Initial Water Table Research Articles

Modelling of shallow water table dynamics using conceptual and physically based integrated surface-water–groundwater hydrologic models

Abstract. We present a new conceptual scheme of the interaction between unsaturated and saturated zones of the MOBIDIC (MOdello Bilancio Idrologico DIstributo e Continuo) hydrological model which is applicable to shallow water table conditions. First, MODFLOW was coupled to MOBIDIC as the physically based alternative to the conceptual groundwater component of the MOBIDIC–MODFLOW. Then, assuming a hydrostatic equilibrium moisture profile in the unsaturated zone, a dynamic specific yield that is dependent on the water table level was added to MOBIDIC–MODFLOW, and calculation of the groundwater recharge in MOBIDIC was revisited using a power-type equation based on the infiltration rate, soil moisture deficit, and a calibration parameter linked to the initial water table depth, soil type, and rainfall intensity. Using the water table fluctuation (WTF) method for a homogeneous soil column, the parameter of the proposed groundwater recharge equation was determined for four soil types, i.e. sand, loamy sand, sandy loam, and loam under a pulse of rain with different intensities. The fidelity of the introduced modifications in MOBIDIC–MODFLOW was assessed by comparison of the simulated water tables against those of MIKE SHE, a physically based integrated hydrological modelling system simulating surface and groundwater flow, in two numerical experiments: a two-dimensional case of a hypothetical watershed in a vertical plane (constant slope) under a 1 cm d−1 uniform rainfall rate and a quasi-real three-dimensional watershed under 1 month of a measured daily rainfall hyetograph. The comparative analysis confirmed that the simplified approach can mimic simple and complex groundwater systems with an acceptable level of accuracy. In addition, the computational efficiency of the proposed approach (MIKE SHE took 180 times longer to solve the three-dimensional case than the MOBIDIC–MODFLOW framework) demonstrates its applicability to real catchment case studies.

Multi-year net ecosystem carbon balance of a restored peatland reveals a return to carbon sink.

Peatlands after drainage and extraction are large sources of carbon (C) to the atmosphere. Restoration, through re-wetting and revegetation, aims to return the C sink function by re-establishing conditions similar to that of an undrained peatland. However, the time needed to re-establish C sequestration is not well constrained due to the lack of multi-year measurements. We measured over 3years the net ecosystem exchange of CO2 (NEE), methane ( ), and dissolved organic carbon (DOC) at a restored post-extraction peatland (RES) in southeast Canada (restored 14years prior to the start of the study) and compared our observations to the C balance of an intact reference peatland (REF) that has a long-term continuous flux record and is in the same climate zone. Small but significant differences in winter respiration driven by temperature were mainly responsible for differences in cumulative NEE between years. Low growing season inter-annual variability was linked to constancy of the initial spring water table position, controlled by the blocked drainage ditches and the presence of water storage structures (bunds and pools). Half-hour at RES was small except when Typha latifolia-invaded drainage ditches were in the tower footprint; this effect at the ecosystem level was small as ditches represent a minor fraction of RES. The restored peatland was an annual sink for CO2 (-90±18gCm-2 year-1 ), a source of CH4 (4.4±0.2gCm-2 year-1 ), and a source of DOC (6.9±2.2gCm-2 year-1 ), resulting in mean net ecosystem uptake of 78±17gCm-2 year-1 . Annual NEE at RES was most similar to wetter, more productive years at REF. Integrating structures to increase water retention, alongside re-establishing key species, have been effective at re-establishing the net C sink rate to that of an intact peatland.

Probabilistic Study of Rainfall-Triggered Instabilities in Randomly Heterogeneous Unsaturated Finite Slopes

Water infiltration destabilises unsaturated soil slopes by reducing matric suction, which produces a decrease of material cohesion. If the porosity of the soil is spatially heterogeneous, a degree of uncertainty is added to the problem as water tends to follow preferential paths and produces an irregular spatial distribution of suction. This study employs the finite element method together with Monte Carlo simulations to quantify the effect of random porosity on the uncertainty of both the factor of safety and failure size of an unsaturated finite slope during and after a rainfall event. The random porosity is modelled using a univariate random field. Results show that, under partially saturated conditions, the random heterogeneity leads to a complex statistical variation of both factor of safety and failure size during the rainfall event. At any given time, the uncertainty about failure size is directly linked to the uncertainty about the position of the wetting front generated by infiltration. Interestingly, the statistical mean of the failed area is smallest when the mean of the factor of safety is lowest. In other words, the slope becomes more likely to fail, but the size of the failure mass tends to be limited. The study also investigates the sensitivity of failure uncertainty to external hydraulic parameters (i.e. initial water table depth, rainfall intensity) and internal soil parameters (i.e. permeability and water retention characteristics). In general, the sensitivity increases when the effect of these parameters on the spatial variation of suction is stronger.

