Stochastic modeling of basins microtopography: analysis of spatial variability and model testing

Microtopography is among the most important factors affecting the performance of basin irrigation system due to its influence on the advance and recession processes. This study is based on field-measured surface elevation of 116 basins in North China. The spatial variability of basins microtopography was analyzed using geostatistics; the spatial structure of basins microtopography can be characterized by a spherical semivariogram model. The correlations between selected basin geometry parameters, mainly the standard deviation (S _d ) of surface elevation differences (SED), and the semivariogram parameters were calculated and allow estimating the semivariogram parameters from basin characteristics. Considering the randomness of SED and, simultaneously, its spatial dependence, a procedure was developed to model the spatial distribution of SED using Monte-Carlo generation and kriging interpolation techniques. The required number of SED generations was also estimated depending upon the S _d of SED. The SED stochastic generation model was tested by comparing the advance, recession, flow water depths and performance parameters observed in an experimental basin with those simulated using measured and model generated SED data. Results show that estimation errors from using generated data are similar to those resulting from observations. Thus, SED generated data may be used for assessing the impacts of microtopography on irrigation performance.     

Effects of water infiltration and storage in cultivated soil on surface irrigation

Surface irrigation analysis and design require the knowledge of the variation of the cumulative infiltration water Z (L) (per unit area) into the soil as a function of the infiltration time t (T). The purpose of this study is to evaluate water infiltration and storage under surface irrigation in an alluvial clay soil cultivated with grape yield, and to determine if partially wetted furrow irrigation has more efficient water storage and infiltration than traditional border irrigation. The two irrigation components considered were wet (WT) and dry (DT) treatments, at which water applied when available soil water reached 65% and 50%, and the traditional border irrigation control. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. The infiltration (cumulative depth, Z and rate, I) was functioned to opportunity time (t_o) in minute for WT and DT treatments as: Z_WT = 0.528 t_o^0.6, Z_DT = 1.2 t_o^0.501, I_WT = 19 t_o^−0.4, and I_DT = 36 t_o^−0.498. The irrigation efficiency and soil water distribution have been evaluated using linear distribution and relative schedule depth. Coefficient of variation (CV) was 5.2 and 9.5% for WT and DT under furrow irrigation system comparing with 7.8% in border, respectively. Water was deeply percolated as 11.88 and 19.2% for wet and dry furrow treatments, respectively, compared with 12.8% for control, with no deficit in the irrigated area. Partially wetted furrow irrigation had greater water-efficiency and grape yield than both dry furrow and traditional border irrigations, where application efficiency achieved as 88.1% for wet furrow irrigation that achieved high grape fruit yield (30.71 Mg/ha) and water use efficiency 11.9 kg/m³.     

Evaluation of surface irrigation as a function of water infiltration in cultivated soils in the Nile Delta

As sources of irrigation water are decreasing, efficient use of surface irrigation is essential. The purpose of this study is to determine if partially-wetted furrow irrigation has more efficient water storage and infiltration than traditional border irrigation in an alluvial clay soil under cultivated grape production. The two irrigation components considered were wet (WT) and dry (DT) treatments, at which water was applied when available soil water reached 65 % and 50 %, and the traditional border irrigation control. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. Coefficient of variation (CV) was 5.2 and 9.5 % for WT and DT under furrow irrigation system comparing with 7.8 % in border, respectively. Water was deeply percolated as 11.9 and 19.2 % for wet and dry furrow treatments respectively, compared with 12.8 % for control, with no deficit in the irrigated area. Partially-wetted furrow irrigation had greater water-efficiency and grape yield than dry furrow and traditional border irrigation, where application efficiency achieved as 88.1 % for wet furrow irrigation that achieved high grape fruit yield (30.71 Mg /ha). The infiltration (cumulative depth, Z and rate, I) was functioned to opportunity time (t ₀ ) in minute for WT and DT treatments as: Z _WT ?=?0.528?t ₀ ^0.6, Z _DT ?=?1.2?t ₀ ^0.501, I _WT ?=?19?t ₀ ^?0.4, I _DT ?=?36?t ₀ ^?0.498. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. The irrigation parameters and coefficients, and soil water distribution have been also evaluated.     

