Applying MODFLOW Model for Drainage Problem Solution: A Case Study from Jahir Irrigated Fields, Israel

High water table and soil salinization processes are common in irrigated fields in Israel. Subsurface drainage systems are a common technique to solve soil salinity problems. Subsurface drainage models can contribute to the efficiency of the drainage system as it can assist in the selection of the proper drainage system and its proper placement in the field. In this study we used the MODFLOW groundwater flow model to simulate groundwater levels in Jahir irrigated fields, the Jordan Valley, Israel. Using a three-layer groundwater flow model, the most efficient drainage system was found to be a combination of deep drains with relief wells and a pump placed in the area with soil salinity problem and upward hydraulic pressure. It was found that simulated drainage system can yield nearly 200,000?m3 of water per year. Given certain information, a spatially distributed groundwater flow model such as MODFLOW can provide more reliable information than different analytical solutions for planning of an effective subsurface drainage system.     

Comparison of Models for Computing Drainage Discharge

The WAVE model describes the transport and transformations of matter and energy in the soil, crop, and vadose environment. A lateral field drainage subprogram was added to the WAVE model to simulate lateral subsurface drainage flow. The subsurface drainage is considered as the drainage provided by evenly spaced parallel drains with a free outlet: drain tubing or ditch. The rate of subsurface water movement into drain tubes or ditches depends on the hydraulic conductivity of the soil, drain or ditch spacing, hydraulic head in the drains, profile depth, and water table elevation. Hooghoudt's steady-state equation was selected for incorporation in the WAVE model. The subsurface drainage subprogram was calibrated and validated by comparison with the SWAP model (The Netherlands) and DRAINMOD (the United States) and partially by using 7 years of drain outflow data from an experimental field under fallow and cropped conditions. The comparative study revealed that the three models performed equally well and that the models were reliable and accurate tools for predicting the drainage flux as a function of rainfall-evapotranspiration and local conditions. The WAVE model, in comparison to the SWAP and DRAINMOD model, provided as good a prediction of the lateral subsurface drainage flow to drains. The statistical analysis between each model and observed data revealed that the three models were able to predict with sufficient accuracy the observed drainage discharge. The DRAINMOD model, however, has the advantage of giving a more accurate estimate of the discharge, resulting in a more precise modeling. The models were consistent in predicting water table levels, but they could not be verified against field data because of a lack of suitable measurements.     

Water Management of Irrigated-Drained Fields in the Jordan Valley South of Lake Kinneret

The Jordan Valley is one of the primary regions for growing winter crops of fruit and vegetables in Israel and Jordan. Control of water management in these fields is obtained by solid-set irrigation systems and subsurface drainage. Detailed field observations were conducted at a location near the Jordan River, south of Lake Kinneret. Water table heights were measured by approximately 100?piezometers. An exiting wide spacing (160?m) subsurface drainage system was monitored and the total drainage discharge from this regional drainage system to Lake Kinneret was measured. Rainfall, irrigation, and evapotranspiration rates were measured and overall hydrological balance was conducted. The old irrigation method in the region was border irrigation with very high leaching fraction and poor irrigation efficiency. During the 1970s the irrigation method was changed to computer operated drip irrigation. The leaching fraction was reduced and irrigation efficiency increased. Reduction of the total drainage discharge to Lake Kinneret by a factor of about 10 was observed. Water table rise under hand moving sprinkler and soil-set drip irrigation methods were measured and compared for assessment of salinization of the root zone by upward movement of groundwater. The result indicates the strong effect of irrigation time interval on the extent of these rises. The effect of irrigation mode on the extent of water table rises was measured at the field by comparing that under hand moving sprinkler irrigation to that under water solid set drip method. This effect depends, among other variables, on the irrigation time interval, a fact which complicates prediction of water table rise under different irrigation practices. These field results support previous theoretical analysis by the writers and highlighted the interrelationship between irrigation practice and drainage design. The effect of water table drawdown towards the Jordan River was monitored and found to be about 4.6%. The strong influence of the Jordan River on water table height at the drained field is magnified by the existence of sandy layers in the soil profile. This observed gradient may be used for the estimation of lateral seepage flow from the irrigated agricultural field towards the adjacent Jordan River. This study provides a useful source of data for future studies in similar situations.     

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.     