Numerical modelling of hydro-mechanical behaviour of ground settlement due to rising water table in loess

The numerical simulation of collapsible settlement in loess soil subjected to rising ground water table is presented in this paper. A coupled hydro-mechanical model is proposed. Comparisons between the results of numerical simulations and those of oedometer and in situ water immersion field test in Lanzhou, northwest China, reveal good agreement, which validates the proposed model formulation. Factors that influence the ground settlement of loess including initial elevation of ground water table, rising water height and velocity are then evaluated. The results of the analyses reveal that the most critical situation of largest possible ground settlement due to ground water rising in loess involves initial water table elevation of 10 m and rising water velocity of 0.5 m/year. Two upper bound lines of predicted maximum possible ground settlement are proposed to facilitate a preliminary quick evaluation of ground settlement due to rising water under different water table scenarios in loess.

Peat depth as a control on moss water availability under evaporative stress

AbstractNorthern peatlands are a vital component of the global carbon cycle, containing large stores of soil organic carbon and acting as a long‐term carbon sink. Moss productivity is an important factor in determining whether these wetlands will retain this function under future climatic conditions. Research on unsaturated water flow in peatlands, which controls moss productivity during periods of evaporative stress, has focused on relatively deep bog systems. However, shallower peatlands and marginal connective wetlands can be essential components of many landscape mosaics. In order to better understand factors influencing moss productivity, water balance simulations using HYDRUS‐1D were run for different soil profile depths, compositions, and antecedent moisture conditions. Our results demonstrate a bimodal distribution of peatland realizations, either primarily conserving water by limiting evapotranspiration or maximizing moss productivity. For sustained periods of evaporative stress, both deep water storage and a shallow initial water table delay the onset of high vegetative stress, thus maximizing moss productivity. A total depth of sand and peat of 0.8 m is identified as the threshold above which increasing peat depth has no effect on changing vegetative stress response. In contrast, wetlands with shallow peat deposits (less than 0.5 m thick) are least able to buffer prolonged periods of evaporation due to limited labile water storage and will thus quickly experience vegetative stress and so limit evaporation and conserve water. With a predicted increase in the frequency and size of rain events in continental North America, the moss productivity of shallow wetland systems may increase, but also greater moisture availability will increase the likelihood they remain as wetlands in a changing climate.

Field and numerical experiment of an improved subsurface drainage system in Huaibei plain

New requirements are put forward for agricultural drainage system due to frequent floods and cultivated land shortage in Huaibei plain, China. The improved subsurface drainage is a more efficient drainage system by laying high permeability materials as filter above the drains based on conventional subsurface drainage whose function is limited by soil hydraulic conductivity. Field experiments was used to evaluate the performance of the improved subsurface drainage preliminarily and numerical experiments was used to explore the capacity of the improved subsurface drainage deeply. Based on calibration and validation by field experiment data, HYDRUS model was used to evaluate the impacts of design parameters of filter hydraulic conductivity, filter width and height, drain spacing and depth on improved subsurface drainage discharge with constant ponding depth. Then, water table depths at different distances from the pipe drain for improved and conventional subsurface drainage were simulated under initial conditions of saturated soil and no surface ponding. Besides, the daily water balance under improved subsurface drainage had been also studied. The result of field experiment showed that the discharge of improved subsurface drainage was about 1.9 times of the conventional subsurface drainage discharge under conditions of same surface ponding depths. The results of numerical experiments indicated that the improved subsurface drainage had a real-time drainage function for the reason that cumulative outflow increased by about 87% than conventional subsurface drainage within 12h after beginning draining. The improved subsurface drainage lowered water table to an appropriate depth faster than conventional ones, which could provide a more favourable soil moisture condition for crop growth. Furthermore, through daily water balance analysis of improved and conventional subsurface drainage with different rainfalls and initial water table depths, the results showed that subsurface drainage could reduce surface runoff effectively, especially for improved subsurface drainage. Good drainability of the improved subsurface drainage was beneficial to decrease the amount of soil water storage after rainfall and helpful to shorten subsequent draining time of water table drawdown. The research results could provide scientific basis for improved subsurface drainage design and lay a good foundation for its application. Meanwhile, it would be beneficial to enrich agricultural drainage technologies and promote development of agricultural drainage in China.

