基于土壤入渗水量分布特性的微喷灌系统组合分析

通过显色示踪方法研究了微喷条件下入渗水量分部模式,在此基础上探讨了微喷组合布置形式。试验结果显示喷洒水量分布为2次曲线情况下,入渗后水量分部符合4次曲线;同时分布峰值位置沿半径方向向外侧偏移,而含水率变化量在垂直方向分布差异性较小。依据实际入渗水量分布情况,采用正方形组合方案对系统的灌溉效率进行评价,组合间距为1.1倍有效喷程时,均匀系数最大。基于入渗水量分布进行微喷灌组合将能有效地提高灌水质量和效率。     

Wind effects on solid set sprinkler irrigation depth and yield of maize (<Emphasis Type="Italic">Zea mays</Emphasis>)

A field experiment was performed to study the effect of the space and time variability of water application on maize (Zea mays) yield when irrigated by a solid set sprinkler system. A solid set sprinkler irrigation layout, typical of the new irrigation developments in the Ebro basin of Spain, was considered. Analyses were performed (1) to study the variability of the water application depth in each irrigation event and in the seasonal irrigation and (2) to relate the spatial variability in crop yield to the variability of the applied irrigation and to the soil physical properties. The results of this research showed that a significant part of the variability in the Christiansen coefficient of uniformity (CU), and wind drift and evaporation losses were explained by the wind speed alone. Seasonal irrigation uniformity (CU of 88%) was higher than the average uniformity of the individual irrigation events (CU of 80%). The uniformity of soil water recharge was lower than the irrigation uniformity, and the relationship between both variables was statistically significant. Results indicated that grain yield variability was partly dictated by the water deficit resulting from the non-uniformity of water distribution during the crop season. The spatial variability of irrigation water depth when the wind speed was higher than 2 m s^–1 was correlated with the spatial variability of grain yield, indicating that a proper selection of the wind conditions is required in order to attain high yield in sprinkler-irrigated maize.     

Field evaluation of crop yield as affected by nonuniformity of sprinkler-applied water and fertilizers

The determination of target uniformity for sprinkler irrigation system should consider the impacts of nonuniformity of water and fertilizers on crop yield. Field experiments were therefore conducted in north China plains to address the impacts of nonuniformly applied water and fertilizers on winter wheat yield. Irrigation water and fertilizers were applied through a solid set sprinkler system. Three experimental plots were used with seasonal Christiansen uniformity coefficients (arithmetic mean of individual CUs) ranging from 62 to 82%. Each plot was divided into $\text{3}\text{m}\text{×3}\text{m}$ grids. Sprinkler water depth and concentration of fertilizer solution for each grid was measured both below and above the canopy for each individual irrigation event. The spatial distribution of soil moisture for each experimental plot was also measured periodically to determine irrigation times and amounts. On harvest, grain yield and total nitrogen content of plant stems were measured for each grid. The experimental results showed that the uniformity of fertilizer applied increased with sprinkler water uniformity. The distributions of both fertilizers and water applied through sprinkler system can be represented by a normal distribution function. Field experiments also demonstrated that the uniformity of sprinkler-applied water and fertilizers has insignificant effect on winter wheat yield for the studied uniformity range. The current standard for sprinkler uniformity (for example, the target CU is equal to or higher than 75% in China) is high enough for obtaining a reasonable crop yield in dry sub-humid regions.     

Irrigation uniformity related to horizontal extent of root zone

Summary Harmonic analysis is used to derive the component waves of a given water distribution map. These components are then subjected to smoothing by root systems of various sizes, to obtain the effective variances and uniformity coefficients for these root systems. This approach helps to explain, for instance, why the effective uniformity by trickle irrigation is high, while the detailed actual distribution is very nonuniform; why the actual uniformity of under-canopy sprinkling of orchards need not be very high; or why it is usually better to have the rows of field crops parallel to the shorter spacing of the sprinklers. It is observed that ordinary distribution maps contain little variance in the shorter wave-lengths, thus suggesting a reduction in the number of collectors necessary for pattern determination. Another conclusion based on the same observation is that when plants spacing is half the sprinkler's spacing, a spatial shift between the crop and the irrigation system may markedly affect the effective uniformity.     

