1. Introduction
Improvements in intensity prediction for tropical cyclones (TCs) have notably lagged the advances made in TC track predictions over the last few decades (Landsea and Cangialosi 2018). However, over the last decade, and in large part due to advancements made in the Hurricane Forecast Improvement Program (Gall et al. 2013), the skill of intensity predictions from dynamical models has started to increase, becoming competitive with statistical-dynamical models (Cangialosi et al. 2020). Dynamical models continue to struggle with the prediction of large intensity fluctuations caused by processes such as rapid intensification and eyewall replacement cycles (ERCs). Since large intensity changes are thought to originate from TC inner core dynamics (Gall et al. 2013), improvements to the horizontal grid spacing, model parameterizations, and analyzed storm structure from improving data assimilation (DA) techniques should provide more accurate forecasts for these events.
The ERC is a common process in mature TCs that acts to modulate their intensity and wind field size. TCs that undergo this process are characterized by concentric eyewalls (Houze et al. 2007; Sitkowski et al. 2011; Willoughby et al. 1982). With a large set of aircraft reconnaissance data, Sitkowski et al. (2011) demonstrated that most ERCs can be broken into three distinct phases. The first, labeled “intensification,” occurs when a secondary wind maximum develops radially outward of the primary wind maxima. Both wind maxima contract inward while intensifying. This phase is completed when the primary wind maximum reaches its peak intensity. The second phase, or “weakening” phase, is characterized by the secondary wind maxima continuing to contract and intensify while the primary eyewall weakens, ending when the intensity of the two wind maxima equal each other. Last, the third phase, or “re-intensification” phase, is marked by the further intensification of the secondary wind maximum while the primary wind maximum begins to decay. When the primary wind maximum is no longer detected, the ERC is completed. The TC is left with the former secondary wind maximum as the new primary wind maximum, which usually resides at greater radius than the original. In most cases, ERCs lead to the broadening of the TC vortex (Maclay et al. 2008; Sitkowski et al. 2011), which can have forecasting implications depending on the TC’s proximity to land (Irish et al. 2008). Two notable hurricanes, Katrina (2005) and Ike (2008), weakened before landfall as a result of an ERC but saw an expansion of their wind fields that affected the spatial extent of storm surge impacts.
Currently, the only objective tool available to forecasters for predicting the onset and intensity/structural changes associated with ERCs are statistical models (Kossin and Sitkowski 2009, 2012), making successful prediction of ERC events with dynamical modeling important for the advancement of TC intensity prediction. In addition, the development of advanced DA techniques is expected to provide more realistic analyzed TC structure to help identify when a TC is likely to undergo intensity changes associated with ERCs. Most of the modeling studies of ERCs focus on the mechanisms responsible for one of their phases (Didlake et al. 2017), with the most frequent one being secondary eyewall formation given its importance for the subsequent intensity changes. Modeling studies of ERCs have consisted of both idealized (Kepert 2013; Rozoff et al. 2008; Terwey and Montgomery 2008; Wang 2008a,b; Zhou and Wang 2009, 2011) and real cases (Abarca and Corbosiero 2011; Houze et al. 2007; Zhang et al. 2005). Of the modeling studies for real cases, there has been a focus on the ability of the model to capture general features of the ERC. For example, Abarca and Corbosiero (2011) and Houze et al. (2007) demonstrated that features of the ERC conceptual model such as the establishment of a secondary eyewall, contraction of the secondary eyewall, and decay of the primary eyewall could be qualitatively captured in their numerical simulations of Hurricanes Katrina and Rita, respectively. This result demonstrated the potential of convection allowing models to capture key processes associated with the ERC. These early studies, however, did not examine how realistic the forecasts were compared with observations during the ERC. Specifically, these studies did not study the accuracy of ERC predictions in terms of the timing of phase changes and the overall morphology of the TC structure in comparison with available observations. One of the goals of this study is to investigate and verify against observations the ability of HWRF, with the advanced assimilation of inner core Doppler radar (ICDR) observations, to analyze and predict an ERC event for a real case of Hurricane Matthew (2016).
To obtain the accurate prediction of ERC events, more accurate analyses of TC kinematic and thermodynamic structures are expected to initialize the numerical model through the advancement of data assimilation. Over the last decade, the implementation of ensemble-based DA for TC prediction (Aksoy et al. 2012, 2013; Dong and Xue 2013; Li et al. 2012; Lu et al. 2017a,b; Torn 2010; Weng and Zhang 2012; Zhang et al. 2009) along with the assimilation of high-resolution TC inner core observations has shown promise for TC prediction. More skillful intensity predictions as well as more realistic analyzed and predicted storm structure are demonstrated by assimilating the aircraft-born TDR observations for both case (Aksoy et al. 2012; Lu et al. 2017b; Weng and Zhang 2012) and systematic studies (Aksoy et al. 2013; Lu et al. 2017a; Zhang et al. 2011). Another source of high spatial and temporal resolution inner core observations is from coastal ground-based radar surveillance stations (hereinafter GBR for “ground-based radar”) that can sample TCs near and during landfall. Numerous studies have shown improvements to the analyzed TC structure and intensity forecasts after the assimilation of GBR observations (Dong and Xue 2013; Li et al. 2012; Wang et al. 2014, 2016; Zhao and Xue 2009; Zhang et al. 2009; Zhu et al. 2016).
Most studies assimilating TDR or GBR observations have prioritized improvements to the track and intensity forecasts, as well as more realistically analyzed and predicted storm structure. Different from these early studies, this study places an emphasis on exploring the impact of assimilating these observations on the prediction specifically associated with the ERC process. During the ERC of Hurricane Matthew, it was sampled by both GRB and TDR with differing temporal availabilities. Another goal of the study is to investigate the relative impact of assimilating the TDR and GBR observations on the analysis and prediction of the ERC process of Matthew. To the best knowledge of the authors, studies comparing these two sources of data for hurricane prediction are limited. HWRF has assimilated TDR observations operationally since 2013 (Sippel 2019) while GBR observations began operational use in 2020 (Sippel 2021). Each set of observations offers their own benefits and drawbacks, which are listed in Table 1. The relative impact of assimilating the GBR and TDR observations for TC prediction specifically associated with the ERC process is left unanswered. This study makes the first attempt to address this question.
