Inertio Gravity Research Articles

Modal Decomposition of the Global Response to Tropical Heating Perturbations Resembling MJO

Abstract The paper presents four ensembles of numerical experiments that compare the response to monopole and dipole heating perturbations resembling different phases of the Madden–Julian oscillation (MJO). The results quantify the Rossby and inertio-gravity (IG) wave response using the normal-mode function decomposition. The day 3 response is characterized by about 60% variance in the IG modes, with about 85% of it belonging to the Kelvin waves. On day 14, only 10% of the response variance is due to the Kelvin waves. Although the n = 1 Rossby mode is the main contributor to the Rossby variance at all time scales, the n > 1 Rossby modes contribute over 50% of the balanced response to the MJO heating. In the short range, dipole perturbations produce a response with the maximal variance in zonal wavenumbers k = 2–3 whereas in the medium range the response maximizes at k = 1 in all experiments. Furthermore, the medium-range response to the heating perturbation mimicking MJO phase 6 is found also over Europe.

Systematic decomposition of the MJO and its Northern Hemispheric extratropical response into Rossby and inertio‐gravity components

The Madden–Julian Oscillation (MJO) is the dominant form of intraseasonal variability in the Tropics. The MJO is a complex convectively coupled phenomenon, which is still poorly represented in the current generation of climate models, and our understanding of its essential dynamics and its influence on the midlatitude circulation is still incomplete. Here, we use a normal‐mode decomposition method to decompose the MJO systematically into Kelvin, inertio‐gravity (IG), and Rossby‐wave components in the ERA‐Interim reanalysis data for the period 1980–2015 to provide a climatology of the eight MJO phases for the Kelvin, IG, and Rossby‐wave components.Our analysis shows that the Rossby modes provide a larger contribution to the magnitude of the MJO in terms of geopotential height and winds than the Kelvin wave and IG modes. Moreover, the kinetic energy associated with the Rossby modes of the MJO accounts for about 93% of the kinetic energy. Our decomposition also shows that the Kelvin wave is the dominant mode in the unbalanced wave part, which is flanked by Rossby waves on both sides of the Equator, consistent with previous studies. The extratropical response to the MJO also consists of both IG and Rossby‐wave components in the Northern Hemisphere (NH). The midlatitude MJO response is also linked to well‐known teleconnection patterns like the North Atlantic Oscillation and the Pacific–North American pattern. The transient NH atmospheric response is fast, of the order of 5–7 days. While the extratropical response is dominated by Rossby waves, IG waves also show a prominent response in the NH.

Estimating Subseasonal Variability and Trends in Global Atmosphere Using Reanalysis Data.

A new measure of subseasonal variability is introduced that provides a scale‐dependent estimation of vertically and meridionally integrated atmospheric variability in terms of the normal modes of linearized primitive equations. Applied to the ERA‐Interim data, the new measure shows that subseasonal variability decreases for larger zonal wave numbers. Most of variability is due to balanced (Rossby mode) dynamics but the portion associated with the inertio‐gravity (IG) modes increases as the scale reduces. Time series of globally integrated variability anomalies in ERA‐Interim show an increase in variability after year 2000. In recent years the anomalies have been about 2% above the 1981–2010 average. The relative increase in variability projecting on the IG modes is larger and more persistent than for the Rossby modes. Although the IG part is a small component of the subseasonal variability, it is an important effect likely reflecting the observed increase in the tropical precipitation variability.

Indonesian rainfall variability during Western North Pacific and Australian monsoon phase related to convectively coupled equatorial waves

The Indonesian archipelago which has over 15,000 islands, lies in the tropics between Asia and Australia. This eventually alters the rainfall variability over the region, which was influenced by the Asian-Australian monsoon and controlled by intraseasonal variabilities such as convectively coupled equatorial waves (CCEW), i.e., Kelvin, n = 1 equatorial Rossby (ER), mixed Rossby gravity (MRG), and n = 1 Westward inertio gravity (WIG), including the Madden–Julian Oscillation (MJO). This study examines a 15-year 3B42 data for trapping CCEW and MJO in the region of Indonesia during both active and extreme Western North Pacific (WNP) and Australian (AU) monsoon phases, which are then compared with 30-year rainfall anomalies among 38 synoptic stations over Indonesia. The space–time spectral analysis is employed to filter each wave including the MJO in the equator, then proceeding with the empirical orthogonal function (EOF) method to seek each wave peak which then coincides with WNP and AU monsoon peaks over Indonesia. It is concluded that an extreme monsoon classification has proven to control rainfall activity related to the CCEW and MJO at 60.66% during December through February (DJF)-WNP for only the significant wave perturbation value. Meanwhile, the CCEW and MJO significantly increase/decrease precipitation at Day 0 for about 37.88% from the total of Day 1st to Day end. Although the contribution of the CCEW and MJO does not profoundly influence rainfall activity during monsoon phase over Indonesia, they still modulate weather condition for more than 50%. On the other hand, a complex topography with a number of land–sea complexities is capable of influencing the rainfall variability in the region as a negative relationship is associated with the CCEW and MJO either during DJF-WNP or July through August (JAS)-AU monsoon phase.