Simplified Impedance Model for Adhesively Bonded Piezo-Impedance Transducers

The electromechanical impedance technique employs surface-bonded lead zirconate titanate piezoelectric ceramic patches as impedance transducers for structural health monitoring and nondestructive evaluation. The patches are bonded to the monitored structures using finitely thick adhesive bond layer, which introduces shear lag effect, thus invariably influencing the electromechanical admittance signatures. This paper presents a new simplified impedance model to incorporate shear lag effect into electromechanical admittance formulations, both one-dimensional and two-dimensional. This provides a closed-form analytical solution of the inverse problem, i.e. to derive the true structural impedance from the measured conductance and susceptance signatures, thus an improvement over the existing models. The influence of various parameters (associated with the bond layer) on admittance signatures is investigated using the proposed model and the results compared with existing models. The results show that the new model, which is far simpler than the existing models, models the shear lag phenomenon reasonably well besides providing direct solution of a complex inverse problem.     

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.     

Soil Salinity Modeling over Shallow Water Tables. I:?Validation of LEACHC

Soil salinity is a very common problem in today's irrigated agriculture. High salinity levels adversely impact crop yields and reduce overall soil quality. The presence of a saline shallow water table can be a major contributor to this problem. The LEACHC version of LEACHM is one of the few numerical models that considers independent movement of individual ions along with their detailed chemistry. This model has apparently not previously been tested under saline shallow water table conditions. LEACHC was evaluated using both lysimeter and field data from the literature. The model performed reasonably well in simulating solute transport above a saline shallow water table. For both data sets used in model validation, less reactive ions (sodium and chloride) were predicted well while calcium concentrations were underpredicted. For the field data, the model predicted soil electrical conductivity (EC) profiles better than most of the individual ions. The water content profiles associated with the field data were also predicted quite well. Based on these results, LEACHC was selected as a simulation tool for evaluating the effects of management practices on salinity transport in crop root zones above a saline shallow water table.     

Transient Ditch Drainage of Two-Layered Soil

The analytical solution to the problem of transient drainage without replenishment for a two-layered soil, by applying Girinsky's potential, has been presented. The effect of various parameters on drainage has been evaluated, and a set of relationships has been developed that may help in the design of drainage in layered soils. The proposed analytical solutions have been experimentally investigated on a vertical Hele-Shaw model in which the two-layered soil conditions were simulated. The comparison of results of proposed analytical solutions with the experimentally observed ones in the Hele-Shaw model showed that the experimentally observed and predicted midpoint water tables were found to be in good agreement for the entire duration of the experiment. The proposed theoretical model may be utilized for transient design of a drainage system in a two-layered soil.     

Turbulent Flow Over and Within a Porous Bed

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re k-ε turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability K ranging from 5.5490×10?7 to 4.1070×10?4?m2 and porosity ? from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for ? = 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.     

Drainage of Sloping Lands with Variable Recharge Model Validation and Applications

Semianalytical transient equations describing the behavior of water tables in subsurface drained soils when drains rest on a sloping impervious barrier have been derived previously and represent the bases of the SIDRA model. To validate (SIDRA), water table elevations and drainflow rates have been monitored for six years in the French Alps on fields with a slope of 8%. The predicted drain flow rates and water table shapes compare reasonably well with data of a drainage experiment site but the improvement provided by taking the slope into consideration was limited. Running the model with different slopes confirmed that high water table elevations and peak flows were not significantly changed with a slope of 8%. As could be predicted from the analysis in steady state, low water table elevations were the most affected by slope. With the soil parameters of the field experiment and from an analysis in tail recession conditions, it was shown that there is a clear threshold of 12% slope below which the slope has no significant influence and can be neglected in drainage design.     

Centrifuge Modeling of Nonaqueous Phase Liquid Movement and Entrapment in Unsaturated Layered Soils

Four geotechnical centrifuge tests with different soil layered systems were performed to investigate the movement and entrapment of water and of light nonaqueous phase liquids (LNAPLs) in unsaturated layered soil deposits. The tests were performed at 20 g and a vadose zone condition was created during the centrifuge tests by lowering the water table from the initially water saturated condition. During the water drainage stage, the water distribution within the models and the dynamic air–water capillary pressure saturation relationships of the three sands were obtained using tensiometers and resistivity probes. After achieving the unsaturated condition, a model LNAPL (Soltrol 220? or silicon oil) was injected near the soil surface and the movement and entrapment were monitored during the redistribution stage until the LNAPL reached the top of the water table. Complex LNAPL preferential flow and entrapment patterns were observed in the layered models with different textural interfaces due to the relative movement of all three phases [water, nonaqueous phase liquid (NAPL), and air]. The centrifuge tests data coupled with the numerical analyses show that NAPL properties, subsurface soil structures, initial water saturation, and NAPL infiltration rate affect the variation in entrapment conditions in heterogeneous unsaturated soil deposits.     

