Journal of Irrigation and Drainage Engineering

The simulation of fertigation in furrows and level furrow systems faces a number of problems resulting in relevant restrictions to its widespread application. In this paper, a simulation model is proposed that addresses some of these problems by: (1) implementing an infiltration model that adjusts to the variations in wetted perimeter; (2) using a friction model that adjusts to different flows and which uses an absolute roughness parameter; (3) adopting an equation for the estimation of the longitudinal diffusion coefficient; and (4) implementing a second-order TVD numerical scheme and specific treatments for the boundary conditions and the junctions. The properties of the proposed model were demonstrated using three numerical tests focusing on the numerical scheme and the treatments. The application of the model to the simulation of furrows and furrow systems is presented in a companion paper, in which the usefulness of the innovative aspects of the proposed model is demonstrated.

Furrow fertigation can be an interesting practice when compared to traditional overland fertilizer application. In the first paper of this series, a model for furrow fertigation was presented. The simulation model combined overland water flow (Saint-Venant equations), solute transport (advection-dispersion), and infiltration. Particular attention was paid to the treatment of junctions present in level furrow systems. In this paper, the proposed model is validated using five furrow fertigation evaluations differing in irrigation discharge, fertilizer application timing, and furrow geometry. Model parameters for infiltration and roughness were estimated using error minimization techniques. The error norm was based on observed and simulated values of advance time, flow depth, and fertilizer concentration. Model parameters could be adequately predicted from just one discharge experiment, although the use of more experiments resulted in decreased error. The validated model was applied to the simulation of a level furrow system from the literature. The model adequately reproduced irrigation advance and flow depth. Fertigation events differing in application timing were simulated to identify conditions leading to adequate fertilizer uniformity.

GESTAR is an advanced computational hydraulic software tool specially adapted for the design, planning, and management of pressurized irrigation networks. A summary is given of the most significant characteristics of GESTAR. The hydraulic solver for quasi-steady scenarios uses specific strategies and incorporates several new features that improve the algorithms for pipe network computation, overcoming some of the problems that arise when attempting to apply drinking water software, using the gradient method, to irrigation systems. It is shown that the gradient method is a nodal method variant, where flow rates are relaxed using head loss formula exponents. Although relaxation produces a damping effect on instabilities, it is still unable to solve some of the numerical problems common to the nodal methods. In this contribution the results of the research on computational strategies capable of dealing with low resistance elements, hydrant modelling, multiple regulation valves, numerous emitters, and pumps with complex curves are presented, obtaining accurate results even in conditions where other software fails to converge. GESTAR incorporates all these computational techniques, achieving a high convergence rate and robustness. Furthermore, GESTAR’s solver algorithm was easily adapted to incorporate inverse analysis options for optimum network control and parameter calibration. Illustrative examples are provided, documenting the improved numerical techniques and examples of GESTAR’s performance in comparison with EPANET2, a widely used gradient method-based hydraulic solver.

To efficiently manage the water supply for paddy rice and to reduce the inundation damage from floods, it is necessary to enhance our understanding of the characteristics of the surface water hydraulics in an irrigated paddy field. In this study, a two-dimensional numerical model is used, and the model’s applicability for simulating surface irrigation and drainage is evaluated. The model’s Manning roughness coefficient is estimated, taking into account the growth stage of the paddy rice; the simulation results are in good agreement with the observations. Model simulations reveal that the initial ponding depth affects the wave propagation and the increase in water depth during irrigation. There are few differences in piezometric heads among the positions except for those close to the outlets during drainage. Constructing drainage ditches in a paddy field reduces the drainage time to 24 h. Also, the study results reveal that it is preferable to determine the appropriate water management measures by considering the characteristics of the surface water hydraulics of paddy fields to reduce costs and labor input.

The FAO-56 Penman-Monteith combination equation (FAO-56 PM) has been recommended by the Food and Agriculture Organization of the United Nations (FAO) as the standard equation for estimating reference evapotranspiration $\left({\mathrm{ET}}_0\right)$ . The FAO-56 PM equation requires the numerous weather data that are not available in the most of the stations. This paper examines the potential of FAO-56 PM equation in estimating the ${\mathrm{ET}}_0$ under humid conditions from limited weather data. For this study, full weather data sets were collected from six humid weather stations from Serbia, South East Europe. FAO-56 reduced-set PM ${\mathrm{ET}}_0$ estimates were in closest agreement with FAO-56 full set PM ${\mathrm{ET}}_0$ estimates at the most of locations. The difference between FAO-56 full set PM ${\mathrm{ET}}_0$ estimates and FAO-56 PM reduced-set ${\mathrm{ET}}_0$ estimates generally increases by increasing the number of estimated weather parameters. Overall results indicate that FAO-56 reduced-set PM approaches mostly provided better results compared to Turc equation, adjusted Hargreaves equation and temperature-based RBF network. This fact strongly supports using the FAO-56 PM equation even in the absence of the complete weather data set. The minimum and maximum air temperature data and local default wind speed value are the minimum data requirements necessary to successfully use the FAO-56 PM equation under humid conditions.

