Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds

We present a statistical cloud scheme based on the subgrid-scale distribution of the saturation deficit. When analyzed in large-eddy simulations (LES) of a typical cloudy convective boundary layer, this distribution is shown to be bimodal and reasonably well-fitted by a bi-Gaussian distribution. Thanks to a tracer-based conditional sampling of coherent structures of the convective boundary layer in LES, we demonstrate that one mode corresponds to plumes of buoyant air arising from the surface, and the second to their environment, both within the cloud and sub-cloud layers. According to this analysis, we propose a cloud scheme based on a bi-Gaussian distribution of the saturation deficit, which can be easily coupled with any mass-flux scheme that discriminates buoyant plumes from their environment. For that, the standard deviations of the two Gaussian modes are parametrized starting from the top-hat distribution of the subgrid-scale thermodynamic variables given by the mass-flux scheme. Single-column model simulations of continental and maritime case studies show that this approach allows us to capture the vertical and temporal variations of the cloud cover and liquid water.     

An efficient optimum interpolation analysis scheme

Abstract

One of the characteristics of the optimum interpolation analysis scheme is that a matrix problem that depends on the number of observations has to be solved for each grid‐point value that is calculated. In data‐rich regions, this matrix can be quite large and in general, a limit on its size has to be imposed in order to avoid an excessive amount of computation.

In the proposed univariate analysis scheme, the autocorrelation function has been approximated by the second‐order and fourth‐order Taylor series expansion of the Gaussian Hill function. It is shown that the weights given to the observations can then be evaluated analytically by resolving associated systems of order 4 and 9, respectively.

When 24 pieces of data are used, the proposed schemes are, respectively, 6 and 3 times faster than an optimum interpolation analysis scheme using the Gaussian autocorrelation function. Furthermore, the analyses produced by those 3 schemes are almost identical. The search radius being limited, the proposed schemes are useful and worth while only over data‐dense areas.     

On the influence of non-Gaussianity on turbulent transport

Non-Gaussianity effects, first of all the influence of the third and fourth moments of the velocity probability density function, have to be assessed for higher-order closure models of turbulence and Lagrangian modelling of turbulent dispersion in complex flows. Whereas the role and the effects of the third moments are relatively well understood as essential for the explanation of specific observed features of the fully developed convective boundary layer, there are indications that the fourth moments may also be important, but little is known about these moments. Therefore, the effects of non-Gaussianity are considered for the turbulent motion of particles in non-neutral flows without fully developed convection, where the influence of the fourth moments may be expected to be particularly essential. The transport properties of these flows can be characterized by a diffusion coefficient which reflects these effects. It is shown, for different vertical velocity distributions, that the intensity of turbulent transport may be enhanced remarkably by non-Gaussianity. The diffusion coefficient is given as a modification of the Gaussian diffusivity, and this modifying factor is found to be determined to a very good approximation by the normalized fourth moment of the vertical velocity distribution function. This provides better insight into the effect of fourth moments and explains the varying importance of third and fourth moments in different flows.     

PERMAFROST ZONATION AND CLIMATE CHANGE IN THE NORTHERN HEMISPHERE: RESULTS FROM TRANSIENT GENERAL CIRCULATION MODELS

Numerous studies have demonstrated that both global patterns and local details of permafrost distribution are highly responsive to climatic fluctuations, at several temporal and spatial scales. Permafrost currently underlies about one fourth of the land area of the northern hemisphere, and many qualitative predictions have been made for a severe reduction of this area in response to global warming. A map of permafrost distribution compiled using the frost index, a dimensionless number that can be related to the zonal arrangement of permafrost, shows very good correspondence with a recently published empirical map. The frost index was used in conjunction with three transient general circulation models to compile maps of permafrost zonation for conditions in the mid-21st century. Although regional patterns and local details differ substantially between the three scenarios, all result in reductions in the area occupied by each permafrost zone. Localized expansions of the area underlain by permafrost are apparent from two of the scenarios. Reductions in the areal extent of equilibrium permafrost predicted from two of the three transient models are much less than those indicated by runs using 2 × CO models.     