Benefits and drawbacks of the two different ICDR observation types used for TC prediction.
ICDR observations for Matthew do not become available until after a secondary eyewall has been established. For this reason, the scope of this study is confined to the ending of the weakening phase and entirety of the re-intensification phase. However, the ability of the DA cycling to establish Concentric eyewall structure resembling observations, and the impact of such an establishment on the subsequent forecasts, are still important steps toward the improvement of TC intensity forecasts associated with ERCs. An in-depth description of the ERC of Matthew and the timing of phases relative to ICDR observation availability is given in section 2a.
In this study, the analysis and prediction of Hurricane Matthew’s ERC are examined using HWRF and an hourly, continuously cycled GSI-based hybrid 3D ensemble-variational (3DEnVar) DA scheme (Wang 2010; Wang et al. 2013) with the assimilation of GBR and TDR radial velocity observations as the storm paralleled Florida’s east coast on 6–7 October 2016. In summary, the primary scientific objective of this study is to assess the impacts of assimilating GBR and TDR radial velocity observations individually, as well as in combination, on the analysis and forecast of Hurricane Matthew’s concentric eyewall structure and evolution throughout the weakening and re-intensification phases of the ERC.
The remainder of this study is outlined as follows. Section 2 discusses Hurricane Matthew and its ERC evolution in depth, as well as the experimental setup, DA specifics, and detailed information on the GBR and TDR observations. In section 3, the results of experiments performing continuous cycling with different ICDR observations are discussed to address the scientific objective of this study. Section 4 concludes the study with a summary of the results.
2. Data and methods
a. Hurricane Matthew
On 6–7 October 2016, Matthew paralleled the east coast of Florida while undergoing an ERC that was sampled by multiple coastal WSR-88D stations. Figure 1 shows the evolution of composite reflectivity from 1500 UTC 6 October to 1500 UTC 7 October where a transition from a concentric to single eyewall TC is evident. To provide a quantitative description of Matthew’s intensity and structural changes during its ERC, the method of Sitkowski et al. (2011) is used with slight modifications.1 In short, this method fits single and double Rankine vortex profiles to flight level observations in order to obtain the radial location and intensity of the primary and secondary wind maxima. Figure 2 shows the evolution of the intensity and radius of Matthew’s concentric eyewalls from flight-level2 reconnaissance (FL RECON) as a function of time. Cubic polynomials are fit to the data using least squares method. The cubic fits to these data will be used often throughout the study as proxies for the radial location of each eyewall and for trends in intensity.
Multiple-Radar/Multiple-Sensor composite reflectivity of Hurricane Matthew approximately every 3 h from 1500 UTC 6 Oct to 1500 UTC 7 Oct showing a transition from concentric to single eyewall structure.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
Evolution of (a) radius and (b) intensity of Hurricane Matthew’s primary and secondary wind maxima from FL RECON data calculated using the method of Sitkowski et al. (2011). The different phases of the ERC are labeled and bounded by black vertical dashed lines. Cubic polynomials are fit to the radius and intensity data points for both wind maxima using least squares to show trends in their evolution. Color shadings in the background represent the temporal availability of ICDR observations used for DA.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
The time period in which hourly DA cycling will be performed in this study is from 1500 UTC 6 October to 1500 UTC 7 October, corresponding to the green shaded area representing the GBR availability in Fig. 2. Evidence of a secondary wind maximum is first seen around 0300 UTC 6 October at a radius of 80–120 km (Fig. 2a). Up to just before the start of GBR availability, around 1300 UTC 6 October, Matthew is in the intensification phase, with the primary eyewall’s radius contracting from about 30 to 20 km while intensifying from about 45 to 55 m s−1. The start of the weakening phase happens immediately after the primary eyewall reaches its maximum intensity around 1300 UTC 6 October, marked by the first black vertically dashed line in Fig. 2. Matthew’s secondary eyewall continues to contract and intensify in this phase while the primary eyewall weakens. The two eyewalls equal each other in intensity around 0300 UTC 7 October, signifying the end of the weakening phase and start of the re-intensification phase. Matthew’s secondary eyewall continues to contract and strengthen further during the re-intensification phase. The primary eyewall is last detected around 1300 UTC 7 October, marking the end of the ERC. GBR observations provide sampling of Matthew’s inner core during both the weakening and re-intensification phases of the ERC, while the TDR availability is limited to the period from 1900 UTC 6 October to 0100 UTC 7 October during the weakening phase only. More details about the GBR and TDR observations and their spatial and temporal distributions are given in section 2c.
b. Model system description and system configuration
In this study, the GSI-based, dual resolution hybrid 3DEnVar system for the 2018 version of HWRF (Lu et al. 2017b) is used with a 13.5/4.5/1.5-km grid spacing configuration. The ensemble Kalman filter uses horizontal and vertical localizations of 500 km and 400 hPa, respectively. The GSI 3DEnVar uses horizontal and vertical localizations of 60 km and 550 hPa, respectively. For additional details on the HWRF modeling system and parameterizations used, the reader is referred to Biswas et al. (2018). The cycling system configuration is outlined in Fig. 3. Continuous hourly DA cycling is performed for a 24-h period starting from 1500 UTC 6 October. Available ICDR observations are assimilated with a 1-h interval depending on the respective experiment. After each hourly DA update, a 48-h free forecast is initialized and launched with hourly output, resulting in a total of 25 free forecasts for each experiment. The following steps are taken to spin up the cycling DA system. The 40 ensemble members and 1 control member are initialized from the operational GFS at 0600 UTC 6 October, followed by a 6-h forecast to 1200 UTC 6 October. Vortex relocation (VR) is then performed and followed by DA updates with only “conventional” observations. In short, VR is a bogusing method to move the background storm to its observed location before performing DA or launching a forecast (Biswas et al. 2018). The types of observations assimilated are discussed in section 2c. A 3-h forecast is then launched to 1500 UTC 6 October, the first analysis time of the hourly cycling. Before the hourly cycling starts, vortex relocation is performed for the last time. For more details on HWRF’s vortex relocation technique, see Biswas et al. (2018).
