2.1 Aircraft measurements of vertical wind

We analyze data from aircraft campaigns that simultaneously measured ice water content (IWC) and high-rate (sampled faster than 1 Hz) vertical wind in and above the TTL, which we define, for the purpose of this study, as the atmospheric layer between 14 and 18 km altitude and between 30^∘ N and 30^∘ S. Five NASA campaigns meet these criteria, namely the Airborne Tropical TRopopause EXperiment (ATTREX; Jensen et al., 2017) 2013 and 2014 (we treat these different years of ATTREX as two different campaigns), Pacific Oxidants, Sulfur, Ice, Dehydration, and cONvection (POSIDON), the Tropical Composition, Cloud and Climate Coupling experiment (TC4; Toon et al., 2010), and the Cirrus Regional Study of Tropical Anvils and Cirrus Layers – Florida Area Cirrus Experiment (CRYSTAL-FACE; Jensen et al., 2004). TC4 and CRYSTAL-FACE used multiple aircraft, but only data from the WB-57 meet our criteria. We only include data within the TTL or above the TTL in our analysis.

Figure 1Map of mean top-of-atmosphere outgoing longwave radiation from CERES, with flight tracks from the five campaigns used in this study overlaid.

Figure 1 shows flight tracks from these five campaigns, overlaid on time mean outgoing longwave radiation (OLR) from the entire Clouds and the Earth's Radiant Energy System (CERES) level 3 satellite-based dataset (Doelling et al., 2013; NASA/LARC/SD/ASDC, 2017), which spans nearly 22 years. Smaller OLRs indicate more frequent deep convection. The frequency of deep convection during the flight campaigns may be different than for the entire CERES dataset due to seasonal and interannual variability. ATTREX 2013 is an outlier in that the majority of its sampling was over the tropical east and central Pacific, which has infrequent deep convection. TC4, CRYSTAL-FACE, and POSIDON sampled primarily close to deep convection near Costa Rica, near Florida, and over the tropical west Pacific, respectively. ATTREX 2014 consisted of two transit flights that sampled far from deep convection over the east and central Pacific and six science flights that sampled close to deep convection over the tropical west Pacific.

All campaigns measured vertical wind at 20 Hz using NASA's Meteorological Measurement System (MMS) instrument (Scott et al., 1990). The MMS estimates the vertical wind as the difference between the vertical speed of air relative to the aircraft and the vertical aircraft speed. These are estimated from pressure sensors and aircraft parameters including pitch, roll, and heading. MMS vertical wind data sometimes exhibit discontinuities when the aircraft switches from one maneuver to another (such as from an ascent to a descent) and must be corrected to minimize artifacts caused by this behavior. Following recommendations from Jonathan Dean-Day and Rei Ueyama from NASA, the aircraft data are separated into flight legs or maneuvers, which are stretches of time when the airplane has a near-constant attack angle, and the vertical wind along each flight leg is demeaned and detrended.

Demeaning and detrending does not introduce significant biases for sufficiently long flight legs because, in the TTL, vertical winds averaged over regions of similar size to a flight leg are typically of the order of a centimeter per second. This estimate is based on analyzing vertical winds in the TTL from ERA5 reanalysis averaged over 1^∘ × 1^∘ or about 100 km × 100 km boxes (not shown). While ERA5 should probably not be trusted in detail for such a purpose, here it is only used to make an order-of-magnitude estimate. We found that 99.9 % of these boxes have mean vertical wind with magnitudes less than 10 cm s⁻¹, and 62.5 % have mean vertical wind with magnitudes less than 1 cm s⁻¹. The small-scale vertical winds that are the focus of this study have magnitudes of at least 25 cm s⁻¹. Additionally, in the rare event that the mean wind exceeds 10 cm s⁻¹ over a 100 km segment of the atmosphere, that mean wind is unlikely to be measured well by the aircraft. Flight legs that are less than 100 km long are removed, as demeaning and detrending those legs could remove some small-scale variability and bias our results.

Figure A1 in Appendix A shows corrected and uncorrected vertical wind data for an example flight, demonstrating both the biases in the uncorrected data and the effectiveness of our data-correction procedure in removing them. Correcting the MMS data is necessary for constraining the magnitude of the vertical wind, but high-frequency (> 1 Hz) vertical wind variance is well constrained in the uncorrected data because the biases in vertical wind have frequencies lower than 1 Hz.

