Journal of Irrigation and Drainage Engineering

Surface fertigation is widely practiced in irrigated crop production systems. Lack of design and management tools limits the effectiveness of surface fertigation practices. The availability of a process-based coupled surface–subsurface hydraulic and solute transport model can lead to improved surface fertigation management. This paper presents the development of a coupled surface–subsurface solute transport model. A hydraulic model described in a previous paper by the writers provided the hydrodynamic basis for the solute transport model presented here. A numerical solution of the area averaged advection–dispersion equation, based on the split-operator approach, forms the surface solute transport component of the coupled model. The subsurface transport process is simulated using HYDRUS-1D, which also solves the one-dimensional advection–dispersion equation. A driver program is used for the internal coupling of the surface and subsurface transport models. Solute fluxes calculated using the surface transport model are used as upper boundary conditions for the subsurface model. Evaluation of the model is presented in a companion paper.

The development of a coupled surface–subsurface solute transport model for surface fertigation management is presented in a companion paper (Part I). This paper discusses an evaluation of the coupled model. The numerical solution for pure advection of solute in the surface stream was evaluated using test problems with steep concentration gradients. The result shows that the model can simulate advection without numerical diffusion and oscillations, an important problem in the solution of the advection–dispersion equation in advection dominated solute transport. In addition, a close match was obtained between the numerical solution of the one-dimensional advection–dispersion equation and a simplified analytical solution. A comparison of field data and model output show that the overall mean relative residual between field observed and model predicted solute breakthrough curves in the surface stream is 16.0%. Excluding only two outlier (in the graded basin data) reduces the over all mean relative residual between field observed and model predicted breakthrough curves to 5.2%. Finally, potential applications of the model in surface fertigation and salinity management are highlighted.

Analytical expressions have been developed relating water distribution indexes in trapezoidal drip irrigation units to design variables which define these units: lengths and diameters of pipes, emitter and lateral spacing, slopes, emitter flow equation parameters, and equivalent lengths characterizing local losses. The proposed expressions are founded in classical hydraulics. They are more accurate than predictions in irrigation practice and are easier to handle than the simulation models frequently proposed to irrigation technicians. Unit design and irrigation decision making and evaluation can thus be furthered. An example for the application of the proposed expressions is presented. First, lateral and submain diameters are determined for different shapes of irrigation units to achieve a given water application uniformity. The irrigation time to supply the desired irrigation depth is then calculated. Results are finally compared with values obtained by simulations that take into account hydraulic and manufacture variations in the unit.

In this paper, unsteady flow into a multiaquifer well due to stream stage changes and varying pumping rate is analyzed. The well is located at such a distance that the radius of influence touches the stream boundary; hence, pumping induces seepage from the stream to the aquifer. The discrete kernel approach, which is based on Duhamel’s principle, has been applied to find the interaction among stream, aquifers, and pumping well for constant as well as varying stream stage. The analytical expression for a damped sinusoidal flood wave passing in a fully penetrating stream has been used for obtaining the aquifer response. By applying image-well theory, the finite aquifer and well system has been transformed into an infinite aquifer and well system. The principle of superposition, which is applicable to a linear system, has been used to analyze the interaction processes among the three components of the system. The interaction of the stream, aquifers, and well with each other are analyzed during pumping, after stoppage of pumping, as well as during passage of a flood wave in the stream.

A steady-state theory is presented for predicting flow into an auger hole partially penetrating a homogeneous and anisotropic confined aquifer that is underlain by an impermeable layer. The developed equations can be directly applied (i.e., without resorting to a coordinate transformation) to translate the rate of rise of the water in a pumped auger hole into directional conductivities of soil. The study shows that the conductivity values calculated by neglecting the confining pressure of an artesian aquifer (i.e., by applying the existing unconfined auger-hole seepage theories to experimental auger data obtained from a confined aquifer) may lead to serious error; hence, the confining head of an aquifer must be considered while the conductivity values are computed. Further, the distance of the outer layer also plays an important role in determining the flow to an auger hole penetrating a confined aquifer, and this parameter must therefore be included in the theoretical analysis of the problem. The validity of the proposed theory is checked by comparing a few results obtained from the theory with corresponding results obtained from numerical and analytical works. The developed theory is an addition to already existing auger-hole seepage theories for water-table aquifers; together with the available theories, the proposed solution is expected to cover the most commonly encountered auger hole experimental flow situations in the field.

