1. Introduction
Economic and population growth, changes in eating habits and rural and urban drifts put pressure on water resources [
1]. In addition, water, energy and food are inextricably inter-linked and are vital for the subsistence and development of human beings [
2,
3]. Therefore, it is important for researchers to find a way to promote sustainable water use and meet the needs of the growing population. Changes in the availability of water resources strongly affect food production, especially in developing countries, which have experienced several resource shortages [
4]. However, due to various factors, such as irrigation methods and technologies, water equipment and the uneven distribution of water resources in China, it is difficult to further the improvement of agricultural water use efficiency; therefore, the maximization of the irrigation water value is of great significance for agricultural development in arid areas [
5]. For example, the goal of sustainable utilization can be achieved by using the economic value of water as a starting point for the optimal allocation of water for crop irrigation and exploring a reasonable agricultural water plan [
5]. It can also provide a basis for the improvement of the utilization efficiency of irrigation water and can contribute to addressing water scarcity and food security issues [
6,
7].
The rise of intelligent algorithms in recent years has provided new ideas to solve the complex models of irrigation water resources. In the last century, Hall and Nathan [
8] proposed a dynamic programming model to solve the water allocation of supply, considering dollar benefits, cost, etc. They were followed by other researchers who proposed different intelligent algorithms to solve the optimal configuration problems [
9,
10,
11,
12,
13,
14,
15]. However, an intelligent algorithm for the optimal solution of global water distribution is often difficult to achieve due to the complexity and variability of certain factors such as objective function and constraint conditions. Jin et al. [
16] and Leela Krishna et al. [
17] proposed the Genetic Algorithm and Non-Linear Programming (GA-NLP) hybrid algorithm and the dynamic double-interval programming model and achieved the global optimal solution. The traditional intelligent algorithm for multi-objective optimization of water distribution in the channel system was not optimal; therefore, Sun et al. [
18] did not rely on the objective function and optimized a small number of parameters to solve the optimal type of method. In the process of “constant flow, control open”, Civicioglu [
19] proposed the backtracking-search algorithm for the optimization model of water distribution in an irrigation area and provided a solution for the water distribution scheme, which had the shortest water distribution time and the most stable water flow delivery. It was different from other algorithms because of its simple structure and single control parameter. Its performance was not sensitive to the initial value of the control parameter. Moreover, it was efficient, fast and capable of solving multi-model problems and was suitable for different types of optimization problems [
20,
21].
Reasonable planning of water distribution schedules for canal systems can reduce losses caused by water seepage and improve the utilization efficiency of irrigation water. Although many algorithms can optimize water distribution schemes, few studies have verified the feasibility of these optimization results in flow dynamics. Qi et al. [
22] proposed that to optimize the configuration of water resources, real-time risk dispatching, intelligent management technology and coupling technology can be strengthened. When the water distribution scheme was initiated, the water level and flow rate of the canal changed along with time and process due to unsteady flow, which reflected the channel flow [
23]. To calculate the optimization of water allocation in irrigation districts, only the utilization efficiency of water resources was considered; the real-time transition process of water flow during the actual operation in the current situation was not considered. However, field experiments are usually site-specific, expensive and time consuming, and the water distribution scheme of an irrigation district is not easily measured until reliability is assured. Therefore, establishing the numerical simulation of channel hydrodynamics based on the optimized water distribution model will be an effective and feasible method.
The basic theory for channel hydrodynamic simulation is the de Saint-Venant system of equations, which was proposed by Laplace and Lagrange [
24]. It provided new ideas for the subsequent studies of unsteady flow problems in open channels. The in-depth studies of many researchers at home and abroad have proposed and improved various solutions for solving equations, laying a solid foundation to develop the numerical simulation of open channel hydrodynamics. With continuous development in the theory and the gradual popularization of modern computer technologies, the numerical simulation of unsteady flow has been fully developed and various calculation models have been proposed. There are many kinds of solving algorithms for open channel hydrodynamic simulation. Various algorithms have been gradually matured after years of applications and improvements. However, the verification of solution feasibility by coupling the optimal water distribution process with the hydrodynamic simulation is a common practice. Considering the uniqueness of the backtracking-search algorithm (BSA), in this study some channels of the Xiying Irrigation District in the Shiyang River basin were taken as the research objects, and the results of the BSA were coupled with the hydrodynamic simulation in order to optimize and analyze the regional irrigation regime. On the basis of Sun et al. [
18], the problem of implementation was considered after the optimization of the solution. The operations of the hydrodynamic calculation model and the output of the results were used to analyze the feasibility of the scheme given by the BSA. On the basis of the new irrigation feasible scheme and the hydrodynamic information, the variation in the opening degree of each gate was calculated to provide a reference for a water-saving and efficient irrigation system in Xiying.