Throughout this study, we use the vertical wind variance as a proxy for turbulence (Atlas et al., 2020). Many studies (e.g., Gultepe and Starr, 1995; Muhlbauer et al., 2014; Podglajen et al., 2017) have used an estimate of the turbulent eddy dissipation rate (ϵ) instead of vertical wind variance to identify and quantify turbulence. ϵ must be computed from a power spectrum of the aircraft vertical wind. The estimate of ϵ is sensitive to the algorithm used to make the power spectrum (e.g., Fourier decomposition or wavelet analysis), how ϵ is estimated from the power spectrum (e.g., fitting a line or integrating the power spectrum), and the assumed Kolmogorov constant. Vertical wind variance is straightforward to calculate and conveys the same information. Within the inertial range of turbulence, it is proportional to ${\mathit{ϵ}}^{\mathrm{2}/\mathrm{3}}$, with a constant of proportionality that is dependent on the aircraft speed and the sampling frequency (Gultepe and Starr, 1995). Figure A1d–e show the vertical wind variance and the reported values of ϵ for an example flight to show that the same turbulent patches are clearly evident in both metrics.

2.2 Aircraft measurements of TTL cirrus cloud microphysics

For all campaigns analyzed, ice water content (IWC) is computed as a difference between total water and water vapor. The cloud laser hygrometer (CLH; Davis et al., 2007) measured total water, and a combination of the Harvard Lyman-α (Weinstock et al., 1994) and the Jet Propulsion Laboratory (JPL) laser hygrometer (May, 1998) measured water vapor during CRYSTAL-FACE and TC4. The reported IWC has a detection limit of about 10⁻¹ mg m⁻³. The NOAA water instrument (Thornberry et al., 2015) measured both total water and water vapor during POSIDON and ATTREX 2013 and 2014. The reported IWC has a detection limit close to 2 × 10⁻³ mg m⁻³. Nonzero IWCs that are below the detection limit are uncertain.

IWC and ice crystal number concentration (NI) are tightly linked in TTL cirrus clouds, which tend to have ice size distributions that are more similar than their ice crystal number concentrations. Figure 2 shows percentiles of IWC binned by NI from POSIDON and ATTREX 2014. NI was measured by the Fast Cloud Droplet Probe (FCDP; for particles 3–24 µm; Lance et al., 2010) and the Two-Dimensional Stereo probe (2D-S; for particles 25–3005 µm; Lawson et al., 2006) for both campaigns. The detection limits for the FCDP and the 2D-S, for an aircraft speed of 100 m s⁻¹ and assuming sample areas of 0.03 and 80 mm², respectively, are about 33 and 0.1 L⁻¹ s⁻¹. Median IWC varies nearly linearly with median NI, and the median ice crystal size, assuming single-sized spherical ice particles, varies between about 19 µm (dashed magenta line) and 24 µm (dashed cyan line).

Figure 2Statistics of ice water content (IWC) are shown as a function of ice crystal number concentration (NI) for 1 Hz data from POSIDON and ATTREX 2014. The solid line is the median, the dotted lines are the 5th and 95th percentiles, and the shaded area spans the range of the 25th to 75th percentiles. Colored dashed lines indicate constant mean particle mass. The legend lists the mean masses and the corresponding mean equivalent sphere radii for each colored line.

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IWC and NI have been quality checked and compiled into a single dataset (Krämer et al., 2020a), as described in Krämer et al. (2020b). Since ATTREX 2013 sampled mainly clear sky, it was not included in the analysis by Krämer et al. (2020b). We still use IWC from this campaign, but we note that it has not been subjected to the same quality control as the other campaigns.

3.1 Small-scale vertical wind variability in all campaigns

We analyze the 1 Hz vertical wind (${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$) in this section and high-frequency (> 1 Hz) vertical wind variance (σ²w₁) in the next section for all five flight campaigns separately. ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ is sensitive to both gravity wave activity and turbulence, whereas σ²w₁ is sensitive mainly to turbulence.

Throughout these two sections, we split the data up into categories based on IWC, distance to deep convection cores, and height. Figure B1 shows distributions of these variables for the five flight campaigns, and Appendix B discusses our choice of categories. We split the IWC into three categories, i.e., clear sky (IWC = 0.0), low-IWC cirrus clouds (between 0.0 and 1 mg m⁻³), and high-IWC cirrus clouds (IWC > 1 mg m⁻³). Clear sky and low-IWC cirrus clouds cannot be perfectly discriminated by the measurements, particularly for CRYSTAL-FACE and TC4, which have an IWC detection limit of 0.1 mg m⁻³.