Emitter discharge variability of subsurface drip irrigation in uniform soils: effect on water-application uniformity

Emitter discharge of subsurface drip irrigation (SDI) decreases as a result of the overpressure in the soil water at the discharge orifice. In this paper, the variation in dripper discharge in SDI laterals is studied. First, the emitter coefficient of flow variation CV _q was measured in laboratory experiments with drippers of 2 and 4 L/h that were laid both on the soil and beneath it. Additionally, the soil pressure coefficient of variation CV _hs was measured in buried emitters. Then, the irrigation uniformity was simulated in SDI and surface irrigation laterals under the same operating conditions and uniform soils; sandy and loamy. CV _q was similar for the compensating models of both the surface and subsurface emitters. However, CV _q decreased for the 2-L/h non-compensating model in the loamy soil. This shows a possible self-regulation of non-compensating emitter discharge in SDI, due to the interaction between effects of emitter discharge and soil pressure. This resulted in the irrigation uniformity of SDI non-compensating emitters to be greater than surface drip irrigation. The uniformity with pressure-compensating emitters would be similar in both cases, provided the overpressures in SDI are less than or equal to the compensation range lower limit.     

控水控肥对微喷灌三七土壤磷素的影响

通过3个控水水平和4个控肥水平正交试验,对2017—2019年泸西县大栗树村三七典型种植区控水控肥条件下微喷灌三七土壤全磷和速效磷运移分布及其储量特性进行试验研究.结果表明:不同灌水量全磷以三七植株为中心沿水平方向和土壤深度增大均逐渐减小,水平方向最大值出现范围在0~10 cm,土壤深度最大值出现范围在0~20 cm.速效磷沿水平方向和土壤深度增大均先减小后增大,沿水平方向和土壤深度方向最大值出现范围均在0~20 cm.不同施肥量全磷和速效磷以三七植株为中心沿水平方向和土壤深度增大均先减小后增大,处理W3F2全磷和速效磷水平方向和土壤深度方向最大值出现范围在0~10 cm.不同灌水量全磷和速效磷分布均匀系数均随灌水量增加先减小后增大,处理W3F2全磷和速效磷分布均匀系数最小,分别为46.77%和62.70%,处理CK全磷偏态系数为负值,其余处理全磷和速效磷偏态系数均为正值.不同施肥量全磷和速效磷分布均匀系数均随施肥量增加先减小后增大,处理W2F3全磷分布均匀系数最小,为46.83%;处理W2F4速效磷分布均匀系数最小,为68.68%;处理W2F1速效磷偏态系数为负值,其余处理全磷和速效磷偏态系数均为正值.不同灌水量全磷和速效磷储量在土壤表层0~20 cm最大,全磷和速效磷储量均随土壤深度增加而减少,随灌水量增加而增加.不同施肥量全磷和速效磷储量均随施肥量增加先增大后减小,处理W2F3全磷和速效磷储量平均值最大.该研究对三七土壤水肥高效利用和调控提供技术支持,对三七高产优质种植具有指导意义.     

Control of irrigation amounts using velocity and position of wetting front

A new approach for the estimation and control of the quantity of water applied in an irrigation is presented in which irrigation is stopped when the wetting front reaches a critical depth, Z _L. An expression for calculating the critical depth Z _L was developed. A major parameter in this expression is the velocity of advance of the wetting front, V, which was shown to be directly related to the application rate, IR, and inversely related to the initial soil water content, _i. A depth probe (patent pending) was designed, constructed and tested for the purpose of monitoring the position of the wetting front during infiltration and redistribution and for computing the value of V. Equations developed for relating the velocity of advance of the wetting front to _i as well as for estimating the value of the critical depth Z _L were successfully tested under conditions of uniform distribution of the initial soil water content. An iterative learning process which utilizes the real time output from the depth probe during each irrigation and is therefore capable of handling realistic field conditions where nonuniformity is the rule is presented. The acquired information is used to estimate a critical depth of the wetting front, Z _L, for a planned final wetted depth, Z _F, during each irrigation. This process is incorporated in the depth probe and is used to stop irrigation and thus control the quantity of water applied.     

