Empirical evidence for deep convection related stratospheric cirrus clouds over North America

. Cirrus clouds in the lowermost stratosphere affect stratospheric water vapor and the Earth’s radiation budget. The knowledge of its occurrence and driving forces is limited. To assess the distribution and possible formation mechanisms of stratospheric cirrus clouds (SCCs) over North America, we analyzed SCC occurrence frequencies observed by the Cloud-Aerosol Lidar and Infrared Pathﬁnder Satellite Observations (CALIPSO) instrument during the years 2006 to 2018. Possible driving forces such as deep convection are assessed based on Atmospheric Infrared Sounder (AIRS) observations during the 5 same time. Results show that at nighttime, SCCs are most frequently observed during the thunderstorm season over the Great Plains from May to August (MJJA) with a maximum occurrence frequency of 6.2 %. During the months from November to February (NDJF), the highest SCCs occurrence frequencies are 5.5 % over the North-Eastern Paciﬁc, western Canada and 4.4 % over the western North Atlantic. Occurrence frequencies of deep convection from AIRS, which includes storm systems, fronts, mesoscale convective systems and mesoscale convective complexes at mid- and high latitude, show similar hotspots like the 10 SCCs, with highest occurrence frequencies being observed over the Great Plains in MJJA (4.4 %) and over the North-Eastern Paciﬁc, western Canada and the western North Atlantic in NDJF ( ∼ 2.5 %). Both, seasonal patterns and daily time series of SCCs and deep convection show a high degree of spatial and temporal relation. Further analysis indicates that the maximum fraction of SCCs related to deep convection is 74 % over the Great Plains in MJJA and about 50 % over the western North Atlantic, the North-Eastern Paciﬁc and western Canada in NDJF. We conclude that, locally and regionally, deep convection 15 is the leading factor related to occurrence of SCCs over North America. In this study, we also analyzed the impact of gravity waves as another important factor related to the occurrence SCCs, as the Great Plains is a well-known hotspot for stratospheric gravity waves. In the cases where SCCs are not directly linked to deep convection, we found that stratospheric gravity wave observations correlate with SCCs in as much as 30 % of the cases over the Great Plains in MJJA, about 50 % over the North-Eastern Paciﬁc, western Canada and up to 90 % over eastern Canada and the north-west Atlantic in NDJF. Our results provide 20 better understanding of the physical processes and climate variability related to SCCs and will be of interest for modelers as SCC sources such as deep convection and gravity waves are small-scale processes that are difﬁcult to represent in global general circulation models.

tion and strong storm systems from infrared nadir sounder observations. To detect deep convection at latitudes below ± 60 • from AIRS measurements, Aumann et al. (2003) used a brightness temperature threshold of 210 K for the 1231 cm −1 (8.1 µm) radiance channel. Hoffmann and Alexander (2010) increased the threshold to 220 K to better identify convective systems at midlatitudes, which appear at higher tropopause temperatures at these latitudes. Later, Hoffmann et al. (2013) pointed out that ambiguous detections at different latitudes and seasons are likely caused by using a constant threshold for detection. Therefore, 160 varying thresholds, which are based on monthly and latitudinally mean tropopause temperatures from the NCAR/NCEP reanalysis, have been used in their work. Following this approach, we use co-located tropopause temperatures from the ERA-Interim reanalysis to achieve further improved identification of deep convective events. By considering the vertical grid spacing of the ERA-Interim reanalysis and a sensitivity test (Appendix A), an offset of +7 K on top of the tropopause temperature (T T P ) was selected as a threshold to detect deep convection events from AIRS brightness temperature measurements (BT AIRS ) at 165 1231 cm −1 here, (1) Note that the term 'deep convection' used in this work does not only refer to convection from tropical storms, but also to strong convective events from various sources such as storm systems and fronts, mesoscale convective systems and mesoscale convective complexes at mid-and high latitudes. Sensitivity tests on deep convection detection can be found in Appendix A.

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Mean brightness temperatures in the carbon dioxide 4.3 µm waveband have previously been used to detect stratospheric gravity wave signals from AIRS observations (e.g., Hoffmann and Alexander, 2010;Hoffmann et al., 2013;Yue et al., 2013;Hoffmann et al., 2018). In order to reduce noise and to improve the detection sensitivity, we averaged measurements of 42 AIRS channels from 2322.6 to 2345.9 cm −1 and 2352.5 to 2366.9 cm −1 . In the next step, background signals from planetary waves and large-scale temperature gradients are removed by means of a low pass filter. To identify gravity wave events, a 175 variance filter was then applied to the 4.3 µm brightness temperature perturbations. Gravity wave events are detected based on a threshold of 0.05 K 2 for the noise-corrected 4.3 µ brightness temperature variances. The detection method described here is sensitive to a broad range of gravity wave horizontal wavelengths (50 to 1000 km), but limited to vertical wavelengths of about 15 km or longer. The method can be used to detect gravity waves in the middle and upper stratosphere (30 -40 km of altitude) (Hoffmann and Alexander, 2010;Hoffmann et al., 2013Hoffmann et al., , 2018. However, as gravity waves typically propagate upward from 180 their tropospheric sources into the stratosphere, the detections also provide information about gravity waves at tropopause levels. 3 Results Sun and Huang, 2015; Qu et al., 2020). Investigating the relationship between SCCs and deep convection will provide further 195 insights into the potential mechanism of SCC formation and water vapour transport into the stratosphere over North America.

