Physical parameterizations in global atmospheric and ocean models typically include free parameters that are not theoretically or empirically constrained. New methods are required to determine the optimal parameter combinations for such models in an objective, exhaustive, yet computationally feasible manner. Here we propose to apply computationally inexpensive radial basis function (RBF) surrogate models to minimize a “cost,” or error, function of an atmospheric model or a physical parameterization. The RBF is iteratively updated as more input‐output pairs are obtained during the optimization. The approach is used to optimize the eddy‐diffusivity/mass‐flux boundary‐layer parameterization of the convective boundary‐layer in a single‐column model framework. The optimization based on surrogate models is able to identify parameter combinations that reduce the error of the untuned default setting by 41%. The probability to detect a low‐error solution increases rapidly especially over the first tens of single‐column model evaluations. In comparison, a quadratic polynomial model only yields an error reduction of 17% since (a) high‐order parameter interactions are not accounted for and (b) the construction of the polynomial is not based on an iterative sampling approach. The RBF surrogate models achieve this 17% error reduction for 40% of the polynomial model's cost. Interestingly, one of the emerging optimal settings describes a pure mass flux parameterization without eddy‐diffusivity component. A second optimal solution is characterized by a plume fractional area of 20–30% and an eddy‐mixing time scale of ∼700 s.

中文翻译：

---

使用替代模型优化涡流扩散/质量通量浅积云和边界层参数化

全球大气和海洋模型中的物理参数化通常包括不受理论或经验约束的自由参数。需要新的方法以客观，详尽，但在计算上可行的方式确定此类模型的最佳参数组合。在这里，我们建议应用计算上便宜的径向基函数（RBF）替代模型，以最小化大气模型或物理参数化的“成本”或误差函数。随着优化过程中获得更多的输入输出对，RBF会进行迭代更新。该方法用于优化单列模型框架中对流边界层的涡流扩散/质量通量边界层参数化。基于代理模型的优化能够识别参数组合，从而将未调整的默认设置的错误减少41％。检测低错误解决方案的可能性迅速增加，尤其是在前十个单列模型评估中。相比之下，二次多项式模型仅产生17％的误差减少，因为（a）不考虑高阶参数交互作用，并且（b）多项式的构造不基于迭代采样方法。RBF替代模型可将误差降低17％，而多项式模型的成本却可降低40％。有趣的是，其中一种新兴的最佳设置描述了没有涡流扩散成分的纯质量通量参数化。