发表机构
University of California Merced（加州大学默塞德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对海洋湖泊模型中难以直接测量的深度相关扩散系数，本文提出基于伴随的非精确高斯-牛顿反演方法，利用温盐剖面数据同时优化拟合，并通过合成与真实数据验证其准确性和鲁棒性。
AI 中文摘要
海洋湖泊为研究湍流混合、生物混合和潮汐交换等物理过程如何在相对孤立的生态系统中调节热量、氧气和营养物质的垂直输送提供了独特的机会。有效扩散系数表征了整体混合程度，在海洋湖泊模型中至关重要，但难以直接测量。本文研究了从合成和真实的垂直温度与盐度剖面测量数据中推断随深度变化的扩散系数的问题。为此，我们构建了一个由屏蔽泊松方程（类似于亥姆霍兹方程）描述的海洋湖泊模型所支配的反问题。该反问题被表述为一个非线性最小二乘优化问题，其中代价泛函量化了观测剖面与恢复剖面之间的失配。为了改善离散化问题的条件数，我们添加了Tikhonov正则化项，并使用L曲线方法选择正则化参数。我们采用基于伴随的非精确高斯-牛顿法求解该问题。为了利用这些剖面中的互补信息，该公式同时优化了两个数据集的拟合。通过全面的合成研究，我们考察了重建扩散系数的准确性以及该方法对噪声的鲁棒性。此外，我们将该框架与物理信息神经网络进行了对比，突出了各自的优势和局限性。当应用于真实的海洋湖泊数据时，伴随方法在密度分层强烈的区域重建出较小的扩散系数，这与物理预期一致。结果表明，所提出的方法为海洋湖泊动力学的精确建模提供了基础。
英文摘要
Marine lakes offer a unique opportunity to study how physical processes, such as turbulent mixing, biomixing, and tidal exchanges, regulate the vertical transport of heat, oxygen, and nutrients in relatively isolated ecosystems. The effective diffusion coefficient characterizes the overall mixing and is critical in models of marine lakes, but it is difficult to measure directly. This paper addresses the problem of inferring the depth-dependent diffusion coefficient from synthetic and real measurements of vertical temperature and salinity profiles. To do so, an inverse problem governed by a marine lake model described by the screened-Poisson equation (similar to Helmholtz) is formulated. The inverse problem is formulated as a nonlinear least-squares optimization problem, where the cost functional quantifies the misfit between the observed and recovered profiles. A Tikhonov regularization term is added to improve the conditioning of the discretized problem, with a regularization parameter chosen using the L-curve method. We solve this problem using an adjoint-based inexact Gauss-Newton method. To leverage the complementary information in these profiles, the formulation optimizes the fit across both datasets simultaneously. The accuracy of the reconstructed diffusion coefficient and the method's robustness to noise are investigated through comprehensive synthetic studies. Additionally, we contrast this framework with physics-informed neural networks, highlighting the advantages and limitations of each. When applied to real marine lake data, the adjoint method reconstructed a smaller diffusion coefficient in regions of strong density stratification, in line with physical expectations. The results indicate that the proposed approach provides a foundation for accurate modeling of marine lake dynamics.
