## Convectively Coupled Equatorial Waves (CCEWs)

•October 20, 2012 • 1 Comment

Convectively Coupled Tropical Waves (CCEWs)

Reconstructed Codes by  Sandro Lubis
(Former) Graduate Student at the Institute of Meteorology, University of Leipzig, Leipzig, Germany
and (Former) Postgraduate Student at the GEOMAR – Helmholtz Centre for Ocean Research Kiel, Kiel, Germany

Updated: January, 2016

## Journal !!:

Lubis, S.W and Jacobi, C. (2015), The modulating influence of convectively coupled equatorial waves (CCEWs) on the variability of tropical precipitation. Int. J. Climatol., 35: 1465–1483. doi:10.1002/joc.4069

## Attention !!:

This blog was designed under Linux operating system thus I apologize this page will not look nice if you are using another operating system.

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“Forced Stationary Waves”

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[NEW]* Theoretical structure of “Atmospheric Forced Stationary Waves” at the equator. The heating response Q is the forcing term which is proportional to the vertical derivative of the diabatic heating and the dissipation rate (representing Rayleigh friction), and Newtonian cooling is assumed to 0.2 (nondim). The background atmosphere was assumed to be at restOnce the set of forcing functions for u, v and $\Phi$, namely (0, 0, Q), are given by a linear combination of the eigenfunctions , it is straightforward to calculate the responses of u, v and $\Phi$ to the forcing.

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“Free Equatorial Waves”

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Theoretical Structure of Equatorially Trapped Waves of Matsuno’s  normal modes superimposed with divergence and convergence fields. All fields have been nondimensionalized by using the equatorial radius of deformation.  Any further queries regarding the calculation can be found in this manuscript (part of my bachelor thesis): Sandro_Manuscript — [Click the button below to see my calculations related to equatorial waves and also the figure to see an animation related to cloud convective regions associated with Convergence Fields].

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“2D Theoretical Structures”

 >>ERn=1 >> MRG n=0 >> EIG=0 >>  EIGn=1 >> WIGn=1 >> Kelvin n=-1 >>EIGn=2 >> WIGn=2 >> ERn=2 >>  EIGn=3 >> WIGn=3 >> ERn=3

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“2D Theoretical Animations”

Animations of the Equatorially Trapped Waves of Matsuno’s  normal modes superimposed with divergence and convergence fields. The black solid lines indicate the convergence, while the divergence fields are represented by the dashed lines. Theoretical geopotential height structures are shown in color contours.

 >>Kelvin n=-1 >> ERn=1 >> EIGn=0 >> MRG n=0 >>  EIGn=1 >> WIGn=1 >>EIGn=2 >> WIGn=2 >> ERn=2 >>  EIGn=3 >> WIGn=3 >> ERn=3

Equatorial Planetary Waves Amplitudes associated with Height perturbations for (a) Kelvin (Yellow), (b) MRG (red), (c) EIG n=0 (green), (d) Rossby waves n=1 (purple), (d) WIG n=1 (blue) and (e) WIG n=2 (white). All scales and fields have been nondimensionalized. X is nondimensionalized latitude and Y is amplitude.

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“Observational Evidences”

“Convectively Coupled Equatorial Waves (CCEWs)”

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CCEWs play a crucial role in controlling the tropical weather system, as they modulate or organize the convection and a substantial portion of tropical rainfall and fuel the tropical cyclone geneses (e.g. Kiladis et al. 2009; Schreck et al. 2013, Kim and Alexander 2013 etc).

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“2D Observational Variances of CCEWs”

Spatial distributions of the Filtered OLR  variance 1981-2010 (30 years) for various parts of the wavenumber-frequency domain of interest. [All Season Variance]

 ERn=1 MRG n=0 Kelvin EIGn=0 WIGn=1 WIGn=2 TDD MJO

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“2D Observational Snapshots in NCEPR2 & ERA”

[NEW]* Snapshots and Animations of the space-time filtered OLR assoaciated with CCEWs.  Please kindly contact me for any further queries regarding the isolation technique. Reference vector is 1 m/s

NCEP-R2 [2.5 deg]

 ER Waves n=1 Kelvin Waves n=-1 TDD like-waves MRG waves n=0

ERA Interim – ECMWF [1.5 deg]

 ER Waves n=1 Kelvin Waves n=-1 TDD like-waves MRG waves n=0

XXX

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“2D Animations of CCEWs in OLR, U, V,  and Z”

