Journal of Irrigation and Drainage Engineering

With a view to alleviate waterlogging, minimize maintenance costs, improve conveyance efficiency, etc., numerous unlined channels in India are replaced by parallel‐running, cup‐shaped (round‐bottom), brick‐lined (rigid boundary) channels. The operation of these newly lined channels manifests sediment deposition all along the wetted perimeter. This is quite surprising because: (1) The grade and concentration of sediment entering these lined channels (from their parent unlined branch canals) remain the same as in the case of unlined channels; (2) water surface or bed slopes are unchanged because the channel command is the same; and (3) the roughness coefficient rather appreciably decreases on account of the lining. This paper examines the causes responsible for sediment deposition in lined channels and suggests the most efficient shape of conveyance for sediment transport with no deposition. The rectangular section placed with its longer side horizontal is shown to be the most efficient for sediment transport, followed by the conventional trapezoidal section. The cup‐shaped section should not be used since it is the least efficient for sediment transport. Criteria for determining the limiting concentration of transported sediment are also suggested.

A basis for comprehensive analytical models, equations, and their solutions for border or furrow irrigation advance is derived. This basis consists of an analytical solution of the zero‐inertia (ZI) differential equations, which assumes a moving momentum representative cross section in the water body. It takes into account the time‐varying character of infiltration and does not contain any restrictions on the infiltration formula used. Subsequently, this solution is specifically developed for a zero‐inertia model of border irrigation advance (ZIMBA). It proved efficient in three types of application: (1) Simulation of irrigation advance in sloping borders; (2) replacing within a numerical model of the cumbersome, but widely used mass‐balance techniques for calculating the flow in the tip region of the wave; and (3) generating initial values for starting a numerical simulation of border irrigation. The results of ZIMBA are compared to observed values and to results of a full hydrodynamic model. For the data analyzed here, the prediction error always remains below 4%.

This paper presents a local optimal control technique (control of an individual gate) for operation of an irrigation canal with a single reach. By using the concepts of control theory, an expression for an upstream gate opening of an irrigation canal reach operated based upon a constant‐level control is obtained. In the derivation, the canal reach between two gates is divided into N nodes, and the finite‐difference forms of the continuity and the momentum equations are written for each node. The Taylor series is applied to linearize the equations around the initial steady state or equilibrium conditions. The linearized equations are then arranged to form a set of equations of the form $\mathbf{\delta }\dot{\mathbf{x}}\mathbf{/}\mathbf{\delta }\mathbf{t}=\mathbf{A}\mathbf{\delta }\mathbf{x}+\mathbf{B}\mathbf{\delta }\mathbf{u}$, which is called the state equation in control theory jargon. The linear quadratic regulator theory is applied to derive an expression of the form $\mathbf{\delta }\mathbf{u}=\mathbf{K}\mathbf{\delta }\mathbf{x}$ for the optimal gate opening to bring the system back to the equilibrium condition in the presence of disturbances. The response of the linearized system is simulated in the presence of known constant disturbances and found to be acceptable as long as the disturbances are less than 20% of the original flow rate in the canal reach. The results obtained from the optimal control theory are currently being evaluated using an unsteady open‐channel flow model.

An analysis of water‐delivery schedules is made based on a water‐balance simulation approach using a crop growth simulation model. Five rotational schedules of two, three, four, five, and six weeks were compared to an on‐demand schedule in terms of evapotranspiration, total water applied, and yield. Simulated yields for on‐demand and a two‐week rotation schedule are comparable. Longer rotation schedules resulted in yield decreases. Modifying the rotation schedule in critical growth periods saved water and resulted in minimum yield losses. The best modified rotation schedule produced 94% of the on‐demand yield.

