1. Introduction
Tropical cyclones (TCs) remain the costliest natural disasters across the United States (Klotzbach et al. 2018; Grinsted et al. 2019). Despite overall improvements in TC intensity forecasting in recent years, forecasting of rapid intensification (RI) events has not improved at the same rate (Cangialosi et al. 2020; DeMaria et al. 2021). RI is widely defined as an increase in maximum winds of at least 30 kt (1 kt ≈ 0.51 m s−1) in 24 h, which is approximately the 95th percentile of all 24-h intensity changes (Kaplan and DeMaria 2003). With the introduction of the Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria and Kaplan 1994) the environment and internal structure of TCs have been intensively studied to contribute to the improvement of intensification forecasts, including a specific focus on RI with the SHIPS RI Index (SHIPS-RII; Kaplan and DeMaria 2003).
Two major environmental parameters, vertical wind shear (hereafter referred to as “shear”) and moisture, have been included in the SHIPS-RII in different formulations. Shear, defined as the vector difference between the 850- and 200-hPa winds, was originally calculated within a standard environmental annulus of 200–800 km from the storm center (DeMaria et al. 2005). Since 2010, a radius of 0–500 km has been used, together with a vortex removal algorithm (Kaplan et al. 2010, 2015). The 850- and 200-hPa levels have long been used as the reference levels for calculating shear due to the higher reliability of satellite-based atmospheric motion vectors (AMVs) estimated at those levels (Velden and Sears 2014). To consider some variability at the lower and upper levels, and the levels where the AMVs are most reliable, several studies calculated the shear using the average of the 300–150-hPa layers as the top and the 850–700-hPa or 925–700-hPa layer as the bottom, and both were well correlated with single-level shear (Sears and Velden 2012; Velden and Sears 2014; Rios-Berrios and Torn 2017). Nevertheless, it is meaningful to ask whether the relationship between TC intensity change and shear is sensitive to how the shear is defined, via the vertical level selection and the annulus within which the shear is computed. Moisture in the original SHIPS-RII was computed as the average relative humidity (RH) between the 700- and 850-hPa levels in the standard environment annulus of 200–800 km (Kaplan and DeMaria 2003), and this has been replaced by total precipitable water (TPW) in an upshear region of the TC (Kaplan et al. 2015). SHIPS text files produce RH in the environmental annulus using the average of the 500–700-hPa layer, and we will use those and other levels to examine the moisture around TCs.
There has been consensus that RI is more likely in environments with weaker shear, moister midlevels, and higher sea surface temperatures (SSTs) (e.g., Kaplan and DeMaria 2003; Kaplan et al. 2010; Hendricks et al. 2010; Rios-Berrios and Torn 2017). While this has been confirmed in many observational, reanalysis, and model studies, there are still many nuances in the environment preceding RI events. Hendricks et al. (2010) found that environments around RI and non-RI storms were quite similar in the North Atlantic. Using observations and synthetic hurricane events, Kowch and Emanuel (2015) concluded that high intensification rates are governed by random environmental and internal variability. A composite of global TCs under moderate shear between 1982 and 2014 found that intensifying events moved within environments of greater midtropospheric moisture and more easterly shear (Rios-Berrios and Torn 2017). Idealized TC simulations focused solely on the influence of shear found that upper-level shear is less detrimental for TC intensification (Finocchio et al. 2016). Analysis of Northern Hemisphere wind profiles also found that the deep layer shear is mostly controlled by the 200-hPa winds (Finocchio and Majumdar 2017). Using 14 Global Ensemble Forecast System ensemble members, Alvey et al. (2020) found that the shear value alone was not responsible for whether the TC intensified or not. A modeling study using different environmental shear profiles found that at a shear stronger than 7.5 m s−1, TCs did not undergo RI, and that the stronger the shear, the larger the spread in the onset time of RI among model members (Tao and Zhang 2015). Shear direction is also of importance for intensification. DeMaria (2010) found it to be most important as a function of latitude, with low latitude storms having an optimal shear direction from the northeast and higher latitude storms from the southwest. However, Ritchie and Frank (2007) and Zeng et al. (2010) found that easterly shear has a smaller effect on TC intensification than westerly shear. Most of these studies reinforce the notion that the entire vertical wind profile may not only be more representative of the real-world environment, but also more useful for understanding TC intensification than the standard definition of 850–200-hPa shear (also suggested by Onderlinde and Nolan 2017; Ryglicki et al. 2018a,b; Chan et al. 2019; Dai et al. 2021).
The combined role of increasing shear and decreasing moisture on TC intensity change has been examined, including the ventilation hypothesis (Tang and Emanuel 2012). Using an ensemble of TC simulations, Munsell et al. (2013) corroborated this hypothesis by finding that the weakest TCs had significantly drier midlevels and increased shear than the strongest TCs, which inhibited both alignment and convection from wrapping around the vortex, concluding that there is a complicated relationship between dynamic and thermodynamic factors (also suggested by Alland et al. 2021a,b). Bhatia et al. (2022) found that the mean probability (5.3%) for Atlantic TCs to undergo RI is exceeded when RH ≥ 60.4% and shear ≤ 9.2 m s−1. Using an advanced artificial intelligence system trained on the entire SHIPS developmental dataset, shear was found to be of very high importance, but RH ranked relatively low (Wei and Yang 2021). In contrast, an unsupervised learning technique on Atlantic TCs between 2004 and 2016 found that mid and upper-level RH served as an important factor in identifying the onset of RI, especially within the inner core (Mercer et al. 2021). Conflicting results on the importance of moisture and shear in intensification, which may partly be a result of different methodologies and datasets, nonetheless prompts further analysis of the various ways that TCs may be modulated by their environment.
In addition to understanding the relationships between the intensification rate at the time of onset and the environmental parameters (and their variations), the evolution of these parameters during the intensification process warrants further understanding. Using an idealized simulation, Ryglicki et al. (2019) found that the shear in the inner core within a 0–200-km radius decreased the most prior to intensification compared with a 0–500-km radius and a 200–500-km annulus. Also using idealized simulations, Dai et al. (2021) corroborated that intensification begins after the shear decreases. These findings are also evident in SHIPS and reanalysis data (Ryglicki et al. 2021; Wang and Jiang 2021). Other studies found that during the intensification period, environmental shear values were generally similar regardless of intensification rate (Shi and Chen 2021; Richardson et al. 2022). However, Shi and Chen (2021) did find that for moderate shear cases, the local shear computed within a 0–200-km radius, decreased 24 h prior to intensification onset. As for the evolution of moisture during the intensification process, Wu et al. (2012) found decreasing mid- to lower-tropospheric RH for three annuli from a near to far TC environment leading up to maximum intensity, for all quadrants around the TC. On the other hand, composites of TPW showed no difference during the intensification process below 500 hPa, although differences were present at 400 hPa (Richardson et al. 2022). Wu et al. (2015) noted that it is important to distinguish moisture in the inner core versus outer rainbands as well as different locations around the TC to better quantify its influence on intensification; a recommendation that we follow in this paper.
