Eastward Inertio-gravity Waves Research Articles

Dynamic and thermodynamic modulations of the convectively coupled equatorial waves by the MJO

The convectively coupled equatorial waves (CCEWs), including the Kelvin, mixed-Rossby gravity (MRG), eastward inertio-gravity (EIG), and westward inertio-gravity (WIG) waves, are dominant synoptic-scale waves in the tropics. In this study, the modulation of the CCEWs by the MJO is examined with observational data from 1985–2005 over the Indian Ocean (IO), Maritime Continent (MC), and Western Pacific (WP). We find that the MRG wave is strengthened (weakened) to the west (east) of the MJO convection. In contrast, the Kelvin, WIG and EIG waves are mostly strengthened over the MJO convective center. As MJO modulates the background vertical wind shear and moisture fields, a further analysis was conducted to reveal the relationship between the background dynamic and thermodynamic field changes and the wave intensity change. A significant negative correlation between the MJO-scale vertical wind shear and the MRG intensity variation suggests that the MRG wave is primarily modulated by the dynamic field. The intensity changes of the WIG and EIG waves are significantly correlated to the MJO moisture field. The Kelvin wave, which has both quasi-geostrophic and gravity wave nature, is modulated by both the MJO-scale vertical wind shear and specific humidity.

Possible impact of equatorially trapped waves on the tropical cyclone drift

The effect of equatorially trapped waves on the movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model in a beta-plane approximation. According to recent studies, equatorially trapped waves contribute to the genesis of TCs. It is thus natural to assume that these waves affect also the movement of the TC. The effect of three types of equatorially trapped waves, namely Kelvin, Rossby, and n = 0 eastward inertio-Gravity (EIG) waves, on the TC trajectory is investigated with a focus on the sensitivity on some key physical parameters such as the wavenumber and wavespeed. Using a simple barotropic model forced by a prescribed baroclinic flow, the barotropic response to equatorially trapped waves is simulated for a period of 50 days, under various wave parameter configurations. This response is then used as a background flow where TC’s can evolve and propagate. TC-like flows are injected into this wavefield background at arbitrary times during the simulation, and the TC trajectories are tracked and recorded for 48h after the injection time. The resulting TC trajectory patterns with respect to the injection times and wave parameters appear to be stochastic and the mean paths and the associated standard deviations are calculated and reported here. The statistics are different for different wave types. Kelvin waves make shorter length of TC trajectories and small divergence of direction. On the contrary, Rossby waves cause rather dramatic changes in the TC path and yield longer trajectories. Meanwhile, TCs in EIG waves maintain fairly the same direction and typically have longer trajectories though less dramatic. A robustness test using a random forcing instead has also been conducted.

A Systematic Comparison of Tropical Waves over Northern Africa. Part II: Dynamics and Thermodynamics

AbstractThis study presents the first systematic comparison of the dynamics and thermodynamics associated with all major tropical wave types causing rainfall modulation over northern tropical Africa: the Madden–Julian oscillation (MJO), equatorial Rossby waves (ERs), tropical disturbances (TDs, including African easterly waves), Kelvin waves, mixed Rossby–gravity waves (MRGs), and eastward inertio-gravity waves (EIGs). Reanalysis and radiosonde data were analyzed for the period 1981–2013 based on space–time filtering of outgoing longwave radiation. The identified circulation patterns are largely consistent with theory. The slow modes, MJO and ER, mainly impact precipitable water, whereas the faster TDs, Kelvin waves, and MRGs primarily modulate moisture convergence. Monsoonal inflow intensifies during wet phases of the MJO, ERs, and MRGs, associated with a northward shift of the intertropical discontinuity for MJO and ERs. This study reveals that MRGs over Africa have a distinct dynamical structure that differs significantly from AEWs. During passages of vertically tilted imbalanced wave modes, such as the MJO, TDs, Kelvin waves, and partly MRG waves, increased vertical wind shear and improved conditions for up- and downdrafts facilitate the organization of mesoscale convective systems. The balanced ERs are not tilted, and rainfall is triggered by large-scale moistening and stratiform lifting. The MJO and ERs interact with intraseasonal variations of the Indian monsoon and extratropical Rossby wave trains. The latter causes a trough over the Atlas Mountains associated with a tropical plume and rainfall over the Sahara. The presented results unveil which dynamical processes need to be modeled realistically to represent the coupling between tropical waves and rainfall in northern tropical Africa.

