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

Restrepo，DMS-1109856 Mariano，DMS-1108949 拉格朗日方法的基础上的离散核滤波器（DKF）和EnhancedBred矢量（EBV），使用本地估计，保持显着的动力学特征，检测到的观测和数值模拟，开发的前向拉格朗日轨迹预测（LTP）和逆源估计问题，是在许多不同的科学学科的基础。 这些非线性滤波问题是非高斯的，并且可以具有高维状态空间。 DKF是基于粒子滤波器，它不会遭受合奏崩溃，因为它有一个内置的再生过程中的参数化的扩散过程，定义了预测的主要分支。 该方法对预测分支进行线性化，但在分析阶段不做高斯假设。 EBV算法用于找到预测分支的最佳选择，从而显著提高了该方法应用于重要现实世界问题的效率，例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，鱼苗运输和渔业连接，预测海冰运动，人类定居，绘制入侵物种，监测小行星的运动等等 流体流动和流动轨迹的观测，如果观测是从独立于流动的固定点进行的，则称为欧拉;如果观测是从随流动本身移动的点进行的，则称为拉格朗日。 同样，如果流动通过固定的计算网格，则流动的计算模拟称为欧拉，如果网格随流动移动，则称为拉格朗日。 研究人员开发了一种方法来预测流体流动的轨迹，这些轨迹受到随机扰动。 他们将该方法应用于捕获特征至关重要的两个问题：飓风/台风跟踪和美国海岸警卫队的搜索和救援。 这两个问题都具有重大的社会意义，因为具有更严格误差条的更优解决方案可以挽救生命和金钱。 出于实用性的原因，他们寻求一种有效的方法，该方法也能够（1）融合海洋环流的多平台观测和数值模型模拟，以改进模型的欧拉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，以及（2）处理已经存在的集合，融合来自主要业务模型（如NCEP GFS、GFDL、UKMET、ECMWF、NOGAPS等）的飓风路径预报集合，以改进对热带气旋（飓风、台风）路径的预测。 该方法可以帮助制作最先进的不确定性地图，这对搜索和救援飞行规划至关重要，并有助于减少飓风预测的“不确定性锥”。

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.