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Presents a response to the comments made on an article about an algorithm for hydraulic calculation in irrigation laterals. Problems identified in the article; Types of SBS simulations proposed in the paper; Reason for the disagreement pointed out by the discussers.

The nonlinear Muskingum model is a hydrologic flood-routing method useful when the storage flow relation departs from the classic linear assumption. This paper extends versions of the nonlinear Muskingum model by introducing a parameterized initial storage condition. The extended nonlinear Muskingum values have an increased number of degrees of freedom that allows an enhanced capacity to accurately predict outflow hydrographs provided that parameter estimation is optimized as proposed in this work. The parameters of the nonlinear Muskingum models are estimated with the weed optimization algorithm (WOA), and the excellent performance of the extended nonlinear Muskingum models is demonstrated with several types of hydrographs using several criteria of statistical efficiency. The implementation results show that the nonlinear Muskingum model's predictions outperform those of the best results reported with other routing models for the examples presented in this paper. [ABSTRACT FROM AUTHOR]

Previous research on canal automation has dealt with the control of single, in-line canals, while canal operators typically have to control an entire network of canals. Because the branches in a network are hydraulically coupled with each other, control of a branching canal network based on separate controllers for each branch may not be the most effective control strategy. A methodology by which existing automatic control systems could be modified to control branching canal networks is provided in a companion paper. This paper presents results of hydraulic simulations of the new methodology to estimate the controllability of a large portion of the branching canal network operated by the Salt River Project (SRP). Two types of controllers were used for this study: (1) linear quadratic regulator (LQR) and (2) model predictive control (MPC). Both controllers used the same underlying process model [integrator-delay (ID) model], and both controllers were capable of feedback and feedforward control. Under feedback control alone, both controllers gave similar performance, but were unable to effectively control the overall system because of the long delay times. When feedforward control was added to the feedback controller, both of these control systems were able to effectively control the branching canal network operated by SRP. For the LQR controller, the volume compensation method for routing known demand change was used as the feedforward controller. For the MPC controller, the ID model was used as the feedforward controller. Slight differences were noted between the performance of the two feedforward controllers. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of the development of a distributed linear quadratic Gaussian (LQG) controller for a water delivery canal. The control structure proposed relies on a set of LQG control agents interconnected through a communication network. Each of these local control agents controls a canal reach made of a pool and the corresponding downstream gate and receives information (output signal and control moves) only from the corresponding canal reach and the ones that are adjacent to it. An algorithm is proposed to achieve coordinated action of the different local control agents. This distributed control structure is compared with centralized multivariable LQG control. Several aspects with incidence on performance are addressed, including the modification of the quadratic cost to ensure a constraint on closed-loop poles, the use of a nonlinear filter to limit noise effects, and the impact of a quantization commonly forced in gate position. Experimental results obtained in a pilot canal are presented. [ABSTRACT FROM AUTHOR]

Hydraulic methods can model channel flow with high accuracy using data related to channel geometry and flow regime that render the computational effort burdensome. In contrast, hydrologic methods apply simplifying assumptions in their algorithms for flow routing. This paper implements genetic programming (GP) to calculate hydrographs in simple and compound channels. Predicted hydrographs for the simple and compound channels are compared with those predicted by a Muskingum model and a one-dimensional (ID) coupled characteristic-dissipative-Galerkin (CCDG-1D) procedure. Results show that the differences between predicted hydrographs by GP and modeled hydrographs by the Muskingum and CCDG-1D methods are similar in simple and compound channels. Moreover, GP yields acceptable predicted hydrographs with decreased computational burden. These results indicate that the proposed GP method is effective in the prediction of open-channel flow. [ABSTRACT FROM AUTHOR]

Multicropping is the practice of growing two or more crops in the same space during a single growing season. Planning rules are mathematical equations that use previous experiences of a water resource system to balance the system's water supply and demand, and calculate multicrop areas in various periods. In this paper, linear and nonlinear planning rules are developed for optimal multicrop irrigation areas associated with reservoir operation policies in a reservoir-irrigation system. Reservoir operations are related to water allocations to each irrigated area by considering inflow and storage volume of the reservoir as the water supply in a monthly operation period. Evolutionary algorithms (EAs) can determine optimal multicropping patterns planning rules by considering various mathematical patterns. In this paper, three EAs, namely, (1) genetic algorithm (GA), (2) particle swarm optimization (PSO), and (3) shuffled frog leaping algorithm (SFLA) are employed and compared to maximize the total net benefit of the water resource system by supplying irrigation water for a proposed multicropping pattern over the planning horizon. Results show that the SFLA achieves the best solution, with the maximum value of the objective function in both linear and nonlinear planning rules compared to the GA and PSO. Moreover, the best yield of nonlinear rules is 45.52% better (higher) than that obtained by linear rules. [ABSTRACT FROM AUTHOR]

