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Note: Please see pdf for full abstract with equations. Finding a direct solution to the widely used Green-Ampt (G-A) one dimensional infiltration model has been subject of efforts for more than half a century. We derived an accurate explicit formula that appears be so far the simplest proposed model in the literature. Our approach builds upon simulating the Valiantzas’s G-A infiltration model by a second order polynomial. The proposed equation is F = Kt (0.70635 + 0.32415 √1+9.43456(S2/K2t)), with F, K, S and t being cumulative infiltration, saturated hydraulic conductivity, sorptivity and time, respectively. Relative errors (ɛ) by the application of this equation generally do not exceed ±0.3% in most practical infiltration problems faced in water resources engineering. It was both numerically and mathematically shown that absolute errors > 0.3% could only occur if Kt/F > 0.904, a criteria that could practically be the case for light textured soils like sand and loamy sand if they are exposed to long infiltration times, i.e., 6 hr and 19 hr in our examples, respectively. A simple linear adjustment model is proposed as Fadj ≅ 0.9796F + 0.335 S2/K to account for these uncommon real-World conditions. The linear adjustment assures that ɛ remains within the ± 0.3% range even under imaginary infiltration timings. Due to its simplicity and accuracy, the proposed equation here should find application among hydrologists, natural resource scientists and engineers who desire to easily derive accurate estimations of the Green-Ampt infiltration model.

Knowledge about biomass partitioning of maize grown in arid and semi-arid climates is scarce and yet essential to select a robust and effective deficit irrigation management (DIM) strategy for these regions. The objectives of this study were to: i) investigate the effects of different levels of water application under two DIM strategies on the root and aboveground characteristics, the response factor to water stress (Ky) and irrigation water use efficiency (IWUE) of silage maize at different growth stages, and ii) determine the best DIM strategy that would maximize biomass productivity. Field pot experiments were conducted in Isfahan, Iran, during 2009 and 2010. The two DIM strategies were fixed irrigation interval-variable irrigation depth (M1), and variable irrigation interval-fixed irrigation depth (M2). Each DIM strategy was tested at four water-deficit levels, including: severe, moderate, mild, and a full-irrigation. In M1, irrigation intervals were consistent for all irrigation treatments but were varied over the growing season. Treatment effects were measured at the 10-leaf, 16-leaf, tasseling, milk, and silage harvest crop growth stages. There was significant effect of irrigation and growth stage on total aboveground biomass (TB), leaf area (LA), root biomass (RB), and root:shoot ratio (RSR) for both DIM strategies during the two years. For M2, there was significant difference in TB, LA, RB, and RSR between all irrigation levels at all growth stages. TB production was on the average around 25% higher for M1 compared to M2, even though total applied irrigation water was only 6% higher for M1. Comparing the two DIMs showed that RSR and Ky were both higher for M2, indicating that the crop was more sensitive to this strategy. In conclusion, M1 was selected as the best management practice since it had more favorable effects on improving the IWUE and also on the development of maize roots during the growing season.

The traditional catch-can technique for measuring water depth application under sprinkler irrigation systems has the limitation of being unable to monitor the continuous variation of wind drift and evaporation losses (WDEL) under changing weather conditions. Such information is essential to better manage the agricultural water by improving the global water application uniformity under moving irrigation machines. Three parallel, long, impermeable water collection strips were constructed underneath a stationary linear move irrigation system to address this issue. The sprinkler discharge efficiency (SDE ≈ 1- WDEL) was monitored over 5-min intervals (SDE5min) during Apr-Aug of 2014-on a bare experimental plot. Experiments were conducted on a discrete basis for about 1040 h total in order to collect more than 11,600 SDE5min data points. It was found that the SDE5min is very dynamic and can experience abrupt changes up to 16.5% as a result of sudden changes in wind speed and direction. The maximum and minimum observed SDE5min during the study period were 97.5 and 73.6%, respectively. The difference between maximum and minimum SDE5min during a day/night cycle was controlled by solar radiation and maximum wind speed. The average hourly SDE (SDEhr) for data collected at predawn, morning, afternoon, and evening were 89.5, 87.7, 86.9 and 88.8%, respectively. Overall, the daily SDE was mainly controlled by air temperature and varied between 81.8 and 91.8%, indicating that ∼8–18% of the daily applied water was lost on average. A multiple linear regression model was developed to help predict the SDEhr as a function of weather parameters. The model indicated wind speed, temperature and relative humidity as the best explanatory variables and predicted the SDEhr with an absolute error just over 4%. Because the difference between maximum and minimum SDEhr over a full experimental day could be as high as 22%, this magnitude of error was considered to be acceptable for wind drift and evaporation loss estimation.

