Journal of Irrigation and Drainage Engineering

Four methods of estimating daily reference evapotranspiration $\left({\mathrm{ET}}_o\right)$ were evaluated with the data collected from 2004 to 2006 in a Maritime weather station, the Potato Research Centre, Fredericton, N.B., Canada. We tested two models [i.e., the FAO-56 Penman–Monteith (PM) and the Priestley–Taylor (PT) equations] and two Class A pan methods (Cuenca and Snyder equations). In order to assess the Evaporation Pan methods, an automatic Class A Pan system was installed in a grassed field surrounded by potato fields and continuously measured from 2004 to 2006. The results from three growing seasons (years 2004–2006) indicated that both evaporation pan methods generated lower estimations of ${\mathrm{ET}}_o$ compared to the PM and PT methods. The PT method produced the highest ${\mathrm{ET}}_o$ estimation. The Snyder method showed a better agreement with the PM $(r^2>0.56)$ . However, the agreement varied from year to year with an $r^2$ value range of 0.4–0.7. $K_{\mathrm{pan}}$ coefficients (a factor to convert pan observation to ${\mathrm{ET}}_o$ ) varied from 0.78 to 0.94. In general, the Cuenca generated lower $K_{\mathrm{pan}}$ values (0.83) than the Snyder method (0.87). Compared to the PM, the PT method overestimated ${\mathrm{ET}}_o$ , which may be related to the absence of humidity adjustment in the model. Furthermore, the research suggested that the time step played an important role in the estimation of ${\mathrm{ET}}_o$ in this region. The PM method at daily time step was simple but intended to overestimate ${\mathrm{ET}}_o$ by 10% compared to the hourly time-step method. In summary, when Class A Pan data are available, the Snyder equation can be used to calculate $K_{\mathrm{pan}}$ with an acceptable accuracy. If the PM method is used to estimate ${\mathrm{ET}}_o$ when pan observations are unavailable, a reduction of 10% to the calculated ${\mathrm{ET}}_o$ at daily time step could be applied to improve the accuracy of ${\mathrm{ET}}_o$ estimation.

Reliable estimates of reference evapotranspiration $\left({\mathrm{ET}}_0\right)$ are key elements for efficient water resource management, and estimating ${\mathrm{ET}}_0$ , based on “Class ‘A’ pan evaporation” data is common in arid climates. A pan coefficient $\left(K_p\right)$ , which depends on the distance (or fetch) of green vegetation or fallow soil around the pan $\left(F\right)$ , wind run $\left(U\right)$ , and relative humidity (RH), is used to convert from pan evaporation to ${\mathrm{ET}}_0$ . Several researchers have developed models for estimating $K_p$ values for pans surrounded by green vegetated fetch, but there is only one equation to estimate $K_p$ values for dry fetch conditions. The equation is complex, so the objective of this research was to develop a new simple equation to estimate $K_p$ under fallow soil fetch conditions. The new $K_p$ equation and the more complex equation were compared with tabular values published by the United Nations Food and Agriculture Organization. The new equation performed slightly better at matching the tabular $K_p$ values than the complex equation. The equation derivation and evaluation are presented.

Water uptake by plants is one of the major components of water balance of the vadose zone that greatly influences the contaminant and moisture movement in variably saturated soils. In this study, a nonlinear macroscopic root water uptake model that includes the impact of soil moisture stress is developed. The model incorporates the spatial and temporal variation of root density in addition to the dynamic root depth considerations. The governing moisture flow equation coupled with the water extraction by plants term is solved numerically by an implicit finite-difference method. The simulation is performed for various physical scenarios subjected to different boundary conditions. The model is tested first without considering the water uptake and results are compared with observed data available in the literature for two cases. A nonlinear water uptake term is subsequently incorporated in the model which is then simulated for corn crop for constant root depth under various characteristic moisture availability environments. Results show that the water extraction rate is closely related to the soil moisture availability in addition to the root density. The plants are observed to extract moisture mainly from the upper root dense soil profile when water content is in an optimal range, otherwise, the peak of the uptake moves to other soil layers where the moisture is easily available. Finally, the model is applied to a corn field and simulated results are validated with field data. The simulated moisture content for 2 months of crop growing season shows a reasonably good agreement with the observed data.