The paper reviews several methods to convert discharge into gate opening. A control algorithm for one or several reaches of an irrigation canal sometimes uses a discharge as the control action variable even though the device to be manipulated is a gate or a weir. In this case a slave controller has to convert the discharge into a gate opening or a sill elevation in the case of a weir. This is usually done by inverting the static relation between discharge and gate opening. An improved method can be based on the characteristics theory to estimate the deviations of the water levels. However, both methods underestimate the gate opening deviations required to deliver a desired discharge deviation, because water levels vary continuously over time when the gate is operated. The paper proposes a method to take into account this dynamic behavior of the pool-gate interaction by using a simple linear model for the pools’ dynamics, the integer delay zero model. The proposed method enables us to better estimate the gate opening necessary to get a desired average discharge. The method is evaluated in simulation and on a gate of the Gignac Canal, located in the South of France. A dimensionless analysis of the problem is finally performed to evaluate the methods’ applicability. [ABSTRACT FROM AUTHOR]

Grass establishment on railway embankment steep slopes for erosion control in Central Queensland, Australia, is aided by drip lateral irrigation systems. The effective field values of the lateral parameters may be different from the manufacturer supplied ones due to manufacturing variations of the emitters, environmental factors, and water quality. This paper has provided a methodology for estimating drip lateral effective parameter values under field conditions. The hydraulic model takes into account the velocity head change and a proper selection of the friction coefficient formula based on the Reynolds number. Fittings and emitter insertion head losses were incorporated into the hydraulic model. Pressure measurements at some locations within the irrigation system, and the inlet discharges, were used to calibrate the lateral parameters in a statistical framework that allows estimation of parameter uncertainties using the Metropolis algorithm. It is observed that the manufacturer’s supplied parameters were significantly different from the calibrated ones, underestimating pressures within the irrigation system for a given inlet discharge, stressing the need for field testing. The parameter posterior distributions were found to be unimodal and nearly normally distributed. The emitter head loss coefficient distribution being very significant suggests the need to incorporate it into the hydraulic modeling. Although the example given in this paper relates to steep slopes, the methodologies are general and can be applied to any use of drip laterals. [ABSTRACT FROM AUTHOR]

Discusses research on gradually varied flow computation in cyclic looped channel networks. Algorithm for steady and gradually varied flows in looped channel networks; Computational efficiency of the proposed algorithm; Comparison of solution time for the solution technique and band solver for different bandwidths.

The canal delivery system in the Left Hemidelta area of the Ebro River in Spain consists of a tree-shaped net of open canals. The overall system can be quickly isolated in the case of an emergency by closing the upstream pool. Transients, in which the initial state is hydraulically far from the final state, are difficult to handle and cannot be made in only one gate movement in order to protect the canal lining. Therefore, they have to be as smooth as possible. GoRoSo is a feedforward control algorithm for irrigation canals based on sequential quadratic programming. With this tool, it is possible to calculate the gate trajectories that smoothly carry the canal from the initial state to the final state by keeping the water depth constant at checkpoints. The paper shows the efficient implementation of GoRoSo in both the closure and opening operations of the canal delivery system. [ABSTRACT FROM AUTHOR]

An accuracy-based learning classifier system (XCS), as described in a companion paper (Part I: Design), was developed and evaluated to produce operational rules for canal gate structures. The XCS was applied together with a genetic algorithm and an unsteady hydraulic simulation model, which was used to predict responses to gate operation rules. In the tested cases, from 100 to 2,000 XCS simulations, each involving thousands of hydraulic simulations, were required to produce satisfactory rules. However, the overall fitness of the set of rules increased monotonically as XCS simulations progressed. Initial fitness started at an arbitrary value, and rules increased in strength by better achieving operational objectives during the training process. Fewer XCS iterations were required to increase the fitness as the rule population evolved. Calculated water depths approached the respective target depths for variable water delivery demand through turnout structures in the simulated canal systems. The water depth achieved stabilization inside a dead band of ± 8% of the target depth after applying different turnout demand hydrographs to each reach. The calculated depth was inside the dead band 92% of the time in Reach 1, and 73% of the time in Reach 2 for the constant supply experiment. The water depth was inside the dead band 100% of the time in Reach 1, and 76% of the time in Reach 2 for the variable-supply experiment. [ABSTRACT FROM AUTHOR]

A downstream controller is designed for an irrigation canal reach using a design technique called quantitative feedback control theory (QFT). The performance of this controller is compared to a proportional, integral, derivative (PID) controller and a linear quadratic regulator (LQR) controller. In this study, the QFT controller is designed for a single canal reach because it best demonstrates how a controller is designed. Previous research for this canal model provided data for comparison. For the operating conditions that are defined in this paper, the QFT controller is shown to have slightly better performance than the PID controller and better performance than the LQR controller. When the canal hydraulic roughness is increased, the QFT controller still performed better than the PID controller. [ABSTRACT FROM AUTHOR]

A typical irrigation scheduling problem is one of preparing a schedule to service a group of outlets which may be serviced simultaneously. This problem has an analogy with the classical earliness/tardiness problem in operations research. In previously published work an integer program was used to solve this problem, however such scheduling problems belong to a class of combinatorial problems known to be computationally demanding (N-P hard). This is widely reported in operations research. Hence integer programs can only be used to solve relatively small problems usually in a research environment where considerable computational resources and time can be allocated to solve a single schedule. For practical applications metaheuristics such as genetic algorithms, simulated annealing, or tabu search methods need to be used. However as reported in the literature, these need to be formulated carefully and tested thoroughly. This paper demonstrates the importance of robust testing of one such genetic algorithm formulated to solve the irrigation scheduling problem with simultaneous outlets serviced against an integer program formulated to solve the same problem. [ABSTRACT FROM AUTHOR]

