Collaborative Research: Lagrangian data blending for hurricane tracking and source estimation

基于离散核滤波器（DKF）和集成繁殖向量（EBV）的拉格朗日方法，该方法使用局部估计器，保留了观测和数值模拟中检测到的重要动态特征，用于前向拉格朗日轨迹预测（LTP）和逆源估计问题，这是许多不同科学学科的基础。这些非线性滤波问题是非高斯的，可以具有高维的状态空间。DKF基于粒子滤波，由于在扩散过程的参数化中有一个内置的再生过程，该过程定义了预测的主要分支，因此它不会遭受系综崩溃。该方法对预测的分支进行线性化处理，但在分析阶段不做高斯假设。EBV算法用于寻找预测分支的最佳选择，从而显着提高了该方法的效率，可用于解决重要的现实问题，如溢油建模和污染源识别，大气中放射性气体的运输和扩散，鱼类幼虫运输和渔业连通性，预测海冰运动，人类殖民，绘制入侵物种和监测小行星运动等。对流体流动和流动轨迹的观察，如果从与流动无关的固定点上进行，则称为欧拉式；如果从与流动一起运动的点上进行，则称为拉格朗日式。同样地，如果流动在一个固定的计算网格中移动，那么流动的计算模拟称为欧拉式，如果网格随着流动移动，则称为拉格朗日式。研究人员开发了一种方法来预测流体流动的轨迹，这是受随机扰动。他们将该方法应用于捕捉特征至关重要的两个问题：飓风/台风跟踪，以及美国海岸警卫队的搜索和救援。这两个问题都具有重要的社会意义，因为更优的解决方案和更严格的误差可以节省生命和金钱。出于实用性的考虑，他们寻求一种有效的方法，该方法也能够(1)融合多平台观测和海洋环流的数值模式模拟，以改善欧拉模型的诊断变量和拉格朗日轨迹的预测，以及相关的估计不确定性；(2)处理现有的集合，融合来自主要业务模型(如NCEP GFS， GFDL， UKMET， ECMWF，NOGAPS等)，以提高对热带气旋（飓风、台风）路径的预测。该方法可以帮助生成最先进的不确定性地图，这对于搜索和救援飞行计划以及减少飓风预测的“不确定性锥”至关重要。

Restrepo, DMS-1109856Mariano, DMS-1108949 A Lagrangian methodology based on a Discrete Kernel Filter (DKF) and the Ensemble Bred Vector (EBV) that uses local estimators that preserve significant dynamical features, detected by observations and in numerical simulations, is developed for the Forward Lagrangian Trajectory Prediction (LTP) and inverse source estimation problems that are fundamental in many different scientific disciplines. These nonlinear filtering problems are non-Gaussian and can have large-dimensional state spaces. DKF is based upon a particle filter and it does not suffer ensemble collapse because it has a built-in regeneration process in the parameterization of the diffusion process that defines the primary branches for prediction. The method linearizes about branches of prediction, yet makes no Gaussian assumption in the analysis stage. The EBV algorithm is used to find the best choices for branches of prediction, thus increasing the efficiency of the method significantly for application to important real-world problems such as oil spill modeling and pollution source identification, transport and dispersion of radioactive gases in the atmosphere, fish larvae transport and fishery connectivity, predicting sea ice motion, human colonization, mapping invasive species, and monitoring asteroid movements, to name a few. Observations of fluid flows and the trajectories of the flows are called Eulerian if the observations are taken from points fixed independent of the flows, and Lagrangian if they are taken from points that move with the flows themselves. In the same way, a computational simulation of a flow is called Eulerian if the flow moves through a fixed computational grid, and Lagrangian if the grid moves with the flow. The investigators develop a method to predict the trajectories of fluid flows, which are subject to random perturbations. They apply the method to two problems where capturing features is critical: hurricane/typhoon tracking, and US Coast Guard search and rescue. Both of these problems are of great societal importance because more optimal solutions with tighter error bars can save both lives and money. For reasons of practicality they seek an efficient method that is also capable of (1) fusing multi-platform observations and numerical model simulations of ocean circulation for improving both the Eulerian, diagnostic variables of the model and prediction of Lagrangian trajectories, as well as the associated estimation uncertainties, and (2) handling already existing ensembles, fusing hurricane track forecast ensembles from the leading operational models (such as NCEP GFS, GFDL, UKMET, ECMWF, NOGAPS, others) to improve predictions of the path of tropical cyclones (hurricane, typhoon). The method can help produce state-of-the-art uncertainty maps that are critical in search and rescue flight planning and for reducing the "cone of uncertainty" for operational hurricane predictions.