Water table fluctuation in response to transient recharge from a rectangular basin

A problem of water-table fluctuation in a finite two-dimensional aquifer system in response to transient recharge from an overlying rectangular area is studied. An analytical solution is obtained by using the method of finite Fourier transform to predict the transient position of the water-table. The solution for constant rate of recharge is shown as a special case of the present solution. Effects of variation in the rate of recharge on the growth of two-dimensional groundwater mound is illustrated with the help of a numerical example.Notation A half width of the aquifer [L] - B half length of the aquifer [L] - D half width of the recharge basin [L] - e specific yield - h varying water-table height [L] - h ₀ initial water-table height [L] - h weighted mean of the depth of saturation [L] - K hydraulic conductivity [LT^–1] - L half length of the recharge basin [L] - P(t) time varying rate of recharge [LT^–1] - P ₁ +P ₀ initial rate of time varying recharge [LT^–1] - P ₁ final rate of time varying recharge [LT^–1] - t time of observation [T] - x, y coordinate axes - decay constant [T^–1]     

An analytical solution for water-table fluctuation in a finite aquifer due to transient recharge from a strip basin

Two cases of water-table fluctuation in a finite aquifer in response to transient recharge from a strip basin are investigated. In the first case the aquifer is bounded by open water-bodies, whereas in second one the aquifer is bounded by impermeable boundaries on both sides. Analytical solutions are presented to predict the transient position of the water-table. The solutions are obtained by using finite Fourier sine and cosine transforms.Notations A width of the aquifer [L] - e specific yield - h variable water-table height [L] - h ₀ initial water-table height [L] - weighted mean of the depth of saturation [L] - K hydraulic conductivity [LT^–1] - m,n integers - P ₁ +P ₀ initial rate of transient recharge [LT^–1] - P ₁ final rate of transient recharge [LT^–1] - P constant rate of recharge [LT^–1] - x ₁ distance of left boundary of the strip basin [L] - x ₂ distance of right boundary of the strip basin [L] - t time of observation [T] - decay constant [T^–1]     

On the prediction of groundwater mound formation due to transient recharge from a rectangular area

Recharge to the aquifer leads to the growth of a groundwater mound. Therefore, for the proper management of an aquifer system, an accurate prediction of the spatio-temporal variation of the water table is very essential. In this paper, a problem of groundwater mound formation in response to a transient recharge from a rectangular area is investigated. An approximate analytical solution has been developed to predict the transient evolution of the water table. Application of the solution and its sensitivity to the variation of the recharge rate have been illustrated with the help of a numerical example.Notations a = Kh/e [L²/T] - A = aquifer's extent in the x-direction [L] - B = aquifer's extent in the y-direction [L] - e = effective porosity - h = variable water table height [L] - h ₀= initial water table height [L] - h = weighted mean of the depth of saturation [L] - K = hydraulic conductivity [L] - m, n = integers - P = constant rate of recharge [L/T] - P ₁+P₀= initial rate of transient recharge [L/T] - P ₁= final rate of transient recharge [L/T] - s = h ²–h ₀ ² [L²] - t = time of observation [T] - x,y = space coordinates - x ₂–x₁= length of recharge area in x-direction [L] - y ₂–y₁= width of recharge area in y-direction [L] - z = decay constant [T^-1]     

Analytical solutions of unsteady drainage problems for soils subjected to variable recharge from a semi-confined aquifer