The determination of critical depth and the position of control sections is important in open-channel hydraulics. Calculation of critical depth in open channels is useful not only for determining the condition of a flow but also for hydraulic design and analysis of experimental and analytical results. In this study, unlike the conventional approaches, an alternative method, based on a genetic algorithm (GA), for the calculation of critical depth in conduits is presented. In our model, the governing equations are transferred into an objective function that is then minimized using a GA in order to calculate critical depth. This method does not have the limitations of existing empirical and semiempirical methods and can be used for any prismatic or nonprismatic open-channel cross section. The concepts presented in this paper can be generalized for solving other tortuous hydraulic engineering equations and problems. [ABSTRACT FROM AUTHOR]

Most of the research on the design of feedback controllers for irrigation canals has been concentrated on single, in-line canals with no branches. Because the branches in a network are hydraulically coupled with each other, it may be difficult to automatically control a branching canal network by designing separate feedback controllers for each branch and then letting them run simultaneously. Thus feedback control of an entire branching canal system may be more efficient if the branching flow dynamics are explicitly taken into account during the feedback controller design process. This paper develops two different feedback controllers for branching canal networks. The first feedback controller was developed using linear quadratic regulator theory and the second using model predictive control. Both algorithms were able to effectively control a simple branching canal network example with relatively small flow changes. [ABSTRACT FROM AUTHOR]

This paper presents a genetic algorithm (GA) model for obtaining an optimal operating policy and optimal crop water allocations from an irrigation reservoir. The objective is to maximize the sum of the relative yields from all crops in the irrigated area. The model takes into account reservoir inflow, rainfall on the irrigated area, intraseasonal competition for water among multiple crops, the soil moisture dynamics in each cropped area, the heterogeneous nature of soils, and crop response to the level of irrigation applied. The model is applied to the Malaprabha single-purpose irrigation reservoir in Karnataka State, India. The optimal operating policy obtained using the GA is similar to that obtained by linear programming. This model can be used for optimal utilization of the available water resources of any reservoir system to obtain maximum benefits. [ABSTRACT FROM AUTHOR]

Reference crop evapotranspiration (ETo) is a key variable in procedures established for estimating evapotranspiration rates of agricultural crops. As per internationally accepted procedures outlined in the United Nations Food and Agriculture Organization's Irrigation and Drainage Paper No. 56 (FAO-56), using the Penman–Monteith (PM) combination equation is the recommended approach to computing ETo from ground-based climatological observations. Applying of the PM equation requires converting input climate and site data into a number of parameters, and FAO-56 recommends exact procedures for estimating these parameters. However, a plethora of alternative procedures for estimating parameters exist in literature. As a consequence, it is likely that ambiguous results may be obtained from the FAO-56 PM equation because of the adoption of such alternative (nonrecommended) supporting equations. The purpose of the present study is to evaluate differences that could arise in FAO-56 ETo estimates if nonrecommended equations are used to compute the parameters. Using historical climate records from 1973 to 1992 of a station located in the humid tropical region of Karnataka State, India, monthly ETo estimates computed by FAO-56 recommended procedures were statistically compared with those obtained by introducing alternative procedures for estimating parameters. In all, 13 alternative algorithms for ETo estimation were formulated, involving modified procedures for parameters associated with weighting factors, net radiation, and vapor-pressure-deficit terms of the PM equation. For the 240-month period considered, nine of these algorithms yielded ETo estimates that were in close correspondence with FAO-56 estimates as indicated by mean absolute relative difference (AMEAN) values within 1% and maximum absolute relative difference (MAXE) values within 2%. The remaining four algorithms, involving nonrecommended procedures for the vapor-pressure-deficit and net-radiation parameters, yielded considerably different ETo estimates, giving rise to AMEAN values in the range of 2 to 8% and MAXE values ranging between 8 and 28%. The results of this study highlight the need for strict adherence to recommended procedures, especially for estimating of vapor-pressure-deficit and net-radiation parameters if consistent results are to be obtained by the FAO-56 approach. [ABSTRACT FROM AUTHOR]

In the past, studies involving optimal design of composite channels have employed Horton’s equivalent roughness coefficient, which uses a lumped approach in assuming constant velocity across a composite channel cross section. In this paper, a new nonlinear optimization program (NLOP) is proposed based on a distributed approach that is equivalent to Lotter’s observations, which allows spatial variations in velocity across a composite channel cross section. The proposed NLOP, which consists of an objective function of minimizing total construction cost per unit length of a channel, is solved using genetic algorithm (GA). Several scenarios are evaluated, including no restrictions, restricted top width, and restricted channel side slopes, to account for certain site conditions. In addition, the proposed NLOP is modified to include constraints on maximum permissible velocities corresponding to different lining materials of the composite channel cross section, probably for the first time. The proposed methodology is applied to trapezoidal and triangular channel cross sections but can be easily extended to other shapes or compound channels. Optimal design graphs are presented to determine the channel dimensions of a composite trapezoidal channel cross section. The results obtained in this study indicate that cost savings up to 35% can be achieved for the unconstrained velocity case and up to 55% for the limiting velocity case when the proposed NLOP is solved using GA as compared with the existing NLOP solved using either the classical optimization solution technique or GA. [ABSTRACT FROM AUTHOR]