ASSESSMENT OF WATER TABLE MODEL ON OIL PALM AREA IN A HILLY LAND

The aim of this research is to assess performance of developed water table model on oil palm area in a hilly land. The model requires some data of initiatial condition, input model, and physical parameters of the soils and crops. Initial data includes leaf area index, latitude geography position, initial water table, and the deep of impermeable soil layer. Input model includes daily weather data (rainfall, temperature, solar radiation, and wind speed). Soil physic parameters includes bulk volum density at each soil layers, and run-off of the soil surface. The crop parameters includes rainfall interception of crown and stem plants. Daily water table measurement was carried out at 3 points of wells located in one line hilly catena (30 – 70 m above sea level) with slope about of 15% (top, middle, and foot). The area was the 20 years old oil palm planting area, soil type was Typic Hapludult with coarse to fine soil texture, hydraulic conductivity was classified as fast. The water table in this area was located in unconfined aquifer zone. The results showed that outputs of the model were 3 - 4% higher than the actual values observed on the top hill, 7 – 8% lower than the actual values on the middle sloping of the hill, and 7 – 7.5% lower than the actual values on the foot hill. The high rate of run-off at the top might have reduced the water inflow (through infiltration process) to the system, causing output values of the model were higher than the actual values. On the other hand, the water inflow from the top to the lower area might have increased the water inflow to the system, so that the actual values were higher than the output values of the water table model. Adjustments of parameters mainly run-off rate and hydraulic potential gradient on sloping and hilly physiography might increase the accuracy of the model.

ASSESSMENT OF WATER TABLE MODEL ON OIL PALM AREA IN A HILLY LAND

The aim of this research is to assess performance of developed water table model on oil palm area in a hilly land. The model requires some data of initiatial condition, input model, and physical parameters of the soils and crops. Initial data includes leaf area index, latitude geography position, initial water table, and the deep of impermeable soil layer. Input model includes daily weather data (rainfall, temperature, solar radiation, and wind speed). Soil physic parameters includes bulk volum density at each soil layers, and run-off of the soil surface. The crop parameters includes rainfall interception of crown and stem plants. Daily water table measurement was carried out at 3 points of wells located in one line hilly catena (30 – 70 m above sea level) with slope about of 15% (top, middle, and foot). The area was the 20 years old oil palm planting area, soil type was Typic Hapludult with coarse to fine soil texture, hydraulic conductivity was classified as fast. The water table in this area was located in unconfined aquifer zone. The results showed that outputs of the model were 3 - 4% higher than the actual values observed on the top hill, 7 – 8% lower than the actual values on the middle sloping of the hill, and 7 – 7.5% lower than the actual values on the foot hill. The high rate of run-off at the top might have reduced the water inflow (through infiltration process) to the system, causing output values of the model were higher than the actual values. On the other hand, the water inflow from the top to the lower area might have increased the water inflow to the system, so that the actual values were higher than the output values of the water table model. Adjustments of parameters mainly run-off rate and hydraulic potential gradient on sloping and hilly physiography might increase the accuracy of the model.

Deriving Effective Soil Water Retention Characteristics from Shallow Water Table Fluctuations in Peatlands

Core Ideas This is a new approach for determining in situ peat soil water retention characteristics. It only requires data on water table changes, precipitation, and microrelief. Water table rises are used to invert for water retention parameters. Applicability is demonstrated for field data from a peatland. This approach should be applicable to other shallow groundwater systems.We have developed a novel and simple approach that can be used to derive effective in situ soil water retention characteristics from field monitoring time series in peatlands. The simplicity of the approach is given by the very limited data requirements, which comprise only precipitation, water table, and, if relevant, microrelief data. Our approach is built on two main assumptions: (i) for shallow groundwater systems, the soil moisture profile is always close to hydrostatic equilibrium; and (ii) during short time periods of high precipitation, the water storage change due to lateral fluxes is small compared with the precipitation input. Given these assumptions, the height of a water table rise due to a precipitation event mainly depends on the soil water retention characteristics, the precipitation amount, the initial water table depth, and, if present, the microrelief. In this study, this dependency was used to determine the effective van Genuchten parameters by Bayesian inversion assuming a uniform soil profile. We applied our concept to field data from a peatland with microrelief. Results indicated that observations of water table rises caused by precipitation events can contain sufficient information to constrain the soil water retention characteristics around monitoring wells in peatlands to plausible ranges. In principle, the approach should also be applicable to other shallow groundwater systems. Application limits and potential systematic errors are discussed.