The effect of four different irrigation levels on the marketable yield and economic return of summer-growth lettuce was evaluated during 2005 and 2006 in Eastern Sicily, Italy. The viability of deficit irrigation was evaluated by estimating optimum applied water levels. Actual evapotranspiration $\left({\mathrm{ET}}_a\right)$ was estimated by combining pan evaporation measures and the Penman–Monteith approach $\left({\mathrm{ET}}_{0\text{-}\mathrm{PM}}\right)$ . The highest marketable yield of lettuce was recorded for plots receiving 100% ${\mathrm{ET}}_{0\text{-}\mathrm{PM}}$ . For deficit irrigated plots, reductions in crop production were ascribed to a decrease in lettuce weight. Crop coefficients equal to 1 determined maximum crop production values. Crop water use efficiency was maximum at a 100% ${\mathrm{ET}}_{0\text{-}\mathrm{PM}}$ level of water applied, corresponding to yield of $0.3\mathrm{t}{\mathrm{ha}}^{-1}{\mathrm{mm}}^{-1}$ . Irrigation water use efficiency reached its maximum at a 40% ${\mathrm{ET}}_{0\text{-}\mathrm{PM}}$ level, with values of 0.54 and $0.44\mathrm{t}{\mathrm{ha}}^{-1}{\mathrm{mm}}^{-1}$ during 2005 and 2006, respectively. Water applied and marketable yield of lettuce showed a significant quadratic relationship. Cost functions had a quadratic form during 2005 and a linear form during 2006. In the land-limiting condition the optimal economic levels fit the agronomic ones well. In the water-limiting condition, ranges of water deficit of 15–44% and 74–94% were as profitable as full irrigation, thus contributing to appreciable water savings.

Popup sprinkler irrigation systems are usually installed in golf courses, orchards, and lawns. Evaluation of these systems is considered essential to identifying any necessary improvements. To this end some performance indicators have evolved for comparison of the existing performance with established design criteria of the system. The irrigation uniformity and application efficiency of any irrigation system are important factors which are strongly affected by pressure and wind speed. In this study, the water application uniformity, system efficiency, water application rates, jet losses, and soil infiltration characteristics were considered as the basic performance indicators. The low quarter distribution uniformity of the system varied from 43 to 57% and the application efficiency was found to be only 34–47%. The Christiansen uniformity coefficient varied from 61.7 to 68.9% for different operating pressures. More losses were found for day time irrigation than for night time irrigation. Surface runoff was observed at the bottom of the mounds due to high infiltration at their tops. Overall performance of the system was found unsatisfactory and some changes are suggested for its improvement.

Although the Darcy–Weisbach equation combined with the Colebrook–White semitheoretical formula for calculating the friction coefficient is a highly accurate generalized pipe-water flow resistance equation, most users prefer the use of simple, explicit power law form formulas. Because of their simplicity (despite their limitations) the purely empirical power formulas of Hazen–Williams and Manning remain the most popular pipe flow resistance equations used in routine hydraulic engineering applications. In this paper, a new simple power law form formula is derived to approximate the generalized Darcy–Weisbach combined with the Colebrook–White equation. The two main pipe flow parameters, such as the discharge (or velocity) and the diameter, appeared explicitly in the proposed formula. The suggested power-form formula compared with the Darcy–Weisbach and Coolbrook–White equation yields a maximum relative error of about $\pm 4.5\%$ . The power-form suggested formula is dimensionally homogeneous and its accuracy is sufficient for practical engineering applications. A correction factor is introduced for the variation of kinematic viscosity with temperature. The usefulness of the formula is demonstrated in an application concerning the optimal design of a delivery pipeline with pumping. The power form of the friction formula facilitates the formulation of the problem leading to the derivation of a simple equation from which the economic diameter is explicitly calculated.