Evapotranspiration and irrigation effeciency of mature orange orchards in Valencia (Spain)

Actual evapotranspiration (ETc) of three mature sweet orange orchards (cv. Salustiana and Washington Navel on sour orange), under border irrigation and typical cultural practices was measured by the water balance method during 1981 to 1984. Soil water content was measured at 7 to 10 day intervals using a neutron meter and soil sampling of the 0–10 cm surface layer. Zero flux plane was calculated by measurements with mercury tensiometers. Irrigation water in these and other 5 similar orchards was measured by broad crested weirs. Rainfall and other climatic data for calculation of reference evapotranspiration by FAO's methods (ETo) were collected in a nearby meteorological station. Average yearly ETc ranged from 750 to 660 mm and mean monthly maximum was 3.7 and 3.2 mm/day in July for Salustiana and W. Navel orchards, respectively.ETo estimates for the different methods used were highly correlated (r ²0.94). Monthly crop coefficients (Kc) based on pan evaporation ranged from 0.5–0.6 in spring and summer to 0.8 in autumn and were about 10% higher than those for Penman or radiation methods. Average annual Kc for the three plots studied was 0.64, 0.61 and 0.51, respectively, and correlated well (r ²=0.99) with tree ground cover. Irrigation efficiency was about 50% for orchards with soils with less water holding capacity and more applied water per irrigation and 70–80% in orchards with deeper soils or with a higher water holding capacity. Increasing irrigation frequency and applying smaller amounts of water per irrigation with good uniformity can improve on-farm irrigation efficiency.     

Soil moisture distribution patterns under surface and subsurface drip irrigation systems in sandy soil using neutron scattering technique

This study was carried out at the experimental field station of the Atomic Energy Authority in Anshas, Egypt, by the aim of assessing the soil moisture status under surface and subsurface drip irrigation systems, as a function of the variation in the distance between drippers along and between laterals. Moisture measurements were carried out using neutron moisture meter technique, and water distribution uniformity was assessed by applying Surfer Model. The presented data indicated that the soil moisture distribution and its uniformity within the soil profile under surface drip was to great extent affected by the distance between drippers rather than that between laterals. Generally, the soil moisture distribution under using 30-cm dripper spacing was better than of that under 50 cm. Under subsurface drip irrigation, the allocation of the irrigation system was the factor that dominantly affected the moisture trend under the studied variables. Installing the system at 30 cm from the soil surface is the one to be recommended as it represents the active root zone for most vegetable crops, beside it leads to a better water saving in sandy soils than that allocated at 15 cm depth.     

Cotton root growth as affected by changes in soil water distribution and their impact on plant tolerance to drought