In drainage of agricultural lands, the upward vertical recharge from a semi-confined aquifer depends on the difference of the piezometric heads on the two sides of the semi-impermeable layer through which this recharge takes place. This means that the recharge through the semi-impermeable base depends on the unknown height of the unsteady water table. In the nonhomogeneous Boussinesq equation, which describes the drainage problems, the downward uniform rate of the recharge from rain or irrigation and the recharge from the semiconfined aquifer are expressed by two terms. By solving the Boussinesq equation expressions for the nondimensional height of the water table and the nondimensional discharge of the drains per unit drained area are obtained for three different initial conditions. Some known solutions are shown as special cases of the present solutions. Variation of nondimensional water table heights at half distance of the drain spacing and the nondimensional discharge of the drains with nondimensional time have been graphically illustrated with the help of synthetic examples.Notation B _s thickness of the semi-impervious layer [L] - c hydraulic resistance of the semi-impervious layer [T] - D depth of the drains from the base [L] - d _e equivalent depth [L] - h=h(x, t) height of the water table [L] - h ₀ initial height of the water table [L] - h _t water table height at mid-distance of drains att [L] - h _j ,h _k water table height at mid-distance of drains at timej andfk, respectively [L] - H ₀ piezometric head in the semi-confined aquifer [L] - K hydraulic conductivity of the soil [LT^–1] - K _s hydraulic conductivity of the semi-impervious layer [LT^–1] - k ₀,k ₁,k ₂ nondimensional constants - L distance between the drains [L] - q ₀ upward recharge per unit surface area through the semi-impervious layer [LT^–1] - q _t discharge per unit drainable area of drains at timet [LT^–1] - R,R ₀ recharge per unit surface area from rain or irrigation during the unsteady and steady-state, respectively, [LT^–1] - S specific yield of the soil - t time of observation [T] - x distance measured from the drain [L] - leakage factor [L] - nondimensional distance - nondimensional time     

Combined analytical solution of overland flow and sediment transport

With reference to the kinematic wave theory coupled with the hypothesis of constant linear velocity for the rating curve, rising limb analytical solutions have been calculated for overland flow, over an Hortonian-infiltrating surface, and sediment discharge. These analytical solutions are certainly easier to use than the numerical integration of the basic equations and they may be used to obtain an initial evaluation of the parameters of more complex models generally devised for complicated cases.Notation a exponent of the Horton law [T^–1] - b exponent of the rill erosion equation - B inter-rill erosion coefficient [ML^–m–2T ^m–1] - c sediment concentration [ML^–3] - c _o reference sediment concentration [ML^–3] - E _I inter-rill erosion [ML^–2T^–1] - E _R rill erosion [ML^–2T^–1] - f _c final infiltration rate of the soil [LT^–1] - f _o initial infiltration rate of the soil [LT^–1] - h flow depth [L] - h _o reference flow depth [L] - i infiltration rate [LT^–1] - k rill erosion coefficient [ML^–1–b T^–1] - K integration constant - L() Laplace transformation - m exponent of the inter-rill erosion equation - n Manning's coefficient [L^–1/3T] - p rainfall intensity [LT^–1] - q water discharge per unit width [L²T^–1] - q _s sediment discharge per unit width [ML^–1T^–1] - t time [T] - t _p ponding time [T] - x distance along the flow direction [L] Greek Letters coefficient of the stage-discharge equation [L^2–T^–1] - exponent of the stage-discharge equation - rill erosion coefficient [L^–1]     

