Diurnal variations of tropical cyclone outer region size growth

Various aspects of tropical cyclones (TCs) fluctuate with the diurnal cycle. TC size is critical to the extent of its damage, but diurnal variations in the growth of the outer region size have largely remained unexplored. This paper examines the diurnal variations in the growth of the radius of gale‐force winds (34 kt; R34) by analyzing best‐track data from 2001 to 2019 for both North Atlantic TCs and global TCs outside of the North Atlantic region. Statistically significant diurnal variations was found for R34 growth, with the maximum 6‐h growth rate occurring at 2100–0300 local solar time (LST) for North Atlantic TCs, and at 0300–0900 LST for global TCs excluding the North Atlantic which experienced rapid intensification (≥30 knots within 24 h). The higher R34 6‐h growth rates during the night were linked to a larger extent of very deep convective clouds with infrared brightness temperatures <208 K during this time.


| INTRODUCTION
Diurnal cycles have been well-recognized in various aspects of tropical cyclones (TCs).Among all TC aspects, the diurnal variations of the upper-level cirrus canopy and precipitation of TCs have been studied the most, largely due to the abundance of satellite observations (e.g., Bowman & Fowler, 2015;Browner et al., 1977;Ditchek, Molinari, et al., 2019;Dunion et al., 2014;Kossin, 2002;Leppert & Cecil, 2016;Muramatsu, 1983;Wu, Ruan, et al., 2015;Wu & Ruan, 2016;Zhang & Xu, 2021).Other TC aspects which exhibit diurnal cyclic behavior include TC lightning (Ditchek, Corbosiero, et al., 2019), overshooting top density in TCs (Sun et al., 2021), the boundary layer inflow of mature hurricanes (Zhang et al., 2020), TC intensification rate (Wu et al., 2020), the contraction of the radius of maximum wind (RMW) and eye size during TC intensification (Lee et al., 2020;Muramatsu, 1983;Tang et al., 2019;Wu & Hong, 2022).While the inner-core size of a TC, as represented by the RMW, has been found to have a significant diurnal cycle, the diurnal cycle of changes in the TC outer region size, if any, is much less explored.
The size of the TC outer region, which determines the potential extent of TC impacts, is as important as the TC intensity (Irish et al., 2008).The outer region size is usually described by the radius of gale-force winds (34 kt or 17 m/s; R34; 1 kt = 0.514 m/s).Based on the satellite infrared (IR) imagery, Knaff et al. (2014) developed an objective algorithm for TC size estimation.Wu and Ruan (2016) found that the mean extent of very deep convective clouds with IR brightness temperatures (BT) <208 K reaches a maximum in the early morning, and TC cloud top BT between 208 and 240 K reaches a maximum in the afternoon.Given that diurnal cycles of TC cloud top BT have been well-recognized, it remains an open question as to whether or not a diurnal signal of changes in TC outer region size also exists via the established linkage between TC clouds and TC outer region size.
Although there are extensive studies on TC diurnal variations, to our knowledge, only Dunion et al. (2014) briefly mentioned that the 50-kt wind radius tends to increase more in the afternoon than early morning for the Atlantic major hurricanes without speculating upon any physical reasoning.To date, it is still unknown if the diurnal cycle of TC outer region size growth is a general feature for global TCs, and whether the diurnal cycle of the TC outer region wind field expansion happens in tandem with RMW contraction at the storm center.The main objectives of this study are to examine the diurnal variations of outer region wind radius growth of global TCs and to investigate the possible reason for the detected diurnal variations of TC outer region size growth.

| DATA AND METHODS
A TC best-track dataset was obtained from the International Best Track Archive for Climate Stewardship (IBTrACS).The best-track data for the North Atlantic and the eastern North Pacific were provided by the National Hurricane Center (NHC), and the other basins were provided by the US Navy's Joint Typhoon Warning Center (JTWC).The 6-hourly records of TC center position (latitude and longitude), intensity (maximum 1-min mean sustained surface wind speed), and R34 were included in the best-track data.Best-track data were recorded regularly at 0000, 0600, 1200, and 1800 coordinated universal time.The intensity was discretized at 5-kt intervals, and R34s for each quadrant were assessed at 5 nautical mile (nmi) intervals.Longitude data were used to adjust the best-track data to local solar time (LST).Best-track data for 2001-2019 were used because TC size data were available for most ocean basins after 2001.