Cross-sectional dimensions of the most hydraulically efficient lined canals are evaluated based on an analysis of a generalized trapezoidal shape that reduces to two standard sections with rounded bottom vertices used in India, as well as to the commonly used trapezoidal section with sharp bottom vertices. The method of Lagrange multipliers is applied to find the dimensions of optimal sections when the only constraint imposed is that of uniform flow and normal depth and, in addition, when values of either channel side slope, bottom width, top width, or supply depth are specified as well. The analytic solutions obtained for the generalized trapezoidal section are shown to match known solutions for limiting cases including those for sections in the shape of sharp-cornered trapezoids, rectangles, triangles, and semicircles. Solutions presented will be useful for evaluating standard cross-sectional shapes used for lined canals in India, as well as other sections that can be obtained from the generalized trapezoid with rounded bottom vertices.

Dealing with climate variability in a river basin presents many challenges in managing a water resources system. Occurrence of severe and persistent droughts deplete reservoirs storage to critical levels, which may lead to future water supply disaster. This paper illustrates certain benefits of using long-lead streamflow forecasts as well as restriction rules for reservoir operation to help manage the water resources system in the Zayandeh-rud River Basin in Iran. An approach is developed for activating restrictions on allocating water to agricultural demands during a drought and predicting low flow regimes using long-lead forecasts. The long-lead forecasts could utilize valuable hydroclimatic information such as the El-Nino southern Oscillation and northern Atlantic Oscillation to predict seasonal streamflow values. Hedging rules for optimal water supply releases is developed based on the benefit functions of release and carryover storage at each agricultural season. Hedging rules are triggered by different levels of drought indices determined by the predicted water availability at the beginning of each agricultural season. The method is used on an historical data set of hydroclimatic variables of the system to simulate the real time operation of the Zayandeh-rud Reservoir. The utility of the method is demonstrated for operating the Zayandeh-rud Reservoir from the drought mitigation point of view. Furthermore, the proposed model is compared to a stochastic dynamic programming model by investigating different indices such as drought duration, drought severity, drought loss, and reliability of agricultural water demands allocation. The results indicate that the use of the proposed approach can significantly reduce the vulnerability of the system during hydrological droughts and increases the long-term benefits of agricultural water demand allocation.

The variation of the saturated hydraulic conductivity with time, as a function of temperature, has been studied involving field measurement at the College of Aboureyhan Research farm. The College of Aboureyhan is a part of the University of Tehran and the above-mentioned farm is located in the lowland of the southeast of Tehran, Iran. For the purposes of this research study it was planned to measure and record the field data in a plot of $18{\mathrm{m}}^2$ . The hydraulic conductivity data were measured in 18 test points inside the study area using the inverse auger-hole method. Experiments were carried out from August 16, 2005 to June 14, 2006. The recorded filed data were then used to calculate the saturated hydraulic conductivity data using Excel software. The relationship between soil temperature, water temperature, and also water’s viscosity with hydraulic conductivity, respectively, were determined. The results of the statistical analysis involving SAS software demonstrated that the variation of temperature can considerably affect the saturated hydraulic conductivity values. The results showed that the lowest values of $K_s$ were obtained in the winter when the water, soil, and air temperature were minimal and these values increased when the temperature increased. The effect of the means of daily $K$ values (values measured in each sample date $K_d$ ) and their corresponding soil temperature adjusted values on drain spacing was determined compared with the average of total $K$ values. The maximum over- and underestimation of drain spacing was 19.1 and 23.3%, respectively, for measured values. These estimations were 9 and 16% for adjusted ones. Also, using the average values of $K$ measured in the soil temperature range of $17–23°\mathrm{C}$ resulted in a lower over- or underestimation of drain spacing.

