In this study, a particle copula Metropolis-Hastings (PCMH) approach was developed for reliable uncertainty quantification of hydrological predictions. The proposed PCMH approach employs a mixed particle evolution scheme, which integrates the Gaussian perturbation and copula-based dependent sampling methods. The Metropolis ratio is then employed to determine the acceptance of the candidate samples. The applicability of PCMH is elaborated for a long-term data assimilation case at the River Ouse in UK. Multiple hydrological models and different uncertainty settings in inputs, outputs and sample sizes are tested by the PCMH, particle filter (PF) and particle Markov chain Monte Carlo (PMCMC) approaches. The results indicate that the developed PCMH approach is able to generate more reliable results with less accuracy fluctuation than PF and PMCMC for both deterministic and probabilistic predictions from all the hydrological models. The mean values and the associated variation intervals of NSE over the total 270 runs for PCMH, PF and PMCMC are 0.752 (variation interval of [0.534, 0.866]), 0.661 (variation interval of [0.080, 0.879]), and 0.655 (variation interval of [0.247, 0.824]), respectively. For the probabilistic predictions evaluated by CRPS, the mean values and fluctuation ranges from PCMH, PF and PMCMC are respectively 15.215 ([8.624,31.549]), 18.758 ([8.595, 43.536]), 19.308 ([10.848, 37.799]). These results suggested that the proposed PCMH method would be more robust than PF and PMCMC in generating reliable hydrologic predictions and be less influenced by the hydrologic model structures, uncertainty scenarios, and its inherent randomness. Moreover, the PCMH method can also show better robustness than the copula-based particle filter method since the particle evolution scheme of PCMH would balance extreme samples from copula sampling procedure by mixing samples from Gaussian perturbation and remove unacceptable candidates through the Metropolis acceptance criterion.

在这项研究中，开发了一种粒子 copula Metropolis-Hastings (PCMH) 方法，用于对水文预测进行可靠的不确定性量化。所提出的 PCMH 方法采用混合粒子演化方案，该方案集成了高斯扰动和基于 copula 的相关采样方法。然后使用 Metropolis 比率来确定候选样本的接受度。在英国乌斯河的一个长期数据同化案例中详细阐述了 PCMH 的适用性。通过 PCMH、粒子滤波器 (PF) 和粒子马尔可夫链蒙特卡罗 (PMCMC) 方法测试多个水文模型和输入、输出和样本大小的不同不确定性设置。结果表明，对于所有水文模型的确定性和概率性预测，与 PF 和 PMCMC 相比，所开发的 PCMH 方法能够以更小的精度波动产生更可靠的结果。在 PCMH、PF 和 PMCMC 的总共 270 次运行中，NSE 的平均值和相关变化区间为 0.752（变化区间 [0.534, 0.866]）、0.661（变化区间 [0.080, 0.879]）和 0.655（变化区间[0.247, 0.824]) 的区间。对于 CRPS 评估的概率预测，PCMH、PF 和 PMCMC 的平均值和波动范围分别为 15.215 ([8.624,31.549])、18.758 ([8.595, 43.536])、19.308 ([10.848, 37.799])。这些结果表明，所提出的 PCMH 方法在生成可靠的水文预测方面比 PF 和 PMCMC 更稳健，并且受水文模型结构、不确定性情景及其固有随机性的影响较小。此外，PCMH 方法还可以显示出比基于 copula 的粒子滤波方法更好的鲁棒性，因为 PCMH 的粒子演化方案将通过混合来自高斯扰动的样本来平衡来自 copula 采样过程的极端样本，并通过 Metropolis 接受标准去除不可接受的候选者。