Model predictive control (MPC) is a popular control algorithm in the process control industry that is particularly suited to the automatic control of irrigation water delivery systems because it explicitly accounts for the long delay times encountered in open-channel flow. In addition, a feedforward routine is easy to implement in MPC and many of the constraints that canal operators face can be directly incorporated into the MPC scheme. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on ASCE test canal 1 using a remote downstream control configuration of MPC. The MPC algorithm effectively controls ASCE test canal 1, and its performance was similar to that of other proposed controllers. When there were no minimum gate movement constraints, MPC was fairly robust because the controller performance did not significantly degrade under untuned conditions. In the presence of minimum gate movement constraints, the water levels continually oscillate around the water level setpoint. Using the configuration presented in this paper, the feedforward portion of MPC does not perform as well as other proposed feedforward routines. This underperformance is related to the simplifications made by the underlying process model and not to MPC itself. [ABSTRACT FROM AUTHOR]

The article discusses a study on water cycle algorithm (WCA) performance in optimization of reservoir systems. The study compares the results of WCA application using the three mathematical benchmark test function problems such as Sphere, Bukin6, and Rosenbrock with results from a genetic algorithm (GA). The study shows WCA to have better performance and capability than GA. Also discussed are issues on the study including lack of information on WCA parameters and carryover constraint.

This paper presents the application of a distributed model predictive controller (DMPC) to the control of an accurate model of an actual irrigation canal in Spain. The canal is modeled using the Saint-Venant equations and implemented using the well-known Simulation of Irrigation Canals (SIC) modeling software for irrigation canals. The DMPC algorithm has been implemented in Matlab and interfaced to SIC. In the distributed-control algorithms, the local controllers exchange information so that their control policies are optimal in the sense of getting the best value of a performance index. The results show that the proposed distributed-control algorithm obtains better control performance than a more-conventional decentralized control scheme without information exchange. This better performance translates directly into money and resource savings. [ABSTRACT FROM AUTHOR]

To predict hydraulic jump characteristics for channel design, jump height may be determined by calculating the subcritical sequent depth from momentum theory. In closed conduits, however, a hydraulic jump may fill the conduit entirely before the expected sequent depth is reached. This paper reviews momentum theory as applicable to closed-conduit hydraulic jumps and presents general solutions to the sequent depth problem for four commonly shaped conduits: rectangular, circular, elliptical, and pipe arch. It also provides a numerical solution for conduits of any shape, as defined by the user. The solutions assume (1) the conduits are prismatic, fairly horizontal, and relatively frictionless within the jump length; (2) the pressure is hydrostatic and the velocity is uniform at each end of the jump; (3) the effects of air entrainment and viscosity are negligible; and (4) atmospheric conditions exist at the entrance. The implications of these assumptions are discussed briefly. In practice, the derived solutions may be used to predict the size and location of potential hydraulic jumps within culvert barrels or storm water sewers to facilitate a cost-effective design for energy dissipation. [ABSTRACT FROM AUTHOR]

The present work aims at taking us closer to the study of the influence of the spatial configuration of the irrigated zone on the unit cost (€/ha) of a layout irrigation network design. The layout analyzed in this paper is carried out by means of the algorithm, based on the graph theory which eliminates the skill or experience of the designer, thus giving rise to homogeneous results. These layouts are sized using the method of the modified economic series. Then, the irrigated zone is studied by applying spatial analysis techniques and calculating a series of variables that may have some effects on the cost (€/ha) of the network. Finally, we look for the existing relationship between the spatial variables and the cost by using the statistical technique of multiple regression analysis. Variables such as accessibility of supply, location of the network origin, total irrigated area, density of irrigable plots, perimeter, or hydrants spatial point pattern are extremely important in the cost of the network. The statistical model explains more than 99% of the variability found in unit cost. The equation obtained may be very useful before performing a design, in order to find out a suitable location of the network origin, as well as to check if the design of a single network is preferred to the alternative of dividing it into several smaller networks. Moreover, it would also be interesting to verify if the hydrant spatial point pattern as a whole is appropriate. [ABSTRACT FROM AUTHOR]

A patchy aquifer or an aquifer with a finite thickness skin can be considered as a radial two-zone aquifer system, which can be characterized by five parameters, i.e., the thickness of the first zone and four aquifer parameters including the transmissivity and storage coefficient for each of the first and second zones. This paper proposes an approach based on an analytical solution of a constant-flux pumping in a confined two-zone aquifer and the simulated annealing algorithm to determine the five parameters simultaneously. The estimated results for the five parameters are fairly good even assuming the aquifer as a single-zone system at the beginning of the data analysis. The estimated results indicate that the first-zone parameters are much more difficult to accurately identify than the second-zone parameters due to insufficient early-time data and high correlation of the sensitivities among the first-zone parameters. However, the problem of inaccurate results obtained at the first-zone can be significantly improved if more densely temporal drawdown measurements are used. [ABSTRACT FROM AUTHOR]

