Some aspects of the interpretation of spectra in meteorology

The meaningfulness of spectral presentations, and of spectral peaks in particular, is considered by the use of simple examples. First, we derive analytically the spectra of sinusoidal finite-length waves and subject the spectra to several area-conserving transformations. The peak of the logarithmic spectrum (power density per unit natural logarithm of frequency) is shown to be the most appropriate for defining the scales (or frequencies) of the waves. The advantage of the logarithmic spectrum becomes even more apparent when a wave consisting of the positive part of a sine wave is considered. In that case, the conventional frequency presentation is misleading because in addition to the erroneous location of the spectral peak, an increase of power density towards low frequencies occurs, giving the spectra the appearance of red noise. For the same wave, it is shown that the logarithmic spectrum has a single peak at the position corresponding with the actual wave frequency.     

Internal gravity waves in a stably stratified boundary layer

Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.     

A simple spectral model for the modification of turbulence in flow over gentle hills

A model is presented which calculates the changes of the velocity variances and stress uw in flow over gentle isolated hills. At intermediate frequencies spectra of the velocity components are modified according to rapid distortion theory. At low frequencies spectral densities change in proportion to the square of the mean wind. The inner and outer layer of the flow are distinguished. Streamline curvature effects are accounted for in the vertical velocity variance and the covariance.The sensitivity of the model to several parameters is investigated. Then, its results are compared with measurements of turbulent flow over various hills and an escarpment. The model is able to simulate the structure of the modified variance and covariance fields although larger differences occur at individual positions. The calculated modified spectra compare well with observed spectra.     

红外高光谱观测值反演云参数

最小局部比辐射率变化MLEV算法根据在红外长波10～15 μm 区, 云的吸收、发射和散射具有相对有限的局部谱变化的特征, 利用对云敏感的长波红外辐射观测值来同时反演单层云的云顶高度和有效云比辐射率谱。先给定一些假想的云高初始猜测, 最佳的云高和比辐射率谱解使得用这些不同云高计算得到的比辐射率谱的局部变化最小, 该算法适用于高光谱(光谱分辨率从0.25～1 cm-1) 的大气红外探测器。通过用两种不同方案的内部比较及与激光雷达观测和MODIS业务云高产品的对比验证, 说明对卫星红外高光谱观测资料采用MLEV算法同时反演单层云的云顶高度和云有效比辐射率谱是非常有效的, 尤其是对中高云。     

Taylor's hypothesis and spectra of velocity and temperature derivatives in a turbulent shear flow

Spectral densities of temporal velocity and temperature derivatives, measured in the atmospheric turbulent boundary layer and on the axis of a turbulent plane jet, are compared with the spectral densities of the ratios of these derivatives and of the local longitudinal instantaneous velocity. The comparison between the spectral densities, when both are normalized such that the areas under the spectra are equal, shows that the corrected spectrum is lower than the measured spectrum at frequencies larger than about one-seventh of the Kolmogorov frequency while the opposite trend is observed at low frequencies. A qualitatively similar result has been obtained when the measured velocity derivative spectrum is compared with that corrected using Lumley's method. While the unnormalized spectral densities and moments of the derivatives, as corrected by Lumley's method are smaller than the corresponding measured quantities, the opposite trend is found when the correction is made by dividing the temporal derivative by the longitudinal instantaneous velocity.     

Variation of the spectrum of wind ripple on coastal waters under the action of internal waves

The mechanism of flattening of surface wind waves in the centimetre wavelength range under the action of internal waves and in the presence of surfactants is considered. It is shown that internal waves give rise to perturbations of surfactant concentration proportional to the orbital velocities of wave particles. Accordingly, the damping coefficient of centimetre wavelength ripples is also modulated. Evolution of the wind wave spectrum is described by the energy balance equation. In the right-hand side of the equation the Phillips excitation mechanism, the Miles mechanism with a nonlinear spectrum limitation, and the dissipation caused by a surface-active film are taken into account. Assuming that the energy source and sink balance of the wind wave spectrum over the centimetre wavelength range is local, relative spectra (contrasts) for the case of gentle breeze are calculated. It is shown that the spectral components of ripples in the slicks can be order less than the uperturbed spectrum values.     

