Water Table Fluctuation in the Presence of a Time-Varying Exponential Recharge and Depth-Dependent ET in a Two-Dimensional Aquifer System with an Inclined Base

An analytical solution is presented for water table fluctuation between ditch drains in presence of exponential recharge and depth-dependent evapotranspiration (ET) from groundwater table in a two-dimensional gently sloping aquifer. The groundwater head above the drain is small compared to the saturated thickness of the aquifer. A sound mathematical transformation is devised to transform the two-dimensional groundwater flow equation into a simple form, which makes possible to obtain an analytical solution. The transient midpoint water table variations from the proposed solution compare well with the already existing solutions for horizontal aquifer. A numerical example is used to illustrate the combined effect of depth-dependent ET coupled with a time-varying exponential recharge on the water table fluctuation. The inclusion of a depth-dependent ET in the solution results in water table decline at a faster rate as compared to the case when ET is not considered. With an increase in slope of the aquifer base, water table profiles become asymmetric and the water table divide shifts towards the lower drain. The height of the water table profiles increases on moving away from the boundary of the aquifer and the highest level of the ground water table is obtained in the central portion of the aquifer basin due to the presence of drainage ditches on the aquifer boundary. When the effect of ET is incorporated in combination with recharge, the analytical solution results in accurate and reliable estimates of water table fluctuations under situations subjected to a number of controlling factors. This study will be useful for alleviation of drainage problems of the aquifers receiving surface recharge and surrounded by streams.     

Water Table Rise in Sloping Aquifer due to Canal Seepage and Constant Recharge

Analytical solutions of the linearized Boussinesq equation and a fully implicit finite-difference numerical solution of the nonlinear Boussinesq equation were obtained to study transient and steady-state water table rise in a homogeneous, isotropic, and incompressible unconfined sloping aquifer. The rise was due to seepage from two canals located at different elevations above the sloping impermeable barrier and constant recharge from the land surface. Proposed analytical solutions were verified with existing analytical solutions for a horizontal aquifer and were found in close agreement. The effect of recharge and slope of the impermeable barrier on water table rise predicted by both analytical and numerical solutions was studied by considering a numerical example. The effect of the linearization of the Boussinesq equation on water table rise was also studied by comparing the water table heights predicted by the numerical solution with those computed from the analytical solution. The analytical solution overestimates water table elevations compared to those obtained from the numerical solution, and the difference in water table in the middle region decreases with increase in time.     

Analytical Solution for Transient Water Table Heights and Outflows from Inclined Ditch-Drained Terrains

This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated aquifer. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. As this solution represents the groundwater table shape more realistically, this water table profile is used as an initial condition in the derivation of the second analytical solution for the groundwater table height, and the in- and outflow into the ditches. The solutions allow the calculation of the transient behavior of the groundwater table, and its ouflow, due to changing percolation rates or water level heights in both ditches.     

Modeling Evapotranspiration of Two Land Covers Using Integrated Hydrologic Model

Modeling evapotranspiration (ET) distribution in shallow water table environments is of great importance for understanding and reproducing other hydrologic fluxes such as runoff and recharge. Unfortunately, ET distribution can be the most difficult hydrologic process to analyze. The partitioning of ET into upper zone ET, lower zone ET, and groundwater ET is complex because it depends on land cover and subsurface characteristics. One comprehensive distributed parameter model, integrated hydrologic model (IHM), builds on an improved understanding and characterization of ET partitioning between surface storages, vadose zone storage, and saturated groundwater storage. It provides a smooth transition to satisfy ET demand between the vadose zone and the deeper saturated groundwater. In this paper, the IHM was used to analyze ET contribution from different regions of the vadose zone and saturated zone. Rigorous testing was done on two distinct land covers, grass land and forest land, at a study site in West-Central Florida. Sensitivity analysis on the key parameters was investigated and influence of parameters on ET behavior was also discussed. Statistics with the root mean square error and mean bias error for forest total ET were about 1.46 and 0.04 mm/day, respectively, and 1.61 and 1.07 mm/day for grass total ET. Modeling results further proved that ET distributions from the upper and lower soil and water table, while incorporating field-scale variability of soil and land cover properties, can be predicted reasonably well using IHM model.     