Quantifying peat carbon accumulation in Alaska using a process‐based biogeochemistry model

AbstractThis study uses an integrated modeling framework that couples the dynamics of hydrology, soil thermal regime, and ecosystem carbon and nitrogen to quantify the long‐term peat carbon accumulation in Alaska during the Holocene. Modeled hydrology, soil thermal regime, carbon pools and fluxes, and methane emissions are evaluated using observation data at several peatland sites in Minnesota, Alaska, and Canada. The model is then applied for a 10,000 year (15 ka to 5 ka; 1 ka = 1000 cal years before present) simulation at four peatland sites. We find that model simulations match the observed carbon accumulation rates at fen sites during the Holocene (R2 = 0.88, 0.87, 0.38, and −0.05 using comparisons in 500 year bins). The simulated (2.04 m) and observed peat depths (on average 1.98 m) were also compared well (R2 = 0.91). The early Holocene carbon accumulation rates, especially during the Holocene thermal maximum (HTM) (35.9 g C m− 2 yr− 1), are estimated up to 6 times higher than the rest of the Holocene (6.5 g C m− 2 yr− 1). Our analysis suggests that high summer temperature and the lengthened growing season resulted from the elevated insolation seasonality, along with wetter‐than‐before conditions might be major factors causing the rapid carbon accumulation in Alaska during the HTM. Our sensitivity tests indicate that, apart from climate, initial water table depth and vegetation canopy are major drivers to the estimated peat carbon accumulation. When the modeling framework is evaluated for various peatland types in the Arctic, it can quantify peatland carbon accumulation at regional scales.

Models and influencing factors of the delay phenomenon for rainfall on slope stability

The effect of rainfall on the slope may continue and the most unstable state may occur after the rainfall has stopped. This phenomenon can be described as the delay phenomenon. This paper reports on the models and influencing factors of the delay phenomenon using numerical methods. Two representative models of landslides occurring after rainfall were set up to illustrate the mechanisms of the delay phenomenon. Parametric studies were made to quantify the impact of soil types, the depth of initial water table, anisotropic conductivity, rainfall intensity and rainfall pattern on the delay phenomenon. The results indicated that slope soils with slightly smaller water-entry value and slower permeation rate of rainwater have a higher probability of generating the delay phenomenon. The most noticeable delay phenomenon was observed when the anisotropy ratio ky/kx = 0.5 and the saturated hydraulic conductivity of soil have similar value with rainfall intensity. Besides, the delay phenomena were the most likely to occur when rainfall intensity peak was near to the time when rainfall stopped.

The effects of rainfall on the stability of soil slopes in Khanh Vinh district, Khanh Hoa province

This study presents a procedure for calculating the change of the safety factor for unsaturated slopes of homogenous, residual soils suffering from rainfall infiltration within Khanh Vinh district, Khanh Hòa province. Rainfall is supposed as a main trigger caused failure of the potential sliding slopes. Rainwater into the slope due to infiltration caused an increase in moisture content and negative pore water pressure; a decrease in matric suction and in shear strength on the failure surface. Thus, slopes are reduced stability and can be failed. Soil permeability and rainfall intensity were found to be the primary factors controlling the instability of slopes due to rainfall, while the initial water table location and slope geometry only played a secondary role. A numerical model of analysis coupled seepage-stability used to simulate the seepage and slope stability under conditions of specific environment such as soil permeability, rainfall intensity, water table location and slope geometry in the study area. The relationships between safety factor and rainfall intensity, soil permeability, angle slope, high slope were identified to provide a good indication for the management of landslide hazards under the effects of rainfall.

Influence of lowland forests on subsurface salt accumulation in shallow groundwater areas.

In flat sedimentary plains in areas with a sub-humid climate, tree planting on grasslands and arable lands creates strong hydrological shifts. As a result of deep rooting and high water uptake of trees, groundwater levels drop and subsurface salt accumulation increases. Tree planting has expanded globally and in Hungary it reached rates of 15 000 ha year(-1), being focused mainly in the Great Hungarian Plain where forests replace grasslands and crops in a region with widespread shallow groundwater. We performed soil and groundwater observations in 31 pairs of forest and control plots in the region, including gradients of initial water table depth and salinity, soil layering, and tree species and age. Accumulated tree biomass was positively correlated with soil salinization rates following tree planting, being also affected by species (poplar > common oak > black locust) and stand age. Differences among tree species effects appeared to be related to their growth rates. Due to downward deep percolation and salt leaching episodes during the Hungarian winters, the observed salt accumulation rates were lower than those described under similar settings in the warmer Argentine Pampas.

