大气污染物浓度变化的非线性特征分析

研究了大气污染物浓度变化的非线性动力学特征,首次详细考察了污染物浓度时间序列的谱分布、结构函数、自相关函数、时间变化曲线的分数维、相空间中吸引子的关联维及最大Lyapunov指数.此外,当前在国际上得到广泛应用的小波分析方法也能对揭示污染物浓度变化的非线性特征提供很好的帮助.     

The regional dynamical model of the atmospheric ozonosphere

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Progress in the Study of Nonlinear Atmospheric Dynamics and Predictability of Weather and Climate in China (2007--2011)

Recent progress in the study of nonlinear atmospheric dynamics and related predictability of weather and climate in China (2007-2011) are briefly introduced in this article. Major achievements in the study of nonlinear atmospheric dynamics have been classified into two types:(1) progress based on the analysis of solutions of simplified control equations, such as the dynamics of NAO, the optimal precursors for blocking onset, and the behavior of nonlinear waves, and (2) progress based on data analyses, such as the nonlinear analyses of fluctuations and recording-breaking temperature events, the long-range correlation of extreme events, and new methods of detecting abrupt dynamical change. Major achievements in the study of predictability include the following:(1) the application of nonlinear local Lyapunov exponents (NLLE) to weather and climate predictability; (2) the application of condition nonlinear optimal perturbation (CNOP) to the studies of El Nin o-Southern Oscillation (ENSO) predictions, ensemble forecasting, targeted observation, and sensitivity analysis of the ecosystem; and (3) new strategies proposed for predictability studies. The results of these studies have provided greater understanding of the dynamics and nonlinear mechanisms of atmospheric motion, and they represent new ideas for developing numerical models and improving the forecast skill of weather and climate events.     

The Role of Wake Production on the Scaling Laws of Scalar Concentration Fluctuation Spectra Inside Dense Canopies

The scalar concentration fluctuations within a plane parallel-to-the-ground surface were measured inside a model canopy composed of densely arrayed rods using the laser-induced fluorescence technique. Two-dimensional scalar concentration spectra were computed and were shown to exhibit an approximate ?3 power-law scaling at wavenumbers larger than those associated with wake production during quiescent instances when von Karman vortex streets dominated the flow. However, during instances when sweeps disrupted the flow, the spectral exponents increased above ?3. The ?3 power-law for these concentration fluctuation spectra measurements was shown to be consistent with a simplified spectral budget for locally homogeneous and isotropic turbulence augmented with a relaxation time scale similarity argument that assumed a constant enstrophy injection rate and wake generation mechanism. Hence, the origin of this ?3 power-law scaling here differs from the well-known ?3 power-law result for the so-called inertial diffusive range derived for the scalar concentration spectrum at small Prandtl numbers.     

Characteristics Of Chaotic Attractors In Atmospheric Boundary-Layer Turbulence

In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible.     

A Wavelet-Based Correction Method for Eddy-Covariance High-Frequency Losses in Scalar Concentration Measurements

Eddy-covariance (EC) scalar-flux measurements suffer from unavoidable biases introduced by high-frequency losses in the sampled scalar concentration fluctuations. This bias alone leads to an underestimation of scalar fluxes by as much as 20% in some cases, especially when a closed-path gas analyzer is used to sample concentration far from the inlet location. A novel method that directly corrects for these high-frequency losses using only the sampled scalar-concentration time series is proposed and tested. The sampled concentration fluctuation time series is adjusted, point-by-point, in the wavelet half-plane for each EC averaging interval (??30?min). Similarity between scalars (and temperature) is not necessary and a pre-defined theoretical shape of the cospectrum is not required, making this method attractive at meteorologically non-ideal sites. When closed-path gas analyzers are used to measure H₂O concentration fluctuations, the method is shown to reproduce the dependence of the attenuation on air relative humidity. Nevertheless, the method is not able to account for excessively large spectral attenuation that occurs close to the spectral peak, as might be the case with long tubes and high relative humidity. Since the method corrects the original scalar concentration time series and not the cospectrum, other flow statistics??such as variances and integral time scales??are also adjusted. The proposed method can be used synergistically with conventional high-frequency cospectral correction methods given the differences in assumptions and approaches among these methods. When the conventional and the proposed methods agree, added confidence to the estimate of the high frequency correction is gained, and vice versa.     

