Tropical cyclones (TCs), driven by heat exchange between the air and sea, pose a substantial risk to many communities around the world. Accurate characterization of the subsurface ocean thermal response to TC passage is crucial for accurate TC intensity forecasts and for an understanding of the role that TCs play in the global climate system. However, that characterization is complicated by the high-noise ocean environment, correlations inherent in spatio-temporal data, relative scarcity of in situ observations, and the entanglement of the TC-induced signal with seasonal signals. We present a general methodological framework that addresses these difficulties, integrating existing techniques in seasonal mean field estimation, Gaussian process modeling, and nonparametric regression into an ANOVA decomposition model. Importantly, we improve upon past work by properly handling seasonality, providing rigorous uncertainty quantification, and treating time as a continuous variable, rather than producing estimates that are binned in time. This ANOVA model is estimated using in situ subsurface temperature profiles from the Argo fleet of autonomous floats through a multi-step procedure, which (1) characterizes the upper ocean seasonal shift during the TC season; (2) models the variability in the temperature observations; (3) fits a thin plate spline using the variability estimates to account for heteroskedasticity and correlation between the observations. This spline fit reveals the ocean thermal response to TC passage. Through this framework, we obtain new scientific insights into the interaction between TCs and the ocean on a global scale, including a three-dimensional characterization of the near-surface and subsurface cooling along the TC storm track and the mixing-induced subsurface warming on the track's right side.

翻译：热带气旋（TC）由海气热交换驱动，对全球许多社区构成重大风险。准确描述TC过境引起的海洋次表层热响应，对于精确的TC强度预报以及理解TC在全球气候系统中的作用至关重要。然而，由于海洋环境的高噪声特性、时空数据固有的相关性、现场观测数据的相对稀缺性，以及TC引发信号与季节性信号的相互干扰，这种特征刻画变得异常复杂。我们提出了一种通用的方法论框架来应对这些挑战，将季节性平均场估计、高斯过程建模和非参数回归等现有技术整合到ANOVA分解模型中。重要的是，我们通过恰当处理季节性因素、提供严格的量化不确定性、并将时间视为连续变量（而非生成时间分箱的估计值），改进了以往的研究。该ANOVA模型利用Argo自主浮标阵列的现场次表层温度廓线，通过多步骤程序进行估计：（1）刻画TC季节期间上层海洋的季节性变化；（2）对温度观测值的变异性进行建模；（3）利用变异性估计值拟合薄板样条函数，以考虑观测值之间的异方差性和相关性。样条拟合揭示了TC过境引起的海洋热响应。通过这一框架，我们获得了关于全球尺度上TC与海洋相互作用的新的科学见解，包括沿TC风暴路径的近表层和次表层冷却的三维特征描述，以及风暴路径右侧混合诱导的次表层增温现象。