Impact of Direct Radar Reflectivity Data Assimilation on the Simulation of Mesoscale Descending Inflow and Secondary Eyewall Formation in Hurricane Matthew (2016)

The impact of assimilating ground‐based radar reflectivity on the rainband structure and secondary eyewall formation (SEF) of Hurricane Matthew (2016) is investigated within the framework of the Hurricane Weather Research and Forecasting model and its hybrid three‐dimensional ensemble‐variational data assimilation (DA) system. Compared to the control experiment (no radar reflectivity DA), the radar reflectivity DA experiment shows a clear signal of concentric eyewall and eyewall replacement cycle. Results demonstrate that radar reflectivity DA improves the stratiform rainband analysis, resulting in the mid‐level cooling associated with mesoscale descending inflow (MDI). The MDI further contributes to the low‐level acceleration maximum with boundary layer dynamics and triggers new convective updrafts in the SEF region. Momentum budget analysis also suggests that the mean vertical advection of absolute angular momentum plays an important role in the local momentum tendency in the SEF region in Hurricane Matthew (2016).

One aspect of the aforementioned asymmetric rainband processes is the existence of a mesoscale descending inflow (MDI).The MDI was first found by Didlake and Houze (2013) in the stratiform rainbands of Hurricane Rita (2005).Didlake et al. (2018) later also found a similar MDI in Hurricane Earl (2010) and hypothesized a pathway to explain how the asymmetric MDI leads to an axisymmetric secondary eyewall development.During the transition, a persistent MDI could be found in mature stratiform rainband precipitation regions in the DL quadrant and then descended into the boundary layer by the latent cooling from melting and evaporation below the stratiform rainband.This MDI in the boundary layer locally produced tangential wind acceleration and enhanced convection through boundary layer dynamics in the outer range, where the axisymmetric SEF was established.
More recently, Yu et al. (2021) further examined the MDI pathway to SEF during the early stage of Hurricane Matthew (2016) by a high-resolution with convection-permitting numerical model initialized using an ensemble-Kalman filter DA system.By conducting absolute momentum budget analysis, they confirmed that the MDI is driven by midlevel cooling below the stratiform regions and brings absolute angular momentum to the boundary layer, leading to the tangential acceleration in the boundary layer and the following axisymmetrization of the secondary eyewall.
To have a more accurate prediction of SEF, a full understanding of initial TC structures including kinematic and thermodynamic aspects is anticipated in the simulation through the advancement of data assimilation (DA).During the last decade, many studies (Zhang et al., 2009;Torn, 2010;Aksoy et al., 2012Aksoy et al., , 2013;;Li et al., 2012;Weng & Zhang, 2012;Dong & Xue, 2013;Lu et al., 2017aLu et al., , 2017b;;Green et al., 2022) have demonstrated significant improvements to both analysis and forecast of TC structure and intensity after the assimilation of radar observations.Green et al. (2022) conducted hourly DA cycling for Hurricane Matthew (2016) by assimilating ground-based (GBR) and tail-Doppler (TDR) radar velocity observations, respectively.They found that the forecasts from the GBR experiment show a better structure and intensity improvement for the entire eyewall replacement cycle compared to the TDR experiment due to the less consistent TDR analyses during downwind legs.
The purpose of this study is to examine the impact of assimilating radar reflectivity on the asymmetric rainband processes and SEF of Hurricane Matthew (2016).Two experiments with and without the radar reflectivity observations DA are conducted by utilizing a state-of-the-art high-resolution numerical simulation and DA system.As in Green et al. (2022), hourly and continuous DA cycling is performed before SEF.This study will mainly focus on the asymmetric stratiform rainband processes that contribute to SEF before the onset of SEF.In contrast to Green et al. (2022), the experiment in this study focuses on the assimilation of the radar reflectivity from the ground-based radar.This experiment design aims to provide insights into the role of radar reflectivity DA in SEF through the asymmetric rainband and hydrometeor processes.The rest of the paper is organized as follows.A brief description of the numerical method including the DA method and experiments is given in Section 2. The detailed analyses of simulations are shown in Section 3. Discussion and conclusions are summarized in Section 4.