Runoff-denoted drought index and its relationship to the yields of spring wheat in the arid area of Hexi corridor, Northwest China

A drought index is defined based on the inland river runoff from Hexi corridor, Gansu Province, Northwest China. The relationship between this drought index and yields of spring wheat is examined. The data used in this study include the following: monthly runoff data during 1959-2004 from the hydrological stations at Changmapu, Yingluoxia and Jiutiaoling on the three representative inland rivers in the Hexi corridor belt; the yields of spring wheat, monthly temperature and precipitation from three agro-meteorological stations in Jiuquan, Zhangye and Wuwei; and monthly precipitation data from three meteorological stations at Tole, Qilian and Menyuan.The runoff, following the Pearson type III distribution, is normalized to translate into the standard normal distribution as function of Z. Z is the variable in normalizing process. According to the characteristic of standard normal distribution of Z, a runoff-denoted drought index (Z_rd hereafter) is defined. The grades of Z_rd are determined by the standard normal distribution theoretical frequencies of Z. In order to validate the drought grades, runoff drought indices are compared with the atmospheric dryness indices determined by the precipitation. Results indicate that the division of drought categories based on runoff is rational and thus reliable. The Z_rd, as it considers both temperature and rainfall in upstream mountains, is close to reality.Based on the relationship between the drought grade and water usage, suggestions are made for irrigation in the area. Five grades of Z_rd are then translated into 4 grades of runoff irrigation drought index (Z_ir). The relationship between Z_ir and tendency-free yield (i.e. climate yield) of spring wheat from the Hexi Corridor irrigation zones at station Jiuquan, Zhangye and Wuwei is investigated. Results show that the Z_ir represents an anti-phase trend of the climate yields of the crops. As a conclusion, Z_ir can be utilized to qualitatively predict the trend of the wheat yield. An empirical yield model is created using a multi-variable regression method.     

Rapid field evaluation of drip and microspray distribution uniformity

The Cal Poly ITRC irrigation evaluation programs have been widely used to assess the global distribution uniformity (DU) of drip and microsprayer irrigation systems. The field procedures and formulas used in the program are presented in this paper. The system DU is estimated by mathematically combining the component DU values. DU components include pressure differences, other causes (such as manufacturing variation, plugging, and wear), unequal drainage, and unequal application rates. Results are presented from evaluations by several entities, including Cal Poly ITRC. Cal Poly evaluations of 329 fields provided an average DU_lq of 0.85 for drip and 0.80 for microspray. Approximately 45% of the non-uniformity was due to pressure differences, 52% was due to other causes, 1% due to unequal drainage, and 2% due to unequal application rates. The data show that with good design and management, it is possible to have high system DU values for at least a 20-year system life.     

Characterizing microtopographical effects on level-basin irrigation performance

Microtopography has long been recognized as one of the key variables in level-basin irrigation performance, although little effort has been devoted to establish its relevance. In this work, experimental data are used to quantify the influence of microtopography on irrigation performance. An irrigation evaluation was performed on a small level-basin (256 m²) LASER levelled to zero slope. Irrigation depth was gravimetrically measured and estimated at the 49 nodes of a regular network. Data from the irrigation evaluation and a two-dimensional flat-bed model were used to estimate irrigation depth. Irrigation times, soil surface elevation and distance to the inlet were estimated at the same nodes, and a correlation matrix was computed. Results showed that soil surface elevation was highly and significantly correlated with the times of advance (0.725⁷¹), recession ( −0.815⁷¹) and opportunity ( −0.852⁷¹), and with the measured irrigation depth ( −0.583⁷¹). Distribution uniformity using soil water measurements was 71.0%. Estimates from the irrigation evaluation and the two-dimensional model were 85.3% and 94.9%, respectively. The irrigation evaluation procedure could explain 30⁷¹% of the measured variability in irrigation depth. A large part of the unexplained variance in measured irrigation depth seems to be due to the spatial variation of infiltration properties. Predictions by the two-dimensional model were not significantly related to the measured values. A simple method was devised to estimate microtopography-adjusted irrigation performance from the results of a flat bed model and the standard deviation of elevation. Microtopography can have an important effect on level-basin irrigation performance. Models not considering this variable may incur large errors when simulating irrigation performance.     

