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Convectively coupled equatorial waves (CCEWs) are modes of tropical variability that are often seen as potentially beneficial for sub‐seasonal predictions. Quantifying this potential has been proven difficult in operational forecast systems because tropical variability tends to be poorly represented in such models. The European Center for Medium‐Range Weather Forecasts (ECMWF) is a potential exception because it has been shown to have much improved representation of the tropics. Here, ECMWF reforecasts are used to investigate the predicted evolution of CCEWs and how they might impact sub‐seasonal predictions. It is shown that the ECMWF system is able to generate variability consistent with various modes of CCEWs, but CCEWs tend to be weaker in amplitude and their propagation characteristics often deviate from observations. This study suggests that model advancements aimed at improving the deterministic representation of CCEWs are still needed in order to better understand and utilize tropical sources of sub‐seasonal predictive skill. Plain Language Summary: Accurate weather forecasts leverage on proper characterization of the current state of the atmosphere and on predictable atmospheric phenomena that constrain the evolution of that state. Tropical weather forecasting is challenging in both aspects: observations are more sparse than in the extratropics, and the evolution of the atmosphere is constrained by large‐scale forcings such as tropical rainfall. This study focuses on the contribution of equatorial waves to low latitude weather forecast skill because these types of disturbances are known to modulate tropical rainfall, which feed back strongly onto the disturbances themselves. The main finding is that the initial state tends to be fairly well represented in forecast systems; however, within a day or two the amplitude of these waves becomes weaker than in observations, which is a decay time much faster than their typical one‐to‐three week lifetimes. Along with errors in the waves propagation characteristics, this loss of amplitude suggests that equatorial waves do not impact precipitation forecast within the models as much as theory and observations imply they should. Key Points: Convectively coupled equatorial waves (CCEWs) are a potential source of global sub‐seasonal precipitation skillOperational forecast model's representation of CCEWs has greatly advanced over the last two decadesDeviations from observations often attenuate the role of CCEWs as sources of sub‐seasonal predictive skill [ABSTRACT FROM AUTHOR]

The composite structure of the Madden-Julian oscillation (MJO) has long been known to feature pronounced Rossby gyres in the subtropical upper troposphere, whose existence can be interpreted as the forced response to convective heating anomalies in the presence of a subtropical westerly jet. The question of interest here is whether these forced gyre circulations have any subsequent effects on divergence patterns in the tropics and the Kelvin-mode component of the MJO. A nonlinear spherical shallow water model is used to investigate how the introduction of different background jet profiles affects the model's steady-state response to an imposed MJO-like stationary thermal forcing. Results show that a stronger jet leads to a stronger Kelvin-mode response in the tropics up to a critical jet speed, along with stronger divergence anomalies in the vicinity of the forcing. To understand this behavior, additional calculations are performed in which a localized vorticity forcing is imposed in the extratropics, without any thermal forcing in the tropics. The response is once again seen to include pronounced equatorial Kelvin waves, provided the jet is of sufficient amplitude. A detailed analysis of the vorticity budget reveals that the zonal-mean zonal wind shear plays a key role in amplifying the Kelvin-mode divergent winds near the equator, with the effects of nonlinearities being of negligible importance. These results help to explain why the MJO tends to be strongest during boreal winter when the Indo-Pacific jet is typically at its strongest. [ABSTRACT FROM AUTHOR]