A Systematic Comparison of Tropical Waves over Northern Africa. Part I: Influence on Rainfall

Abstract Low-latitude rainfall variability on the daily to intraseasonal time scale is often related to tropical waves, including convectively coupled equatorial waves, the Madden–Julian oscillation (MJO), and tropical disturbances (TDs). Despite the importance of rainfall variability for vulnerable societies in tropical Africa, the relative influence of tropical waves for this region is largely unknown. This article presents the first systematic comparison of the impact of six wave types on precipitation over northern tropical Africa during the transition and full monsoon seasons, using two satellite products and a dense rain gauge network. Composites of rainfall anomalies in the different datasets show comparable modulation intensities in the West Sahel and at the Guinea Coast, varying from less than 2 to above 7 mm day−1 depending on the wave type. African easterly waves (AEWs) and Kelvin waves dominate the 3-hourly to daily time scale and explain 10%–30% locally. On longer time scales (7–20 days), only the MJO and equatorial Rossby (ER) waves remain as modulating factors and explain about up to one-third of rainfall variability. Eastward inertio-gravity waves and mixed Rossby–gravity (MRG) waves are comparatively unimportant. An analysis of wave superposition shows that low-frequency waves (MJO, ER) in their wet phase amplify the activity of high-frequency waves (TD, MRG) and suppress them in the dry phase. The results stress that more attention should be paid to tropical waves when forecasting rainfall over northern tropical Africa.

The Relationship between Equatorial Mixed Rossby–Gravity and Eastward Inertio-Gravity Waves. Part I

Abstract The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature Tb and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection. Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered Tb isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric Tb signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the Tb patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.

The Relationship between Equatorial Mixed Rossby–Gravity and Eastward Inertio-Gravity Waves. Part II

Abstract Space–time spectral analysis of tropical cloudiness data shows strong evidence that convectively coupled n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) occur primarily within the western/central Pacific Ocean. Spectral filtering also shows that MRG and EIG cloudiness patterns are antisymmetric with respect to the equator, and they propagate coherently toward the west and east, respectively, with periods between 3 and 5 days, in agreement with Matsuno’s linear shallow-water theory. In contrast to the spectral approach, in a companion paper it has been shown that empirical orthogonal functions (EOFs) of 2–6-day-filtered cloudiness data within the tropical Pacific Ocean also suggest an antisymmetric pattern, but with the leading EOFs implying a zonally standing but poleward-propagating oscillation, along with the associated tropospheric flow moving to the west. In the present paper, these two views are reconciled by applying an independent approach based on a tracking method to assess tropical convection organization. It is shown that, on average, two-thirds of MRG and EIG events develop independently of one another, and one-third of the events overlap in space and time. This analysis also verifies that MRG and EIG cloudiness fields tend to propagate meridionally away from the equator. It is demonstrated that the lack of zonal propagation implied from the EOF analysis is likely due to the interference between eastward- and westward-propagating disturbances. In addition, it is shown that the westward-propagating circulation associated with the leading EOF is consistent with the expected theoretical behavior of an interference between MRGs and EIGs.

A Systematic Relationship between the Representations of Convectively Coupled Equatorial Wave Activity and the Madden–Julian Oscillation in Climate Model Simulations

Abstract The relationship between a model’s performance in simulating the Madden–Julian oscillation (MJO) and convectively coupled equatorial wave (CCEW) activity during wintertime is examined by analyzing precipitation from 26 general circulation models (GCMs) participating in the MJO Task Force/Global Energy and Water Cycle Experiment (GEWEX) Atmospheric System Study (GASS) MJO model intercomparison project as well as observations based on the Tropical Rainfall Measuring Mission (TRMM). A model’s performance in simulating the MJO is determined by how faithfully it reproduces the eastward propagation of the large-scale intraseasonal variability (ISV) compared to TRMM observations. Results suggest that models that simulate a better MJO tend to 1) have higher fractional variances for various high-frequency wave modes (Kelvin, mixed Rossby–gravity, and westward and eastward inertio-gravity waves), which are defined by the ratios of wave variances of specific wave modes to the “total” variance, and 2) exhibit stronger CCEW variances in association with the eastward-propagating ISV precipitation anomalies for these high-frequency wave modes. The former result is illustrative of an alleviation in the good MJO models of the widely reported GCM deficiency in simulating the correct distribution of variance in tropical convection [i.e., typically too weak (strong) variance in the high- (low-) frequency spectrum of the precipitation]. The latter suggests better coherence and stronger interactions between these aforementioned high-frequency CCEWs and the ISV envelope in good MJO models. Both factors likely contribute to the improved simulation of the MJO in a GCM.

