A semi‐analytical model for solute transport in layered dual‐porosity media

The vulnerability of groundwater from chemical leaching through soil is a concern at some locations. Because measurements are laborious, time‐consuming, and expensive, simulation models are frequently used to assess leaching risks. But the significance of simulated solute movement through a layered soil is questionable if vertical homogeneity of physical soil properties has been assumed. In the present study, a semi‐analytical model for solute leaching in soils is presented. The model is relatively simple, but it does account for soil layers having different physical properties. The model includes the mobile‐immobile model (MIM) to describe one‐dimensional (1‐D) nonequilibrium, transient solute transport under steady‐state flow conditions. The MIM is rewritten as a second‐order differential equation and solved by a numerical scheme. Differing from fully analytical or fully numerical solutions, the new approach solves the differential equation numerically with respect to time and analytically with respect to distance. Numerical experiments for a single layered soil profile show that the semi‐analytical solution (SA‐MIM) is numerically stable for a wide range of parameter values. The accuracy of SA‐MIM predictions is comparable to that of analytical solutions. Numerical experiments for a multilayered profile indicate that the model correctly predicts effluent curves from finite layered soil profiles under steady‐state flow conditions. The SA‐MIM simulations with typical parameter values suggest that neglecting vertical heterogeneity of flow paths in a layered soil can lead to inaccurate prediction of soil‐solute leaching. The quality of predictions is generally improved if parameter estimates for the different soil layers are considered. However, the mobile‐immobile‐parameter estimates obtained in a number of previous studies may not be transferable to a field situation that is characterized by a slow and steady flow of water. Further field experiments to determine mobile‐immobile parameters under such conditions are desirable.     

Two models for the leaching of a non-reactive solute to a mole drain

Two models of solute leaching to a mole-pipe drainage system are described. The first model is research-oriented. It simplifies two-dimensional water and solute flow to a mole drain by dividing the soil between the mid-mole plane and the mole into notional compartments. Solute movement between compartments is assumed to occur by convection and mechanical dispersion. Within each compartment a mobile and immobile solute phase is defined, with diffusion occurring between them. Rainfall intensity (over approximately hourly intervals) and basic soil hydraulic data are needed as inputs. An explicit finite-difference solution to the water and solute mass-balance and flux equations is used. The second simpler model is management-oriented. It uses daily time steps, and assumes the soil solution behaves as if it were well-mixed system. It requires only daily rainfall and evaporation data, the drainage coefficient of the mole-pipe system, and the soil macroporosity as inputs. In both models a source/sink term accounts for additions of solute in rainfall and fertilizer, and extraction by plant uptake. The models were used to simulate leaching losses of chloride to a mole-pipe drainage system in a silt loam under pasture, following the application of potassium chloride to the soil surface. The first model simulated leaching better immediately after ertilizer application, and during bypass flow induced by heavy rain. However, both models were able to simulate the measured losses over a 2-year period equally well.     

Simulation of solute leaching in soils of differing permeabilities

Abstract. The model described divides the soil into layers and considers two categories of water, mobile and immobile, in each layer. It has two main parameters, one a measure of the soil's capacity to hold water and thence to retain solutes against leaching, and the other a measure of the ease with which water can pass through the soil and carry solutes with it. These are, in effect, capacity and rate parameters, and the model is unusual in having both. They can be estimated from the percentages of clay and other soil components. The rate parameter varied appreciably between plots in the field but in a consistent manner. The model has been validated against field experiments following the vertical movement of solute applied to the soil surface and allowed to leach, and the paper includes one such test.     

土壤溶质迁移的指数函数模型

边界层方法是描述土壤溶质迁移的简单方法,通过边界层距离与时间的关系可以估计溶质迁移参数。基于边界层方法,研究了土壤溶质迁移的数学模拟及相应参数估计问题。假定土壤溶质浓度剖面为指数函数,得到了描述溶质浓度分布的指数函数模型。各参数对边界层距离的影响分析表明,应选取较小的孔隙水流速度、短历时推求土壤溶质迁移参数;对不同模型预测土壤溶质分布进行比较,结果表明,在短距离处指数型解与精确解的误差比其它都要小。误差分析表明了指数函数模型的有效性和实用性。     

