated layer was found to move down to different depths at different sites. The movement, averaged over the forty sites is found to be 96 cm, indicating that the average recharge for the year 1971 (a year of normal monsoon) was 21.5 cm of water.     

The measurement of tritium activity in natural waters

The concentrations of tritium have been determined in wet precipitations occurring over the Indian subcontinent during 1961–64, using a sensitive method for counting of tritium activity discussed in Part I* of this paper. The tritium concentrations varied significantly during the period of observation; highest concentrations were observed during 1963. An analysis of the data reported here, in conjunction with those available for concentrations of H³ and Sr⁹⁰ in rains at higher latitudes, reveals that these nuclides which were originally placed at high altitudes in the polar regions during late 1962, were deposited chiefly at 30°–90° latitudes during 1963 and 1964 respectively in relative proportions of 1 and 0·6. The data show that the largest gradients in their zonal deposition occur at about 35°–40° N latitude and that to a first approximation, their deposition per unit area in 1963 or 1964 was practically uniform, separately in the 30°–90° and 0°–30° latitude regions. This observation suggests the existence of two well-defined cells, which are internally well mixed: the meridional transport to low latitudes occurs as a result of interaction between these cells. The annual deposition rates of Sr⁹⁰ as observed during 1963 and 1964 suggest a mean time of 3 months for exchange of air between the two cells, in good agreement with the values deduced for mid-months of the year on the basis of analysis of bomb produced C¹⁴ data. The tritium and strontium data for the inland, coastal and island stations are analysed to evaluate the importance of (i) the re-evaporation of tritium from continents, and (ii) the molecular exchange of atmospheric tritium with oceanic water. Process (i) probably plays a significant role over the continents throughout the year; its effect, however, is experimentally visible only during June to September. The estimated concentration of H³ in evaporated water suggests that the precipitated water mixes very slowly with that in the soil; limits on the equivalent amount of exchangeable soil water are given. It is shown that the relative wet deposition of H³ and Sr⁹⁰ atisland andcoastal stations is similar to their estimated concentration ratio in upper level tropospheric air. Furthermore, the relative concentrations of H³ and Sr⁹⁰ at continental and occanic stations differ only to the extent expected due to reinjection of H³ over continents. Thus, if one takes into account the recycling of H³ at continental stations (which results in about a 50% higher apparent deposition on an annual basis), one is led to the conclusion that process (ii) is rather unimportant; an upper limit of 30% on the fraction of tritium removed over oceans by molecular exchange is deduced. The mean annual concentration of Sr⁹⁰ in wet precipitation is lower at oceanic stations compared to that at continental stations. This could be due to meteorological effects peculiar to oceanic areas,e.g., higher rainfall and quick recycling of evaporated water. Otherwise, one must postulate a significant removal of Sr⁹⁰ (and H³) by ocean spray and jet action.     

Quantifying fate and transport of nitrate in saturated soil systems using fractional derivative model

Natural soil systems usually exhibit complex properties such as fractal geometry, resulting in complex dynamics for the movement of solutes and colloids in soils, such as the well-documented non-Fickian or anomalous diffusion for contaminant transport in saturated soils. The development of robust mathematical models to simulate anomalous diffusion for reactive contaminants at all relevant scales presents a contemporary problem in computational hydrology. This study aims to develop and validate a novel fractional derivative, advection-dispersion-reaction equation (fADRE) with first order decay to quantify nitrate contaminants transport in various soil systems. As an essential nutrient for crop growth, nitrogen in various forms (i.e., fertilizers) is typically applied to agricultural plots but a certain fraction or excess that is converted to nitrate or nitrite will serve as a critical pollutant to surface-water and groundwater. Applications show that the fADRE model can consider both hydrological and biogeochemical processes describing the fate and transport of nitrate in saturated soil. Here “fate” is a commonly used terminology in hydrology to describe the transformation and destination of pollutants in surface and subsurface water systems. The model is tested and validated using the results from three independent studies including: (1) nitrate transport in natural soil columns collected from the North China Plain agricultural pollution zone, (2) nitrate leaching from aridisols and entisols soil columns, and (3) two bacteria (Escherichia coli and Klebsiella sp.) transport through saturated soil columns. The qualitative relationship between model parameters and the target system properties (including soil physical properties, experimental conditions, and nitrate/bacteria physical and chemical properties) is also explored in detail, as well as the impact of chemical reactions on nitrate transport and fate dynamics. Results show that the fADRE can be a reliable mathematical model to quantify non-Fickian and reactive transport of chemicals in various soil systems, and it can also be used to describe other biological degradation and decay processes in soil. Hence, the mathematical model proposed by this study may help provide valuable insight on the quantification of various biogeochemical dynamics in complex soil systems, but needs to be tested in real-world applications in the future.     

Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory

Incomplete information is notoriously common in planning soil and groundwater remediation. For making decisions groundwater flow and transport models are commonly used. However, uncertainty in prediction arises due to imprecise information on flow and transport parameters like saturated/unsaturated hydraulic conductivity, water retention curve parameters, precipitation and evapo-transpiration rates as well as factors governing the fate of pollutant in soil like dispersion, diffusion, degradation and chemical transformation. Different methods exist for quantifying uncertainty, e.g. first and second order Taylor’s Series and Monte-Carlo method. In this paper, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. The application of the fuzzy set theory is demonstrated through pesticide (endosulfan) transport in an unsaturated layered soil profile. The governing partial differential equation along with fuzzy inputs, results in a non-linear optimization problem. The solution gives complete membership functions for flow (suction head) and pesticide concentration in soil column.     

An analysis of moisture diffusion according to Fick’s law and the tensile mechanical behavior of a glass-fabric-reinforced composite

The properties of moisture diffusion parameters and their effect on the tensile mechanical behavior of a fabric composite (glass fiber/epoxy resin) in the warp and weft directions were investigated. The water up take by specimens conditioned in a humid environment under different relative humidities (0, 60, and 96% RH) at a constant temperature of 60°C was evaluated by weight gain measurements. The water absorption followed Fick’s diffusion law in the fabric composite. A comparison between the values obtained for the moisture diffusion coefficient and the equilibrium moisture content at the laboratory and those given by Loos and Springer showed that the parameters depended not only on the nature of materials, but also on environmental conditions. The effect of moisture absorption on tensile characteristics of the composite, which was tested in uniaxial tension in the warp and weft directions at constant imposed displacement rates up to failure, showed a significant reduction in the ultimate tensile strength of the specimens conditioned at 96% RH. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 43, pp. 479-488, May-June, 2009.     

Radon concentration of air over the Eastern Arabian Sea

The radon concentrations of air samples collected during the South West monsoon period at altitudes up to 4 km over the Arabian Sea at two locations,i.e., 0–50 km and 300–400 km west of Bombay, are reported. Radon was extracted from air, using a simple single stage apparatus. The concentration of radon in the monsoon air mass was found to range around 80–100 dpm/m³ STP, indicative of its recent continental origin. The results suggest that the coastal monsoon air mass, up to 400 km west of Bombay coast, is generally homogeneous and vertically well mixed. During the post-monsoon condition, a strong gradient in the radon concentration in the vertical is observed. The concentration of radon decreases from 157 dpm/m³ at sea level to 35 dpm/m³ at about 3·7 km altitude, suggesting a vertical turbulent diffusion coefficient of ～6×10⁴ cm²/sec. In contrast, the near absence of vertical gradient of radon in the monsoon air mass indicates that the vertical turbulence is much stronger during the monsoon period.     

A decision tool for optimal irrigated crop planning and water resources sustainability

In the present study, the conjunctive use policies of surface and ground water resources are developed for minimizing water shortage in an irrigation district subject to constraints on groundwater withdrawals and crop planning capacities. An integrated soil water balance algorithm is coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. Various options of conjunctive use water resources along with current and proposed cropping patterns have been explored by Koohdasht Irrigation District (KID), a semi-arid region in I.R. Iran. The analysis provides various scenarios, which can help managers in decision-making for the optimum allocation plans of water resources within the irrigation area. The results reveal that the proposed model, as a decision tool for optimal irrigated crop planning and water resources sustainability, may be used for maximizing the overall net benefits and global water productivity of an irrigation district considering an allowable annual recharge of groundwater. Findings indicate the importance of the conjunctive water management modeling, which can be easily implemented and would enhance the overall benefits from cropping activities in the study area.     

