Comparison of numerical, analytical, and empirical models to estimate wetting patterns for surface and subsurface drip irrigation

Due to increasing competition for water resources by urban, industrial, and agricultural users, the proportion of agricultural water use is gradually decreasing. To maintain or increase agricultural production, new irrigation systems, such as surface or subsurface drip irrigation systems, will need to provide higher water use efficiency than those traditionally used. Several models have been developed to predict the dimensions of wetting patterns, which are important to design optimal drip irrigation system, using variables such as the emitter discharge, the volume of applied water, and the soil hydraulic properties. In this work, we evaluated the accuracy of several approaches used to estimate wetting zone dimensions by comparing their predictions with field and laboratory data, including the numerical HYDRUS-2D model, the analytical WetUp software, and selected empirical models. The soil hydraulic parameters for the HYDRUS-2D simulations were estimated using either Rosetta for the laboratory experiments and inverse analysis for the field experiments. The mean absolute error (MAE) was used to compare the model predictions and observations of wetting zone dimensions. MAE for different experiments and directions varied from 0.87 to 10.43 cm for HYDRUS-2D, from 1 to 58.1 cm for WetUp, and from 1.34 to 12.24 cm for other empirical models.     

果树蓄水坑灌法单坑水分入渗数值模拟及分析

根据果树生理特性与土壤水动力学理论，建立了非恒定水位复杂边界条件下的蓄水单坑均质土入渗及土壤水分运动的数学模型，并采用交替方向隐式差分法进行求解。其模拟结果与实测结果吻合较好，表明利用该方法模拟蓄水单坑的水分入渗问题是可行的。用本模型模拟了不同条件下的入渗过程，并对入渗规律的影响因素进行了分析，为蓄水坑灌理论与灌水技术要素的深入研究做了一些基础性的工作。     

The soil water balance of rainfed and irrigated oats,Italian rye grass and rye using the CropSyst model

Crop growth models have been used in simulating the soil water balance for purposes of irrigation management and yield predictions. The application of CropSyst, a cropping systems simulation model, was evaluated for Cedara, South Africa. Simulations included soil water balance of fallow land and rainfed and irrigated winter crops [oats (Avena sativa), Italian ryegrass (Lolium multiflorum) and rye (Secale cereale)]; and irrigation scheduling of the winter crops. Soil, plant, weather and management inputs were used for the soil water balance simulations. Model crop parameters were used from past experiments or obtained from model documentation, with a slight modification to account for varietal differences. The fallow land soil water simulations were more accurate for dry than for wet soil. For all three winter crops, the model consistently over-estimated the soil water content in the upper layers, with a good agreement for the deeper layers until a large precipitation event occurred to which the model responded more slowly than that observed. Simulations using model-scheduled irrigation based on 0.4 and 0.6 maximum allowable depletion criteria indicated that the observed applied irrigation in the field was more than that required. Soil water depletion and accumulated transpiration simulations were similar in both the observed and model-scheduled irrigations, but total soil evaporation and percolation were greater in the case of the observed than the model-scheduled irrigations. Irrigation scheduling using crop growth models may assist in avoiding over- or under-application of irrigation applications by ensuring efficient utilization of rain and irrigation.     

Numerical evaluation of subsurface trickle irrigation with brackish water

In this study, an assessment for a proposed irrigation system in the El-Salam Canal cultivated land, Egypt, was conducted. A numerical model (HYDRUS-2D/3D) was applied to investigate the effect of irrigation amount, frequency, and emitter depth on the wetted soil volume, soil salinity levels, and deep percolation under subsurface trickle irrigation (SDI) of tomato growing with brackish irrigation water in three different soil types. The simulations indicated that lower irrigation frequency increased the wetted soil volume without significant increase in water percolates below the plant roots. Deep percolation decreased as the amount of irrigation water and emitter depth decreased. With the same amount of irrigation water, the volume of leached soil was larger at lower irrigation frequency. The salinity of irrigation water under SDI with shallow emitter depth did not show any significant effect on increasing the soil salinity above tomato crop salt tolerance. Based on the results, it appears that the use of SDI with brackish irrigation water is an effective method for growing tomato crop in El-Salam Canal cultivated land especially with shallow emitter depth.     

