A QBO Cookbook: Sensitivity of the Quasi-Biennial Oscillation to Resolution, Resolved Waves, and Parameterized Gravity Waves

An intermediate complexity moist general circulation model is used to investigate the sensitivity of the quasi-biennial oscillation (QBO) to resolution, diffusion, tropical tropospheric waves, and parameterized gravity waves. Finer horizontal resolution is shown to lead to a shorter period, while finer vertical resolution is shown to lead to a longer period and to a larger amplitude in the lowermost stratosphere. More scale-selective diffusion leads to a faster and stronger QBO, while enhancing the sources of tropospheric stationary wave activity leads to a weaker QBO. In terms of parameterized gravity waves, broadening the spectral width of the source function leads to a longer period and a stronger amplitude although the amplitude effect saturates in the mid-stratosphere when the half-width exceeds (Formula presented.) m/s. A stronger gravity wave source stress leads to a faster and stronger QBO, and a higher gravity wave launch level leads to a stronger QBO. All of these sensitivities are shown to result from their impact on the resultant wave-driven momentum torque in the tropical stratosphere. Atmospheric models have struggled to accurately represent the QBO, particularly at moderate resolutions ideal for long climate integrations. In particular, capturing the amplitude and penetration of QBO anomalies into the lower stratosphere (which has been shown to be critical for the tropospheric impacts) has proven a challenge. The results provide a recipe to generate and/or improve the simulation of the QBO in an atmospheric model

Tropical Background and Wave Spectra: Contribution of Wave–Wave Interactions in a Moderately Nonlinear Turbulent Flow

&amp;lt;p&amp;gt;Variability in the tropical atmosphere is concentrated at wavenumber&amp;amp;#8211;frequency combinations where linear theory indicates wave modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small-scale convection triggering large-scale waves via wave&amp;amp;#8211;wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow-water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only antisymmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave modes, and also provides a solid footing for the common assumption that the background spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as &amp;amp;#8722;5/3. However, it does explain why the cascade should be toward lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave modes are important for tropical dynamics.&amp;lt;br&amp;gt;It also explains why&amp;amp;#160; in satellite observations and reanalysis data, the symmetric component is stronger than the anti-symmetric component, as any bias in the small-scale forcing from isotropy, whether symmetric or antisymmetric, leads to symmetric bias in the large-scale spectrum regardless of the source of variability responsible for the onset of the asymmetry.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Shamir, O., C. Schwartz, C.I. Garfinkel, and N. Paldor,&amp;amp;#160;The power distribution between symmetric and anti-symmetric components of the tropical wavenumber-frequency spectrum, JAS,&amp;amp;#160;https://doi.org/10.1175/JAS-D-20-0283.1&amp;amp;#160;.&amp;lt;br&amp;gt;Garfinkel, C.I., O. Shamir, I. Fouxon, and N. Paldor,&amp;amp;#160;Tropical background and wave spectra: contribution of wave-wave interactions in a moderately nonlinear turbulent flow, JAS,&amp;amp;#160;https://doi.org/10.1175/JAS-D-20-0284.1.&amp;lt;br&amp;gt;Shamir, O., C.I. Garfinkel, O. Adam, and N. Paldor,&amp;amp;#160;A note on the power distribution between symmetric and anti-symmetric components of the tropical Brightness Temperature spectrum in the wavenumber-frequency plane&amp;amp;#160;, JAS,doi: 10.1175/JAS-D-21-0099.1.&amp;lt;/p&amp;gt;</jats:p

Planetary (Rossby), Inertia-Gravity (Poincar&amp;#233;) and Kelvin waves on the f-plane and &amp;#946;-plane in the presence of a uniform zonal flow

&amp;lt;p&amp;gt;A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/&amp;amp;#946;-plane or on the equatorial &amp;amp;#946;-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the &amp;amp;#946;&amp;amp;#8211;effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincar&amp;amp;#233;) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the &amp;amp;#8220;no mean-flow&amp;amp;#8221; phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincar&amp;amp;#233; modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincar&amp;amp;#233; modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem.&amp;amp;#160;&amp;lt;/p&amp;gt;</jats:p

The power distribution between symmetric and anti-symmetric components of the tropical wavenumber-frequency spectrum