土壤溶质锋运移的解析解

为了推求土壤溶质锋运移与时间的关系 ,假设土壤溶质运移发生在溶质输入内边界至溶质锋之间 ,应用拉普拉斯变换方法求解输入内边界到溶质锋边界的对流—弥散方程 ( CDE)。溶质锋浓度解与半无限精确解的比较表明 ,在内边界至溶质锋边界内具有良好的一致性。溶质锋运移解的一个重要应用是估计实验室和田间条件的溶质运移参数。这个新的参数估计方法要求土壤中溶质锋随时间运移数据。如果应用有色示踪剂 ,溶质锋运移可以目测 ;如果应用其他示踪剂 ,可以通过 TDR或其它仪器测量示踪剂通量或体积浓度 ,确定溶质锋的深度。这个新的方法简单易行、节省时间 ,而且能够应用到实验和田间条件。     

区域农田土壤质地剖面的随机模拟模型

冲积土壤剖面的质地层次分层是该类土壤的重要特性,对农田水分转化和溶质运移具有重要影响。本文论据已取得的研究结果,采用Ｍａｒｋｏｖ链理论提出了区域冲积土壤质地层次的随机模拟模型－ＭＣ模型和ＭＣ－ＬＮ模型,采用蒙特卡罗方法模拟了研究区的土壤质地剖面,并与实测结果进行了对比。     

塿土水分入渗、再分布过程反应性溶质(NH_4~ )运移特征研究

利用土柱切割法研究（土娄）土水分入渗、再分布过程反应性溶质（NH4 ）运移特征。在水分入渗初期,土壤剖面溶质分布曲线为斜线,随入渗时间延长,土壤剖面溶质分布曲线上部逐渐出现垂直于横坐标的垂直线段。与水分入渗、再分布相比,溶质（NH4 ）入渗、再分布明显滞后;水分入渗深度增加,水溶质入渗距离比增加,溶质入渗滞后程度增大。入渗液浓度增大,溶质入渗滞后程度及溶质入渗阻滞因子减小,相应的土壤吸持溶质的反应速率常数增大,表观活化自由能减小。不同再分布时间的土壤剖面溶质分布曲线具有交点（溶质再分布等浓度点）,且该交点随入渗液浓度增大而加深。水分再分布过程中,溶质再分布等浓度点的土壤溶质吸持量基本不变,而其上部的土壤吸持量减小,下部的土壤吸持量增大。     

(土娄)土水分入渗、再分布过程反应性溶质(NH4+)运移特征研究

利用土柱切割法研究Lou土水分入渗、再分布过程反应性溶质（NH4^ )运移特征。在水分入渗初期，土壤剖面溶质分布曲线为斜线，随入渗时间延长，土壤剖面溶质分布曲线上部逐渐出现垂直于横坐标的垂直线段。与水分入渗、再分布相比，溶质（NH4^ )入渗、再分布明显滞后；水分入渗深度增加，水溶质入渗距离比增加，溶质入渗滞后程度增大。入渗液浓度增大，溶质入渗滞后程度及溶质入渗阻滞因子减小，相应的土壤吸持溶质的反应速率常数增大，表观活化自由能减小。不同再分布时间的土壤剖面溶质分布曲线具有交点（溶质再分布等浓度点），且该交点随入渗液浓度增大而加深。水分再分布过程中，溶质再分布等浓度点的土壤溶质吸持量基本不变，而其上部的土壤吸持量减小，下部的土壤吸持量增大。     

Estimating leaching losses from sub-surface drained soils

Abstract. Leaching losses of solutes can be calculated if two variables, the amount of water passing through the soil and the concentration of solute in that water (a flux concentration), are known. Two simple approaches, soil extraction and suction cup sampling, were used to estimate the concentration of solutes in the water moving through a silt loam soil. The results were compared with actual concentrations measured in the drainage water from a sub-surface (mole-pipe) drained soil.
Seasonal leaching losses were calculated as the sum of the products of estimated monthly drainage and the estimated average monthly solute concentration in the soil solution. These results were compared with the leaching losses measured in drainage water from the mole-pipe system. For non-reactive solutes such as bromide (an applied solute) and chloride (a resident solute), the suction cup data provided better estimates of the leaching losses than did the soil extraction data. The leaching losses calculated using volume-averaged soil solution concentrations (obtained by soil extraction) overestimated the loss for the resident solute, but under-estimated the loss for the surface-applied solute. On the other hand, the data for non-reactive solutes suggest that measurements on suction cup samples may be representative of the flux concentration of a solute during leaching. For nitrate, a biologically reactive solute, there was no clear pattern in the differences between the estimated and measured leaching losses. The flux-averaged concentration in the drainage water was about midway between those measured in the suction cup samples and in the soil solution.     