膜孔灌土壤湿润体水分分布与入渗特性数值模拟

以非饱和土壤水分运动理论为基础,建立了膜孔灌土壤水分运动的数学模型,并用SWMS-3D软件进行求解,利用室内试验对模拟结果进行分析验证,模拟值与实测值基本吻合,所建模型合理。用所建立的模型和方法对一定灌水技术要素组合下的土壤湿润体水分分布、膜孔入渗量进行数值模拟,结果表明：除膜孔间距大时,膜孔附近土壤水分分布不均匀程度增大外,土壤质地、容积密度、初始含水率、膜孔直径和灌溉水深对膜孔灌土壤水分分布模式影响较小。土壤质地、容积密度对膜孔灌的入渗特性影响显著,土壤初始含水率和灌溉水深对其影响较小。膜孔控制区域内的平均入渗水深主要受开孔率和膜孔直径的影响。     

微咸水灌溉改良盐碱地的可行性研究

针对水资源短缺和盐碱地不断恶化等问题，微咸水灌溉农作物在理论上受到大量关注，在实践上也有良好效果，但鲜有微咸水投入改良盐碱地的理论实践，缺少一定的理论指导。对目前国内外微咸水灌溉开发和利用研究进展进行综述，总结微咸水灌溉技术的实践情况，阐明微咸水灌溉对作物、环境和土壤水盐运动的影响，详细论述微咸水灌溉提升作物产量和改良盐碱地的成果，分析其灌溉改良盐碱地的可行性，并提出微咸水灌溉改良盐碱地的研究方向和实践操作。      

Average concentration of soluble salts in leached soils inferred from the convective–dispersive equation

The convective–dispersive, or advective–dispersive, equation (CDE) has long been the model of choice for solute transport in soils. Using the average concentration of soluble salts in soil profile to evaluate changes in salinity due to irrigation can be beneficial when spatial variability of soil salinity at selected depths is larger than spatial variability of soil salinity in the layer encompassing these depths, and when soil salinity is evaluated with electric conductivity measurements that give layer-average rather than depth-specific salinity values. The objective of this work was to present analytical solutions of the CDE that express the average soluble salt content in soil profile as the function of time, water flux, and solute dispersion parameter. The solutions were developed for both semiinfinite and finite domain and implemented in a computer code. Examples are presented of using these solutions to develop a nomogram for the dispersion coefficient estimation and to evaluate the applicability of the semiinfinite domain solution to soil monolith leaching experiments. In cases when the CDE application is justified, the analysis of the salt leaching based on the average salt concentrations in soil profile provides estimates of the effective salt dispersion parameter useful in land evaluation and soil reclamation.     

Monitoring and modelling the three-dimensional flow of water under drip irrigation

The interpretation of soil water dynamics under drip irrigation systems is relevant for crop production as well as on water use and management. In this study a three-dimensional representation of the flow of water under drip irrigation is presented. The work includes analysis of the water balance at point scale as well as area-average, exploring uncertainties in water balance estimations depending on the number of locations sampled. The water flow was monitored by detailed profile water content measurements before irrigation, after irrigation and 24 h later with a dense array of soil moisture access tubes radially distributed around selected drippers. The objective was to develop a methodology that could be used on selected occasions to obtain ‘snap shots’ of the detailed three-dimensional patterns of soil moisture. Such patterns are likely to be very complex, as spatial variability will be induced for a number of reasons, such as strong horizontal gradients in soil moisture, variations between individual sources in the amount of water applied and spatial variability is soil hydraulic properties. Results are compared with a widely used numerical model, Hydrus-2D. The observed dynamic of the water content distribution is in good agreement with model simulations, although some discrepancies concerning the horizontal distribution of the irrigation bulb are noted due to soil heterogeneity.     

Simulation of soil water dynamics under subsurface drip irrigation from line sources

A mathematical model which describes water flow under subsurface drip lines taking into account root water uptake, evaporation of soil water from the soil surface and hysteresis in the soil water characteristic curve θ(H) is presented. The model performance in simulating soil water dynamics was evaluated by comparing the predicted soil water content values with both those of Hydrus 2D model and those of an analytical solution for a buried single strip source. Soil water distribution patterns for three soils (loamy sand, silt, silty clay loam) and two discharge rates (2 and 4 l m⁻¹ h⁻¹) at four different times are presented. The numerical results showed that the soil wetting pattern mainly depends on soil hydraulic properties; that at a time equal to irrigation duration decreasing the discharge rate of the line sources but maintaining the applied irrigation depth, the vertical and horizontal components of the wetting front were increased; that at a time equal to the total simulation time the discharge rate has no effect on the actual transpiration and actual soil evaporation and a small effect on deep percolation. Also the numerical results showed that when the soil evaporation is neglected the soil water is more easily taken up by the plant roots.     