Methodology for Estimating Specific Yield in Shallow Water Environment Using Continuous Soil Moisture Data

A methodology for estimating specific yield in shallow water environments using continuous soil moisture data is introduced. An accurate estimate of specific yield is critical for management of water resources affecting well yields, water levels, and rates of water level decline. The study area is located in an intensive small-scale hydrologic monitoring field site in Hillsborough County, Florida. Data from four soil moisture monitoring stations were studied. The objectives of this paper are to describe a methodology to obtain precise estimates of the specific yield that can be obtained by a fitting procedure and to determine functional relationships between measured soil parameters and soil moisture storage variability. Estimated specific yield values varied from zero, when the water table was near land surface, to a maximum that was close to drainable porosity consistent with a humid shallow water environment, where sensitive ecosystems and wetlands are dependent on a seasonal hydroperiod of water table fluctuations. The results will be incorporated into regional integrated surface and ground water models that are being applied successfully in West-Central Florida.     

Influence of Subsurface Drainage on Soil Temperature in a Cold Climate

Soil temperature during springtime is an important factor for crop establishment and growth in poorly drained soils of northwest Minnesota. In this region, shallow water tables causing spring planting delays and excess water conditions during the growing season, may have contributed to significant unplanted cropland and yield reductions in recent years. Temperature is a regulating factor for many biological and chemical processes in the soil. One of the most commonly cited benefits of subsurface drainage on poorly drained soils is faster soil warm-up in the spring. Previous studies of this phenomenon do not provide definitive conclusions concerning the influence of soil drainage on soil temperature. The results of three site years of field observations of soil temperatures from drainage research plots at two locations in northwest Minnesota are presented herein. Replicated soil temperature and water table depths were measured continuously at five depths for two drain spacings and an undrained treatment. Subsurface drainage was found to significantly increase soil temperatures in both a coarser textured Vallers loam soil and a finer textured Hegne silty clay loam soil. Up to 4°C temperature increases occurred primarily between May and July with the greatest increases at 30–60?cm depths. Treatments with narrow drainage spacing showed a greater spring temperature increase than treatments with wider drainage spacings.     

CFD Predictions and Experimental Comparisons of Pressure Drop Effects of Turning Vanes in 90° Duct Elbows

This paper presents new results for numerical predictions of air flow and pressure distribution in two commonly used elbows: (1) 90° mitered duct elbows with turning vanes having 0.05 m radius, 0.038 m vane spacing and (2) 90° mitered duct elbows without turning vanes, in 0.2×0.2?m (8?in.×8?in.) duct cross section using the STAR-CD computational fluid dynamics (CFD) code. A k-ε turbulence model for high Reynolds number and k-ε Chen model were used for that purpose for comparative purposes. The simulation used 13 different Reynolds numbers chosen between the range of 1×105 and 2×106. To validate the CFD results, the results of two experimental papers using guided vanes were compared with simulated vane runs under the same condition. The first experimental study used a 0.6×0.6?m (24?in.×24?in.) square elbow with 0.05 m radius, 0.038 m vane spacing and air velocities at 2.54 m/s (500 fpm) and 25.4 m/s (5,000 fpm), the second experiment used a 0.81×0.2?m (32?in.×8?in.) rectangular elbow geometry with 0.05 m radius, 0.038 m vane spacing with air velocities from 10.16 m/s (2,000 fpm) to 13.97 m/s (2,750 fpm). For Reynolds numbers (1.00–2.00)×105 the pressure drop difference between vaned and unvaned elbows was found to be 35 Pa as compared to 145 Pa. The simulations also agreed reasonably well with published experimental results. For the 0.6×0.6?m (24?in.×24?in.) square elbow and 0.81×0.2?m (32?in.×8?in.) rectangular elbow with vanes, the difference in pressure drop was 3.9 and 4.1% respectively and indicates that CFD models can be used for predictive purposes in this important HVAC applications area.     

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.     