The main objective of this study was to analyze the sensitivity of the monthly reference crop evapotranspiration (ETo) trends to key climatic factors (minimum and maximum air temperature (T max and T min), relative humidity (RH), sunshine hours (t sun), and wind speed (U 2)) in Iran by applying a qualitative detrended method, rather than the historical mathematical approach. Meteorological data for the period of 1963–2007 from five synoptic stations with different climatic characteristics, including Mashhad (mountains), Tabriz (mountains), Tehran (semi-desert), Anzali (coastal wet), and Shiraz (semi-mountains) were used to address this objective. The Mann–Kendall test was employed to assess the trends of ETo and the climatic variables. The results indicated a significant increasing trend of the monthly ETo for Mashhad and Tabriz for most part of the year while the opposite conclusion was drawn for Tehran, Anzali, and Shiraz. Based on the detrended method, RH and U 2 were the two main variables enhancing the negative ETo trends in Tehran and Anzali stations whereas U 2 and temperature were responsible for this observation in Shiraz. On the other hand, the main meteorological variables affecting the significant positive trend of ETo were RH and t sun in Tabriz and T min, RH, and U 2 in Mashhad. Although a relative agreement was observed in terms of identifying one of the first two key climatic variables affecting the ETo trend, the qualitative and the quantitative sensitivity analysis solutions did never coincide. Further research is needed to evaluate this interesting finding for other geographic locations, and also to search for the major causes of this discrepancy.

The increased need for water and food security requires the development of new approaches to save water through irrigation management strategies, particularly for center pivot irrigation. To do so entails monitoring of the dynamic variation in wind drift and evaporation losses (WDELs) of irrigation systems under different weather conditions and for relatively long time periods. The historical catch can method has limited our ability to address this goal. Here, a new and easy-to implement methodology, called the strip test, was developed and validated against the catch can technique. Our results showed strong agreement between the catch can method and the strip test for determining the average water application efficiency (WAE ≈ 1-WDEL). Because the strip test method was measured for shorter intervals compared to the catch can method, the variables influencing WAE were able to be compared during each test. WAE had a large variance over time, which was controlled, in part, by wind speed (>4 m s−1). Site-specific characterisation of WDEL is needed to apply this technique. Once applied, it can provide a better understanding of WAE behaviour over the time, and enhance the capability of predicting results for the optimising water use in sprinkler irrigation.

A simple analytical method was developed for directly calculating the thermodynamic wet-bulb temperature from air temperature and the vapor pressure (or relative humidity) at elevations up to 4500 m above MSL was developed. This methodology was based on the fact that the wet-bulb temperature can be closely approximated by a second-order polynomial in both the positive and negative ranges in ambient air temperature. The method in this study builds upon this understanding and provides results for the negative range of air temperatures (−17° to 0°C), so that the maximum observed error in this area is equal to or smaller than −0.17°C. For temperatures ≥0°C, wet-bulb temperature accuracy was ±0.65°C, and larger errors corresponded to very high temperatures (Ta ≥ 39°C) and/or very high or low relative humidities (5% < RH < 10% or RH > 98%). The mean absolute error and the root-mean-square error were 0.15° and 0.2°C, respectively.

The uniform distribution of water delivered through microirrigation emitters on a lateral line is an important objective that greatly affects a system’s efficiency. Among the various uniformity parameters, distribution uniformity (DU) is one of the most frequently used indexes in industry. In this study, an easy-to-use analytical method for directly calculating the DU of tapered microirrigation laterals laid on horizontal or uphill slopes is developed. The proposed equations are derived assuming that the system’s hydraulic characteristics and the ground slope are the only factors affecting the DU. A comparison test with a numerical stepwise solution indicates that the proposed analytical method is reasonably accurate and can be used to evaluate the system uniformity. The results also show that the accuracy of the method increases as the total number of outlets increases or the value of the emitter exponent approaches unity.

Sayed Hossein Sadeghi; Troy Peters; and Freddie R. Lamm Postdoctoral Research Associate, Dept. of Crop and Soil Sciences, Washington State Univ., Pullman, WA 99164 (corresponding author). E-mail: s.hossein.sadeghi@wsu.edu Extension Irrigation Specialist and Associate Professor, Washington State Univ., 24106 N. Bunn Rd., Prosser, WA 99350. E-mail: troy_peters@ wsu.edu Professor and Research Irrigation Engineer, Kansas State Univ., P.O. Box 505, Colby, KS 67701. E-mail: flamm@ksu.edu

In pressurized irrigation systems the total long-term costs can often be minimized by dividing the pipeline into segments of different diameters. To properly design such a system requires a...