**Filtered OLR Anomalies **

 Animations Animations Animations MJO Total Kelvin Waves n=-1 Total ER Waves n=1 Total MRG Waves n=0 TDD/ Easterly Waves Sym_Kelvin_Waves Sym_ER_Waves Anti_Sym_ER_Waves Anti_Sym_MRG_Waves

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**Filtered OLR & 850 hPa Wind Perturbations**

 Animations Animations Animations MJO Total Kelvin Waves n=-1 Total ER Waves n=1 Total MRG Waves n=0 TDD/ Easterly Waves Sym_Kelvin_Waves Sym_ER_Waves Anti_Sym_ER_Waves Anti_Sym_MRG_Waves

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**Filtered Geopotential Height & 850 hPa Wind Perturbations**

 Animations Animations Animations MJO Total Kelvin Waves n=-1 Total ER Waves n=1 Total MRG Waves n=0 TDD/ Easterly Waves Sym_Kelvin_Waves Sym_ER_Waves Anti_Sym_ER_Waves Anti_Sym_MRG_Waves

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**Filtered Geopotential Height & 200 hPa Wind Perturbations**

 Animations Animations Animations MJO Total Kelvin Waves n=-1 Total ER Waves n=1 Total MRG Waves n=0 TDD/ Easterly Waves Sym_Kelvin_Waves Sym_ER_Waves Anti_Sym_ER_Waves Anti_Sym_MRG_Waves

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===== Spaca-Time Spectra Diagram (STSD) =====

****[Through Decomposition]****

****[Without Decomposition] ****

A. The Entire Calendar Years

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B. Extended Summer and Winter

To ﬁnd the dominant wave modes, the spectrum from each season is divided by the
annual mean of red noise (background).

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C. Seasonal Spectra

Note: Contour begins at a value of 2.1 for which the spectral signatures are statistically signiﬁcantly above the background at the 95% level (based on 500 dof)– WK99.

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****[With Doppler Shifting Effect]****

XXX

Composite Analysis of CCEWs in OLR

Briefly, time series of raw OLR data are regressed onto a time series of filtered data (in this case Kelvin waves filtered OLR, MRG, and ER).

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===== Spaca-Time Cross-Spectra Diagram (STCSD) =====

Space Time Cross Spectra OLR and Zonal Wind at 850 hPa  level with period of 96 days was chosen for the Fst Fourier Transform (FFT) with 65-day overlap and taper.

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“Theory: Phase Angles of Kelvin and MRG Waves”

Constant Phase Angle of Kelvin Waves (n=-1) and MRG Waves (n=0)

Solving for particular “n” meridional wave mode number, we will find a set of frequency-vertical wavenumber relations for specific “n” that can reveal the slope of constant wave phase angle at the (Z,X) plane and at the (Z,t) plane in which Z is denoted as altitude, X is longitude, and t is time. The following figure is a vertical structure of free Kelvin waves and MRG n=0 in Z,X plane and Z,t plane in a constant N troposphere respectively, with Lz=6 km, he=10, H=7.3 km and dt/dz=-7 K/km. All units have been nondimensionalized using m* ≡ |m|β/Nk^2, ω* ≡ ωk/β, z*=z(Nk^2/β), t*=t(β/k), and x*=x/√(N/|m|β). The contours indicate the geopotential perturbations associated with the wave amplitude.

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Vertical Group Velocity of Kelvin Waves

Theoretical structure of vertical group velocity values (Cgz) for dry Kelvin waves in a constant N (Brunt–Väisälä frequency) troposphere and lower stratosphere with doppler shifting effect. Related articles: Kiladis et al. 2009 and Yang et al. 2011

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The equatorial planetary waves (hereafter, EPW) are generated by diabatic heating due to organized tropical large-scale convective heating in the equatorial belt . Although they do not contain as much energy as other typical tropospheric weather disturbances,EPW causes predominant disturbances in the equatorial atmosphere , e.g.,  induces mean-meridional circulation, modulates the climatological cold tropopause, affects the patterns of low level moisture convergence, controls the distribution of convective heating and convective storms in large longitudinal distances and also plays important role in the heat balance of the equatorial belt.  Matsuno (1966) developed a model of quasi-geostrophic motions in the equatorial area to explain the characteristic of EPW by applying a single layer of homogeneous incompressible fluid with free surface and assuming that Coriolis parameter to be proportional to the latitude. His work concerned on mathematical analyses of the simplified hydrodynamical equations, meanwhile Lindzen (1967)  used the β-planes approximation and Laplace’s Tidal Equation to describe planetary waves in the equator and mid-latitudes. Both of theses works are very fundamental to explain the main characteristic of equatorial planetary waves in the atmosphere.