Numerical investigation of irrigation scheduling based on soil water status

Improving the sustainability of irrigation systems requires the optimization of operational parameters such as irrigation threshold and irrigation amount. Numerical modeling is a fast and accurate means to optimize such operational parameters. However, little work has been carried out to investigate the relationship between irrigation scheduling, irrigation threshold, and irrigation amount. Herein, we compare the results of HYDRUS 2D/3D simulations with experimental data from triggered drip irrigation, and optimize operational parameters. Two field experiments were conducted, one on loamy sand soil and one on sandy loam soil, to evaluate the overall effects of different potential transpiration rates and irrigation management strategies, on the triggered irrigation system. In both experiments, irrigation was controlled by a closed loop irrigation system linked to tensiometers. Collected experimental data were analyzed and compared with HYDRUS 2D/3D simulations. A system-dependant boundary condition, which initiates irrigation whenever the matric head at a predetermined location drops below a certain threshold, was implemented into the code. The experimental model was used to evaluate collected experimental data, and then to optimize the operational parameters for two hypothetical soils. The results show that HYDRUS 2D/3D predictions of irrigation events and matric heads are in good agreement with experimental data, and that the code can be used to optimize irrigation thresholds and water amounts applied in an irrigation episode to increase the efficiency of water use.     

石羊河流域咸水灌溉对土壤物理性质的影响

为揭示咸水灌溉对土壤水力特性的影响机制,探求西北内陆干旱地区的合理灌溉模式,对石羊河流域中游地区开展制种玉米咸水灌溉田间试验,通过设置4种灌溉水矿化度水平(0.71,3.00,6.00,9.00 g/L),研究土壤盐分对土壤容重、孔隙度、质地和饱和导水率的影响.研究结果表明:对土壤进行咸水灌溉会引起土壤容重、孔隙度的改变,从而改变土壤饱和导水率.随着灌水次数的增多,各个处理土壤容重都越来越大,孔隙度越来越小,从而使得饱和导水率越来越小.此外咸水灌溉还会引起土壤质地的改变,特别是黏粒含量的增大,会使土壤饱和导水率减小.研究成果对咸水资源的高效利用及农业的可持续发展,具有重要的理论意义和实用价值.     

地下滴灌条件下土壤水分运动模型

本文分析了线水源条件下地下滴灌土壤水运动的物理过程，认为其土壤水运动是一垂直毛管的平面二维流动；在此基础上，建立了饱和──非饱和土壤水二维流动的数学模型。采用ＡＤＩ法，结合Ｐ－Ｃ法对模型进行求解。计算结果与室内试验基本相吻合。     

Analysis of AET and yield predictions under surface and buried drip irrigation systems using the Crop Model PILOTE and Hydrus-2D

Innovative irrigation solutions have to face water scarcity problems affecting the Mediterranean countries. Generally, surface (DI) or subsurface drip irrigation systems (SDI) have the ability to increase water productivity (WP). But the question about their possible utilisation for crops such as corn would merit to be analysed using an appropriate economic tool. The latter would be necessary based on the utilisation of a modelling approach to identify the optimal irrigation strategy associating a water amount with a crop yield (Yc). In this perspective, a possible utilisation of the operative 1D crop model PILOTE for simulating actual evapotranspiration (AET) and yield under a 2D soil water transfer process characterizing DI and SDI was analysed. In this study, limited to a loamy soil cultivated with corn, the pertinence of the root water uptake model used in the numerical code Hydrus-2D for AET estimations of actual evapotranspiration (AET) under water stress conditions is discussed throughout the Yc = F(AET) relationship established by PILOTE on the basis of validated simulations. The conclusions of this work are (i): with slight adaptations, PILOTE can provide reliable WP estimations associated to irrigation strategies under DI and SDI, (ii): the current Hydrus-2D version used in this study underestimates AET, compared with PILOTE, in a range varying from 7% under moderate water stress conditions to 14% under severe ones, (iii): A lateral spacing of 1.6 m for the irrigation of corn with a SDI system is an appropriate solution on a loamy soil under a Mediterranean climate.A local Yc = F(AET) relationship associated with a Hydrus-2D version taking into account the compensating root uptake process could result in an interesting tool to help identify the optimal irrigation system design under different soil conditions.     

Use of kinematic wave theory to model irrigation on cracking soil

Border irrigation in Australia is characterised by excessive run-off and variable water use efficiencies. This paper discusses an analytical irrigation model that, because of its simplicity, represents a tool for improving water management in border irrigation. Infiltration data on four replicate 75-m² plots were obtained from one irrigation of perennial pasture on a duplex, red-brown earth. Infiltration was characterised by high initial and low final rates. Kostiakov, modified Kostiakov, Horton, Philip and linear infiltration functions were fitted to the data. The linear function fitted the data well, and the parameters have physical interpretation. Consequently, an analytical kinematic wave model of border irrigation that incorporates the linear infiltration function is discussed. The analytical model was compared to more complex numerical models of border irrigation. The analytical model does not require a computer and performed sufficiently well to have application for border irrigation management in the field. Received: 6 January 1993     