Wind radii estimates made by operational centers are based on all available information, including in situ observations (e.g., ships, buoys, station reports, aircraft reports), remotely sensed data (e.g., active and passive sensors on aircraft and satellite platforms) data scenes, and TC-specific applications (e.g., algorithms that prescribe circulations based on intensity, forward speed, patterns in satellite images, etc.; Knaff et al., 2021).Although aircraft reconnaissance for TCs in the Atlantic basin is typically carried out every 12 h, alternative observations can also provide valuable information for estimating wind radii using 6-hourly satellite imagery when aircraft reconnaissance is not feasible.In the absence of aircraft reconnaissance, an estimation of the wind radii can provide a reasonable fit to TC aircraft observations (Holland et al., 2010).R34 for the global TCs in the besttrack dataset had a nonlinear relationship with intensity (figure not shown), which was consistent with the result using the Multiplatform Tropical Cyclone Surface Wind Analysis (MTCSWA, Knaff et al., 2011) data for TCs in the western North Pacific (Wu, Tian, et al., 2015).To further evaluate the reliability of R34 on a diurnal scale, we used the Tropical Cyclone Observations-Based Structure (TC-OBS) dataset to examine the diurnal variation of R34 growth in the North Atlantic Ocean.More than half of TCs in TC-OBS were calibrated by aircraft observations (Vigh et al., 2016).To analyze the diurnal variations of R34 growth in TCs calibrated by aircraft observations without rounding to an artificial threshold, we excluded cases in TC-OBS where TC parameters were not calibrated by aircraft observations and had the same values as the best track.We were only able to use TC-OBS data from 2001 to 2014 for validation, as the dataset is not available after 2014. Figure 1 shows the variations in mean TC R34 growth over the course of a day during 2001-2014 in the North Atlantic Ocean in the TC-OBS dataset calibrated by aircraft observations and best-track dataset.For the TC-OBS dataset (best-track dataset), the mean R34 was 111.9 nmi (95.1 nmi), and the mean R34 growth rate was 6.4 nmi per 6 h (5.3 nmi per 6 h).Although there were some differences in mean R34 and mean R34 growth rates between the two datasets, the diurnal variation in R34 growth rate was similar.The highest R34 growth rate occurred during 2100-0300 LST (7.3 nmi per 6 h for TC-OBS dataset and 6.9 nmi per 6 h for best-track dataset), although the standard error was large in TC-OBS due to the small sample size.The R34 growth in the North Atlantic Ocean from 2001 to 2014 showed the consistent nocturnal preference in the TC-OBS dataset calibrated by aircraft observations and the best-track dataset, which provided some confidence on the reliability of R34 in the best-track dataset.The limited availability of aircraft observations made it impractical to evaluate the reliability of the best-track dataset for other basins.Moreover, the growth life cycles of TC sizes in the North Atlantic Ocean were different from those in other regions, as reported by Knaff et al. (2014).Therefore, we analyzed the diurnal variations of R34 growth separately for North Atlantic TCs and global TCs, excluding those in the North Atlantic.
Diurnal variations of deep convection over the ocean and over the land are different (Yang & Slingo, 2001), therefore the diurnal variations of TC R34 growth related to deep convection might be different over the land from over the ocean.This study focused on the open ocean, so any storm with a center <300 km from the land was not considered.Only R34 growth during the period from TC genesis to its lifetime maximum values was analyzed.TCs that had 24-h decreases in R34 were not included.Overall, 80.3% of R34 increased or remained unchanged in 24 h during the period from TC genesis to its lifetime maximum values.Only the records containing R34 measurements in four quadrants were kept.The average value of the four quadrants was defined as the R34 value.Each selected TC must have had at least five consecutive R34 records covering a whole day.Under these criteria, 7933 R34 data were identified, and the R34s at 0000, 0600, 1200, and 1800 coordinated universal time had approximately the same sample sizes.The R34 changes over a 6-h interval were calculated using the forward difference method.The forward difference (ΔR34 t ) was calculated by subtracting the current R34 (R34 t ) from the R34 6 h later (R34 t+1 ), that is, 4R34 t ¼ R34 tþ1 À R34 t .Rapid intensification (RI) was defined as an increase in maximum sustained wind ≥30 kt in 24 h (Kaplan & DeMaria, 2003).RI TCs refer to TCs that experienced RI at least once in their lifetime, and non-RI TCs refer to TCs that did not experience RI in their lifetime.For RI TCs (non-RI TCs), the mean lifetime maximum intensity was 100.1 kt (58.3 kt), the mean lifetime maximum R34 was 116.1 nmi (87.5 nmi), the mean R34 was 92.8 nmi (78.4 nmi), and the mean R34 growth rate was 6.3 nmi per 6 h (5.3 nmi per 6 h).Diurnal variations of R34 changes for RI TCs and non-RI TCs were analyzed separately for global TCs excluding the North Atlantic, because most RI storms exhibited at least one diurnal signal of active convective area (Lee et al., 2020).Statistical significances of differences in this study were based on two-tailed Student's t test.