MJO and Convectively Coupled Equatorial Waves Simulated by CMIP5 Climate Models

Abstract This study evaluates the simulation of the Madden–Julian oscillation (MJO) and convectively coupled equatorial waves (CCEWs) in 20 models from the Coupled Model Intercomparison Project (CMIP) phase 5 (CMIP5) in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) and compares the results with the simulation of CMIP phase 3 (CMIP3) models in the IPCC Fourth Assessment Report (AR4). The results show that the CMIP5 models exhibit an overall improvement over the CMIP3 models in the simulation of tropical intraseasonal variability, especially the MJO and several CCEWs. The CMIP5 models generally produce larger total intraseasonal (2–128 day) variance of precipitation than the CMIP3 models, as well as larger variances of Kelvin, equatorial Rossby (ER), and eastward inertio-gravity (EIG) waves. Nearly all models have signals of the CCEWs, with Kelvin and mixed Rossby–gravity (MRG) and EIG waves being especially prominent. The phase speeds, as scaled to equivalent depths, are close to the observed value in 10 of the 20 models, suggesting that these models produce sufficient reduction in their effective static stability by diabatic heating. The CMIP5 models generally produce larger MJO variance than the CMIP3 models, as well as a more realistic ratio between the variance of the eastward MJO and that of its westward counterpart. About one-third of the CMIP5 models generate the spectral peak of MJO precipitation between 30 and 70 days; however, the model MJO period tends to be longer than observations as part of an overreddened spectrum, which in turn is associated with too strong persistence of equatorial precipitation. Only one of the 20 models is able to simulate a realistic eastward propagation of the MJO.

Performance of the HOMME dynamical core in the aqua-planet configuration of NCAR CAM4: equatorial waves

Abstract. A new atmospheric dynamical core, named the High Order Method Modeling Environment (HOMME), has been recently included in the NCAR-Community Climate System Model version 4 (CCSM4). It is a petascale capable high-order element-based conservative dynamical core developed on a cubed-sphere grid. We have examined the model simulations with HOMME using the aqua-planet mode of CAM4 (atmospheric component of CCSM4) and evaluated its performance in simulating the equatorial waves, considered a crucial element of climate variability. For this we compared the results with two other established models in CAM4 framework, which are the finite-volume (FV) and Eulerian spectral (EUL) dynamical cores. Although the gross features seem to be comparable, important differences have been found among the three dynamical cores. The phase speed of Kelvin waves in HOMME is faster and more satisfactory than those in FV and EUL. The higher phase speed is attributed to an increased large-scale precipitation in the upper troposphere and a more top-heavy heating structure. The variance of the n=1 equatorial Rossby waves is underestimated by all three of them, but comparatively HOMME simulations are more reasonable. For the n=0 eastward inertio-gravity waves, the variances are weak and phase speeds are too slow, scaled to shallow equivalent depths. However, the variance in HOMME is relatively more compared to the two other dynamical cores. The mixed Rossby-gravity waves are feeble in all the three cases. In summary, model simulations using HOMME are reasonably good, with some improvement relative to FV and EUL in capturing some of the important characteristics associated with equatorial waves.