The capability of mature cotton plants (Gossypium hirsutum L.) to adjust to progressive drying of their root zone by promoting root growth to adjacent wetted zones, and the implications of this process on irrigation design were investigated. Field grown plants that developed shallow root systems in response to a drip irrigation management of daily, surface soil wettings were exposed 85 days after emergence (DAE), while in the flowering stage, to a sudden change in water distribution in the form of deep soil wetting (DSW) followed by termination of irrigation. The shallow rooted plants (SRP) failed to respond to further surface soil wetting and the progressive drying of the profile by rapid root growth to the deeper-wetted zones; consequently, the SRP suffered from water deficiency for at least two weeks, evidenced by a gradual decrease in their leaf water potential (L_w). Potted plants responded similarly. Daily irrigations of the pot surface with water amounts similar to those lost by evapotranspiration led to the development of a system in which most of the roots and available water became concentrated at the pot's upper section. A transition to irrigation from the bottom of the pot led to a reversed soil-water content gradient and failed to promote rapid root spreading to the deeper-wetted layers, in spite of the accelerated drying of the upper zone. The slow deepening of the root system was accompanied by water-stress symptoms as indicated by a considerable reduction in dry matter production. The root shoot ratio in these plants was not much greater than in non-stressed plants in which the surface wetting was continued. This indicated that preferential root growth relative to the shoot did not occur in response to the progressive drying of the shallow root zone. Rewetting of the root zone after a long period of soil water deficiency failed to promote rapid recovery of the root system in the form of root regrowth in this zone. It was concluded that the capability of mature cotton plant roots to adjust their growth to large changes in water distribution in the soil, is slow and that this should be taken into account when determining an irrigation regime in which the depth at which water is applied is changed during the growing season.Contribution from the Agricultural Research Organization, Volcani Center, Bet Dagan, Israel; No. 343-E, 1992 series     

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.     

A model of crop yield response to irrigation water salinity: theory,testing and application

A relationship between crop yield and irrigation water salinity is developed. The relationship can be used as a production function to quantify the economic ramifications of practices which increase irrigation water salinity, such as disposal of surface and sub-surface saline drainage waters into the irrigation water supply system. Guidelines for the acceptable level of irrigation water salinity in a region can then be established. The model can also be used to determine crop suitability for an irrigation region, if irrigation water salinity is high. Where experimental work is required to determine crop yield response to irrigation water salinity, the model can be used as a first estimate of the response function. The most appropriate experimental treatments can then be allocated. The model adequately predicted crop response to water salinity, when compared with experimental data.Abbreviations A Crop threshold rootzone salinity in Equation of Maas and Hoffman (dS/m) - B Fractional yield reduction per unit rootzone salinity increase (dS/m)^–1 - C_i Average salinity of applied water (dS/m) - C_r Average salinity of rainfall (dS/m) - C_s Linearly averaged soil solution salinity in the rootzone (dS/m) - C_se Linearly averaged soil saturation extract salinity in the rootzone (dS/m) - C_w Average salinity of irrigation supply water (dS/m) - C_z Soil solution salinity at the base of the crop rootzone (dS/m) - C Mean root water uptake weighted soil salinity in equation of Bernstein and François (1973) (dS/m) - E_p Depth of class A pan evaporation during the growing season (m) - ET_a Actual crop evapotranspiration during the growing season (m) - ET_m Maximum crop evapotranspiration during the growing season (m) - I The total depth of water applied during the growing season (including irrigation water and rainfall) (m) - K Empirical coefficient in leaching equation of Rhoades (1974) - K_c Crop coefficient for equation of Doorenbos and Pruit (1977) to estimate crop water use - K_y Yield response factor in equation of Doorenbos and Kassam (1974) - LF The leaching fraction - Ro Depth of rainfall runoff during the growing season (m) - R Depth of rainfall during the growing season (m) - W Depth of irrigation water applied during the growing season (m) - Y Relative crop yield - Y_a Actual crop yield (kg) - Y_m Maximum crop yield (kg) - /z Dimensionless depth for equation of Raats (1974), and empirical coefficient for the leaching equation of Hoffman and van Genutchen (1983)     

喷灌和软管灌溉两用机组水量分布特性与试验

喷灌和软管灌溉两用轻小机组具有喷灌和软管灌溉两种灌水方式,且有高度可升降、喷幅可调等特点.采用理论分析和试验验证相结合的方法,对该机组水量分布特性进行了研究,分析了影响机组水量分布特性的因素,计算了机组在配置喷灌和软管灌溉系统时的喷灌强度、均匀系数,结果表明,影响机组水量分布均匀性的主要因素是所配置灌水器的水量分布特性、灌水器配置间距、行走速率、土壤和地形、风速等.在室内试验时,机组喷灌均匀系数达95%以上,软管灌溉均匀系数达90%,可满足灌溉需要.     