Optimization-simulation models for the design of an Irrigation project

Optimization-simulation models were used for the systems analysis of a water resources system. The Karjan Irrigation reservoir project in India was taken as the system. Two types of optimization models, i.e., linear programming, and dynamic programming (continuous and discontinuous) were used for preliminary design purposes. The simulation technique was used for further screening. The linear programming model is most suitable for finding reservoir capacity. Dynamic programming (continuous and discontinuous models) may be used for further refining the output targets and finding the possible reservoir carry-over storages, respectively. The simulation should then be used to obtain the near optimum values of the design variables.Notations a ₁ Unit irrigation benefit [Rs.10⁵ L^–3] - B ₁ Gross annual irrigation benefit [Rs.10⁵] - B _1,t Gross irrigation benefit in periodt [Rs.10⁵] - C ₁ Annual capital cost of irrigation [Rs.10⁵] - C ₁ Annual capital cost function for irrigation [Rs.10⁵ L^–3] - C _1,t Fraction of annual capital cost for irrigation in periodt [Rs.10⁵] - C ₂ Annual capital cost of reservoir [Rs.10⁵] - C ₂ Annual capital cost function for reservoir [Rs.10⁵ L^–3] - C _2,t Fraction of annual capital cost for reservoir in periodt [Rs.10⁵] - El _t Reservoir evaporation in timet [L³] - f _t Optimal return from staget [Rs.10⁵] - g _t The return function for periodt [Rs.10⁵] - I _t Catchment inflow into the reservoir in periodt [L³] - I _t Water that joins the main stem just above the irrigation diversion canal in timet [L³] - _t Local inflow to the reservoir from the surrounding area in timet [L³] - Ir Annual irrigation target [L³] - K _t Proportion of annual irrigation targetIr to be diverted for irrigation in timet - K _t Amount by whichK _t exceeds unity is the fraction of the end storage which is assigned to reservoir evaporation losses - L Loss in irrigation benefits per unit deficit in the supply [Rs.10⁵ L^–3] - L ₁ Lower bound on annual irrigation target,Ir [L³] - L ₂ Lower bound on reservoir capacity,Y [L³] - N Number of time periods in the planning horizon - O _t Total water release from the reservoir in periodt [L³] - O _t ^* The optimal total water release from the reservoir in timet [L³] - _t Secondary water release from the reservoir in timet [L³] - O _t Reservoir release to the natural channel in timet [L³] - Od _t Irrigation demand in timet [L³] - Om ₁ Annual OM cost of irrigation [Rs.10⁵] - Om ₁ Annual OM cost function for irrigation [Rs.10⁵ L^–3] - Om _1,t Fraction of annual OM cost for irrigation in periodt [Rs.10⁵] - Om ₂ Annual OM cost of reservoir [Rs.10⁵] - Om ₂ Annual OM cost function for reservoir [Rs.10⁵ L^–3] - Om _2,t Fraction of annual OM cost for reservoir in periodt [L³] - Omin_t Lower bound onO _t in timet [L³] - Omax_t Upper bound onO _t in timet [L³] - P _t Precipitation directly upon reservoir in timet [L³] - S _t Gross/live reservoir storage at the end of timet (gross storage in the linear program and live storage in the dynamic program) [L³] - S _t–1 Gross/live reservoir storage at the beginning of timet [L³] - t Any time period - Tr_t Transformation function - U ₁ Upper bound onIr [L³] - U ₂ Upper bound onY [L³] - Y Total capacity of reservoir at maximum pool level [L³] - Ya Fixed active (live) capacity of the reservoir (Y-Yd) [L³] - Ya _t Active (live) capacity (Ymax_t –Ymin_t) of the reservoir in timet [L³] - Yd Dead storage of the reservoir [L³] - Ymax_t Capacity up to the normal pool level of the reservoir in timet [L³] - Ymax_t Live capacity up to the normal pool level of the reservoir in timet [L³] - Ymin_t Capacity up to the minimum pool level of the reservoir in timet [L³] - Ymin_t Live capacity up to the minimum pool level of the reservoir in timet [L³]     

