Observed radar reflectivity in convectively coupled Kelvin and mixed Rossby-gravity waves

GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

Observed Radar Reflectivity in Convectively Coupled Kelvin

and Mixed Rossby-gravity waves

A. Swann,1A. H. Sobel,2 S. E. Yuter,3 and G. N. Kiladis,4

Propagating disturbances in the tropical atmosphereexhibiting characteristics of linear equatorial waves havebeen shown to be “coupled” to convection. In somecases, a rain event at a specific location can be asso-ciated with a particular wave of sufficiently large am-plitude. Rain events spanning three years at KwajaleinAtoll, Republic of the Marshall Islands, 8.72oN 167.73oE,are classified by associated wave type (i.e. Kelvin ormixed Rossby-gravity (MRG)) using space-time spectral-filtered outgoing longwave radiation (OLR). Contouredfrequency by altitude diagrams (CFADs) of radar for theclassified dates were compared between the two groups.The Kelvin wave accumulated CFAD has a distribu-tion shifted to lower reflectivities suggesting that Kelvinstorms likely contain a larger fraction of stratiform toconvective area compared to MRG storms.

1. Introduction

Convectively coupled waves are large-scale tropical dis-turbances associated with deep convection which havedispersion properties predicted by dry linear equatorialwave theory. The deep convection associated with a par-ticular type of convectively coupled wave is detectableby its distinct signature in the frequency-wavenumberspectrum of observed outgoing longwave radiation (OLR)[Wheeler and Kiladis 1999]. In some cases, specific con-vectively coupled wave types can be associated with spe-cific storm events at a particular location [Straub and Ki-ladis 2002; Sobel et al. 2004]. Here, we examine whetherconvective systems associated with two wave types maybe different in some way that is detectable from theirstatistical distributions of volumetric radar reflectivities.Our approach has some similarities to that of Petersenet al. [2003] who examined differences between convec-tive systems occurring in different phases of the samewave type, but we look instead at differences across wavetypes. The results may present clues as to how the large-scale environment influences deep convection, which isthe essence of the convective parameterization problem.

1Department of Earth and Planetary Science, Universityof California, Berkeley, California, USA

2Department of Applied Physics and AppliedMathematics and Department of Earth and EnvironmentalSciences, Columbia University, New York, New York, USA

3Department of Marine, Earth, and Atmospheric Sciences,North Carolina State University, Raleigh, North Carolina,USA

4NOAA/Earth System Research Laboratory, Boulder,Colorado, USA

Copyright 2006 by the American Geophysical Union.0094-8276/06/$5.00

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X - 2 SWANN ET AL.: STRUCTURE OF CONVECTIVELY COUPLED WAVES

2. Data

We use volumetric radar data from the scanning S-band Doppler radar on Kwajalein Island, Republic ofthe Marshall Islands, 8.72oN 167.73oE [Houze et al.2004, Yuter et al. 2005] to examine the precipitationstructures associated with different convectively coupledwave types over the western Pacific tropical open ocean.The radar data were quality-controlled to remove non-meteorological echo and echoes within 157 km range fromthe radar were interpolated to a Cartesian grid with 2 kmspatial scale in the horizontal and vertical. The time se-ries of near surface echo area > 20 dBZ is used to estimatethe area of precipitation that would be measurable fromsurface gauges (> 0.5 mm/hr). Additionally, the area ofradar echo at each height was tabulated for each radarvolume. The joint probability distribution of reflectivitywith height, referred to as a contoured frequency by al-titude diagram [CFAD, Yuter and Houze 1995], is usedto characterize the statistical properties of the ensembleof radar echoes occurring in association with each wavetype. The CFAD distills the observed three-dimensionalradar reflectivity into a format that facilitates compari-son of the bulk microphysical properties between groupsof storms. At each height, the CFAD consists of a nor-malized probability density function (PDF) of radar echointensity at that level. Our analysis uses radar scansmade approximately every 6 minutes over the rainy sea-son (July-December) for the four years 1999-2002.

OLR data from NOAA polar-orbiting satellites [Lieb-mann and Smith, 1996] are used to identify large-scalepropagating disturbances and to classify rain events asbeing associated with particular wave types. Wheeler andKiladis [1999] (hereafter WK99) describe a space-timespectral analysis using these OLR data. In the space-time domain they remove a red noise background spec-trum, and find zonally propagating waves on synopticto intraseasonal time scales. Figure 1 from Straub andKiladis [2002] shows wave filtering using windows pre-scribed for Kelvin waves and figure 3 from WK99 showsthe same but for MRG waves. The method used to cre-ate wave-associated OLR for this analysis follows thesestudies, differing from WK99 only in that the total OLR,not just the symmetric component, is filtered and parti-tioned. This alternate method better captures the struc-ture of the waves about the equator.

