Lagrangian gravity wave spectra in the lower stratosphere of current (re)analyses

Due to their increasing spatial resolution, numerical weather prediction (NWP) models and the associated analyses resolve a growing fraction of the gravity wave (GW) spectrum. However, it is unclear how well this "resolved" part of the spectrum truly compares to the actual atmospheric variability. In particular, the Lagrangian variability, relevant, for example, to atmospheric dispersion and to microphysical modeling in the upper troposphere-lower stratosphere (UTLS), has not yet been documented in recent products. To address this shortcoming, this paper presents an assessment of the GW spectrum as a function of the intrinsic (air parcel following) frequency in recent (re)analyses (ERA-Interim, ERAS, the ECMWF operational analysis and MERRA-2). Long-duration, quasi-Lagrangian balloon observations in the equatorial and Antarctic lower stratosphere are used as a reference for the atmospheric spectrum and are compared to synthetic balloon observations along trajectories calculated using the wind and temperature fields of the reanalyses. Overall, the reanalyses represent realistic features of the spectrum, notably the spectral gap between planetary and gravity waves and a peak in horizontal kinetic energy associated with inertial waves near the Coriolis frequency f in the polar region. In the tropics, they represent the slope of the spectrum at low frequency. However, the variability is generally underestimated even in the low-frequency portion of the spectrum. In particular, the near-inertial peak, although present in the reanalyses, has a reduced magnitude compared to balloon observations. We compare the observed and modeled variabilities of temperature, zonal momentum flux and vertical wind speed, which are related to low-, mid- and high-frequency waves, respectively. The probability density function (PDF) distributions have similar shapes but show increasing disagreement with increasing intrinsic frequency. Since at those altitudes they are mainly caused by gravity waves, we also compare the geographic distribution of vertical wind fluctuations in the different products, which emphasizes the increase of both GW variance and intermittency with horizontal resolution. Finally, we quantify the fraction of resolved variability and its dependency on model resolution for the different variables. In all (re)analysis products, a significant part of the variability is still missing, especially at high frequencies, and should hence be parameterized. Among the two polar balloon datasets used, one was broadcast on the Global Telecommunication System for assimilation in NWP models, while the other consists of independent observations (unassimilated in the reanalyses). Comparing the Lagrangian spectra between the two campaigns shows that the (re)analyses are largely influenced by balloon data assimilation, which especially enhances the variance at low GW frequency.