Occurrence frequencies of SCCs and deep convection
The occurrence frequencies of SCCs and deep convection for the summer season, i. e., May to August (MJJA), and the winter season, i. e., November to February (NDJF), were calculated from CALIPSO measurements between 2006 and 2018 as the ratio of the number of detections to the total number of profiles in 4 • × 6 • (latitude × longitude) grid boxes (Fig. 2). As the CALIPSO measurements have a better signal-to-noise ratio at nighttime than at daytime (Winker et al., 2009;Hunt et al., 200 2009), which has a significant impact on the detection of SCCs (Pan et al., 2009;Zou et al., 2020), we focus on the analysis of nighttime data in this study. North Atlantic with maximum occurrence frequencies of 4.4 % (Fig. 2b). These occurrence frequencies are in agreement with  (Zou et al., 2020), in which the SCCs were retrieved with the same detection method and tropopause data.
The patterns of the occurrence frequencies of deep convection from AIRS, which were calculated as the ratio between the number of deep convection pixels and the total number of pixels in each grid box, are quite similar to the CALIPSO SCC 210 observations (Fig. 2). High occurrence frequencies of deep convection occur over the Great Plains in MJJA with maximum value of 4.4 % (Fig. 2c) and over the North-Eastern Pacific, western Canada and the western North Atlantic in NDJF reaching 2.5 % (Fig. 2d).

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Even though at midlatitudes the SCC occurrence maxima are slightly shifted downwind (eastward) compared to the deep convection maxima, the occurrence frequencies overall indicate a high degree of relation between SCCs and deep convection.

Temporal correlations of SCCs and deep convection
The

SCCs related to deep convection
In this section, the relations between SCCs and deep convection are investigated in more detail by analyzing the fraction of SCC observations occurring in the same grid box with deep convection on the same day at nearly the same time, considering that both AIRS and CALIPSO are in the A-Train (Fig. 6). The fraction of SCCs related to deep convection is defined as the ratio 250 of day numbers with SCCs and deep convection both detected to the total number of days with SCC detections. In MJJA, most SCC observations are directly related to deep convection over the Great Plains with the highest fraction up to 74 % (Fig. 6a).
In NDJF, the SCCs observations over the western Atlantic Ocean (up to 50 %) and secondly over the North-Eastern Pacific and western Canada with maximum fraction of 44 % are mostly related to deep convection. Regions with a high degree of relation between SCCs and deep convection agree best with the regions with large occurrence frequencies of deep convection,

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indicating that deep convection is the main factor related to the formation of SCCs in the study area.

SCCs related to gravity waves
The summertime deep convection over the Great Plains is known to induce gravity waves (Hoffmann and Alexander, 2010) and gravity waves are known to contribute to cirrus formation (Jensen et al., 2016). To address potential sources for the SCCs not 285 directly related to deep convection as found in Fig. 8, we analyzed the SCC relation with gravity waves. An example of SCCs induced by gravity waves is shown in Fig. 11. The top of the SCCs is located about 1.2 km above the tropopause according to the CALIPSO observations. The AIRS 4.3 µm brightness temperature variances around the SCCs are about 0.06 K 2 , which exceeds the significance level of AIRS to detect stratospheric gravity waves. The stratospheric gravity waves were likely caused by a convective system to the west of the SCCs as indicated by the propagation direction of the waves patterns (Fig. 11).

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Counting only SCCs connected with gravity waves in absence of deep convection in the same grid box, Fig. 12 shows the occurrence frequencies of gravity waves as well as the fraction of SCCs related to gravity waves. In contrast to deep convection, gravity waves are more often detected in NDJF over eastern Canada and the north-west Atlantic (> 30 %) (Fig. 12b). In MJJA,  Canada and 90 % over eastern Canada and the north-west Atlantic (Fig. 12d). In MJJA, the influence of gravity waves on occurrence of SCCs is weaker ( maximally 30 % over the Great Plains, Fig. 12c), as deep convection plays a more important role.

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The result that up to 74 % of SCCs in MJJA over the Great Plains and about 50 % in NDJF over the western Atlantic Ocean, the North-Eastern Pacific, and western Canada are correlated with deep convection implies that deep convection is the major source for SCCs in these regions for the respective seasons. This finding appears plausible, as for tropical SCCs, there is a clear relation with the seasonally varying deep convection (Pan and Munchak, 2011). During the thunderstorm season in MJJA, the region over the Great Plains is known to produce extraordinarily strong convection at midlatitudes. Their tropopause reaching 305 cloud occurrence frequency is comparable with (daytime)/even higher than in (nighttime) the tropical deep convection hotspots