城市地下水资源可持续开发利用模型研究

根据地下水可持续开发利用原则,运用系统分析方法建立了地下水可持续开发利用模型,首先,运用有限元分析法对地下水运动偏微分方程进行离散,导出了地下水运动的数值方程,使得地下水运动方程能够与系统分析方法相结合建立城市地下水可持续开发利用模型;然后,以地下水位下降最小为目标函数,以各井的出水能力及时段内的需水量作为约束条件,建立了城市地下水优化利用模型,为城市地下水资源可持续开发利用提供新的规划管理方法.     

On fractal nature of groundwater level fluctuations due to rainfall process

Hourly resolution time series of groundwater level fluctuations are analyzed after removing the seasonal cycle. It is found that fluctuations of groundwater levels have fractal scaling and a persistent behavior. We show also that groundwater level fluctuations exhibit non-Gaussian heavy tailed probability distribution that is well fitted by the Lévy stable distribution. Implications of the present results on the groundwater system modeling as a fractional Lévy motion and the connection with the anomalous diffusion inside the soil are discussed.     

Hydrogeochemical modeling for groundwater management in arid and semiarid regions using MODFLOW and MT3DMS: A case study of the Jeffara of Medenine coastal aquifer,South-Eastern Tunisia

The study of water quality and the quantification of reserves and their variations according to natural and anthropogenic forcing is necessary to establish an adequate management plan for groundwater resources. For this purpose, a modeling approach is a useful tool that allows, after calibration phase and verification of simulation, and under different scenarios of forcing and operational changes, to estimate and control the groundwater quantity and quality. The main objective of this study is to collect all available data in a model that simulates the Jeffara of Medenine coastal aquifer system functioning. To achieve this goal, a conceptual model was constructed based on previous studies and hydrogeological investigations. The regional groundwater numerical flow model for the Jeffara aquifer was developed using MODFLOW working under steady-state and transient conditions. Groundwater elevations measured from the piezometric wells distributed throughout the study area in 1973 were selected as the target water levels for steady state (head) model calibration. A transient simulation was undertaken for the 42 years from 1973 to 2015. The historical transient model calibration was satisfactory, consistent with the continuous piezometric decline in response to the increase in groundwater abstraction. The developed numerical model was used to study the system's behavior over the next 35 years under various constraints. Two scenarios for potential groundwater extraction for the period 2015–2050 are presented. The predictive simulations show the effect of the increase of the exploitation on the piezometric levels. To study the phenomenon of salinization, which is one of the most severe and widespread groundwater contamination problems, especially in coastal regions, a solute transport model has been constructed by using MT3DMS software coupled with the groundwater flow model. The best calibration results are obtained when the connection with the overlying superficial aquifer is considered suggesting that groundwater contamination originates from this aquifer. Recommendations for water resource managers

• The results of this study show that Groundwater resources of Jeffara of Medenine coastal aquifer in Tunisia are under immense pressure from multiple stresses.
• The water resources manager must consider the impact of economic and demographic development in groundwater management to avoid the intrusion of saline water.
• The results obtained presented some reference information that can serve as a basis for water resources planning.
• The model runs to provide information that managers can use to regulate and adequately control the Jeffara of Medenine water resources.

     

On convergence of finite volume schemes for one-dimensional two-phase flow in porous media

This paper deals with development and analysis of finite volume schemes for a one-dimensional nonlinear, degenerate, convection-diffusion equation having application in petroleum reservoir and groundwater aquifer simulation. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze and compare three families of numerical schemes corresponding to explicit, semi-implicit, and implicit discretization of the diffusion term and a Godunov scheme for the advection term. L^∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the schemes satisfy a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem. Results of numerical experiments using the present approach are reported.     

Man-made plutonium in freshwater and marine environments

Significant concentrations of plutonium isotopes are found in lake and coastal marine sediments accumulating at rates of 1–5 mm/yr. The activity levels of^{239, 240}Pu range between 0·7–3·3 dpm/g for post 1960 sediments. The measured and the calculated integrated activities of²³⁹Pu in the lake sediments are in agreement. This suggests that plutonium is chemically reactive in freshwater environments and it is removed to sediments from the water column shortly after its injection. A delay of about three years has been observed between the peak of plutonium fallout and its incorporation in the varved sediment from Santa Barbara basin. Based on this observation the mean size of particles transporting plutonium to the basin sediments is estimated to be about three microns. The usefulness of plutonium isotopes as a tracer nuclide for estimating sedimentation rates for the last two decades have been evaluated.     