Flowchart showing configuration of the DA cycling performed for all experiments.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
c. Description of experiments and ICDR observations
To address the scientific objectives for this study, four different experiments are performed following the flowchart in Fig. 3. Each experiment is identical up to the 1500 UTC 6 October analysis time, after which each experiment will assimilate different sets of observations available to them. Each experiment will assimilate a set of “conventional observations,” which we define to be all observations contained in the following files obtained from the operational datastream: prepbufr, satwndbufr, tcvital, and satellite radiance files. Note that FL RECON observations are not assimilated. Instead, these observations are used as independent verifications for the analyses created by assimilating the Doppler radar observations.
The “Control” experiment only assimilates the conventional observation set, providing a baseline for which to compare experiments that assimilate ICDR observations. The “GBR,” “TDR,” and “GBTDR” experiments assimilate the conventional observation set, along with GBR, TDR, and the combination of GBR and TDR observations, respectively. Note, the TDR observations are only assimilated when they are available. In contrast, the two experiments with GBR observations will have availability throughout the entirety of the hourly cycling. The four experiments are selected in order to assess the effects of cycling with different sets of ICDR observations on the analysis and prediction of the ERC of Matthew.
GBR and TDR observations offer different temporal and 3D observational distributions throughout the hourly cycling. As briefly discussed previously, GBR observations of Matthew’s inner core region are available throughout the entire cycling period, and cover a portion of the weakening and the entirety of the re-intensification periods of the ERC. TDR observations, in contrast, are only available for about a 7-h period from 1900 UTC 6 October to 0100 UTC 7 October, which is typical for any TDR mission. This period of TDR availability exists only in the weakening phase.
Differences in the 3D observational distributions between the GBR and TDR observations are shown in Fig. 4. During the 24-h cycling period, the peak in horizontal distribution of the GBR observations relative to the storm center is located at larger radii (Fig. 4a), decreasing slowly as Matthew approaches radars on Florida’s east coast. The peak in GBR vertical observation distribution lies in the middle to upper levels, around 6–8 km above ground level (AGL), and slowly moves downward as Matthew gets closer to the radar stations (Fig. 4b). The horizontal and vertical observation distributions for TDR are much different than those of the GBR observations. The peak in horizontal distribution is dependent on the location of the aircraft relative to the storm center (Fig. 4c). During penetration legs, the peak in the horizontal distribution is located closer to the storm center [see Fig. 2 of Aksoy et al. (2012)]. Alternatively, during downwind legs, the horizontal distribution peaks at larger radii. The vertical distribution for the TDR observations is consistently located around 1 km AGL, with the number of observations within 100 km of the storm center dependent on the position of the plane. Overall, these differences in temporal, horizontal, and vertical distribution of both types of ICDR observations aid in the interpretation of results from the DA cycling.
(left) Horizontal and (right) vertical distributions of (a),(b) GBR and (c),(d) TDR radial velocity observations for select analysis times (every 3 h for GBR and every hour for TDR) during their availabilities. For vertical distributions, only observations within 100 km of the storm center are considered. Note that similar colored lines between the GBR and TDR distributions do not indicate that they are from the same analysis time.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
GBR observations are available from five different WSR-88D locations for each hourly cycle. For the first 12 h of cycling (1500 UTC 6 October–0200 UTC 7 October) GBR observations are used from Key West, Miami, Melbourne, Tampa Bay, and Jacksonville, all in Florida. For the last 12 h of cycling (0300 UTC 6 October–1500 UTC 7 October), Charleston, SC observations are assimilated while Key West observations are dropped. These GBR sites are selected to save computational cost given the number of experiments conducted. To obtain the GBR observations, Level 2 radar data are postprocessed using Py-ART software (Helmus and Collis 2016) to perform quality control and de-aliasing with the “regional” method. Following this, an additional manual check is performed to ensure poorly de-aliased scans are removed. TDR observations are obtained from the NCEP operational datastream, which have already been quality controlled and de-aliased. Before assimilation, GBR and TDR observations are thinned into 10 km × 10 km × 0.5 km and 9 km × 9 km boxes, respectively. Note, GBR observations are thinned every 0.5 km in the vertical direction, whereas TDR observations are not thinned in the vertical direction. GBR and TDR observations are, respectively, assigned an observation error of 2 m s−1 following Li et al. (2012) and an observation error of 3 m s−1 following Weng and Zhang (2012).
3. Results
a. Analysis of Matthew’s concentric eyewall structure and storm evolution
In this section, the process in which GBR observations correct an initially incorrect storm structure are detailed. Then, relative impacts of assimilating the two types of ICDR observations are exemplified at the 1900 UTC analysis time. Last, the overall evolution of the analyses’ 1-km azimuthally averaged tangential wind evolution is discussed for the four experiments.
The background storm structure at the first analysis time (1500 UTC 6 October) is broad and has only one wind maximum (Fig. 5), which is inconsistent with the composite reflectivity observations at the time (Fig. 1a). In addition, the maximum 10-m wind (Vmax) and minimum sea level pressure (MSLP) are about 32 kt (1 kt ≈ 0.5 m s−1) lower and 23 hPa higher than the National Hurricane Center’s best track (Landsea and Franklin 2013) estimate, respectively. This is due to no assimilation of ICDR observations, and no vortex modification being done up to this point. GBR observations from Miami, Florida (Fig. 5), are consistent with the horizontal and vertical observation distributions in Fig. 4, showing limited horizontal coverage of Matthew and a lack of observations in the lower levels due to the storm’s distance from coastal radars.