A Three-Dimensional Multivariate Modal Analysis of Atmospheric Predictability with Application to the ECMWF Ensemble

Abstract A new methodology for the analysis of ensemble prediction systems (ENSs) is presented and applied to 1 month (December 2014) of ECMWF operational ensemble forecasts. The method relies on the decomposition of the global three-dimensional wind and geopotential fields onto the normal-mode functions. The ensemble properties are quantified in terms of the 50-member ensemble spread associated with the balanced and inertio-gravity (IG) modes for forecast ranges every 12 h up to 7 days. Ensemble reliability is defined for the balanced and IG modes comparing the ensemble spread with the control analysis in each scale. Modal analysis shows that initial uncertainties in the ECMWF ENS are largest in the tropical large-scale modes and their spatial distribution is similar to the distribution of the short-range forecast errors. Initially the ensemble spread grows most in the smallest scales and in the synoptic range of the IG modes but the overall growth is dominated by the increase of spread in balanced modes in synoptic and planetary scales in the midlatitudes. During the forecasts, the distribution of spread in the balanced and IG modes grows toward the climatological spread distribution characteristic of the analyses. In the 2-day forecast range, the global IG spread reaches 60% of its asymptotic value while the same percentage of the global balanced spread is reached after 5 days of forecasts. An underdispersiveness of the system is suggested to be associated with the lack of tropical variability, primarily the Kelvin waves.

Systematic decomposition of the Madden‐Julian Oscillation into balanced and inertio‐gravity components

AbstractWe present a new method for the three‐dimensional multivariate decomposition of the Madden‐Julian Oscillation (MJO) into balanced and inertio‐gravity (IG) components. The method analyzes global fields with no filtering involved, and it provides a quantitative comparison between the contribution of the Rossby, Kelvin, and other balanced and IG modes to the MJO circulation and its teleconnections. Results based on the ERA Interim reanalysis data and the multivariate MJO index show that the Rossby mode with the lowest meridional index is the largest contributor to the MJO circulation over the Pacific. A smaller role of the Kelvin mode is diagnosed over the Indian Ocean and the maritime continent. The MJO teleconnections in the polar stratosphere appear associated with the leading balanced vertical modes. The presented method shows new ways of evaluating the MJO structure and its global impacts in weather and climate models.

Normal-mode function representation of global 3-D data sets: open-access software for the atmospheric research community

Abstract. This article presents new software for the analysis of global dynamical fields in (re)analyses, weather forecasts and climate models. A new diagnostic tool, developed within the MODES project, allows one to diagnose properties of balanced and inertio-gravity (IG) circulations across many scales. In particular, the IG spectrum, which has only recently become observable, can be studied simultaneously in the mass and wind fields while considering the whole model depth in contrast to the majority of studies. The paper includes the theory of normal-mode function (NMF) expansion, technical details of the Fortran 90 code, examples of namelists which control the software execution and outputs of the software application on the ERA Interim reanalysis data set. The applied libraries and default compiler are from the open-source domain. A limited understanding of Fortran suffices for the successful implementation of the software. The presented application of the software to the ERA Interim data set reveals several aspects of the large-scale circulation after it has been partitioned into the linearly balanced and IG components. The global energy distribution is dominated by the balanced energy while the IG modes contribute around 10% of the total wave energy. However, on sub-synoptic scales, IG energy dominates and it is associated with the main features of tropical variability on all scales. The presented energy distribution and features of the zonally averaged and equatorial circulation provide a reference for the validation of climate models.