Establishment of shallow and restricted root systems in cotton and its impact on plant response to irrigation

Summary The effects of frequent and shallow soil wetting by surface drip irrigation on root growth, morphology, and location, and their impact on plant sensitivity to irrigation management were studied in cotton (Gossypium hirsutum L.). Daily drip irrigation, which wetted the 0 to 40-cm soil depth, encouraged root development mainly around the drippers. Water extraction took place mostly from 0 to 20 cm below the drippers, where the roots were concentrated. Shallowness of root growth was not altered by the expansion and deepening of the wetted soil zone which resulted from an increase in amount of irrigation water. The shallow and restricted root system was characterized by a high fraction of thin roots (less than 1 mm dia.) which comprised almost 90% of the root dry matter. Root proximity to the drippers and the limited amount of water in the rooted soil led to a sensitive and quick response of the plants to small amounts of irrigation. A supply of 1.0 mm H₂O given at midday to 70 day-old plants resulted in a leaf water potential (L _w) increase from –1.64 to –1.32 MPa over a 20-min period. This amount of irrigation comprised 15% of the average daily quantity. A 24 h delay in irrigation to 80 dayold plants was enough to decrease L _w from –1.41 to –2.42 MPa. This decrease was caused by a soil water deficit of less than 6 mm H₂O. Extending the irrigation delay to 72 h affected yield and earliness, although the deficient amount of water was supplied over the several days after the treatment. A strong response to minor, but continuous, differences in the daily irrigation amount was detected. Differences in irrigation of less than 1 mm H₂O per day applied during the whole growth season substantially affected L _w, yield and earliness. It was concluded that the establishment of a shallow and restricted root system resulted in strong dependence of the plants on frequent and sufficient supply of water, and temporary minor changes in irrigation affected plant water status and productivity.     

射流式喷头水量分布动态仿真及试验

【目的】研究工作压力,喷头组合间距、组合斱式和旋转速度对射流式喷头及多喷头组合喷灌均匀性系数(CU)和分布均匀系数(DU)的影响。【斱法】采用不同工作条件下单喷头和多喷头组合喷灌水量分布的动态仿真代码,对射流式喷头开展了水力性能试验;研究了射流式喷头在不同工作压力及安装高度条件下对喷灌强度、水量分布的影响;建立了水量峰值强度与工作压力的回归关系式;模拟了单喷头在正斱形和三角形组合喷灌下的空间水量分布。【结果】喷头在1.5 m安装高度、100~300 kPa压力条件下,水量峰值集中在5 mm/h附近,标准偏差(STD)为0.23。喷头在100 kPa工作压力,安装高度为1.1、1.3 m的水量峰值强度分别可高达8.9、10.5mm/h。不同工作压力下的单喷头喷灌的DU和CU标准偏差分别为15.5%、9.3%,且DU对压力的变化相对更为敏感。【结论】在实际喷灌工程中正斱形组合喷灌的间距应小于8m,三角形组合喷头之间的间距应布置在8m附近,此时的喷灌均匀度最高,单个喷灌设备覆盖范围最广,成本最低。     

Spatial and temporal distributions of nitrogen and crop yield as affected by nonuniformity of sprinkler fertigation