Comparison of surge and continuous furrow methods for cotton in the Harran plain

This study compares surge flow with conventional steady flow irrigation in 130–160 m field lengths in order to analyze the potential of the former for reducing deep percolation and tailwater runoff together with the improvement of irrigation efficiency. The field experiment comprises of four surge treatments with two inflow rates of 0.0498 and 0.12 m³/min (Q₁ and Q₂), and two cycle ratios of 0.33 and 0.50 (CR₁ and CR₂), respectively, with 30 min on-times, along with two steady flow treatments with the same inflow rates. Surge flow irrigation of the level furrows was successfully managed under the field conditions with decreases in the total water applications (2–22%) and the water intake (14–25%), except in the treatments of surge S₁₁ (Q₁ CR₁) with 9% increase in the latter together with 21–38% decrease in the tailwater runoff and 19–70% decrease in the calculated deep percolation below the root zone of 1.20 m depending on inflow rates and cycle ratios of the permeable Harran soils. Surge flow reduced the water intake of a surface soil loosened by tillage by 13–23% as compared to continuous flow, thus manifesting an incomparable advantage to the level furrow systems.     

Assessing basin irrigation and scheduling strategies for saving irrigation water and controlling salinity in the upper Yellow River Basin, China

Water saving in irrigation is a key concern in the Yellow River basin. Excessive water diversions for irrigation waste water and produce waterlogging problems during the crop season and soil salinization in low lands. Supply control and inadequate functionality of the drainage system were identified as main factors for poor water management at farm level. Their improvement condition the adoption of water saving and salinity control practices. Focusing on the farm scale, studies to assess the potential for water savings included: (a) field evaluation of current basin irrigation practices and further use of the simulation models SRFR and SIRMOD to generate alternative improvements for the surface irrigation systems and (b) the use of the ISAREG model to simulate the present and improved irrigation scheduling alternatives taking into consideration salinity control. Models were used interactively to define alternatives for the irrigation systems and scheduling that would minimize percolation and produce water savings. Foreseen improvements refer to basin inflow discharges, land leveling and irrigation scheduling that could result in water savings of 33% relative to actual demand. These improvements would also reduce percolation and maintain water table depths below 1 m thereby reducing soil salinization.     

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.     

Two-dimensional zero-inertia model of surface water flow for basin irrigation based on the standard scalar parabolic type

The two-dimensional zero-inertia equations for basin irrigation were formulated as a standard scalar diffusion equation subject to Neumann boundary conditions. The formulation can handle anisotropic variations in hydraulic resistance. A numerical solution was developed using finite-volume method on unstructured triangular cells. The simulation performance of the constructed model was validated based on typical experimental data. The complete hydrodynamic model of basin irrigation was selected as the comparative model. The validated results show that the constructed model can successfully simulate the basin surface water flow when the basin surface microtopography condition is relatively smooth. Similar results were found in terms of both the water quantity conservation and convergence rate. Moreover, the computational efficiency of the constructed zero-inertia model is approximately 17 times of the complete hydrodynamic model of basin irrigation. Therefore, the constructed zero-inertia model has good simulation performance.     