新疆砾石地葡萄滴灌带合理设计及布设参数的数值分析

为了摸清新疆含砾石复杂土壤条件下土壤水分运动规律,优化葡萄滴灌系统设计中的各项设计参数及合理布设,该文通过田间交汇试验确定合适的滴头间距为30 cm,并借助Hydrus-2D数值模型确定了土壤水力参数,同时运用该数值模型模拟了不同滴头流量和滴灌带水平间距布设形式下地表滴灌土壤水分分布特征。根据土壤湿润体特征结合葡萄根系分布规律,确定新疆砾石地葡萄滴灌系统合理的滴头流量为2.5～3.0 L/h,滴灌带水平间距为60 cm。该结果可为新疆砾石地复杂土壤葡萄滴灌系统的科学设计和田间合理布设提供参考。     

波涌灌土壤的粒度组成研究

本文通过对宝鸡峡灌区波涌灌和连续灌前后大量土壤取样的粒度组成分析认为，灌水对农田土壤粒度组成的时空分布的影响是个长期的效应。波涌灌灌水技术参数，除入沟、畦流量外，放、停水时间及循环率对土壤的粒度组成没有明显的影响。灌水过程中入渗携带的极少的细颗粒并不是波涌灌表层土壤导水率降低的原因。     

叶尔羌河灌区冬小麦灌溉试验与分析

以叶尔羌河灌区地下水均衡场内２０ 个试验小区两年的冬小麦田间灌溉试验为基础,对田间土壤水量平衡,冬小麦产量、水分生产率与耗水量关系,冬小麦产量与供水量关系等进行了分析。还根据试验成果应用Ｊｅｎｓｅｎ 模型拟合了冬小麦水分生产函数     

Soil sodicity as a result of periodical drought

Soil sodicity development is a process that depends nonlinearly on both salt concentration and composition of soil water. In particular in hot climates, soil water composition is subject to temporal variation due to dry–wet cycles. To investigate the effect of such cycles on soil salinity and sodicity, a simple root zone model is developed that accounts for annual salt accumulation and leaching periods. Cation exchange is simplified to considering only Ca/Na exchange, using the Gapon exchange equation. The resulting salt and Ca/Na-balances are solved for a series of dry/wet cycles with a standard numerical approach. Due to the nonlinearities in the Gapon equation, the fluctuations of soil salinity that may be induced, e.g. by fluctuating soil water content, affect sodicity development. Even for the case that salinity is in a periodic steady state, where salt concentrations do not increase on the long term, sodicity may still grow as a function of time from year to year. For the longer term, sodicity, as quantified by Exchangeable Sodium Percentage (ESP), approaches a maximum value that depends on drought and inflowing water quality, but not on soil cation exchange capacity. Analytical approaches for the salinity and sodicity developing under such fluctuating regimes appear to be in good agreement with numerical approximations and are very useful for checking numerical results and anticipating changes in practical situations.     

NaCl溶液处理亚热带土壤水分特征曲线差异与模型优选

携带大量盐分的低质水长期灌溉导致土壤存在极大的物理化学特性退化风险,为了探究盐分对土壤水分特征曲线影响的差异性,采用压力膜法对亚热带地区粘性潮土、沙性潮土、红壤、紫色土、水稻土等5种土壤进行室内测定,对比分析了各土壤在0、5、10、15 g/L等4个钠盐浓度水平下土壤水分特征曲线的差异,并利用RETC软件结合数理统计方法确定了各土壤不同钠盐浓度水平下相应的最优拟合模型。结果表明:钠盐处理均可提高各土壤的持水能力,且粘粒含量较高的土壤影响显著;钠盐处理减少了粘性潮土、沙性潮土和红壤的有效含水率,分别最大减少了40.8%、30.5%、31.5%,却提高了紫色土、水稻土有效含水率,分别最大提高了45.7%、28.9%。粘粒含量少或低浓度盐溶液处理的土壤水分特征曲线以BC模型拟合最优,而粘粒含量多且高浓度盐溶液处理的以DP-M模型拟合最优。     

灌溉水量对无压灌溉水分运移的影响

通过试验,分析研究了不同灌溉水量对无压灌溉入渗过程中水分运移的影响。试验表明,无压灌溉湿润体形状近似为球体,且与土壤类型、气象条件等外界因素无关,提出了用灌溉水量估计湿润体大小的经验方程;湿润体内水平和垂直方向含水率分布规律表明,各层或各深度范围内含水率变化趋势相近,湿润体内固定点处的含水率在灌水过程中几乎不发生变化,灌溉水量的增加只是用来扩大湿润体的大小。研究结果对无压灌溉灌水定额的制定具有重要指导意义。