Observational evidence of two extratropical pathways to forcing tropical convective disturbances is documented through a statistical analysis of satellite-derived OLR and ERA5 reanalysis. The forcing mechanism and the resulting disturbances are found to strongly depend on the structure of the background zonal wind. Although Rossby wave propagation is prohibited in easterlies, modeling studies have shown that extratropical forcing can still excite equatorial waves through resonance between the tropics and extratropics. Here this "remote" forcing pathway is investigated for the first time in the context of convectively coupled Kelvin waves over the tropical Pacific during northern summer. The extratropical forcing is manifested by eddy momentum flux convergence that arises when extratropical eddies propagate into the subtropics and encounter their critical line. This nonlinear forcing has similar wavenumbers and frequencies with Kelvin waves and excites them by projecting onto their meridional eigenstructure in zonal wind, as a form of resonance. This resonance is also evidenced by a momentum budget analysis, which reveals the nonlinear forcing term is essential for maintenance of the waves, while the remaining linear terms are essential for propagation. In contrast, the "local" pathway of extratropical forcing entails the presence of a westerly duct during northern winter that permits Rossby waves to propagate into the equatorial east Pacific, while precluding any sort of resonance with Kelvin waves due to Doppler shifting effects. The intruding disturbances primarily excite tropical "cloud plumes" through quasigeostrophic forcing, while maintaining their extratropical nature. This study demonstrates the multiple roles of the extratropics in forcing in tropical circulations and illuminates how tropical–extratropical interactions and extratropical basic states can provide be a source of predictability at the S2S time scale. Significance Statement: This study seeks to understand how circulations in the midlatitudes excite the weather systems in the tropics. Results show that the mechanisms, as well as the types of tropical weather systems excited, are strongly dependent on the mean large-scale wind structure. In particular, when the large-scale wind blows from east to west, a special type of eastward-moving tropical weather system, the Kelvin wave, is excited owing to its resonance with remote eastward-moving weather systems in the extratropics. On the contrary, when the average wind blows from west to east, midlatitude systems are observed to intrude into the lower latitudes and directly force tropical convection, the cloud plumes, while maintaining their extratropical nature. These results speak to how the midlatitudes can excite distinct types of tropical weather systems under different climatological wind regimes. Understanding these tropical weather systems and their interactions with the midlatitudes may ultimately help to improve predictions of weather beyond 2 weeks. [ABSTRACT FROM AUTHOR]

Tropical precipitation and circulation are often coupled and span a vast spectrum of scales from a few to several thousands of kilometers and from hours to weeks. Current operational numerical weather prediction (NWP) models struggle with representing the full range of scales of tropical phenomena. Synoptic to planetary scales are of particular importance because improved skill in the representation of tropical larger-scale features such as convectively coupled equatorial waves (CCEWs) has the potential to reduce forecast error propagation from the tropics to the midlatitudes. Here we introduce diagnostics from a recently developed tropical variability diagnostics toolbox, where we focus on two recent versions of NOAA's Unified Forecast System (UFS): operational GFSv15 forecasts and experimental GFSv16 forecasts from April to October 2020. The diagnostics include space–time coherence spectra to identify preferred scales of coupling between circulation and precipitation, pattern correlations of Hovmöller diagrams to assess model skill in zonal propagation of precipitating features, CCEW skill assessment, plus a diagnostic aimed at evaluating moisture–convection coupling in the tropics. Results show that the GFSv16 forecasts are slightly more realistic than GFSv15 in their coherence between precipitation and model dynamics at synoptic to planetary scales, with modest improvements in moisture convection coupling. However, this slightly improved performance does not necessarily translate to improvements in traditional precipitation skill scores. The results highlight the utility of these diagnostics in the pursuit of better understanding of NWP model performance in the tropics, while also demonstrating the challenges in translating model advancements into improved skill. [ABSTRACT FROM AUTHOR]

The circulation associated with convection of the Madden‐Julian Oscillation (MJO) has been suggested to have an impact on its propagation by a number of previous studies. This circulation contains both flanking Rossby waves to the rear and a Kelvin wave leading the convective center. In this study, individual MJO convective envelopes from a 40‐year database are tracked, a technique to scale the MJO by its zonal wavelength is employed, and statistical methods are used to assess how the MJO circulation pattern might impact its eastward propagation downstream. Results suggest that continuous eastward propagation of the MJO is favored when a strong Kelvin wave circulation is present east of MJO convection, indicated by both an easterly zonal wind anomaly and negative geopotential height anomaly. In addition to the known significance of having Kelvin wave easterly wind anomalies, the results of this study highlight that the existence of negative geopotential height is important to supporting moistening and MJO propagation. It is found that importance of the Kelvin wave signal to MJO propagation depends on the region that the MJO is located over. Kelvin wave circulation east of MJO convection enhances moistening to support continuous eastward propagation of the MJO, mainly through meridional moisture advection due to the coupling between the Kelvin wave and Rossby‐like disturbances east of the active convection. The roles of boundary layer convergence and vertical moistening are also discussed. Key Points: A new method is introduced to quantify the strength of Kelvin circulation response to the Madden‐Julian Oscillation (MJO) with varying zonal scalesThe MJO is most likely to continue its propagation when both zonal wind and geopotential signals of the Kelvin circulation are presentMeridional moisture advection is most important in supporting MJO eastward propagation [ABSTRACT FROM AUTHOR]

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 β$$ \beta $$‐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. [ABSTRACT FROM AUTHOR]