Water measurement in irrigation canals is frequently hindered by low head availability and high capital investment costs associated with construction of compatible hydraulic structures. Often irrigation systems have circular sliding gates in place used as diversion and flow control structures. The Fresno Irrigation District investigated the feasibility of using such circular gates (Armco Model 101) as flow metering stations in the 1920s. This early work demonstrated that circular gates could be used simultaneously for both flow control and as flow measurement structures. The original work is compiled by USBR as 10,500 data points and is presented in tabular fashion for gate diameters varying from $20.3\text{to}121.9\mathrm{cm}$ $(8–48\mathrm{in.})$ . An analytical equation of the form $Q=C_D(y,D)yD\sqrt{2gH}$ , [where $C_D(y,D)$ is a discharge function which depends on the gate displacement $y$ and the nominal gate diameter $D$ , $g$ represents the gravitational acceleration, and $H$ is the hydraulic headloss through the crescent-shaped orifice] accurately predicts most tabulated values. Equations are provided to compute the discharge function for nominal gate diameters varying from $20.3\text{to}121.9\mathrm{cm}$ $(8–48\mathrm{in.})$ for gate displacements between $5.1\mathrm{cm}$ $\left(2\mathrm{in.}\right)$ and fully open conditions. The precision of the proposed algorithms are excellent (predicted values are within $\pm 5\%$ of the corresponding reported values 95% of the time) for gates greater than $30.5\mathrm{cm}$ $\left(12\mathrm{in.}\right)$ .

This paper presents a comparison of two algorithms—the forward-elimination and branch-segment transformation equations—for separating out end-node variables for each branch to model both steady and unsteady flows in branched and looped canal networks. In addition, the performance of the recursive forward-elimination method is compared with the standard forward-elimination method. The Saint–Venant equations are discretized using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved using the Newton–Raphson method. The algorithm using branch-segment transformation equations is found to be at least five times faster than the algorithm using the forward-elimination method. Further, the algorithm using branch-segment transformation equations requires less computer storage than the algorithm using the forward-elimination method, particularly when only nonzero elements of the global matrix are stored. Comparison between the Gauss-elimination method and the sparse matrix solution technique for the solution of the global matrix revealed that the sparse matrix solution technique takes less computational time than the Gauss-elimination method.

The study aimed to determine the number of cultivation cycles required to reform the plough sole once it has been destroyed or removed from the paddy. An ad hoc infiltration column experiment, which is a cylinder of $50\mathrm{cm}$ in diameter and $140\mathrm{cm}$ long, was setup to simulate the processes of ploughing and compaction, the two major forces exerted by a tractor, for developing a plough sole in rice paddy. Three experimental conditions were investigated, namely developing the plough sole by ploughing, compaction, and a combination of ploughing and compaction. The results of the change in the infiltration rate, soil dry bulk density, and weight percentage of clay in an experimental soil column were measured and evaluated. The experimental results show that, the infiltration rate decreases to 63, 29, and 2% of its initial value with ploughing eight times, compaction 30 times, and combination of ploughing and compaction 14 times, respectively. Moreover, the soil bulk density increases from 1.51 to 1.53, 1.61, and $1.71\mathrm{g}{\mathrm{cm}}^{-3}$ , respectively. Finally, the weight percentage of clay in the plough sole as a result of clay particles moving down from above and increases from 6.2 to 8.2, 6.2, and 14.8%, respectively, over the experimental period. The ploughing rearranged clay content distribution and the compaction increased soil bulk density. Applying these two practices in sequence effectively increased the soil bulk density and reduced the infiltration rate. The results also indicate that after 14 ploughing and compaction the infiltration rate did not further decrease, suggesting that the soil structure could no longer be changed and the plough sole had successfully been reformed. The quantitative result of this work provides valuable information on how to rehabilitate a plough sole once it has been destroyed and needs to be reformed from the paddy field.

Critical depth is an important parameter in the analysis of varied flow in canals and natural streams. For triangular, rectangular, and parabolic channel sections it is possible to express critical depth analytically. However, for many practical sections, including the trapezoidal section, the governing equations are implicit in the critical depth. For these sections the critical depth is presently obtained either by trial and error procedure, or by using empirical equations based on curve fitting. In this Technical Note exact analytical solutions of critical depth for the trapezoidal open channel section have been obtained in the form of fast converging infinite series.

Sprinkler irrigation is a widely studied subject in scientific and technical literature. Initially studies were mainly conducted experimentally, whereas more recently we can say that the use of simulation models is the rule. To calibrate such models, experimental data of high precision are required to prevent possible errors in simulations. In sprinkler irrigation evaluation the collectors play a central role and should be designed to minimize the perturbation of water application it is measuring. Using the fluid dynamics software program Fluent, several designs of collectors have been analyzed to assess their capabilities for precise water collection under a horizontal wind. The analysis was performed in two steps: (1) evaluation of airflow perturbation due to collector and (2) calculation of collection rate for different droplet diameters and wind velocity on two selected collectors (one minimizing airflow perturbations, one easy to manufacture). The collector design producing the best results was used to create a mold for manufacturing collectors out of injected plastic material.