Methane Flux Influenced by Experimental Water Table Drawdown and Soil Warming in a Dry Boreal Continental Bog

To quantify the effects of water table drawdown and soil warming on CH4 fluxes, we used a static chamber technique during the growing seasons (May–October) of 2011–2013 at hollow and hummock microforms at three sites of a continental bog near the town of Wandering River, Alberta, Canada: (1) Control, (2) Experimental drained, and (3) old Drained. To simulate climatic warming, we used open top chambers to passively warm half of the hollows and half of the hummocks at each of the water level treatment sites. Water table drawdown significantly reduced CH4 flux by 50% in 3 years and 76% in 13 years of drainage. The hollows showed greater reduction of efflux as compared to hummocks. A persistent functional relationship of CH4 flux with water level was found across all sites in all years. The relationship revealed that the contribution of change in vegetation type at hollows and hummocks to CH4 production and emission was relatively less important than that of the water level. Hummocks and hollows responded to warming differently. At the control, experimental and drained sites, warming increased flux at hollows by 16, 21 and 26%, and reduced flux at hummocks by 4, 37, and 56%, respectively. The combined effect of lowered water table and warming on CH4 emission was overall negative, although the interaction between the two contributing factors was not significant. Therefore, whereas climatic warming and subsequent lowering of water table are expected to reduce CH4 efflux from dry ombrotrophic bogs of Alberta, different microforms at these bogs may respond differently with accelerated emissions at warmed, wetter (hollows) and reduced emissions at warmed, drier (hummocks) microforms. Overall, CH4 efflux from Alberta’s dry continental bogs that are not underlain by permafrost might be affected only slightly by the direct effect of predicted climate warming, although initial water table position will be an important control on the overall response.

Space–time prediction of rainfall-induced shallow landslides through a combined probabilistic/deterministic approach, optimized for initial water table conditions

In landslide-prone areas the magnitude of events is related to recurring rainfall intensity. In a large sector of the Sannio Apennines (Southern Italy), predictive mapping of recurrent shallow landslides was undertaken by combining deterministic and probabilistic predictive approaches. This, with the aim to minimize the negative influence of the uniform distribution of the initial water table depth in steady condition that usually influence the theoretical instability resulting from the application of methods for large-scale estimation. The deterministic approach was performed by means of the Transient Rainfall Infiltration and Grid-based Regional Slope-stability model to obtain triggering maps in multi-temporal transient pore-water pressures. The optimized physical modeling was validated by back-analysis on large-magnitude landslide events which occurred in 2003 by means of the introduction of two cross-mapping correlation indexes. Subsequently, different predictive scenarios were proposed for different probabilistic return periods of the rainstorm events. The output data permitted the definition of a linear log regression curve to estimate the theoretical instability of the study area. This curve is defined as a function of cumulative precipitation, duration and return periods of the possible rainfall events.

Air and water flows induced by pumping tests in unconfined aquifers with low‐permeability zones

AbstractAir flows from the atmosphere into an unconfined aquifer when the water table falls during pumping tests. Pumping test results in unconfined aquifers may be significantly affected by low‐permeability zones (LPZs) near the initial water table position, because they restrict the downward movement of air. A transient, three‐dimensional air–water two‐phase flow model is employed to investigate numerically the effects of local heterogeneity on pumping test results in unconfined aquifers. Two cases of local heterogeneities are considered herein: a LPZ around the pumping well and on one side of the pumping well. Results show that the drawdown with the LPZ is significantly greater than that of the homogeneous aquifer. The differences in drawdown are the most significant at intermediate times and gradually diminish at later times. The LPZ significantly reduces air flow from the atmosphere to the aquifer. The pore air velocity in the LPZ is very low. The air pressure at the observation point under the LPZ when air begins to enter is significantly lower than the air pressure of the homogeneous aquifer at the same point. After that, the air pressure increases quickly and then increases slowly. The time for the air pressure to reach the atmospheric pressure is significantly longer. Copyright © 2013 John Wiley & Sons, Ltd.