Simulation of calcium leaching and desorption in an acid forest soil

The aim of the study was to evaluate effects of mobile and immobile water and diffusion‐limited transport on the binding and release of ions in soils. The desorption and leaching of calcium in a humic layer of a densely rooted acid forest soil under a beech stand was studied in laboratory experiments by leaching soil columns with a desorption solution and recycling the leachate through the columns. Radioactive tracers were added and monitored in the leachate to evaluate desorption and leaching characteristics of the soil. Parallel experiments were conducted with chloride and calcium to determine transport and desorption parameters independently. The experimental data were then analysed with a transport model, taking into account effects of mobile and immobile soil water fractions, and in the case of calcium assuming an equilibrium Langmuir adsorption isotherm. The transport was highly dependent on the mobility of the soil water, and in particular the fraction of the soil water to which the chemical was confined as a result of ionic properties. For chloride an excluded soil water phase had to be taken into account to explain the experimental findings. Immobile or mobile water and solute transfer and transport properties were not sufficient to explain non‐equilibrium effects in the adsorption reactions. Desorption curves agreed with results from batch experiments, provided the leaching experiments were done in such a way that equilibration between the soil solution and the solid matrix adsorption sites was reached, otherwise desorption was delayed and the calculated isotherms do not represent actual equilibrium adsorption–desorption conditions.     

棉花膜下滴灌土壤水盐运移规律数值模拟

通过棉花桶栽试验,获取棉花全生育期土壤蒸发蒸腾量以及土壤含水率、含盐量变化规律。以土壤水分运动基本方程和溶质运移对流-弥散方程为基础,在考虑棉花根系吸水和土壤蒸发蒸腾条件下,对膜下滴灌棉花全生育期时段内土壤中水盐运移规律进行了数值模拟,并与实测的土壤含水率和含盐量进行了对比分析。其结果显示:土壤表层和深层的土壤含水率和含盐量模拟值与实测值均存在不同程度的偏差,而中间层土壤含水率和含盐量的模拟值较接近实测值。因此,只要能够获得足够的精确的大田实测资料,就可以将该模型应用于棉花膜下滴灌土壤水盐运移规律的实际预测。     

Simulation of Water and Chloride Transport in Field Lysimeters

In a lysimeter study in the field with soil samples of a Fluvisol the transport of chloride was monitored under high frequency irrigation. The results of this investigation were used for verification of two computer models of different complexity. One was a transient state water and solute movement model the other a simplified steady state model. It was demonstrated that both models predicted nearly equally well the chloride concentrations in the drainage water. For many practical situations, the simple model may be all that is needed to predict the downward movement of solutes in field soils.     

犁底层深度对膜下滴灌土壤水盐运移影响的模拟研究

为了探寻膜下滴灌条件下犁底层深度对土壤水盐运移的影响规律,采用室内土柱模拟试验与数值模拟相结合的方法,对不同犁底层深度（无犁底层,CK;25 cm深度,PB25;30 cm深度,PB30;35 cm深度,PB35;40 cm深度,PB40;45 cm深度,PB45）下土壤水盐运移规律进行了研究,结果表明:犁底层可以阻碍水分运移,降低水分入渗速率且有一定的阻水性,蒸发结束后PB处理表层10 ~ 20 cm土壤含水率比CK处理大;犁底层有一定的抑盐作用,CK处理上部10 ~ 20 cm土层的“洗盐”效果比PB处理好,蒸发结束后上部10 ~ 20 cm土层盐分最大的是PB30处理,最小的是PB45处理;利用HYDRUS-1D模型对膜下滴灌条件下犁底层对土壤水盐运移的变化规律进行模拟,经过实测数据验证,模拟效果较好。在现行以旋耕为主的传统耕作模式下,可根据不同作物根系吸水和耐盐的特点适度深耕打破犁底层,为作物生长创造适宜的水盐环境。研究结果可为新疆地区盐碱地改良、农业生产可持续发展提供参考。     

Modelling water flow through undisturbed soil cores using a transfer function model derived from 3HOH and Cl transport

Large undisturbed soil cores (20 cm diam. × 25–30 cm long) were irrigated at rates of 0.5–4 cm h^?1 with 0.005 M CaCl₂ solution labelled with ³HOH. The cores were used at varying initial water contents and flow in all cases was unsaturated. Breakthrough curves for Cl and ³HOH were markedly asymmetric and unlike those reported for columns of packed aggregates. The data could be satisfactorily described using a density distribution function of the logarithm of cumulative drainage D. The mean and standard deviation of In D were estimated by a curve-fitting procedure from Cl and ³HOH effluent concentrations in each core. The mean pore water velocity and fraction of the soil water that participated in solute transport (the mobile volume) were also calculated. The apparent velocity of Cl movement was always greater than that of ³HOH which suggested that the mobile volume involved in convective and diffusive transport of Cl was less than that for ³HOH. We suggest that Cl and ³HOH diffused at different rates out of flowing water films in a relatively few large conducting channels into essentially immobile water within the surrounding soil matrix. The difference in mobile volume for Cl and ³HOH was used to calculate the perimeter of voids in any horizontal cross-section of the soil through which water flowed, assuming a planar interface between the mobile and immobile water.     

