使用可微天气模式的长窗四维变分法（4DVar）进行再分析
Long-window 4DVar for reanalysis using a differentiable weather model
AI总结：
本研究提出一种省略传统背景误差项的长窗4D-Var再分析方法，利用可微天气模式NeuralGCM，经三个月循环实验，其500百帕位势高度误差显著小于20CRv3。
AI中文摘要：
大气再分析通过复杂的数据同化系统将观测值与模式预报相结合。本研究验证，可微天气模式是否能基于长窗四维变分数据同化（4D-Var）公式实现更简单、更准确的方法，该方法省略了传统的背景误差项。该方法利用自动微分寻找最优的NeuralGCM初始条件，以最小化对分布在2至7天重叠窗口内的实际地表气压观测值的拟合误差，假设无模式误差。从2015年1月1日开始，以6小时间隔循环三个月，得到的稳定再分析结果在500百帕位势高度上的误差小于使用集合卡尔曼滤波同化相同观测值的《二十世纪再分析第三版》（20CRv3）。每个窗口的误差均小于20CRv3，其中四天窗口的分析误差约比20CRv3小55%；在不依赖未来观测的四天窗口结束时，误差仍约比20CRv3小38%。超过四天后分析结果略有下降，我们将此归因于模式误差的重要性不断增加。
英文摘要：
Atmospheric reanalyses combine observations with model forecasts using complex data assimilation systems. We test whether a differentiable weather model permits a simpler and more accurate method based on a long-window four-dimensional variational data assimilation (4D-Var) formulation that omits the conventional background-error term. The method uses automatic differentiation to find optimal NeuralGCM initial conditions that minimize the misfit to real surface-pressure observations distributed across overlapping windows of two to seven days, assuming no model error. Cycling at 6-hour intervals for three months beginning 1 January 2015 yields a stable reanalysis with smaller error relative to ERA5 in 500-hPa geopotential height than the Twentieth Century Reanalysis version 3 (20CRv3), which uses an ensemble Kalman filter to assimilate the same observations. Every window produces smaller errors than 20CRv3, with analysis error for the four-day window approximately 55% smaller than for 20CRv3. At the end of the four-day window, which does not benefit from future observations, error remains approximately 38% smaller than 20CRv3. Analyses degrade slightly beyond four days, which we attribute to the increasing importance of model error.