Figure 3Distributions of 1 Hz mean vertical wind (${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$), for corrected data from all campaigns, shown in separate rows. Campaign names and the number of 1 Hz samples are given in the leftmost column. Second, third, and fourth columns split the data into categories (relative frequencies are shown in pie charts) based on IWC, distance from deep convection, and height in the TTL, respectively. Standard deviations of fitted normal distributions (σ) are printed on all panels.

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Figure 3 shows probability distributions of ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ for each campaign separately. The first column shows the distribution for all campaign data with the campaign name and the number of 1 Hz samples included in the analysis printed over the plots. The second, third, and fourth columns show probability distributions of ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ split into categories based on the IWC, distance to deep convective cores, and height in the TTL, respectively, with pie charts showing the distribution of data across the different categories. Normal distributions are fitted to all probability distributions and the fitted standard deviations (σ) are printed on the plots.

Values of σ vary between 0.17 and 0.4 m s⁻¹ for all campaign data (first column of Fig. 3). Differences in vertical wind variability across the set of campaigns may arise from sampling closer to or farther from deep convection, the properties of the deep convection (e.g., land vs. ocean and shallow vs. deep), interannual, seasonal, and geographic variability in the upper troposphere and TTL, including the quasi-biennial oscillation (QBO) phase, and sampling different heights within the TTL. CRYSTAL-FACE, which sampled near-convection in the Florida region, has the widest distribution of ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ (the most vertical wind variability). ATTREX 2013, which sampled the tropical east and central Pacific, usually far from deep convection, has the least variability. Because the five campaigns sampled such different conditions, it is plausible that they approximately span the vertical wind variability to be expected anywhere in the TTL outside of the immediate vicinity of deep convection.

The remaining columns of Fig. 3 partition the data from each experiment into categories of IWC, distance from deep convection, and height and compare the distributions of ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ across these categories. Within ATTREX 2014, POSIDON, and CRYSTAL-FACE data, high-IWC cirrus clouds have wider ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ distributions (top three rows of second column of Fig. 3), and this result is insensitive to the threshold used to define high-IWC cirrus clouds (not shown). In general, vertical wind variability increases closer to deep convection (third column of Fig. 3). An exception is ATTREX 2013, where vertical wind variability is low, regardless of the distance from deep convection. The first column of Fig. B2 shows the same analysis for clear-sky data only; the results are the same. Thus, the increase in vertical wind variability close to deep convection is not caused by a higher occurrence of cirrus cloud close to deep convection. There is no consistent relationship between vertical wind variability and height across the five campaigns or between the analysis of all data (Fig. 3) and clear-sky data (Fig. B2).

3.2 Turbulence in all campaigns

Figure 4 shows distributions of high-frequency (> 1 Hz) vertical wind variance (σ²w₁). σ²w₁ is the variance of the 20 sub-samples within each second of data and a proxy for turbulence. The distributions are split into the same categories based on IWC, distance from deep convection, and height, as in Fig. 3. We define σ²w₁ greater than an empirical detectability threshold of 0.01 m² s⁻² as turbulent. This turbulence threshold is typically lower than the one used by Podglajen et al. (2017), who analyzed strong turbulence rather than just detectable turbulence. This can be seen by comparing the shaded yellow regions of the flight tracks shown in Fig. A1d and e. Our methodology therefore flags turbulence with a much higher frequency. To facilitate comparison with Podglajen et al. (2017) and test the robustness of our results to the turbulence threshold used, Fig. B3 shows a version of Fig. 4 but with distributions of ϵ instead of σ²w₁ and with a turbulence threshold for ϵ of 10⁻³ m² s⁻³. The sensitivity of turbulence to environmental categories is qualitatively similar to Fig. 4, but the implied turbulence frequency is an order of magnitude smaller. We would need to increase our threshold high-frequency vertical wind variance to over 0.1 m² s⁻² (not shown) to obtain comparable results. We choose our comparably weak detectability threshold because we aim to associate all vertical wind anomalies exceeding 25 cm s⁻¹ with a particular type of small-scale vertical wind variability. Using a strong turbulence threshold would result in many of these periods going undetected. Additionally, the infrequency of strong turbulence would result in poorer sampling statistics.