In the context of sustainable watershed management, natural fibers mixed with soil have applications in irrigation and drainage projects such as river levees, contour bunds, temporary canal diversion works, temporary check dams, soil structures, stream restoration, etc., for controlling seepage. In this study, a number of experiments were carried out for determining the seepage velocity and piping resistance of different types of soils mixed randomly with coir fibers. Three types of soils are used in this study. The experiments were carried out for various hydraulic heads, fiber contents, and fiber lengths. Discharge velocity and seepage velocity of flow of water through soil is calculated in each case and compared with plain soil. It is observed that fibers reduce the seepage velocity of plain soil considerably and thus increase the piping resistance of soil. Regression equations based on experiments are developed for quantifying the seepage velocity and piping resistance considering hydraulic gradient, fiber contents, and fiber lengths. Suitability of coir fibers for field applications with typical examples is also highlighted. The results show that coir fiber mixed soil can be used to increase the piping resistance and reduce seepage velocity in the above mentioned applications.

Experiments were performed to evaluate flow and head variations along perforated screens ( $10–30\mathrm{mm}$ in diameter) using sand tanks which were connected and a perforated screen extended through these tanks to form a model collector well lateral up to $2.6\mathrm{m}$ in length. Hydraulic heads and discharge along the lateral and production rates of the model collector well were measured as the water level in the well, the lateral length, and diameter, and the hydraulic conductivity of the filter sand were varied. A mathematical model was developed to predict the axial flow velocity distribution and the discharge intensity variation along the lateral using the head distribution. Results showed that the production rate increased as the lateral length and diameter and the drawdown at the well increased. However, the production rate increase was not linearly related to these factors. When larger-diameter laterals were used, the axial flow velocity in the laterals decreased. This caused the hydraulic heads along the lateral to become more flattened, resulting in a lateral of high efficiency in terms of water production. This condition is similar to the assumption of the uniform discharge intensity along the lateral that many researchers have used in the analysis of the horizontal wells. Under the conditions of this study, a critical axial flow velocity was determined to be $1\mathrm{m}∕\mathrm{s}$ . Hydraulic efficiency decreased drastically when the velocity exceeded $1\mathrm{m}∕\mathrm{s}$ . The roughness coefficient (the Manning’s $n$ value) of the lateral varied as a function of factors such as axial velocity and discharge intensity, and it ranged from 0.010 to 0.015.

A regression analysis was performed on measured lag times from gauged watersheds to develop a lag time equation. The watersheds are part of the Agricultural Research Service’s database. They are located in several states and are comprised of varying terrain. The goal of the analysis was to develop a lag time equation that is useful in hydrologic modeling. The study included measurements from approximately 10,000 direct runoff events from 52 watersheds to determine which watershed parameters are best for predicting lag time. The lag time was found to correlate strongly with the longest hydraulic length of the watershed. Therefore an equation was developed that used only this parameter. The inclusion of any other watershed characteristics in the equation did not improve its ability to predict the lag time. Finally, the National Resource Conservation Service procedures for calculating watershed lag time were used to determine the lag times of the watersheds. These estimated lag times were then compared with the measured lag time of the watershed. It was found that the use of these methods generally underpredicted the true lag time of a watershed.

The hydraulic characteristics of multi- and single-barrel circular culverts were compared in this study. One-, two-, and three-barrel culverts configurations, operating under inlet control, were tested in the laboratory with various approach conditions and barrel spacing (horizontal and vertical). The single-barrel head-discharge relationship was consistent with the average head-discharge relationship of the individual barrels in a multibarrel culvert configuration with a uniform upstream approach flow and uniform invert elevations. For the nonuniform approach flow condition, the single-barrel model overpredicted the average-barrel flow by up to 10%. With the middle barrel installed at a lower elevation than the outside barrels, in submerged flow the single-barrel head discharge relationship was consistent with the outside barrels, but the middle barrel was up to 7% more efficient than the single-barrel discharge. The flow rate variations are attributed, in part, to a reduction in approach flow contraction entering the center culvert in the three-culvert configuration and a nonuniform distribution of intermittently forming surface vortices at the culvert inlets. The results of a state (United States) Department of Transportation survey regarding multiple culvert use are also presented.