Contributions of equatorial wave modes and parameterized gravity waves to the tropical QBO in HadGEM2

AbstractThe contributions of the equatorial waves to the quasi‐biennial oscillation (QBO) are investigated using Hadley Centre Global Environment Model version 2 (HadGEM2). A gravity wave parameterization that couples its source spectrum to the convection is used. The equatorial wave modes are identified in the spectral domain, based on their distinct characteristics associated with momentum and heat fluxes. The Kelvin waves and parameterized gravity waves (PGWs) transport westerly momentum into the equatorial stratosphere by ∼0.35 and 0.8 mPa, respectively, while easterly momentum is carried primarily by the PGWs (∼0.75 mPa). The resolved inertio‐gravity (IG) waves transport both easterly and westerly momentum by ∼0.2 mPa. In the lowermost stratosphere, gradual dissipation of the Kelvin waves occurs, and the remaining waves induce eastward forcing in the westerly shear layer by 3–5 m s−1 month−1. The PGWs primarily dissipate within the sheared layer and provide large easterly and westerly forcing in the middle stratosphere (∼17 m s−1 month−1), while the forcing in the lower stratosphere is comparable to the Kelvin wave forcing. The IG wave forcing is small because of the small wave dissipation rate. The Rossby and mixed Rossby‐gravity (MRG) waves contribute to the westerly‐to‐easterly QBO transition by ∼2 m s−1 month−1. The magnitudes of the simulated Kelvin and Rossby wave forcings are comparable with the Modern‐Era Retrospective Analysis for Research and Applications, whereas the MRG and IG wave forcings are underestimated in the lower stratosphere. Differences between the simulation and reanalysis and the uncertainties in both are discussed.

Balance properties of the short‐range forecast errors in the ECMWF 4D‐Var ensemble

AbstractIn this paper the normal‐mode function framework is applied to the representation of time‐averaged structure of short‐term forecast error variances in the 20‐member ensemble based on the 4D‐Var assimilation system of ECMWF. The applied methodology provides an attractive way to measure the balance by splitting forecast error variances into parts projecting on the balanced and inertio‐gravity (IG) circulations; the approach is particularly suitable for the Tropics, where IG circulation dominates on all scales.A little over 50% of the global forecast error variance at short range is balanced. The component of the variance associated with eastward IG modes dominates over the westward IG modes on all zonal scales but the difference gets larger as the zonal wave number increases. There is a major difference in the vertical variance distribution between the balanced and IG modes. A large part of the balanced variance projects on to the barotropic structure in the troposphere, while the IG variances are found in vertical modes that have equatorially trapped horizontal structures corresponding to equivalent depths between a few tens and few hundred metres. The variance growth between 3 h and 12 h range is substantially different in the balanced, eastward and westward IG modes. The balanced variance growth dominates whereas the variance growth in the westerly IG modes is small. In the eastward IG modes, the variance growth is most significant in the large‐scale equatorial Kelvin mode.

Impact of the Vertical Resolution of Analysis Data on the Estimates of Large-Scale Inertio-Gravity Energy

AbstractThis paper deals with the large-scale inertio-gravity (IG) wave energy in the operational ECMWF analyses in July 2007. Energy percentages of the IG waves obtained from the standard-pressure-level data are compared to those derived from various discretizations of the model-level data. The results show a small albeit systematic increase of the IG energy percentage as the vertical level density increases from the standard-pressure levels toward the model-level density; the small relative change is explained by the sufficient vertical resolution to resolve the large-scale IG waves in the tropics that make the majority of the global IG energy on large scales. A relatively larger increase of the IG energy is obtained when the mesospheric model levels are included; however, the analyses at these levels in July 2007 are less reliable. Furthermore, two numerical methods for the normal-mode function (NMF) decomposition are shown to provide similar results. The decomposition of atmospheric analyses into the NMF series is proposed as a tool to analyze the spatial and temporal variations of the large-scale equatorial waves and their role in global energetics.

An Assessment of MJO and Tropical Waves Simulated by Different Versions of the GAMIL Model

Simulated outgoing longwave radiation (OLR) outputs by two versions of the grid-point atmospheric general circulation model (GAMIL) were analyzed to assess the influences of improvements in cloud micro- physics and convective parameterization schemes on the simulation of the Madden-Julian oscillation (MJO) and other tropical waves. The wavenumber-frequency spectral analysis was applied to isolate dominant modes of con- vectively coupled equatorial waves, including the MJO, Kelvin, equatorial Rossby (ER), mixed Rossby-gravity (MRG), and inertio-gravity (IG) waves. The performances of different versions of the GAMIL model (version 1.0 (GAMIL1.0) and version 2.0 (GAMIL2.0)) were evalu- ated by comparing the power spectrum distributions of these waves among GAMIL1.0, GAMIL2.0, and observa- tional data. GAMIL1.0 shows a weak MJO signal, with the maximum variability occurring separately at wavenumbers 1 and 4 rather than being concentrated on wavenumbers 1-3, suggesting that GAMIL1.0 could not effectively capture the intraseasonal variability. However, GAMIL2.0 is able to effectively reproduce both the symmetric and anti-symmetric waves, and the significant spectra of the MJO, Kelvin, and MRG waves are in agreement with observational data, indicating that the ability of GAMIL2.0 to simulate the MJO and other tropical waves is enhanced by improving the cloud mi- crophysics and convective parameterization schemes and implying that such improvements are crucial to further improving this model's performance.  Keywords: GAMIL model, MJO, tropical waves Citation: Mao, J.-Y., and L.-J. Li, 2012: An assessment of MJO and tropical waves simulated by different ver- sions of the GAMIL model, Atmos. Oceanic Sci. Lett., 5, 26-31.