Interaction of Stream and Sloping Aquifer Receiving Constant Recharge

An analytical solution and finite-element numerical solution of a linearized and nonlinear Boussinesq equation, respectively, were obtained to describe water table variation in a semi-infinite sloping∕horizontal aquifer caused by the sudden rise or fall of the water level in the adjoining stream. Transient water table profiles in recharging and discharging aquifers having 0, 5, and 10% slopes and receiving zero or constant replenishment from the land surface were computed for t = 1 and 5 days by employing analytical and finite-element numerical solutions. The effect of linearization of the nonlinear governing equation, recharge, and slope of the impermeable barrier on water table variation in a semi-infinite flow region was illustrated with the help of a numerical example. Results suggest that linearization of the nonlinear equation has only a marginal impact on the predicted water table heights (with or without considering constant replenishment). The relative errors between the analytical and finite-element numerical solution varied in the range of ?0.39 to 1.59%. An increase in slope of the impermeable barrier causes an increase in the water table height at all the horizontal locations, except at the boundaries for the recharging case and a decrease for the discharging case.     

Drainage of Sloping Lands with Variable Recharge: Analytical Formulas and Model Development

Semianalytical transient equations for shallow subsurface transverse drainage systems installed in sloping lands are developed. They provide a general relationship between drain flow rates, water table elevations, and recharge rates. This relationship demonstrates that, depending on the recharge intensity, several drain flow rates can be observed at a given water table elevation. The recharge contribution is shown to depend on a water table shape factor and to decrease when the water table is low or the slope is steep. For very steep slopes, the recharge intensity no longer influences the drain flow rate. These equations can be used to confirm previous results obtained in steady-state conditions and to determine precisely under which conditions slope needs to be considered in drainage design. They have been incorporated into the field drainage model SIDRA, which simulates hourly values of water table elevations and drain flow rates. The model predictions are compared with the predictions of a steady-state equation and a numerical model, which solves the Boussinesq equation (SLOP model).     

Agroecological Impacts from Salinization and Waterlogging in an Irrigated River Valley

Extensive field data and calibrated flow and salt-transport models characterize the spatial and temporal patterns of salinity and waterlogging in an irrigated western river valley. Over three irrigation seasons, average seasonal aquifer recharge from irrigated fields in a 50,600?ha study area ranges from 0.59?to?0.99?m, including contribution from precipitation. The salinity of irrigation water varies from 618?to?1,090?mg/L. The water table is shallow, with 16 to 33% of irrigated land underlaid by an average water table less than 2?m deep. Average water table salinity ranges from 2,680?to?3,015?mg/L, and average soil salinity from 2,490?to?3,860?mg/L. Crop yield reductions from salinity and waterlogging range from 0 to 89% on fields, with regional averages ranging from 11 to 19%. Annual salt loading to the river from subsurface return flows, generated in large part by dissolution from irrigation recharge, averages about 533?kg/irrigated?ha?per?km. Upflux from shallow water tables under fallow ground contributes to about 65?million?m3 (52,600?acre-ft) per year of nonbeneficial consumption. Beyond problem identification, the developed database and models provide a basis for effectively addressing these problems through a systematic and comparative assessment of alternative solutions.     