This paper presents a simple and quick method for estimating furrow infiltration using a single advance point based on the volume balance equation. The furrow infiltration and water front advance along the furrow are assumed to follow the modified Kostiakov infiltration and power advance equations, respectively. The volume balance equation, including these equations, is simplified to a function containing two parameters, i.e., the exponents of power advance and Kostiakov infiltration equation (with a prior-known basic infiltration rate). These parameters are estimated by minimizing the function to zero using a quasi-Newton search algorithm, provided with Excel Solver. The estimated exponents are used to determine the Kostiakov infiltration parameters. The proposed one-point method is tested with seven independent furrow irrigation evaluation data sets and the estimated cumulative infiltration is compared with the observed counterparts. Performance of the proposed method was evaluated using the root-mean-square error and index of agreement (Ia). The results show that the proposed one-point method estimated cumulative infiltration is closer to the observed; the method performed as good as Valiantzas’ method. Shepard’s method did not perform well for the tested data sets. The algorithm and the results of the proposed method reveal that the proposed method can be used as a tool for quick estimation of furrow infiltration using a single advance point. [ABSTRACT FROM AUTHOR]

This paper develops a nonlinear programming model to optimally design a settling basin for a small-scale drainage area with a minimum total cost. It is assumed that the shape of the settling basin is rectangular parallelepiped, and it is connected to an open channel at both ends. Therefore, the decision variables include the scales of the settling basin (i.e., length, width, and height) and the scales of the channel (i.e., width and height). The design trap efficiency requirement, which must be greater than or equal to the required one of the considered watershed, makes up the main constraint. Other constraints consist of the upper and lower bounds of the decision variables, the equations for computing the trap efficiency, and the average flow velocity in the settling basin. The objective function is to minimize the total annual cost, which is the sum of the land, capital, and maintenance-operation cost. The developed model is solved by using a genetic algorithm. This model is applied to a subwatershed of the Wu-She Reservoir watershed in central Taiwan. The obtained results effectively demonstrate the applicability and practicability of the model. [ABSTRACT FROM AUTHOR]

A cost effective channel section for a specified flow rate, roughness coefficients, longitudinal slope, and various cost parameters can be determined using an optimization technique. However, the derived optimal channel section may not be feasible for construction because of in situ conditions. The local soil conditions may not support the optimal side slope of the channel and if constructed, the slope may fail. It is therefore necessary to also incorporate the criteria for side slope stability in designing an optimal open channel section. In this paper, a new methodology has been developed to design a stable and optimal channel section using hybrid optimization techniques. A genetic algorithm based optimization model is developed initially to determine the factor of safety of a channel slope for given soil parameters. This optimization model is then externally linked with a separate sequential quadratic programming based optimization model to evaluate the parameters of the stable and optimal channel section. Solution for various example problems incorporating different soil parameters are illustrated to demonstrate the applicability of the developed methodology. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Energy costs constitute the largest expenditure for nearly all water utilities worldwide and can consume up to 65% of a water utility’s annual operating budget. One of the greatest potential areas for energy cost savings is in the scheduling of pump operations. This paper presents a new management model, WAPIRRA Scheduler, for the optimal design and operation of water distribution systems. The model makes use of the latest advances in genetic algorithm (GA) optimization to automatically determine annually the least cost of pumping stations while satisfying target hydraulic performance requirements. Optimal design and operation refers to selecting pump type, capacity, and number of units as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a given set of demand curves. The optimization process consists of three main steps: (1) generating randomly an initial set of pump combinations to start the optimization process for a given demand-duration curve; (2) minimizing the total annual cost, which consists of operation and maintenance costs and depreciation cost of the initial investment, by changing the set and discharge of pump sets based on the provided model; and (3) achieving the final criterion to stop the optimization process and reporting the optimized results of the model. Computational analysis is based upon one major objective function and solving it by means of a computer program that is developed following the GA approach to find the optimized solution of generated equations. Application of the model to a real-world project shows considerable savings in cost and energy. [ABSTRACT FROM AUTHOR]

This paper presents an efficient solution technique for one-dimensional unsteady flow routing through a general channel network system—dendritic, looped, divergent, or any combination of such networks. The finite difference method is used to solve the de St. Venant equations in all the branches of the network simultaneously. The number of equations to be solved at a time during any iteration is reduced to only four times the number of branches of the network. This results in a significant reduction in storage requirements and solution time. Importantly, the algorithm does not require any special node numbering schemes and the nodes can be numbered independently for each branch. The algorithm is also suitable for programming on a parallel-processing computer. [ABSTRACT FROM AUTHOR]

Presents a response by the authors on the comment to their study titled "Gradually Varied Flow Computation in Cyclic Looped Channel Networks." Comparison between the computational efficiency of the authors and D. J. Sen et al.; Advantages of the computation method proposed by the authors; Purpose of the derivation of the computational efficiency.

The article discusses an article about the most hydraulically efficient riprap-lined drainage channels. In the article, a minimization problem was solved and was presented in a dimensionless form. It was solved numerically utilizing a variant of the generalized reduced gradient (GRG) algorithm. It is noted that a numerical solution carried out by a software application was the optimization strategy recommended by the discussers.