AbstractA yet unexplained feature of the tropical wavenumber-frequency spectrum is its parity distributions, i.e., the distribution of power between the meridionally symmetric and anti-symmetric components of the spectrum. Due to the linearity of the decomposition to symmetric and anti-symmetric components and the Fourier analysis, the total spectral power equals the sum of the power contained in each of these two components. However, the spectral power need not be evenly distributed between the two components. Satellite observations and reanalysis data provide ample evidence that the parity distribution of the tropical wavenumber-frequency spectrum is biased towards its symmetric component. Using an intermediate-complexity model of an idealized moist atmosphere, we find that the parity distribution of the tropical spectrum is nearly insensitive to large-scale forcing, including topography, ocean heat fluxes, and land-sea contrast. On the other hand, we find that a small-scale (stochastic) forcing has the capacity to affect the parity distribution at large spatial scales via an upscale (inverse) turbulent energy cascade. These results are qualitatively explained by considering the effects of triad interactions on the parity distribution. According to the proposed mechanism, any bias in the small-scale forcing, symmetric or anti-symmetric, leads to symmetric bias in the large-scale spectrum regardless of the source of variability responsible for the onset of the asymmetry. As this process is also associated with the generation of large-scale features in the Tropics by small-scale convection, the present study demonstrates that the physical process associated with deep-convection leads to a symmetric bias in the tropical spectrum.</jats:p

Equatorial waves on the &amp;#946;-plane in the presence of a uniform zonal flow: Beyond the Doppler shift

&amp;lt;p&amp;gt;Numerical solutions of the eigenvalue equation associated with zonally propagating waves of the Linearized Rotating Shallow Water Equations are derived in a channel on the equatorial &amp;lt;em&amp;gt;&amp;amp;#946;&amp;lt;/em&amp;gt;-plane in the presence of a uniform mean zonal flow. The meridionally varying mean height field is in geostrophic balance with the prescribed mean zonal flow. In addition to the trivial Doppler shift of the free waves&amp;amp;#8217; phase speeds, the mean state causes the dispersion curves of each of the free Rossby and Poincar&amp;amp;#233; waves to coalesce in pairs of modes when the zonal wavenumber increases. For large zonal wavenumber or large mean flow, the latitudinal variation of the waves&amp;amp;#8217; amplitudes differs from that of free waves i.e., Hermite Functions (in wide channels) and Harmonic Functions (in narrow channels) do not describe the amplitude structure. For large mean speed and for large zonal wavenumber the eigenvalue problem loses its Sturm-Liouville structure and the eigenfunctions have multiple extrema between successive zeros of the function itself. In contrast to free Kelvin waves, in the presence of a mean flow the meridional velocity component of these waves does not vanish identically. For zonal stratospheric winds of order 20 m s&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt; and for gravity wave speed of order 25 m s&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt; the phase speed with mean wind can be twice that of the classical theory with no mean zonal wind.&amp;lt;/p&amp;gt;</jats:p

Tropical background and wave spectra: contribution of wave-wave interactions in a moderately nonlinear turbulent flow

AbstractVariability in the tropical atmosphere is concentrated at wavenumber-frequency combinations where linear theory indicates wave-modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small scale convection triggering large scale waves via wave-wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only anti-symmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave-modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave-modes, and also provides a solid footing for the common assumption that the back-ground spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as -5/3. However it does explain why the cascade should be towards lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave-modes are important for tropical dynamics.</jats:p

A note on the power distribution between symmetric and anti-symmetric components of the tropical Brightness Temperature spectrum in the wavenumber-frequency plane

AbstractA recent study observed the existence of a salient bias towards the symmetric part of the tropical wavenumber-frequency spectrum. Examination of the tropical Brightness Temperature (BT) spectrum in this note shows that its parity difference, i.e., the difference between its symmetric and anti-symmetric components, is concentrated in regions of the wavenumber-frequency plane corresponding to the spectral bands suggested by Wheeler and Kiladis (1999). In terms of the difference between the spectral power in the symmetric and anti-symmetric components, the spectral bands corresponding to Kelvin waves, Madden-Julian Oscillation, and Rossby waves explain about 31%, 21%, and 13% of the symmetric bias, respectively, while the combined contribution of all the other bands is negligible. The “background” spectrum after filtering out all the spectral bands explains the remaining 35% of the symmetric bias. As these spectral bands were originally designed for filtering convectively coupled equatorial waves, the findings of this note may help estimate the contributions of different wave features to the symmetric bias in the tropical BT spectrum. In addition, these findings may also help better understand the processes responsible for generating the tropical background spectrum.</jats:p