Impact of Shallow Groundwater on Evapotranspiration Losses from Uncultivated Land in an Irrigated River Valley

In many agricultural regions of the West, decades of intensive irrigation have produced shallow water tables under not only cultivated fields but also the nearby uncultivated land. It is possible that the high water tables under the uncultivated lands are substantially increasing evapotranspiration (ET) rates, which would represent an unnatural and potentially nonbeneficial consumptive use. The objective of this paper is to quantify loss of water that occurs from uncultivated lands in a semiarid irrigated river valley (the Lower Arkansas River Valley in southeastern Colorado). A remote-sensing algorithm is used to estimate actual ET rates on 16 dates on the basis of Landsat satellite images. On the same dates, water table depths, soil moisture values, and soil water salinities are measured at up to 84 wells distributed across three study sites. On the basis of a water balance of the root zone, it is estimated that 78% of the ET is supplied by groundwater upflux at these sites. It is also observed that the ET and groundwater upflux decrease with increasing water table depth. A regression analysis indicates that the spatial variations in ET are most closely related to variations in vegetation-related attributes, whereas soil moisture and water table depths also explain substantial amounts of the variation. Valley-wide implications for reducing nonbeneficial ET through water table control also are discussed.     

Water Table Profiles and Discharges for an Inclined Ditch-Drained Aquifer under Temporally Variable Recharge

This paper presents the solution of the linearized Boussinesq equation for an inclined, ditch-drained aquifer, with a temporally varying recharge rate. Water-table profiles and flow rates into the ditches are calculated. As an initial condition the steady-state profile for a constant recharge rate is used, and the linearized Boussinesq equation is solved for a different recharge rate. Then, at a specified time, the transient water table profile is used as initial condition for the Boussinesq equation with a new recharge rate. The transient solution at a new specified time is then used as the initial condition for the Boussinesq equation with a different recharge rate, and so on. Using the Darcy equation, analytical expressions for the flow rates into the ditches can be obtained. The solution allows the calculation of the transient behavior of the groundwater table and its flow rates due to temporally variable recharge rates.     

Soil Salinity Modeling over Shallow Water Tables. II: Application of LEACHC

Root zone salinity is one of the major factors adversely affecting crop production. A saline shallow water table can contribute significantly to salinity increases in the root zone. A soil salinity model (LEACHC) was used to simulate the effects of various management alternatives and initial conditions on root zone salinity, given a consistently high water table. The impact of water table salinity levels, irrigation management strategies, soil types, and crop types on the accumulation of salts in the root zone and on crop yields was evaluated. There were clear differences in soil salinity accumulations depending upon the depth and salinity of the water table. In general, increasing water table depth reduced average soil profile salinity, as did having lower salinity in the water table. Among the four irrigation strategies that were compared, the 14-day irrigation interval with replenishment of 75% of evapotranspiration (ET) resulted in the lowest soil salinity. With a 4-day interval and 50% ET replenishment, a wheat yield reduction of nearly 40% was predicted after three years of salt accumulation. Soil type and crop type had minimal or no impact on soil salinity accumulation. Under all conditions, soil water average electrical conductivity increased during the 3-year simulation period. This trend continued when the simulation period was extended to 6 years. Under the conditions shown to develop the highest average soil salinity (high water table, low irrigation), an annual presowing irrigation of 125 mm caused a nearly 50% reduction in soil salinity at the end of the 6-year simulation period, as compared with the soil salinity given no presowing irrigation.     

Analysis of Seepage from Polygon Channels

An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and a Schwarz-Christoffel transformation. The symmetry about the vertical axis has been utilized in obtaining the solution for half of the seepage domain only. The solution also includes relations for variation in seepage velocity along the channel perimeter and a set of parametric equations for the location of phreatic line. From this generalized case, particular solutions have also been deduced for rectangular and triangular channels with a drainage layer at finite depth and trapezoidal, rectangular, and triangular channels with a drainage layer and water table at infinite depth. Moreover, the analysis includes solutions for a slit, which is also a special case of polygon channels, for both cases of the drainage layer. These solutions are useful in quantifying seepage loss and/or artificial recharge of groundwater through polygon channels.     