Figure 4Same as Fig. 3 except showing distributions of high-frequency (> 1 Hz) vertical wind variance (σ²w₁). The percentage of data exceeding the turbulent threshold (0.01 m² s⁻²; vertical dotted line) for each category is shown on each plot.

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Using our variance-based algorithm, the frequency of turbulence varies between about 6 % and 12 % for all campaign data (first column of Fig. 4). ATTREX 2014 and POSIDON, which both sampled the TTL mainly above the tropical west Pacific, have about twice as frequent turbulence as CRYSTAL-FACE and TC4, even though the latter campaigns have more vertical wind variability. Thus, turbulence accounts for a larger proportion of the vertical wind variability sampled during ATTREX 2014 and POSIDON than during TC4 and CRYSTAL-FACE.

The frequency of turbulence for clear-sky data (dark blue line; second column in Fig. 4) varies between about 5 % and 10 % and is typically just slightly lower than the all-sky frequency, implying that clear-air turbulence accounts for much of the turbulence in the TTL. The frequency of turbulence for high-IWC cirrus clouds is at least 3 times that for clear-sky data (second column in Fig. 4). High-IWC cirrus clouds have more turbulence than clear-sky data, independently of the threshold used for turbulence and the threshold used to define high-IWC cirrus clouds (not shown).

Increased turbulence can account for much of the widening of the vertical wind distribution within high-IWC cirrus clouds (seen in Fig. 3) for ATTREX 2014, POSIDON, and CRYSTAL-FACE.

In all campaigns, turbulence is least frequent further than 500 km away from convection (third column of Fig. 4), which is consistent with the findings of Podglajen et al. (2017). In all campaigns, except TC4, turbulence is most frequent within 100 km of convection. Column 3 in Fig. B2 shows that the same is true for clear-sky data. However, the differences in the frequency of turbulence between the two other categories (100–500 km and > 500 km) are largely diminished in the clear-sky data. If a stricter threshold is used for turbulence, then the results are the same except for ATTREX 2013, where the differences in the amount of turbulence within 100 km of convection, and between 100 and 500 km, are diminished (not shown).

Turbulence is enhanced below 15.5 km in all campaigns, except ATTREX 2013, which has enhanced turbulence between 15.5 and 17 km. Podglajen et al. (2017) found that turbulence was enhanced below 15.5 km, mainly within 500 km of deep convection (Fig. 9 in their paper). Consistent with these results, ATTREX 2013 has the most sampling further than 500 km away from deep convection (Figs. 3 and B1). These results are insensitive to the turbulence threshold used.

In this section and in the preceding section, we analyzed aircraft data from the TTL from five NASA aircraft campaigns that took place in different years, seasons, and geographical areas and sampled a different range of distances from deep convection and heights within and above the TTL. Across all campaigns, the probability distribution of ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{1}}$ is well approximated as a normal distribution, with a standard deviation between 0.17 and 0.56 m s⁻¹, depending on the distance from deep convection, the height in the TTL, and the presence of cloud. Vertical wind variability, which is influenced by both turbulence and gravity wave activity, is largest during CRYSTAL-FACE, but the frequency of turbulence is largest during ATTREX 2014 and POSIDON. That means that the increased vertical wind variability during CRYSTAL-FACE is due to increased gravity wave activity. It is unlikely that these differences are purely due to different sampling strategies across the campaigns, and we encourage future studies to investigate the causes of geographical differences in the frequency of turbulence and small-scale gravity wave activity.

We verified that several findings reported in Podglajen et al. (2017) about the frequency of turbulence in ATTREX 2013 and 2014 are true across our entire set of campaigns, including that turbulence is enhanced closer to deep convection, below 15.5 km in the TTL when close to deep convection, and above 15.5 km when far away from deep convection. Furthermore, we analyzed turbulence in clear-sky and cloudy data separately and found that turbulence is strongly enhanced within high-IWC TTL cirrus clouds.

3.3 Sources of small-scale vertical wind variability during ATTREX

Level (constant-altitude) flight legs are useful for separately detecting turbulence and gravity wave activity and for performing spectral analyses because they do not conflate horizontal and vertical scales of variability. Gravity waves often have smaller vertical wavelengths than horizontal wavelengths (Bramberger et al., 2022), so the scale separation between gravity wave activity and turbulence is more pronounced in the horizontal.

