AI 中文总结
针对大气流动模拟中莫宁-奥布霍夫相似理论表面参数的不确定性问题，采用贝叶斯方法推断参数并量化不确定性，在数据稀疏场景下表现优于最小二乘方法，可降低预测误差与概率评分。
AI 中文摘要
在大气流动模拟中，网格间距通常比地表粗糙元的尺寸大一个数量级。地表形态和粗糙度对流动的未解析效应由有效表面参数表征，并作为地表通量边界条件指定，最常通过基于莫宁-奥布霍夫相似理论（MOST）的公式实现。已知这些表面参数同时依赖于地表和流动特性，但通常被估计为确定性量，未表征相关不确定性。本研究采用贝叶斯方法推断MOST的表面参数并量化其不确定性。对于单独推断的空气动力学粗糙度长度$z_0$，正态-正态共轭更新以闭式形式得到后验和后验预测分布。我们首先在大涡模拟生成的理想化常规中性边界层上验证该方法，其中$z_0$为预设值，并量化先验和观测相关选择对推断后验的影响。随后将该方法应用于大气辐射测量南方大平原观测站的野外观测数据，从中推断按月、风向以及两者联合条件的$z_0$分布。通过利用训练年份内所有近中性观测样本统计量构建的先验，我们证明在数据稀疏条件下，$z_0$的贝叶斯推断方法相比当前实践的最小二乘廓线拟合方法具有优势。对未见过的观测的预测（以后验均值评估）可降低数据稀疏风向上的均方根误差和平均绝对误差，而后验预测分布则持续降低约20%-30%的连续秩概率评分。
英文摘要
In simulations of atmospheric flow, the grid spacing typically exceeds the size of the roughness elements at the surface by an order of magnitude. The unresolved effects of surface morphology and roughness on the flow are represented by effective surface parameters and specified as a surface flux boundary condition, most often through a formulation based on Monin-Obukhov similarity theory (MOST). These surface parameters are known to depend on both surface and flow properties, yet they are generally estimated as deterministic quantities with no characterization of associated uncertainty. In this study, we use a Bayesian approach to infer surface parameters for MOST and quantify their uncertainties. For the aerodynamic roughness length $z_0$ inferred in isolation, a normal-normal conjugate update yields the posterior and posterior predictive distributions in closed form. We first demonstrate our method on idealized conventionally neutral boundary layers generated by large-eddy simulation, where $z_0$ is prescribed, and quantify how prior- and observation-related choices shape the inferred posterior. We then apply the method to field observations from the Atmospheric Radiation Measurement Southern Great Plains observatory, from which we infer $z_0$ distributions conditioned on month, on wind direction, and on both jointly. By leveraging a prior informed by sample statistics of all near-neutral observations in the training years, we demonstrate the advantage of the Bayesian inference method for $z_0$ relative to the state-of-practice least-squares profile-fitting method in conditions of data sparsity. Predictions for unseen observations-evaluated at the posterior mean-reduce root mean squared error and mean absolute error in data-sparse wind directions, while posterior predictive distributions consistently reduce the continuous ranked probability score by approximately $20$-$30\%$.
Comments19 pages, 9 figures, 1 table