Gaussian components of cloud amount frequency distributions

Summary Interannual variability of meteorological conditions produces cloud amount sequences that statistically cannot be regarded as samples from the same population. Consequently in order to treat cloud amount distributions the traditional methods of mathematical statistics are useless. In this paper a method is presented that enables to approximate the cloud amount histograms by means of mixtures of Gaussian components. When a component can be found that is common to the histograms of different years, it may be regarded as a characteristic of a quasistationary cloudiness regime that is induced by stable meteorological conditions above the respective target area during the given period.The procedure to separate a cloud amount frequency distribution into Gaussian components is demonstrated on the basis of an example of March–May cloudiness analysis in the mid-ocean regions of the belt 0°–13.5° S. The monthly mean cloud amount data in the (500 km)² squares have been determined from Nimbus-7 short-wave albedo measurements in 1979–1986. It has been demonstrated that even in the years that are not affected by the El Niño event the interannual variability of the autumn cloud amount histograms is essential at the 95% significance level. But separating the frequency distributions into Gaussian components, a part can be found that is common to all the autumns and, thus, may be regarded as a characteristic of the contemporary climate.With 6 Figures     

用一维时间序列确定吸引子维数应注意的两个问题

该文给出了严格自相似和统计自相似的区别，并由此讨论了用一维时间序列确定吸引子维数应注意的两个问题，即维数计算公式中的标度范围及比例系数问题和双对数图与Ｄ－ｍ图的关系问题。     

青藏高原晴空行星反照率与地面反照率关系的研究

本文利用了大气-地球系统的物理模型推导了晴空行星反照率与地面反照率之间的相互关系,指出当仅考虑一次地面反射时,行星反照率是地面反照率的一次线性函数,当考虑到大气与地面的多次反射时,两者的关系设为二次抛物线函数,并利用1986年中美青藏高原联合考察期间的地面辐射资料以及同期NOAA-9的GAC资料对上述关系进行了试验,结果表明,两种关系都能较好地反映出青藏高原行星反照率与地面反照率之间的关系,但二次函数表现的物理意义更为明确。 青藏高原作为一个特殊的地理类型,其行星反照率与地面反照率的相互关系与全球纬向平均相比较也有明显的差异,本文讨论了这些差异的物理意义,同时分别讨论了该地区可见光和近红外这二个通道的滤过反照率与地面分光谱反照率之间的关系。 青藏高原晴空反照率与地面反照率关系的研究为利用AVHRR资料反演青藏高原地面反照率的数值分布图提供了理论依据和具体方法。     

REYNOLDS EXCHANGE IN THE ATMOSPHERIC MULTI-SCALE MOTIONS

In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con-cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynoldsexchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.Inorder to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynoldsequations is given in which the subscale motions are described by Langevin equation as the air particles are moving inthe Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchangecoefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperatureand other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be-tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancyand/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the correspondingelements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo-tions.     

关于不同尺度大气运动中的雷诺交换

本文从多尺度分解概念出发,建立了多尺度Reynolds方程组。证明了平均运动的Reynolds交换项应为各级子平均运动非线性项的平均和。文中将子尺度运动处理为描述质点个别运动的Langevin形式以避免Euler方式导致的高阶闭合困难,简单地得到了K闭合表示,给出了动量、热量、质点交换系数的表达式并阐明了它们之间差异的形成原因。此外本文还给出了表现无序脉动量在导向力(如浮力、科氏力)作用下建立有序平均量梯度的负K值及其存在条件,解释了大气中大尺度运动的一些负粘性现象。     

A model for sensible heat flux probability density function for near-neutral and slightly-stable atmospheric flows

The probability density function for sensible heat flux was measured above a uniform dry lakebed (Owens lake) in Owens Valley, California. It was found that for moderately stable to near neutral atmospheric stability conditions, the probability density function exhibits well defined exponential tails. These exponential tails are consistent with many laboratory boundarylayer measurements and numerical simulations. A model for the sensible heat flux probability density function was developed and tested. A key assumption in the model derivation was the near Gaussian statistics of the vertical velocity and temperature fluctuations. This assumption was verified from time series measurements of temperature and vertical velocity. The parameters for the sensible heat flux probability density function model were also derived from mean meteorological and surface conditions using surface-layer similarity theory. It was found that the best agreement between modeled and measured sensible heat flux probability density function was at the tails. Finally, a relation between the intermittency parameter, the probability density function, and the mean meteorological conditions was derived. This relation rigorously links the intermittency parameter to mean meteorological conditions.     

