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Discrete second order adjoints in atmospheric chemical transport modeling

机译：大气化学迁移模型中的离散二阶伴随

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Atmospheric chemical transport models (CTMs) are essential tools for the study of air pollution, for environmental policy decisions, for the interpretation of observational data, and for producing air quality forecasts. Many air quality studies require sensitivity analyses, i.e., the computation of derivatives of the model output with respect to model parameters. The derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis. While the traditional (first order) adjoint models give the gradient of the cost functional with respect to parameters, second order adjoint models give second derivative information in the form of products between the Hessian of the cost functional and a vector (representing a perturbation in sensitivity analysis, a search direction in optimization, an eigenvector, etc.). In this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three-dimensional atmospheric CTMs. The tools include discrete second order adjoints of Runge-Kutta and of Rosenbrock time stepping methods for stiff equations together with efficient implementation strategies. Numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis, optimization, uncertainty quantification and the calculation of directions of maximal error growth in three-dimensional atmospheric CTMs. (c) 2008 Elsevier Inc. All rights reserved.
机译：大气化学迁移模型（CTM）是研究空气污染，制定环境政策，解释观测数据和产生空气质量预报的重要工具。许多空气质量研究都需要进行灵敏度分析，即，相对于模型参数计算模型输出的导数。通过伴随灵敏度分析，可以有效地计算成本函数（在模型输出中定义）相对于大量模型参数的导数。传统的（一阶）伴随模型给出了成本函数相对于参数的梯度，而二阶伴随模型则给出了成本函数的Hessian与向量之间的乘积形式的二阶导数信息（表示灵敏度的扰动）分析，优化中的搜索方向，特征向量等）。在本文中，我们讨论了离散二阶伴随灵敏度方法的数学基础，并提出了一套完整的计算工具，用于在三维大气CTM中进行二阶灵敏度研究。这些工具包括用于刚性方程的Runge-Kutta和Rosenbrock时间步进方法的离散二阶伴随函数以及有效的实现策略。数值示例说明了这些计算工具在重要应用中的使用，例如灵敏度分析，优化，不确定性量化和三维大气CTM中最大误差增长方向的计算。 （c）2008 Elsevier Inc.保留所有权利。

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