最大熵谱的优良特性和预报误差过滤系数阶数的确定

最大熵谱分析比通常谱分析分辨率高,峰值偏离小,特别适宜于短资料或长周期的谱分析,这对气候分析和中长期过程的周期分析是有显著意义的。最大熵谱分析的预报误差过滤系数的阶数,可以在最终预报误差(FPE)m的前后两个极小值的谱估计一致的条件下,用前一个极小值的m数来确定。     

A Simple Physically-Based Model for Wind-Turbine Wake Growth in a Turbulent Boundary Layer

A systematic evaluation is conducted of the smoothed spectrum, which is a spectral estimate obtained by averaging over a window of contiguous frequencies. The technique is extended to the ogive, as well as to the cross-spectrum. It is shown that, combined with existing variance estimates for the periodogram, the variance—and therefore the random error—associated with these estimates can be calculated in a straightforward way. The smoothed spectra and ogives are biased estimates; with simple power-law analytical models, correction procedures are devised, as well as a global constraint that enforces Parseval’s identity. Several new results are thus obtained: (1) The analytical variance estimates compare well with the sample variance calculated for the Bartlett spectrum and the variance of the inertial subrange of the cospectrum is shown to be relatively much larger than that of the spectrum. (2) Ogives and spectra estimates with reduced bias are calculated. (3) The bias of the smoothed spectrum and ogive is shown to be negligible at the higher frequencies. (4) The ogives and spectra thus calculated have better frequency resolution than the Bartlett spectrum, with (5) gradually increasing variance and relative error towards the low frequencies. (6) Power-law identification and extraction of the rate of dissipation of turbulence kinetic energy are possible directly from the ogive. (7) The smoothed cross-spectrum is a valid inner product and therefore an acceptable candidate for coherence and spectral correlation coefficient estimation by means of the Cauchy–Schwarz inequality. The quadrature, phase function, coherence function and spectral correlation function obtained from the smoothed spectral estimates compare well with the classical ones derived from the Bartlett spectrum.     

Intraseasonal zonal wind fluctuations seen through Indian radiosonde observations

Summary Twice-daily radiosonde records for Calcutta, Madras, Nagpur, New Delhi, Trivandrum, and Visakhapatnam have been quality checked and analyzed for intraseasonal activity in the summer monsoon. The records for all six cities end on 30 June 1978 and are 17–27 years long.Spectra were estimated by smoothing periodograms and by using the maximum entropy method (MEM), which entails fitting an autoregressive (AR) model. We show how confidence limits can be placed on an average of MEM spectral estimates using the Central Limit Theorem and how this helps pick the orders of the AR models to be tried. We donot favor use of Akaike's Final Prediction Error in choosing the model order, because it can grossly underestimate the AR model order needed to resolve low frequency peaks.MEM spectra of zonal wind based on thirtieth order AR models have large peaks around 30 day time scales. 10–20 day activity is identifiable but is much less prominent. On average, 3–5 day time scales are part of the spectral continuum and do not have a significant spectral peak.Time-height diagrams of filtered zonal wind show that a deep layer of the troposphere acts in phase on 30–50 day time scales over India. The shortest vertical length scale is over southern India and the longest is over northern India. Vertical phase propagation is irregular except over Nagpur, where it is generally upward. Empirical orthogonal functions indicate that vertically in phase activity has more variance (kinetic energy) than the first baroclinic mode.With 10 Figures     

North-Eastward propagating 25–50-day mode and its link with Indian summer monsoon activity

Summary Spatio-temporal characteristics of the 25–50-day oscillations are investigated using the empirical orthogonal function (EOF) decomposition and spectral analysis with the Maximum Entropy Method (MEM). Daily pressure values over India during 1978 are used in this study. Power spectra of the temporal coefficients of the two leading EOFs show the existence of a low frequency oscillation with a period range 25–50-day over all India. An analysis using extended empirical orthogonal function (EEOF) indicates North-Eastward propagating 25–50-day mode. The analysis EOF has allowed to establish a relationship between the 25–50-day oscillation and the activity of the summer monsoon. The North-Eastward propagation of this mode is also confirmed by the simple EOF analysis.With 9 Figures     

Non-harmonic spectral analysis to investigate periodicity in hydrologic and climatologic time series

Summary Some hydrologic, climatologic and artificially generated time series are analyzed for periodic components using a nonharmonic (NH) method of spectral estimation. The NH spectra are compared with those obtained by using the traditional Blackman and Tukey (BT) and Fast Fourier Transform (FFT) methods and with the relatively recent Maximum Entropy (ME) and Autoregressive Moving Average (ARMA) methods. The NH method appears to be promising.With 12 Figures     