Background structure of Matthew at 1500 UTC 6 Oct before hourly cycling is started: (a) horizontal tangential winds at 1 km AGL and (b) west–east vertical cross section of tangential winds. GBR observations from the Miami station for the 1500 UTC 6 Oct analysis time are plotted as black dots. All GBR observations from closest volume scan to analysis time are plotted in (a), whereas only those within 10 km of the cross section are plotted in (b).
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
In Fig. 6, the process in which the initially inconsistent storm structure (Fig. 5) is corrected via the assimilation of GBR observations is shown from 1500 to 1800 UTC 6 October. At 1500 UTC, positive analysis increments are maximized in the middle to upper levels of the background (Fig. 6a), acting to contract and strengthen the tangential wind field in the middle to upper levels while leaving the lower-level wind structure largely intact (Fig. 6b). During the 1-h time integration to 1600 UTC, the contracted wind field in the upper levels is extended downward to the surface, leaving a more realistic wind structure (Fig. 6c). This pattern of correction continues for the next three cycles while lower-level coverage of GBR observations slowly improves, allowing for analysis increments to extend to the surface. At the 1800 UTC analysis time, the first evidence of coherent concentric eyewall structure is seen in both the background and analysis (Figs. 6g,h). Figure 6h shows primary and secondary wind maxima located around 20–25 and 50 km from the storm center, respectively. Consistent with observational studies (Bell et al. 2012; Houze et al. 2007), the primary eyewall is vertically deeper and has no outward tilt with height while the secondary eyewall is shallower and tilts outward with height. Despite their limited lower-level coverage, assimilation of GBR observations demonstrate that the concentric eyewall structure can be established through continuous hourly cycling.
Evolution of cross sections from 1500 to 1800 UTC 6 Oct for the GBR experiment. All cross sections are taken at a 45° angle relative to a parallel. (a),(c),(e),(g) Background tangential winds (contour fill), storm-relative analysis increments (contoured in black every 10 kt), and GBR observations within 10 km of cross section plane. (b),(d),(f),(h) The analysis tangential wind field.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
Relative impacts of assimilating the two different ICDR observation types are compared at the 1900 UTC 6 October analysis time (Fig. 7). With the TDR observations available at this time, clear comparisons can be made on the effects of assimilating the two ICDR observation types together and separately. In the GBR experiment, the magnitude of the analysis increments to the 3 km AGL tangential wind field (Fig. 7c) are small relative to the other two experiments and the previous analysis times for this experiment (Fig. 6), indicating the large structural changes associated with correcting the initial background have subsided. Relative to FL tangential winds, the locations of the primary wind maxima on both sides of the center and the secondary wind maximum on the right side of center are located too radially inward (Fig. 7a). Diagnostics suggest that the spuriously small eye is due to the lack of GBR observation coverage at the lower levels. The level of peak coverage of GBR observations is about 7 km AGL (Fig. 4b), indicating that the vertical levels containing the most intense winds are not being sampled. As a result, corrections to the lower-level wind field are made through information spreading via the BEC structure and can be limited due to the vertical/horizontal localizations.
Comparison of (c),(e),(g) background and (d),(f),(h) analysis 3 km AGL horizontal tangential winds. In (c), (e), and (g), storm-relative analysis increments of 3 km AGL tangential wind are contoured every 10 kt with the zero contour omitted. (a) The tangential winds from FL RECON observations along with the tangential wind profiles for the four experiments. (b) Tangential winds from the Hurricane Research Division dual Doppler wind analysis at 3 km AGL.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
The TDR experiment has the largest analysis increments to the horizontal 3 km AGL tangential wind field at the 1900 UTC analysis time (Fig. 7e). The background is similar to the initial storm structure at 1500 UTC (Fig. 5), with the initially inconsistent structure not yet corrected. Figure 7e shows positive increments to the 3 km AGL tangential wind inside the area of largest wind gradient associated with the eyewall, which results in a contraction of the wind field to establish a primary wind maximum about 25 km from the center. Negative increments occur at the radius of maximum wind in the west and south parts of the storm, and just inside the radius of maximum winds in the east and north parts, consistent with the establishment of a secondary wind maximum in the northeast side of the storm. This is confirmed in by the tangential wind profile (Fig. 7a). Relative to the GBR and GBTDR experiments, the primary wind maxima of TDR are not as intense and are located more radially outward. However, its position and intensity of the secondary wind maxima compares favorably to the FL RECON observations.
The GBTDR experiment at this analysis time allows for a direct comparison with the GBR experiment, because the two have identical backgrounds at the 1900 UTC analysis time. With this being the first analysis time in which TDR observations are available, any differences between the GBR and GBTDR analyses can be directly attributed to the additional assimilation of TDR observations. Analysis increments (Fig. 7g) are negative inside and at the radius of the primary wind maximum, acting to shift this maximum radially outward. In addition, negative increments are located at and just inside the radius of the secondary wind maximum in the northeast part of the storm, acting to weaken the secondary wind maximum and shift it radially outward. The differences between the FL profiles in the GBR and GBTDR (Fig. 7a) show the deficiencies in the GBR experiment background are corrected in the GBTDR experiment, with the location of the primary wind maximum on either side of the center being shifted radially outward, and the secondary wind maximum on the right side of center being weakened and moved radially outward. Diagnostics reveal that the corrections to the lower-level wind field are due to the increased lower-level coverage from the TDR observations, as the plane was flying a penetration leg during the DA time window (Fig. 4c). The TDR’s superior 3D observation coverage at this analysis time complements the GBR observations, demonstrating one of the potential benefits of assimilating GBR and TDR observations simultaneously when they sample different regions of the storm.