Deep percolation and nitrate leaching are important considerations in the design of sprinkler systems. Field experiments were therefore conducted to investigate the influence of nonuniformity of sprinkler irrigation on deep percolation and spatial distributions of nitrogen and crop yield during the growing season of winter wheat at an experiment station in Beijing, China. Three experimental plots of a sandy clay loam soil in the 0–40 cm depth interval and a loamy clay soil below 40 cm were irrigated with a sprinkler irrigation system that had a seasonal averaged Christiansen irrigation uniformity coefficient (CU) varying from 72 to 84%. Except for the fertilizer applied before planting, fertilizer was applied with the sprinkler irrigation system. The corresponding seasonal averaged CU for fertigation varied from 71 to 85%. Daily observation of matrix water potentials in the root zone showed that little deep percolation occurred. Consequently, the effect of sprinkler uniformity on deep percolation was minor during the irrigation season for the soil tested. Intensive gravimetric soil core samplings were conducted several times during the irrigation season in a grid of 5 m × 5 m for each plot to determine the spatial and temporal variation of NH₄-N and NO₃-N contents. Soil NH₄-N and NO₃-N exhibited high spatial variability in depth and time during the irrigation season with CU values ranging from 23 to 97% and the coefficient of variation ranging from 0.04 to 1.06. A higher uniformity of sprinkler fertigation produced a more uniform distribution of NH₄-N, but the distribution of NO₃-N was not related to fertigation. Rather it was related to the spatial variability of NO₃-N before fertigation began. At harvest, the distribution of dry matter above ground, nitrogen uptake, and yield were measured and the results indicated that sprinkler fertigation uniformity had insignificant effects on the parameters mentioned above. Field experimental results obtained from this study suggest that sprinkler irrigation if properly managed can be used as an efficient and environment-friendly method of applying water and fertilizers.     

平移式喷灌机行走速度及喷灌均匀度试验研究

为研究低压喷灌下喷灌机行走速度合理取值以及喷灌均匀度对土壤含水率均匀度的影响,以自行研制的轻小型平移式喷灌机为研究对象,通过室内单喷头试验和田间喷灌试验,探究了特定灌水定额下喷灌机的工作压力与行走速度关系,并对其水量分布、喷灌均匀度以及土壤含水率均匀度随时间变化进行了分析.结果表明：通过确定灌水定额能够计算出平移式喷灌机的行走速度和工作压力：当灌水定额分别为10,15,20 mm时,40~120 kPa喷灌压力下喷灌机行走速度最小为17.27 m/h,最大为58.65 m/h;增大喷灌压力能小范围提高均匀度,40 kPa工作压力均匀度为0.696,60~120 kPa喷灌压力下均匀度变化范围为0.731~0.788,喷灌水在土壤中的二次分布均匀度明显高于地表喷灌均匀度,40 kPa喷灌压力下喷后6 h土壤含水率均匀度达到0.906,24 h后达到0.953,可相应降低喷灌均匀度设计值以降低运行成本,节约能耗.     

Effect of irrigation methods,management and salinity of irrigation water on tomato yield,soil moisture and salinity distribution

The increasing demand for irrigation water to secure food for growing populations with limited water supply suggests re-thinking the use of non-conventional water resources. The latter includes saline drainage water, brackish groundwater and treated waste water. The effects of using saline drainage water (electrical conductivity of 4.2–4.8 dS m⁻¹) to irrigate field-grown tomato (Lycopersicon esculentum Mill cv Floradade) using drip and furrow irrigation systems were evaluated, together with the distribution of soil moisture and salt. The saline water was either diluted to different salinity levels using fresh water (blended) or used cyclically with fresh water. The results of two seasons of study (2001 and 2002) showed that increasing salinity resulted in decreased leaf area index, plant dry weight, fruit total yield and individual fruit weight. In all cases, the growth parameters and yield as well as the water use efficiency were greater for drip irrigated tomato plants than furrow-irrigated plants. However, furrow irrigation produced higher individual fruit weight. The electrical conductivity of the soil solution (extracted 48 h after irrigation) showed greater fluctuations when cyclic water management was used compared to those plots irrigated with blended water. In both drip and furrow irrigation, measurements of soil moisture one day after irrigation, showed that soil moisture was higher at the top 20 cm layer and at the location of the irrigation water source; soil moisture was at a minimum in the root zone (20–40 cm layer), but showed a gradual increase at 40–60 and 60–90 cm and was stable at 90–120 cm depth. Soil water content decreased gradually as the distance from the irrigation water source increased. In addition, a few days after irrigation, the soil moisture content decreased, but the deficit was most pronounced in the surface layer. Soil salinity at the irrigation source was lower at a depth of 15 cm (surface layer) than that at 30 and 60 cm, and was minimal in deeper layers (i.e. 90 cm). Salinity increased as the distance from the irrigation source increased particularly in the surface layer. The results indicated that the salinity followed the water front. We concluded that the careful and efficient management of irrigation with saline water can leave the groundwater salinity levels unaffected and recommended the use of drip irrigation as the fruit yield per unit of water used was on average one-third higher than when using furrow irrigation.     