Periodic signals in Spanish monthly precipitation data

Summary Forty-two monthly rainfall time series from Spain have been analyzed for the presence of cycles and regional patterns. The study was carried out by means of periodicity tests devised by Whittle, Hannan, Bartlett, Siegel, and Priestley. These tests contribute to a mixed spectrum analysis leading to the evaluation of signals versus the background of coloured noise (autocorrelation). Also, a direct maximum entropy method (MEM) for estimating spectra was applied to the series, in particular an autoregressive (AR) power spectral density (psd) estimation, and an autoregressive moving average (ARMA) psd estimation, with parameters obtained by exact maximum likelihood estimator (MLE).With 4 Figures     

Maximum entropy spectra of some rainfall and river flow time series from southern and central India

Summary Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

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Zusammenfassung In hydrologischen und klimatologischen Zeitreihenanalysen stellt die Maximale Entropie Spektralanalyse (MESA) eine Alternative zur traditionellen Blackman-Tukey (BT) und schnellen Fouriertransformation (FFT) dar. Es werden die maximalen Entropiespektra der jährlichen Niederschlagszeitreihe in Mangalore und Waltair und die monatlichen Durchflußzeitreihen der Flüsse Godavari und Krishna (Indien) präsentiert und mit den Spektren, die man durch BT und FFT erhält, verglichen. Eine kürzlich entwickelte Entscheidungsregel wurde herangezogen, um die Filterlänge für MESA zu bestimmen. Der Einfluß der Filterlänge auf die maximalen Entropiespektra wird ebenfalls diskutiert.

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With 6 Figures     

Analysis of precipitation series for Belgrade

Summary Precipitation is a very variable climatic element. It is highly variable, both spatially and temporally at different scales (interannual and intra-annual). The search for cyclicity in the climatic record can resolve some of the complexities of the atmospheric system. This paper takes the example of the Belgrade precipitation series (1889–2000) to illustrate how trend and spectral analysis can provide information on climate variability as expressed through this particular variable.The annual, seasonal and monthly precipitation series of the Belgrade-Observatory station were analyzed by means of the Mann-Kendall test and the spectral analysis. The power spectra were calculated using the autocorrelation spectral analysis, the maximum entropy spectral analysis and the multitaper method.The influence of large-scale phenomena such as the El-Niño Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO) on the Belgrade precipitation series was investigated.     

Signature of quasi–biennial oscillation and long-period equatorial disturbances in the lower atmosphere over Thiruvananthapuram

Summary An attempt has been made in this paper to examine different modes of oscillation in the wind field during different seasons over Thiruvananthapuram (lat. 8.29° N, long. 76.59° E, located at the extreme southwest coast of India) based on daily upper air observations for the period from January 1997 to December 1999. A power spectral analysis is carried out with the upper air data of the station. The study shows that one and half cycle of Quasi–Biennial Oscillation (QBO) and the power spectra of the meridional wind component exhibit peaks between the period of four days and seven days (corresponding frequency range between 0.25 day⁻¹ and 0.15 day⁻¹) during all seasons. The seasonal variation of these large-scale oscillations over the station depends upon the background mean zonal flow, which in turn closely related to the QBO structure. The time sequence of power spectra shows that the disturbances with periods between four days and seven days dominantly prevail in the upper troposphere and lower stratosphere throughout the year. The regimes of high power spectral intensity in this period range are maintained in the levels where the mean zonal flow (westerly or easterly) weakens and changes with height. The study establishes the fact that disturbances (mixed Rossby-gravity waves) acquire maximum power in the winter season whereas the south-west monsoon exhibits minimum spectral intensity when spreading of energy over a frequency range takes place.     

A spectral and lag-correlation analysis of turbulence in a deciduous forest canopy

The processes influencing turbulence in a deciduous forest and the relevant length and time scales are investigated with spectral and cross-correlation analysis. Wind velocity power spectra were computed from three-dimensional wind velocity measurements made at six levels inside the plant canopy and at one level above the canopy. Velocity spectra measured within the plant canopy differ from those measured in the surface boundary layer. Noted features associated with the within-canopy turbulence spectra are: (a) power spectra measured in the canopy crown peak at higher wavenumbers than do those measured in the subcanopy trunkspace and above the canopy; (b) peak spectral values collapse to a relatively universal value when scaled according to a non-dimensional frequency comprised of the product of the natural frequency and the Eulerian time scale for vertical velocity; (c) at wavenumbers exceeding the spectral peak, the slopes of the power spectra are more negative than those observed in the surface boundary layer; (d) Eulerian length scales decrease with depth into the canopy crown, then increase with further depth into the canopy; (e) turbulent events below crown closure are more correlated with turbulent events above the canopy than are those occurring in the canopy crown; and (f) Taylor's frozen eddy hypothesis is not valid in a plant canopy. Interactions between plant elements and the mean wind and turbulence alter the processes that produce, transport and remove turbulent kinetic energy and account for the noted observations.     