3. Results and Discussion
3.1. Water Distribution Scheme Given by BSA
According to the water distribution requirements of the Xiying Canalization in 2008, it was ensured that the irrigation time was controlled within 15 days. The irrigation water distribution time and flow rate (as shown in
Figure 4 and
Figure 5, respectively) were obtained by the BSA model using the basic parameters as input. Under the constraint of meeting the 15 days upper limit of irrigation time, the BSA model selected the irrigation sequence of each branch canal, gave the corresponding irrigation start and end times and also reduced the irrigation cycle, as shown in
Figure 4.
Figure 5 shows the respective working flow of the five branch canals, which met the constraints of the no-rush and no-sediment operations of the channel. It was in line with the actual operation of the field. The bar chart of the amount of unused water obtained under single backtracking is shown in
Figure 6. This meant that the amount of unused water was uneven, which was due to a higher number of available branch canals using the BSA model in the early stages. Therefore, it was easier to make the remaining flow reach zero in the unit time. The accumulation curve of unused water, shown in
Figure 6, showed that there was a pause platform in the third retrospective, which was due to the fact that the time used for the ten times backtracking was extremely short. Even if the flow rate of the unused water was high, it was impossible to accumulate a large amount of unused water in a short time.
The optimization results clearly showed that the BSA could complete the irrigation task in a short time by optimizing the water distribution of the canal system. It was conducive to the more efficient and economical use of water resources in irrigation districts. Increasing water resources beyond the limits of crop growth will not increase crop yields. Quantitative and efficient irrigation of irrigation areas enables the precise and cautious use of field water, rather than more fearless and optimistic water use. A balanced water supply must be maintained in order to sustain the agricultural water resources instead of more supply, and the traditional water supply programs must be reformed and optimized. With the efficient and economical use of irrigation water resources, irrigation water could also be used to reduce the pressure of urban water use or used as ecological water to better meet ecological needs. This takes into account the sustainability of water resources in other sectors and areas and reflects our commitment to promoting the sustainability of more water resources through the optimal management of agricultural water.
However, to propose a water distribution scheme for an actual irrigation district, optimal water use should be considered along with verification from practical aspects and simple economical use. For the verification of water use schemes in large-scale irrigation districts, it is not feasible to select field verification. With change in the irrigation area, performing an equal proportion of the experimental model for analysis cannot be adjusted in time and is also uneconomical. The effect of the BSA scheme in the scope of the Xiying main canals and its branch canals was evaluated from the simulation point of view through the numerical simulation of the channel water level and flow rate of the retrospective water distribution scheme.
3.2. Unsteady Flow Information Based on Simulation
The simulation area adopted relative elevation. The relative elevation in the simulation starting point of the total main channel was set to 100 m, while other required elevations were calculated according to the longitudinal slope. The simulation duration of each channel was set to 200 min, the time step was taken for 1 s and the downstream normal water depth operation mode was adopted. The upstream flow of Canal ZGQ (as shown in
Figure 1) was set to a design flow of 8.41 m
3/s by considering the efficiency of irrigation. The water flow dispatched from other branch channels was allocated according to the optimized water distribution scheme, i.e., the gate of each tributary was opened and closed according to the time shown in
Figure 4, while the diversion flow of each branch canal was increased from 0 to the operating flow (as shown in the column in
Figure 5) and remained stable. The calculations were performed according to the above conditions and the simulation results are shown in
Figure 7.
