In this study, we use measurements from over 4,735 globally distributed Global Navigation Satellite System receivers to track the progression of traveling ionospheric disturbances (TIDs) associated with the 15 January 2022 Hunga Tonga‐Hunga Ha'apai submarine volcanic eruption. We identify two distinct Large Scale traveling ionospheric disturbances (LSTIDs) and several subsequent Medium Scale traveling ionospheric disturbances (MSTIDs) that propagate radially outward from the eruption site. Within 3,000 km of epicenter, LSTIDs of >1,600 km wavelengths are initially observed propagating at speeds of ∼950 and ∼555 ms−1, before substantial slowing to ∼600 and ∼390 ms−1, respectively. MSTIDs with speeds of 200–400 ms−1 are observed for 6 hrs following eruption, the first of which comprises the dominant global ionospheric response and coincides with the atmospheric surface pressure disturbance associated with the eruption. These are the first results demonstrating the global impact of the Tonga eruption on the ionospheric state.

The accuracy of horizontal winds and temperature in the equatorial lower stratosphere is evaluated in different (re)analyses (European Centre for Medium‐Range Weather Forecasts (ECMWF) operational analysis, ERA Interim, and Modern‐Era Retrospective Analysis for Research and Applications) using an independent data set collected at low latitudes during long‐duration balloon flights in early 2010. The three analyzed wind products are found significantly less accurate than in the extratropics, with periods of ≳0.3em103.0235ptm/sdisagreement with the observations lasting several days. To highlight the dynamical context in which the major disagreement events occur, case studies are carried out. The events are shown to be related to an improper representation of large‐scale equatorial Kelvin and Yanai wave packets with vertical wavelengths smaller than 5 km. Such events can induce large errors on trajectories computed with analyzed winds relatively to the actual (balloon) trajectory: 4000 km separation after 5 days of calculation. Reasons for analyses inaccuracy are discussed. The vertical resolution of the underlying model likely plays a role, but the main factor responsible for deficiencies appears to be the lack of wind observations. Indeed, errors in analyzed winds during the campaign have a strong longitudinal structure, with root‐mean‐square errors twice as large over the Indian Ocean and western Pacific, poorly covered by radiosounding stations, as over the Maritime Continent or South America. For the ECMWF analysis, this structure mirrors that of the analysis increments, which have largest amplitudes over observed regions. We argue that the reported events are more likely to happen during maximum shear phases of the quasi‐biennial oscillation.

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.

SUMMARYThis paper seeks to represent the tropical short-range forecast error covariances of the European Centre for Medium-Range Weather Forecasts (ECMWF) model in terms of equatorial waves. The motivation for undertaking this investigation is increasing observational evidence indicating that a substantial fraction of the tropical largescale variability can be explained by equatorially trapped wave solutions known from shallow-water theory. Shortrange forecast differences from a data-assimilation ensemble were taken to serve as a proxy for background errors.It was found that the equatorial waves coupled to convection can explain on average 60-70% of the error variance in the tropical free atmosphere. The largest part of this explained variance is represented by the equatorial Rossby (ER) modes, and a significant percentage pertains to the equatorial inertio-gravity (EIG) modes. Eastwardpropagating EIG modes have maximum variance in the stratosphere, where the short-wave variance in westwardmoving waves is particularly small. This feature is most likely related to the phase of the quasi-biennial oscillation during the study period, suggesting that significant temporal variations could be present in longer-term time series of such statistics.The vertical correlations for ER modes display characteristics similar to those of their extratropical counterparts: correlations narrow towards shorter scales and in the stratosphere. However, the present statistics do not display the significant increase with altitude of the horizontal correlation scale for the height field which is typical for global, quasi-geostrophic statistics commonly used in current data-assimilation schemes. Furthermore, tropospheric ER correlations are vertically asymmetric and deeper for the n = 1 mode than for higher modes. Most likely, deep convection, acting as a generator of equatorial wave motion, is the dominant mechanism underlying these results.In spite of its relatively small contribution to the tropospheric variance, the Kelvin-wave coupling plays a decisive role for determining the characteristics of the horizontal correlation near the equator. EIG modes also play an important role for the tropical mass-wind coupling; these waves have a major impact by reducing the meridional correlation scales and the magnitudes of the balanced height-field increments.

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-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)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(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.