The extended Kostiakov equation is intensively used in surface irrigation applications. Traditionally, the extended Kostiakov infiltration formula is calibrated for specific field conditions. However, there is a dependence of the extended Kostiakov coefficients on both initial and boundary conditions. In this paper, a new simplified methodology is developed to account extended Kostiakov $\kappa$ variation for these effects. The purely empirical extended Kostiakov equation is transformed to a form of a modified version of the classical Philip two-term equation. This modification relates a physical parameter, the soil sorptivity $S$ , with the purely empirical coefficient $\kappa$ of the extended Kostiakov formula. Then, the variation of the sorptivity $S$ for various water levels and initial water contents is given theoretically by a simple algebraic equation. The proposed correction was compared with numerical infiltration data with varying initial (water content) and boundary conditions (ponding depth) for two contrasting soils. Results indicate that the corrected infiltration curves converge well with the simulated ones.

The study presents hydrologic simulations assessing the potential impact of climate change on subsurface drainage and its pattern in Iowa’s subsurface drained landscapes. The contemporary (representing the decade of 1990s) and future (representing the decade of 2040s) climatic scenarios were generated by downscaling the projections of global climatic model HadCM through two regional climatic models RegCM2 and HIRHAM to a regional grid box of $52–55{\text{km}}^2$ , which contains Perry, IA. These climatic scenarios were used to drive the field scale deterministic hydrologic model DRAINMOD to simulate subsurface drainage from one of Iowa’s predominant hydric soils, WEBSter, cultivated with Continuous Corn (WEBS_CC), and equipped with a conventional drainage system (30-m drain spacing at 1.2-m drain depth). The simulation results consistently indicate an increase in subsurface drainage from WEBS_CC under future climatic scenario as compared to contemporary climatic scenario. This increase in subsurface drainage would be more in the winter months (from December to March) and early spring months (from April to May) than summer and fall months. Since subsurface drainage is a primary carrier of nitrate-nitrogen $\left({\text{NO}}_3–\text{N}\right)$ from the agricultural lands, the extrapolation of this study simulations suggest that there would be a potential for increased ${\text{NO}}_3–\text{N}$ loss from Iowa’s subsurface drained landscapes under future (in the decade of 2040s) climatic conditions.

The Dupuit-Forchheimer approximation is used in an investigation of steady-state water-table heights due to accretion in ditch-drained lands resting on an undulating impermeable bed that slopes away from a peak midway between drainage ditches toward a lower level at the drains. Analytical expressions are obtained for the water-table profiles assuming both horizontal flow and flow parallel to the impermeable base. These are compared with numerical results obtained for the Laplace solution of the flow problem that show the equipotentials to be better approximated as being normal to the base than vertical. There is good agreement for large slopes between the water-table heights obtained assuming one-dimensional flow parallel to the sloping base and the two-dimensional numerical results. Poorer agreement is obtained as the slope becomes less with results approaching those given by assuming horizontal flow which always results in underestimates. At small accretion rates agreement is obtained with both Dupuit-Forchheimer analyses and the Laplace solution. The maximum height of the water table above the base decreases and is closer to the drain as the slope increases.

The Revised Universal Soil Loss Equation (RUSLE) is used often by erosion control planners to estimate the soil loss from urban construction sites when sizing sediment ponds and determining the soil loss under vegetative mats. This project used the existing, complete-year rainfall record for 27 sites in the state of Pennsylvania to compare the USDA isoerodent maps to the annual rainfall erosivity, $\mathit{R}$ , values calculated using the USEPA equations for the National Resource Conservation Service Type II rainfall. The USDA and USEPA maps showed a general trend of increasing median annual $\mathit{R}$ from west-to-east and north-to-south. A trend analysis relating the median $\mathit{R}$ values calculated during this project to geographic location had similar, large-scale geographic trends as the USDA and USEPA maps. However, the $\mathit{R}$ values more closely followed a combination of the annual rainfall pattern and topography (the Appalachian mountains bisect the state). Two case studies of the impacts of these calculations were developed to show the impact of using different values of $\mathit{R}$ on the design of sediment ponds and predicting vegetation establishment. The results of these scenarios indicate that the source of data to predict R can affect the frequency and cost of sediment pond maintenance and may under-predict the protection level required of a vegetated erosion control mat.