Half-hourly, globally merged IR BT data were provided by the Climate Prediction Center of the United States National Centers for Environmental Prediction (NCEP) (Janowiak et al., 2001).These IR BT data were merged and calculated using data from all available geostationary satellites with a 4-km pixel resolution between 60 N and 60 S. The half-hourly data were averaged to give hourly images to decrease the number of data gaps caused by satellite eclipse periods.The IR BTs were adjusted to LST according to longitude, consistent with the best-track data.

| RESULTS
Variations in mean TC R34 growth over the course of a day from 2001 to 2019 are shown in Figure 2, in which North Atlantic TCs and global TCs excluding the North Atlantic are presented separately.In North Atlantic, the R34 increased by 6.22, 5.30, 4.17, and 4.76 nmi in 6 h at 2100-0300, 0300-0900, 0900-1500, and 1500-2100 LST, respectively.The mean R34 growth rate during nighttime (2100-0900 LST) was higher than that during daytime (0900-2100 LST).The maximum R34 growth rate at 2100-0300 LST was significantly 49% higher than the minimum at 0900-1500 LST, with a 95% confidence level (p-value <0.05).These results suggest that R34 is more likely to grow during nighttime for TCs in North Atlantic.In other basins, diurnal variations of R34 changes for RI TCs and non-RI TCs were analyzed separately.For RI TCs, the R34 increased by 6.51, 7.36, 6.08, and 6.53 nmi in 6 h at 2100-0300, 0300-0900, 0900-1500, and 1500-2100 LST, respectively.The maximum R34 growth rate at 0300-0900 LST was significantly higher than during daytime at the 90% confidence level (p-values <0.1).For non-RI TCs, the mean increases of R34 were 5.03, 5.52, 5.26, and 5.62 nmi in 6 h at 2100-0300, 0300-0900, 0900-1500, and 1500-2100 LST, respectively.The R34 growth for non-RI TCs were significantly smaller than that for RI TCs during nighttime at the 95% confidence level (p-values <0.05).No statistically significant variations were detected in the mean R34 growth rate for non-RI TCs.RI TCs in the western North Pacific, eastern North Pacific, and southern Indian Oceans showed a preference for R34 growth during nighttime, but this was not statistically significant.However, RI TCs in the global basin, excluding the North Atlantic, also exhibited a preference for R34 growth during nighttime with statistical significance.The lack of statistical significance in the western North Pacific, eastern North Pacific, and southern Indian Oceans may be attributed to the limited number of samples.Nevertheless, the confidence in the diurnal variations for North Atlantic TCs is higher due to the availability of aircraft observations, which ensured the reliability of the best track data.
One possible explanation for the growth in the outer region size of a TC is the absolute angular momentum transport caused by the heating-induced secondary circulation within the boundary layer (Chan & Chan, 2013;Holland & Merrill, 1984;Ruan & Wu, 2022), as the change in the 15 m/s wind radius was roughly proportional to the inflow at the 15 m/s wind radius (Tsuji et al., 2016).Given the linkage between very deep convective clouds and the change in TC outer region size, it was necessary to examine the role of areal extent of very deep convective clouds on diurnal variations of R34 growth in RI TCs. Figure 3a shows the radial distribution of very deep convection with IR BT < 208 K during daytime (0900-2100) and nighttime (2100-0900) TCs in the North Atlantic.The radial distance from the TC center (r) was normalized to R34 (R = r/R34).In general, the coverage of very deep convective clouds decreased as the distance from the storm center increased, except that the highest occurrence frequency of very deep convection for RI TCs located between 0.2 < R ≤ 0.4.The coverages of the very deep convective clouds were 2%-3.6%larger during nighttime than daytime at each interval annulus.Diurnal variations of very deep convective cloud coverage with IR BT <208 K within 200 km (approximately the mean R34) of the storm center for North Atlantic TCs are shown in Figure 3b.The maximum coverage of very deep convective clouds occurred at 2100-0300 LST (12.8%), which was significantly larger than the minimum coverage at 0900-1500 LST (10.5%) at the 95% confidence level (p-value <0.05).The higher R34 growth rate at 2100-0300 LST (Figure 2a) appears to be associated with the highest deep convective clouds located within R34 at 2100-0300 LST.