Monitoring and Modeling Flow and Salt Transport in a Salinity-Threatened Irrigated Valley

Saline high water tables pose a growing threat to the world’s productive irrigated land. Much of this land lies along arid alluvial plains, where solutions must now be developed in the context of changing constraints on river management. Findings are presented from the preliminary phase of a project aimed at developing, through well-conceived data collection and modeling, strategies to sustain irrigated agriculture in the salinity-threatened lower Arkansas River Basin of Colorado. Extensive field data from a representative subregion of the valley reveal the nature and variability of water table depth and salinity, irrigation efficiency and salt loading, and soil salinity. The shallow water table had an average salinity concentration of 3,100 mg/L and an average depth of 2.1 m, and was less than 1.5 m deep under about 25% of the area. Evidence reveals low irrigation efficiencies and high salt loading under each of six canals serving the subregion. Water table depths less than 2.5–3 m contributed to soil salinity levels that exceed threshold tolerances for crops under about 70% of the area. Preliminary steady-state modeling indicates that only limited improvement can be expected from vertical drainage derived from increased pumping, or from decreased recharge brought about by reduced overirrigation. Investments in canal lining, horizontal subsurface drainage, and improved river conditions also will need consideration.     

Pan Evaporation to Reference Evapotranspiration Conversion Methods

Reference evapotranspiration (ET0) is often estimated from evaporation pan data as they are widely available and of longer duration than more recently available micrometeorologically based ET0 estimates. Evaporation pan estimation of ET0 ( = KpEpan) relies on determination of the pan coefficient (Kp), which depends on upwind fetch distance, wind run, and relative humidity at the pan site. The Kp estimation equations have been developed using regression techniques applied either to the table presented in FAO-24 or to the original data upon which this table was based (from lysimeter studies in Davis, Calif.). Here, the relative performances of the FAO-24 table and six different Kp equations are evaluated with respect to reproducing the original data table using the FAO-24 table as a standard. Evaporation pan- and CIMIS-based estimates of ET0 are also compared for stations having ranges of mean humidities (48–66%) and mean wind runs (156–193 km/day) located in the Sacramento and San Joaquin valleys, and for a coastal station (Point Heuneme) near Ventura, Calif., having a greater mean humidity (71%). In comparing the means, standard deviations, root-mean-square errors, and linear regression coefficients, five of the six equations reproduced the original data table with approximately the same accuracy as the FAO-24 table. Use of either Kp table slightly underestimated measured ET0 at the coastal site, while the Cuenca, Allen-Pruitt, and Snyder Kp equations most closely approximated the average measured ET0 at all seven sites.     

Monthly Water Resources and Irrigation Planning: Case Study of Conjunctive Use of Surface and Groundwater Resources

The Tehran metropolitan area is one of the mega cities of the world and has an annual domestic water consumption close to one billion cubic meters. The sewer system mainly consists of traditional absorption wells. Therefore, the return flow from the domestic consumption has been one of the main sources of groundwater recharge. Some part of this sewage is drained into local rivers and drainage channels and partially contaminates the surface runoff and local flows. These polluted surface waters are used in conjunction with groundwater for irrigation purposes in the southern part of the Tehran. In this paper, a systematic approach to surface and groundwater resources modeling in the study area, with its complex system of water supply, groundwater recharge, and discharge, is discussed. A dynamic programming optimization model is developed for conjunctive use planning. The objective function of this model is developed to supply the agricultural water demands, to reduce pumping costs, and to control groundwater table fluctuations. To develop the response function of the aquifers located in the study area, a mathematical model for simulation of the Tehran aquifer water table fluctuations has been developed and calibrated with the available data. Different scenarios are defined to study the long-term impacts of the development projects on conjunctive use policies and water table fluctuations. Comparison of the results showed how significant is the effects of an integrated approach to the surface and groundwater resources allocation in Tehran metropolitan area. The proposed model is a useful tool for irrigation planning in this region.     

