Ensemble forecasting at NMC and the breeding method

The breeding method has been used to generate perturbations for ensemble forecasting at NMC since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. A combination of bred perturbations and lagged forecasts provided a daily set of 14 global forecasts valid to 10 days. In March 1994, the ensemble was expanded to 7 independent breeding cycles on the new Cray C90 supercomputer, and the forecasts extended to 16 days, This provides 46 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. We point out that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first guess forecasts, is "scaled down" at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred modes are superpositions of the leading local (time dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property of the leading LLVs is that all random perturbations assume their structure after a transientperiod. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred modes from independent breeding cycles. Off-line experimental runs with a 10-member ensemble (5 independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04-0.11 in AC in forecasts at and beyond 7 days, together with the potential for estimation of the skill, suggest that this system will be a useful operational forecast tool. The results and methodology discussed should be applicable to the new operational ensemble configuration; where 17 independent forecasts are performed every day. The two methods used so far to produce operational ensemble forecasts, i.e., breeding and the adjoint (or "optimal perturbations"). technique applied at ECMWF, have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred modes are estimates of fastest sustainable growth and as such they represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth and are less likely to occur in analysis error fields. A major practical difference between the two methods for ensemble forecasting is that breeding is much simpler and far less expensive than the adjoint technique. Zoltan Toth and Eugenia Kalnay. "April 7, 1995." Also available online in PDF via the NOAA Central Library. Includes bibliographical references (pages 25-28).自1992年12月起，该繁殖型扰动方法（breeding method）已被用于美国国家气象中心（National Meteorological Center, NMC）的集合预报（ensemble forecasting）扰动生成工作。彼时，系统仅运行单轮繁殖循环，搭配一对经繁殖的预报结果。将繁殖型扰动与滞后预报相结合，可每日生成14组有效期长达10天的全球预报。1994年3月，依托新型克雷C90（Cray C90）超级计算机，该集合预报系统扩展至7个独立繁殖循环，预报有效期也延长至16天，由此可每日生成46组独立的全球预报，有效期达两周。为实现高效的集合预报，对控制分析场引入的初始扰动需充分采样可能的分析误差空间。本文指出，分析循环与繁殖循环具有相似性：其对真实大气的演变起到非线性扰动模型的作用。初猜预报中传递的扰动（即分析误差），会通过定期应用观测资料被“尺度缩减”。正因如此，与大气演变状态相关的增长型误差会在分析循环中发展，并主导后续的预报误差增长。繁殖型扰动方法正是模拟了分析循环中增长型误差的发展过程：将两个非线性预报结果的差异场随大气分析场的演变向前传递，并定期进行尺度缩减。从构造原理来看，繁殖模态是大气主要局地（时变）李雅普诺夫向量（Lyapunov vectors, LLVs）的叠加。主要李雅普诺夫向量的一项重要特性是：所有随机扰动在经过一段过渡阶段后，都会趋近于其结构。当开展多个独立的繁殖循环时，单个（及区域）主要李雅普诺夫向量的相位与振幅均为随机分布，这保证了来自不同繁殖循环的全球繁殖模态之间具有准正交性。针对由5个独立繁殖循环生成的10成员集合预报开展的离线试验结果表明，集合平均预报效果优于经最优平滑处理的控制预报，以及随机生成的集合预报，且与中期双水平分辨率控制预报的表现不相上下。此外，在空间与时间域中，均发现集合离散度与预报误差之间存在潜在的实用关联。在7天及更长时效的预报中，距平相关系数（Anomaly Correlation, AC）的评分提升了0.04至0.11，加之其具备估算预报技巧的潜力，这表明该系统将成为一款实用的业务预报工具。本文讨论的研究结果与方法，可推广至当前的新型业务集合预报配置——该配置每日可生成17组独立预报。目前用于生成业务集合预报的两种方法，即本文所采用的繁殖方法，以及欧洲中期天气预报中心（European Centre for Medium-Range Weather Forecasts, ECMWF）所应用的伴随（或称“最优扰动”）技术，二者存在诸多显著差异，但均致力于估算快速增长扰动的子空间。繁殖模态是快速可持续增长的估算值，因此它们代表了大概率出现的增长型分析误差。而最优扰动则是估算瞬态快速增长的向量，在分析误差场中出现的可能性更低。两种方法在集合预报实践中的主要差异在于，繁殖方法远比伴随技术简单，且计算成本更低。本文作者为佐尔坦·托特（Zoltan Toth）与欧仁尼·卡奈（Eugenia Kalnay），发表日期为1995年4月7日。该文献可通过美国国家海洋和大气管理局（National Oceanic and Atmospheric Administration, NOAA）中央图书馆在线获取PDF版本，包含25至28页的参考文献。