A frequency-wavenumber spectral analysis technique has been performed to identify convectively coupled equatorial planetary waves (CCEWs) signals in the atmosphere using  one of proxies of tropical convection (in this case OLR) and other related variables such as geopotential height and wind velocity at 850 hPa and 200 hPa . The dispersion diagram was obtained by performing a two dimensional space and time spectral analysis  during 31 years. The wavenumber–frequency spectrum for unfiltered/filtered daily anomalies are divided by an estimate of the red background in order to normalize the data following Wheeler & Kiladis (1999, JAS) and Wheeler & Weickmann (2001, Monthly Weather Review) and then separated into  symmetric and anti-symmetric component. Data starts to cluster into different categories Kelvin waves, Mixed Rossby Gravity waves, Equatorial Rossby waves, TDD etc. It’s shown by spectral peaks tending to lie along the dispersion curves for shallow water equatorial waves (black lines) with flow background U=0. Should be noted in this case, anomalies are calculated from Smooth Daily Climatology by following this common procedure: (1) perform an FFT to get real and imaginary coefficients. (2) arbitrarily retain the 1st ‘nHarm’ coefficients. No change in coefficients. (3) set the (nHarm+1) real and imaginary coefficientsto 0.5 of the original values. Set all others to 0.0. Presumably these are high frequency noise. (4) Do a back transform with coefficients as described in (3) . .The procedure of filtering process for each waves meets the following criteria:  MJO : Wave numbers 1to 5; period of 30-96 days, Kelvin waves: Wave numbers 1 to 14; period of 2.5-30 days; equivalent depth of 8-90m. ER waves: Wave numbers -1 to -10; period of 5-48 days; equivalent depth of 0-90m. MRG waves: Wave numbers -1 to -10; period of 3-10 days; equivalent depth of 8-90m. For each case, missing values are filled using linear interpolation in space and time.  Contours are in a space-time filtered of the shaded field for each modes of the waves.

Horizontal Structure of CCEWs

Experiment 1. Equatorial Kelvin Waves period 2.5–17 days, wavenumber 1-14 and equivalent depth 8-90 m. Remarks: Propagation Direction is Eastward.

Experiment 2. Equatorially trapped Rossby waves period 9–72 days, wavenumber 1-10 and equivalent depth 0-90 m. Remarks: Propagation Direction is westward.

Experiment 3. Mixed Rossby-Gravity waves (MRG) period 3–10 days, wavenumber 1-10 and equivalent depth8-90 m. Remarks: Propagation Direction is westward.

==Quartet Filter in Hovmöller Diagram==

In this section, I personally called it as Quartet Filter. Quartet Filter in Hovmöller Diagram is shown to perform 2D FFT filter in space and time related to the time evolution of the waves in the average latitude. Contours are filtered in space-time. Data are first detrended and tapered in time, and filtered using 2-dimensional fast Fourier transform (FFT).  The procedure of filtering process for each waves follows this criteria: Kelvin Filtering: Wave numbers 1 to 14; period of 2.5-30 days; equivalent depth of 8-90m. MJO Filtering: Wave numbers 1 to 5; period of 30-96 days ER Filtering: Wave numbers -1 to -10; period of 5-48 days; equivalent depth of 8-90m. Black dashed lines indicate convectively active phases of MJO associated to negative anomalies of OLR.

==Dispersion Curves==

Theoretical dispersion curves (solid lines) are depicted for U=0 and separated into two components about the equator : symmetric and asymmetric

Figure 1. Wavenumber–frequency spectrum for unfiltered daily OLR and filtered anomalies of OLR [1980-2011, divided by an estimate of the red background following Wheeler & Kiladis (1999, JAS). The panel on the left shows signals that are anti-symmetric about the equator, while the panel on the right shows those that are symmetric. Spectral peaks tend to lie along the dispersion curves for shallow water equatorial waves (black lines). The unfiltered Omega shown above just to verify the constructed diagram that  has been created.