奇异交叉谱分析及其在气候诊断中的应用

提出了一种新的用于气候诊断的奇异交叉谱分析方法（记为SCSA）。从理论上证明,它是一类时频域相结合的广义交叉谱分析,也是奇异谱分析（SSA）的一个推广。SCSA可获得比经典交叉谱更为强化的耦合振荡信号,并在时域上描述两个系统之间各种耦合振荡信号的时变特征,因而可将频域上的耦合振荡信号在时域上加以合成和分解,包括非线性耦合振荡的弱信号,这对短期气候预报十分有益。文中实例证明,SCSA比经典交叉谱分析有更为优良的特性。     

Wavelet analysis of a centennial (1895–1994) southern Brazil rainfall series (Pelotas, 31°46′19″S 52°20′ 33″W)

In this work we apply the wavelet transform to the Pelotas (southern Brazil) total annual rainfall series (1894–1995). Classical, wavelet and cross-wavelet analyses were performed in the El Niño Southern Oscillation (ENSO), Quasi-Biennial Oscillation (QBO), sunspot number (Rz) and Pelotas rainfall time series. Classical spectral analysis for Pelotas has shown a large number of short periods – between 2.2–5.6 years (yr) and periods at 8.9, 11.7 and 24.9 yr. Further, we have found that the Pelotas rainfall wavelet spectrum shows the most significant periodicities around 2–8 yr, but they have an intermittent character. Cross-wavelet spectrum showed that: rainfall and QBO series are correlated at 2–3 yr (QBO) scales and this cross-power is continuous along the time series interval; rainfall and SOI have higher cross-power around 4–8 yr, but this signal is sporadic; rainfall and sunspot number (Rz) showed higher cross-power around the 11-yr solar cycle period, but this cross-power is sporadically high and low; finally, the rainfall cross-spectrum with the double sunspot number (Rz22) revealed a high cross-power around 20–22 yr which is more persistent in duration, compared to the 11-yr period. These wavelet results are compared with classical spectral analysis and with previous work results. We concluded that the phenomenon that influences most of Pelotas rainfall variability is ENSO, but only a minor part of the variance (～30%) can be described by a simple multi-linear dependence on solar/ENSO/QBO phenomena, this result could imply that non-linear coupling among sun and internal climatic variability (QBO, ENSO) has an important role in the local/regional climate variations.     

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     

Concentration fluctuation measurements in tracer plumes using high and low frequency response detectors

A set of tracer experiments designed to compare two concentration fluctuation detectors and measure fluctuation statistics at high frequencies is described. A detector which has been used in several previous fluctuation experiments (the TIP photoionisation detector manufactured by Photovac of Canada) is compared with another with a much higher frequency response (the flame ionisation detector — FID — made by Cambustion of the UK). Good agreement is found and results show that the signal optimization system used in previous work with the TIP provides an accurate enhancement of the instrument output, thus improving confidence in the results of previous papers. They also confirm that the TIP detector is able to resolve most of the concentration variance in most situations of interest, but not at very short range. Measurements of the high frequency end of the fluctuation spectrum using the FID show inertial-convective subrange behaviour at frequencies not resolved by the TIP, supporting earlier work. Fluctuation spectra measured very close to the source are also shown to have a characteristic +2/3 power law behaviour (when nSc (n) is plotted against n) at lower frequencies, in agreement with theoretical predictions.     