Overall, the GBR experiment demonstrates that having ICDR observations available earlier and continuously can overcome its limited lower-level coverage, making corrections to Matthew’s structure before the TDR observations become available. At the analysis time when TDR is available and has sufficient horizontal coverage, TDR can correct the structure of the storm more quickly due to its better vertical coverage. At those analysis times, the GBTDR experiment shows the ability of the GBR and TDR observations to complement each other in terms of their vertical and horizontal observation distributions, as they are directly sampling different parts of the storm.
To assess overall structural evolution of each experiment for the entirety of the cycling from 1500 UTC 6 October to 1500 UTC 7 October, a Hovmöller diagram of azimuthally averaged 1 km AGL3 tangential winds of the model analyses is shown in Fig. 8. The cubic fits of wind radii from Fig. 2a serve as observed locations of the primary and secondary wind maxima. The cubic fits for the secondary wind maxima here will have an outward radial bias in relation to the 1 km AGL wind maxima due to it being obtained from 3 km AGL winds, and the secondary eyewalls outward tilt with height. Nevertheless, cubic fits provide the best possible proxy verification for the ERC Matthew to the best knowledge of the authors.
Hovmöller diagrams of azimuthally averaged tangential wind at 1 km AGL for the analyses in the four different experiments. Black dots indicate local maxima in the azimuthally averaged tangential wind field. The dashed black line represent the cubic fits to the FL RECON wind observations radius data from Fig. 2a for identifying locations of the primary and secondary wind maxima throughout the cycling times. Blue horizontal dashed lines represent the bounds of TDR availability, which are displayed on each of the three ICDR experiments’ panels.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
Throughout the 24-h period of cycling, Control shows no ability to establish concentric eyewall structure, or to accurately represent the structural changes associated with the evolution of the ERC. This result demonstrates that without any ICDR observations, the kinematic structure cannot be corrected. In contrast to the Control, the GBR and GBTDR experiments (Figs. 8c,d) are able to correct the initial background by establishing dual wind maxima by 1800 UTC 6 October, with the primary and secondary wind maxima located around 20 and 70 km, respectively, in the azimuthal average. Subtle differences exist between azimuthally averaged wind structure between GBR and GBTDR experiments throughout the rest of the cycling. The GBR experiment tends to pull the primary wind maximum too far radially inward (Fig. 8c) for several analysis times in the 1800 to 0200 UTC time period, whereas the GBTDR tends to keep the local maximum closer to the cubic fit. In addition to these differences, the GBR establishes a stronger secondary wind maximum earlier than in GBTDR (e.g., 2300 UTC 6 October). This difference takes place in the period of TDR cycling, suggesting that the weaker azimuthally averaged winds associated with the secondary eyewall in the GBTD experiment are tied to the addition of the TDR observations. The strengthening and contraction of the secondary wind maxima in these two experiments are similar and consistent with the re-intensification phase of the ERC. Both the GBR and GBTDR have similar contraction rates and radial locations of the secondary wind maximum. Overall, without having knowledge of the entire 3D kinematic structure of the observed storm for the entirety of the cycling time, it is difficult to identify which of the two experiments is more realistic. However, while benefits of TDR were shown to be complementary to the GBR observations in terms of lower-level coverage at 1900 UTC 6 October, the addition of the TDR observations to the GBR experiment does not drastically change the azimuthally averaged structural evolution throughout the 24-h cycling time in the GBTDR experiment, at least at the lower levels.
In the TDR experiment, the establishment of dual wind maxima, as discussed previously, does not occur until the 1900 UTC 6 October analysis time. Before that, only a single wind maximum is analyzed identical to the Control (Fig. 8b). During the period when the TDR observation becomes available, dual wind maxima are established in the azimuthal mean. However, the placement and evolution of both azimuthally averaged wind maxima are more poorly represented than in GBR and GBTDR. In the later cycles when the TDR observations are unavailable again, the evolution of the ERC as represented by the TDR experiment does not properly represent the contraction and strengthening associated with the re-intensification phase. These deficiencies in the TDR analyses are hypothesized to result from two reasons. The first is that the TDR observations are only available for a limited period of time as compared with the GBR observations. The second is the inconsistent horizontal coverage of TDR observations from analysis time to analysis time even during the period when TDR observations are available (Fig. 4c). When the TDR observations in the DA time window are taken from a downwind leg, they are less useful for inner core structural corrections due to incomplete sampling. The TDR, however, does offer improvements over the Control. Comparison of the TDR with the GBR or GBTDR experiments highlights the importance of continuous availability of ICDR observations. Earlier ICDR observation availability allows for faster corrections to establish concentric eyewall structure, and longer duration of coverage results in the correct evolution of the storm structure during the re-intensification phase.
b. Forecasted structure and intensity changes throughout Matthew’s ERC
In this section, structure and intensity forecasts for the four experiments are discussed. Cubic fits to the FL RECON wind observations radius data from Fig. 2a are again used as the proxy for the verification of the primary and secondary wind maxima locations. It will also be demonstrated that the structure and intensity changes for many of the forecasts from the GBR and GBTDR experiments show the correct features and trends associated with the ending of the weakening phase and transition to the re-intensification phase. Last, the importance of initialized concentric eyewall structure is exemplified.
The structural forecasts for all free forecasts from the cycling period are summarized in Fig. 9. As a direct result of the Control’s inability to accurately analyze Matthew’s concentric eyewall structure (Fig. 8a), it is also unable to capture the correct structural changes associated with the weakening and re-intensification phases of the ERC in its forecasts (Fig. 9a). In the TDR forecasts, the time average indicates that the forecasts fail to capture a relative wind maximum associated with the primary eyewall in the vicinity of the cubic fit. Around 2100 UTC 6 October, the average wind field bulges radially inward, which is a result of four consecutive forecasts from 1900 to 2200 UTC 6 October that show consistent structural changes with the ERC evolution (not shown). However, given the majority of the TDR forecasts showed structural changes inconsistent with ERC, the two individual maxima in the time average still largely deviate from the FL RECON observed locations. This result is consistent with Fig. 8 where the concentric eyewalls and the ERC evolution do not capture well in TDR cycled analysis.