An Overview of Hurricane Matthew (2016)
Matthew intensified and reached category 4 intensity by 1200 UTC 6 October 2016.The minimum sea level pressure is 937 hPa and the maximum wind speed is 61.7 m s 1 .At 1800 UTC 6 October, the synoptic environment provided a southwesterly vertical wind shear and the deep-layer shear magnitude was about 5 m s 1 .The storm then paralleled and underwent an eyewall replacement cycle along the East Coast of the United States from 6 to 7 October.The evolution of composite reflectivity showed a clear signal of concentric eyewall formation from 1930 UTC 6 October, and the inner eyewall disappeared and was replaced by the secondary eyewall from 0730 UTC 7 October (cf. Figure 9 in Cha et al., 2021).Please refer to Cha et al. (2021) for more details of Hurricane Matthew (2016).

Numerical Model and Data Assimilation
For the study, we use the 2018 version of Hurricane Weather Research and Forecasting (HWRF) (Lu, Wang, Tong, & Tallapragada, 2017) with the Gridpoint Statistical Interpolation (GSI)-based, dual resolution hybrid three-dimensional ensemble-variational (3DEnVar) system (Wang, 2010;Wang et al., 2013).The horizontal and vertical localization in cut-off radii of 55 km (500 km) and 550 hPa (400 hPa) are used in the GSI 3DEnVar, respectively.The horizontal grid spacing configuration for domains 1-3 is 13.5/4.5/1.5 km with 75 vertical model levels.See Biswas et al. (2018) for further details such as model physics and parameterizations.
The configuration of the initial DA cycling is similar to those of Green et al. (2022) (cf. Figure 3 in their manuscript).The initial DA spin-up procedure includes 40 ensemble members and a control member initialized from the operational GFS at 0600 UTC 6 October, followed by a 6-hr forecast to 1200 UTC 6 October.The hourly DA cycling starts from 1500 UTC 6 October after a 3-hr forecast.For the control experiment (CTL), only conventional observations such as prepbufr files, satellite radiances, tcvital, and satellite winds are assimilated.The radar reflectivity experiment (DBZ) assimilates these conventional observations and the radar reflectivity from the ground-based radar (GBR).Both experiments have hourly DA cycling from 1500 to 1800 UTC and a 12hr free forecast initialized at 1800 UTC 6 October.The assimilation of radar reflectivity follows the GSI EnVar direct reflectivity DA approach proposed and developed by Wang andWang (2017, 2021).For other details and information on the GBR observations please refer to Green et al. (2022).

Analysis Results
Figures 1a-1d show the plan view of reflectivity analysis near 5 and 6 km altitude for CTL and DBZ experiments, and Figure 1f display the assimilated observed reflectivity from National Climatic Data Center (NCDC).At 1700 UTC 6 October, Matthew is located about 50 km north of Bahama Island and moving toward the northwest in about 23 km per hour with a 5 m s 1 southwesterly environmental vertical wind shear (black arrow in Figure 1f).Compared to the reflectivity analysis in the CTL experiment (Figures 1a and 1c) which the radar observation was not assimilated, the overall reflectivity analysis in the DBZ experiment (Figures 1b and 1d) is close to the observations.This consistency includes the eyewall convection, moat, and spiral rainbands, while the intensity of some individual convections is underestimated (cf.Figures 1d and 1f).Since MDI is induced by stratiform clouds in the DL quadrant, we use a simple cloud partitioning algorithm to examine the differences in stratiform clouds between both experiments.Based on the reflectivity criteria for cloud partitioning proposed by Steiner et al. (1995) and Qi et al. (2013).(a) the reflectivity is greater than 30 dBZ at 10°C or above; (b) the reflectivity is greater than 40 dBZ at 0°C or above.If either of these criteria is met, the cloud is identified as a convective cloud.Using this simple cloud partitioning, the cloud in the DL quadrant in the CTL experiment is mostly convective cloud (see the yellow part in Figure 1a and the red part in Figure 1c).In contrast, only the primary eyewall and some convection to the northern Great Abaco Island are identified as convective clouds (Figures 1b  and 1d) in the DBZ experiment.This comparison in cloud partitioning suggests that radar reflectivity DA can contribute to the successful simulation of stratiform clouds through hydrometeor processes, creating a favorable environment for MDI (Figures 1b and 1d) in the DBZ experiment.In addition to stratiform clouds, the primary eyewall size and location are accurately captured by radar DA in the DBZ experiment.Without radar reflectivity DA in the CTL experiment, the eye is larger than observed, and the eyewall location differs significantly from the observation (cf.Figures 1c and 1f).This prerequisite is also crucial for SEF.
