Vertical Normal Mode Transforms: Theory and Application

Fulton, Scott R.; Schubert, Wayne H.

doi:10.1175/1520-0493(1985)113<0647:vnmtta>2.0.co;2

Cited by 79 publications

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“…The primitive equations, linearized about a basic state of zero or constant wind, can be solved by separation of variables (e.g., Matsuno, 1966;Gill, 1982;Kasahara, 1984;Fulton and Schubert, 1985). Separate equations governing vertical and horizontal structure are obtained.…”

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

“…The vertical spectral transform was performed with the code of Fulton and Schubert (1985), which uses a realistic virtual temperature stratification (in this case a mean sounding from the tropical western Pacific). Note that it is important to use consistent heating and stratification profile measurements, since convective heating profiles physically depend on the stratification profile (e.g., Mapes, 1997a).…”

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

“…The various plotting symbols in Fig. 2a correspond to different discretizations of the vertical spectrum of the observed mean heating profile, obtained by moving the artificial atmospheric lid in the Fulton and Schubert (1985) transform to various altitudes (35,25,15,5, and 1mb). The spectrum can be well represented by two main spectral bands, one centered at c-52m/s and one at c-23m/s (as in Fig.…”

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

“…Internal heating projects only weakly onto this external mode (Geisler and Stevens, 1982;Lim and Chang, 1983;Fulton and Schubert, 1985). Furthermore, the external mode's high value of c makes this weak response spread rapidly over an enormous area, so the amplitude is quite weak everywhere.…”

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

“…Observed divergence in tropical MCSs in nearly equal to bd. This quantity can be converted to Fulton and Schubert's (1985) 'forced geopotential' ct-the rate of change of geopotential if heating went directly into temperature changes-byct=c2g-1sd. The conversion to heating rate profiles, using Fig.…”

Section: Magnitude Acid Size O F the Mcs Heatingmentioning

confidence: 99%

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The Large-Scale Part of Tropical Mesoscale Convective System Circulations

Mapes

1998

Journal of the Meteorological Society of Japan

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The linear response of the tropical troposphere to a heat source resembling a moderately large mesoscale convective system (MCS) is modeled. The spectral representation of vertical structure, with and without rigid lids atop the atmosphere, is illustrated graphically and discussed physically. The spectrum characterizing a mean radar-observed MCS heating profile in an unbounded, realistically stratified atmosphere can be well approximated with just two spectral bands. The equations governing the wind and height amplitudes of each spectral band are linear shallow-water equations, combined with a time-dependent spatial smoothing that accounts for the finite spectral widths of the bands. This spectral band smoothing mimics the tropospheric smoothing effects of the preferential upward propagation of high horizontal wavenumber components.During the period from 0-72 hours after the MCS, the flow evolves from initially circular expanding wavelike rings, toward the planetary-wave patterns studied by Matsuno, Gill, and others. This size expansion is not truly an "up-scale" evolution: the red horizontal spectrum of scales excited by a meso-sized heat source merely undergoes phase evolution with time. Small scales do preferentially propagate upward, however. An interesting feature strongly excited by an equatorial MCS is a zonally elongated inertio-gravity motion along the equator, which cools the troposphere 48 hours after a brief heating event. This oscillation has a large zonally-symmetric component.The linear solutions developed here are superposed to obtain estimates of the wind and temperature changes forced by satellite-observed ensembles of MCSs. Low-level winds comparable to observed Australian monsoon winds spin up from rest in just 2-3 days, while some of the monsoon convective heating escapes into the equatorial waveguide as downwelling Kelvin and mixed Rossby-gravity waves.Synthetic data constructed from model fields illustrate how observing systems experience the effects of MCS heating events. Deep vertical motion on tropical rawinsonde-array scales responds rapidly to convective heating, with a response time (1-2h) small compared to the observed lifetime of MCSs (6-12h). These results indicate that rawinsonde array observations of a "quasi-equilibrium" between largescale vertical motion and convection may be due to the rapid response of the former to the latter, not vice versa as has sometimes been supposed.

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Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

Section: Spectral Representation Of the Vertical Dimension: Backgroundmentioning

confidence: 99%

Section: Magnitude Acid Size O F the Mcs Heatingmentioning

confidence: 99%

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The Large-Scale Part of Tropical Mesoscale Convective System Circulations

Mapes

1998

Journal of the Meteorological Society of Japan

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Balanced dynamics of deep and shallow Hadley circulations in the tropics

Gonzalez

Rojas

2014

J Adv Model Earth Syst

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This paper examines the dynamics of large-scale overturning circulations in the tropical atmosphere using an idealized zonally symmetric model on the equatorial b-plane. Under certain simplifications of its coefficients, the elliptic partial differential equation for the transverse circulation can be solved by first performing a vertical transform to obtain a horizontal structure equation, and then using Green's function to solve the horizontal structure equation. When deep diabatic heating is present in the Intertropical Convergence Zone (ITCZ), the deep Hadley circulation is of first-order importance. In the absence of deep diabatic heating, the interior circulation associated with Ekman pumping cannot penetrate deep into the troposphere because the resistance of fluid parcels to horizontal motion (i.e., inertial stability) is significantly smaller than their resistance to vertical motion (i.e., static stability). In this scenario, only a shallow Hadley circulation exists. The shallow overturning circulation is characterized by meridional velocities as large as 7 m s 21 at the top of the boundary layer, in qualitative agreement with observations in the tropical easternPacific. The meridional asymmetry between the winter and summer deep and shallow Hadley cells is attributed to the anisotropy of the inertial stability parameter, and as the ITCZ widens meridionally or as the forcing involves higher vertical wave numbers, the asymmetry between the winter and summer cells increases.

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Influence of the basic state zonal flow on convectively coupled equatorial waves

Dias

Kiladis

2014

Geophysical Research Letters

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Observational data are used to test the hypothesis that the basic state modulates the dispersion properties of convectively coupled equatorial waves (CCEWs). This hypothesis is based on shallow water theory, which predicts that the zonal speed of propagation of such tropospheric equatorial modes is altered by the equivalent depth and the basic zonal flow. Localized space‐time spectra are calculated to investigate how CCEW spectral peaks vary across the tropics and how they are affected by the variations in zonal wind observed geographically and by season. Doppler shifting by the basic state barotropic zonal flow is readily identified. Once this Doppler shifting is taken into account, the equivalent depths of CCEWs inferred from global power spectra are surprisingly uniform, both geographically and temporally. However, there are also detectable modulations that appear consistent with changes in vertical shear of the zonal flow, along with other shifts that are not as easily explained.

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Vertical Normal Mode Transforms: Theory and Application

Cited by 79 publications

References 0 publications

The Large-Scale Part of Tropical Mesoscale Convective System Circulations

The Large-Scale Part of Tropical Mesoscale Convective System Circulations

Balanced dynamics of deep and shallow Hadley circulations in the tropics

Influence of the basic state zonal flow on convectively coupled equatorial waves

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