Asymmetries in environmental moisture have also been investigated. Observations and simulations of TCs have found upshear moistening to be characteristic of intensifying TCs, especially in moderate shear (Rios-Berrios et al. 2016b; Rios-Berrios and Torn 2017; Zawislak et al. 2016; Rios-Berrios et al. 2018). Zawislak et al. (2016) found that the lower RH values upshear needed to increase for the storm to intensify. Several ensemble studies also observed a cyclonic evolution of moisture from downshear to upshear for intensification (Rios-Berrios et al. 2016a,b; Leighton et al. 2018). In reanalysis data, Richardson et al. (2022) found that RI events have ∼8% larger RH at 400 hPa in the upshear-left quadrant prior to onset than more slowly intensifying storms. Using an ensemble of simulations of Hurricane Edouard (2014), Alvey et al. (2020) found that in the ensemble members where Edouard intensified, advection of water vapor progressed from downshear left to upshear left. This result is consistent with Tao et al. (2017) who used 16 years of Tropical Rainfall Measuring Mission satellite data to find that RI events are associated with increased rainfall, first in the upshear left quadrant 12 h before onset, and which then cyclonically rotates around during RI. Greater RH in RI than steady-state events occur in the upshear half within 200 km of the storm center (Rios-Berrios and Torn 2017).
The broad goal of this study is to differentiate how shear and RH progress during the onset of different intensification rates, within three defined annuli near and around TCs. While several prior studies have compared intensification rates, they have mostly done so with RI versus steady state or a subset of slower intensification rates. Our study encompasses all intensifying TCs in the North Atlantic from 1980 to 2021, and we will present the distribution of shear and moisture and their respective evolutions, for three different intensification brackets. We will compare the shear and RH distributions in different annuli, building on Rios-Berrios and Torn (2017) and Ryglicki et al. (2019) who found differences in these parameters within 200 km of the TC center compared with the environment. We will also investigate the evolution from 48 h before to 48 h after onset, building on Wang and Jiang (2021) and Richardson et al. (2022) who investigated mean values at more limited times. Finally, we will also investigate the climatological evolution of moisture in shear-relative quadrants, expanding beyond several aforementioned studies that used observations or model simulations of single TCs, as well as the evolution of the shear direction itself.
Following an introduction to the data and calculations performed in this study in section 2, in section 3 we will present the distributions of shear and RH across the different annuli and intensification rates at onset and compare the average shear in different RH environments. The evolution of shear and RH prior to and through each intensification process will be presented in section 4, followed by the evolution of RH in different shear-relative quadrants in section 5. The evolution of shear direction in the environment is presented in section 6. Section 7 investigates the sensitivity of the evolution of shear and RH to the different levels for calculations. Finally, conclusions are provided in section 8.
2. Data and methods
a. Best track and intensification rates
Environments within and around Atlantic TCs between 1980 and 2021 are analyzed. Six-hourly TC times are chosen based on the National Hurricane Center best track database (HURDAT2; Landsea and Franklin 2013) storm classification as either a tropical depression, tropical storm, or hurricane that had intensified at least 5 kt in the past 24 h. The previous 24-h intensification from HURDAT2 is used to classify storm times into slightly intensifying [SI, 5–10 kt (24 h)−1], moderately intensifying [MI, 15–25 kt (24 h)−1] ,and rapidly intensifying [RI, ≥30 kt (24 h)−1]. An event must be classified as a TC at onset, and subsequently through the 24-h intensification period, but may be an invest or other low pressure system up to 48 h before or after onset. Each consecutive 6-h period is the beginning of a new event, and therefore a singular TC may undergo multiple SI, MI, and RI events across its lifetime. An additional criterion is introduced to correctly identify the onset time of RI: intensification of at least 5 kt in the first 6 h post-onset. This criterion ensures an accurate onset point of RI for storms that may meet the 30 kt (24 h)−1 threshold but are not intensifying in the first 6–12 h of that period. Waiting 6 h before identifying a new RI event or only including the first event did not affect the overall distributions of the environmental variables in section 3 or time series in section 4. Consequently, all RI events, including multiple consecutive events, are included. The first RI event will be investigated separately to identify any differences between it and continuous events. The total event numbers at onset are presented in the first row of Table 1. For the time series analysis, a homogeneous set was created where an event must exist for the entire 4-day period of analysis. These case numbers are presented in the second row of Table 1.
Number of events per intensification rate for all cases at onset, a homogeneous set for time series analysis, and by environmental shear strength within the homogeneous set.
b. Reanalysis data and annuli selection
Gridded 0.25° × 0.25° European Centre for Medium-Range Weather Forecast version 5 (ERA5; Hersbach et al. 2020) data are used throughout this study. First, the 850–200-hPa shear and 500–700-hPa average RH, consistent with the definitions used in SHIPS, are computed. These variables are averaged within the SHIPS environment (referred to as “standard” here) of a 200–800-km annulus from the best track TC center. We first analyzed the distributions of shear and RH in annuli made of combinations of inner radii ranging from 0 to 300 km, every 50 km, and outer radii ranging from 500 to 800 km, every 100 km. These tests yielded minimal dependence on the inner and outer radius combination for the TC environment. The 100–600-km annulus is chosen to represent a “middle” environment and will be compared with the standard environment. A radius of 0–250 km is used to represent the “inner core” as a contrast to the two environmental annuli and to investigate how shear and RH are modulated by the TC itself. Given that the eye and near-eye region of TCs are not well resolved within ERA5, a radius of 0–250 km is used to average data over a large enough area to reduce statistical noise. Visualization of the three annuli is presented in Fig. 1 to give the reader a sense of their spatial extent around the TC.
Average 500–700-hPa RH centered at the storm center with the black, blue, and purple circles representing the 200–800-km annulus, 100–600-km annulus, and 0–250-km radius, respectively. The white arrow represents a westerly shear vector with the white dashed line perpendicular to it to showcase the shear-relative quadrants.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
c. Shear strength, moisture asymmetries, and additional depths
RH data are separated into three shear categories based on Rios-Berrios and Torn (2017). Weak shear is defined as the lowest 25% of all standard environmental shear values (<9 kt). Strong shear is defined as the top 25% (>20 kt), with moderate being in between, and relevant homogeneous case numbers are presented in Table 1. The standard environment is used to ensure that the same cases are being considered even when investigating the middle environment or inner core, whose shear values may fall outside the prescribed ranges for each category.
RH is further investigated in shear-relative quadrants around the storm. The shear direction calculated within the standard annulus is used as the basis for establishing the quadrants. For example, for a westerly shear vector, the quadrants moving cyclonically around from the upper right are as follows: downshear left (DSL), upshear left (USL), upshear right (USR), and downshear right (DSR) (Fig. 1). The standard shear vector is used for all three annuli for consistency such that RH data are computed within the same area relative to the TC regardless of annulus. The shear vector itself for the middle and standard environments is also examined relative to onset across the three intensification rates. The inner core shear vector is not included due to complexities in the inner core processes of TCs.
In addition to the shear computed between 850 and 200 hPa, shallower (925–400-hPa) and deeper (925–150-hPa) ranges are examined in section 7. Calculations of average RH in section 7 are performed for the 700–850-hPa layer to correspond to the original moisture in SHIPS-RII, a 600–800-hPa layer to evaluate lower- to midtropospheric moisture, and a 400–800-hPa layer for a deeper midtroposphere.
