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：对于海洋学应用，概率预报通常需要处理：i) 高维复杂模型，以及ii) 非常稀疏的空间观测。例如，在海上搜救行动中，漂移轨迹的短期预测对于高效定义搜索区域至关重要，但现场浮标观测仅提供非常稀疏的点测量值，且任务仍在进行中。统计最优预报（包括一致的不确定性表述）依赖于贝叶斯数据同化方法，以充分利用复杂的数学模型和稀疏的空间数据。为确定适用于该背景的数据同化方法，我们讨论了局地化策略，并比较了两种用于空间稀疏观测应用的最新基于集合的方法。第一种方法是集合变换卡尔曼滤波器的一个版本，其中我们针对稀疏点数据定制了局地化方案。第二种方法是隐式等权粒子滤波器，该方法近期已在相关海洋学应用中得到测试。首先，我们研究了一个用于污染物平流与扩散的线性时空模型，其中解析卡尔曼滤波器提供了参考基准。接下来，我们考虑了一个简化的海流海洋模型，并进行了状态估计与漂移预测。通过比较基于集合的方法在多个技能评分（包括预测偏差与精度、分布覆盖率、秩直方图、空间连通性以及漂移轨迹预测）上的表现，获得了深入见解。