Forecasting and optimizing furrow irrigation management decision variables

Furrow irrigation can be better managed if the management decision variables (irrigation time and amount; inflow rate and cutoff) can be determined ahead of time. In this study, these decision variables were forecast and optimized using 1 day ahead grass reference crop evapotranspiration (ET₀) forecasts, based on the ARMA (1,1) time-series model, with a seasonal furrow irrigation model for both homogeneous and heterogeneous infiltration conditions. Heterogeneity in infiltration characteristics was restricted to variations along the furrow length as opposed to variations between furrows. The results obtained were compared with their counterparts using the observed ET₀ for the same period during the 1992 cropping season. Seasonal performance (application efficiency, inflow, runoff and deep percolation volumes) and economic return to water (yield benefits minus seasonal water related and labor costs) were affected by infiltration conditions, while irrigation requirement and bean yield were unchanged. In a given infiltration case, seasonal performance, irrigation schedules, bean yield and economic return to water were comparable (lower than 4% difference) for the two ET₀ conditions. For each ET₀ condition, individual irrigation events resulted in different irrigation designs (inflow rate and cutoff time) except inflow rates with heterogeneous infiltration. Differences in inflow volume were less than 2% and 5%, respectively, for homogeneous infiltration and heterogeneous infiltration. For the conditions studied, furrow irrigation management decision variables can be forecast and optimized to better manage the irrigation system, because irrigation performance was the same for both (forecast and observed) ET₀ cases. Received: 9 October 1999     

Methods for estimating irrigation needs of spring wheat in the middle Heihe basin,China

Understanding reference crop evapotranspiration (ET₀) is essential in planning the most effective use of water resources in the arid northwest China. The objective of the present work in the middle Heihe River basin were: (1) to determine the best model for calculating the areal distribution of reference crop evapotranspiration in this region, and (2) to estimate the spatial distribution of the irrigation requirements of spring wheat. Note that eight commonly used formulates were tested and that FAO-Penman was the best.The irrigation amount of spring wheat in 2000 was estimated by three steps. First, DEM-based and GIS-assisted methods were employed to estimate the spatial distribution of reference crop evapotranspiration (ET₀) according to FAO-Penman model. Then, spring wheat evapotranspiration (ET) was calculated by ET₀ and crop-coefficient (K_c). Finally, the maximum irrigation amount of spring wheat was estimated with the spring wheat evapotranspiration and precipitation in the different growing stage. The maximum irrigation has temporal–spatial variation. Temporally the irrigation amount appears the largest in June when it is the peak period of spring wheat development. The irrigation amount is the smallest in July because spring wheat was in late-season stage. In April, spring wheat was in seedling stage during which the water demand is also small. Spatially the irrigation amount increases from southeast to northwest.     

Effects of partial root-zone irrigation on the nitrogen absorption and utilization of maize

To investigate the dynamic change of plant nitrogen (N) absorption and accumulation from different root zones under the partial root-zone irrigation (PRI), maize plants were raised in split-root containers and irrigated on both halves of the container (conventional irrigation, CI), on one side only (fixed partial root-zone irrigation, FPRI), or alternatively on one of two sides (alternate partial root-zone irrigation, APRI). And the isotope-labeled ¹⁵N-(NH₄)₂SO₄ was applied to one half of the container with (¹⁴NH₄)₂SO₄ to the other half so that N inflow rates can be tracked. Results showed that APRI treatment increased root N absorption in the irrigated zone significantly when compared to that of CI treatment. The re-irrigated half resumed high N inflow rate within 5 days after irrigation in APRI, suggesting that APRI had significant compensatory effect on N uptake. The amount of N absorption from two root zones of APRI was equal after two rounds of alternative irrigation (20 days). The recovery rate, residual and loss percentages of fertilizer-N applied to two zones were similar. As for FPRI treatment, the N accumulation in plant was mainly from the irrigated root zone. The recovery rate and loss percentage of fertilizer-N applied to the irrigated zone was higher and the residual percentage of fertilizer-N in soil was lower if compared to those of the non-irrigated zone. The recovery rate of fertilizer-N in APRI treatment was higher than that of the non-irrigated zone but lower than that of the irrigated zone in FPRI treatment. In total, both FPRI and APRI treatments increased N and water use efficiencies but only consumed about 70% of the irrigated water when compared to CI treatment.     

