Improved Monthly Frequency Method Based on Copula Functions for Studying Ecological Flow in the Hailang River Basin, Northeast China

Climate change has intensified extreme hydrological events in cold regions, threatening the stability of river ecosystems. The traditional monthly frequency method for calculating ecological flow assumes equal guarantee rates across all months, overlooking the complex nonlinear dependencies between interannual and intermonthly flows. This approach may result in flow values for certain months during low-flow years exceeding those of corresponding months in high-flow years, failing to align with actual hydrological patterns. This study integrates Copula functions with the monthly frequency method to establish an improved ecological flow calculation framework, accurately characterizing the statistical correlation between interannual and intermonthly flow variability. The Hailang River basin in Northeast China was selected as the study area. First, the SWAT model was employed to simulate natural runoff processes from 1956 to 1965. The calibration phase demonstrated excellent performance (R2 = 0.84, NSE = 0.83), and the validation phase also met standards (R2 = 0.82, NSE = 0.81). The improved method selected optimal Copula functions for each month through rigorous statistical tests (AIC, BIC, RMSE, and K-S test), establishing joint probability distributions for annual and monthly average flows. The results indicate that different Copula types better align with monthly hydrological seasonal characteristics: Gaussian Copula suits February, May, and July; t-Copula suits August; Clayton Copula from September to December; Gumbel Copula for January, March, April, and June. Through conditional probability relationships (P(X0≥x0, 90%) = 0.9), the monthly guarantee rate range determined by the improved method spans 81.83% to 90.08%, significantly outperforming the uniform 90% guarantee rate employed by traditional methods. Verification using the Tennant method confirmed that ecological flows throughout the year met “excellent” or higher standards. Ecological flows exhibited pronounced seasonal variation, ranging from 6.2 m3/s during winter to spring to 96.93 m3/s during summer to autumn, providing scientific basis for basin-scale ecological water management. This study establishes a reliable methodological framework for ecological flow management in cold-region rivers.