ATTREX 2014's flight strategy involved repeatedly flying parallel to the ground at a height of about 14.2 km, typically through cloud, and performing a slow ascent and a quick descent (Fig. A1). ATTREX 2013 sometimes employed this flight strategy and sometimes performed ascents and descents with no level legs in between. There are 52 level legs that are at least 100 km long in the ATTREX 2014 dataset and 13 in the ATTREX 2013 dataset, which are the focus of the rest of this study. In this section, we present an algorithm to distinguish between turbulence and gravity wave activity, and we investigate how the presence of turbulence and gravity wave activity varies with distance to deep convection, IWC, and NI. In the following section, we perform spectral analyses of vertical wind on level leg data from ATTREX 2014 and simulated vertical winds from four global storm-resolving models from the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains summer experiment (DYAMOND-1; Stevens et al., 2019) to evaluate simulated small-scale vertical wind variability over the tropical west Pacific.

Gravity wave activity occurs on a wide range of horizontal scales from 1 km to thousands of kilometers. We define long-wavelength gravity wave activity (LW GWA) as having dominant wavelengths between 5 and 100 km and short-wavelength gravity wave activity (SW GWA) as having smaller wavelengths. The purpose of making this distinction is that SW GWA has horizontal length scales that overlap with turbulence, whereas LW GWA does not.

We separate the level legs from ATTREX into non-overlapping 25 s or 5 km segments (the aircraft travels at about 200 m s⁻¹ during level legs). LW GWA occurs on spatial scales larger than 5 km, so we classify each entire level leg into one of two categories, i.e., (1) negligible LW GWA and (2) LW GWA. All 5 km segments within a level leg receive the same classification.

Turbulence and SW GWA occur on scales smaller than 5 km, so we classify each 5 km segment into one of three different categories, i.e., (1) negligible sub 5 km variability, (2) turbulence, and (3) SW GWA. Because SW GWA and turbulence occur on similar spatial scales, we can only detect turbulence in the absence of SW GWA. We detail the classification of level legs and 5 km segments in Appendix C.

Figure 5Four example vertical wind time series for 100 km long segments from ATTREX 2014 level legs. All plots show the time series of high-rate (20 Hz/10 m) vertical wind and 5 km mean vertical wind (${\stackrel{\mathrm{‾}}{w}}_{\mathrm{25}}$). In the top time series for each example, high-rate vertical wind is in gray and ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{25}}$ is in black. Horizontal dashed purple lines indicate 0.0, 0.5, and −0.5 m s⁻¹. In the bottom time series for each example, ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{25}}$ is colored green if there is long-wavelength gravity wave activity, and the high-rate vertical wind is colored cyan and red where there is short-wavelength gravity wave activity and turbulence, respectively.

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Figure 5 shows four example time series of vertical wind for four different level legs from the ATTREX 2014 dataset. In the upper time series plot for each example, the 20 Hz vertical wind is shown in gray, and the mean vertical wind for the 5 km segments (${\stackrel{\mathrm{‾}}{w}}_{\mathrm{25}}$) is shown in black. In the second row under each example, the 20 Hz vertical wind is color coded according to the sub 5 km variability classifications, and ${\stackrel{\mathrm{‾}}{w}}_{\mathrm{25}}$ is color coded according to the LW GWA classification (for the entire level leg). Examples 2 and 3 have LW GWA, whereas examples 1 and 4 have negligible LW GWA. All of the 5 km segments in examples 1 and 2 have negligible sub 5 km variability, whereas in example 3 they are all turbulent. Example 4 has one intermittent patch of turbulence and one patch of SW GWA. These small-scale vertical motions are typically associated with temperature anomalies of up to 0.5 K for SW GWA and 0.1–0.2 K for turbulence (not shown; for an example, see Fig. 5 in Podglajen et al., 2017).

Figure 6Analysis of 5 km segments from ATTREX 2013 and 2014 level legs. (a) Frequency of atmospheric conditions. The most common conditions are labeled. (b) Histograms of (top to bottom) NI, IWC, and distance from deep convection, showing the contributions from different atmospheric conditions. Black lines indicate thresholds also used below in panel (c). (c) Pie charts showing the relative frequency of categories of (top to bottom) NI, IWC, and distance to deep convection for the three most frequent atmospheric conditions.