A water policy intercomparison model for a region with three seasons

A water policy model is proposed as a solution to the problem of obtaining maximum net benefit from providing irrigation and urban water in regions where the major source of supply is groundwater. In essence, the model introduces an innovative scheme based on two types of penalties. These intervene when either watertable elevation falls below a critical value during the operation of a system of wells or a remote source is used to partially cover the needed amount of water expected from the basic groundwater source. Another specific idea of the model is the consideration, for southern regions, of a three-season division in the climatic character of a year. The algorithm is illustrated by a numerical example in which five possible alternatives are compared. The conclusion of the study (although a function of regional economics, natural conditions, as well as specific zonal water policy constraints) reveals a compromise between limiting the amount provided from remote sources and confining the aquifer operation to critical values of the water-table elevation.Notation B benefits from water use, 10³ US$ - C sum of total costs, 10³ US$ - CMR total maintenance-repair cost, 10³ US$ - CO total cost of operation, 10³ US$ - C _HO unit cost of operation per hour, US$ hr^–1 - C _y unit average cost of a repaired pump, US$/(year × well) - d screen diameter for each well, m - H _G average groundwater elevation, m - H _{W cr} critical water elevation value in wells, m - H _{W dj} hydraulic head deficit in wells (belowH _{W cr} ), m - H _{W j} seasonal water elevation in each well, m - j current season - K average hydraulic conductivity of the aquifer, m s^–1 - NB net benefit, 10³ US$ - Ns maximum number of seasons - N _HO number of hours of operation per well and month - N _{W j} number of wells in operation over a seasonj - n _j number of months over each seasonj - P sum of total penalties, 10³ US$ - PH total penalty for pumping whenH _{W dj} >0, 10³ US$ - PQ total penalty for remote source use, 10³ US$ - P _RSj unit penalty for remote source use, 10³ US$ month^–1 - P _{W dj} unit penalty for pumping whenH _{W dj} >0, 10³ US$ month^–1 - pRM percentage of repaired and maintained pumps yearly, % - Q _iRj discharge needed for irrigation use, m³ s^–1 - Q _Nj total discharge needed by users, m³ s^–1 - Q _Pj total seasonal yield capacity of the battery, m³ s^–1 - Q _RSj discharge covered from remote sources, m³ s^–1 - Q _UWj discharge needed for urban water use, m³ s^–1 - Q _j seasonal operated pumping rate in each well, m³ s^–1 - Q _waj weighted average of pumping rate at timet _j , m³ s^–1 - S _Y average specific yield of the aquifer - S _cr critical drawdown value in wells, m - S _j seasonal drawdown in each well - T average transmissivity of the aquifer, m² s^–1 - t _OPj current duration of system operation - t _j –t _j–1 duration of each seasonj     

Impact of Treated Wastewater Reuse on Agriculture and Aquifer Recharge in a Coastal Area: Korba Case Study

Treated wastewater (TWW) reuse has increasingly been integrated in the planning and development of water resources in Tunisia. The present study aimed the evaluation of the environmental and health impact that would have the reuse of TWW for crops direct irrigation or for the recharge of the local aquifer in Korba (Tunisia). For this purpose water analyses were carried on the TWW intended for the aquifer recharge and on underground water of this area. As for underground water before recharge, no contamination by organic matter or heavy metals is shown but high salinity, nitrate, potassium and chloride concentrations are detected. The bacteriological analyses show the occurrence of faecal streptococcus, thermo-tolerant coliforms, total coliforms and E coli, but absence of salmonella. These results indicate that this water is not suitable for irrigation worse still for drinking purpose. The monitoring of TWW pollutants has demonstrated that oxygen demands (COD and BOD) do not exceed the Tunisian standards for TWW used in agriculture (NT 106.03) except for August when samples reach high values (COD = 139 mg O₂ L^− 1, BOD = 34). It is also the case for temperature, electrical conductivity (EC), salinity and pH. Heavy metal concentrations are under the detection limit. The determination of nutrients shows relatively low concentrations of nitrates, nitrites and orthophosphate (the maxima in mg L^− 1 are respectively 6.6, 5.6 and 0.92) whereas the potassium levels are high (up to 48.8 mg L^− 1) and the ammonia levels very high, reaching 60.6 mg L^− 1. As for bacteriological pollution, while no salmonella and intestinal nematods are detected, high concentrations of total coliforms, thermo-tolerant coliforms, faecal streptococci and E. coli are analysed. Consequently, the better use of TWW in this region would be the use of infiltration basins for the recharge of the deteriorated aquifer by TWW. It would give the opportunity to better the quality of the TWW reaching the groundwater by an additional treatment for bacteriological and suspended solid (TSS) contaminants while being an alternative water for the aquifer recharge and a coastal barrier against seawater intrusion.     

