Three-dimensional normal mode functions: open-access tools for their computation in isobaric coordinates (p-3DNMF.v1)

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An analysis of the energy equation of the three‐dimensional normal modes of the atmospheric circulation provides evidence on the behaviour of the most important equatorial waves which compose the Madden–Julian Oscillation. They are the equatorial Rossby waves of zonal wavenumber 1 and 3 and the Kelvin waves of zonal wavenumber 1. In the mean, the equatorial Rossby waves gain energy by convective heating and atmospheric column stretching and transfer it to the circulation field, whereas the Kelvin waves draw energy from the circulation field and dissipate it by surface friction. The convergence associated with the Kelvin waves contributes to the moisture fuelling of the convection centre. Therefore, the coupling between equatorial Rossby and Kelvin waves is mediated by convective heating/column stretching excitation of Rossby waves and moisture convergence by Kelvin waves.

“…Observing the vertical structures in figure 3 of Marques et al . (2020) and considering the tropical tropopause at 100 hPa, one sees that, in the troposphere, the modes

k = 5

and 6 have a first baroclinic structure. The second node of the mode

k = 7

occurs at a pressure of 122 hPa, near the tropical tropopause.…”

Section: Resultsmentioning

confidence: 96%

(l_{r} = 0)

was assigned to index 0, the equatorial Rossby mode

(l_{r} = 1)

to index

-

1, and so on.…”

Section: Resultsmentioning

confidence: 99%

“…Following Tanaka (1985) and Marques et al . (2020), the global atmospheric circulation

(u, v, ϕ)

{(u, v, ϕ)}^{T} = \sum_{k = 0}^{\infty} \sum_{l = 0}^{\infty} \sum_{n = prefix- \infty}^{\infty} w_{n l k} (t) X_{k} Π_{n l k} (λ, θ, p) .

…”

Section: Methodsmentioning

confidence: 99%

“…Using the scaling matrix

X_{k}

given by

X_{k} = [\begin{matrix} \sqrt{g h_{k}} & 0 & 0 \\ 0 & \sqrt{g h_{k}} \\ 0 & 0 & g h_{k} \end{matrix}],

where g is the gravity acceleration and

h_{k}

is the equivalent height, the expansion coefficients

w_{n l k}

Section: Methodsmentioning

confidence: 99%

“…For each equivalent height,

h_{k}

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

The equatorial wave skeleton of the Madden–Julian Oscillation

Castanheira

Marques

2021

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Identification of equatorial waves using Hough function vectors

Castanheira

Marques

2023

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Equatorial waves are essential features of the tropical atmosphere dynamics, and their diagnosis is relevant for both operational and climate analysis. Here, we present a method for the identification of equatorial waves using the multivariate spatial structures of the eigensolutions of the linearized shallow‐water equations over the sphere, named Hough function vectors. The method does not require any a priori space–time filtering to separate westward‐ and eastward‐moving waves, and it can be applied to instantaneous or daily circulation fields. The wave types (Kelvin, Rossby, mixed Rossby–gravity, inertio‐gravity) are unambiguously identified by the intrinsic dynamical relationship between the horizontal wind components and geopotential fields represented in the multivariate meridional structures of the Hough function vectors. Both free and convectively coupled equatorial waves can be diagnosed. Moreover, different time filterings can be applied a posteriori, depending on the purposes of the analysis. This article is written as a proof of concept, and direct comparisons are made with results of other methods recently reviewed in a work published in this journal.

On the indices of the normal modes of Laplace's tidal equations for zonal wavenumber zero

Castanheira

2024

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The normal modes of Laplace's tidal equations seem to be a consolidated subject in the literature. However, up until now, no mode for the zonal wavenumber zero, (i.e., independent of longitude) had been identified as a mixed Rossby–gravity mode with physical meaning. Moreover, the meridional structures of westward gravity modes were not considered to be similar to the meridional structures of the corresponding inertio‐gravity modes for non‐zero wavenumbers (k>0). Here, a mixed Rossby–gravity mode with zero zonal wavenumber () is identified for the first time, and a new classification of the normal modes for the zonal wavenumber zero is proposed. Under the new classification, all the meridional structures corresponding to zero wavenumber modes are similar to the meridional structures of their respective non‐zero wavenumber modes. Moreover, using the new classification, all modes of a given type show smooth frequency variations with the zonal wavenumber, which approach asymptotically the analytic dispersion curves from the ‐plane shallow‐water equations as the fluid height tends to zero.