Optimal allocation model of surface water and groundwater based on queuing theory in irrigation district

The conjunctive use of groundwater and surface water for agricultural irrigation is one of the main irrigation patterns of most irrigation districts in China.The input parameters of current optimization models of groundwater are usually crisp numbers, which are too simple to truly reflect the impacts of the groundwater utilization variance on irrigation areas over time.In order to obtain more reasonable results, this study aims to develop a model for the conjunctive use of groundwater and surface water model considering the uncertainties of the application of groundwater.In general, there are only a few growth stages during which crops are irrigated by groundwater, and the relationship between crop areas irrigated by groundwater and the duration of surface water irrigation can be described as Poisson distribution.The queuing theory was used to express the uncertainty of the groundwater exploitation, and the(M/M/C):(∞/∞/FCFS) model was adopted.Based on the analyses of the queuing behavior, an optimal irrigation water allocation model was established.The model takes into account two levels of canal system including main canals and trunk canals.The objective of the model is to minimize irrigation duration, subjected to a series of constrains including surface water availability, groundwater availability, permitted flux of main canals, permitted flux of trunk canals, irrigation duration of channels, irrigation area of subareas, etc.It is difficult to solve the model using conventional solution method because of the complexity and the nonlinearity of the structure of the model.Therefore, the particle swarm optimization algorithm which can solve above problems was adopted to obtain the optimal water allocation schemes for the five main channels.Results from applying the model to a case study in the Shijin Irrigation District in Hebei demonstrate the feasibility and the applicability of the developed model.The results showed that the optimal irrigation duration is 25.6 days which is better than the previous irrigation durations(40 days on average).Channel B1 is the key channel for the efficiency improvement of the whole irrigation system since its irrigation period occupies most of the optimal irrigation duration.The reason is that the design flux of channel B1(16 m3/s) is small, while its controlled irrigation area(13 983 ha) is the largest among all subareas.The other channels are free in the adjustment of irrigation time.Channel B2 and B5 can be irrigated over a few days, which are 10.4 and 13.4 days.Channel B5 has the shortest irrigation duration(12.2 days), which illustrates that water supply capacity of channel B5 is the strongest compared with other irrigation areas in all channels.All channels are under full load working conditions during 13.4~22.7 days, thus it is particularly important to maintain the operation of the whole irrigation system.Subdistrict C1 can be irrigated by surface water during the whole period because it is the nearest to the canal head of the main canal.Subdistrict C5 is allocated with relatively more amounts of groundwater and its irrigated area by groundwater accounts for 43% of the whole irrigation area.This is because subdistrict C5 is farthest to the canal head of the main canal and has the minimum surface water use efficiency.The flux of all the canals are approximately equal to the corresponding design values, among which, the flux of B1 and B5 are higher than their design values but within the scope of 1.2 times of the design values.Accordingly, the water supply capacity of these two canals should be first adjusted in terms of improving the irrigation capacity of the whole system.However, as the area of B5 is the smallest, leading to the adjusting effect of B5 may not be as obvious as that of B1.Overall, most of the subareas are irrigated by surface water, occupying 93% of whole irrigation area.The study can reflect the variance of groundwater for irrigation over time and provide modelling reference for the establishment of the conjunctive use of surface water and groundwater in most irrigation districts of China.