Time average for all deterministic free forecasts for 1 km AGL azimuthally averaged winds. To obtain the time average at each date, the field from any forecast valid at that date is averaged over. This will mean that each date will have a different number of valid forecasts/analyses over which to average. Dashed black curves are cubic fits to the FL RECON wind observations radius data from Fig. 2a. Black dots represent local maxima in the time averaged field at each date.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
In direct contrast to the Control and TDR experiments, the GBR and GBTDR experiments show superior ability in capturing the primary and secondary wind maxima in their forecasts as verified against the FL RECON observations. Primary wind maxima are captured as distinct local maxima in the time averages from 1700 to 0000 UTC indicating the forecast of the primary eyewall and its decay are happening consistently during the forecasts. In both experiments the secondary wind maxima is captured in the forecasts, with very similar contraction rates and their radial positioning. The superior analysis structure of the GBR and GBTDR experiments in Figs. 8c and 8d result in realistic structural forecasts starting earlier (1600 UTC, not shown), and more frequently than TDR. The time averaged forecasts capture both eyewalls more consistently throughout the cycling than TDR, and have more accurate radial positions in comparison with observations. These results highlight the importance of proper initialization of dual wind maxima for the ability to capture the ERC in the forecasts. It should be noted that the time averaged structural forecasts in Fig. 9 do not account for the variability in the forecasts. Features including the location of each eyewall, the time taken for the primary eyewall to decay, the contraction rate of the secondary eyewall, and the strength of each eyewall can vary considerably from analysis time to analysis time.
The qualitative results for structural forecasts shown in Fig. 9 are verified quantitatively in Fig. 10 against the independent GBR radial wind observations. The GBR and GBTDR experiments have lower average radial velocity root-mean-square differences (RMSD) throughout the 12 h of lead times than the Control and TDR experiments. On average, the RMSD values for the TDR experiment are smaller or similar for lead times 0–3 h but are larger at select lead times after that in compared with the Control. These results are largely due to the Control having consistent single eyewall forecasts whose structure near the end of the ERC is more consistent with observations than are the TDR forecasts.
RMSD between GBR radial velocity observations and radial velocity of the experiments using the coastal radars at Miami, Melbourne, and Jacksonville. RMSDs are averaged for each lead time.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
The Vmax intensity forecasts are examined in Fig. 11. Forecasts for the Control (Fig. 11a) are consistent with the structural forecasts in Fig. 9a. The average of the intensity forecasts (gray curves) shows general intensification until roughly 0900 UTC 7 October, followed by weakening thereafter. The prolonged period of general intensification in the time averaged forecasts until 0900 UTC 7 October is inconsistent with Matthew’s general weakening intensity trend at the time as indicated by the best track. The GBR and GBTDR experiments show four distinct phases of intensity trends in their time mean. Given their similarity, the GBR experiment is discussed in detail.
The 10-m maximum wind speed (Vmax) for all free forecasts from 1500 UTC 6 Oct to 1500 UTC 7 Oct. Dotted lines represent free forecasts initialized before 1900 UTC 6 Oct. Each intensity forecast is marked with a dot at the analysis time to track how the analysis Vmax evolves. The gray curve represents the time average of all analyses/forecasts valid at each date. The black line with dots is the best track for Matthew. Vertically dashed black lines represent the bounds of the different ERC phases from FL observations (Fig. 2), which are labeled at the bottom of (c) and (d), with the last vertical line representing the end of the ERC.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
From 1500 to 2000 UTC 6 October, a strengthening trend is shown by the time mean. At 2100 UTC 6 October, the analysis Vmax strengthens to about 125 kt, about 7 kt stronger than best track at the time. This period of intensification in the analyses and forecasts represent the adjustment of the initially weak vortex through the continuous DA cycling using GBR observations. This is consistent with the structural changes in Fig. 9c, where the establishment of two wind maxima is taking place as evidenced by two local maxima in the time mean. Following this strengthening, a weakening trend from 2000 UTC 6 October to 0200 UTC 7 October is seen, followed by a strengthening trend from 0200 to 1100 UTC 7 October. Although the best track does not show the two periods of intensity change, they are argued later to be a result of the free forecasts correctly capturing the weakening and re-intensification phases of the ERC. Such timing of the variation of the Vmax is consistent with the structural variation shown in Fig. 9c. From 2000 UTC 6 October to 0200 UTC 7 October, the time mean of GBR forecasts in Fig. 9c show the weakening of the primary wind maxima and the strengthening of the secondary wind maxima associated with the weakening phase of the ERC, in which the maximum wind is still located in the primary eyewall. From 0200 to 1100 UTC 7 October, the secondary eyewall in the time mean of the forecasts (Fig. 9c) becomes stronger than the primary eyewall and begins to intensify while it contracts. Last, after 1100 UTC 7 October, the intensity trend switches to weakening associated with deteriorating environmental conditions after the ERC is complete, which is also consistent with the mean structural forecasts in Fig. 9c. These four phases of intensity trends in the time mean are seen in the GBTDR experiment with slight differences in the timing of the phase changes.
The average of the TDR intensity forecasts in Fig. 11 do not show the intensity variation trends seen in GBR and GBTDR. This is consistent with the structural forecasts by TDR where the structural changes with the weakening and re-intensification of the ERC are only captured by limited cycles (Fig. 9b). It is also noted that unlike GBR and GBTDR, the adjustment of the initial vortex intensity from 1500 to 2000 UTC 6 October is not as drastic as GBR and GBTDR.
