## 1 Introduction  
Irrigation area water measurement technology is a core technology in irrigation area water monitoring and information construction [1]. Accurate flow measurement can improve the water supply capacity of all levels of channels and reduce water loss, which is the foundation of scientific water allocation and the modern management of irrigation areas [2, 3]. In recent years, Ningxia has vigorously carried out modernization transformation of irrigation areas and installed over 4000 sets of measurement and control gates, involving more than 20 domestic and foreign manufacturers. The measurement and control gate is a new type of measurement and control facility that integrates flow measurement and control. It adopts the principle of the ultrasonic time difference method for real-time flow measurement. The Ningxia Yellow Diversion Irrigation Area has the largest number of measurement and control gates in China and the measurement accuracy problem is the most prominent in this area. However, due to the large number of manufacturers involved, there are significant differences in the flow measured by different types of equipment. In addition to the Ningxia Yellow Diversion Irrigation Area, other irrigation areas in China also suffer from the problem that the measurement accuracy of the measurement and control gate cannot be calibrated [4]. There is an urgent need to find a way to calibrate and adjust the flow measured by the measurement box. The integrated measurement and control gate is designed based on the gate outflow principle. However, the traditional gate overflow formula requires selecting different flow calculation formulas based on different water flow patterns in practical applications. When the flow pattern changes rapidly or when it is difficult to distinguish between different flow patterns, this will lead to a large deviation between the calculated value and the measured value. In order to improve the accuracy of water measurement in irrigation areas, researchers have improved traditional flow calculation formulas or calibrated them for specific channels. [PERSON] et al. [5] calibrated the water level-flow relationship of the main canal in Heping Irrigation District, Qing'an County, Heilongjiang Province, by using the uniform flow formula of the open channel. They also compared the calculated values with the measured flows and verified the correctness of the calibrated water level-flow relationship curve. [PERSON] et al. [6] improved the \"six-point method\" of cross-section flow measurement for large channels in irrigation areas. They obtained the \"one-point method\" flow formula for the surface flow velocity at the center vertical line, which is applicable to wide shallow trapezoidal channels. The improved formula improves the efficiency of flow measurement and can obtain instantaneous flow. [PERSON] et al. [7] compared three commonly used river flow calculation methods using the measured flow velocity and flow data from the Feilaixia Hydrological Station. They proposed that adding a velocity observation point in the river section can significantly improve the calculation accuracy of the traditional water level-flow method. [PERSON] et al. [8] proposed a free outflow flow coefficient formula for the gate hole of Huaidian Gate in Huaihe River Basin on the basis of comparing five different functional forms of gate flow calculation formulas. This calculation formula adopts a segmented function form, which can improve the adaptability and calculation accuracy of traditional flow coefficient calculation formulas. [PERSON] et al. [9] established a unified flow calibration model for flat gates and verified the effectiveness of the model by using the Flow-3D three-dimensional simulation model and field measurement data of large-scale control gates. The above flow calculation models or flow coefficient calibration models are for specific flow patterns or fixed structure channels, and their scope of application is relatively limited.