A study of vertical velocity distributions in the planetary boundary layer

Until recently, pollution dispersion models have made predictions on the basis that the pollutant concentration is Gaussian. Such is not the case for convective conditions where the observed vertical velocity distribution is skewed towards the updraught portion of the distribution. One recent dispersion model assumes that the observed distribution can be synthesized by superimposing two Gaussians of appropriate means, variances and amplitudes.In the current paper, two techniques for deriving the constituent distributions are investigated. The first technique is based on conditionally sampling the vertical velocity time series and partitioning the vertical velocity samples into two sets — one set recorded when the sensor was experiencing an updraught and the other when the sensor was experiencing a downdraught. The second method consists of fitting two Gaussian distributions to the observed data and adjusting these using an iterative procedure until a specified tolerance is achieved.Both techniques give similar results which compare favourably with results obtained by other researchers. Assumptions, as well as advantages and disadvantages of each technique are also discussed.     

A Markov-chain model for winterstrength in the upper Danube Region

A Markov-chain model is fitted to the series of winter-strength parameters of five stations in the upper Danube Region. The validity of the model is tested by an appropriate Gaussian test-statistic. Having calculated the matrices of transition probabilities, boundaries for them are derived from the theory of Markov-chains as well as means of the first transition times with their standard deviations; further, forecasts are derived for the next but one winter. As in all cases the standard deviations for prognostic values are rather large one should be very careful in making annual forecasts, which is also demonstrated by a testforecast.     

Near-surface wind estimates using statistics from a planetary boundary-layer model

This paper shows the possibilities of a procedure for estimating near-surface wind statistics, by means of the numerical integration of a simple boundary-layer model with a second-order turbulent closure. Standard and easily available synoptic data are used as initial and boundary conditions. The development of this methodology is impelled by increasing requirements of a quick and precise knowledge of the wind characteristics in many regions of South America, which confronts the serious limitation of a reduced number of extended observational series, scattered over a vast continent. In order to evaluate the methodology, near-surface wind statistics from observed data at two locations are compared with model output statistics. Relative errors are about 0.2 for daily mean velocities and about 0.1 for weekly mean velocities, observed and computed time series being highly correlated in both cases. Calculated frequency distribution of wind directions is in good agreement with the observed one, and the absolute mean error in the daily mean wind direction is about 20 deg. Even though a wide variety of large-scale synoptic situations has been indirectly considered through boundary conditions, basic model output statistics resemble fairly well those observed at different levels between the surface and 100 m.     

对流层下部的湍流微結构

本文利用等人的风速模涨落的观測資料,分析了100—1470米高的湍流結构。得到下面主要結果:(1)各个高度上水平风速模涨落的概率分布近于正态律.(2)局地各向同性湍流理論的結論适用于所述高度范围內的小湍涡区.并且,在几百米高度以下,結构函数适合“2/3規律”的最大尺度常常与高度相当,甚至会超过高度好多倍.(3)在高于几百米的地方,适合“2/3規律”的最大尺度小于高度,且随高度沒有呈現系統性变化。 文中也討論了所用記录的代表性。     

1921～2010年天津气温和降水量序列的多尺度分析

基于集成经验模态分解(EEMD)方法,对1921~2010年天津年平均气温和降水量序列进行了多尺度分析。并结合功率谱对年平均气温和年降水量及其本征模态函数(IMF)分量进行周期分析。结果表明:天津年平均气温的变化主要是由第1、第2本征模态分量和趋势项构成,即准5 a和2~3 a的振荡与"先降后升"的长期趋势变化起主要作用。而第4、第5本征模态分量则反映出天津近90年来气温年代际尺度的冷暖变化,它们对1920年代至1940年代的暖期以及1950年代至1970年代的冷期有重要贡献。降水量的变化主要由第1、第2本征模态分量构成,即4.5 a、准9 a和2~3 a的振荡起主要作用。与气温序列相比,降水序列中年代际尺度的变化和长期趋势的贡献明显要小得多,但也反映了1980年代以后降水减少的趋势。     

层结大气中重力惯性波的非线性周期解

本文在动量无辐散近似下的层结大气中,考虑密度空间分布的不均匀性引入非线性项,并假设解为行波形式,得到了一个二阶非线性系统。应用本系统不仅可以得到刘式适等(1984)所得到的一切结果,而且可以证明一次近似系统存在周期解时,非线性系统也存在周期解,且避免了应用级数展开时所带来的一些数学问题。文中还讨论了非线性系统的一系列近似解。     

RECONSTRUCTING MIDDLE-TIBET CLIMATE DURING THE LAST 600 YEARS BY DENDROCLIMATOLOGICAL METHOD*

Based on four tree-ring chronologies which was analyscd with appropriate collection and accurate dating in the middle Tibetan Plateau,an essential procedure on reconstruction of past climate has been pointed out in this paper.First,the response function of each dendrochronology has been built and used to estimate how ring-width growth responds to variations in monthly climatic change.Second,the climate factors which could be produced with different tree-ring series have been selected.Then,the transfer function equation,including a new set of orthogonal variables,can be used to reconstruct local past temperature or precipitation.It should be emphasized that prior growth has been considered in the relationship between climate factor and tree-ring chronology,Besides,some different periods for calibration and verification have been divided.And some statistics and other kinds of proxy data have been adopted as test approaches.As a result,the variations of air temperature during the last 600 years and precipitation during the last 340 years were reconstructed by combining the same types of tree-ring series in the middle Tibet.     