Water Productivity from Integrated Basin Modeling

It is obvious that real water saving measures are only possible if the current water resources are clearly understood. For a basin in western Turkey, simulation modeling at three different scales, field, irrigation scheme and basin level was performed to obtain all terms of the water balance. These water balance numbers were used to calculate the Productivity of Water (PW) at the three levels. The four performance indicators considered were: PW_irrigated (yield / irrigation), PW_inflow (yield / net inflow), PW_depleted (productivity / depletion), and PW_process (productivity / process depletion), all expressed in kg yield per m³ water. For the two cotton fields considered at the field scale level, the more upstream field performed better than the field at the tail-end. This was partly a result of the difference in climatic condition, but was mainly due to the location of the two fields: upstream vs. downstream. At the irrigation scheme level PW_irrigated was higher than at the individual cotton field, since non-irrigated crops were also included. Other PW values were lower as crops more sensitive to drought were also found in the irrigated areas. Basin scale PWs are lower than those at the irrigation scheme, as large areas of the basin were covered with less productive land covers. It is concluded that performance indicators are useful ways of representing water dynamics with clearly understandable numbers, and that it is important to consider all the spatial scales at the appropriate level of detail.     

Water use efficiency and economic feasibility of growing rice and wheat with sprinkler irrigation in the Indus Basin of Pakistan

With a population of more than 150 million, Pakistan cannot meet its need for food, if adequate water is not available for crop production. Per capita water availability has decreased from 5600 m³ in 1947 to 1000 m³ in 2004. Water table has gone down by more than 7 m in most parts of the country. Present need is to identify and adopt measures, that will reduce water use and increase crop production. This study was conducted in farmers’ fields during 2002–2004 to evaluate the water use efficiency and economic viability of sprinkler irrigation system for growing rice and wheat crops. Yields and water use were also measured on adjacent fields irrigated by basin flooding, which were planted with the same crop varieties. Sprinkler irrigation of rice produced 18% more yield, while reducing consumption of water to 35% of that used in the traditional irrigation system. Sprinkler irrigation of wheat resulted in a water use efficiency of 5.21 kg of grain per cubic meter of water used compared to 1.38 kg/m³ in the adjacent flooded basins. Benefit–cost analysis showed that adoption of rain-gun sprinkler irrigation for rice and wheat is a financially viable option for farmers. While these findings show large potentials for improving water use efficiency in crop production they also indicate that a large portion of the water applied in traditional flooded basin irrigation is going to groundwater recharge, which has high value near large cities which draw their water from the aquifer.     

影响水平畦田灌溉质量的灌水技术要素分析

在开展激光控制土地精细平整技术应用的基础上 ,根据田间畦灌试验资料 ,对影响水平畦田灌溉质量的灌水技术要素进行分析和评价 ,给出适宜于水平畦田灌溉方法应用的田间技术参数组合方式。结果表明 ,在较佳的田间微地形条件下 ,通过选择合理的地面纵坡和畦田规格 ,采用适宜的入畦流量并加强田间灌溉管理 ,可达到改进和提高水平畦田灌溉系统性能的目的     

Analysis of surface irrigation systems with WinSRFR—Example application

WinSRFR is an integrated software package for analyzing surface irrigation systems. Software functionalities and technical features are described in a companion article. This article documents an example application. The analyzed field is a graded basin (close-ended border) irrigation system. The event analysis tools of WinSRFR are used first to evaluate performance of the irrigation system and estimate its infiltration and hydraulic roughness properties. Performance contours in the Operations Analysis World are then used to optimize irrigation system inflow rate and cutoff time. The adequacy of the existing design is examined with the performance contours provided in the Physical Design World. Hydraulic and practical constraints are considered in finding an optimal operation or design solution. Finally, sensitivity analyses are used to demonstrate the robustness of the solutions.     

Determination of infiltration rate from border irrigation advance and recession trajectories

A volume-balance technique utilizing irrigation advance and recession functions, numerical integration, and an optimization procedure was developed to determine infiltration parameters. The procedure is simple yet rational and accounts for spatial variability of soil characteristics. The required data are flow rate, the coefficients and exponents of the advance and recession functions, and inflow shut-off time. In a field experiment on a clay loam soil (typical of southern Alberta) at the Lethbridge Research Centre, infiltration rates estimated by this technique were similar and in close agreement with those measured with a ring infiltrometer. Except for two border strips, there were no significant mean differences between simulated (I_s) and measured (I_m) infiltration rates. In the two non-conforming border strips, field measured infiltration rates were higher than those simulated with the volume balance approach, most likely due mainly to spatial variability of soil characteristics and partly to lateral flow which occasionally occurs when measuring infiltration with a ring infiltrometer.     