A schematic is presented in Fig. 2 to orient the reader on connections between the intensification rates, annuli, and all environmental variable calculations.
Schematic representing the relationships between intensification rates, annuli, and environmental variables analyzed in this study. The colors for the intensification rates RI (blue), MI (orange), and SI (green) as well as the symbols for inner core (cross), middle (square), and standard (circle) will be consistent in all figures shown. Red lines represent connections using shear direction. Purple lines represent connections with shear strength.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
d. Addressing inconsistencies between HURDAT, ERA5, and SHIPS
Slocum et al. (2022) found that the median offset between the ERA5 calculated TC position, based on the 850-hPa height and mean sea level pressure, and the best track position, is ∼25 km, approximately one grid point in ERA5. They also found the offset of the TC center within ERA5 caused an average deviation of 0.8 kt of shear (Slocum et al. 2022). When comparing ERA5-based shear and midlevel RH with SHIPS output for the North Atlantic, Slocum et al. (2022) found that ERA5 has a 0.5-kt positive bias for shear and ERA5 RH is ∼2% drier than SHIPS. Comparing ERA5 with dropwindsonde data, they also found relatively small biases. Prior to compiling the shear and RH for our full sample, we compared the ERA5-derived values to SHIPS for several TCs. We found deviations similar to those identified by Slocum et al. (2022). Given that SHIPS input is taken from the Global Forecasting System (GFS), slight discrepancies between the ERA5 and SHIPS values are expected. Since the overall sensitivities are only minor, and we are taking averages of large areas, we are confident in using the HURDAT for storm center location and ERA5 data for calculations of shear and RH.
3. Probability density functions
Normalized probability density functions (PDFs) for RI (blue), MI (orange), and SI (green) are plotted on top of each other. Given the substantial overlap of the shear and RH distributions for each of the intensification rates, the smoothed curve of the PDF for each distribution is also given to provide readers with a general idea of the probability for each intensification rate, even if the specific bar cannot be seen. The maximum of the smoothed curve (mode) corresponds closely to the value of highest probability of occurrence, and deviates by only a few knots of shear and percent of RH from the mean value. For each of our statistics, the patterns of the mode and mean values are similar. Since the mean is computed from all values including the extrema, it will be used for all discussion in this paper. Relative probability plots are computed for each annulus as follows: at a given bin, the RI, MI, and SI event numbers are divided by the summation of the three.
a. Shear
PDFs for shear at onset of all intensification rates for the inner core (Fig. 3a), middle (Fig. 3b), and standard environment (Fig. 3c) exhibit the same pattern for each annulus. Consistent with previous studies, the mean shear value within the standard annulus decreases from SI to MI to RI, with values of 16.7, 14.2, and 11.6 kt, respectively. The middle environment and inner core exhibit the same pattern of decreasing shear at faster intensification rates, providing additional support that RI is more likely at lower shear. A similar pattern exists when comparing the same intensification rate across the different annuli. The shear decreases closer to the storm center, with the mean values of shear being 11.6, 10.7, and 9 kt for the standard, middle, and inner core, respectively, for RI. When looking at the relative probability for an RI event, the highest probability occurs at shear values < 5 kt (Figs. 3d–f), much lower than the average value. Figures 3d–f also show that with increasing shear, the relative probability of both RI and MI decrease, but SI increases.
(top) PDFs and (bottom) relative probability plots of shear for the (a),(d) inner core; (b),(e) middle; and (c),(f) standard environments for RI (blue), MI (orange), and SI (green). The black line in the relative probability plots indicates total numbers of cases at each value.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
The Kolmogorov–Smirnov test (K-S test; Andrade and Estévez-Pérez 2014) and Welch’s t test are conducted to identify whether the PDFs and their respective mean values are statistically significantly different across intensification brackets and annuli. All combinations show statistical significance at the 5% levels except for the PDFs and associated mean values of shear in RI between the middle and standard environment.
b. Relative humidity
For each of the three annuli, the PDFs of RH are not as obviously discernible between intensification rates although their means occur at significantly different values (Fig. 4). The inner core exhibits the largest mean RH at 77.2%, 75.2%, and 72.0% for RI, MI, and SI, respectively (Fig. 4a), while the standard environment has the lowest RH at 57.8%, 56.4%, and 54.3%, respectively (Fig. 4c), and the middle environment falls between the two (Fig. 4b). Hence, only a few percent separate RI from SI within each radius, with RI having the highest RH, consistent with previous studies.
As in Fig. 3, but for relative humidity.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
The PDFs of RH for the three annuli have different shapes in contrast to the respective PDFs of shear that have similar shapes with distinctive peaks. In the inner core, the modal RH values for RI and MI are similar (∼81%), with a higher probability density for RI, whereas the corresponding PDF for SI has a less distinct peak at its maximum value with a consistent probability density across most RH values (Fig. 4a). The highest relative probability for RI and MI is also 81% for the inner core (Fig. 4d). For the two environmental annuli, the distributions for the three intensification rates overlap much more than for the inner core and all shear PDFs. From the relative probabilities, RH in RI peaks between 70% and 80%, and SI experiences the lowest probability in that same range (Figs. 4e,f). Via the K-S test, all distributions of RH by intensification rate and annulus are significantly different from each other at the 5% level.
The relative probability plots further illustrate the rarity of RI events in general. At values deemed to be more favorable for RI, the difference in probability between RI and SI is the smallest, but MI and SI still have a higher relative probability of occurrence.
c. First RI event
Multiple RI events within one TC usually consist of several consecutive time steps satisfying the RI definition. Since accurately forecasting the first RI event can be considered the most important, it is of interest to evaluate if and how the environment within and around the TCs changes with successive RI events. Even though there are some shear and RH values that occur more frequently for the first RI than all events and vice versa, the K-S test relays that there is no significant difference between the two groups (Fig. 5). In other words, the shear and RH value at the onset of RI is equally distributed for both groups.
PDFs of (top) shear and (bottom) RH with all RI events (dark blue bars and line) and only the first RI event (cyan bar and black line) for the (a),(d) inner core; (b),(e) middle; and (c),(f) standard environment.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
d. Shear by relative humidity
Previous results, and other studies, have shown that RI is more likely to occur at higher RH and lower shear. To determine if the average shear decreases in conjunction with increasing RH, mean shear was calculated within the following RH bins: ≤39%, 40%–49%, 50%–59%, 60%–69%, 70%–79%, and ≥80%.1 There is a general negative correlation between shear and RH, ranging from a correlation coefficient of −0.1 for the two environments in RI to −0.39 for inner-core MI (Fig. 6). The relatively low correlation can be partly explained by the values that do not follow the overall pattern. For the standard environment, the lowest shear value (9.7 kt) occurs in the lowest RH bin (≤39%). In contrast, the second lowest shear value (10.2 kt) occurs in the second highest RH bin (60%–69%). For the middle environment in RI, the lowest mean shear value (9.4 kt), occurs in the 70%–79% RH bin, and the second lowest shear value (10.1 kt), occurs in the lowest RH bin (≤49%), also suggesting that there is no reliable pattern. However, calculating mean RH by 5-kt shear bin demonstrated that higher shear is associated with lower mean RH across all intensification rates and annuli, showcasing that the variability stems from the RH environment.
