Hurricane predictability: are there simple linear invariants within these complex nonlinear dynamical systems?

Summary Forecasting the tracks of hurricanes is a problem of immense importance. It is a major scientific exercise in solving the complicated set of mathematical equations that govern the behavior of atmospheric flow in general and hurricanes in particular. Moreover, hurricanes rank as the most devastating of all natural phenomena, in terms of loss of life and destruction of property. Hitherto, unlike many other atmospheric and oceanic systems, hurricanes have defied rapid advances in prediction of their motion, and progress has been of the order of a mere one percent or so reduction per annum in mean 48 hour forecast position errors over the past two decades. A research program aimed at estimating inherent and actual mean absolute forecast position errors, has produced an apparent paradox. Despite the fact that the equations governing hurricane motion are a complex, coupled, nonlinear set of dynamical equations, there is very strong evidence for the existence of an underlying simple, linear, invariant behavior. The original aim of the research program was to determine the lower limits of mean hurricane forecast position errors and to quantify them out to 72 hour leadtime. The appearance of the paradox meant that the focus shifted first to examining and explaining the paradox. Attention then turns to showing that the mean forecasts errors are still a very large 40 to 50 percent lower than the mean position errors currently being achieved in practice by state-of-the-art models numerical weather prediction (NWP) models. Revised December 14, 1999     

数值天气预报———另类途径的必要性和可行性

通过讨论省 (甚至地、市) 气象部门要不要开展数值天气预报工作的问题, 认为不是所有的地方都要开展, 只是那些希望搞科研型业务、迫切要求提高当地高影响天气的预报准确率的地方要开展。对于如何开展的问题, 提出不是去重复类似于主流途径的做法, 而是开辟另类途径, 并阐述了另类途径的内容、方法和意义。强调开展另类途径无需构建模式 (这是非常困难的工作), 只需运转现成的模式, 借助所关心的现象的历史数据来改造现成模式, 使之本地化, 是完全可行的。     

一个可供现代数学分析研究的气候动力学模型

针对以往大气动力学方程和气候动力学方程数学研究所使用模式的不足之处,本文作了改进,使数学模型更接近于实际情况。这些包括,（1）取大气上界气压为零,而非某个正的（小）常数;（2）消除了整层无辐散近似,从而使地面气压为直接的预报量,但在地面气压预报方程中加入了水平湍流扩散项（平滑）;（3）对大气运动的内热源的辐射传输过程和水汽相变过程作了合理的处理,而非看作已知的外强迫,用适当的方法可以用解析函数较好地逼近这些过程。另外还提出合理的边界条件。我们的目的是要证明这样提出的初—边值问题的解的存在性,以后还可研究其基本性质和长期行为。     

Stochastic precipitation generator with hidden state covariates

Time series of daily weather such as precipitation, minimum temperature and maximum temperature are commonly required for various fields. Stochastic weather generators constitute one of the techniques to produce synthetic daily weather. The recently introduced approach for stochastic weather generators is based on generalized linear modeling (GLM) with covariates to account for seasonality and teleconnections (e.g., with the El Niño). In general, stochastic weather generators tend to underestimate the observed interannual variance of seasonally aggregated variables. To reduce this overdispersion, we incorporated time series of seasonal dry/wet indicators in the GLM weather generator as covariates. These seasonal time series were local (or global) decodings obtained by a hidden Markov model of seasonal total precipitation and implemented in the weather generator. The proposed method is applied to time series of daily weather from Seoul, Korea and Pergamino, Argentina. This method provides a straightforward translation of the uncertainty of the seasonal forecast to the corresponding conditional daily weather statistics.     

正压大气中尺度半平衡和准平衡动力学模式

应用描写正压大气运动的基本方程组，分析了中尺度大气运动的物理特征，指出非平衡强迫运动是引起中尺度重要天气演变的根本原因。中尺度动力学方程组是中尺度动力学理论研究的基础，因此，结合中尺度大气运动的基本特征，依据严格的尺度分析理论和摄动理论，简化基于流体力学和热力学的大气动力学方程组使之能够恰当地描述出中尺度运动的基本特征，对于中尺度动力学的发展是极为必要的。基于非线性平衡方程所得到的半平衡和准平衡动力学模式分别与半地转和准地转模式极为相似，它们可以较精确地描述中尺度大气运动的基本特征，因而，可作为中尺度动力学研究的理论基础。将准平衡动力学模式应用于中尺度涡旋系统的研究，结论表明中尺度平衡涡旋系统主要是受梯度风控制，其流场和气压场的发展演变则由一个演化方程来描写，获得了较为理想的结果。     

天气数值预报中过去资料的使用问题

本文指出在天气数值预报中要解的天气方程组与我们能有的求解条件是不相配称的.因此需要研究如何把方程组化成最合适的形式而最充分地利用可能有的定解条件(特別是最可靠最完全的气象量测的分布)以使预报效果最好.在某些情形下,天气数值预报可以提成“演变”问题,从而可能使用过去的资料.作为某一气象量的初值问题,天气数值预报也可能使用一部分过去资料.而在以前的天气数值预报是并不使用过去天气资料的.本文最后讨论了这样提法的意义.     