Prediction of annual reference evapotranspiration using climatic data

It is important to determine how well ET_o can be estimated from easily observed E_pan (free water evaporation measured by a pan) measurements and the other climatic data. Our objectives are to predict annual ET_o with E_pan data (with a calibrated k_p (=ET_o/E_pan)) and with a 4-variable regression function method. The significance of the trends of E_pan, ET_o and k_p series were detected. The whole data series (ET_o, E_pan, mean temperature, sunlight hours, relative humidity and wind speed) were divided into the early (L-5) years for calibrating k_p and coefficients of a 4-variable function and the last 5 years for predicting ET_o. From the results, significance of series trends decreased when using the modified Mann-Kendall (MMK) test compared to the Mann-Kendall (MK) method. For ET_o, five out of six sites showed significant trends according to the MK statistic Z, and two sites were significant in trend combining with the MMK statistic Z*(j). For E_pan, two sites were significant in trends according to Z, and zero sites were significant in trends combining with Z*(j). For k_p, two sites were significant in trends according to Z, and no sites were significant in trends combining with Z*(j). Thus the calibrated k_p can be treated as a constant when using the E_pan method. The predicted annual ET_o using the E_pan and the multi-variable methods showed generally good agreements with the estimated annual ET_o (based on monthly PM equation) with low relative errors (RE). Mean ET_o values were well predicted by both methods. When using E_pan method, RE ranged from −14.7 to −3.3% for Urumqi, from 17.6 to 21.7% for Xning, from 1.8 to 10.7% for Lanzhou, from 4.7 to 17.0% for Huhehaote, from −7.4 to 9.1% for Beijing, and from −8.6 to 2.3% for Changchun. RE of predicting annual ET_o with 4-variable regression function were even lower compared to E_pan method. The main error source of the predictions came from the deviation between calibrated k_p and the actual k_p of the predicted years when using E_pan method and from random fluctuations of climatic data when using the 4-varible regression function. In conclusion, the MMK test was a robust method for trend detection because it considered serial time dependence. Insignificant trend of the k_p series supports the choice of a mean value as the calibrated k_p and for ET_o predictions. The E_pan method is recommended for prediction of annual ET_o.     

Temporal and spatial variations of evapotranspiration for spring wheat in the Shiyang river basin in northwest China

The methods for estimating temporal and spatial variation of crop evapotranspiration are useful tools for irrigation scheduling and regional water allocation. The purpose of this study was to develop a method for mapping spatial distribution of crop evapotranspiration and analyze the temporal and spatial variation of spring wheat evapotranspiration in the Shiyang river basin in Northwest China in the last 50 years. DEM-based methods were employed to estimate the spatial distribution of spring wheat evapotranspiration (ET_c). Reference crop evapotranspiration (ET₀) was calculated with the Penman–Monteith equation using meteorological data measured from eight stations in the basin. Crop coefficient (K_c) was determined from measured evapotranspiration in spring wheat season in the region. The results showed that ET_c gradually increased in the upper reaches of the basin in the last 50 years, while the middle reaches showed a significant decreasing trend, and in other regions, no significant trend was found. These changes can be attributed to expansion of irrigation areas and climate change. The multiple regression analysis between ET_c and altitude, latitude, and aspect were carried out for eight weather stations and the relationships were used to map ET_c for the basin. The spatial variations of ET_c were analyzed for three typical growing seasons based their precipitation. Results showed that long-term average ET_c over cultivated land was increasing from 270 mm in southwest mountainous area to 591 mm in northeast oasis of the basin, and the relative error between the estimated ET_c in spring wheat growing season by reference evapotranspiration (ET₀) and crop coefficient (K_c), and the interpolated ET_c was within 11.1%.