Although the radial distribution of very deep convection in global TCs, excluding those in the North Atlantic, was similar to North Atlantic TCs, the coverage of deep convective clouds at each interval annulus was significantly greater (as shown in Figure 3c).The coverage of very deep convective clouds within the radius of R34 was significantly larger for RI TCs than non-RI TCs at the 95% confidence level (p-values <0.05).The differences between the coverages of very deep convection for RI TCs and non-RI TCs were relatively small at radii larger than 1.2.The coverages of the very deep convective clouds were larger during nighttime than daytime for both RI and non-RI TCs.For RI (non-RI) TCs, the mean coverages of very deep convective clouds were 4.6%-5.9%(4.1%-8.1%)larger during nighttime than during daytime at each interval annulus.For both RI TCs and non-RI TCs, the maximum coverage of very deep convective clouds within 200 km occurred at 0300-0900 LST (Figure 3d), resulting in the higher R34 growth rate of RI TCs at 0300-0900 LST (Figure 2b).However, no diurnal signals were detected in R34 growth for non-RI TCs.The difference in diurnal patterns of R34 growth between North Atlantic TCs and global RI TCs outside the North Atlantic region, which exhibit a higher R34 growth rate at 2100-0300 LST and 0300-0900 LST, respectively, may be linked to variations in the timing of the peak occurrence of the very deep convective clouds located within R34.
An example of the diurnal cycle of R34 growth for Typhoon Haima ( 2016 western Pacific and grew to a powerful category 5 on the Saffir-Simpson wind speed scale (Figure 4a).Typhoon Haima rapidly intensified 2100 LST 15 October and 1500 LST October, from a tropical storm to a category 3, with an R34 growth from 87 nmi to 175 nmi (Figure 4a).Typhoon Haima reached a peak intensity of 145 kt at 0300 LST on 19 October, with an R34 of 190 nmi, and reached the maximum R34 of 230 nmi at 1400 LST on 20 October.As shown in Figure 4b, the 6-h increases in R34 were 18 nmi, 10 nmi, 23 nmi, and 13 nmi during the four nighttime periods.During the daytime periods, the 6-h increases in R34 were 7 nmi, 3 nmi, 15 nmi, and 3 nmi.This analysis indicates that Typhoon Haima grew markedly more outer region size during nighttime than daytime over the 2-day period.We focused on the 2-day period because R34 changes during the subsequent period did not show diurnal cycles.
The IR images of Typhoon Haima captured the feature of the diurnal oscillation in the coverage of convective clouds between 2100 LST 15 October 2016 and 1500 LST 17 October 2016 (Figure 5).The areas of cloud cover with IR BT <208 K within 400 km of TC center during nighttime (Figure 5a,b,e,f) were obviously larger than that during daytime (Figure 5c,d,g,h), while the areas of cloud cover with IR BT between 208 K and 240 K were larger during daytime than nighttime.The features shown in Figure 5 were consistent with the previous study (Wu & Ruan, 2016).Preference for R34 growth and larger coverage of very deep convective clouds with IR BT <208 K during nighttime for Typhoon Haima suggested that TC R34 growth was associated with very deep convective clouds with IR BT <208 K.While the areas of very deep convection oscillated from daytime to nighttime, the RMW of Typhoon Haima was almost fully covered with very deep convective clouds, with IR BT <208 K during the analysis period.The very deep convection within RMW is important for RMW contraction and TC intensification (Vigh Schubert, 2009;Wu & Ruan, 2021), however, full coverage of very deep convection in the RMW may lead to the diurnal variations of RMW contraction and TC intensification that are insensitive to the diurnal variations of very deep convection.While evident diurnal variations of R34 growth for Typhoon Haima were found, no marked diurnal variations of RMW contraction and TC intensification were detected between 2100 LST 15 October and 1500 LST 17 October 2016.
While the largest mean growth rate for RI TCs occurred at night (as shown in Figure 2), which was in line with the peak mean intensification (Wu et al., 2020) and RMW contraction rates during RI (Wu & Hong, 2022), diurnal variations in R34 growth, TC intensification, and RWM contraction were rarely detected simultaneously in each storm.This phenomenon was observed in typhoon Haima as well.Both TC intensification and size change involve complicate dynamics and thermodynamics processes.There was no one-to-one relationship between diurnal variations in R34 growth and diurnal variations in TC intensification or RMW contraction during TC intensification period.One possible reason is the location of the very deep convection has different role on TC intensification, RMW contraction and R34 growth.Very deep convection outside the RMW but within the R34 might favors R34 growth (Chan & Chan, 2013;Holland & Merrill, 1984;Ruan & Wu, 2022) but not TC intensification or RMW contraction.This could also be one possible reason for the nonlinear relationship between TC intensity and size in Wu, Tian, et al. (2015).

