Simulating advance distance in border irrigation systems based on the improved method of characteristics

Improving the simulation accuracy of the advance distance based on the method of characteristics is essential to develop numerical solutions for simulating surface irrigation. Instead of volume balance in the traditional method of characteristics (T-MC), the position of critical flow is determined to simulate the advance distance in the improved method of characteristics (I-MC), which is used in border irrigation systems with rapid variation in inflow discharge in the current research. Specifically, the zones of both subcritical and supercritical flow were firstly distinguished to determine the position of the critical flow point, which was also the upstream boundary of the wetting front region, and then the advance distance was calculated by applying the diffusive wave equation in the wetting front region. The results showed that the I-MC accurately simulated the advance distance with high determination coefficients (0.984-0.998) and low errors (root mean square error of 0.35-1.56 min and coefficient of residual mass of 0.01-0.06), which performed much better than the T-MC. The I-MC provided a suitable and simple numerical simulation tool to improve the establishment of numerical surface irrigation models.