Coupling mechanisms between equatorial waves and cumulus convection in an AGCM

In this study, we focused on the difference in appearances of the convectively coupled equatorial waves (CCEWs) in a simulation with the CCSR/NIES/FRCGC AGCM, between two experiments, one with and the other without implementation of the convective suppression scheme (CSS) in the prognostic Arakawa–Schubert cumulus parameterization. Realistic CCEW modes, i.e., Kelvin, Rossby, mixed Rossby-gravity (MRG), and n = 0 eastward inertio-gravity (EIG) wave modes, were reproduced in the with-CSS experiment, while only Rossby-wave-like signals appeared in the without-CSS experiment. By comparing the structures of the Kelvin wave mode and the Rossby wave mode in two runs, it was suggested that the structural difference between these two modes in conjunction with the difference in the controlling factor of cumulus convection determines the CCEW features. The CSS implemented here is such that cumulus convection is suppressed until the cloud-layer-averaged relative humidity exceeds the threshold of 80%. In the without-CSS model, only Rossby wave modes are coupled with the convection. This is because CAPE controls cumulus convection in this model, and the larger frictional convergence of Rossby wave mode prepares CAPE to generate favorable condition for cumulus convection. In the case of the with-CSS model, on the other hand, cumulus convection is largely controlled by the humidity in the free atmosphere. The convergence associated with the equatorial waves can produce the moisture anomaly to overcome the relative humidity threshold, and maintains the favorable condition for cumulus convection once it starts. In this case, not only Rossby waves but also Kelvin, MRG, and n = 0 EIG waves are reproduced more realistically. It is suggested that inclusion of some kind of mechanism connecting the free tropospheric moisture with the convection under the condition of abundant convective available potential energy could be a key factor for realistic coupling between large-scale atmospheric waves and convection.

Tropical Intraseasonal Variability in 14 IPCC AR4 Climate Models. Part I: Convective Signals

Abstract This study evaluates the tropical intraseasonal variability, especially the fidelity of Madden–Julian oscillation (MJO) simulations, in 14 coupled general circulation models (GCMs) participating in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). Eight years of daily precipitation from each model’s twentieth-century climate simulation are analyzed and compared with daily satellite-retrieved precipitation. Space–time spectral analysis is used to obtain the variance and phase speed of dominant convectively coupled equatorial waves, including the MJO, Kelvin, equatorial Rossby (ER), mixed Rossby–gravity (MRG), and eastward inertio–gravity (EIG) and westward inertio–gravity (WIG) waves. The variance and propagation of the MJO, defined as the eastward wavenumbers 1–6, 30–70-day mode, are examined in detail. The results show that current state-of-the-art GCMs still have significant problems and display a wide range of skill in simulating the tropical intraseasonal variability. The total intraseasonal (2–128 day) variance of precipitation is too weak in most of the models. About half of the models have signals of convectively coupled equatorial waves, with Kelvin and MRG–EIG waves especially prominent. However, the variances are generally too weak for all wave modes except the EIG wave, and the phase speeds are generally too fast, being scaled to excessively deep equivalent depths. An interesting result is that this scaling is consistent within a given model across modes, in that both the symmetric and antisymmetric modes scale similarly to a certain equivalent depth. Excessively deep equivalent depths suggest that these models may not have a large enough reduction in their “effective static stability” by diabatic heating. The MJO variance approaches the observed value in only 2 of the 14 models, but is less than half of the observed value in the other 12 models. The ratio between the eastward MJO variance and the variance of its westward counterpart is too small in most of the models, which is consistent with the lack of highly coherent eastward propagation of the MJO in many models. Moreover, the MJO variance in 13 of the 14 models does not come from a pronounced spectral peak, but usually comes from part of an overreddened spectrum, which in turn is associated with too strong persistence of equatorial precipitation. The two models that arguably do best at simulating the MJO are the only ones having convective closures/triggers linked in some way to moisture convergence.

Genesis of Intraseasonal Oscillations and Equatorial Waves

Abstract The particular role of evaporation–wind feedback, and as well cumulus convection and dissipation, in the formation of the Madden–Julian 30–60-day intraseasonal oscillation (MJO) and equatorially trapped waves, including Kelvin, equatorial Rossby, mixed Rossby–gravity, and eastward inertio-gravity waves, has been studied using a global two-level primitive equation instability model. The evaporation has been specified through a bulk aerodynamic formula, and the convection through a generalized Kuo-type parameterization with a moist static stability that is positive everywhere so that wave-conditional instability of the second kind (CISK) is not possible. Both three-dimensional and zonally averaged basic states for January 1979 have been employed, and the e-folding times, periods, structures, and propagation characteristics of these waves have been analyzed and compared with their observed properties. The MJO modes appear to be particularly realistic when the three-dimensional basic state includes e...