The dynamics of a zooplankton–fish system in aquatic habitats

Diel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this paper, we use a temporally periodic reaction–diffusion–advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface water during the night. We establish the persistence theory for both species as well as the existence of a time-periodic positive solution to investigate how zooplankton manage to maintain a balance with their predators via vertical migration. Numerical simulations discover the effects of migration strategy, advection rates, domain boundary conditions, as well as spatially varying growth rates, on persistence of the system.     

Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping

In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L¹-space.     

Radioactive beryllium in the atmosphere and on the earth

It is estimated that about 1,000 nuclei of radioactive Be¹⁰ (2·7 million years half-life) are produced per square meter per second by cosmic ray induced nuclear disintegrations in the atmosphere. The conditions for observing the resulting activity in rain water and in various regions on the earth are favourable and may be useful for measuring sedimentation rates and other geological surface changes during the Tertiary.     

Computational homogenization of non-stationary transport processes in masonry structures

A fully coupled transient heat and moisture transport in a masonry structure is examined in this paper. Supported by several successful applications in civil engineering the nonlinear diffusion model proposed by Künzel (1997) [16] is adopted in the present study. A strong material heterogeneity together with a significant dependence of the model parameters on initial conditions as well as the gradients of heat and moisture fields vindicates the use of a hierarchical modeling strategy to solve the problem of this kind. Attention is limited to the classical first order homogenization in a spatial domain developed here in the framework of a two step (meso–macro) multi-scale computational scheme (FE² problem). Several illustrative examples are presented to investigate the influence of transient flow at the level of constituents (meso-scale) on the macroscopic response including the effect of macro-scale boundary conditions. A two-dimensional section of Charles Bridge subjected to actual climatic conditions is analyzed next to confirm the suitability of algorithmic format of FE² scheme for the parallel computing.     

Modeling the drainage and groundwater table above the collecting pipe through 2D groundwater models

In order to understand the effects of the landfill operation on groundwater flow behavior, 2D horizontal groundwater simulation model was carried out. The model saved the memory of computer and time consumption comparing with 3D groundwater flow model. However, the most difficulty is the assignment of collecting pipe boundary in the study site. Therefore, 2D vertical model was applied to calculate the change of groundwater table above the collecting pipe. This paper paid attention to examine the validation of the assignment of the collecting pipe boundary by applying the results of 2D vertical model. 2D horizontal model was coupled with the recharge model to solve the partial differential equation of groundwater flow. Finite difference method and iterative successive over relaxation were applied. The drainage volume of leachate collection was summed up in the whole landfill site and compared with the average volume of treated waste water. The study demonstrated that the results of 2D vertical model validated and can be applied to 2D horizontal groundwater flow simulation.     

Spectral decompositions in nonlinear coupled diffusion

The solutions of a coupled, linear and nonlinear diffusion equationin a semi-infinite medium are derived using series methods.In addition, perturbation techniques allied to the spectraldecomposition of matrices are used to simplify the analysisand to find semianalytic solutions. The discussion is motivatedby the transmission of heat, moisture, and solute through thestrongly nonlinear medium of soil. Under boundary conditionsrepresenting the daily or seasonal fluctuations, it is shownusing spectral decomposition, despite the nonlinearities, howthe period of oscillation is preserved on passage through themedium. It is also shown how n³ partial differential equationsmay be solved for each of the n coupled variables to determineclosed forms for the first- and second-order perturbation effects.Examples of the solutions are given for the case of the coupledtransport of heat and moisture in soil.     

Existence for a time-dependent rainfall infiltration model with a blowing up diffusivity

A difficulty in the modelling of water infiltration into an unsaturated soil is due to the presence of a diffusion coefficient that blows up at the moisture saturation value. This is put in evidence in some well-known hydraulic models like those of Broadbridge and White and van Genuchten. In this paper, we obtain results concerning the existence, uniqueness and regularity properties of the solution of unsaturated water flow determined by a time-dependent rainfall, with a nonlinear flux boundary condition on the outflow boundary and a singular diffusion coefficient. Some considerations related to the possibility of saturation occurrence and the extension of the results to the model describing the infiltration into an nonhomogeneous stratified soil are finally made.