This paper promotes the view that African easterly waves (AEWs) are triggered by localized forcing, most likely associated with latent heating upstream of the region of observed AEW growth. A primitive equation model is used to show that AEWs can be triggered by finite-amplitude transient and localized latent heating on a zonally varying basic state that is linearly stable. Heating close to the entrance region of the African easterly jet (AEJ) is shown to initiate AEWs downstream. The heating leads to an initial trough that reaches the West African coast about 5-7 days later, depending on the nature of the heating profile. After this, a structure that projects strongly onto the leading linear normal mode of the basic state becomes established, characterized by a number of westward-propagating disturbances that strongly resemble AEWs. The sensitivity of the forced AEWs to the nature and location of the heating profile is examined. AEWs are most efficiently triggered by heating profiles that establish lower tropospheric circulations close to the entrance region of the AEJ. In the present study, this was best achieved by lower tropospheric heating from shallow convection or upper-level heating and lower-level cooling from a strati-form precipitation profile. Both profiles have significant heating gradients in the vertical in the mid-to-lower troposphere. This triggering paradigm for the genesis of AEWs has consequences for the variability and predictability of AEWs at weather and climate time scales. In addition to the nature of the AEJ, often emphasized, it is crucial to consider the nature and variability of upstream heating triggers.

Outgoing longwave radiation (OLR) and low-level wind fields in the Atlantic and Pacific intertropieal convergence zone (ITCZ) are dominated by variability on synoptic time scales primarily associated with easterly waves during boreal summer and fall. This study uses spectral filtering of observed OLR data to capture the convective variability coupled to Pacific easterly waves. Filtered OLR is then used as an independent variable to isolate easterly wave structure in wind, temperature, and humidity fields from open-ocean buoys, radiosondes, and gridded reanalysis products. The analysis shows that while some Pacific easterly waves originate in the Atlantic, most of the waves appear to form and strengthen within the Pacific. Pacific easterly waves have wavelengths of 4200-5900 kin, westward phase speeds of 11.3-13.6 m [s.sup.-1], and maximum meridional wind anomalies at about 600 hPa. A warm, moist boundary layer is observed ahead of the waves, with moisture lofted quickly through the troposphere by deep convection, followed by a cold, dry signal behind the wave. The waves are accompanied by substantial cloud forcing and surface latent heat flux fluctuations in buoy observations. In the central Pacific the horizontal structure of the waves appears as meridionally oriented inverted troughs, while in the east Pacific the waves are oriented southwestnortheast. Both are tilted slightly eastward with height. Although these tilts are consistent with adiabatic barotropic and baroclinic conversions to eddy energy, energetics calculations imply that Pacific easterly waves are driven primarily by convective heating. This differs from African easterly waves, where the barotropic and baroclinic conversions dominate.

Vertical structures of 2-day waves and the Madden-Julian oscillation (MJO) are projected onto vertical normal modes for a quiescent tropical troposphere. Three modes capture the gross tropospheric structure of 2-day waves, while only two modes are needed to represent most of the baroclinic structure of the MJO. Deep circulations that project onto the first baroclinic mode are associated with deep cumulonimbus and stratiform rainfall. Shallow circulations that project onto higher wavenumber modes are associated with precipitating shallow cumulus and congestus and stratiform rainfall. For both disturbances the horizontal divergence contributed by shallow modes is an important factor in the column-integrated moist enthalpy budget. These modes converge moist static energy for a time prior to when deep circulations export moist static energy. These results highlight the importance of properly representing the effects of shallow cumulus, congestus, and stratiform precipitation in theories of convectively coupled waves and in atmospheric models.

A primitive equation model is used to study the linear normal modes of the African easterly jet (AEJ). Reanalysis data from the summertime mean (June-September; JJAS) flow is used to provide zonally uniform and wavy basic states. The structure and growth rates of modes that grow over West Africa on these basic states are analyzed. For zonally uniform basic states, the modes resemble African easterly waves (AEWs) as in many previous studies, but they are quite baroclinic and surface intensified. For wavy basic states the modes have a longitudinal structure determined by the AEJ. They have a surface-intensified baroclinic structure upstream and a deep barotropic structure downstream, as confirmed by energy conversion diagnostics. These modes look remarkably similar to the composite easterly wave structures found by the authors in a companion paper. The similarity extends to the phase relationship of vertical velocity with streamfunction, which resembles OLR composites, suggesting a dynamical influence on convection. Without damping, the mode for the wavy basic state has a growth rate of 0.253 [day.sup.-1]. With a reasonable amount of low-level damping this mode is neutralized. It has a period of 5.5 days and a wavelength of about 3500 km. Further results with monthly mean basic states show slight variations, as the wave packet essentially follows displacements of the jet core. Experiments focused on specific active and passive years for easterly waves (1988 and 1990) do not yield significantly different results for the modes. These results, and in particular, the stability of the system, lead to the conclusion that barotropic-baroclinic instability alone cannot explain the initiation and intermittence of AEWs, and a finite-amplitude initial perturbation is required.