考虑水迁移率动态变化改进土壤溶质地表流失模型

农田土壤溶质的地表径流流失是农业面源污染的重要组成部分,为了更加有效预测和控制农田土壤溶质的流失,该文将水迁移率考虑为随土壤侵蚀变化而变化的函数,并修改Hydrus-1D代码数值求解土壤溶质的地表径流浓度值。利用两组已经发表的试验数据对改进的模型进行校验,研究结果表明该文模拟值与观测数据的相关系数r≥0.81,残差绝对均值和均方根差与原模型的模拟值相比,分别平均减少了35.42和60.77 mg/L,该文改进的模型能更好地模拟土壤溶质的地表径流流失规律。该文的研究成果将为实际预防和控制农业面源污染提供参考。     

Modelling water and solute transport in macroporous soil. I. Model description and sensitivity analysis

A detailed mechanistic model of water movement and transport of non-reactive solute in a macroporous soil is described. One important feature of the model is that it may be run in either one or two flow domains using the same values for the hydraulic properties characterizing the soil. Water and solute movement in the micropores is calculated with the Richards and convection-dispersion equations and, in two domains, this is coupled to fluxes of water and solute in the macropores by empirical interaction terms. These interaction terms are redundant in the one-domain model, which simply reduces to the non-steady state convection-dispersion equation. A sensitivity analysis is presented showing how it is possible to identify conditions under which a macropore flow domain may need to be considered. In part II (Jarvis et al., 1991), the model is evaluated under field conditions in chloride breakthrough experiments in soil monolith lysimeters.     

Solute leaching in a sandy soil with a water-repellent surface layer: A simulation

Many sandy soils in the Netherlands have a water-repellent surface layer covering a wettable soil with a shallow groundwater table. Fingers form in the water-repellent surface layer and rapidly transport water and solutes to the wettable soil in which the streamlines diverge. Although several field observations are available, this system has not yet been studied systematically. In this paper, we present a model with a steady-state water flow to which solutes are added as a pulse. The model predicts the flow through the distribution zone and through the finger in the water-repellent surface layer with a closed form solution and transport in the wettable subsoil numerically. Model calculations show that the travel time through the water-repellent surface layer and the thickness and hydraulic conductivity of the wettable soil have the strongest effect on the arrival time of the solute pulse at groundwater level. The calculations also show that, assuming transport in the wettable subsoil to take place in fingers, the travel time is considerably shorter than when the diverging flow in the wettable soil is included.     

Salt-Water Transport in Unsaturated Soils Under Crop Planting： Dynamics and Numerical Simulation

A laboratory salt-water dynamics experiment using unsaturated soils in packed silt loam and clay soil columns with different soil texture profiles and groundwater levels under crops were conducted to study the changes of salt-water dynamics induced by water uptake of crops and to propose the theoretical basis for the regulation and control of saltwater dynamics as well as to predict salinity levels. The HYDRUS 1D model was applied to simulate the one-dimensional movement of water and salt transport in the soil columns. The results showed that the salts mainly accumulated in the plow layer in the soil columns under crops. Soil water and salt both moved towards the plow layer due to soil water absorption by the crop root system. The salt contents in the column with lower groundwater were mostly greater than those with high groundwater. The water contents in the soil columns increased from top to the bottom due to plant root water uptake. The changes in groundwater level had little influence on water content of the root zone in the soil columns with crop planting. Comparison between the simulated and the determined values showed that model simulation results were ideal, so it is practicable to do numerical simulation of soil salt and water transport by the HYDRUS 1D model. Furthermore, if the actual movement of salt and water in fields is to be described in detail, much work needs to be done. The most important thing is to refine the parameters and select precise boundary conditions.     

基于两组负水头入渗数据推求Brooks-Corey模型中的参数

非饱和土壤水分运动和溶质运移的研究需要准确的土壤水动力特性信息，然而土壤水动力特性的测定往往费时费力且较难。该研究假设土壤水力动力特性可用Brooks-Corey模型来描述，结合Darcy定理和质量守恒推导了基于两组负水头下入渗数据来估计Brooks-Corey模型参数的方法。利用负水头下一维土壤水分运动中累计入渗量和湿润峰之间的关系实现了参数的求解，大量的数值模拟数据检验了该方法，并与Wang的方法进行了比较和分析，结果表明本研究提供了一种简单而且精确的确定土壤水动力参数方法。