Analysis of the Moberg et al. (2005) hemispheric temperature reconstruction

The Moberg et al. (Nature 433(7026):613–617, 2005. doi:10.1038/nature03265; M05) reconstruction of northern hemisphere temperature variations from proxy data has been criticised; the M05 method may artificially inflate low-frequency variance relative to reality. We test this assertion by undertaking several pseudoproxy experiments in three climate model simulations—one control run and two forced simulations that include several time-varying radiative forcings. The pseudoproxy series are designed to have the same variance spectra as the real M05 proxies, primarily to mimic the low-resolution character of several series. A simple composite-plus-scale (CPS) method is also analysed. In the CPS case all input data behave like annually resolved proxies. The spectral domain performance of both M05 and CPS is found to be dependent on the noise type and noise level in pseudoproxies, on the variance spectrum of the climate model simulation, and on the degree of data smoothing. CPS performs better than M05 in most investigated cases with the control run, but leads to deflated low-frequency variance in some cases. With M05, low-frequency variance tend to be inflated for the control run but not for one of the forced runs and only very slightly with the other forced simulation. Hence, the M05 approach does not routinely inflate low-frequency variance. In our experiment, the M05 approach performs better in the spectral domain than CPS when applied to forced climate model simulations. The results underscore the importance of evaluating the variance spectrum of climate reconstructions.     

Mesoscale spatial and temporal variability of meteorological observations from an array of buoys in JASIN-1978

Observations of wind speed and direction, air and sea temperatures and solar radiation were obtained from an array of buoys in JASIN-1978 conducted in the area northwest of Scotland in the summer of 1978. The observations were analyzed to show spatial and temporal variability in the mesoscale fields. Spectra of wind speed and air and sea temperatures were computed to illustrate the distribution of variance over periods ranging from 3.5 min to 40 days. When plotted on log-log graphs, the spectral estimates generally decreased with slopes between –3/2 and –2 with increasing frequency. Spectra of air and sea temperatures had a peak at the diurnal period but not the wind speed spectrum. When plotted in variance-preserving form, the spectrum of wind speed was consistent with a spectral gap and was qualitatively similar to other observations of low-frequency spectra. On the basis of auto- and cross-correlation analyses, it appeared that mesoscale eddies propagated through the array of buoys with the mean wind speed except during times of frontal passages. The cross-correlation between wind speed and air temperature showed evidence of horizontal roll vortices or some other forms of organized convection.     

Proof of the monotonicity of grid size and its application in grid-size selection for mesoscale models

Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices.Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

Power and cross-power spectral studies of electric parameters under fair weather conditions in the atmospheric surface layer

Power spectral and cross-spectral studies of atmospheric electrical parameters for different months of the year are presented. The data represent fair weather conditions and the frequency range is from 0.01 to 0.3 cph. The analysis shows spectral peaks in the atmospheric electric parameters for frequencies corresponding to the diurnal wave; in many cases large variances are noted for the frequencies 0.083, 0.125 and 0.17 cph. Annual cycles in the spectra are also observed. In general, fairly small variances are obtained for frequencies above 0.05 cph. High coherences for the atmospheric electric parameters are observed in the lower frequency part of the spectra and in some cases in other parts as well (i.e., 0.083, 0.125 and 0.17 cph). Phase relationships of the electric components are also presented.     

0.1~40 MHz地闪、 云闪及NBE事件的辐射场频谱特征分析

利用宽带傅立叶分析法对2008年7月30日和8月4日两次雷暴过程中, 距离观测点5~20 km范围内的55次负地闪回击过程, 33次云内闪电过程以及20次双极性窄脉冲事件（NBE）的电磁辐射信号进行了观测分析, 得到地闪回击、 云闪放电初始阶段以及双极性窄脉冲事件在0.1~40 MHz频带宽度下的电磁辐射能量谱密度。结果表明, 这三类闪电放电过程的辐射频谱波形均呈现出随频率增加、 幅值减小的趋势, 但在辐射强度和衰减速率上存在一定的差异。负地闪回击幅频波形在6~28 MHz频段上衰减速率相对缓慢; 云闪初始阶段在全频带上始终遵循f-1.2~f-1.4之间的衰减率递减, 且其频谱幅值与地闪回击的辐射能量谱幅值相差不大; NBE事件在0.1~40 MHz频带中辐射能量谱幅值基本都明显大于其他两类闪电放电过程, 特别是在10 MHz以上的HF、 VHF频带上其差异可达到20 dB。     