The mean structure of African easterly waves (AEWs) over West Africa and the adjacent Atlantic is isolated by projecting dynamical fields from reanalysis and radiosonde data onto space-time-filtered satellite-derived outgoing longwave radiation. These results are compared with previous studies and an idealized modeling study in a companion paper, which provides evidence that the waves bear a close structural resemblance to the fastest-growing linear normal mode of the summertime basic-state flow over Africa. There is a significant evolution in the three-dimensional structure of AEWs as they propagate along 10[degrees]N across West Africa. At this latitude, convection occurs in northerly flow to the east of the Greenwich meridian, then shifts into the wave trough, and finally into southerly flow as the waves propagate offshore into the Atlantic ITCZ. In contrast, to the north of the African easterly jet along 15[degrees]N convection remains in southerly flow throughout the waves' trajectory. Along 10[degrees]N over West Africa, the location of convection is consistent with the adiabatic dynamical forcing implied by the advection of perturbation vorticity by the mean thermal wind in the zonal direction, as in the companion paper. Offshore, and along 15[degrees]N, the relationship between the convection and dynamics is more complex, and not as easily explained in terms of dynamical forcing alone.

A statistical study of the three-dimensional structure of the Madden Julian oscillation (MJO) is carried out by projecting dynamical fields from reanalysis and radiosonde data onto space-time filtered outgoing longwave radiation (OLR) data. MJO convection is generally preceded by low-level convergence and upward motion in the lower troposphere, while subsidence, cooling, and drying prevail aloft. This leads to moistening of the boundary layer and the development of shallow convection, followed by a gradual and then more rapid lofting of moisture into the middle troposphere at the onset of deep convection. After the passage of the heaviest rainfall, a westerly wind burst region is accompanied by stratiform precipitation, where lower tropospheric subsidence and drying coincide with continuing upper tropospheric upward motion. The evolution of the heating field leads to a temperature structure that favors the growth of the MJO. The analysis also reveals distinct differences in the vertical structure of the MJO as it evolves, presumably reflecting changes in its vertical heating profile, phase speed, or the basic-state circulation that the MJO propagates through. The dynamical structure and the evolution of cloud morphology within the MJO compares favorably in many respects with other propagating convectively coupled equatorial waves. One implication is that the larger convective envelopes within the Tropics tend to be composed of more shallow convection along their leading edges, a combination of deep convection and stratiform rainfall in their centers, and then a preponderance of stratiform rainfall along their trailing edges, regardless of scale or propagation direction. While this may ultimately be the factor that governs the dynamical similarities across the various wave types, it raises questions about how the smaller-scale, higher-frequency disturbances making up the MJO conspire to produce its heating and dynamical structures. This suggests that the observed cloud morphology is dictated by fundamental interactions with the large-scale circulation.

The dynamics of the 2-day wave, a type of convectively coupled disturbance that frequents the equatorial western Pacific, is examined using observations and a linear primitive equation model. A statistical composite of the wave's kinematic and thermodynamic structure is presented. It is shown that l) the wave's wind and temperature perturbations can be modeled as linear responses to convective beating and cooling, and 2) the bulk of the wave's dynamical and convective structure can be represented with two vertical modes. The observations and model results suggest that the 2-day wave is an n = 1 westward-propagating inertio-gravity wave with a shallow equivalent depth (14 m) that results from the partial cancelation of adiabatic temperature changes due to vertical motion by convective beating and cooling.