Next, the vertical cross-sections of tangential and vertical wind are shown at 17 UTC in the DL and upshear-right quadrants to investigate the existence of MDI.Both upward motion and convection are stronger to the DL quadrant (right part in the figure) but weaker to the upshear-right.This eyewall asymmetry due to vertical wind shear has also been found in several previous studies (e.g., Black et al., 2002;Corbosiero & Molinari, 2002, 2003;Frank & Ritchie, 1999, 2001).Along the downshear-left, a slantwise downdraft is located outward between 100 and 200 km radii, and the strongest downdraft is at about 5 km height.These results are consistent with the findings of MDI in Didlake et al. (2018) (see Figures 17 and 18 in their manuscript).The MDI comes from larger radii (more than 150 km radius) and descends due to the latent cooling in the stratiform region in the DL quadrant (Figures 1b and 1d).Results from Figure 1 suggests that radar reflectivity DA improves the spiral rainband and stratiform region associated with the development of the MDI.
Given the existence of MDI in the DBZ experiment, the difference of TC radial structure in CTL and DBZ experiments are examined.Figure 2 displays the radius-height plots of azimuthally averaged tangential and radial winds.Throughout the first hour of the forecast, the CTL experiment (Figures 2a-2d) shows no concentric eyewall structure, implying that the concentric eyewall cannot be established by only the conventional observations DA for Matthew.The maximum tangential wind increases and extends upward starting between 54 and 72 km radii near the boundary layer top, with an eyewall contraction.In contrast, the DBZ experiment has a local tangential wind maximum and a strong outflow above the inflow boundary layer at around 55 km radius by 1800 UTC 6 October (Figure 2e).After a one-hour forecast, the secondary eyewall has been formatted, with dual tangential wind maximum and dual radial inflow maximum located around 20 and 60 km radii.These concentric eyewall structures are consistent with the observations of Matthew in Cha et al. ( 2021) (see their Figure 6a).Note that the TC in the DBZ experiment is weakening during the one-hour forecast.This weakening is due to SEF and eyewall replacement cycle and has been documented by previous studies (e.g., Cha et al., 2021;Green et al., 2022).
Given the importance of the MDI at 1700 and 1800 UTC 6 October and SEF from 1800 UTC 6 October, the spatial and temporal evolution of SEF and MDI are examined.First, Figures 3a and 3b show the time-radius diagrams of axisymmetric composite reflectivity of the two experiments.As in Figures 2a-2d, the control experiment still fails to capture the concentric eyewall structure.Throughout all forecast time, only one eyewall structure is located around 54 km radius and the TC intensity change is limited.The TC structure and intensity are consistent with the radius and magnitude of maximum tangential wind in Figures 2a-2d.On the other hand, a distinct contraction of the secondary composite reflectivity maximum is shown in the DBZ experiment (Figure 3b).The TC also experiences weakening and reintensification during the forecast hours.These forecasts point out several aforementioned typical features in the context of an eyewall replacement cycle process.This concentric eyewall evolution is similar to the observations of Matthew in Cha et al. (2021) (see their Figure 9a).Second, prior to SEF, Figures 3c and 3d demonstrate the azimuth-time evolution of the vertical wind integrated along the radius (r = 90-120 km) and altitude (z = 2-6 km).At 1700 UTC 6 October, both CTL and DBZ experiments had downdraft in the DR quadrant.However, from 1720 UTC 6 October, only the DBZ experiment shows a clear signal of strong downdrafts in the DL quadrant, with the radial inflow in this region (not shown).This representative existence of asymmetric MDI prior to SEF implies that the MDI not only accelerates the tangential wind in the outer region but enhances secondary eyewall convection, which is consistent with the results in Didlake et al. (2018) and Yu et al. (2021).In all, these results suggest that radar reflectivity DA plays an important role in the development of MDI and SEF.