This paper documents an experimental study conducted to evaluate the performance of two commonly used sediment treatment control products, albeit with contrasting treatment technologies: a fiber roll or wattle (i.e., three-dimensional filter) and a perforated pipe wrapped by a pervious geosynthetic material (i.e., boundary filter). Emphasis was placed on (1) simulating field conditions and (2) describing performance via runoff, sediment yield, and particle-size measurements. Scaling problems typically associated with erosion experiments were minimized by using standard-size products (not scaled models) and a large-scale erosion bed with overhead rainfall simulators, with which dominant forms of soil erosion and sediment transport were attained. The results indicate that the experimental procedures and measurements utilized are appropriate for quantifying the erosion control performance of the products tested. In particular, the measurements revealed the important role of installation quality on BMP performance. Results also indicate that the magnitudes of peak discharge and total runoff from compacted, bare soils on steep slopes can approach values typical of highly impervious surfaces.

A particularly useful generalized numerical solution for detention basin design is presented and sets the stage for practical applications for roof detention and the rationale and use of such a solution for detention basin design more generally. The generalized numerical solution provides results that can be applied to practical problems in certain cases and demonstrates the general importance of storm duration. The method utilizes a trapezoidal inflow hydrograph, which includes the important effect of storm duration based on the modified rational method. Convenient charts are presented to display the relationship between the variables. The derivation provides the basis for specializing the method to provide generalized curves applicable to storage detention on roofs. Although the results presented herein are more generalized than those presented by other writers, certain other methods are shown to compare favorably for special cases. An added perspective is provided on some of those other methods. Soil Conservation Service TR-55 curves are included in the comparisons, which demonstrates their limitations. An example demonstrates application of the generalized curves.

To predict the characteristics of flows over circular spillways, a turbulence model based on the Reynolds stress model (RSM) is presented. Circular spillways are used to regulate water levels in reservoirs. The flow over the spillway is rapidly varied with highly curvilinear streamlines. The isotropic eddy-viscosity models such as $k\text{-}\epsilon$ models are based on the Boussinesq eddy viscosity approximation that assumes the components of the turbulence Reynolds stress tensor linearly vary with the mean rate of strain tensor. Hence, they cannot very precisely predict the characteristics of flows over the spillway. On the other hand, the non-isotropic turbulence models such as the turbulence Reynolds stress models (RSM) that calculate all the components of the Reynolds stress tensor can accurately predict the characteristics of these flows. The $k\text{-}\epsilon$ models and RSM were applied in the present study to obtain the flow parameters such as the pressure and velocity distributions as well as water surface profiles. The previously published experimental results were used to validate the simulation predictions. For flow over a circular spillway, RSM appears to properly validate the characteristics of the flow under various conditions in the field, without recourse to expensive experimental procedures.

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.

Two grassed bioretention cells including internal storage zones (ISZs) were monitored for $16\text{months}$ in central North Carolina. Each cell had a surface area of $106{\mathrm{m}}^2$ and fill media depths were 0.75 and $1.05\mathrm{m}$ for the north (North) and the south (South) cells, respectively. Asphalt parking lot inflow and outflows were analyzed for nitrogen and phosphorus forms and fecal coliform (FC). Outflow volumes and peak flows for individual storms were generally less than those of inflow. Overall, except for $\mathrm{N}{\mathrm{O}}_{2,3}–\mathrm{N}$ , effluent nitrogen species event mean concentrations (EMCs) and loads were significantly $(\alpha =0.05)$ lower than those of the inflow, and nitrogen species load reductions ranged from 47 to 88%. Apart from fall and winter, during which a longer hydraulic contact time seemed to be needed, the ISZs appeared to improve denitrification. Total phosphorus (TP) and $\mathrm{O}\mathrm{P}{\mathrm{O}}_4-\mathrm{P}$ EMCs were significantly lower than those of the inlet. Reductions were 58% (South) and 63% (North) for TP and 78% (North) and 74% (South) for $\mathrm{O}\mathrm{P}{\mathrm{O}}_4–\mathrm{P}$ . There was no significant difference in TP and $\mathrm{O}\mathrm{P}{\mathrm{O}}_4–\mathrm{P}$ loads between the inlet and the two outlets. Moreover, effluent concentrations for both phosphorus species were low, relative to other studies. The best nutrient EMC and load reductions occurred during the warm and humid seasons. When considering effluent concentrations in addition to removal rates, the grassed cells showed promising results for FC and nutrient pollution abatement when compared to conventionally vegetated bioretention (trees, shrubs, and mulch) previously studied in North Carolina.

A linear combination of traditional discharge equations for simple rectangular and/or triangular weirs is proposed to describe the discharge equations of compound broad-crested (CBC) weirs. The CBC weirs are composed of rectangular, triangular, and/or truncated triangular weirs. Dimensionless discharge equations have been also derived. Laboratory experiments on discharge relations for flows over four CBC weirs were conducted in this study in order to calibrate the proposed discharge equations. The experiments were carried out under the conditions of the $H_1∕H_2$ -ratio of water heads above upper and lower crests less than 0.54, and a dimensionless discharge less than 2.174. The result shows that the differences between the calculated discharges by the proposed equations and the measured ones are less than 3% for flows over these CBC weirs under the present experimental conditions.