一个检测水中冻结核含量的新装置

为了检测降水物中冻结核的相对浓度,在Vali均匀水滴冻结实验方法的基础上,研制了一种可自动检测冻结信号和处理实验数据的装置。其主体是由一组热电偶制冷的冷台,49个热敏元件等间隔地贴在冷台上,其中一个贴上小型的Pt100测温元件,另一个作为信号参考,其他47个热敏元件各滴上一个被测水滴。试验进行时冷台和水滴线性降温,降温率由818P4欧陆控温仪控制。每个水滴冻结时释放的潜热被热敏元件检测,经电路转换为电压信号,全部水滴冻结产生的一串等值信号由计算机实时跟踪监测。可得到水滴冻结的温度谱和时间谱。通过软件计算可方便地推导出水中所含冻结核的微分和积分浓度的温度谱。与以前的同类装置相比,提高了效率和检测精度。文中简要地介绍了该系统的结构、软件功能、试验程序,并给出了几种人工和自然水样的初步检测结果。这个装置对检测水中冻结核和播云催化剂研究都是有用的。人工冰核(如AgI)常用于人工增雨作业,如果对催化前后的降水样品取样检测它们的冻结核含量,可能发现其中的差别,有助于评估播云效果。     

An analysis of the vertical structure equation in sigma coordinates

Abstract

An analysis of the vertical structure equation of sigma coordinate primitive equation models is given that brings together and extends the work of several authors. We derive the vertical structure equation, and obtain its solution for a two‐parameter family of vertical structure profiles that includes those of previous studies. For this family, it is shown that in the limiting case of an unbounded atmosphere the spectrum becomes partially continuous, rather than entirely discrete as in the bounded case. A criterion is obtained for the validity of the linearization used to derive the vertical structure equations, and it turns out that this criterion is satisfied by all but one of the previous studies. Asymptotic expansions are derived and used to explain two observations of Wiin‐Nielsen (1971a), viz. why the equivalent depths of the internal modes are relatively insensitive to the precise choice of lower boundary condition, and why one choice in particular leads to the elimination of the external mode; these asymptotic expansions also yield surprisingly accurate numerical values for the equivalent depths. Finally, the projection of atmospheric data onto modes found by direct numerical approximation of the vertical structure equation is shown, particularly for the least grave modes, to be very sensitive to resolution; consequently care must be exercised when interpreting the results of data projection studies that use this approach.     

Secular variation of the Pacific Decadal Oscillation,the North Pacific Oscillation and climatic jumps in a multi-millennial simulation

Outputs from a 10,000-year simulation with a coupled global climatic model for present climatic conditions have been used to investigate the behaviour of the Pacific Decadal Oscillation (PDO), the North Pacific Oscillation (NPO) and related phenomena. The analysis reveals a wide range of temporal variability for these Oscillations, suggesting that observations to date provide only a limited sample of possible outcomes. In addition, the simulation suggests that the current observed phase relation between the PDO and NPO may not be typical of longer-term variability. Climatic jumps appear to be a ubiquitous feature of climatic variability, and while, as observed, the most common interval between such jumps is about 20 years, intervals of up to 100 years occur in the simulation. The probability density functions of the PDO and NPO are very close to Gaussian, with the PDO being represented by an auto-regressive function of order one, while the NPO consisted of white noise. An FFT analysis of PC1 of the PDO revealed periodicities concentrated near 10 years, while for the NPO the principal periodicities were decadal to bidecadal. Global distributions of the distributions of the correlations between PC1 or the NPO and selected climatic variables were similar, and in agreement with observations. These correlations highlight the inter-relationships between these two Oscillations. The above correlations were not necessarily stable in time for a given geographical point, with transitions occurring between positive and negative extremes. Climatic jumps were identified with transitions of both the PDO and NPO, with magnitudes of importance as regards climatic perturbations. Spatial patterns of the changes associated with such jumps have global scales, and the need to consider the implications of these jumps in regard to greenhouse induced climatic change is noted.