Given the distinct patterns of MDI and SEF in the DBZ experiment, the dynamical processes of how MDI contributes to SEF are examined.The axisymmetric angular momentum budget is performed to quantify the dynamical processes.Following Yu et al. (2021), the absolute angular momentum equation is where ∂ c /∂t is the local time derivative following the storm center, (r,λ,z) is storm-following cylindrical coordinate, the overbar is azimuthal mean about the storm center, the prime symbol is a deviation from the azimuthal mean, M ST = rv ST +(1/2)fr 2 is the axisymmetric storm-relative absolute angular momentum, u ST and v ST are the storm-relative radial and tangential winds, w is vertical wind, p is pressure, ρ is density, and F λ is surface friction along the tangential direction.The term on the left-hand side is the storm-relative angular momentum change, and the right-hand side indicates the terms of radial and vertical mean advections, radial and vertical eddy momentum advections, and contributions from the pressure gradient force and the surface friction, respectively.
Figures 4a and 4b display the actual angular momentum changes of Equation 1 during 1800 UTC 6 October for the CTL and DBZ experiments.As shown in Figure 4a for the CTL experiment, the majority of absolute angular momentum increases near the primary eyewall region between 36 and 54 km radii at the boundary layer top.This positive tendency is consistent with the acceleration and extension of the maximum tangential wind associated with the eyewall contraction (cf.Figures 2a-2d).This consistency suggests that the positive angular momentum change contributes to the tangential acceleration.On the other hand, the angular momentum change in the DBZ experiment (Figure 4b) has a broadscale increase between 54 and 108 km radii.This distinct pattern is located outside of the secondary eyewall and has a local maximum of around 850 hPa near a 90 km radius.Note that the momentum tendency is negative near the primary eyewall region, which is consistent with the weakening shown in Figures 2e and 2f.These results suggest that all major tangential acceleration and deceleration are well represented by the absolute angular momentum tendency.Note also that Figures 4c and 4d show the integrated angular momentum changes, which are the sum of the first four right terms of Equation 1.The pressure gradient term and friction term are negligible.The diagnosed momentum term is forward integrated using 1-hr model output.While the integrated momentum changes are broadly consistent with the actual momentum changes in Figures 4a and 4b, both experiments show inconsistencies.Such inconsistencies are likely due to the coarse 1-hr model output used for integration.
To understand which specific terms contribute to the main change of absolute angular momentum, Figures 4e  and 4f display the mean vertical advection term in Equation 1 for the CTL and DBZ experiments.Only the mean vertical advection term is shown here since the mean vertical advection is the dominant contributor and causes the major change of absolute angular momentum in the outer eyewall region during 1800 UTC 6 October.Otherwise, the mean radial advection has the primary contribution to the inner eyewall region and is offset by the friction term in the boundary layer.The contributions from the eddy flux and baroclinic pressure gradient terms are small and limited.In the CTL experiment, the mean vertical advection term has an anticipated positive contribution that concentrates near a 54 km radius, where the primary eyewall is located.On the other hand, the mean vertical advection contribution in the DBZ experiment has two local maxima near 72 and 90 km radii at around 850 hPa.These vertical advection maxima are consistent with the positive angular momentum tendency in Figure 4b, implying that the mean vertical advection term plays an important role in the absolute angular momentum tendency in the DBZ experiment.Note that the MDI, although asymmetric and confined to a specific quadrant, is characterized by a dominance of mean advection contribution over nonlinear eddy flux terms.This momentum budget analysis reveals that the MDI is not solely an asymmetric feature contributing exclusively through nonlinear eddy term.This feature was also found by Yu et al. (2021).
Moreover, the latent cooling resulting from the organized stratiform rainband due to radar reflectivity DA enhances the MDI air to become more descending, leading to a strong MDI in the DBZ experiment.The MDI further brings high absolute angular momentum into the boundary layer, resulting in a local tangential acceleration.This local tangential wind acceleration in the boundary layer leads to a local radial inflow maximum adjacent to outside the tangential wind maximum, with a local updraft maximum adjacent to inside the tangential wind maximum by boundary layer dynamics (Li & Wang, 2021a, 2021b).As a result, the secondary eyewall is thus established.