The artificial recharge of groundwater: A solution by successive variations of steady states

The artificial recharge of groundwater aims at the modification of water quality, an increase of groundwater resources, and the optimization of the exploitation and recovery of contaminated aquifers. The purpose of this work is to develop a new mathematical model for the problem of an artificial recharge well, using the method of successive variations of steady states. Applying this method, one arrives at an expression of time as a double integral. This integral contains the time-dependent radius of the recharge boundary and the piezometric head of the well, calculated with the finite-element method. The new model is simple and useful, and can be applied to many practical problems, using the designed dimensionless graphs.Notations A area of the finite element (m²) - c the Euler constant (0.5772156649...) - e index of the finite element - E _i the exponential integral function - F _j nodal values of the functionF - h piezometric head, (m) - h ₀ piezometric head at timet=0 (m) - h _w piezometric head on the well contour (m) - i, j, k nodal indices of the finite element - K hydraulic contactivity (ms^–1) - N _i interpolation function - Q discharge (m³ s^–1) - r cylindrical coordinate (m) - r ₀ the action radius of the well (m) - r _w the radius of the well (m) - S the effective porosity - t the time (s) - T the transmissivity of the aquifer (m²s^–1) - V the stored water volume (m³) - x, y, dummy variables     

On the predictability of the water-table variation in a ditch-drainage system

The irrigation in regions of brackish groundwater in many parts of the world results in the rise of the water-table very close to the groundsurface. The salinity of the productive soils is therefore increased. A proper layout of the ditch-drainage system and the prediction of the spatio-temporal variation of the water table under such conditions are of crucial importance in order to control the undesirable growth of the water-table. In this paper, an approximate solution of the nonlinear Boussinesq equation has been derived to describe the water-table variations in a ditch-drainage system with a random initial condition and transient recharge. The applications of the solution is discussed with the help of a synthetic example.Notations a lower value of the random variable representing the initial water-table height at the groundwater divide - a+b upper value of the random variable representing the initial water-table height at the groundwater divide - h variable water-table height measured from the base of the aquifer - K hydraulic conductivity - L half width between ditches - m ₀ initial water-table height at the groundwater divide - N(t) rate of transient recharge at time t - N ₀ initial rate of transient recharge - P N ₀/K - S Specific yield - t time of observation - t ₀ logarithmic decrement of the recharge function - T Kt/SL - x distance measured from the ditch boundary - X x/L - Y h/L - Y mean of Y - Y Variance of Y     

Water table fluctuation with a random initial condition

The nonlinear Boussinesq equation is used to understand water table fluctuations in various ditch drainage problems. An approximate solution of this equation with a random initial condition and deterministic boundary conditions, recharge rate and aquifer parameters has been developed to predict a transient water table in a ditch-drainage system. The effects of uncertainty in the initial condition on the water table are illustrated with the help of a synthetic example. These results would find applications in ditch-drainage design.Notation A / tanh t - a lower value of the random variable representing the initial water table height at the mid point - a+b Upper value of the random variable representing the initial water table height at the midpoint - B tanh t - C 4/ - h variable water table height - h mean of the variable water table height - h _m variable water table height at the mid point - h _m mean of the variable water table height at the mid point - K hydraulic conductivity - L half spacing between the ditches - m ₀ initial water table height at the mid point - N Uniform rate of recharge - S specific yield - t time of observation - x distance measured from the ditch boundary - (4/SL)(NK)^1/2 - (L/4)(N/K)^1/2 - dummy integral variable     

Brackish groundwater resources in Bahrain: Current exploitation,numerical evaluation and prospect for utilization