The claim that the intensity trends from the GBR and GBTDR free forecasts are consistent with structural changes in the weakening and re-intensification phase of the ERC is examined further in Fig. 12. For the first 7 h of the GBTDR forecast, the primary eyewall is the dominant feature, with the secondary eyewall being noticeably weaker (Fig. 12a). During this time, the azimuthally averaged 10-m wind intensity becomes gradually weaker, with a brief uptick in intensity around forecast hours 4–5. Figure 12b shows the decreasing trend in Vmax during these time periods and verifies that the radius of maximum wind is occurring inward of 25 km (blue), corresponding to the primary eyewall. This weakening of the primary eyewall, while still being the stronger of the two, is typical of the weakening phase of the ERC, and is captured in both Vmax and in structural changes in the Hovmöller (Fig. 12a).
Hovmöller diagram from GBTDR experiment initialized at 1900 UTC 6 Oct of (a) azimuthally averaged 10-m tangential winds and (b) the corresponding scatterplot of the Vmax forecast, with colors corresponding to the radial distance relative to 25 km from the storm center. The thin dashed curves in (b) represent the cubic fits to the wind maximum of the primary and secondary eyewalls from the FL RECON observations in Fig. 2. Black horizontal dashed lines indicate the observed phase changes in the ERC as in Fig. 2.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
The switch from the weakening phase to the re-intensification phase happens between forecast hours 7 and 8, as denoted by the gray horizontal dashed line (Fig. 12b). The timing of the switch matches closely to that of the verifying cubic fits to the FL RECON observations with the former being only 1 h earlier. Leading up to this time, the secondary wind maximum in the Hovmöller diagram can be seen intensifying and contracting. At forecast hour 8, the secondary wind maximum overtakes the primary wind maximum in intensity, as evidenced by the color of the intensity markers in the scatterplot turning a darker red. This indicates the Vmax values are now located around 40–45 km in radius, consistent with the location of the secondary wind max represented by the azimuthal averaged tangential winds at this time. The forecasted Vmax begins to intensify up to forecast hour 21, with all Vmax values located in the secondary eyewall (red), consistent with the contraction and intensification of the secondary eyewall in the azimuthal mean. The downward trend in intensity after forecast hour 21 is associated with the weakening caused by environmental conditions, also consistent with the cubic fits.
The correspondence between the structural changes seen in the Hovmöller diagrams (Fig. 9) and the point intensity forecasts (Fig. 11) demonstrate the capability of the model to capture structure and intensity changes during the weakening and re-intensification phases of the ERC. Because the maximum 10-m wind (Vmax) can be found at any point horizontally in a concentric eyewall TC, it could realistically be found in either eyewall, especially during the transition from the weakening to re-intensification phase. Therefore, an ideal Vmax forecast capturing the intensity changes associated with these two ERC phases will resemble the maximum value of either eyewall’s intensity. Graphically, this is represented by the maximum of the two cubic fits in Fig. 2b). The example shown in Fig. 12 demonstrates that this specific GBTDR forecast is capturing the point intensity and structural changes as expected. Because these changes are tied to the evolution of the decay of the primary eyewall and the strengthening and contraction of the secondary eyewall, capturing these subtle intensity changes will help signal the oncoming changes to the TC’s wind structure. These subtle intensity changes associated with the ERC phase changes occur on a shorter time scale than 6 h and are therefore not captured by best track.
The performance of the four experiments in capturing the timing of the downward and upward intensity trends and the location of the contracting eyewalls is further evaluated in Fig. 13. In these experiments, the switch from downward to upward intensity trends corresponds with a transition from blue to red intensity markers (Figs. 13c,d). Physically, this represents the location of Vmax switches from the primary (blue markers) to secondary eyewall (red markers). Similar to Fig. 12, the intensity changes can be understood conceptually as the forecasts capturing the maximum value of the cubic fits given the Vmax will be located in whichever eyewall is strongest at the time. During the re-intensification of the GBR and GBTDR forecasts, the color of the Vmax points switches from darker to lighter red, indicating that the secondary eyewall is contracting inward. In contrast to GBR and GBTDR, the TDR does not show as clear of a switch in the radius of the Vmax forecasts. Some contrast in the colors of the Vmax points exist around 0200 UTC 7 October, which correspond to the four previously mentioned forecasts from this experiment that show realistic structural and intensity changes. However, after 0200 UTC 7 October, the Vmax points colors tend to be mixed between blue and red, as many of the forecasts are not capturing the ERC.
Vmax intensity forecasts initialized after 1800 UTC 6 Oct, with colors corresponding to the Vmax distance from 25-km radius from the storm center, as in Fig. 12b. The gray curve represents the time average of all analyses/forecasts valid at each date. The cubic fits for FL wind maxima are overlaid on each panel to show approximate trends of the two eyewalls. They do not serve as a proxy for the 10-m wind intensity.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
In additional to the statistical evaluation of the impact of the initial structure of the wind field after assimilating the ICDR observations, mechanisms for the decay of the primary eyewall and the strengthening and contraction of the secondary eyewall during the ERC in an axisymmetric framework are briefly discussed using a comparison of free forecasts between the Control and GBR experiments (Fig. 14). With initialized concentric eyewall structure in the GBR experiment (Fig. 14b), the evolution of the wind field can be partially explained with balanced (Shapiro and Willoughby 1982; Willoughby et al. 1982) and unbalanced dynamics (Huang et al. 2012; Smith et al. 2009). Throughout the GBR forecast, the secondary eyewall’s contraction and strengthening occurs via the advection of higher absolute angular momentum surfaces from the radial inflow toward the center. The secondary eyewall is also strengthened in the boundary layer via the unbalanced dynamics mechanism (not shown), acting to cause rapid deceleration of the radial inflow in the boundary layer at the secondary eyewall, helping to increase the strength of the transverse circulation of the secondary eyewall. As the secondary eyewall continues to strengthen, the radial inflow is cut off from reaching the primary eyewall, resulting in high angular momentum air not being able to advance toward the primary eyewall, as evidenced by the decreased positive angular momentum advection near the storm’s center. The process spins down the primary eyewall, resulting in primary wind maximum being almost completely decayed by forecast hour 16 (Fig. 14f). In the Control experiment, this process does not occur, as only a single, broad eyewall is initialized.