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Each 5 km segment can have three possible sub 5 km classifications, with or without LW GWA. We show the frequency of each combination of classifications in Fig. 6a. Hatching indicates LW GWA, and the color represents the sub 5 km variability classification. The following three situations are most common: (1) negligible LW GWA with negligible sub 5 km variability (quiescent), (2) LW GWA with negligible sub 5 km variability (LW GWA only), and (3) LW GWA with turbulence. These situations occur 24 %, 50 %, and 21 % of the time, respectively. LW GWA is present 75 % of the time. Turbulence occurs preferentially with LW GWA, such that only 5 % of turbulent segments (11 % for clear-sky data) do not have LW GWA (Fig. 6a). SW GWA also occurs preferentially with LW GWA, as only 7 % of segments with SW GWA do not also have LW GWA (these segments are represented by the thin sliver in cyan between the areas of the pie chart labeled as quiescent and as LW GWA with turbulence).

Figure 6b shows histograms of 5 km mean (from top to bottom) NI, IWC, and distance to deep convection. The extra column on the left-hand side of the histograms for NI and IWC corresponds to NI = 0 and IWC = 0, respectively, and the black lines show thresholds defining high NI (> 20 L⁻¹) and high IWC (> 1 mg m⁻³), which is also used in the category definitions of Fig. 6c. Segments classified as LW GWA with turbulence are most common, and segments classified as quiescent are rarely seen within high-NI and high-IWC cirrus clouds or within 500 km of convection (to the left of the black line on the histogram for the distance to deep convection).

Figure 6c shows pie charts of 5 km mean NI, IWC, and distance from deep convection for the three most common conditions from Fig. 6a, with categories used to simplify the analysis. There are fewer total samples in the pie charts for the distance to deep convection than there are in the pie charts for IWC and NI because brightness temperature data are occasionally missing over the tropical west Pacific.

The likelihoods of occurrence of high-NI cirrus clouds, given quiescent conditions, LW GWA only, and LW GWA with turbulence, are 0.9 %, 16 %, and 40 %, respectively. Thus, high-NI cirrus clouds are about 20 times more likely when there is gravity wave activity and 50 times more likely when there is also turbulence, compared to quiescent conditions. The likelihoods of occurrence of high-IWC cirrus clouds, given quiescent conditions, LW GWA only, and LW GWA with turbulence, are 0.7 %, 14 %, and 32 %, respectively. Thus, high-IWC cirrus clouds are also about 20 times more likely when there is gravity wave activity and about 50 times more likely when there is also turbulence, compared to quiescent conditions. High-NI and high-IWC cirrus clouds co-occur with low-frequency gravity wave activity 99 % of the time.

The fractions of 5 km segments within 500 km of convection with quiescent conditions, LW GWA only, and LW GWA with turbulence are 4 %, 15 %, and 48 %, respectively. Thus, turbulence is enhanced closer to deep convection to a much greater extent than LW GWA.

Turbulence co-occurs with high-NI cirrus clouds 40 % of the time and with high-IWC cirrus clouds 32 % of the time (Fig. 6c). However, turbulence is not a necessary condition for high-NI and high-IWC cirrus clouds, as they occur in the absence of turbulence about half of the time. In general, the presence of turbulence is much more highly correlated with the presence of LW GWA than with the presence of high-NI and high-IWC cirrus clouds.

3.4 Evaluating vertical wind variability in global storm-resolving models

Recently, advances in computing power have made it possible to run global atmospheric models with horizontal grid spacing below 5 km. These models are referred to as global storm-resolving models (GSRMs) because they explicitly resolve deep convection rather than using a deep convective parameterization. Since deep convection is a major source of both gravity waves and the water vapor and ice that form TTL cirrus clouds, this makes GSRMs attractive for studying TTL cloud formation processes, including lifting within gravity waves. However, GSRMs do not resolve turbulence, which they typically parameterize in some form. In this section, we use ATTREX observations to address whether TTL vertical winds simulated by GSRMs are sufficiently realistic to form a credible dynamical environment for TTL cirrus cloud formation and evolution.