The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology,the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction.To address this,it is important to invest in the development of global nonhydrostatic models.Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores,which can subsequently degrade the accuracy of the calculations.A new nonhydrostatic global spectral model,which utilizes the Eulerian spectral method,is developed here from NCAR Community Atmosphere Model 3.0(CAM3.0).Using Janjic's hydrostatic/nonhydrostatic method,a global nonhydrostatic spectral method for the primitive equations has been formulated and developed.In order to retain the integrity of the nonhydrostatic equations,the atmospheric curvature correction and eccentricity correction are considered. In this paper,the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out,which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration,as well as better simulation ability for short-term idealized integration.Then,a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes.The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind,temperature,and 500-hPa height.     

中尺度自忆模式在强降水预报中的应用

根据大气自忆性原理提出的回溯时间积分格式应用于中尺度格点模式MM5,构建了中尺度自忆模式SMM5并做了短期强降水预报的实验.结果表明,SMM5模式与MM5模式相比,由于使用了多个时刻的场资料,预报精度有了明显的提高, SMM5预报的最大雨区的中心位置与降水量也比MM5更接近实际观测场.     

The unique,well posed reduced system for atmospheric flows: Robustness in the presence of small scale surface irregularities

It is well known that the primitive equations (the atmospheric equations of motion under the additional assumption of hydrostatic equilibrium for large scale motions) are ill posed when used in a limited area on the globe. Yet the atmospheric equations of motion for large scale motions are essentially a hyperbolic system that with appropriate boundary conditions should lead to a well posed system in a limited area. This apparent paradox was resolved by Kreiss through the introduction of the mathematical Bounded Derivative Theory (BDT) for any symmetric hyperbolic system with multiple time scales (as is the case for the atmospheric equations of motion). The BDT uses norm estimation techniques from the mathematical theory of symmetric hyperbolic systems to prove that if the norms of the spatial and temporal derivatives of the ensuing solution are independent of the fast time scales (thus the concept of bounded derivatives), then the subsequent solution will only evolve on the advective space and time scales (slowly evolving in time in BDT parlance) for a period of time. The requirement that the norm of the time derivatives of the ensuing solution be independent of the fast time scales leads to a number of elliptic equations that must be satisfied by the initial conditions and ensuing solution. In the atmospheric case this results in a 2D elliptic equation for the pressure and a 3D equation for the vertical component of the velocity.Utilizing those constraints with an equation for the slowly evolving in time vertical component of vorticity leads to a single time scale (reduced) system that accurately describes the slowly evolving in time solution of the atmospheric equations and is automatically well posed for a limited area domain. The 3D elliptic equation for the vertical component of velocity is not sensitive to small scale perturbations at the lower boundary so the equation can be used all of the way to the surface in the reduced system, eliminating the discontinuity between the equations for the boundary layer and troposphere and the problem of unrealistic growth in the horizontal velocity near the surface in the hydrostatic system.     

大气动力学方程组的定性理论及其应用

基于完整的湿大气动力学方程组,利用无穷维动力系统的新理论和新方法,系统讨论了强迫耗散的非线性大气系统的定性理论及其应用。将完整的强迫耗散非线性湿大气动力学方程组化为Hilbert空间中一个等价的算子方程,研究了算子的性质及其物理意义,在此基础上得到湿大气系统全局吸引子的存在性定理,揭示出系统向外源的非线性适应特征,并把结果推广到有地形动力作用和非定常外源强迫的情形。同时探讨了大气方程组惯性流形的存在,大气多平衡态产生的根源以及强迫、耗散和非线性对系统解的渐近行为的影响。在理论结果的基础上,提出强迫耗散的非线性动力系统中存在三类时间边界层、方程组简化准则、分解算法的算子约束原则以及支撑吸引子基底的少数自由度的构造方法,探讨了理论在非线性发展方程差分格式的设计和计算稳定性分析、多平衡态的数值分析、数值模式延伸预报的改进、短期气候预测以及一类中尺度系统分析与预测中的应用,指出描述长期过程动力学模式的必备条件,给出初值与模式相协调的合理解释。最后,对今后的研究方向作了展望。     