Border Irrigation Field Experiment.?I: Water Balance

This paper presents the results from a detailed field experiment of water movement on a border-irrigated bay in northern Victoria, Australia, an area characterized by shallow ground-water tables and salinization problems. The objective of the study was to quantify the impact of changes in irrigation management on salt and water movement within and from the bay and on recharge to the region's shallow ground-water table. Results showed that the evapotranspiration volume almost wholly explained the soil moisture changes between irrigation events and that deep drainage was negligible. Infiltration was mainly confined to the advanced stages of irrigation, with the soil rapidly becoming saturated across the bay, due to the presence of soil cracks. Such findings suggest that more efficient management of border irrigation supply to the bay will not lead to the lowering of the shallow ground-water table—conclusions that have important implications for irrigation management.     

Evaluating Regional Solutions to Salinization and Waterlogging in an Irrigated River Valley

Potential solutions to high soil salinity levels and waterlogging problems are investigated on a regional scale using calibrated finite-difference flow and mass transport modeling for a portion of the Lower Arkansas River Valley in Colorado. A total of 38 alternatives incorporating varying degrees of recharge reduction, canal seepage reduction, subsurface drainage installation, and pumping volume increases are modeled over three irrigation seasons (1999–2001). Six performance indicators are used to evaluate the effectiveness of these alternatives in improving agroecological conditions, compared to existing conditions. Predicted average regional decrease in water table elevation (as great as 1.93 m over the irrigation season) is presented for selected alternatives, as well as the spatial mapping of results. Decrease in soil salinity concentration (with regional and seasonal average reduction as high as 950 mg/L) is also predicted and mapped. Estimated groundwater salinity changes, reduction in total salt loading to the river, increase in average regional crop yield, and changes in net water consumption indicate the potential for marked regional-scale enhancements to the irrigation-stream-aquifer system.     

Unsteady Solution for Well Recharge in a Low Diffusive Aquifer

Finite aquifer solution exists for the constant head in a fully penetrating well. Their use for well recharge is limited, as they do not permit simultaneous computation of unsteady wellhead pressure and variable recharge rate. In the present paper semianalytical solutions are presented for well recharge under variable head boundary condition. These solutions were developed using the method of separation of variables and Duhamel’s convolution theorem. The solution developed in the paper was verified with the Jacob-Lohman solution and subsequently validated using field data pertinent to constant-head boundary conditions. Subsequently for variable head boundary condition such an appropriate background was found missing in the literature.     

Tide-Induced Water Table Fluctuations in Coastal Aquifers Bounded by Rhythmic Shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer’s properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.     

Processes Governing Flow and Chemical Characteristics of Discharges from Free-Draining, Underground Coal Mines

In the Uniontown Syncline of Southwestern Pennsylvania, discharges from unflooded, free-draining coal mines are acidic with high sulfate concentrations. Flow and water quality data obtained in 1998–2000 for an unflooded mine discharge in the Uniontown Syncline were evaluated using a tank reactor fill-and-draw model to describe seasonal variations in outflows over time observed for the mine as well as to simulate discharge water quality. The hydraulic model was coupled to a chemical mass balance using estimates of recharge water quality and in-mine chemical production∕loss. Field data indicated that the concentrations of sulfate, iron, and acidity were fairly constant even when flow varied greatly. Flow-related mass production functions for these constituents were obtained by fitting the field data. The hydraulic–chemical model was used to simulate sulfate and acidity production from pyrite dissolution and total carbonate loss in the mine. Model simulations indicated that in-mine acid production correlated with recharge rate, due to the sustained presence of oxygen which drives pyrite dissolution, and that recharge water chemistry had a significant influence on discharge characteristics. For the mine studied, alkaline recharge water mitigates the acidity of the discharges.     

Multidimensional Infiltration with Arbitrary Surface Fluxes

A new solution to the multidimensional linearized Richards equation was derived using a Fourier integral transform. Exponential functional forms k = kseαψ and θ = θr + (θs ? θr)eαψ were used to represent the hydraulic conductivity and pressure relation and the soil water release curve. The analytical solutions consider the conditions of time dependence and nonuniform distribution of rainfall intensity and arbitrary initial water content distribution with a water table. The analytical solutions can be used to predict the ponding time and to obtain the volumetric water content distribution over time and space.