Improving the methodology for spectral analysis of climatic time series

The paper discusses a methodology able to estimate both the discrete and continuous spectra without any assumption on the shape of spectral densities. The approach to estimate the spectral density is based on a robust smoothing of the periodogram. Bandwidth, a quantity similar to the width of spectral windows traditionally used in spectral analysis, is estimated locally in contrast to intuitively chosen global window lengths. Detection and estimation of frequencies forming discrete spectra are also addressed. The procedure is applied to Central England temperature (CEt), North Atlantic Oscillation (NAO) index and Oxygen Isotope of North Greenland Ice Core Project (δ¹⁸O of NGRIP) data. Annual and half annual cycles were detected in CEt data, whilst 118.2- and 41.7-ky cycles were found in δ¹⁸O of NGRIP. This latter periodicity is almost as intense as the dominant longer cycle. Several local peaks of spectral densities were recognised in each time series that mostly cover earlier results. However, a few previous findings at low frequencies have not been reinforced by the present method. Identification of modest local peaks or discrete amplitudes at low frequencies is an extremely challenging task as climatic data generally have spectral densities rising to low frequencies.     

Multifractal analysis of 1-min summer rainfall time series from a monsoonal watershed in eastern China

Multifractal analysis can provide parameters associated with different scales of rainfall, which may be useful for setting up parsimonious downscaling models of rainfall, or for revealing climate-specific properties. Time series of rain rate with 1-min resolution collected from ten stations over a monsoon watershed in eastern China were used to study the multifractal properties. The power spectra estimated by fast Fourier transform (FFT) and discrete Haar wavelet transform (DWT) showed three scaling regimes: the sub-hourly scaling regime with β?≈?1.2, the scaling regime from 1 h to 1 day with β close to 0.6, and the low-frequency spectra plateau with β?≈?0.1. From the hyperbolic tails of exceeding probability distributions, the estimated values of parameter q _c are in 2–2.5, which were consistent with the critical order of K(q) curves. The statistical moments display two main scaling regimes: the high-frequency regime from 3 min to 5 days and the scaling regime beyond 5 days. The scales of 5–10 days seem a transitional regime. The reason that the regimes, revealed by the power spectra, disagree with the statistical moments may be that both FFT and DWT power spectra have limited abilities of analyzing low-frequency scaling but are sensitive to the properties in high-frequency scales. The H values estimated for the regime of sub-hourly scales are larger than 0.4, and the values for the regime 1 h–1 day are close to 0.1. For the low-frequency scales beyond 1 day, negative H is obtained by DWT power spectra. The parameters of universal multifractal models were also estimated. The values of α for the scaling range of 1 min–5 days are 0.486?±?0.047, and for the low-frequency scaling range, its values are 0.808?±?0.323. For the high- and low-frequency scaling ranges, the values of C ₁ are 0.5 and 0.169, respectively, which is different from the values for daily rainfall series collected at the same rain gages.     

中国三峡地区汛期降水量的正态性研究

为了分析三峡地区降水量序列的正态性和谱结构,对降水量的常见各种变换进行试验性研究。试验包括单站降水量、降水量的平方根、立方根和Γ分布概率值等非线性变换,以及级别变换。研究区域多站平均降水量、区域降水量的主分量、区域降水量的非线性变换后的主分量和区域降水量的级别变换后的主分量等序列。研究发现三峡地区单站降水量的各种变换不改变序列原始谱结构,仅影响概率分布的偏度和峰度,使其较好地遵从正态分布,其中以Γ分布的变换以及级别变换在分布的偏度上为最好。 区域降水量的各种变换的综合指数(区域平均值和主分量)正态性及谱结构分析表明,除区域平均值变换后不改变原单站序列的谱结构外,主分量的综合指数能改变原单站序列的谱结构,同时也影响概率分布的偏度和峰度,使其能较好地遵从正态分布。其中以降水量的立方根和Γ分布概率变换以及级别变换,在分布的偏度上有较好的效果。     