基于进化方向遗传算法的四维变分资料同化方法

数值天气预报模式初始时刻要素场的变分同化问题是一个非线性最优化问题。利用进化方向遗传算法（EDGA）求解该最优化问题，并对理想初始场作数值模拟，结果表明模拟的效果较好。     

Radar data assimilation of the GRAPES model and experimental results in a typhoon case

Constructing β-mesoscale weather systems in initial fields remains a challenging problem in a mesoscale numerical weather prediction (NWP) model. Without vertical velocity matching the β-mesoscale weather system, convection activities would be suppressed by downdraft and cooling caused by precipitating hydrometeors. In this study, a method, basing on the three-dimensional variational (3DVAR) assimilation technique, was developed to obtain reasonable structures of β-mesoscale weather systems by assimilating radar data in a next-generation NWP system named GRAPES (the Global and Regional Assimilation and Prediction System) of China. Single-point testing indicated that assimilating radial wind significantly improved the horizontal wind but had little effect on the vertical velocity, while assimilating the retrieved vertical velocity (taking Richardson's equation as the observational operator) can greatly improve the vertical motion. Experiments on a typhoon show that assimilation of the radial wind data can greatly improve the prediction of the typhoon track, and can ameliorate precipitation to some extent. Assimilating the retrieved vertical velocity and rainwater mixing ratio, and adjusting water vapor and cloud water mixing ratio in the initial fields simultaneously, can significantly improve the tropical cyclone rainfall forecast but has little effect on typhoon path. Joint assimilating these three kinds of radar data gets the best results. Taking into account the scale of different weather systems and representation of observational data, data quality control, error setting of background field and observation data are still requiring further in-depth study.     

雷达资料同化在局地强对流预报中的应用

采用ARPS模式的资料分析系统ADAS同化多普勒雷达径向速度和反射率因子资料,分析两者对初始场的改进作用,并应用于WRF中尺度模式中对2012年8月21日江西省一次局地强对流过程进行了模拟试验。分析结果表明:（1）ADAS同化系统能够利用雷达径向速度和反射率因子资料有效增加初始场中的中小尺度风场信息和云、水物质含量,并通过湿绝热或非绝热初始化对温度场、湿度场和风场进行调整,使初始场在动力和热力上达到平衡。（2）同化径向速度后对改善模式初始场的动力场有重要贡献,而对大气水凝物和降水的预报影响较小;同化反射率因子的主要作用是调整初始场中的水凝物场和热力场,有效缩短了模式的“ spin-up”时间,明显改进了定量降水预报;同时同化雷达径向速度和反射率因子后,初始场中快速调整出了中小尺度风场水平辐合、垂直运动以及合理的温、湿分布,对3小时内雨带形状、降水落区及定量降水的预报与实况更接近。（3）模拟试验表明,同时同化径向速度和反射率因子能成功模拟出本次对流单体风暴的中β尺度三维空间分布结构及其演变过程,中低层切变线的辐合抬升强迫作用是对流单体风暴组织、发展和维持的主要动力机制之一,对流凝结潜热加热在对流单体风暴的发生发展中发挥了重要作用。因此,雷达资料同化对提高临近数值天气预报的准确率以及对强对流天气系统的模拟能力具有重要意义。     

预报科学

世界各国和各地区的环境预报中心的主要任务是向本国、本地区和全球公众发布科学的环境预报,包括天气、水、气候和空间天气的预报。气象学家与其他科学家合作,一起制作可靠、及时、准确的分析结果、指导意见、预报及预警,以确保人们的生命和财产安全,促进全球经济的发展,以满足人们日益增长的对环境信息的需求。为了更准确地制作预报、更好地服务大众以及最大限度地减少生命和财产损失,这里提出了＂预报科学＂思想。预报科学包括现代观测系统的资料收集、观测与预报信息的实时交流、各种科学技术的发展、无缝隙预报以及公共服务等。预报科学可以概括为三个相互独立的部分,即科学性、工程性和艺术性,且三者存在相互作用。总之,天气预报是大气与环境服务的重要组成部分;预报科学的科学性、工程性和艺术性均服务于天气预报、服务于人民。     