Figure 2. Zonal wavenumber-frequency power spectra of the (a) antisymmetric component and (b) symmetric component of  unfiltered daily OLR 1980-2011.

Figure 3.  Zonal wavenumber-frequency spectrum of the base-10 logarithm of the ‘‘background’’ power calculated by averaging the individual power spectra of unfiltered daily OLR 1980-2011 in Figs. 2a and 2b, and smoothing many times with a 1-2-1.

Comparation to the Theoretical Structure of Tropical Waves

In this section,  two dimensional structure of EPW based on the linear wave theory has been experimented with specific frequency and modes. For details explaination please go directly to this article: Free Atmospheric Planetary Waves on an Equatorial β-plane Part I: Theoretical Background and Simulation.Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Rossby waves mode n= 1, which satisfies this general analytic solution:

Simulation of geopotential field and horizontal wind perturbations corresponding to Kelvin waves mode n= -1 with zonal wavenumber (k) =1.0 and  Yanai waves mode n= 0 with zonal wavenumber (k)=1.0.

Theoretical dispersion relation for free equatorial planetary waves (EPW) in nondimensionalized wavenumber and frequency (Kelvin waves, Yanai waves, Rossby waves, East Poincare ́ waves (EIG) and West Poincare ́ waves (WIG).

–Sandro Lubis–

My special acknowledgement to Dr. Carl J. Schreck, III

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## The Storm Tracks in ERA

The Storm Track

By Sandro Wellyanto Lubis

Former Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany, PhD Candidate in GEOMAR, Kiel, Germany

Storm tracks are the atmospheric zones where extra-tropical cyclones grow and decay. A measure of strength and direction of the storm tracks can be quantified in a number of ways. One such way is track the lows as they move across the oceans and compile statistics about the tracks over a long period of time. Following figures are one of methods to indetify the storm tracks using transient poleward temperature flux and transient geopotential height covariance flux.

The 700mb transient poleward temperature flux from observations for 55 Northern Hemisphere winters (1958-2012). The measure reaches a maximum over the North Atlantic and North Pacific Oceans, the storm track regions where extra-tropical cyclones are most frequent and most intense.

Transient 250mb covariance of geopotential height flux for 55 Northern Hemisphere winters DJF (1958-2012), on a pressure level which is at a height of a few kilometres up into the atmosphere

## Planetary Waves

Planetary Waves

By Sandro Lubis

updated: January 2017

Planetary waves can be defined as large-scale atmospheric perturbations or disturbances having zonal wavelengths in the scale of the earth’s radius. Planetary waves have significant influence on the circulation, temperature, and distribution of ozone. Planetary waves are responsible for the prevailing variability in the stratosphere, such as QBO, SSW, and the vacillation of the mean flow at the extratropical latitudes, and also play an important role for the MLT dynamics (Salby 1984, Pogoreltsev et al., 2007, Forbes et al. 2004). Planetary waves are generated by orographic and diabatic heating in the troposphere and also possible forced by irregular thermal or mechanical forcing in the lower atmosphere (Holton 2004, Andrews et al., 1987, Fedulina 2004).

Planetary waves also can be distinguished into two types.  (1) Stationary Planetary Waves (SPWs) are waves whose surfaces of constant phase and amplitude are fixed with respect to the equator and (2) Travelling Planetary Waves (TPWs) are waves that propagate in time and space having incoherent progressive and retrogressive components. The progressive and retrogressive terms arise from the separation technique in space time-frequency domain analysis purposed by Hayashi (1971, 1979). The other types of planetary waves such as quasi-two-day wave and quasi-stationary wave are also exist in the atmosphere. These waves are commonly generated by baroclinic instability or by deposition of zonally asymmetric momentum onto the mean flow.

[CLICK THE ANIMATIONS BELLOW!!]

Figure 1.  Polar stereographic projection of geopotential heights associated with the a westward propagating of 16 -day wave, k=1 for (left) SPWs and right (TPWs) [Part of my master report for the  “middle atmosphere” course from Prof. Ch. Jacobi].