An improved Lewis-Milne equation for the advance phase of border irrigation

Summary The Lewis-Milne (LM) equation has been widely applied for design of border irrigation systems. This equation is based on the concept of mass conservation while the momentum balance is replaced by the assumption of a constant surface water depth. Although this constant water depth depends on the inflow rate, slope and roughness of the infiltrating surface, no explicit relation has been derived for its estimation. Assuming negligible border slope, the present study theoretically treats the constant depth in the LM equation by utilizing the simple dam-break wave solution along with boundary layer theory. The wave front is analyzed separately from the rest of the advancing water by considering both friction and infiltration effects on the momentum balance. The resulting equations in their general form are too complicated for closed-form solutions. Solutions are therefore given for specialized cases and the mean depth of flow is presented as a function of the initial water depth at the inlet, the surface roughness and the rate of infiltration. The solution is calibrated and tested using experimental data.Abbreviations a (t) advance length - c mean depth in LM equation - c _f friction factor - c _h Chezy's friction coefficient - g acceleration due to gravity - h(x, t) water depth - h ₀ water depth at the upstream end - i() rate of infiltration - f(x, t) discharge - q₀ constant inflow discharge - S _f energy loss gradient or frictional slope - S₀ bed slope - t time - u(x, t) mean velocity along the water depth - x distance - Y() cumulative infiltration - (t) distance separating two flow regions - infiltration opportunity time     

Estimations of permissible irrigation rates from soil properties in high frequency irrigation

The effect of irrigation dynamics and soil physical properties on the permissible rate of application was analyzed using the analytic solution of Richard’s equation for periodic flux type boundary conditions typical to high frequency irrigation. Dynamics of irrigation regime was defined by its instantaneous application rate, R ₀, its frequency, and the duty cycle which is the ratio of irrigation duration and irrigation interval (period). Soil properties were saturation, hydraulic conductivity, diffusivity, and Gardner’s soil type coefficient. Fourier Transform was used to derive a closed form analytical expression for the maximal permissible value of R ₀, which would not result in water logging and saturation at soil surface. The analytical expression ties the three irrigation parameters with the above three soil parameters together. Prevention of aeration stress by restricting the moisture content at the soil surface, to become less than the minimal air pore volume (drainable porosity), was also used as an upper constraint of moisture at the surface soil. The effect of irrigation frequency and duty cycle on the permissible R ₀ values was analyzed and computed regarding three soil types: coarse sand, sand, and sandy loam. Under short duration periods of water application resulting from either small values of duty cycle or short irrigation periods (high frequency), or both, the soil surface would not become saturated even for very high R ₀ values. The maximal application depth V _max, depends on both the duty cycle and the frequency. For a given soil, V _max remains essentially constant per irrigation periods of 1 h or less, typical to pulsed irrigation and independent of the duty cycle. For periods longer than 1 day for coarse soils, V _max increases with the duty cycle while for sandy loam soils, the increase in V _max becomes insignificant for duty cycles larger than 0.3. The computed values of maximal R ₀ and V _max based on the water logging concept are much higher than the ones used in irrigation design and should be considered as upper permissible limits only. The permissible values of R ₀ and V _max are much lower if the aeration stress concept is adopted and found in the range used in practice. This analysis may be useful for the design of precision irrigation for high frequency microdrip, high frequency trickle irrigation, as well as for trunk diameter measurement (TDM) irrigation methods.