Mean shear value for each RH bin. Point is plotted at the midpoint of the bin, with the first and last points encompassing cases that also occur at lower and higher RH values, respectively. Cases are separated by intensification rate: RI (blue), MI (orange), SI (green), and by radius: inner core (cross), middle (square), and standard environment (circle).
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
Next, cases per annulus and intensification rate are normalized by shear strength (defined in section 2c) and RH bin (Fig. 7), where the total per row equals 100%. From the environmental RH PDFs (Figs. 4b,c), most values occur between 50% and 70%, and this is corroborated by Fig. 7 where the darkest shades occur in that range. A surprisingly high fraction of cases in strong shear is evident when the environmental RH is 50%–59%, regardless of intensification rate, further indicating that strongly sheared TCs are still able to intensify within the presence of drier air. The general distribution of shear–RH combinations is consistent across the three intensification brackets, suggesting that there is no clear distinction based on intensity change.
Normalized count by percent of total storms per shear strength and annuli for (a) RI, (b) MI, and (c) SI.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
4. Time series
The temporal evolution of the variables relative to intensification onset is important for understanding and potentially forecasting RI versus MI and SI as the environment is not stationary in time. Here, we investigate the environment 48 h prior to and after onset for each intensification rate for our homogeneous set of cases. Due to the small absolute differences, a percent change calculation at a given time relative to onset is computed to complement the actual values. The larger the percent change, the stronger and more obvious the change is in the time series.
a. Shear
The progression of the mean shear and its standard deviation in the standard environment is shown in Fig. 8a. One can imagine the standard deviation, with an average value of 8.5 kt, as representative of the PDFs as there is a large range of shear values that may occur at any time. With such large standard deviations, the progression of shear between the different intensification rates is difficult to generalize. To better discern these differences, not only across intensification rates but also annuli, time series relative to the onset value are illustrated in Fig. 8b. Reductions in shear magnitude prior to onset are at most 2 kt, with the largest reductions 24 h prior to onset evident in the RI cases (Fig. 8b). While it may be difficult to observe a decrease in shear at such small values, the RI environment remains fairly stable between 24 and 48 h prior to RI onset whereas the MI and SI environment is changing (Fig. 8b).
Time series of (a) mean shear and standard deviation for the standard environment and (b) shear deviation relative to onset value with line color and symbols as in Fig. 6.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
All annuli show decreasing shear in the 24 h leading up to RI onset by 15.4%, 7.8%, and 3.0% in the inner core, middle, and standard environments, respectively. Even though this decrease between 24 h prior to onset and onset is insignificant, 218 cases (58%) exhibit a larger decrease in shear within the inner core than in the environment. Conversely, there is an increase in the shear for MI and SI, especially within the environment (Table 2). Only the change in shear within the two environments for SI between 48 h pre-onset and onset are significant. We also note that the average value of shear for RI onset in the homogeneous set is slightly less than for all values at onset, whereas it is larger for MI and SI. Using Welch’s t tests at each time step, annuli and intensification rates that are not significantly different are denoted in Table 3. The difference in the magnitude of change between the inner core and environments, combined with the insignificance between the middle and standard environment for RI and MI, provides evidence that multiple radii may be necessary to more accurately discern between intensification rates.
Percent change in shear relative to the mean onset value (time 0) from 48 h prior, 24 h prior, 12 h prior, 12 h after, and 24 h after onset time.
Welch’s t-test significance for pre-onset times, for annuli and intensification rates that are not significantly different. An “X” denotes nonsignificance at the 5% level at that time for the variables being compared in the second column. Shear direction and 925–125-hPa shear are not included due to nonsignificance for many of the times and variable combinations.
b. Relative humidity
As for shear, a large standard deviation of RH (∼10%) inhibits our ability to identify clear changes in the time series across different intensification rates (Fig. 9a). The differences in RH are more sensitive to the annuli than intensification rate, as was evident for shear. For RI cases, environmental RH decreases by 2%–3% in the 48 h prior to onset and is significant (Fig. 9b). 250 events (66%) exhibit this decrease in the environmental RH at 48 h pre-onset. The inner core RH, conversely, slightly increases by 1.2%, with 211 RI events (56%) experiencing this increase and is the only change between 48 h pre-onset and onset that is insignificant (Table 4). 113 RI events (30%) satisfy both conditions (environmental RH decrease and inner core RH decrease) and 348 independent events (93%) satisfy either requirement. The mean values of RH at onset for the homogeneous set are lower by a few percent compared to all values at onset, indicating that storms with shorter lifespans before intensification have moister midlevels. The opposing pattern of increasing RH in the inner core for RI and MI versus decrease in the environments and for all annuli for SI could allow for the use of multiple annuli to help identify and statistically predict the intensification rate.
As in Fig. 8, but for relative humidity.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
c. Relative humidity by shear environment
Given that the average shear value is moderately negatively correlated with the environmental RH (section 3d), the evolution of RH in the three shear categories is investigated here (Fig. 10). In moderate shear (Fig. 10b), the RH shows a similar progression as for the full dataset (Fig. 9b). The increase in inner-core RH prior to RI onset is larger in moderate shear, and the decrease in RH in the environments is smaller. The change in the inner core and middle environment RH for RI between 48 h pre-onset and onset is insignificant, compared to only the inner core for the entire set. Most cases fall into a moderate shear environment, so this may be a reason behind their similarities.
Time series of relative humidity deviation relative to onset for (a) weak shear, (b) moderate shear, and (c) strong shear. Line color and symbols as in Fig. 6.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
The weak (Fig. 10a) and strong (Fig. 10c) shear environments produce different evolutions of RH relative to onset. For RI cases in weak shear, the inner-core RH only slightly increases. The environmental RH for RI cases in weak shear prior to onset decreases slightly more sharply than for moderate. Another interesting difference for the weak shear cases is that SI has smaller changes within the inner core (Fig. 10a). In strong shear only the inner core for RI sees an increase in RH whereas the rest are decreasing at a larger rate than for other shear environments (Fig. 10c). The percent changes for the different shear environments, as well as all additional calculations presented in this study, are available in the supplemental material. Table 3 indicates that there is no significant difference between MI and SI across the three annuli for most times pre-onset when the environment is separated by the shear. Additionally, for all three annuli for RI, the change in RH from 48 h pre-onset to onset is insignificant. The differing behavior of RH prior to onset based on the environmental shear adds an additional sensitivity that one must consider in addition to the annulus that the RH is computed within.
d. First RI event
The PDFs for the first RI onset displayed no significant differences for either shear or RH across all radii (Fig. 5). The evolution of the environmental shear and RH for the first RI onset is crucial for forecasting, but yet again, there are not many noticeable differences between the first event versus all combined (Fig. 11). Shear for the first RI event tends to be slightly higher than overall (Fig. 11a), and vice versa for RH (Fig. 11b). Deviations relative to the onset value for RH are practically the same whether for the first RI event or for all (Fig. 11d). For shear, on the other hand, the first RI event shows more fluctuations in the pre-onset times than for all RI events (Fig. 11c). This pattern indicates that the shear can be more sensitive to continuous RI events than RH.