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。     

Three-Dimensional Scalar Microfront Systems in a Large-Eddy Simulation of Vegetation Canopy Flow

Large-eddy simulation is used to reproduce neutrallystratified airflow inside and immediately above a vegetation canopy. A passive scalaris released from the canopy and the evolution of scalar concentration above the canopyis studied. The most significant characteristic of the scalar concentration is the repeatedformation and dissipation of scalar microfronts, a phenomenon that has been observedin nature. These scalar microfronts consist of downstream-tilted regions of highscalar concentration gradients. Computer visualization tools and a conditional samplingand compositing technique are utilized to analyze these microfronts. Peaks in positivepressure perturbation exceeding an experimental threshold are found to be effectiveindicators of scalar microfronts. Convergence of the streamwise velocity componentand divergence of the cross-stream velocity component are observed in the immediatevicinity of scalar microfronts, which helps explain their relatively longlifetimes. Many of these three-dimensional features have been observedin previous field studies of canopy flow.     

A Study of Concentration Fluctuations in Instantaneous Clouds Dispersing in the Atmospheric Surface Layer for Relative Turbulent Diffusion: Basic Descriptive Statistics

A series of tracer experiments studying the statistical properties of concentration fluctuations in clouds dispersing in the atmospheric surface layer is described and analyzed. Experiments were conducted at downwind fetches between about 200 and 1200 m, under a wide range of atmospheric conditions ranging from very unstable to moderately stable stratification. The present experiments have addressed basic requirements not met by past field experiments involving instantaneously released clouds; namely, the experiments provided repeat realizations of instantaneously released clouds measured with high-resolution concentration detectors, accompanied by the contemporaneous acquisition of high-quality meteorological and turbulence measurements.Extensive analyses are performed on the cloud concentration data in the framework of relative diffusion. Ensembles of cloud concentration realizations have been constructed. From these ensembles, crosswind and time profiles of the ensemble-mean concentration, concentration variance, ensemble-mean dosage, and dosage variance are obtained. The behaviour of the time profiles of the integral time scale of cloud concentration fluctuations is studied. The use of surface-layer similarity theory for the analysis of the downwind variation of a number of cloud quantities (e.g., cloud size and duration, cloud centre ensemble-mean concentration and dosage, cloud centre concentration and dosage variance, cloud centre integral time scale) is shown to be an effective basis for ordering these quantities. Furthermore, a number of approximate universal relationships describing the behavior of these cloud quantities has been derived. Finally, it is shown that the scaled crosswind and time profiles of ensemble-mean concentration and concentration variance as well as the scaled time profiles of the concentration fluctuation integral time scale exhibit self-similar forms that are independent of atmospheric stratification and downwind fetch.     

Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria

Daily rainfall and temperature data from 47 locations across Nigeria for the 36-year period 1979–2014 were treated to time series analysis technique to investigate some nonlinear trends in rainfall and temperature data. Some quantifiers such as Lyapunov exponents, correlation dimension, and entropy were obtained for the various locations. Positive Lyapunov exponents were obtained for the time series of mean daily rainfall for all locations in the southern part of Nigeria while negative Lyapunov exponents were obtained for all locations in the Northern part of Nigeria. The mean daily temperature had positive Lyapunov exponent values (0.35–1.6) for all the locations. Attempts were made in reconstructing the phase space of time series of rainfall and temperature.     

Coherent Structures Detected in Atmospheric Boundary-layer Turbulence using Wavelet transforms at Huaihe River Basin, China

The presence of coherent structures in turbulent shear flows suggests order in apparently random flows. These coherent structures play an important dynamical role in momentum and scalar transport. To develop dynamical models describing the evolution of such motion, it is necessary to detect and isolate the coherent structures from the background fluctuations. In this paper, we decomposed atmospheric turbulence time series into large-scale eddies, which include coherent structures and small eddies, which are stochastic by using Fourier digital filtering. The wavelet energy computed for the three components of the velocity fluctuations in the large-scale eddies appears to have local maximum values at certain time scales, which correspond to the scales or frequencies of coherent structures. We extract coherent signals from large-scale vortices at this scale by inverse wavelet transform formulae. This method provides an objective technique for examining the turbulence signal associated with coherent structures in the atmospheric boundary layer. The average duration of coherent structures in three directions based on Mexican hat wavelets are 33 s, 34 s and 25 s respectively. Symmetric andanti-symmetric wavelet basis functions give almost the same results. The main features of the structures during the day and night have little difference. The dimensionless durations for u, v and w have linear correlations with each other. These relationships are insensitive to the wavelet basis.     