A new method for calculating total friction head loss in center-pivots with an operational end-gun was developed. The proposed methodology is based on adjusting the previous friction correction factors for center-pivots with end-guns in order to correct their paradoxes and shortcomings. Equations presented in the current work are developed for center-pivots with a finite number of outlets along the lateral and constant outlet spacing and discharge as well as constant discharge and variable spacing. The proposed formulas depend on the number of outlets along the supply pipeline, the exponent of velocity term in the friction formula used and the distance that water is jetted by the end-gun. All equations reduce to the well-established equations for the friction correction factor when the end-gun is turned off. The equations presented here compare well to the stepwise friction calculation method, yet correct slight errors in the way that these friction correction factors were calculated in the past.

Anwar’s friction correction factor, G, and the average correction factor, GAVG, are used to compute the head loss resulting from friction and to calculate the required inlet pressure in horizontal tapered sprinkler laterals with multiple outlets. As a result of their being developed by using a discrete outflow model, which consists of a finite number of operating outlets, the previous approaches for determining these factors required tables or the solving of relatively complex formulas that may be cumbersome. In addition, use of these factors is subject to certain errors when the Darcy-Weisbach equation is used because they are developed assuming a constant friction factor along the lateral. In this study, considering the continuous flow-rate variation concept, at first, two simple and direct equations for calculating the G and the GAVG factor were developed. The proposed equations are then adjusted for the case in which the variability of the friction factor should be considered. The validity of suggeste...

Microirrigation has become quite a common practice in agricultural production in various parts of the world. To achieve the optimum (hydraulic and economic) system performance, designers are often faced with the problem of designing a maximum lateral length which results in a desired coefficient of uniformity (CU) or an allowable pressure head variation (δH). Previous theoretical design approaches are usually based on a constant Darcy–Weisbach (DW) friction factor along the lateral and this assumption can lead to substantial errors. In the research reported in this paper, a new analytical design approach does not require the constant DW assumption for zero-slope laterals while it still takes into account the emitter exponent and the effect of minor friction losses caused by emitters. Assuming a constant friction factor along the lateral might result in errors up to 14% in the calculation of the maximum lateral length. Conversely, the maximum relative error caused by the application of the proposed...

We examined the main and interactive effects of nitrogen (N) and deficit irrigation (DI) on the yield response factor ( K y ), water use efficiency (WUE), and irrigation water use efficiency (IWUE) of silage maize from a semiarid region of Iran. Experiments were conducted in 2003 and 2004 that included three N fertigation rates (0, 150, and 200 kg N ha −1 N0, N150, and N200, respectively) and four irrigation levels (0.7, 0.85, 1.0, and 1.13 of soil water depletion, W1, W2, W3, and W4, respectively). The soil water content measurements showed that most of the water was extracted from the top 60 cm of the soil profile. DI increased WUE for all N fertilizer treatments with the maximum value being observed at the W2 level. The average of the IWUE for the two years of the study showed that the lowest IWUE was 1.38 kg m −3 for the N0W1 treatment, while the highest IWUE was 1.8 kg m −3 for the N200W3 treatment. A linear relationship was observed between evapotranspiration and the total biomass for all N fertilizer levels in 2003 and 2004. The minimum K y to water was obtained from the N0 level as 0.64 in 2003 whereas the maximum K y was recorded from the N200 level as 0.95 in 2004. This reveals that higher N rates application would enhance corn yield sensitivity to water stress. Overall, the sensitivity of the silage maize to water stress was affected by different planting date and nitrogen fertilizer levels. We also discuss emergent trends in water and nutrient management in light of the increased need for food security in the face of changing climate and growing populations.

Based on the mathematical procedure presented in the discussion, the discusser concludes that Eq. (13) [Eq. (7)] is only valid under a limited design case where y 1⁄4 1. He justifies this statement by denoting that it is only under this circumstance that Eq. (12) reduces to (13). In the following, we show that this conclusion is incorrect: 1. Basically our reference equation for evaluating Hav is Eq. (13) and not Eq. (12). Eq. (12) cannot be considered as an exact solution of Hav because it is derived by substituting the following approximation equation