Time series of (a),(c) shear and (b),(d) relative humidity of (top) actual values and (bottom) deviations relative to the onset value for all RI events (dark blue) and first RI event (cyan) with symbols as in Fig. 6.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
5. Shear-relative quadrants
Several observational and modeling studies have noted the importance of upshear moistening before intensification (Rios-Berrios et al. 2016b; Rios-Berrios and Torn 2017; Zawislak et al. 2016; Rios-Berrios et al. 2018). Figure 12 presents the RH time series for each shear-relative quadrant for all radii and intensification rates. The two downshear quadrants (Figs. 12b,d) are moister than the upshear quadrants (Figs. 12a,c). Richardson et al. (2022) found that RI events have ∼8% greater RH in USL prior to onset at the 400-hPa level. Our results show RI events having ∼8% greater RH than SI events at 48 h prior to onset in USL in the standard environment and is the largest out of all quadrants. RH deviations from onset for each quadrant are plotted to better ascertain differences in the evolution of RH (Fig. 13). For RI events, there is a distinctly different behavior in the environment versus the inner core, with the USR quadrant (Fig. 13c) having a different pattern than the rest. During the 24 h prior to RI onset, DSR, DSL, and USL all see a decrease in RH in the two environments of 2%–4% (Figs. 13a,b,d). In contrast, the RH in the USR middle environment increases by 2% and by 0.5% in the standard environment (Fig. 13c). Within the inner core, both right quadrants exhibit an increase in RH in the day prior to onset (with the USR having the largest), whereas DSL experience a decrease and USL a minimal increase.
Time series of relative humidity for (a) upshear left, (b) downshear left, (c) upshear right, and (d) downshear right as depicted in Fig. 1. Line colors and symbols as in Fig. 6.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
As in Fig. 12, but for relative humidity deviations from onset.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
In the day leading up to MI, RH increases in the inner core for all quadrants and only minimally in DSL for SI. Most of the nonsignificance within the quadrants is between MI and SI in the inner core (Table 3). Within the environments, generally the downshear quadrants have a smaller decrease in RH and a larger decrease in the upshear quadrants for MI and SI as compared to RI (Table S4 in the online supplemental material). Separating the environment by shear-relative quadrant has allowed for additional discrimination between intensification rate and annuli, as the moistening of USR during the day prior to onset is only seen in RI events.
With a large, 42-yr climatology, we expect that any patterns that can be discerned from the time series are useful. However, as with the results for the full annulus, many TCs that undergo RI do not experience all the relationships that have been identified. 206, 235, and 191 RI events (55%, 63%, and 51%) experience an increase in RH in the inner core, middle, and standard environment, respectively, of USR within 24 h prior to onset, even though this change is insignificant. In contrast, only 119 RI events (32%) experience an increase in RH in all three radii in USR, with Hurricanes Dorian (2019) and Iota (2020) being two examples (Fig. 14). For Dorian (Fig. 14a), the USR region mostly contains low RH air 24 h prior to onset, yet this region becomes the moistest at onset (Fig. 14b). In Iota, the USR region is already moist at 24 h prior to onset (Fig. 14c), and it experiences a further (small) increase in RH at onset (Fig. 14d). If we consider either moistening in USR and drying in the environment in any of the three other quadrants from 24 h pre-onset, 338 RI events (90%) satisfy that condition. Instead of focusing on one possible evolution for RH during RI, the multiple annuli and quadrants allow for several possibilities which may result in more events being identified correctly as RI.
500–700-hPa average RH for (a),(c) 24 h prior to onset of RI and (b),(d) RI onset for (top) Hurricane Dorian (2019) and (bottom) Hurricane Iota (2020). Circles represent the 200–800-km annulus, the black arrow is the environmental shear direction, and white dotted lines are placed to indicate the quadrants with USR labeled.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
Despite visualization of the RH field around onset, it is still difficult to conclude whether the moistening in the USR quadrant is due to the cyclonic wrapping of convection described in previous studies. It can be a by-product of the TC moving into a generally moister environment or it could be a result of the change in shear direction, which allows the USR quadrant to occupy a new area that was already moist. Given that the USR quadrant is the driest compared to all other quadrants (Fig. 12), any change in shear direction would allow the new USR quadrant to occupy either the moister old USL or DSR quadrant. Figure 14 also depicts the nonuniformity of the RH field around a TC and how using a single average value over such a large environment can remove these nuances that may be important for intensification.
6. Shear direction
Only the magnitude of shear has been considered so far. The direction may provide additional insights into differences between intensification rates, and this is presented in Fig. 15. First, the shear direction for the two environmental annuli is on average westerly for each of the intensification brackets and regardless of whether all cases are considered (Fig. 15a) or they are split between low and high latitudes (Figs. 15b,c). However, the evolution of the shear vector is distinct between the intensification brackets and latitudes. RI storms (blue lines) show the largest change in shear direction for all cases, starting out the most northwesterly and changing over the 48 h leading up to onset of 35.7° and 23.7° for the middle and standard environments, respectively. SI storms (green lines) have the smallest change in direction pre-onset of ∼6°. The shear direction continues to shift through intensification with all cases showing a south of westerly shear direction by the end of the intensification process. For cases south of 20°N, there is a much larger change for both MI and RI cases, starting out far more northeasterly (Fig. 15b). For cases north of 20°N, all intensification rates show minimal change from pre-onset (Fig. 15c). Our results corroborate the findings in DeMaria (2010). The consideration of all cases shows the most significant differences between the intensification brackets, although there is an insignificant difference between the annuli for each intensification rate.
Evolution of wind shear direction (a) all cases, (b) cases south of 20°N at onset, and (c) cases north of and including 20°N at onset for middle (square) and standard (circle) environments for SI (green), MI (orange), and RI (blue). Black outline of shape indicates point 48 h prior to onset, white outline indicates onset, and the end of line indicates 48 h post-onset. The shear direction is plotted such that vector begins at the line and ends in the center.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
While Fig. 15 depicts the average shear direction over all TCs within their respective intensification brackets, the evolution within each storm differs. For Hurricanes Dorian and Iota, the change in shear direction did not follow this pattern and instead moved from a south of westerly shear 24 h prior to onset to a north of westerly shear at onset (Fig. 14). This example shows that a storm may follow the climatological pattern for one variable, in this case RH evolution in shear-relative quadrants, but not shear direction.
7. New levels for shear and RH computations
a. Shear
Different upper and lower levels for shear calculations are investigated to test if the standard 850–200-hPa shear yields the highest discernibility between annuli and intensification rates. The values of the shear deviations relative to onset for 925–400 (Fig. 16a) and 925–125 hPa (Fig. 16b) are similar to standard shear (Fig. 8b). The difference in percent change between 48 and 24 h prior to onset relative to onset for all annuli is ∼1% for standard shear (Table 2), but ∼7% for the 925–400-hPa layer (Table S5). This reveals that the 850–200-hPa shear does not exhibit much change until about 12 h prior to onset whereas in a shallower, lower layer, the shear changes more over the course of the 48 h prior to onset. The change in shear from 48 h pre-onset to onset in the 925–400-hPa layer for all annuli is significant, whereas it is not for the standard shear.