SPWs with zonal wave number 1 and 2 are striking features of the winter middle atmosphere dynamics (Fedulina 2004, Fröhlich 2005, Pancheva et al., 2007). The most prominent traveling waves observed in the atmosphere are traveling Rossby waves or global normal mode with s=1 which is 5-day wave (Andrews, 1987). Traveling planetary waves predominantly propagates westwards. In the middle atmosphere they have zonal wave number between 1 and 4 with periods between 2 days and 16 days (Fröhlich 2005). Many of them are able to propagate upwards through the winter hemisphere into the MLT region. The 5-day waves with zonal wave number 1appears also in the summer hemisphere (Fröhlich 2005, Pogoreltsev et al., 2007).

## Madden – Julian Oscillation (MJO) Part-II

Madden–Julian Oscillation Life Cycle and Phase Diagram

Analysis and Reconstructed Codes by Sandro Lubis  Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany

All computations are made using[ NCAR Command Language (NCL)]

September, 2012

The Madden-Julian Oscillation (MJO) is the leading mode of intra-seasonal variability in the tropical troposphere, characterized by an eastward moving ‘pulse’ of cloud and rainfall near the equator that persists from weekly to monthly timescales. The following analysis follows the standard procedures of investigation MJO defined by US MJO Clivar WG. Generally, there are two main  diagnostics steps pointed out by MJO Clivar WG, Waliser et al., 2009:  Level 1: These diagnostics are meant to provide a basic indication of the spatial and temporal intraseasonal variability that can be easily understood and/or calculated by the non-MJO expert. These diagnostics include assessing variance in preferred frequency bands, spectral analysis over key domains, univariate empirical orthogonal function (EOF) analysis of bandpass filtered data, statistical significance assessment of the EOFs, and lead-lag assessment of the dominant intraseasonal principal component (PC) time series. Level 2: Diagnostics that provide a more comprehensive diagnosis of the MJO through multivariate EOF analysis and frequency wave-number decomposition.

Data used in this analysis was retrieved from datasets consist of three main components: OLR, U200, and U850. V850 is also required for composite analysis of MJO. The daily anomalies are calculated using the first 3 harmonics of the seasonal cycle for 1980–2011.  Afterwards,  the band pass filter has been applied to these original anomalies. Compute the zonal mean of the temporal variance in order to normalize the variances. Then, compute combined EOF and normalize the multivariate EOF 1&2 component time series. Indices (multivariate MJO index)  are obtained by computing (PC1^2+PC2^2).

–Sandro–

## Madden – Julian Oscillation (MJO) Part-I

Filtering Techniques for Monitoring the Madden–Julian Oscillation

Reconstructed Codes by Sandro Lubis
Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany

NCAR Command Language (NCL)]

September, 2012

In this experiment,  Seasonal cycle is  removed by subtracting the first three harmonics of the annual cycle. It is done by following this common procedure: (1) perform an FFT to get real and imaginary coefficients. (2) arbitrarily retain the 1st ‘nHarm’ coefficients. No change in coefficients. (3) set the (nHarm+1) real and imaginary coefficientsto 0.5 of the original values. Set all others to 0.0. Presumably these are high frequency noise. (4) Do a back transform with coefficients as described in (3) . In this case, anomalies are calculated from Smooth Daily Climatology. Annual cycle that contains more harmonics will more closely resemble the actual data. Data was retrieved OLR NOAA from 1980-2011. In order to obtain obvious phenomenon of MJO , filtering technique  in time (20-100 days) and in space-time (k=1-5, 20-100d, Kiladis et all, 2009) are implemented. Missing values are linearly interpolated.

In order to test the reliability of the filter, the specific period was selected in which the phenomenon MJO was clearly visible. 2d FFT technique has been applied to see the direction of propagation of these oscillations.

Filter results in space and time (STSA)  as well as in time (BPF) are shown in the panel diagram below. In general, both filters have almost the same capabilities in isolating OLR anomalies associated with the MJO phenomenon. Filters in space and time  gives a smoother contour and more visible compared to the filter that only applied in time.