Subirrigation Systems to Minimize Nitrate Leaching

Nitrate leaching from corn production systems and the subsequent contamination of ground and surface waters is a major environmental problem. In field plots 75 m long by 15 m wide, the writers tested the hypothesis that subirrigation and intercropping will reduce leaching losses from cultivated corn and minimize water pollution. Nitrate leaching under subirrigation at a depth of either 0.7 m or 0.8 m below the soil surface was compared with leaching under free drainage. The cropping systems investigated were corn (Zea mays L.) monoculture and corn intercropped with annual Italian ryegrass (Lolium multiflorum Lam. cv. Barmultra). The effects of three fertilizer application rates (0, 180, and 270 kg N ha?1) on leaching were investigated in the freely drained plots. The greatest annual loss of NO3?-N in tile drainage water (21.9 kg N ha?1) occurred in freely draining, monocropped plots fertilized with 270 kg N ha?1. Monocropped plots fertilized with 270 kg N ha?1, with subirrigation at 0.7 m depth, resulted in annual nitrate losses into tile drainage of 6.6 kg N ha?1, 70% less than under free drainage. Annual soil denitrification rates (60 kg N ha?1) with subirrigation at 0.7 m were about three-fold greater than under free drainage. Intercropping under free drainage resulted in a 50% reduction in tile drainage loss of NO3?-N compared with monocropping. Off-season (November 1, 1993, to May 31, 1994) tile drainage losses of NO3?-N (7.8 kg N ha?1) from freely draining monocropped plots accounted for 30% of the annual tile drainage losses.     

Study of Variation of Saturated Hydraulic Conductivity with Time

The variation of the saturated hydraulic conductivity with time, as a function of temperature, has been studied involving field measurement at the College of Aboureyhan Research farm. The College of Aboureyhan is a part of the University of Tehran and the above-mentioned farm is located in the lowland of the southeast of Tehran, Iran. For the purposes of this research study it was planned to measure and record the field data in a plot of 18?m2. The hydraulic conductivity data were measured in 18 test points inside the study area using the inverse auger-hole method. Experiments were carried out from August 16, 2005 to June 14, 2006. The recorded filed data were then used to calculate the saturated hydraulic conductivity data using Excel software. The relationship between soil temperature, water temperature, and also water’s viscosity with hydraulic conductivity, respectively, were determined. The results of the statistical analysis involving SAS software demonstrated that the variation of temperature can considerably affect the saturated hydraulic conductivity values. The results showed that the lowest values of Ks were obtained in the winter when the water, soil, and air temperature were minimal and these values increased when the temperature increased. The effect of the means of daily K values (values measured in each sample date Kd) and their corresponding soil temperature adjusted values on drain spacing was determined compared with the average of total K values.?The maximum over- and underestimation of drain spacing was 19.1 and 23.3%, respectively, for measured values. These estimations were 9 and 16% for adjusted ones. Also, using the average values of K measured in the soil temperature range of 17–23°C resulted in a lower over- or underestimation of drain spacing.     

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.     

Interactive Effects of Controlled Drainage and Riparian Buffers on Shallow Groundwater Quality

As a result of recent surface water quality problems in North Carolina, riparian buffers and controlled drainage are being used to reduce the loss of nonpoint source nitrogen from agricultural fields. The effect of controlled drainage and riparian buffers as best management practices to reduce the loss of agricultural nonpoint source nitrogen from the middle coastal plain has not been well documented. The middle coastal plain is characterized by intensive agriculture on sandy soils with deeply incised or channelized streams. A 2-year study was conducted to determine the effectiveness of controlled drainage, riparian buffers, and a combination of both in the middle coastal plain of North Carolina. It was hypothesized that raising the water table near the ditch would enhance nitrate-nitrogen reduction through denitrification. On the sandy soils studied, controlled drainage did not effectively raise the water table near the ditch to a greater degree than observed on the free drainage treatment. Due to random treatment location, the free drainage treatment was installed along a ditch with a shallower impermeable layer compared to the impermeable layer on the controlled drainage treatments (2 m versus 3- to 4-m deep). This resulted in a perched or higher water table on the free drainage treatment. Over 17 storm events, the riparian buffer (free drainage) treatment had an average groundwater table depth of 0.92 m compared to 0.96 and 1.45 m for the combination (riparian buffer and controlled drainage) and controlled drainage treatments, respectively. Nitrate concentration decrease between the field wells and ditch edge wells averaged 29% (buffer only), 63% (buffer and controlled drainage), and 73% (controlled drainage only). Although apparently more nitrate was removed from the groundwater on the controlled drainage treatments, the controlled drainage treatment water table near the ditch was not raised closer to the ground surface compared to the free drainage treatment. Nitrate removal effectiveness was attributed to local soil and landscape properties, such as denitrification in deeper reduced zones of the soil profile.     

Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.