For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term predictions of drift trajectories are essential to efficiently define search areas, but in-situ buoy observations provide only very sparse point measurements, while the mission is ongoing. Statistically optimal forecasts, including consistent uncertainty statements, rely on Bayesian methods for data assimilation to make the best out of both the complex mathematical modeling and the sparse spatial data. To identify suitable approaches for data assimilation in this context, we discuss localisation strategies and compare two state-of-the-art ensemble-based methods for applications with spatially sparse observations. The first method is a version of the ensemble-transform Kalman filter, where we tailor a localisation scheme for sparse point data. The second method is the implicit equal-weights particle filter which has recently been tested for related oceanographic applications. First, we study a linear spatio-temporal model for contaminant advection and diffusion, where the analytical Kalman filter provides a reference. Next, we consider a simplified ocean model for sea currents, where we conduct state estimation and predict drift. Insight is gained by comparing ensemble-based methods on a number of skill scores including prediction bias and accuracy, distribution coverage, rank histograms, spatial connectivity and drift trajectory forecasts.
翻译:对海洋应用而言,概率预测通常必须涉及(一) 高维复杂模型,以及(二) 极为稀少的空间观测。例如,在海上搜索和救援行动中,对漂流轨迹的短期预测对于有效界定搜索区域至关重要,但当地浮标观测只能提供非常稀少的点测量,而任务仍在进行中。统计上的最佳预测,包括一致的不确定性说明,依靠贝叶斯式的数据吸收方法,使数据吸收最佳地利用复杂的漂浮模型和稀少的空间数据。为在这一背景下确定适当的数据同化方法,我们讨论本地化战略,比较两种基于远流轨轨迹的状态最先进的应用方法,以空间稀少的观测为目的。第一种方法是全方位移动轨道观测,我们为稀散点数据设计一个地方化计划。第二种方法是隐含等量的粒子过滤器,最近已经测试了相关的海洋学应用。首先,我们研究一种用于污染模型吸收和扩散的线性空间数据模拟模型的线性空间模型,我们讨论本地化战略并比较两种基于空间稀散观察的基于空间观测范围。第一个方法,其中分析卡勒曼的精确度预测和海洋的预测,我们用一种模拟的预测方法来比较了一种精确的预测,其中的精确的预测,通过测算来比较了海洋的预测的预测,其中的精确的精确度,通过测测测测测测测测测测测测测测测测测测测测测测的测的轨道。