In Bahrain, where water resources available for direct use are finite and the best of its quality has a salinity of over 2.5 g L^–1, utilization of brackish groundwater is an essential part in the management of the country's water resources. Bahrain's brackish water occurs in the Rus-Umm Er Radhuma formations in the form of a lens of a finite lateral extent, with a salinity ranges between 8 and 15 g L^–1. Planning for utilization of brackish groundwater for desalination purposes in Bahrain was based on simulation modeling of the aquifer system using a mixing cell model developed originally in 1983. The model was used to predict the aquifer response to pumping from the proposed wellfield in terms of changes of TDS over a period of 20 years. Construction and operation of the wellfield in 1984 was based on the predicted salinity changes. Over the past 9 uears of wellfield operation (1984–1993), and through continuous monitoring of the aquifer response to pumping, the collected data is used to post-audit the original model by history matching. The calibration process adopted has resulted in a statisfactory agreement between the model output and the observed data. The model is then used to predict the wellfield salinity changes and the aquifer potentiometric levels. The expected life span for the brackish groundwater utilization by the wellfield is redefined through constrained utilization that takes into account salinity deterioration coupled with the effect of head decline on hydraulic interaction between the brackish water and the upper fresh water aquifer. The results suggest that the operation of the wellfield should cease by the year 2007. Construction of a new model that enables testing and evaluating different development scenarios is recommended to aid future management decisions regarding the utilization of brackish groundwater.     

Numerical Solution of 2D Free Surface to Ditch Drains in Presence of Transient Recharge and Depth-Dependent ET in Sloping Aquifer

Water table variations between drains have been investigated by various researchers in response to transient recharge. Recent studies have shown the importance of incorporating the effect of evapotranspiration (ET) in the design of subsurface drainage systems. In arid and semi-arid regions, ET plays a crucial role in lowering the water table resulting in increased drain spacing. In this paper, a numerical solution of two-dimensional free surface flow to ditch drains is presented in presence of transient recharge and depth-dependent ET from land surface for an aquifer with sloping impermeable base. The midpoint water table variations obtained from the proposed solution compare well with experimental results as well as already existing mathematical solution. When ET from the land surface is taken into account in combination with recharge, the model results can provide accurate and reliable estimates of water table fluctuation under complex situations, which are highly related to the hydrology of waterlogged and saline soils.     

Evolution of the Water Table in a Finite Aquifer Due to Transient Recharge from Two Parallel Strip Basins

Understanding the dynamic response of phreatic aquifers due to recharge is most important for the proper management of ground-water systems. In this paper an analytical solution is developed to describe the water-table fluctuation in a finite aquifer system due to transient recharge from two parallel strip basins. Application of the solution in the prediction of spatiotemporal variation of the water table and in the sensitivity analysis of the effects of various controlling parameters on the water-table fluctuation is demonstrated with the help of an example problem.     

An Analytical Solution of Boussinesq Equation to Predict Water Table Fluctuations Due to Time Varying Recharge and Withdrawal from Multiple Basins, Wells and Leakage Sites

Recharging and pumping are the integral part of any scheme of ground water resources development and both processes significantly affect the dynamic behavior of the aquifer system. Leakage from the aquifer’s base, if present, is other process which affects the water table variation. Therefore, an accurate estimation of water table fluctuation induced by recharging, pumping and leakage is pre-requisite to ensure sustainability of groundwater resources. In the present work an analytical solution of a 2-D linearized Boussinesq equation is developed to predict water table fluctuations in the presence of time varying recharge, pumping and leakage from any number of recharge basins, wells and leakage sites of any dimension for any number of recharge and pumping cycles. The rate of time varying recharge (or pumping) is approximated by using a series of linear elements of different lengths and slopes which are dependent on the nature of variation in the recharge (or pumping) rate. Application of the solution in the prediction of water table fluctuation in the presence of time varying recharge, pumping and leakage is demonstrated with the help of a numerical example. These numerical results indicate significant effect of the time varying recharge/pumping rates and leakage on the water table variation. Such information is useful for the proper management of groundwater.     

