The Longitudinal Variation of Equatorial Waves due to Propagation on a Varying Zonal Flow

The general 1D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behavior are found, depending on the sign of the group velocity cg and a wave property B. For B positive, the wave energy and the wavenumber vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang occurs where cg goes to zero. However, for B negative, they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analyzed in detail using the theory. For nondispersive Kelvin waves, B reduces to 2, and an analytic solution is possible. For all the waves considered, B is positive, except for the westward-moving mixed Rossby–gravity (WMRG) wave, which can have negative B as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper-tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However, the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic Oceans are generally not in accord with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher-latitude wave activity

The impacts of convective parameterization and moisture triggering on AGCM-simulated convectively coupled equatorial waves

This study examines the impacts of convective parameterization and moisture convective trigger on convectively coupled equatorial waves simulated by the Seoul National University (SNU) atmospheric general circulation model (AGCM). Three different convection schemes are used, including the simplified Arakawa-Schubert (SAS) scheme, the Kuo (1974) scheme, and the moist convective adjustment (MCA) scheme, and a moisture convective trigger with variable strength is added to each scheme. The authors also conduct a "no convection" experiment with deep convection schemes turned off. Space-time spectral analysis is used to obtain the variance and phase speed of dominant convectively coupled equatorial waves, including the Madden-Julian oscillation (MJO), Kelvin, equatorial Rossby (ER), mixed Rossby-gravity (MRG), and eastward inertio-gravity (EIG) and westward inertio-gravity (WIG) waves. The results show that both convective parameterization and the moisture convective trigger have significant impacts on AGCM-simulated, convectively coupled equatorial waves. The MCA scheme generally produces larger variances of convectively coupled equatorial waves including the MJO, more coherent eastward propagation of the MJO, and a more prominent MJO spectral peak than the Kuo and SAS schemes. Increasing the strength of the moisture trigger significantly enhances the variances and slows down the phase speeds of all wave modes except the MJO, and usually improves the eastward propagation of the MJO for the Kuo and SAS schemes, but the effect for the MCA scheme is small. The no convection experiment always produces one of the best signals of convectively coupled equatorial waves and the MJO.open585

Equatorial waves simulated by the NCAR community climate model

The equatorial planetary waves simulated by the NCAR CCM1 general circulation model were investigated in terms of space-time spectral analysis (Kao, 1968; Hayashi, 1971, 1973) and energetic analysis (Hayashi, 1980). These analyses are particularly applied to grid-point data on latitude circles. In order to test some physical factors which may affect the generation of tropical transient planetary waves, three different model simulations with the CCM1 (the control, the no-mountain, and the no-cloud experiments) were analyzed

Mathematical study of the betaplane model: Equatorial waves and convergence results

We are interested in a model of rotating fluids, describing the motion of the ocean in the equatorial zone. This model is known as the Saint-Venant, or shallow-water type system, to which a rotation term is added whose amplitude is linear with respect to the latitude; in particular it vanishes at the equator. After a physical introduction to the model, we describe the various waves involved and study in detail the resonances associated with those waves. We then exhibit the formal limit system (as the rotation becomes large), obtained as usual by filtering out the waves, and prove its wellposedness. Finally we prove three types of convergence results: a weak convergence result towards a linear, geostrophic equation, a strong convergence result of the filtered solutions towards the unique strong solution to the limit system, and finally a "hybrid" strong convergence result of the filtered solutions towards a weak solution to the limit system. In particular we obtain that there are no confined equatorial waves in the mean motion as the rotation becomes large.Comment: Revised version after referee's comments. Accepted for publication in M\'{e}moires de la Soci\'{e}t\'{e} Math\'{e}matique de Franc

A new theory for tropical instability waves

Large-scale westward propagating waves, so-called "Legeckis" or "Tropical Instabil- ity Waves", are a prominent feature of sea surface temperature images of the equatorial Pacific. Our analyses of satellite altimetry data and long-term moorings reveals that the Legeckis waves can be interpreted as a superposition of two distinct wave modes, a first equatorial Rossby wave and a Rossby-gravity wave. We present evidence that the energy sources for both waves are the mean currents. Our results imply that Legeckis waves can be explained within the framework of linear equatorial waves

The Intricacies of Identifying Equatorial Waves

Equatorial waves (EWs) are synoptic- to planetary-scale propagating disturbances at low latitudes with periods from a few days to several weeks. Here, this term includes Kelvin waves, equatorial Rossby waves, mixed Rossby–gravity waves, and inertio-gravity waves, which are well described by linear wave theory, but it also other tropical disturbances such as easterly waves and the intraseasonal Madden–Julian Oscillation with more complex dynamics. EWs can couple with deep convection, leading to a substantial modulation of clouds and rainfall. EWs are amongst the dynamic features of the troposphere with the longest intrinsic predictability, and models are beginning to forecast them with an exploitable level of skill. Most of the methods developed to identify and objectively isolate EWs in observations and model fields rely on (or at least refer to) the adiabatic, frictionless linearized primitive equations on the sphere or the shallow-water system on the equatorial -plane. Common ingredients to these methods are zonal wave-number–frequency filtering (Fourier or wavelet) and/or projections onto predefined empirical or theoretical dynamical patterns. This paper gives an overview of six different methods to isolate EWs and their structures, discusses the underlying assumptions, evaluates the applicability to different problems, and provides a systematic comparison based on a case study (February 20–May 20, 2009) and a climatological analysis (2001–2018). In addition, the influence of different input fields (e.g., winds, geopotential, outgoing long-wave radiation, rainfall) is investigated. Based on the results, we generally recommend employing a combination of wave-number–frequency filtering and spatial-projection methods (and of different input fields) to check for robustness of the identified signal. In cases of disagreement, one needs to carefully investigate which assumptions made for the individual methods are most probably not fulfilled. This will help in choosing an approach optimally suited to a given problem at hand and avoid misinterpretation of the results

Response of the West African Monsoon to the Madden–Julian Oscillation

Observations show that rainfall over West Africa is influenced by the Madden-Julian Oscillation (MJO). A number of mechanisms have been suggested: 1) forcing by equatorial waves; 2) enhanced monsoon moisture supply; and 3) increased African easterly wave (AEW) activity. However, previous observational studies are not able to unambiguously distinguish between cause and effect. Carefully designed model experiments are used to assess these mechanisms. Intraseasonal convective anomalies over West Africa during the summer monsoon season are simulated in an atmosphere-only global circulation model as a response to imposed sea surface temperature (SST) anomalies associated with the MJO over the equatorial warm pool region. 1) Negative SST anomalies stabilize the atmosphere leading to locally reduced convection. The reduced convection leads to negative midtropospheric latent heating anomalies that force dry equatorial waves. These waves propagate eastward (Kelvin wave) and westward (Rossby wave), reaching Africa approximately 10 days later. The associated negative temperature anomalies act to destabilize the atmosphere, resulting in enhanced monsoon convection over West and central Africa. The Rossby waves are found to be the most important component, with associated westward-propagating convective anomalies over West Africa. The eastward-propagating equatorial Kelvin wave also efficiently triggers convection over the eastern Pacific and Central America, consistent with observations. 2) An increase in boundary layer moisture is found to occur as a result of the forced convective anomalies over West Africa rather than a cause. 3) Increased shear on the African easterly jet, leading to increased AEW activity, is also found to occur as a result of the forced convective anomalies in the model