The feedforward control canal problem is stated as a nonlinear optimization problem with constraints on the gate movements. It is numerically solved with the use of the sequential quadratic problem (SQP) method and the active set. The main objective of the resulting GoRoSo algorithm is the scheduling of the gate openings over a programmed operation scenario, and their calculation relies on the use of the Saint-Venant's complete model over a prediction horizon. A numerical and analytical procedure is developed to quantify the influence of any gate movement over the canal flow conditions for a prediction time horizon. All these influences are lumped together in a global matrix, which is referred to as the hydraulic influence matrix. The GoRoSo algorithm is validated by means of a series of test developed by the ASCE task committee on canal automation algorithms. [ABSTRACT FROM AUTHOR]

A sequential irrigation schedule that honors user demands of duration and minimizes earliness and tardiness is interpreted as a single-machine schedule with earliness and tardiness costs and a common deadline (or fixed interval). A heuristic solution is presented for this irrigation scheduling problem. Four models are presented to reflect the different methods in which an irrigation system at the tertiary unit level may be operated, the first model permits jobs to be noncontiguous, i.e., idle time between jobs is permitted, whereas the others permit contiguous jobs only. The heuristic is tested extensively and the solution quality is compared with either an optimum solution from an integer program or the best available solution obtained from an integer program within allocated computation time. The heuristic is computationally efficient for all models presented, however for schedules with noncontiguous jobs, or where idle time is inserted before and after a contiguous set of jobs, solution quality deteriorates. The work brings the science of single scheduling from operations research into irrigation scheduling and suggests areas for further development. [ABSTRACT FROM AUTHOR]

A discussion on the article "Evolutionary Algorithms for the Determination of Critical Depths in Conduits," by A. Kanan and colleagues, published in the November/December 2008 issue, is presented. The article utilized evolutionary algorithms to identify the critical depth of an open channel section. A definition of evolutionary algorithms is presented. The author argues the use of genetic algorithms to minimize the error function.

This paper presents a combined simulation-optimization model for simulating reservoir operations without any detailed operation rules; it features the integration of a nonlinear, multiple-objective function and a heuristic search method, the Shuffled Complex Evolution method, developed at the University of Arizona. The model is applied to optimal water allocations from both Balan Reservoir and Seomjingang Dam in South Korea, an irrigation reservoir and a multipurpose, multioutlet reservoir, respectively, that primarily supply irrigation water. In the case of the optimal operation of Balan Reservoir, the simulation results show that the optimal release patterns are similar to those of historical operations because the demands for irrigation water are accurately predicted and guide optimal reservoir operations. In addition, the model is successfully applied to establishing a long-term reservoir operation plan. As for the optimal operation of Seomjingang Dam, the reservoir operations are affected by the target water stages, and the model provides reasonable results, irrespective of inflow conditions. Moreover, the model is employed to create a new operation rule that is necessary to adapt to changes in the circumstances related to water management. Consequently, it is concluded that the model is useful for assessing reservoirs' irrigation water supply capacities when establishing operation plans and providing feasible alternatives for new operation rules, and it could be applied to real-time reservoir operations. [ABSTRACT FROM AUTHOR]

The article presents a discussion on a report that described an algorithm for estimating furrow infiltration. The authors proposed a global optimization technique to search for an optimal combination for which the solution is unique. The issues addressed by the discussers were the selection of power coefficients of infiltration and waterfront advance equations for obtaining a unique solution for infiltration estimation.

Flow diversion head works are constructed across rivers to divert flow into irrigation, navigation, or power generation channels. Hydraulic structures, such as weirs or barrages, are integral parts of these diversion head works. The optimal design of these hydraulic structures is generally obtained by considering the deterministic values of hydrogeological parameters. However, there is a high degree of local soil variability and imprecision in the determination of soil parameters, such as the safe exit gradient. The seepage head also exhibits a high degree of variability, depending on complex hydrological and metrological factors. This work considers the hydrogeological parameters safe exit gradient and seepage head as imprecise or uncertain. An optimization-based methodology is presented to incorporate uncertainty in the safe exit gradient and seepage head in the optimization formulation and obtain the optimum structural dimensions that minimize the total cost. The subsurface flow consideration is embedded in the optimization formulation. The nonlinear optimization formulation (NLOF) solution procedure using a genetic algorithm (GA) is implemented to demonstrate the characterization of uncertainty in design and hence, overall cost from the uncertain safe exit gradient and seepage head. The limited evaluation shows the potential applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Flow diversion head works are constructed across rivers to divert flow into irrigation, navigation, or power generation channels. Hydraulic structures, such as weirs or barrages, are integral parts of these diversion head works. The optimal design of these hydraulic structures is generally obtained by considering the deterministic values of hydrogeological parameters. However, there is a high degree of local soil variability and imprecision in the determination of soil parameters, such as the safe exit gradient. The seepage head also exhibits a high degree of variability, depending on complex hydrological and metrological factors. This work considers the hydrogeological parameters safe exit gradient and seepage head as imprecise or uncertain. An optimization-based methodology is presented to incorporate uncertainty in the safe exit gradient and seepage head in the optimization formulation and obtain the optimum structural dimensions that minimize the total cost. The subsurface flow consideration is embedded in the optimization formulation. The nonlinear optimization formulation (NLOF) solution procedure using a genetic algorithm (GA) is implemented to demonstrate the characterization of uncertainty in design and hence, overall cost from the uncertain safe exit gradient and seepage head. The limited evaluation shows the potential applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Location-allocation algorithms allow for situating services in an efficient way in zones where the demand is dispersed across the area. In the present work, the minisum location-allocation algorithm is used to optimize the placement multioutlet hydrants, which are needed to supply irrigation to the region. The objective function aims to minimize the total access costs of the service. Because the total number of hydrants is the same as what currently exists the results can be compared with the presented solution. The proposed model reduces the total distance run to access the service, from 16,177 m to 13,560 m (16.17%), and the objective function (proportional to the cost) by 28.95%. [ABSTRACT FROM AUTHOR]