Figure 7 reflects the changes in the water level in the heads of the five branch canals. The head water levels of each canal had gradually transitioned to a stationary stage after certain fluctuations, as shown in
Figure 7a,b,d. The canals “3GQ” and “4GQ” (as shown in
Figure 1) were connected to the end of the main canal to form a Y-shaped channel; therefore, the water levels were different before the gate, which are shown in
Figure 7c. The water level fluctuated continuously in 200 min simulation time and was difficult to stabilize. Canals 3GQ and 4GQ were located at the end of the primary canal; therefore, the water transfer operation process of the main canal and other secondary canals greatly affected their water level. There were constant fluctuations in the water level before the gate.
Figure 8 shows that the flow discharges varied with time at the end of each secondary channel in the BSA model. The optimization results met the field requirements, and the water was supplied to the sub-regions. The change in the opening degree of each channel gate was calculated according to the calculation correlation of the gate opening degree and the simulated data (as shown in
Figure 9). The scattered point, in
Figure 9, represents the calculated value and shows that it was fitted into the actual running process of the gate (the solid line represents the fitted value), which was basically in line with the running requirements in the actual situation.
Hydrodynamic calculations are used to analyze the feasibility of the optimization results, which means that the given water distribution results are processed into boundary conditions in the MIKE calculation process so that the channel flow can be simulated under the constraints of the water distribution scheme. If the scheme is not reasonable, the boundary conditions will not be successfully coupled to the MIKE 11 and the model will not run. For the Xiying Irrigation District, it was feasible to process the optimization results as boundary conditions. This preliminarily shows that the scheme given by the BSA is feasible.
The hydrodynamic output results were processed and analyzed, and the information flow trends of each typical section conformed to the actual situation. Further analysis and processing of the water flow information gave the change process of the opening degree of each gate, and the calculated value can also fit well with the trend of a polyline that is convenient for actual operation. Through the successful simulation of the water distribution scheme and the analysis of simulation results, it was proved that the BSA scheme was feasible in the Xiying Irrigation District. For other irrigation areas, canals and irrigation systems, considering the safety and economic benefits, this method can still be used for feasibility assessment and analysis before using it in the field.
4. Conclusions
The channel hydrodynamic simulation and backtracking-search algorithm were combined in this study to verify the irrigation scheme of an irrigation district in an arid area, the Xiying Irrigation District, and showed that the hydrodynamic model was suitable for use when the BSA provided a water schedule. On the basis of a previous research study, a model was constructed to estimate the feasibility of optimized results. The hydrodynamic values of each channel flow were subsequently used to calculate the gate opening by using the sluice gate calculation correlation. Finally, the estimated results of that opening were adjusted and matched under the actual operational requirements. Several main conclusions were derived from this study, which are as follows:
(1) The BSA was applied to optimize the water dispatching in the Xiying Irrigation District. The water distribution discharging and the backflow cumulative residual water volume of each channel were obtained. The results shown in
Figure 4 to
Figure 6 show that the water distribution scheme met the optimization conditions of less time and less residual water. From the perspective of water efficiency, this scheme had preliminary feasibility.
(2) According to the hydrodynamic simulation, the water level and flow transition information for the whole canal system was obtained. By the application of MIKE 11 to some typical channels in Yintang Irrigation District, the model calculation results obtained matched the actual measured values of existing irrigation districts and indicated that the hydrodynamic model could be used to verify the water regime of the irrigation districts.
(3) After coupling the water distribution scheme optimization by the BSA with boundary conditions, the developed hydrodynamic calculations of the channel were used as a judgment criterion for the optimal allocation of irrigation water. The consistency in the hydrodynamic model calculations and the final output results showed that the water distribution scheme could be applied practically from the numerical simulation angle. A combination of the calculation correlation of the gate opening degree and the actual operating constraints determined the operation process of the gate.
The water distribution model is a theoretical innovation that also has a high practicability. The hydrodynamic value of unsteady flow provides a basis for the verification of a water distribution optimization scheme. By comparing the feasibilities of different irrigation water schedules from the hydrodynamics point of view, a preferable irrigation system can be chosen in order to overcome the problem of water shortage and realize the sustainable utilization of water.