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Abstract There are different strategies for training neural networks (NNs) as subgrid‐scale parameterizations. Here, we use a 1D model of the quasi‐biennial oscillation (QBO) and gravity wave (GW) parameterizations as testbeds. A 12‐layer convolutional NN that predicts GW forcings for given wind profiles, when trained offline in abig‐dataregime (100‐year), produces realistic QBOs once coupled to the 1D model. In contrast, offline training of this NN in asmall‐dataregime (18‐month) yields unrealistic QBOs. However, online re‐training of just two layers of this NN using ensemble Kalman inversion and only time‐averaged QBO statistics leads to parameterizations that yield realistic QBOs. Fourier analysis of these three NNs' kernels suggests why/how re‐training works and reveals that these NNs primarily learn low‐pass, high‐pass, and a combination of band‐pass filters, potentially related to the local and non‐local dynamics in GW propagation and dissipation. These findings/strategies generally apply to data‐driven parameterizations of other climate processes. 

Abstract The Quasi‐Biennial Oscillation (QBO) dominates the interannual variability in the tropical lower stratosphere and is characterized by the descent of alternating easterly and westerly zonal winds. The QBO impact on tropical clouds and convection has received great attention in recent years due to its implications for weather and climate. In this study, a 15‐year record of high vertical resolution cloud observations from CALIPSO and a 50 hPa zonal wind QBO index from ERA5 are used to document the QBO impact on equatorial (10°S–10°N) clouds. Observations from radio occultations, the CERES instrument, and the ERA5 reanalysis are also used to document the QBO impact on temperature, cloud radiative effect (CRE), and zonal wind, respectively. It is shown that the QBO impact on zonal mean equatorial cloud fraction has a strong seasonality. The strongest cloud fraction response to the QBO occurs in boreal spring and early summer, which extends from above the mean tropopause to ∼12.5 km and results in a significant longwave CRE anomaly of 1 W/m². The seasonality of the QBO impact on cloud fraction is synchronized with the QBO impacts on temperature and zonal wind in the tropical upper troposphere. 

Abstract The ERA5 reanalysis with hourly time steps and ∼30 km horizontal resolution resolves a substantially larger fraction of the gravity wave spectrum than its predecessors. Based on a representation of the two-sided zonal wavenumber–frequency spectrum, we show evidence of gravity wave signatures in a suite of atmospheric fields. Cross-spectrum analysis reveals (i) a substantial upward flux of geopotential for both eastward- and westward-propagating waves, (ii) an upward flux of westerly momentum in eastward-propagating waves and easterly momentum in westward-propagating waves, and (iii) anticyclonic rotation of the wind vector with time—all characteristics of vertically propagating gravity and inertio-gravity waves. Two-sided meridional wavenumber–frequency spectra, which are computed along individual meridians and then zonally averaged, exhibit characteristics similar to the spectra computed on latitude circles, indicating that these waves propagate in all directions. The three-dimensional structure of these waves is also documented in composites of the temperature field relative to grid-resolved, wave-induced downwelling events at individual reference grid points along the equator. It is shown that the waves radiate outward and upward relative to the respective reference grid points, and their amplitude decreases rapidly with time. Within the broad continuum of gravity wave phase speeds there are preferred values around ±49 and ±23 m s⁻¹, the former associated with the first baroclinic mode in which the vertical velocity perturbations are of the same sign throughout the depth of the troposphere, and the latter with the second mode in which they are of opposing polarity in the lower and upper troposphere. 

Abstract This paper describes stratospheric waves in ERA5 and evaluates the contributions of different types of waves to the driving of the quasi-biennial oscillation (QBO). Because of its higher spatial resolution compared to its predecessors, ERA5 is capable of resolving a broader spectrum of waves. It is shown that the resolved waves contribute to both eastward and westward accelerations near the equator, mainly by the way of the vertical flux of zonal momentum. The eastward accelerations by the resolved waves are mainly due to Kelvin waves and small-scale gravity (SSG) waves with zonal wavelengths smaller than 2000 km, whereas the westward accelerations are forced mainly by SSG waves, with smaller contributions from inertio-gravity and mixed Rossby–gravity waves. Extratropical Rossby waves disperse upward and equatorward into the tropical region and impart a westward acceleration to the zonal flow. They appear to be responsible for at least some of the irregularities in the QBO cycle. 

Abstract The dynamics and momentum budget of the quasi-biennial oscillation (QBO) are examined in ERA5. Because of ERA5’s higher spatial resolution compared to its predecessors, it is capable of resolving a broader spectrum of atmospheric waves and allows for a better representation of the wave–mean flow interactions, both of which are of crucial importance for QBO studies. It is shown that the QBO-induced mean meridional circulation, which is mainly confined to the winter hemisphere, is strong enough to interrupt the tropical upwelling during the descent of the westerly shear zones. Since the momentum advection tends to damp the QBO, the wave forcing is responsible for both the downward propagation and for the maintenance of the QBO. It is shown that half the required wave forcing is provided by resolved waves during the descent of both westerly and easterly regimes. Planetary-scale waves account for most of the resolved wave forcing of the descent of westerly shear zones and small-scale gravity (SSG) waves with wavelengths shorter than 2000 km account for the remainder. SSG waves account for most of the resolved forcing of the descent of the easterly shear zones. The representation of the mean fields in the QBO is very similar in ERA5 and ERA-Interim but the resolved wave forcing is substantially stronger in ERA5. The contributions of the various equatorially trapped wave modes to the QBO forcing are documented in Part II. 

The quasi-biennial oscillation (QBO) and sudden stratospheric warmings (SSWs) during the Last Glacial Maximum (LGM) are investigated in simulations using the Whole Atmosphere Community Climate Model version 6 (WACCM6). We find that the period of QBO, which is 27 months in the preindustrial and modern climate simulations, was 33 months in the LGM simulation using the proxy sea surface temperatures (SSTs) and 41 months using the model-based LGM SSTs. We show that the longer QBO period in the LGM is due to weaker wave forcing. The WACCM6 simulations of the LGM, preindustrial, and modern climates do not support previous modeling work that suggests that the QBO amplitude is smaller (larger) in a warmer (colder) climate. We find that SSWs in the LGM occurred later in the year, as compared to the preindustrial and modern climate, but that time of the final warming was similar. The difference in SSW frequency is inconclusive.