The controllability of an irrigation canal depends on its physical characteristics, on the control algorithm used, and on the actual condition of the canal in relation to the algorithm tuning conditions. The flow conditions and controllability in an irrigation canal may change if the hydraulic friction changes. Great variations in friction were observed in an irrigation canal in Spain owing to the presence of Rhizoclonium hieroglyphicum, a type of algae that grows in clear water. Such large variations in friction may have a significant effect on the stability and performance of automatic canal controllers. Using the unsteady-state model Simulation of Irrigation Canal (SIC), the influence of roughness on the performance of the study canal under distant downstream control of its four coupled pools was investigated. A set of proportional-integral (PI) controllers was tuned for different values of Manning's n. The controller's performance under real conditions is sensitive to the roughness conditions under which the control gains were tuned, and a method to robustly tune the gains of the PI controllers is proposed. [ABSTRACT FROM AUTHOR]

The interbasin water transfer project is an alternative to balance the nonuniform temporal and spatial distribution of water resources and water demands, especially in arid and semi arid regions. A water transfer project can be executed if it is environmentally and economically justified. In this study, the feasibility of two interbasin water transfer projects from Karoon River in the western part of Iran to the central part of the country is investigated. An optimization model with an economic objective function to maximize the net benefit of the interbasin water transfer projects is developed. The planning horizon of the model is 23 years (the length of historical data); and it is solved using genetic algorithm. In order to consider environmental impacts of water transfer projects, a water quality simulation model has been used. Then, an Artificial Neural Network model is trained based on the simulation results of a river water quality model in order to be coupled with the optimization model. The outputs of the optimization model are the value of economic gain of the sending (Karoon) basin to offset the loss of agricultural income and environmental costs. The optimal polices for water transfer during the planning horizon has been generated using the coupled simulation-optimization model. Then, operating rules are developed using a K Nearest Neighborhood model for the real time water transfer operation. The results show the significant value of using the proposed algorithm and economic evaluation for water transfer projects. [ABSTRACT FROM AUTHOR]

An experimental program was conducted to determine if a Parshall flume, developed to accurately measure open-channel subcritical flow, could also be used to measure discharge in a supercritical flow regime. Fifteen experimental configurations were tested using two small Parshall flumes [6-in. (15.2-cm) and 9-in. (22.9-cm) crest width] with varying approach channel slopes, approach channel roughness, and flume convergence. It was determined that a single Parshall flume can be used to measure flow (within ±5%) for both supercritical and subcritical flow regimes for a specified range of flows. The original Parshall flume equation was then modified to incorporate crest width, channel slope, channel roughness, and convergence in the prediction algorithm. Unique expressions were developed for both supercritical and subcritical flow regimes to estimate the discharge. A single expression does not appear feasible for accurate discharge measurement for both flow regimes in a Parshall flume at this time. [ABSTRACT FROM AUTHOR]

Pivoting was incorporated in the process of solving the linear system of equations that results after discretizing the Saint- Venant equations using the four-point implicit scheme, and applying the Newton–Raphson algorithm to the resulting set of nonlinear equations. Both exchange of rows only (partial pivoting) and exchange of rows and columns (full pivoting) were investigated using the CanalMan hydraulic model. Partial pivoting was used with the LU (lower and upper) decomposition linear equation solver, whereas full pivoting was used with the Gauss–Jordan elimination algorithm. It was demonstrated that the application of partial and full pivoting to the solution of the linear set of equations during Newton–Raphson iterations can make the difference between convergence and divergence of the solution, and should be applied as needed. However, full pivoting should be used only when needed because it slows the simulation considerably. [ABSTRACT FROM AUTHOR]

Traditional irrigation zones in the east of Spain have been denoted by the high level of parcellation. The layout of the irrigation network design in highly parcelled territories presents an important degree of difficulty, the previous experience of the designer in this task being crucial in the final result. In this work, a new heuristic algorithm for layout of the irrigation network design is presented. We start from a classical graph theory algorithm (Dijkstra’s algorithm) used for solving the shortest path spanning tree problem. This algorithm is modified to assign weights to the arcs and plot limits are used as if they were the arcs of a graph. The algorithm is implemented on a geographical information system, thus creating an application that automatically generates the layout of the irrigation network design. The only necessary initial data are the origin of the network (supply point) and the hydrants (delivery points). The advantage of this heuristic is that the subjectivity introduced for the designer is removed. Moreover, it allows for solving complex problems, and therefore it is applicable to highly parcelled zones, where the number of vertices and edges is so high that it would inhibit calculating capacity of any optimization process. A practical example is presented, in which the layout design obtained by applying the heuristic is compared with the original existing layout. [ABSTRACT FROM AUTHOR]