Use of variance techniques to measure dry air-surface exchange rates

The variances of fluctuations of scalar quantities can be measured and interpreted to yield indirect estimates of their vertical fluxes in the atmospheric surface layer. Strong correlations among scalar fluctuations indicate a similarity of transfer mechanisms, which is utilized in some of the variance techniques. The ratios of the standard deviations of two scalar quantities, for example, can be used to estimate the flux of one if the flux of the other is measured, without knowledge of atmospheric stability. This is akin to a modified Bowen ratio approach. Other methods such as the normalized standard-deviation technique and the correlation-coefficient technique can be utilized effectively if atmospheric stability is evaluated and certain semi-empirical functions are known. In these cases, iterative calculations involving measured variances of fluctuations of temperature and vertical wind velocity can be used in place of direct flux measurements. For a chemical sensor whose output is contaminated by non-atmospheric noise, covariances with fluctuations of scalar quantities measured with a very good signal-to-noise ratio can be used to extract the needed standard deviation. Field measurements have shown that many of these approaches are successful for gases such as ozone and sulfur dioxide, as well as for temperature and water vapor, and could be extended to other trace substances. In humid areas, it appears that water vapor fluctuations often have a higher degree of correlation to fluctuations of other trace gases than do temperature fluctuations; this makes water vapor a more reliable companion or reference scalar. These techniques provide some reliable research approaches but, for routine or operational measurement, they are limited by the need for fast-response sensors. Also, all variance approaches require some independent means to estimate the direction of the flux.This research has been funded as part of the National Acid Precipitation Assessment Program by the U.S. Environmental Protection Agency through IAGDW89930069-01 to the U.S. Department of Energy.     

The Medieval Warm Period, the Little Ice Age and simulated climatic variability

The CSIRO Mark 2 coupled global climatic model has been used to generate a 10,000-year simulation for ‘present’ climatic conditions. The model output has been analysed to identify sustained climatic fluctuations, such as those attributed to the Medieval Warm Period (MWP) and the Little Ice Age (LIA). Since no external forcing was permitted during the model run all such fluctuations are attributed to naturally occurring climatic variability associated with the nonlinear processes inherent in the climatic system. Comparison of simulated climatic time series for different geographical locations highlighted the lack of synchronicity between these series. The model was found to be able to simulate climatic extremes for selected observations for century timescales, as well as identifying the associated spatial characteristics. Other examples of time series simulated by the model for the USA and eastern Russia had similar characteristics to those attributed to the MWP and the LIA, but smaller amplitudes, and clearly defined spatial patterns. A search for the frequency of occurrence of specified surface temperature anomalies, defined via duration and mean value, revealed that these were primarily confined to polar regions and northern latitudes of Europe, Asia and North America. Over the majority of the oceans and southern hemisphere such climatic fluctuations could not be sustained, for reasons explained in the paper. Similarly, sustained sea–ice anomalies were mainly confined to the northern hemisphere. An examination of mechanisms associated with the sustained climatic fluctuations failed to identify a role for the North Atlantic Oscillation, the El Niño-Southern Oscillation or the Pacific Decadal Oscillation. It was therefore concluded that these fluctuations were generated by stochastic processes intrinsic to the nonlinear climatic system. While a number of characteristics of the MWP and the LIA could have been partially caused by natural processes within the climatic system, the inability of the model to reproduce the observed hemispheric mean temperature anomalies associated with these events indicates that external forcing must have been involved. Essentially the unforced climatic system is unable to sustain the generation of long-term climatic anomalies.     

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     

Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes

Summary Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-tie scales ranging from turbulence (centimetersseconds) to climate (kilometers-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures ofself-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. Mathematical models for simulation and prediction of atmospheric flows are nonlinear and do not possess analytical solutions. Finite precision computer realizations of nonlinear models give unrealistic solutions because ofdeterministic chaos, a direct consequence of round-off error growth in iterative numerical computations. Recent studies show that roundoff error doubles on an average for each iteration of iterative computations. Round-off error propagates to the main stream computation and gives unrealistic solutions in numerical weather prediction (NWP) and climate models which incorporate thousands of iterative computations in long-term numerical integration schemes. An alternative non-deterministic cell dynamical system model for atmospheric flows described in this paper predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics. The model provides universal quantification for self-organized criticality in terms of the statistical normal distribution. Model predictions are in agreement with a majority of observed spectra of time series of several standard climatological data sets representative of disparate climatic regimes. Universal spectrum for natural climate variability rules out linear trends. Man-made greenhouse gas related atmospheric warming will result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change.With 11 Figures     