The storage coefficient, transmissivity, and leakage factor are the useful parameters that assess the ground‐water potential of a leaky aquifer. These parameters can be determined with the help of pump test data by using graphical as well as numerical methods. Graphical methods are not very reliable as these are subject to personal error of judgment. On the other hand, numerical methods void of such errors rely on evaluation of the well function either by numerical integration or through approximation valid for small values of the arguments. Due to lack of a full‐range equation for the well function, an entire set of pump test data is rarely used in analysis. In this paper, a high‐accuracy expression for the well function for a leaky artesian aquifer valid for entire range of arguments is developed. A methodology for determination of cutoff error is evolved. By using this approximated well function and minimizing the sum of a criterion function based on the concept of cutoff error, aquifer parameters can be determined.

The conditions of observability and field‐parameter identifiability for surface irrigation advance are examined by analytical' techniques and the linearized zero‐inertia model. The existence and uniqueness of the inverse irrigation problem are established by numerical tests based on a nonlinear estimation algorithm. The limitations are examined for determining the field parameters of intake and surface resistance from, field‐measured values of advance and depth for border‐strip irrigation. The linearized zero‐inertia model proves to be conditionally observable, and the resistance and two infiltration parameters cannot be identified from measurements of the rate of advance alone. All three parameters on the other hand can be identified from measurements of the surface‐water profile. The design of appropriate experiments that lead to observability of the problem is examined and the analytical and numerical limitations of the zero‐inertia model that hinder the inverse solution of surface irrigation advance are identified.

The basic concepts and procedures for the estimation of roughness and infiltration parameters encountered in surface irrigation are presented. A review of existing predictive and nonpredictive parameter‐estimation methods is presented with a formulation of the inverse surface irrigation problem. Conjugate gradient and variable metric techniques are used for the search of the parameter set that minimizes the errors between field observations and the linearized zero‐inertia model. Appropriate constraints that restrict the variation of parameters within physically realistic limits are also imposed on the objective function. The performance and radius of convergence of the search algorithm are studied by numerical tests that demonstrate the steps in the development of the associated objective function and the strategy required for convergence to the correct values of the field parameters. It is concluded that a key role is played by the formulation of the direct problem and its numerical solution, and that the nonlinear field‐parameter search converges quickly when the influence of independent parameters can be decoupled during construction of the objective function.

The controllability of surface irrigation advance is examined by analytical means and numerical tests based on the linearized zero‐inertia model. First, the inflow hydrograph is proved to be identifiable from advance data. Then, it is shown that it is possible to control the advance rate by adjustment of the inflow rate. Field parameter heterogeneities are automatically taken into account, so a predetermined advance trajectory is obtained under arbitrary field conditions. The model utilizes a tentative time increment, during which a trial value for inflow is adopted. The resulting wave advance is simulated by the zero‐inertia model. Discrepancies between the actual and desired advance rate are then used to construct an objective function, whose minimization leads to a correction of the inflow rate for the next time increment of inflow. Finally, examples of self‐adaptive control are presented, in which an irrigation stream is led into a field of unknown parameters. The model uses real‐time information for the identification of the parameters and simultaneous control of the inflow rate to achieve a desired advance rate.

A recirculating furrow infiltrometer is used to determine the effect of three flow rates on infiltration for nontilled beds established on a red‐brown earth soil (heavy clay soil) in the Goulburn‐Murray irrigation region of southeastern Australia. Flow rates are 0.13 L/s (low), 0.38 L/s (medium), and 0.61 L/s (high). Tests are repeated four times at two‐week intervals over the irrigation season. Infiltration measurements are made over 10‐m long furrows for a minimum of five hours of outflow. Increasing the flow rate, with commensurate increases in wetted perimeter and depth of water in the furrow, increases the volume infiltrated into the nontilled beds on these soils. Because of this effect, the depth of water in the furrow should be maintained as high as possible without flooding the surface of the beds. Narrow spacing between furrows and the presence of crop residues in the furrow may also be beneficial. The volume infiltrated, calculated from the Kostiakov‐Lewis equation, decreases with time during the season and is especially evident at the high flow rate.