Recent observational analysis of both individual realizations and statistical ensembles identifies moist convectively coupled Kelvin waves in the Tropics with supercluster envelopes of convection. This observational analysis elucidates several key features of these waves including their propagation speed of roughly 15 m [s.sup.-1] and many aspects of their dynamical structure. This structure includes anomalously cold temperatures in the lower troposphere and warm temperatures in the upper troposphere (below 250 hPa) within and sometimes leading the heating region and strong updrafts in the wave, and an upward and westward tilting structure with height below roughly 250 hPa. Other key features in the wave are that anomalous increases in convective available potential energy (CAPE) and surface precipitation lead the wave while the trailing part of the supercluster is dominated by stratiform precipitation. The main result in this paper is the development of a simple model convective parameterization with nonlinear convectively coupled moist gravity waves, which reproduce many of the features of the observational record listed above in a qualitative fashion. One key feature of the model convective parameterization is the systematic use of two vertical modes with one representing deep convective heating and the other stratiform heating. The other key feature in the model is the explicit parameterization of the separate deep convective and stratiform contribution to the downdrafts, which change equivalent potential temperature in the boundary layer. The effects of rotation on convectively coupled equatorial waves are also included through a suitable linear stability theory for the model convective parameterization about radiative convective equilibrium.

Observations of the horizontal and vertical structure of convectively coupled Kelvin waves are presented and are compared with the predicted structures of moist Kelvin (or gravity) waves in three simple models of coupled wave instability: wave-conditional instability of the second kind (CISK), wind-induced surface heat exchange (WISHE), and stratiform instability. The observations are based on a linear regression analysis of multiple years of ECMWF reanalysis and station radiosonde data. Results suggest that both the wave-CISK and stratiform instability theories successfully predict many important features of observed moist Kelvin waves, but that unrealistic aspects of these models limit their ability to provide comprehensive explanations for the dynamics of these waves. It is suggested that an essential component of any theory for moist Kelvin waves is the second baroclinic mode heat source associated with stratiform precipitation.

Observations are presented that link extratropical Rossby wave disturbances excited in the Southern Hemisphere subtropical jet to the initiation of convectively coupled Kelvin waves in the Pacific intertropical convergence zone (ITCZ) during austral winter. A baroclinic, zonal wavenumber 6, eastward-propagating Rossby wave train in the subtropical jet turns northeastward in the vicinity of Australia, inducing upper tropospheric divergence and vertical motion fields that spread equatorward and induce cloudiness anomalies in the Tropics. Lower tropospheric pressure surges excited from the extratropics also induce Kelvin wave-like geopotential height and temperature anomalies at the surface, providing additional lower tropospheric convergence and vertical motion forcing. The tropical outgoing longwave radiation (OLR) and circulation fields propagate eastward in tandem with the extratropical Rossby wave train at approximately 17 m [s.sup.-1]. Kelvin wave activity in the central Pacific ITCZ thus appears to be associated with eastward-propagating Rossby wave activity in the extratropics, which is traveling at phase speeds similar to those observed in developed convectively coupled Kelvin waves (15-20 m [s.sup.-1]). The longer timescale relationship between subtropical jet activity and Kelvin wave variability in the Tropics is determined through the calculation of monthly averaged composite fields. When Kelvin wave OLR activity is enhanced (suppressed) in the tropical Pacific, eastward-propagating Rossby wave activity in the Kelvin wave phase speed band (8-30 m [s.sup.-1]) is anomalously strong (weak) in the subtropical jet. A case study is presented that suggests that enhanced Kelvin wave activity in the central Pacific ITCZ is associated more strongly with enhanced eastward-propagating Rossby wave activity in the subtropics than with the local thermal and moisture boundary conditions in the tropical Pacific.

We analyze the stratospheric waves in models participating in phase 1 of the Stratosphere–troposphere Processes And their Role in Climate (SPARC) Quasi‐Biennial Oscillation initiative (QBOi). All models have robust Kelvin and mixed Rossby‐gravity wave modes in winds and temperatures at 50 hPa and represent them better than most of the Coupled Model Intercomparison Project Phase 5 (CMIP5) models. There is still some spread among the models, especially concerning the mixed Rossby‐gravity waves. We attribute the variability in equatorial waves among the QBOi models in part to the varying horizontal and vertical resolutions, to systematic biases in zonal winds, and to the considerable variability in convectively coupled waves in the troposphere among the models: only roughly half of the QBOi models have realistic convectively coupled Kelvin waves and only a few models have convectively coupled mixed Rossby‐gravity waves. The models with stronger convectively coupled waves tend to produce larger zonal mean forcing due to resolved waves in the QBO region. Finally we evaluate the Eliassen–Palm (EP) flux and EP flux divergence of the resolved waves in the QBOi models. We find that there is a large spread in the forcing from resolved waves in the QBO region, and the resolved wave forcing has a robust correlation with model vertical resolution. [ABSTRACT FROM AUTHOR]