A Comparison Of The Detailed Structure In Dispersing Tracer Plumes Measured In Grid-Generated Turbulence With A Meandering Plume Model Incorporating Internal Fluctuations

A meandering plume model that explicitly incorporatesinternal fluctuations has been developed and used to model the evolutionof concentration fluctuations in point-source plumes in grid turbulenceobtained from a detailed water-channel simulation. This fluctuating plumemodel includes three physical parameters: the mean plume spread in fixedcoordinates, which represents the outer plume length scale; the meaninstantaneous plume spread in coordinates attached to the instantaneousplume centroid, which represents the inner plume length scale; and, theconcentration fluctuation intensity in the meandering reference frame,which represents the in-plume fluctuation scale. These parameters arespecified in terms of a set of coupled dynamical equations that modeltheir development with downstream distance from the source. Explicitexpressions for the concentration moments of arbitrary integral orderand the concentration probability density function have been obtainedfrom the fluctuating plume model. Detailed comparisons of model predictionsagainst water-channel measurements for the first four concentrationmoments and the concentration probability distributions generally showvery good overall quantitative agreement. Exact quantitative conditions,expressed in terms of the physical parameters of the fluctuating plumemodel, have been derived for the emergence of off-centreline peaks inthe concentration variance profile. These quantitative conditions havebeen illustrated in terms of a diagram of states of the dispersing plume,and the qualitatively different regimes of plume concentration variancebehaviour on this state diagram have been identified and characterized.     

Diagnostic budget study of the internal variability in ensemble simulations of the Canadian RCM

Due to the chaotic and nonlinear nature of the atmospheric dynamics, it is known that small differences in the initial conditions (IC) of models can grow and affect the simulation evolution. In this study, we perform a quantitative diagnostic budget calculation of the various diabatic and dynamical contributions to the time evolution and spatial distribution of internal variability (IV) in simulations with the nested Canadian Regional Climate Model. We establish prognostic budget equations of the IV for the potential temperature and the relative vorticity fields. For both of these variables, the IV equations present similar terms, notably terms relating to the transport of IV by ensemble-mean flow and to the covariance of fluctuations acting on the gradient of the ensemble-mean state. We show the skill of these equations to diagnose the IV that took place in an ensemble of 20 3-month (summer season) simulations that differed only in their IC. Our study suggests that the dominant terms responsible for the large increase of IV are either the covariance term involving the potential temperature fluctuations and diabatic heating fluctuations, or the covariance of inter-member fluctuations acting upon ensemble-mean gradients. Our results also show that, on average, the third-order terms are negligible, but they can become important when the IV is large.     

纬向平均环流预报的系统性误差及其改进

大量的月预报实例分析表明,纬向平均环流(本指高度场纬向平均分量)存在明显的系统性预报误差,且在总误差中占有可观的份额。国内外其它模式也存在类似的现象。为克服这一困难,本尝试了“结合”(hybrid)的途径。应用重构相空间理论和非线性时空序列预测方法,在大量历史资料的基础上,构造了月尺度逐侯纬向平均高度场(零波分量)距平场的非线性预报模型。然后,将非线性预报和谱模式动力预报结合起来,即将非线性预报结果转化为模式需要的颅报量,再在模式积分过程中的每一步取代其相应部分,实施过程订正。初步试验结果表明,这种途样合效地减少了模式纬向环流的预报误差;特别是通过非线性波流相互作用,还改善了部分波动分量的预报。     

Simplified expressions for adjusting higher-order turbulent statistics obtained from open path gas analyzers

When density fluctuations of scalars such as CO₂ are measured with open-path gas analyzers, the measured vertical turbulent flux must be adjusted to take into account fluctuations induced by ‘external effects’ such as temperature and water vapour. These adjustments are needed to separate the effects of surface fluxes responsible for ‘natural’ fluctuations in CO₂ concentration from these external effects. Analogous to vertical fluxes, simplified expressions for separating the ‘external effects’ from higher-order scalar density turbulence statistics are derived. The level of complexity in terms of input to these expressions are analogous to that of the Webb–Pearman–Leuning (WPL), and are shown to be consistent with the conservation of dry air. It is demonstrated that both higher-order turbulent moments such as the scalar variances, the mixed velocity-scalar covariances, and the two-scalar covariance require significant adjustments due to ‘external effects’. The impact of these adjustments on the turbulent CO₂ spectra, probability density function, and dimensionless similarity functions derived from flux-variance relationships are also discussed.     

The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic(or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii(GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach2~(1/2) with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.