–Sandro Lubis–

## Free Atmospheric Planetary Waves on an Equatorial β-plane Part I: Theoretical Background and Simulation

•August 2, 2012 • 1 Comment

Theoretical Simulation of Free Atmospheric Planetary Waves
on an Equatorial $\beta$-plane

+Sandro Wellyanto Lubis and Sonni Setiawan
Department of Geophysics and Meteorology, Bogor Agricultural
University, Bogor 16680, Indonesia
+now in Leipzig Institute for Meteorology, University of Leipzig,
04103 Germany

[ MATLAB – The Language of Technical Computing ]

2011

A simple theoretical model was developed to investigate behavior of equatorial planetary waves (EPW) on a motionless basic state of mean depth H on the equatorial barotropic $\beta$-plane. Based on general nondimensional linearized equations of EPW in equatorial $\beta$-plane, the amplitude of meridional wind perturbation (v’) is maximum at latitude y= $\pm$ 1 for mode n=1 and equal to zero at latitude y = ±1/2$\sqrt{2}$ for mode n=2. The symmetric meridional wind perturbation (v’) with maximum amplitude at latitude y= ± 1 and antisymmetric zonal wind perturbation (u’) are some implications that correspond to simulation of Yanai waves in which the geopotential field perturbation ($\Phi'$) is in the state of geostrophic balance at latitude -1< y <1 or –$(\beta^{-1}\sqrt{gH})^{1/2} > y > (\beta^{-1}\sqrt{gH})^{1/2}$. The simulation of Kelvin waves resulted that either zonal wind or geopotential field has symmetric amplitude and symmetric perturbation relative to Earth’s latitude. Further filtered equatorial waves mode n=1, 2, and 3 showed that there are two classes of EPW which can be classified into high frequency Poincaré modes waves and the low frequency Rossby modes waves.

Figure 1. Simulation of geopotential field and horizontal wind perturbations corresponding to Yanai waves mode n= 0 with zonal wave number (k) = 0.5, =1.0, and 1.5, respectively (left panel) and Simulation of geopotential field and horizontal wind perturbations corresponding to Kelvin waves mode n= -1 with zonal wave number (k) =0.5, =1.0, and 1.5, respectively (right panel).

Figure 2. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Rossby waves mode n= 1, 2, and 3.

Figrure 3. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Eastward Poincaré waves mode n= 1, 2, and 3.

Figure 4. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Westward Poincaré waves mode n= 1, 2, and 3.

Figure 5. Simulation of surface elevation corresponding to Kelvin waves, Yanai waves, Rossby waves, eastward Poincare waves and westward Poincare waves, respectively

Acknowledgements

**********************************************************************************
Sandro and Setiawan gladly acknowledge their gratefulness to Laurel McCoy
(Atmospheric Sciences, University of Missouri-Columbia, USA), Nina
Kargapolova (Institute of Computational Mathematics and Mathematical
Geophysics, Russia), and Davesh Vashishtha (University of Delhi, India) for
their contribution on reviewing this paper. The anonymous reviewers of this
paper provided valuable suggestions, and we truly appreciate them.

## QBO (Quasi-Biennial Oscillation) Part II

•July 29, 2012 • 1 Comment

## QBO (Quasi-biennial Oscillation)

Analysis and Reconstructed Codes by Sandro Lubis
Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany

NCAR Command Language (NCL) and Ferret NOAA]

July, 2012

Figure 1.  Amplitude Spectrum and FFT Phase of QBO (Lubis, 2011)

Data: 1948-2011 NCEP Reanalysis I.

QBO or Quasi-Biennial Oscillation is indicated by zonally symmetric easterly and westerly wind regimes alternating regularly with periods varying from about 24-30 months in the equator. A simple analysis was conducted, zonal wind data from NCEP/NCAR Reanalysis [I] were directly used in order to identify the existence of QBO in the lower middle atmosphere during last decade (1948-2011). The chosen grid was located near the equator at 100 E and 2.5 N. The vertical average of zonal wind were computed due to an indication of the existence of  QBO at 10-70 hPa. This result is consistent with previous studies (Dunkerton, 2003) show that alternating downward propagating westerly and easterly (E) regimes appear around the height of 10-70 hPa layer. Spectral analysis was applied to the average of zonal wind (10- 70hPa) from 1998-2010 giving the result that that the peak of spectral density is observed around 0.03-0.04 Hz month/cycle in other words the period of QBO cycle is obviously detected around 28 month/cycle. A 28 month/cycle is indicated by the max peak of amplitude as shown in figure. The maximum amplitude of QBO is 6.6 m/s and phase angle exceeds 160. The result of this spectral is realistic if it’s compared to the early study pointing out that QBO is associated to the alternating wind regimes repeating at intervals 22 to 34months, with an average period of slightly more than 28months (Baldwin et al., 2001, Holton and Matsuno 1984).

Figure 2.  Zonal wind of QBO in period of 1948-2011 from NCEP/NCAR Reanalysis [I]