A copula-based stochastic simulation method for the penman wind function (PWF) in in-stream evaporation

Accurately estimating in-stream evaporation is crucial for understanding surface water losses, but it remains challenging due to the sparse availability of flux data and the complex dynamics of flowing systems. This study introduces a modeling framework that combines the Penman Wind Function (PWF) with empirical-prior-based stochastic simulation to quantify uncertainty in in-stream evaporation estimates under data-limited conditions. Rather than demonstrating universal transferability of PWF coefficients, this study focuses on identifying how coefficient uncertainty and cross-site transfer bias emerge when reservoir-, stream-, and literature-derived parameters are applied across hydrologically distinct environments. Direct calibration of PWF coefficients using high-resolution flux data from the Andong Stream Experiment Center produced the most reliable estimates ( r = 0.862 , C o E = 0.731 , R M S E = 1.500 m m / d a y ), confirming that site-specific calibration remains the preferred option when local observations are available. To support applications where such observations are unavailable, we constructed a literature-derived empirical prior parameter library of PWF coefficients and used log-space Kernel Density Estimation (KDE) with copula-based Monte Carlo sampling to propagate parameter uncertainty. The literature-derived coefficient pairs were treated as a heterogeneous empirical prior library rather than as homogeneous i.i.d. samples. Copula sensitivity analysis showed that coefficient dependence was weak and model-selection uncertainty was substantial; therefore, the Gaussian copula was used only as a parsimonious working copula and was evaluated against the independence copula. Cross-site application showed that reservoir-derived and ensemble-based coefficients retained part of the temporal co-variation driven by meteorological forcing, but they also produced non-negligible magnitude errors and systematic bias under stream conditions. At Andong, the Yongdam-derived coefficients and copula ensemble showed relatively high correlations but substantially degraded bias and RMSE compared with site-specific calibration, indicating limited coefficient transferability and reservoir-stream aerodynamic regime mismatch. Overall, the proposed framework is best interpreted as an uncertainty-aware baseline estimation approach for data-limited environments, while direct calibration remains the benchmark for reliable in-stream evaporation estimation.