Evolution of azimuthally averaged: tangential winds (purple contours), absolute angular momentum (black contours) (American Meteorological Society 2021), transverse circulation (vectors) (Emanuel 1991), and advection of absolute angular momentum (color shades) for the Control and GBR experiment initialized at 1900 UTC 6 Oct. Two contours in both the azimuthally averaged tangential winds and absolute angular momentum are dashed so that their changes can be tracked.
Citation: Monthly Weather Review 150, 5; 10.1175/MWR-D-21-0234.1
4. Discussion and conclusions
In this study, hourly DA cycling was performed for Hurricane Matthew during a 24-h time period from 1500 UTC 6 October to 1500 UTC 7 October 2016, assimilating GBR and TDR observations together, as well as separately using the HWRF Hybrid 3DEnVar DA system. The goal is to examine the impact of assimilating such data for the analysis and prediction of Matthew’s ERC. Results of this study show that the temporal availability and duration of ICDR observations are important for capturing the correct evolution of Matthew’s ERC. Comparison of the GBR experiment, which has continuous access to GBR observations, and the TDR experiment, which has much limited access to TDR observations, shows stark differences in the establishment of concentric eyewall structure and evolution of the primary and secondary eyewalls throughout the ERC for both the analysis and the forecast (Fig. 8). The GBR experiment corrects the initially inaccurate background storm structure earlier, resulting in the analyzed concentric eyewall structure that evolves consistent with FL RECON observations throughout the rest of the cycling. Specifically, the GBR analysis shows the eventual decay of the primary eyewall and the contraction/strengthening of the secondary eyewall throughout the weakening and re-intensification phases. The TDR experiment, with later and fewer hours of availability of the TDR observations, shows less consistent concentric eyewall structure and the inability to capture the strengthening and contraction of the secondary eyewall after observations become unavailable. Structural evolution of the analyses indicates that without early availability and long duration of ICDR observations, Matthew’s structural changes cannot be analyzed consistently throughout the ERC. In addition, the lack of ICDR observations altogether in the Control experiment shows the complete inability to initialize concentric eyewall structure during the cycling.
Differences in 3D ICDR observation distributions were also shown to affect the initialization of intricate features associated with Matthew’s ERC. The GBR experiment, despite limited lower-level observation coverage, was able to initialize concentric eyewalls through DA cycling that included both corrections to the upper-level wind field and extension of those winds to the surface during the background model integration. A comparison with FL RECON observations shows that although concentric eyewalls were established during the DA cycling, the GBR experiment tends to contract the primary and secondary eyewalls too far radially inward, in part due to the lack of observation coverage at lower levels. The TDR, in comparison, demonstrates the ability to correct the initially inconsistent storm structure to a concentric eyewall TC in only one cycle due to superior horizontal and vertical observation coverage for that cycle despite the underestimation of the primary eyewall strength. However, the TDR horizontal observation distribution can vary drastically from cycle to cycle depending on whether the flight is in a penetration or downwind leg during the DA time window. Limited or incomplete horizontal coverage during downwind legs is hypothesized to contribute to the less consistent TDR analyses during their availability, consistent with the findings of Aksoy et al. (2012).
The simultaneous assimilation of TDR and GBR observations shows the ability to complement each other when their vertical distributions differ. At 1900 UTC 6 October, the deficiencies in the GBR experiment relating to the spuriously small primary eyewall and inwardly displaced secondary eyewall are corrected when the two observation sets are assimilated together. The differences in the structural evolution between the GBR and GBTDR experiments shown throughout the entire cycling period in Fig. 8 are small, with the most noticeable being the earlier intensification of the secondary eyewall in the GBR experiment. These small differences in the azimuthally averaged tangential wind evolution are not completely representative of the differences between the 3D structure of the experiments. However, they do suggest that the dominant structural features in the analyses result from the initial establishment of concentric eyewall structure due to the early availability of the GBR observations, with TDR observations making small contributions to correcting the storm structure thereafter.
The structural and intensity forecasts also suggest that more correct initialization of the concentric eyewall structure is important for making consistent forecasts of realistic structural and intensity changes for the ERC. This was exemplified in the GBR and GBTDR experiments, which were able to capture the decay (strengthening) of the primary (secondary) eyewalls, as well as the intensity trends associated with the weakening and re-intensification phases of the ERC. Despite four realistic forecasts, the TDR experiment that was generally initialized with less realistic concentric eyewall structure was not able to make consistent realistic predictions of either structure or intensity changes throughout the ERC. Correctly initialized concentric eyewall structure was shown to result in the consistent evolution of the two wind maxima through balanced and unbalanced dynamics.
This study is the first to examine the impact of assimilating GBR and TDR observations for the prediction of ERC of a real TC. As an initial study, we designed and performed experiments with a single case. Experiments with more cases should be performed to draw general conclusions. Additionally, improved DA methods such as sub-hourly DA or the 4D approach within a 1-h window should be explored in future work to initialize intricate TC structures such as concentric eyewalls.
Flight-level winds are not pressure adjusted to a reference level as in Sitkowski et al. (2011).
Flight level is approximately 700 hPa, or 3 km above ground level.
1 km AGL is close to the vertical level of maximum winds in tropical cyclones, and this vertical level allows for better contrast to be seen in plots between the primary and secondary eyewalls in terms of tangential winds. Conclusions drawn from the 1 km AGL analysis throughout the paper are consistent with those drawn from 3 km AGL.
Acknowledgments.
This study is supported by NOAA Grant NA16OAR4320115. The experiments are performed on the NOAA supercomputer Jet and University of Oklahoma supercomputer Schooner.
Data availability statement.
All data used in this study, including model and observational data, are archived and available upon request to the corresponding author.
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