Highly Time Resolved Measurements of OH during POPCORN Using Laser-Induced Fluorescence Spectroscopy

Tropospheric hydroxyl radical (OH) concentrations were measured by laser-induced fluorescence (LIF) during the POPCORN field campaign in August 1994 at a rural site in the North East of Germany. Ambient air spectra were recorded by tuning the laser wavelength over a spectral region covering the Q11(3), Q21(3), and P11(1) rotational transitions of the (0-0) band in the A-X system of OH around 308 nm. The observed spectra clearly identify the OH radical in the atmosphere. Besides the OH absorption lines there was no sign of any other narrow-band spectral structure nearby demonstrating the high specificity of the method. For OH measurements with a typical time resolution of 60–100 seconds per data point the laser wavelength was tuned repetitively over small spectral intervals covering the peak position of the P11(1) OH-line and background positions. A total of 2300 measurements were recorded including diurnal cycles of OH with more than 300 data points. The OH as well as the LIF background signal data will be presented. In a first analysis the background signal will be characterized and the correlation between OH and the ozone photolysis frequency will be derived.     

专业气象服务产品自动制作与发布系统

利用地面雨滴谱的连续观测资料,可以分析降水特征和降水的形成机制。对于人工增雨的效果检验工作,雨滴谱资料的分析研究也具有重要的参考价值。目前,山西省人工降雨防雹办公室建设了6300km^2的人工影响天气效果检验示范基地,并且引进了4部德国OTT公司的Parsivel激光降水粒子谱测量系统,分别布设在太谷、汾阳、介休和祁县,这为进行雨滴谱观测研究提供了有利的条件。本文对Parsivel降水粒子谱仪的功能、产品以及在气象领域的应用作简单的介绍,旨在给我们使用此仪器进行降水微结构特征研究提供参考。     

1982—1983年冬季青藏高原地面加热场各分量的谱分析

本文所用资料为1982年11月1日至1983年2月28日青藏高原热源考察资料，改则、拉萨、那曲，甘孜四站的地面热源各分量进行最大熵谱分析。结果表明：地面热源各分量有准两周和准一周周期，由夏至冬地面热源各分量的周期转长。     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

APPLICATION OF MEM SPECTRAL ESTIMATION TO MU RADAR OBSERVATION

Preliminary results of the wind velocity estimation using the Maximum Entropy Method (MEM) to MUradar observation data sets are presented. The comparison of the results from the periodogram method and theMEM shows that the MEM estimation is reliable, and has higher accuracy, resolution and detectability than theestimation from periodogram method. The high accuracy power spectrum obtained by the MEM is veryuseful to studying the atmospheric turbulence structure. However. the MEM needs the longer computingtime for obtaining the high accuracy spectrum. Particularly, the estimation of MEM will bring serious devia-tion at lower signal-to-noise ratio.     

SPECTRAL REFLECTANCE MEASUREMENTS AT THE CHINA RADIOMETRIC CALIBRATION TEST SITE FOR THE REMOTE SENSING SATELLITE SENSOR

A comprehensive field experiment was made with the support of the project of ChinaRadiometric Calibration Site (CRCS) during June-July 1999.Ground reflectance spectra weremeasured at Dunhuang Calibration Test Site in the experiment.More than two thousands ofspectral curves were acquired in a 20km×20km area.The spectral coverage is from 350 nm to2500 nm.The measurement values show that reflectance is between 10% and 33% at the VIS-SWIR spectral region.The standard deviation of reflectance is between 1.0% and 2.0% for thespectral range.Optical characteristics and ground reflectance measurements at the Dunhuang testsite,result analysis and error source were described.In addition,a comparison of the reflectanceobtained in 1999 with those measured in 1994 and 1996 was also made.     

Frequency and directional evaluation of the ocean data gathering program (ODGP) wave spectra at Hibernia

Abstract

The frequency and directional wave‐modelling capability of the Ocean Data Gathering Program (ODGP) deep water spectral wave model is assessed through comparison with WAVEC data gathered at Hibernia. Both qualitative and quantitative analyses indicate better agreement with observations during storms and with the wind‐driven component of the wave spectra. There is statistically poor modelling of the swell. A coherence analysis on derived wave vectors indicates that the ODGP model does not simulate geophysical variability with time‐scales less than about 30 h for overall spectral energy and less than 24 h for wave energy of frequency greater than 0.6 rad s^?1 (0.095 Hz). The signals associated with swell waves are incoherent at nearly all time‐scales.