Time series of shear deviation relative to onset for (a) 925–400- and (b) 925–125-hPa shear for RI (light blue), MI (yellow), and SI (light green). Line symbols are as in Fig. 6.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
b. Relative humidity
In the original SHIPS-RII, moisture was represented by the average RH of the 700–850-hPa layer (Kaplan and DeMaria 2003). Even though it is no longer used, its time series, along with 600–800-hPa and 400–800-hPa layer averages are investigated here as a comparison with the now-standard 500–700-hPa layer (Fig. 17). Within the 700–850-hPa layer (Fig. 17a), all annuli and intensification rates show a decrease in RH throughout the time series; a direct contrast to the 500–700-hPa layer (Fig. 9b). The 600–800-hPa layer (Fig. 17b) is closer to the 500–700-hPa layer, but only has minimal increase in the inner core RH for RI and MI. The 400–800-hPa layer (Fig. 17c), is the most similar to the original, although showing a stronger increase in RH in the inner core prior to RI and MI and a weaker decrease in SI for the environments. The change in RH in the inner core between 48 h pre-onset and onset in the 400–800-hPa layer is significant whereas the change in the two environments is significant for the 600–800-hPa layer. The average RH value at onset for all new layers were larger than for their respective annuli and intensification bracket, but all still fell within one standard deviation of the 500–700-hPa mean (Table S6). This somewhat proves the robustness of the use of the 500–700-hPa layer for TC intensity distinction with the opportunity to expand the midtroposphere to encapsulate the 400–800-hPa layer.
Time series of relative humidity deviation relative to onset for (a) 700–850, (b) 600–800, and (c) 400–800 hPa. Line color and symbols are as in Fig. 16.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-23-0045.1
8. Conclusions
This study investigated vertical wind shear and moisture in and around all North Atlantic intensifying TCs between 1980 and 2021, separating events by slightly, moderately, and rapidly intensifying. The standard 850–200-hPa vertical wind shear and layer-averaged 500–700-hPa RH within a 0–250-km radius were examined to evaluate the relationship within the inner core, and within 100–600-km (“middle”) and 200–800-km (“standard”) annuli to diagnose sensitivities in the environment. The evolution of RH was explored in weak, moderate, and strong shear. A similar analysis for RH was also conducted for shear-relative quadrants to ascertain which areas around the TCs provided the most distinct signals. Last, the direction of the shear vector and the sensitivities to the choices of pressure levels for shear and RH were investigated.
Consistent with results from previous studies (e.g., Kaplan and DeMaria 2003; Kaplan et al. 2010; Hendricks et al. 2010; Rios-Berrios and Torn 2017), we found that the onset of RI is more likely to occur at lower shear and higher RH compared with MI and SI, for each individual annulus. Shear was found to be lowest, and RH highest within the inner core. Average shear values at onset for all intensification rates and radii were found to be of moderate shear strength. The PDFs show immense overlap across intensification rates and annuli, demonstrating that RI may occur over a broad range of environmental combinations, including at high shear and low RH. Most environmental RH values fall within the 50%–70% range for all intensification rates and annuli; however, the relative probability of RI peaks above 70%.
Despite substantial overlap between the PDFs for RI, MI, and SI, Kolmogorov–Smirnov tests confirmed that they are significantly different across all intensification rates and annuli for shear and RH. The one exception is for shear at RI onset between the middle and standard environment. Therefore, the specific environmental annulus that is used to define shear may not be as important as for other variables, such as RH, where distributions were most distinct when comparing annuli within a given intensification bracket. The first RI event classification provided no significant difference in either distributions or time series as compared with all RI events. This essentially may be useful for forecasters as they do not generally need to seek different environmental shear and RH behaviors when forecasting the first versus subsequent RI events.
The time evolution of shear and RH provided additional insight into differences between intensification rates and annuli. Most significantly for shear, the magnitude and timing of the change in shear prior to onset differs per radius and intensification rate. For RH, the inner-core RH increases for RI while it decreases in the environment and all three annuli decrease for SI. For shear-relative quadrants, USR showed the greatest moistening compared with other quadrants which contrasts with previous studies that emphasized the USL. Storms below 20°N showed the largest change in shear direction prior to onset, especially for RI and MI cases, whereas storms above 20°N exhibited minimal change, and all cases fell in between. Regardless of intensification bracket, all storms exhibit a near-westerly shear at onset. Additional shear calculations provided evidence of different timings for the shear decrease prior to RI onset, and a deeper RH layer yielded a stronger ability to discriminate between the intensification categories.
Combining changes over time and significance, we make the following recommendations, in order of importance, for forecasters and intensification models to further assess the adaptability of our results into TC RI forecasting. The significance is focused on the differences between annuli and intensification rate as opposed to individual changes over time, as these displayed less significance across the board. The first is a focus on the increase in USR RH, in contrast to an environmental decrease in the other quadrants, as this occurred for 90% of our homogeneous sample of cases. With the SHIPS-RII already examining an area of ±45° of the upshear area, this suggests a further restriction solely into the USR region. The next would be a focus on the RH in the entire annulus due to the opposing pattern within the inner core and environments. Furthermore, the change from 48 h pre-onset to onset for the two environments for the 500–700-hPa and 600–800-hPa layers are significant, whereas it is so for the inner core for the 400–800-hPa layer, which also shows the largest increase. This perhaps indicates the potential to expand the midtropospheric moisture layer to 800 hPa. The last suggestion would be to look at the shear within the 925–400-hPa layer, a shallower, lower layer than the current 850–200-hPa layer in SHIPS-RII, as all annuli for RI had a significant change between 48 h pre-onset and onset.
For simplicity and initial testing within statistical models such as SHIPS, a radius representing the inner core of the TC can be introduced as an addition to the current environmental annulus. This enables forecasters to identify the role of the distribution of winds and moisture within the TC itself in addition to the larger environment. We also recommend the exploration of whether the temporal changes in shear and RH described in this study are evident in real-time, as we acknowledge that the overall changes are relatively small in the climatology and possibly within uncertainties of our data.
The inner-core relationships investigated in the climatology are limited by the resolution of our dataset and TC center location errors. Inner-core dynamics will be explored in future modeling studies to evaluate how well the reanalysis data matches with a higher-resolution model, and to investigate the processes behind the relationships. Additionally, only two variables are explored, and the TC is modulated by additional conditions, such as SST, that influence its intensification. Furthermore, absolute annuli were used to calculate environmental averages, but the size of the storm may also have an impact on these calculations and can be investigated in future studies.
Overall, this study demonstrates not only that different environments are important for distinguishing between intensification rates, but also that the temporal evolution of wind and moisture varies based on intensification. The fact that these differences in progression of shear and RH are noticeable in a 42-yr climatology is noteworthy, but this does not indicate that all events follow the patterns described. A majority of RI cases can satisfy one of the relationships shown, and as more relationships are added as possibilities, the number of satisfied cases increases, with 93% of RI events seeing either an increase in inner core RH or a decrease in environmental RH from 48 h prior to onset. Different patterns revealed by the annuli and quadrants contribute to the idea that a two-annuli system that can diagnose different parts of the near and far TC environment may be useful for RI forecasting.