Quantifying natural recharge characteristics of shallow aquifers in groundwater overexploitation zone of North China

To improve the accuracy of hydrological simulations in the groundwater overexploitation zone of North China, it is necessary to study the characteristics of shallow aquifer recharge on daily scale. Three shallow aquifer recharge indices were used to quantify shallow aquifer recharge in two ways. The recharge coefficient was used to quantify the amount of shallow aquifer recharge. The recharge duration and water table rise coefficient were used to quantify the recharge temporal process. The Spearman rank correlation coefficient and regression analysis were used to determine the relationships between aquifer water table depth (WTD), rainfall, and shallow aquifer recharge. The Jiangjiang River Basin, a tributary of the Haihe River, was selected as the study area. The results showed that the recharge coefficient first increased, then decreased, and finally leveled off as WTD increased. When WTD was between 5 and 6 m, the recharge coefficient reached its maximum (approximately 0.3). When WTD was greater than 10 m, the recharge coefficient remained stable (around 0.12). With regard to the sources and forms of recharge, preferential flow was dominant in the areas near the extraction wells. In contrast, plug flow became dominant in the areas distant from the wells. With the reduction of rainfall duration, the proportion of preferential flow contributing to aquifer recharge increased. With the increase of rainfall amount, the duration of aquifer recharge lengthened.     

Response of an Unconfined Aquifer Induced by Time Varying Recharge from a Rectangular Basin

An analytical solution is developed to predict spatio-temporal variation of the water table in a 2-D aquifer system which is receiving transient recharge from an overlying basin of rectangular shape. The transient recharge function is approximated by a number of line segments. Application of the solution is demonstrated with the help of an example problem.     

An Empirical Assessment of On-Farm Water Productivity using Groundwater in a Semi-Arid Indian Watershed

Realistic estimation of irrigation volume applied to any crop at farm level generally requires information on event based discharge rates and corresponding periods of irrigation application. Use of mean seasonal discharge rates leads to erroneous estimation of volume due to unaccounted seasonal fluctuations in the water table, upon which the discharge rate of tube well is dependent. In the absence of such information, an alternative approach of estimating farm level water application based upon water table fluctuation data has been adopted in this study. The total actual water extracted during each irrigation event from the watershed was distributed among the farms irrigating crops in proportion to the product of irrigation time and the pump capacity (h_p). Volume of water withdrawal concurrent to an irrigation event was computed based on the water level fluctuations in the wells in conjunction with potential recharge contribution from the surface storage structures to the groundwater aquifer. A production function approach was used to estimate the marginal productivity of water for selected crops at various stages of plant growth. Water, as an input in the production function, encompassed either in-situ soil moisture storage from rainfall or irrigation from groundwater or both. The inter-season as well as intra-season groundwater use, and the consequent groundwater withdrawals were analyzed based on the marginal value and output elasticity of water at different crop growth stages during the season. The cotton crop realized marginal value product of water, ranging from Rs. 1.03/m³ to Rs. 10.43/m³ at different crop growth stages in cotton. Castor crop had the marginal value product ranging from Rs. 2.89/m³ to Rs. 6.81/m³. The availability and use of water, including soil moisture, in the two seasons, coupled with the local harvest prices received, yielded the differential marginal values of water.     

Water-table variation in a sloping aquifer due to random recharge

Variation in the level of the water table is closely linked with recharge. Therefore, any uncertainty associated with the recharge rate is bound to affect the nature of the water-table fluctuation. In this note, a ditch-drainage problem of a sloping aquifer is considered to investigate the effect of uncertainty in the recharge rate on water-table fluctuation. The rate of recharge is taken as an exponentially decaying function with its decay constant as a Gaussian random variable. Expressions for the first two moments of the water-table height, i.e. mean and standard deviation, are presented. By using these expressions, the effect of uncertainty in the recharge rate on the water-table fluctuation has been analyzed with the help of a numerical example.