In the past, various methods have been used to estimate the parameters in the nonlinear three-parameter Muskingum model to allow the model to more closely approximate a nonlinear relation compared to the original two-parameter Muskingum model. In this study, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) technique, which searches the solution area based on mathematical gradients, is introduced. The technique found the best parameter values compared to previous results in terms of the sum of the square deviation between the observed and routed outflows, using the smallest number of computational iterations. A sensitivity analysis showed that the initial values of certain parameters were critical when finding the optimal solution. Although this gradient-based technique makes use of initial value assumptions and involves complicated calculus, different initial values reach the same optimal or near-optimal solution within less time. Moreover, this mathematical technique does not require the algorithm parameters that are essential factors in meta-heuristics such as genetic algorithm or harmony search. The technique also considers the hydrologic parameters to be continuous rather than discrete variables for pure structures. [ABSTRACT FROM AUTHOR]

A three-step computational model for the optimal weekly interseasonal operation of a multipurpose (irrigation, environmental, domestic/industrial) reservoir is developed. Environmental and domestic/industrial uses are evaluated and considered as priority uses that induce deficit irrigation conditions. The spatiotemporal variability of the irrigation water demand at the basin level is accounted for. The objective is the maximization of the interseasonal agricultural profitability at the basin level. The optimal allocation process solves the competition for water on different temporal scales (weekly, seasonal, and interseasonal) and on different spatial scales (in basins among irrigation areas and in irrigation areas among crops). The three steps are simulation model operating at the soil-crop unit level, optimization model operating at the multicrop area level, and optimization model operating at the basin level. This consists of parametric dynamic programming for which an analytical objective function was defined and an analytical solution was determined. This solution replaces the iterative procedure, so that it is possible to account for all the variables without running into the “curse of dimensionality” problem. The environmental use allocation is expressed as a function of a parameter, the variations of which give different environmental protection levels. The validation case study emphasizes the importance of considering the spatiotemporal variability of the demand. This is consistent with the “computationally tractable” model algorithm. [ABSTRACT FROM AUTHOR]

A novel and computationally efficient algorithm is presented to compute the water surface profiles in steady, gradually varied flows of open channel networks. This algorithm allows calculation of flow depths and discharges at all sections of a cyclic looped open channel network. The algorithm is based on the principles of (1) classifying the computations in an individual channel as an initial value problem or a boundary value problem; (2) determining the path for linking the solutions from individual channels; and (3) an iterative Newton–Raphson technique for obtaining the network solution, starting from initial assumptions for discharges in as few channels as possible. The proposed algorithm is computationally more efficient than the presently available direct method by orders of magnitude because it does not involve costly inversions of large matrices in its formulation. The application of this algorithm is illustrated through an example network. [ABSTRACT FROM AUTHOR]

Adequate and reliable estimates of aquifer parameters are of utmost importance for proper management of vital groundwater resources. The pumping (aquifer) test is the standard technique for estimating various hydraulic properties of aquifer systems, viz., transmissivity (T), hydraulic conductivity (K), storage coefficient (S), and leakance (L), for which the graphical method is widely used. In the present study, the efficacy of the genetic algorithm (GA) optimization technique is assessed in estimating aquifer parameters from the time-drawdown pumping test data. Computer codes were developed to optimize various aquifer parameters under different hydrogeologic conditions by using the GA technique. Applicability, adequacy, and robustness of the developed codes were tested using 12 sets of the published and unpublished aquifer test data. The aquifer parameters were also estimated by the graphical method using AquiferTest software, and were compared with those obtained by the GA technique. The GA technique yielded significantly low values of the sum of square errors (SSE) for almost all the datasets under study. The results revealed that the GA technique is an efficient and reliable method for estimating various aquifer parameters, especially in the situation when the graphical matching is poor. Also, it was found that because of its inherent characteristics, GA avoids the subjectivity, long computation time and ill-posedness often associated with conventional optimization techniques. Furthermore, the performance evaluation of the developed GA-based computer codes showed that the fitness value (SSE) of the best point in a population reduces with increasing generation number and population size. The analysis of the sensitivity of the parameters during the performance of GA indicated that a unique set of aquifer parameters was obtained for all three aquifer systems. The GA-based computer programs with interactive windows developed in this study are user-friendly and can serve as a teaching and research tool, which could also be useful for practicing hydrologists and hydrogeologists. [ABSTRACT FROM AUTHOR]

The article discusses the study "Optimum Design and Management of Pressurized Branched Irrigation Networks." The study explores the disadvantages of using a simple genetic algorithm in looking for a global optimum for branched networks. The authors explain that the created modified genetic algorithm has one operator responsible for considering the combinatorial nature of the problem.