Stephan et al. (2019) found that explicit convection simulated with a horizontal grid spacing of 5 km produces more gravity wave momentum flux at 30 km in the tropics and subtropics, where convection is the predominant source of gravity wave activity (Fritts and Alexander, 2003, and references therein), and a wider vertical wind distribution throughout the troposphere, compared to parameterized convection. Müller et al. (2018) found that “convective parameterization inhibits gravity wave generation by convective clouds”. While these studies suggest gravity wave generation and propagation are more realistic in GSRMs than in coarse-resolution models, substantial discrepancies may still exist between GSRMs and the real atmosphere.

In the DYAMOND-1 intercomparison, nine GSRMs were identically initialized from reanalysis and run freely (without nudging) for the 40 d period of 1 August–10 September 2016. Here, we focus on four of those models, namely Nonhydrostatic ICosahedral Atmospheric Model (NICAM), Global System for Atmospheric Modeling (gSAM), Finite-Volume Cubed-Sphere Dynamical Core (FV3), and ICON (Icosahedral Nonhydrostatic Weather and Climate Model). NICAM, gSAM, FV3, and ICON have horizontal grid spacings of 3.25, 5, 3.25, and 2.5 km, respectively. The vertical grid spacing in the TTL is 400 m for NICAM and close to 500 m for the other three models.

Figure 7Snapshots of vertical wind from hour 141 in the DYAMOND-1 simulations. Winds are taken from the model level closest to 14.2 km, and the tropical west Pacific region is shown.

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Figure 7 shows snapshots of vertical wind from the 141st hour of simulation at the vertical levels closest to 14.2 km, which is the same level as the ATTREX horizontal aircraft legs. Figure S1 in the Supplement is an animation of vertical wind snapshots for hours 48–957 of the simulations (allowing 2 d for model spinup), showing that the snapshot in Fig. 7 is representative of the simulations. The models differ substantially in their magnitudes of vertical winds and the dominant scales of vertical wind variability. gSAM is an outlier in having more vertical wind variability than the other models, particularly at the grid scale. ICON has more vertical wind variability than FV3 and NICAM. NICAM has larger dominant scales of horizontal variability than the other models, and FV3 has weak vertical winds in most grid cells but strong gravity wave activity in the vicinity of deep convection.

Figure 8b shows statistics of power spectra of 20 Hz vertical wind from ATTREX 2014 level legs sampling the tropical west Pacific and from the four GSRMs for the same regions and vertical levels shown in Fig. 7. We perform 1-D fast Fourier transforms (FFTs) for both simulations and observations. FFTs are performed separately along the east–west and north–south direction in the GSRMs and then averaged together. The spectra are similar for both directions (not shown). ICON has an unstructured grid. To enable 1-D FFT analysis, it is interpolated to an 0.01^∘ lat–long grid. For the observations only, we use Welch's method for windowed Fourier analysis with a window length of 100 km and a Hann taper to reduce noise in the spectra.

Figure 8(a) Statistics of 1-D power spectral density for the ATTREX 2014 observations over the tropical west Pacific for all measured wavelengths. The increase in power at ∼ 500 m is caused by the oscillation of the aircraft. (b) Statistics of 1-D power spectral density for the ATTREX 2014 observations over the tropical west Pacific (black) and the DYAMOND-1 simulations (blue) for wavelengths between 10 and 100 km. Solid lines are medians, dotted lines are 5th and 95th percentiles, and shaded areas span the ranges of the 25th to 75th percentiles.

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All simulations have too little power in the vertical wind at all wavelengths examined. The power spectra for ICON, FV3, and NICAM decrease strongly towards the grid scale, which is where they are furthest from the observed spectra. gSAM has a flatter spectrum which more closely resembles the observations. However, the grid-scale variability in gSAM has more resemblance to white noise than to gravity wave activity, so it may not be physically meaningful for this analysis.

We do not look at relationships between cirrus cloud properties and vertical wind here because none of the models predict NI, and while all models predict IWC, FV3 outputs it on a different grid than the vertical wind, making comparisons difficult. Nonetheless, our observational analysis showed that small-scale gravity wave activity is a strong control on TTL cirrus cloud microphysics, and our comparison here shows that small-scale gravity wave activity is underrepresented in the evaluated GSRMs. If the GSRMs have enough or too much ice within simulated TTL cirrus clouds compared to the real atmosphere, then that suggests that overproduction of ice within the microphysics schemes is compensating for deficient dynamical contributions to ice production. In this case, the physical mechanisms controlling ice production in simulated TTL cirrus clouds would differ substantially from the real atmosphere.