Balance of the Background-Error Variances in the Ensemble Assimilation System DART/CAM

Abstract This paper quantifies the linear mass–wind field balance and its temporal variability in the global data assimilation system Data Assimilation Research Testbed/Community Atmosphere Model (DART/CAM), which is based on the ensemble adjustment Kalman filter. The part of the model state that projects onto quasigeostrophic modes represents the balanced state. The unbalanced part corresponds to inertio-gravity (IG) motions. The 80-member ensemble is diagnosed by using the normal-mode function expansion. It was found that the balanced variance in the prior ensemble is on average about 90% of the total variance and about 80% of the wave variance. Balance depends on the scale and the largest zonal scales are best balanced. For zonal wavenumbers greater than k = 30 the balanced variance stays at about the 45% level. There is more variance in the westward- than in the eastward-propagating IG modes; the difference is about 2% of the total wave variance and it is associated with the covariance inflation. The applied inflation field has a major impact on the structure of the prior variance field and its reduction by the assimilation step. The shape of the inflation field mimics the global radiosonde observation network (k = 2), which is associated with the minimum variance reduction in k = 2. Temporal variability of the ensemble variance is significant and appears to be associated with changes in the energy of the flow. A perfect-model assimilation experiment supports the findings from the real-observation experiment.

Why do 2-day waves propagate westward?

In observations, the 2-day waves, identified as the convectively coupled equatorial inertio-gravity (IG) waves, only propagate westward. To understand this feature, a simple theoretical model is presented for the convectively coupled equatorial waves (CCEWs). Under the assumption that the convective heating is proportional to the vertical velocity on the first baroclinic mode, the nonlinear governing equation for the meridional velocity of the CCEWs can be derived. The optimal method is used to obtain the dispersion relation from this nonlinear equation, and the results show that the deep convection can slow down the IG waves by decreasing the mean state static stability, but the key leading to the westward propagation of the IG waves is the full meridional variation of the sea surface temperature (SST). The warm SST trapped near the equator excites long westward propagating IG waves, whereas the warm SST trapped near the ITCZ centered at 10° N excites short westward propagating IG waves. This theoretical model provides a simple tool to study the CCEWs in understanding the tropical circulation.

Electromagnetic inertio-gravity waves in the Earth's ionosphere

Propagation of electromagnetic inertio-gravity (IG) waves in the partially ionized ionospheric E- and F-layers is considered in the shallow water approximation. Accounting of the field-aligned current is the main novelty of the investigation. Existence of two new eigen-frequencies for fast and slow electromagnetic waves is revealed in the ionospheric E-layer. It is shown that in F-layer slowly damping new type of inertial-fast magnetosonic waves can propagate. Slowly damping low-frequency oscillations connected with the field-aligned conductivity are found. Broad spectrum of oscillations is investigated.

Studies of inertio‐gravity waves on midlatitude beta‐plane without the traditional approximation

AbstractThe role of the Rossby parameter β due to the meridional variation of the Coriolis parameter f is investigated for inertio‐gravity waves in midlatitudes based on a linear Boussinesq model without the traditional approximation, namely including the role of the horizontal component of the Coriolis vector of the Earth's rotation. Without the β‐effect, it is well established that the non‐traditional Coriolis effects give rise to an additional mode of inertio‐gravity (IG) waves whose frequencies are slightly smaller than the local Coriolis frequency f unlike the traditional IG‐mode whose frequencies are larger than f. The addition of the β‐effect modifies the properties of the sub‐inertial and super‐inertial IG‐modes. These modifications are examined by calculating the model normal modes for a given vertical profile of the buoyancy frequency N. Inclusion of the β‐effect yields the external and internal Rossby modes in addition to the IG‐modes. Presence of the external Rossby mode in this model is a new result, since it does not occur in the traditional version with β nor in the non‐traditional version without β. The normal‐mode properties, including wave frequencies and eigenfunctions, are presented for various values of N. The normal‐mode analysis is complemented by the initial‐value approach to study the evolution of waves generated by forcing. The results of numerical time‐integrations of wave generation in the ocean forced by atmospheric disturbances and by the interaction of tidal flows with bottom topography are presented to reveal a notable role of β for the IG‐waves. Application to atmospheric problems is proposed. Copyright © 2010 Royal Meteorological Society