Factors affecting the measurement of the vertical hydraulic conductivity of a streambed sediment using standpipe tests

AbstractThe vertical hydraulic conductivity (Kv) of a stream or lake sediment is often determined in the field using standpipe tests. Calculation of Kv is based on the assumption that the hydraulic head in the pipe is equal to that of the stream or lake stage. In this work, a modified equation for Kv is developed for the standpipe test which is applicable when this assumption is not valid. The equation involves not only the hydraulic head at different times but also the difference in the hydraulic head (a) between the groundwater level and river stage. The effects of certain factors on Kv, such as the ratio of the hydraulic head at different times (h1/h2), the difference a, and the initial water table height (h0), are also discussed. The results show that when h1/h2 is constant, the relative error (Er) in Kv increases with the ratio a/h2. Furthermore, if a/h2 < 0.05, then for any value of h1/h2, Er is less than 5% using the modified equation. Also, if a/h2 is large, hydraulic head readings with larger h1/h2 ratios must be used to avoid large Er values. The results of a field test also indicate that the error in Kv decreases as the value of h0 increases. Copyright © 2013 John Wiley & Sons, Ltd.

An innovative method for dynamic update of initial water table in XXT model based on neural network technique

The initial subsurface flow of whole basin plays a quite important role in daily rainfall–runoff simulation. However, general physically based rainfall–runoff model, such as the XXT model (a hybrid model of TOPographic MODEL and the Xinanjiang model), is difficult to catch the non-linear factors and take full advantages of previous information of rainfall and runoff that is essential to the initial watershed average saturation deficit of each time step. In order to address the issue, this study selected the initial subsurface flow for the whole time series of the XXT model as the breakthrough point, and used the observed runoff and rainfall data of two days before the present day as the inputs of artificial neural network (ANN) and initial subsurface flow of the present day as the output, then integrated ANN into runoff generation module of XXT model and finally tested the integrated model for daily runoff simulation in large-scale and semi-arid Linyi watershed, eastern China. In addition, this work employ particle swarm optimization (PSO) algorithm to seek the best combination of 6 physical parameters in XXT and a great number of weights in ANN to avoid the local optimization. The results show that the integrated model performs much better than XXT in terms of Nash–Sutcliffe efficiency coefficient (NE) and root mean square error (RMSE). Hence, the new integrating approach proposed here is promising for daily rainfall–runoff modeling and can be easily extended to other process-based models.

Air and water flows in a large sand box with a two-layer aquifer system

The pumping of water from a sand box with a finer layer on the top was studied theoretically and experimentally. The sand box, saturated at its lower portion and initially in hydrostatic equilibrium, was pumped at constant rate. The results show that significant negative air pressure can be generated in the vadose zone during pumping. The negative air pressure increases quickly in the earlier stage of pumping, reaches a maximum, and then gradually becomes zero. The initial water-table depth has a significant effect on the generated negative air pressure. The shallower the initial water table, the larger the vacuum, and the longer the time to reach the maximum vacuum. A transient, three-dimensional model was constructed using TOUGH2-MP to simulate the air-water two-phase flow processes in the sand box. The reasonable match between the numerical solutions and the experimental data indicates that the numerical model can reproduce the dynamic process of air and water flows. The study has implications in pumping test analyses. If the air pressure in the two-layer system is ignored, the drawdown in the system will be underestimated, especially when the upper layer has low permeability and the initial water table is close to the interface of the two layers.

Redistribution of groundwater evapotranspiration and water table around a well field in an unconfined aquifer: A simplified analytical model

Summary Groundwater evapotranspiration (GE) is an essential component for regional water balance in areas with shallow water table. When the depth to water table (DWT) falls due to pumping in a well field, GE will decrease, which also influence the redistribution of water table. A mathematical model of steady radial flow is developed to investigate the problem. The well field is simplified by a circular area with uniformly distributed pumpage. Relationship between GE and DWT is described with a commonly used linear formula when DWT is less than an extinction depth. Analytical solutions for three cases with or without a zero-GE zone (no GE occurs in the zone) are obtained. The redistributions of GE and water table are controlled by three lumped parameters. The analytical model is applied in a case study of the Ordos well field in China, with 55 pumping wells. It sufficiently agrees with a numerical model based on MODFLOW except in the vicinity of individual wells where cones of water table falling appear. The result of GE is not influenced by the discrepancy in water table due to existing of the zero-GE zone. Runge–Kutta solutions of using nonlinear GE formulas are presented and also applied in the case study to compare with the analytical model. They predict almost the same water table distribution and similar redistribution patterns of GE. The analytical model can be applied to determine the protection zone of well fields located in places without strong heterogeneous in topography and initial water table.