A diagnostic curve of unimodal shape is developed for identifying the confined aquifer parameters from early drawdowns. A scaled well function is proposed for the diagnostic curve and computationally simple functions are developed for its accurate approximation. The diagnostic curve may be viewed as an alteration of the Theis’ curve or as the generalization of a previous approach proposed by the writer. Plotting the pumping test data in a convenient form and matching it to the diagnostic curve with a parallel shift of axes identify the aquifer parameters. The unimodal shape of the diagnostic curve facilitates matching and reduces the personal errors. The proposed method is simple, easy to apply, and yields accurate estimates of aquifer parameters from only early drawdowns, which would save considerable time and money involved in conducting a long-duration pumping test. The estimates obtained using the new method are as good as those obtained from much more complex methods. The new method does not require either the initial guess for the parameter values or repetitive evaluation of the well function.

A series of detailed laboratory measurements were made under steady-state flow conditions through a 0.914-m (3-ft) Cutthroat flume in an attempt to more accurately define transition submergence for four standard throat widths. It was found that the change from free to submerged flow, and vice versa, is gradual and that there is no easily observable transition point. The gradual transition between the flow regimes suggested a new calibration approach in which a single equation could more elegantly and more accurately fit the laboratory measurements, eschewing the need for separate free- and submerged-flow equations, and obviating the need to define transition submergence. Such an equation was found, providing greater calibration accuracy up to 95% submergence in 0.914-m Cutthroat flumes.

Block ramps represent structures that produce high energy dissipation and have a unique characteristic of preserving the ecological balance in a river restoration project. The energy dissipation of a block ramp changes with the tailwater level. In this technical note the relative energy dissipation in submerged flow conditions has been investigated. The experiments were conducted at the Hydraulic Laboratory of the University of Pisa, Pisa, Italy on ramps characterized by different block materials, submergence conditions, and ramp slopes. The study shows that the relative energy loss, varying the hydraulic jump location on the ramp, is essentially a function of the scale roughness, the ramp slope, the ratio between the critical water depth, and the ramp height and the ratio between the ramp length and the reduced length in submerged conditions. The differences in energy dissipation for a submerged hydraulic jump in different bed conditions are also investigated.

The specific energy equation has many applications in rectangular open-channel flow problems. The existing methods of solving this equation are as follows: trial-and-error solution, graphical solution, and design tables prepared from the specific energy equation expressed in dimensionless form. No direct solutions are available in the technical literature for this equation to date because it was presumed that finding roots of this equation requires a series of substitutions. In this technical note, the writer develops an analytical solution for transitions located in rectangular open channels: (1) to avoid the inconvenience in available solutions; (2) to derive a less time consuming method; and (3) to achieve more accurate results than those as a result of using existing methods.

Level spreaders are commonly used in combination with riparian buffers as a stormwater best management practice in many parts of the United States. These systems have not been extensively studied in urbanized environments to determine if they can provide a long-term water quality benefit. In winter 2005, 24 level spreaders were evaluated in the Piedmont of North Carolina. Detailed observations were made at 20 of these locations. The results of the study indicate that level spreaders may not be the versatile structure they are perceived to be. No level spreader-riparian buffer system was able to provide diffuse flow through the riparian buffer from the level spreader to the stream. Common causes for failure to maintain diffuse flow included: lack of maintenance (12 cases), poor design (11), riparian topography/content (11), level spreader lip not level (seven), built with easily eroded materials (six), poor construction methods (three), and human interference (two). This field evaluation indicates that level spreader systems may need design revisions, construction guidance, and maintenance requirements before they continue to be used en masse.