The Effect of Tilted Rotation on Shear Instabilities at Low Stratifications

Abstract A linear stability analysis of the inviscid stratified Boussinesq equations is presented given a steady zonal flow with constant vertical shear in a tilted f plane. Full nonhydrostatic terms are included: 1) acceleration of vertical velocity and 2) Coriolis force terms arising from the meridional component of earth’s rotation vector. Calculations of growth rates, critical wavenumbers, and dominance regimes for baroclinic and symmetric instabilities are compared with results from the traditional nonhydrostatic equations, which include a strictly vertical rotation vector, as well as results from the hydrostatic equations. The authors find that for positive zonal z shear, tilted rotation enhances the dominance regime of symmetric instabilities at the expense of baroclinic instabilities and maintains symmetric instabilities at larger scales than previously indicated. Furthermore, in contrast to former studies, it is determined that hydrostatic growth rates for both instabilities are not maximal. Rather, growth rates peak in the fully nonhydrostatic equations for parameter regimes physically relevant and consistent with abyssal ocean stratifications and weak zonal z shears and oceanic measurements of the Labrador Sea and Southern Ocean. In addition, the authors find that zonal shear modifies the frequency range of subinertial inertio–gravity waves. Tilted rotation effects break the base flow shear reflection symmetry present in the traditional and hydrostatic models. Thus, only in the fully nonhydrostatic model does weak negative zonal z shear stabilize the flow and decrease the subinertial frequency range.

A gravity wave analysis near to the Andes Range from GPS radio occultation data and mesoscale numerical simulations: Two case studies

Global maps of potential wave energy per unit mass, recently performed with the Global Positioning System (GPS) Radio Occultation (RO) technique and different satellite missions (CHAMP and SAC-C since 2001, GRACE and COSMIC since 2006) revealed in Argentina, at the eastern side of the highest Andes Mountains, a considerable wave activity (WA) in comparison with other extra-tropical regions. The main gravity wave (GW) sources in this natural laboratory are deep convection (mainly during late Spring and Summer), topographic forcing and geostrophic adjustment. The mesoscale numerical WRF (Weather Research and Forecasting) 2.1.2 model was used to simulate the atmospheric parameters during two representative RO events showing apparent intense WA in this region. The significance of the relative position of the RO lines of sight, the line of tangent points and GW phase surfaces during each event is discussed in relation with the apparent WA detected. The GPS RO technique may not be by itself reliable enough to quantify and locate WA of single events. Nevertheless, it should be considered a useful tool to observe the global WA from statistical studies. We also discuss the relative contribution of high and medium intrinsic frequency mountain waves regularly observed, coexisting with inertio gravity waves, their origin and propagation characteristics.

Electromagnetic inertio-gravity waves in the ionospheric E-layer

The effect of the Ampére force on inertio-gravity (IG) waves in the partially ionized ionospheric E-layer is considered. Electromagnetic IG waves are then studied. It is shown that the free energy necessary for linear instability of electromagnetic IG waves arises from the field-aligned current. Furthermore, it is found that atmospheric vortex motions can induce substantial variations in the geomagnetic field and field-aligned currents.

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.

Asymmetric vertical internal wave propagation

Yearlong data from a single ADCP above the northern extension of the Mid‐Atlantic Ridge are used to investigate vertical internal wave propagation in the open ocean (395–1025 m). Whilst 80% of incoherent semidiurnal tidal (D2) phase propagates downward, 90% of near‐inertial (f) phase propagates upward. Most upward propagating f‐phase is found at sub‐f frequencies σmin(N = f) ≈ 0.74f < σ ≤ 0.99f, N the buoyancy frequency and σmin the lower bound of the inertio‐gravity (IG) wave band following the ‘non‐traditional approach’, which includes the horizontal component of the Earth's rotation in momentum equations. The upper bound of mostly downward propagating D2‐phase coincides with the upper IG‐bound σmax(N = f) ≈ 1.35f. The limited band [σmin, σmax] demonstrates that f and D2 contain special internal waves concerning vertical propagation. It is suggested that this is partially attributable to small‐scale step layering in N, with N = f separating ‘trapping’ from ‘classic propagating’ wave regimes, rendering the mean large‐scale N ≈ 18f less important.