Due to limited data for some annuli at the ends of the distribution, the first bin for the inner core was ≤59%, the first bin for the middle was ≤49%, and the last bin for the standard environment was ≥70%.
Acknowledgments.
This research was supported by the Office of Naval Research Grant N00014-20-1-2075. The authors thank Cameron Masiello and Zachary Michael for their introductory work on analyzing shear and RH. The authors also thank Phil Klotzbach and Brian McNoldy for their comments, and Mark DeMaria and two anonymous reviewers for their reviews.
Data availability statement.
Tropical cyclone best track data are available from the National Hurricane Center best track database at https://www.nhc.noaa.gov/data/. ERA5 data are available through the Climate Data Store at https:/cds.climate.copernicus.eu.
REFERENCES
Alland, J. J., B. H. Tang, K. L. Corbosiero, and G. H. Bryan, 2021a: Combined effects of midlevel dry air and vertical wind shear on tropical cyclone development. Part I: Downdraft ventilation. J. Atmos. Sci., 78, 763–782, https://doi.org/10.1175/JAS-D-20-0054.1.
Alland, J. J., B. H. Tang, K. L. Corbosiero, and G. H. Bryan, 2021b: Combined effects of midlevel dry air and vertical wind shear on tropical cyclone development. Part II: Radial ventilation. J. Atmos. Sci., 78, 783–796, https://doi.org/10.1175/JAS-D-20-0055.1.
Alvey, G. R., III, E. Zipser, and J. Zawislak, 2020: How does Hurricane Edouard (2014) evolve toward symmetry before rapid intensification? A high-resolution ensemble study. J. Atmos. Sci., 77, 1329–1351, https://doi.org/10.1175/JAS-D-18-0355.1.
Andrade, J. M., and M. G. Estévez-Pérez, 2014: Statistical comparison of the slopes of two regression lines: A tutorial. Anal. Chim. Acta, 838, 1–12, https://doi.org/10.1016/j.aca.2014.04.057.
Bhatia, K., and Coauthors, 2022: A potential explanation for the global increase in tropical cyclone rapid intensification. Nat. Commun., 13, 6626, https://doi.org/10.1038/s41467-022-34321-6.
Cangialosi, J. P., E. Blake, M. DeMaria, A. Penny, A. Latto, E. Rappaport, and V. Tallapragada, 2020: Recent progress in tropical cyclone intensity forecasting at the National Hurricane Center. Wea. Forecasting, 35, 1913–1922, https://doi.org/10.1175/WAF-D-20-0059.1.
Chan, K. T. F., D. Wang, Y. Zhang, W. Wanawong, M. He, and X. Yu, 2019: Does strong vertical wind shear certainly lead to the weakening of a tropical cyclone? Environ. Res. Commun., 1, 015002, https://doi.org/10.1088/2515-7620/aaecac.
Dai, Y., S. J. Majumdar, and D. S. Nolan, 2021: Tropical cyclone resistance to strong environmental shear. J. Atmos. Sci., 78, 1275–1293, https://doi.org/10.1175/JAS-D-20-0231.1.
DeMaria, M., 2010: Tropical cyclone intensity change predictability estimates using a statistical-dynamical model. 29th Conf. on Hurricanes and Tropical Meteorology, Tucson, AZ, Amer. Meteor. Soc., 9C.5, https://ams.confex.com/ams/pdfpapers/167916.pdf.
DeMaria, M., and J. Kaplan, 1994: A Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic basin. Wea. Forecasting, 9, 209–220, https://doi.org/10.1175/1520-0434(1994)009<0209:ASHIPS>2.0.CO;2.
DeMaria, M., M. Mainelli, L. K. Shay, J. A. Knaff, and J. Kaplan, 2005: Further improvements to the Statistical Hurricane Intensity Prediction Scheme (SHIPS). Wea. Forecasting, 20, 531–543, https://doi.org/10.1175/WAF862.1.
DeMaria, M., J. L. Franklin, M. J. Onderlinde, and J. Kaplan, 2021: Operational forecasting of tropical cyclone rapid intensification at the National Hurricane Center. Atmosphere, 12, 683, https://doi.org/10.3390/atmos12060683.
Finocchio, P. M., and S. J. Majumdar, 2017: A statistical perspective on wind profiles and vertical wind shear in tropical cyclone environments of the Northern Hemisphere. Mon. Wea. Rev., 145, 361–378, https://doi.org/10.1175/MWR-D-16-0221.1.
Finocchio, P. M., S. J. Majumdar, D. S. Nolan, and M. Iskandarani, 2016: Idealized tropical cyclone responses to the height and depth of environmental vertical wind shear. Mon. Wea. Rev., 144, 2155–2175, https://doi.org/10.1175/MWR-D-15-0320.1.
Grinsted, A., P. Ditlevsen, and J. H. Christensen, 2019: Normalized U.S. hurricane damage estimates using area of total destruction, 1900–2018. Proc. Natl. Acad. Sci. USA, 116, 23 942–23 946, https://doi.org/10.1073/pnas.1912277116.
Hendricks, E. A., M. S. Peng, B. Fu, and T. Li, 2010: Quantifying environmental control on tropical cyclone intensity change. Mon. Wea. Rev., 138, 3243–3271, https://doi.org/10.1175/2010MWR3185.1.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18, 1093–1108, https://doi.org/10.1175/1520-0434(2003)018<1093:LCORIT>2.0.CO;2.
Kaplan, J., M. DeMaria, and J. A. Knaff, 2010: A revised tropical cyclone rapid intensification index for the Atlantic and eastern North Pacific basins. Wea. Forecasting, 25, 220–241, https://doi.org/10.1175/2009WAF2222280.1.
Kaplan, J., and Coauthors, 2015: Evaluating environmental impacts on tropical cyclone rapid intensification predictability utilizing statistical models. Wea. Forecasting, 30, 1374–1396, https://doi.org/10.1175/WAF-D-15-0032.1.
Klotzbach, P. J., S. G. Bowen, R. Pielke Jr., and M. Bell, 2018: Continental U.S. hurricane landfall frequency and associated damage: Observations and future risks. Bull. Amer. Meteor. Soc., 99, 1359–1376, https://doi.org/10.1175/BAMS-D-17-0184.1.
Kowch, R., and K. Emanuel, 2015: Are special processes at work in the rapid intensification of tropical cyclones? Mon. Wea. Rev., 143, 878–882, https://doi.org/10.1175/MWR-D-14-00360.1.
Landsea, C. W., and J. L. Franklin, 2013: Atlantic hurricane database uncertainty and presentation of a new database format. Mon. Wea. Rev., 141, 3576–3592, https://doi.org/10.1175/MWR-D-12-00254.1.
Leighton, H., S. Gopalakrishnan, J. A. Zhang, R. F. Rogers, Z. Zhang, and V. Tallapragada, 2018: Azimuthal distribution of deep convection, environmental factors, and tropical cyclone rapid intensification: A perspective from HWRF ensemble forecasts of Hurricane Edouard (2014). J. Atmos. Sci., 75, 275–295, https://doi.org/10.1175/JAS-D-17-0171.1.