| SUMMARY AND DISCUSSION
Using best-track data, this paper investigated diurnal variations in growth of the radius of gale force winds for global TCs from 2001 to 2019.The radius of gale force winds tended to grow faster during nighttime (2100-0900 LST) than daytime (0900-2100 LST).For North Atlantic TCs, the maximum 6-h R34 growth rate was found at 2100-0300 LST, while for global RI TCs outside the North Atlantic region, the maximum 6-hour growth rate occurred at 0300-0900 LST.The higher R34 growth at night was associated with the higher coverage of very deep convective clouds during nighttime.While the very deep convection within the TC center is important for RMW contraction and TC intensification (Vigh & Schubert, 2009;Wu & Ruan, 2021), this study demonstrated the associated of very deep convection and R34 growth.Although TC intensification, RMW contraction, and R34 growth exhibited a nocturnal preference, we rarely detected diurnal variations in all three phenomena simultaneously in individual storms.
As both the maximum mean R34 growth rate and maximum mean RMW contraction rate occur at night, the extent of the outer-core wind skirt (R34-RMW) for RI TCs tends to grow more at night (results not shown).TC fullness, previously defined as the ratio of the extent of the outer-core wind skirt to the outer-core size of the TC (Guo & Tan, 2017), showed a similar diurnal cycle with a maximum at night (results not shown).
Further research is required to validate the observed diurnal variations in global TCs, excluding those in the North Atlantic, using more accurate observations of wind radii.Additionally, it is important to determine whether diurnal variations in R34 growth are not present in non-RI TCs, or whether the lack of diurnal response is due to statistically significant variations that are difficult to detect with the current best-track data sample size and resolution.

F
I G U R E 1 Mean TC R34 change rate in 6 h (4R34 6h ) during the course of a day in the North Atlantic Ocean during 2001-2014 for (a) the TC-OBS dataset calibrated by aircraft observations and (b) the best-track dataset.Error bars show the standard error.
) is given in Figure 4. Haima was classified as a tropical storm on 15 October 2016 in the F I G U R E 2 Mean R34 change rate in 6 h (4R34 6h ) during the course of a day for (a) North Atlantic TCs and (b) global TCs excluding the North Atlantic during 2001-2019, Error bars show the standard error.Two repeated diurnal cycles are plotted to show the continuity.RI TC (red) and non-RI TC (blue) are shown separately in (b).

F
I G U E 3 (a) Radial distributions of coverage (%) of very deep convective clouds with infrared brightness temperatures <208 K plotted against distance from the center normalized to R34 for North Atlantic TCs.The blue and red lines indicate storms during daytime (0900-2100 LST) and nighttime (2100-0900 LST), respectively.The coverage of very deep convective clouds was calculated within each interval annulus rings.(b) Diurnal variation in coverage (percentage within 200 km of the storm center) of very deep convective clouds with infrared brightness temperatures <208 K for North Atlantic TCs.(c) Same as (a) but for global TCs excluding the North Atlantic, and the dark and light lines represent RI TCs and non-RI TCs, respectively.(d) Same as (b) but for global TCs excluding the North Atlantic, and RI TCs (red) and non-RI TCs (blue) are shown separately.Error bars represent the standard error in each case.
U R E 4 (a) The 6-hourly track of Typhoon Haima (2016) colored by the Saffir-Simpson wind scale based on maximum surface wind speeds.The shading indicates the extent of the R34 during 2100 LST on 15 October and 1500 LST on 17 October.(b) The evolution of R34 and intensity (Vmax) of Typhoon Haima (2016) during 2100 LST on 15 October and 1500 LST on 17 October.The orange, green, and gray lines represent the R34, intensity, and RMW, respectively.Blue and red bars represent the change of R34 in 6 h (4R34 6h ) during daytime and nighttime, respectively.The abscissa denotes the time in the month-day-hour (local solar time) format.Infrared brightness temperature images showing Typhoon Haima (2016) between 2100 LST 15 October 2106 and 1500 LST 17 October 2016.(a), (b), (e), and (f) indicate the nighttime; (c), (d), (g), and (h) indicate the daytime.Black solid (dashed) circles represent the R34 (R34 6 h later), pink circles represent the RMW.The values of R34 and intensity at each moment are given.