Using a Large-Aperture Scintillometer to Measure Absorption and Refractive Index Fluctuations

The contributions of refraction and absorption fluctuations to the measured scintillations are observed for a near-infrared absorption region using a NOAA designed large-aperture scintillometer. The logarithmic amplitude spectra are shown to decay with frequency as f^-8/3 for both the absorption and scattering mechanisms. For the absorption mechanism this is in line with similar observations made at microwave and infrared frequencies. However, for finite transmitting and receiving apertures, theory predicts a stronger decay of the scattering mechanism due to aperture averaging. The spectral shape is characterised by a region of low frequency absorption, higher frequency refraction and separated by a flattish transition zone. The upper observed corner frequency (f_C2) compares well with values calculated using the measured transverse windspeed (v) for a known aperture radius. The lower corner frequency (f_C1) position is shown to be sensitive to the ratio of the real and imaginary part of the refractive index structure parameter, (C _nR ² /C _nI ² )^3/8, and v. The part of the spectrum associated with the absorption scintillations is observed to be much less than that due to refraction through the day until evening, when decreasing C _nR ² causes C _nR ² /C _nI ² to decrease and absorption to become significant. If absorption is ignored, this may have consequences for calculating nocturnal surface fluxes. During unstable, daytime conditions the large aperture scintillometer is most sensitive to refractive scintillations despite having an infrared source transmitting in a lossy atmosphere. But also under these conditions, the low frequency absorption part of the spectrum is observable.     

Radiative Effects on Temperature in the Stable Surface Layer

The interaction between longwave radiation and temperature fluctuations plays a role in the dissipation of temperature variance. This interaction is most easily described by spectral models of atmospheric turbulence and a spectral radiative dissipation function which gives the intensity of the damping at each radiative wavelength and wavenumber k. We have used a Corrsin–Pao closure for the spectral budgets of turbulent kinetic energy and temperature to study the coupling of radiation to turbulence. The spectral radiative dissipation function and a related integral have been fitted by analytical approximations with the correct asymptotic behavior. This resulted in a simple analytical formula for the dimensionless temperature spectrum as a function of Monin-Obukhov stability, and a new dimensionless parameter describing the relative importance of radiation in the temperature spectral budget. The radiative effects both on the temperature spectrum and on the dimensionless temperature variance can then be calculated. Based on typical values of the radiative dimensionless parameters for the surface layer, we conclude that radiative dissipation is probably negligible there.     

Spectral analysis of climatological series in Duero Basin

Summary General harmonic analysis (FFT) and maximum entropy spectral analysis (MEM) are used in order to study annual and monthly values of air temperature, precipitation and insolation in a number of weather stations in Duero Hydrographic Basin. The corresponding spectra estimates were prepared and compared. MEM estimates show better power resolution and a better spectral definition than FFT estimates. Based on the similarity behavior of the spectra, four main climatic zones were clearly defined. Finally, physical interpretation of the main features of the most representative spectra for the four regions was attempted.With 9 Figures     

The local effect of intermittency on the inertial subrange energy spectrum of the atmospheric surface layer

Orthonormal wavelet expansions are applied to atmospheric surface layer velocity measurements. The effect of intermittent events on the energy spectrum of the inertial subrange is investigated through analysis of wavelet coefficients. The local nature of the orthonormal wavelet transform in physical space makes it possible to identify a relationship between the inertial subrange slope of the local wavelet spectrum and a simple indicator (i.e. the local variance of the signal) of local intermittency buildup. The slope of the local wavelet energy spectrum in the inertial subrange is shown to be sensitive to the presence of intermittent events. During well developed intermittent events (coherent structures), the slope of the energy spectrum is somewhat steeper than -5/3, while in less active regions the slope is found to be flatter than -5/3. When the slopes of local wavelet spectra are ensemble averaged, a slope of -5/3 is recovered for the inertial subrange.