Mercer, A. E., A. D. Grimes, and K. M. Wood, 2021: Application of unsupervised learning techniques to identify Atlantic tropical cyclone rapid intensification environments. J. Appl. Meteor. Climatol., 60, 119–138, https://doi.org/10.1175/JAMC-D-20-0105.1.
Munsell, E. B., F. Zhang, and D. P. Stern, 2013: Predictability and dynamics of a nonintensifying tropical storm: Erika (2009). J. Atmos. Sci., 70, 2505–2524, https://doi.org/10.1175/JAS-D-12-0243.1.
Onderlinde, M. J., and D. S. Nolan, 2017: The tropical cyclone response to changing wind shear using the method of time‐varying point‐downscaling. J. Adv. Model. Earth Syst., 9, 908–931, https://doi.org/10.1002/2016MS000796.
Richardson, J. C., R. D. Torn, and B. H. Tang, 2022: An analog comparison between rapidly and slowly intensifying tropical cyclones. Mon. Wea. Rev., 150, 2139–2156, https://doi.org/10.1175/MWR-D-21-0260.1.
Rios-Berrios, R., and R. D. Torn, 2017: Climatological analysis of tropical cyclone intensity changes under moderate vertical wind shear. Mon. Wea. Rev., 145, 1717–1738, https://doi.org/10.1175/MWR-D-16-0350.1.
Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016a: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part I: Katia (2011). J. Atmos. Sci., 73, 71–93, https://doi.org/10.1175/JAS-D-15-0052.1.
Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016b: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part II: Ophelia (2011). J. Atmos. Sci., 73, 1555–1575, https://doi.org/10.1175/JAS-D-15-0245.1.
Rios-Berrios, R., C. A. Davis, and R. D. Torn, 2018: A hypothesis for the intensification of tropical cyclones under moderate vertical wind shear. J. Atmos. Sci., 75, 4149–4173, https://doi.org/10.1175/JAS-D-18-0070.1.
Ritchie, E. A., and W. M. Frank, 2007: Interactions between simulated tropical cyclones and an environment with a variable Coriolis parameter. Mon. Wea. Rev., 135, 1889–1905, https://doi.org/10.1175/MWR3359.1.
Ryglicki, D. R., J. H. Cossuth, D. Hodyss, and J. D. Doyle, 2018a: The unexpected rapid intensification of tropical cyclones in moderate vertical wind shear. Part I: Overview and observations. Mon. Wea. Rev., 146, 3773–3800, https://doi.org/10.1175/MWR-D-18-0020.1.
Ryglicki, D. R., J. D. Doyle, Y. Jin, D. Hodyss, and J. H. Cossuth, 2018b: The unexpected rapid intensification of tropical cyclones in moderate vertical wind shear. Part II: Vortex tilt. Mon. Wea. Rev., 146, 3801–3825, https://doi.org/10.1175/MWR-D-18-0021.1.
Ryglicki, D. R., J. D. Doyle, D. Hodyss, J. H. Cossuth, Y. Jin, K. C. Viner, and J. M. Schmidt, 2019: The unexpected rapid intensification of tropical cyclones in moderate vertical wind shear. Part III: Outflow–environment interaction. Mon. Wea. Rev., 147, 2919–2940, https://doi.org/10.1175/MWR-D-18-0370.1.
Ryglicki, D. R., C. S. Velden, P. D. Reasor, D. Hodyss, and J. D. Doyle, 2021: Observations of atypical rapid intensification characteristics in Hurricane Dorian (2019). Mon. Wea. Rev., 149, 2131–2150, https://doi.org/10.1175/MWR-D-20-0413.1.
Sears, J., and C. S. Velden, 2012: Validation of satellite-derived atmospheric motion vectors and analyses around tropical disturbances. J. Appl. Meteor. Climatol., 51, 1823–1834, https://doi.org/10.1175/JAMC-D-12-024.1.
Shi, D., and G. Chen, 2021: The implication of outflow structure for the rapid intensification of tropical cyclones under vertical wind shear. Mon. Wea. Rev., 149, 4107–4127, https://doi.org/10.1175/MWR-D-21-0141.1.
Slocum, C. J., M. N. Razin, J. A. Knaff, and J. P. Stow, 2022: Does ERA5 mark a new era for resolving the tropical cyclone environment? J. Climate, 35, 7147–7164, https://doi.org/10.1175/JCLI-D-22-0127.1.
Tang, B., and K. Emanuel, 2012: Sensitivity of tropical cyclone intensity to ventilation in an axisymmetric model. J. Atmos. Sci., 69, 2394–2413, https://doi.org/10.1175/JAS-D-11-0232.1.
Tao, C., H. Jiang, and J. Zawislak, 2017: The relative importance of stratiform and convective rainfall in rapidly intensifying tropical cyclones. Mon. Wea. Rev., 145, 795–809, https://doi.org/10.1175/MWR-D-16-0316.1.
Tao, D., and F. Zhang, 2015: Effects of vertical wind shear on the predictability of tropical cyclones: Practical versus intrinsic limit. J. Adv. Model. Earth Syst., 7, 1534–1553, https://doi.org/10.1002/2015MS000474.
Velden, C. S., and J. Sears, 2014: Computing deep-tropospheric vertical wind shear analyses for tropical cyclone applications: Does the methodology matter? Wea. Forecasting, 29, 1169–1180, https://doi.org/10.1175/WAF-D-13-00147.1.
Wang, X., and H. Jiang, 2021: Contrasting behaviors between the rapidly intensifying and slowly intensifying tropical cyclones in the North Atlantic and eastern Pacific basins. J. Climate, 34, 987–1003, https://doi.org/10.1175/JCLI-D-19-0908.1.
Wei, Y., and R. Yang, 2021: An advanced artificial intelligence system for investigating tropical cyclone rapid intensification with the SHIPS database. Atmosphere, 12, 484, https://doi.org/10.3390/atmos12040484.
Wu, L., and Coauthors, 2012: Relationship of environmental relative humidity with North Atlantic tropical cyclone intensity and intensification rate. Geophys. Res. Lett., 39, L20809, https://doi.org/10.1029/2012GL053546.
Wu, L., H. Su, R. G. Fovell, T. J. Dunkerton, Z. Wang, and B. H. Kahn, 2015: Impact of environmental moisture on tropical cyclone intensification. Atmos. Chem. Phys., 15, 14 041–14 053, https://doi.org/10.5194/acp-15-14041-2015.
Zawislak, J., H. Jiang, G. R. Alvey III, E. J. Zipser, R. F. Rogers, J. A. Zhang, and S. N. Stevenson, 2016: Observations of the structure and evolution of Hurricane Edouard (2014) during intensity change. Part I: Relationship between the thermodynamic structure and precipitation. Mon. Wea. Rev., 144, 3333–3354, https://doi.org/10.1175/MWR-D-16-0018.1.
Zeng, Z., Y. Wang, and L. Chen, 2010: A statistical analysis of vertical shear effect on tropical cyclone intensity change in the North Atlantic. Geophys. Res. Lett., 37, L02802, https://doi.org/10.1029/2009GL041788.