Statistical composite maps (figs. 1 and 2) of waveevents were made using anomalous OLR, filtered to re-move periods longer than 30 days, and similarly filtered850 mb wind fields. Wind fields come from the NCEP-NCAR Reanalysis [Kalnay et al., 1996].

3. Methods

3.1. Classification of Rain Events

Rain events at Kwajalein were identified and classifiedinto one of three categories — Kelvin, MRG, and other— using the following algorithm. OLR data filtered toretain only the Kelvin or MRG signal were reduced totime series by averaging over a region around Kwajaleinfrom 165o – 170o W and 0o – 15oN. Smoothed amplitudetime series were created by squaring these wave time se-ries and applying a running mean. The length of therunning mean window was chosen to be proportional tothe lowest frequency retained for each wave type, and was1.5 days for Kelvin, and 5.5 days for MRG.

Event “matches” were chosen as times when both theecho area and wave amplitude series were each above two

SWANN ET AL.: STRUCTURE OF CONVECTIVELY COUPLED WAVES X - 3

standard deviations from the time means over the datarecord. The resulting number of event “matches” wasnot sensitive to small changes in the criteria.

3.2. Composite Spatial Fields

To test the validity of our classification of wave events,we created composite maps of low-level wind and totalOLR anomaly (both filtered to remove periods longerthan 30d) for each wave type. The three-year rain recordat Kwajalein was reduced to 184 total event days bro-ken down into categories of 52 Kelvin days, 48 MRGdays, and 84 “other” days. The identified events fromthe Kelvin and MRG categories were used to create com-posite spatial maps of the 850 hPa winds and OLR duringeach storm. For each storm event (sometimes spanningtwo or three days) and the two days preceding and follow-ing each storm event, the day with a local minimum inwave-filtered OLR was chosen as “day 0” at Kwajalein.The spatial fields from these days, as well as two daysbefore and after, were averaged together to make thecomposite maps. Choosing the day with the minimumin wave OLR helps to align the phase of the storms sothat shared features persist in the mean. Figures 1 and2 show the anomalous OLR for Kelvin and MRG stormsover a 5-day span surrounding the chosen day and figuresS1 and S2 show both the OLR and anomalous winds.We expect to see the fundamental wave patterns derivedfrom the linear shallow water theory as in Matsuno [1966]which can also be seen in figures 6 and 14 from Wheeleret al. [2000] (derived from Matsuno [1966]). In figures1 and 2, the OLR clearly shows propagation past Kwa-jalein with the Kelvin composite propagating eastwardand the MRG composite propagating westward, as ex-pected from theory. The wind patterns (figures S1 andS2) do not conform tightly to the expected theoreticalpatterns in the spatial maps, but do show, for example,strong zonal winds to the East of the OLR maximum inthe Kelvin, and much less zonal wind and more merid-ional wind, with vortical circulations centered approxi-mately on the equator, in the MRG.

The winds are further illustrated by Hovmoeller di-agrams (figures 3 and 4) of zonal winds for the Kelvinwave-associated storms and meridional winds for theMRG-associated storms. In the Kelvin case (figure 3) adivergence in zonal wind is centered at “day 0” but dis-placed eastward in longitude from Kwajalein, near 180o,and the pattern propagates eastward. In the MRG case(figure 4) strong northerlies are centered to the east ofKwajalein near 175oW at “day 0” and propagation iswestward, as expected.

3.3. Composite CFADs

Composite CFADs were made for each wave categoryby averaging at each point in height-reflectivity space allavailable CFADS in the category. The Kelvin categoryCFADs consisted of data from 52 days and the MRG from48 days. The mean CFADs for each group and the sig-nificant difference between them can be seen in figure 5.We use a Monte Carlo simulation to test the significance.Using all Kelvin and MRG event days as a pool (totaling100 event days), groups with equivalent numbers of daysto the Kelvin and MRG groups were drawn randomly,averaged and differenced 1000 times. Our sample differ-ence was considered significant when its absolute valueexceeded that of 950 of the 1000 trial differences (95%significance). Only significant values are plotted in fig-ure 5c. The mean Kelvin CFAD shows a small shift of


the distribution mode to smaller reflectivity values com-pared to the mean MRG at all heights. MRG storms havea wider distribution of reflectivity in the ice layer and arain layer reflectivity distribution skewed to higher val-ues compared to Kelvin. A second normalization schemewas also tested which weights the data from any par-ticular day equally by taking the mean of each day ina group separately before taking the mean of the wholegroup. This method gives very similar results (see figureS3) to the method described above which weights everyCFAD measurement (taken approximately every 6 min-utes) equally.

