On the Optimal Use of WSR-88D Doppler Radar Data for Variational Storm-Scale Data Assimilation

三维变分数据同化（3DVAR）正在达到相当成熟的状态，并正在几个业务气象中心进行业务应用，尽管主要是在大尺度静力流体流动的背景下。由于各种原因（例如，不同的动力约束，变量之间缺乏类似的平衡，以及天气现象的巨大差异），这种技术不能直接扩展到中尺度和风暴尺度上的非流体静力流。在后一个尺度上，特别是对于高度非静力和间歇性的强烈浮力对流，WSR-88D多普勒是唯一能够提供高空间和时间分辨率观测的操作仪器。将这些数据同化到风暴分辨模式中，包括检索雷达不能直接观测到的量，是相当具有挑战性的，但对业务预报的未来具有重要的实际意义。根据该合同，首席研究员将在理论和计算3DVAR框架内研究雷达数据同化的三个关键方面，包括天气研究和预报（WRF）模型的最终使用。主要目标是确定如何将WSR-88D雷达数据与其他观测相结合，最好地用于3DVAR，以预测对流现象。首席研究员将开发增强的3DVAR同化技术，包括检索风、压力和温度场等未观察到的变量的能力。将开发两种单独的检索方法，第一种方法同时获取风和热力学变量，第二种方法采用顺序模式。计划建立不同分析变量的简单平衡方程，探索适合风暴尺度现象的数据同化时间窗。在指定背景误差的背景下，这是变分数据同化的一个关键因素，首席研究员将研究通过指定位移（相位）和振幅方面的误差可能获得的改进。由于风暴尺度结构的间歇性，位移误差的校正至关重要，因此，在将其用于3DVAR分析之前，将开发一种变分相位校正方法来改善背景位移误差。3. 拥有适当质量控制的雷达数据是至关重要的。在这种情况下，使用WSR-88D多普勒观测，速度折叠是一个挑战。首席研究员将开发一种变分算法，其中使用风梯度信息在局部执行去混叠。成本函数将包括以前数据同化周期的背景风场，和/或改进的速度方位角显示（VAD）技术；观测到的径向速度相对于距离和方位角的梯度；并采用平滑性约束来减少地面杂波引起的误差。该方法的关键在于，通过对速度梯度而不是速度本身进行操作，可以很容易地识别和消除混叠歧义。该方法将与应用于理想化和真实数据的几种现有算法进行比较。通过PI作为为新的全社区WRF模型开发变分数据同化系统的主要科学家之一的参与，研究结果将直接用于业务。虽然在此进行的一些工作将使用CAPS先进区域预测系统（由于其成熟度更高），但重点将放在使用WRF进行测试和开发上。

Three-dimensional variational data assimilation (3DVAR) is reaching a considerable state of maturity, and is being used operationally at several operational meteorological centers, though mainly in the context of large-scale hydrostatic flows. Such techniques cannot directly be extended to nonhydrostatic flows on the meso- and storm-scales for a variety of reasons (e.g., different dynamic constraints, the lack of a similar balance among variables, and large differences of weather phenomena). At the latter scales, and, especially for intense buoyant convection that is both highly nonhydrostatic and intermittent, the WSR-88D Doppler is the only operational instrument capable of providing high spatial and temporal resolution observations. The assimilation of such data into storm-resolving models, including the retrieval of quantities that cannot be observed directly by radars, is quite challenging, yet of great practical significance for the future of operational forecasting. Under this award, the Principal Investigator will attack three key aspects of radar data assimilation within a theoretical and computational 3DVAR framework including eventual use by the Weather Research and Forecasting (WRF) model.1. The primary objective is to determine how WSR-88D radar data can best be used in 3DVAR, in combination with other observations, for the prediction of convective phenomena. The Principal Investigator will develop enhanced 3DVAR assimilation techniques which will include the ability to retrieve unobserved variables such as wind, pressure, and temperature fields. Two separate retrieval methods will be developed, the first for obtaining wind and thermodynamic variables simultaneously, and the second in a sequential mode. It is planned to develop a simple balance equation for different analysis variables and explore a suitable data assimilation time window for storm scale phenomenon.2. In the context of specifying background error, which is a critical element of variational data assimilation, the Principal Investigator will investigate what improvements might be gained by specifying the error in terms of displacement (phase) and amplitude. Because of the intermittency of storm-scale structures, correction of the displacement errors is critical, and thus a variational phase correction method will be developed to ameliorate the background displacement error before it is used in 3DVAR analysis. 3. It is critical to have properly quality-controlled radar data. In this context, velocity folding is a challenge in using WSR-88D Doppler observations. The Principal investigator will develop a variational algorithm in which de-aliasing is performed locally using wind gradient information. The cost function will include the background wind field from a previous data assimilation cycle, and/or a modified Velocity Azimuth Display (VAD) technique; the gradient of observed radial velocity with respect to range and azimuth; and a smoothness constraint to reduce errors caused by ground clutter. The key to the method is that, by operating on gradients of velocity rather than the velocity itself, aliasing ambiguities are readily identified and eliminated. This methodology will be compared to several existing algorithms applied to both idealized and real data.The research findings will have a direct path to operations through the PI's involvement as one of the lead scientists in developing the variational data assimilation system for the new community-wide WRF model. Although some of the work to be performed herein will use the CAPS Advanced Regional Prediction System owing to its greater level maturity, emphasis will be placed on testing and development using the WRF.