物理耗散技术及其在MM4中的应用

在传统的流体动力学框架下,数值天气预报问题往往被提为经典牛顿力学的确定论初值问题　。然而大气是多体系统,利用仅对三体以下的系统才能精确描述的理论来处理多体系统的运　动,会引起较大的误差和问题。为此,文中提出了一套在数值天气预报模式中引入“不可逆　热力学算子”的技术,按热力学第二定律的约束方式,来控制多体系统的演变方向,以提高　数值天气预报的精度。例如在ＭＭ４模式中引入不可逆热力学算子后,温度场、湿度场、高度　场及全风速场的平均相对均方根误差减小了约１３％,其中４８　ｈ预报的误差减小两成以上。鉴于文中提出的不可逆热力学算子引入技术是基于描述耗散性的物理定律,而非纯粹出于计算　上的考虑,故名为物理耗散技术。由于它所依据的物理原理对所有流体力学和大气数值模式　均适用,因此该项新技术在地球物理流体力学界将有广阔的应用前景。     

The dynamics of uncertainty: application to parameterization constants in climate models

Climate models, ranging from statistical-dynamical to the explicit-dynamical, contain a range of uncertainties related to the parameterization constants associated with the various forcing terms used therein. Quantifying the impacts of such uncertainties has heretofore received little attention. The impact of this aspect of the dynamics of uncertainty was revealed in a series of dynamical systems of increasing complexity. The inevitability of climate drift was discussed, with one aspect being revealed as the non-Gaussian nature of most forcing terms. For those dynamical systems which are chaotic in nature, it was shown how stochastic dynamic equations can be used to describe the uncertainty, even with uncertainty in the critical forcing terms. The possibility of climate transitions driven by stochastic forcing occurring on much faster time scales (i.e., weather disturbances) has been shown by numerous authors. The caution shown here is that even very small uncertainty in a forcing term occurring on the slow climate time scales can lead to such transitions more easily. Conversely, a deterministic parameterization on the slowly varying time scale may be just slightly incorrect in a particular model formulation and lead to the wrong climatic state. In view of such concerns, the framework for attacking the difficult nonlinear problem of uncertain parameterization constants in complex GCMs is outlined.The National Center for Atmospheric Research is sponsored by the National Science Foundation     

大气边界层的初值形成

采用850毫巴和地面的大尺度天气状况和物理特性作为外参数,将大气边界层下层的地表层进行特殊处理,考虑了层结的作用,其上分成等距15层,考虑地转民随高度线性变化。上下层耦合,建立一个定常平衡初值模型,并将所得的初值作为第一级近似,再利用地面、300、600、900、1500米五个高度测风资料进行动力调整,试图建立一个更加接近实际状态的边界层初值。 文中利用所建立的模型,对大气边界层的一些物理参数的作用进行了分析,并对动力调整过程以及垂直分层的选取等作了讨论。 最后例举华北地区1966年8月23日08时边界层的各层次风场和垂直运动,清楚地显示出边界层内的细致结构。     

热带气旋低层水平流场的平面动力系统分析

利用中国气象局上海台风研究所整理的热带气旋最佳路径资料,热带气旋云图、气象雷达回波图资料,ECMWF ERA-Interim再分析风场资料;并用大气运动方程和天气学原理分析得到热带气旋低层水平流场结构,根据流场建立平面非线性自治动力系统。结果表明,TC在成熟阶段或发展很强时期,由两组二维驻定微分方程组解确定水平流场,TC眼区以内气流沿顺时针方向流动,TC眼区以外气流沿逆时针方向流动。TC眼区内外相反方向风场之间为风向切变圆环,圆环上不断有气旋形成,并存在低空急流,是狂风暴雨出现区域。结论与合成雷达回波观测结果一致。      

台风路径实时数值预报的初步试验

根据国家气象中心建立的台风路径数值预报试验系统，引入了模型台风。模型台风是利用获得的场面参数构成的，然后再叠加到客观分析场上作为台风路径预报的初始场。引入模型台风后，无论是台风中心位置还是其流场、质量场与实际观测比较接近，且预报效果有一定提高。利用模型台风对1992年Eli（9205号）和Janis（9210号）台风进行了实时的预报试验。结果表明对这二个台风的移动趋势基本上能预报出来，预报的台风路径与实况进行了对比，并与气候持续预报作了比较，效果较好。     

Statistical Distribution of Atmospheric Dust Devils on Earth and Mars

Boundary-Layer Meteorology - Numerical weather prediction is often used to supply the mean wind and turbulence fields for atmospheric transport and dispersion plume models as they provide dense...