Other statistics were also computed to compare thetwo groups. Confidence limits were computed by MonteCarlo simulation as described above. The daily meanOLR anomaly was more negative for Kelvin storms thanMRG storms (at 95% significance), but the distribu-tion of echo area sizes were statistically similar betweengroups. Nonetheless, the difference in the CFAD modebetween groups suggests relatively more convective pre-cipitation area (less stratiform precipitation area) inMRG storms compared to Kelvin storms. Since degreeof mesoscale organization is related to stratiform rela-tive area, this in turn implies that Kelvin storms mayhave more developed mesoscale circulations compared toMRG storms. Future work will attempt to determinethe relation between mesoscale organization and stormintensity by partitioning the precipitation explicitly intoconvective and stratiform components.

4. Conclusions

All major rain events (rainfall > 2 standard deviationsfrom the mean) at Kwajalein were classified into one ofthree groups associated with large-scale wave dynamics,Kelvin, MRG, and “other”. Rain events were assignedto these categories by finding coincident large anomaliesof the appropriate signs in both the smoothed amplitudefiltered OLR time series for the wave in question andthe time series of surface 20 dBZ radar echo area. TheCFADs were composited based on the wave-associatedstorm dates; then, the Kelvin and MRG groups werecompared by taking the difference of the mean CFADfor each group. These mean CFADs show detectable dif-ferences according to wave type, with the mode of theKelvin CFAD shifted to lower reflectivities compared toMRG. This suggests that MRG storms may have moreconvective precipitation area relative to total storm areacompared to Kelvin storms.

At present, this is purely an observational result, forwhich we do not have an explanation. We can think ofvarious ways in which waves alter the large-scale envi-ronment in which deep cumulus convection occurs. Forexample, waves induce vertical motion, which can al-ter the temperature and humidity profiles; alter sur-face winds (and thus surface fluxes); and advect mois-ture. Different wave types presumably act, via these var-ious mechanisms, in different ways, leading to differencesin mesoscale convective dynamics which manifest them-selves in our results. For example, a wave which propa-gates faster, relative to the mean flow, will have less timeto interact with the surrounding air mass compared toone which propagates slower. A slower wave will havemore time to modify the air mass in which it is traveling,potentially allowing humidity feedbacks to be more effec-tive [Sobel and Horinouchi, 2000]. Whether this or someother difference in large-scale wave forcing is responsible


for the differences in convection which we observe, andhow those forcing differences lead to the convection dif-ferences, is a matter for future research.

Acknowledgments. This work was supported by NASAgrant NNG04GA73G, and by an NSF IGERT fellowshipto A. Swann at Columbia University. We would like tothank Catherine Spooner and Timothy Downing for their helpwith data acquisition and radar data processing respectively,Cristina Perez for her comments and assistance editing, andMark Cane, Anthony Del Genio and Brian Mapes for dis-cussions. This work was completed primarily while the firstauthor was a student at Columbia University.

References

Kalnay, E., et al. (1996), The NCEP/NCAR 40-year reanalysisproject, Bull. Am. Met. Soc., 77, 437–471.

Liebmann, B., and C. A. Smith (1996), Description of a com-plete (interpolated) outgoing longwave radiation dataset,Bull. Am. Met. Soc., 77, 1275–1277.

Matsuno, T. (1966), Quasi-geostrophic motions in the equa-torial area, J. Meteor. Soc. Jpn., 44, 25–43.

Petersen, W. A., et al. (2003), Convection and easterly wavestructures observed in the eastern Pacific warm pool duringEPIC-2001, J. Atmos. Sci., 60, 1754–1773.

Schumacher, C., and R. A. Houze (2000), Comparison of radardata from the TRMM satellite and Kwajalein oceanic val-idation site, J. Appl. Meteor., 39, 2151–2164.

Sobel, A. H., and T. Horinouchi (2000), On the dynamics ofeasterly waves, monsoon depressions, and tropical depres-sion type disturbances, J. Meteor. Soc. Jpn., 78, 167–173.

Sobel, A. H., et al. (2004), Large-scale meteorology and deepconvection during TRMM KWAJEX, Mon. Wea. Rev.,132, 422–444.

Straub, K. H., and G. N. Kiladis (2002), Observations of a con-vectively coupled Kelvin wave in the eastern Pacific ITCZ,J. Atmos. Sci., 59, 30–53.

Wheeler, M., and G. N. Kiladis (1999), Convectively coupledequatorial waves: Analysis of clouds and temperature in thewavenumber-frequency domain, J. Atmos. Sci., 56, 374–399.

Yuter, S. E., and R. A. Houze (1995), 3-Dimensional Kine-matic and Microphysical Evolution of Florida Cumulonim-bus.2. Frequency-Distributions of Vertical Velocity, Reflec-tivity, and Differential Reflectivity, Mon. Wea. Rev., 123,1941–1963.

