【摘要】 基于数字流域的分形拓扑结构，引入分形网络谱间隙理论与异质平均首次通过时间(MFPT)标度律，解析了非平稳径流随机过程的收敛特性与演化机制；融合模糊马尔可夫链与非平稳隐马尔可夫-多项式回归，构建了径流状态动态转移演化模型，并建立了完整的参数估计与训练校验方法．在此基础上，从信息几何与渐近分析双重视角，严格证明了变差稳定性原理(VSP)相较于MSE准则的物理一致性与统计优越性．构建了从流域分形结构、非线性随机过程到预报不确定性量化的完整机理链，形成了分形-随机统一的径流预报理论体系，实现了径流预报从黑箱拟合向白箱机理解析的范式转换，为气候变化背景下流域水资源系统的自适应调控提供了数学理论基础与方法支撑．更多还原

【Abstract】 Based on the fractal topology structure of digital watersheds, the fractal network spectral gap theory and heterogeneous mean first pass time(MFPT) scaling law were introduced to analyze the convergence characteristics and evolution mechanism of nonstationary runoff stochastic processes. A dynamic transition evolution model of runoff state was constructed by integrating fuzzy Markov chain and non-stationary hidden Markov polynomial regression, and a complete parameter estimation and training verification method was established. On this basis, from the dual perspectives of information geometry and asymptotic analysis, the physical consistency and statistical superiority of the variational stability principle(VSP) over the MSE criterion were rigorously proven. A complete mechanism chain was constructed from the fractal structure of the watershed, nonlinear stochastic processes to the quantification of forecast uncertainty, forming a fractal stochastic unified theoretical system for runoff forecasting. The paradigm shift of runoff forecasting from black box fitting to white box mechanism analysis was achieved, providing a mathematical theoretical basis and methodological support for the adaptive regulation of watershed water resources systems under the background of climate change.更多还原