A. Swann, Department of Earth and Planetary Science,University of California-Berkeley, 307 McCone Hall #4767Berkeley, CA 94720-4767. ([email protected])


Figure 1. Composite map of anomalous OLR for Kelvinwave-associated storms. The middle panel shows a com-posite of spatial variables on the storm day designated as“day 0”, and the top and bottom panels show compositesfor two days preceding and following “day 0” respectively.Negative OLR values are shaded with dotted contour in-tervals of 3.4 Wm−2 and positive OLR values contouredwith solid lines at the same interval and a maximum of27.1 Wm−2. The location of Kwajalein is identified by awhite dot.

Figure 2. Same as figure 1 but for MRG wave-associatedstorms using contour intervals of 3.5 Wm−2 and a maxi-mum of 23.3 Wm−2.

Figure 3. Composite Hovmoeller diagram of zonal wind(filtered to remove periods greater than 30d and averagedfrom 0 to 15N) for Kelvin wave-associated storms. Nega-tive wind directions are shaded with dotted contour linesand positive wind anomalies are contoured with solidlines. The time axis is as in figure 1 and the longitude ofKwajalein is identified by a black line.

Figure 4. Same as figure 3 but for meridional winds forMRG wave-associated storms.

Figure 5. The mean CFADs of reflectivity for Kelvin and MRG wave-associated storm days are shown in panels (a)and (b) respectively. Panel (c) shows the significant difference between panels (a) and (b) as determined by Monte Carlosimulation. Despite falling outside the significant region, the contour interval for zero has been drawn with a think blackline to highlight the negative and positive regions. Each CFAD consists of a PDF of reflectivity at each height multipliedby 100 so that values are in percent.


Figure 6. Composite map of anomalous 850 mb windand anomalous OLR for Kelvin wave-associated storms.Panel (b) shows a composite of spatial variables on thestorm day designated as “day 0”, and panels (a) and (c)show composites for two days preceding and following“day 0” respectively. Negative OLR values are outlinedwith dotted contour intervals of 3.4 Wm−2 and positiveOLR values contoured with solid lines at the same in-terval and a maximum of 27.1 Wm−2. A wind arrowbar corresponding to 1 m/s wind speed is located in thelower right of each panel. The location of Kwajalein isidentified by a white dot.

Figure 7. Same as figure S1 but for MRG wave-associated storms using contour intervals of 3.5 Wm−2

and a maximum of 23.3 Wm−2.

100oE 120oE 140oE 160oE 180oW 160oW 140oW 120oW 12oS 6oS 0o 6oN 12oN 18oN

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Figure 1.Composite map of anomalous OLR for Kelvin wave-associated storms. The middle panel shows a composite of spatial variables on the storm day designated as “day 0”, and the top and bottom panels show composites for two days preceding and following “day 0” respectively. Nega-tive OLR values are shaded with dotted contour intervals of 3.4 Wm-2 and positive OLR values contoured with solid lines at the same interval and a maximum of 27.1 Wm-2. The location of Kwajalein is identified by a white dot.

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Figure 2.Same as figure 1 but for MRG wave-associated storms using contour intervals of 3.5 Wm-2 and a maximum of 23.3 Wm-2.

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Figure 3.Composite Hovmoeller diagram of zonal wind (filtered to remove periods greater than 30d and averaged from 0 to 15N) for Kelvin wave-associated storms. Negative wind directions are shaded with dotted contour lines and positive wind anomalies are contoured with solid lines. The time axis is as in figure 1 and the longitude of Kwajalein is identified by a black line.

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Figure 4.Same as figure 3 but for meridional winds for MRG wave-associated storms.

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Figure 5.The mean CFADs of reflectivity for Kelvin and MRG wave-associated storm days are shown in panels (a) and (b) respectively. Panel (c) shows the significant difference between panels (a) and (b) as determined by Monte Carlo simulation. Despite falling outside the significant region, the contour interval for zero has been drawn with a think black line to highlight the negative and positive regions. Each CFAD consists of a PDF of reflectivity at each height multiplied by 100 so that values are in percent.

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(a) (b) (c)

(a) (b) (c)

Figure S1.Composite map of anomalous 850 mb wind and anomalous OLR for Kelvin wave-associated storms. The middle panel shows a composite of spatial variables on the storm day designated as “day 0”, and the top and bottom panels show composites for two days preceding and follow-ing “day 0” respectively. Negative OLR values are outlined with dotted contour intervals of 3.4 Wm-2 and positive OLR values contoured with solid lines at the same interval and a maximum of 27.1 Wm-2. A wind arrow bar corresponding to 1 m/s wind speed is located in the lower right of each panel. The location of Kwajalein is identified by a white dot.


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Figure S2.Same as figure S1 but for MRG wave-associated storms using contour intervals of 3.5 Wm-2 and a maximum of 23.3 Wm-2.


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Observed radar reflectivity in convectively coupled Kelvin and mixed Rossby-gravity waves

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