Discussion and Conclusions
In this study, the impact of assimilating radar reflectivity on SEF of Hurricane Matthew ( 2016) is examined.To achieve the goal, two experiments were performed with hourly DA cycling from 1500 UTC to 1800 UTC 6 October 2016 using the HWRF Hybrid 3DEnVar DA system.The first experiment (CTL) only assimilates baseline observations including conventional observations, satellite radiances and winds, and tcvital minimum sea level pressure.Compared to the CTL experiment, the second experiment (DBZ) additionally assimilates the radar reflectivity based on the ground-based radar observations.Results show that in contrast to the CTL experiment which fails to simulate the concentric eyewall structure, the DBZ experiment successfully establishes SEF and the subsequent eyewall replacement cycle.We hypothesize that radar reflectivity DA improves the reflectivity of the stratiform rainband of Hurricane Matthew, leading to a more accurate hydrometeor distribution.The improved stratiform rainband then enhances the mesoscale descending inflow (MDI) by the latent cooling from melting and evaporation below the stratiform rainband.
The MDI further contributes to the low-level acceleration maximum with boundary layer dynamics and triggers new convective updrafts in the SEF region.The primary findings in this study are shown as follows.
• Prior to SEF, radar reflectivity DA in the DBZ experiment improves the reflectivity of the stratiform rainband to be more organized with fitting to GBR observations than that in the CTL experiment.These stratiform rainbands are in the DL quadrant.The improvement of the reflectivity also results in a more accurate hydrometeor distribution for the stratiform rainbands.• A more accurate hydrometeor of the stratiform rainbands can produce latent cooling from melting and evaporation, causing the MDI air to become more negatively buoyant in the DBZ experiment.This result helps explain that while the MDI can be found in both CTL and DBZ experiments, the MDI in the DBZ experiment is stronger and broader than that in the CTL experiment.• The MDI then brings high absolute angular momentum into the boundary layer in the SEF region.The associated local tangential acceleration is triggered, leading to SEF by boundary layer dynamics after the establishment of the secondary tangential wind maximum in the DBZ experiment.
The results from this study confirm the occurrence of asymmetric MDI in Hurricane Matthew (2016), which is located in the DL quadrant resulting from the interaction between the spiral rainband and vertical wind shear.Radar reflectivity DA further enhances the MDI into the boundary layer, resulting in SEF by the local tangential acceleration in the DBZ experiment.These results are re-confirmed by the comparison between the CTL and DBZ experiments with the analysis from the absolute angular momentum budget.Note that the only difference between the CTL and DBZ experiments is whether the radar reflectivity observations are assimilated, implying the importance of radar reflectivity DA in capturing the subtle structure of the spiral rainband in the DL quadrant as well as the primary eyewall location and size, which lead to subsequent more realistic SEF and eyewall replacement cycle.Although assimilating GBR observations demonstrate more skillful predictions of intensity and structure for the analyzed TC, certain challenges persist.In terms of data availability, GBR is only accessible for TCs close to land and provides less uniform three-dimensional spatial coverage.Advancement of DA algorithms taking into account multiscales (Wang et al., 2021) and non-Gaussianity (Feng et al., 2020).
This study first examines the impact of assimilating radar reflectivity for the prediction and simulation of SEF.
While the impacts of radar reflectivity DA in this study provide new insights into the SEF process in Hurricane Matthew ( 2016), continued research is certainly needed to examine the hypothesized pathway.Other asymmetric rainband processes due to radar reflectivity DA may also contribute to SEF.A more robust relationship between the asymmetric MDI and axisymmetric SEF also requires further validation.As an initial study, these examinations will be the subject of future work.

Data Availability Statement
The operational data sets, including the control and ensemble analysis and forecast from the Global Forecast System (GFS, 2003) used in this study, can be found from (Wang et al., 2013).The level-II GBR observations (Crum et al., 1993) can be ordered from National Centers for Environmental Information (NCEI, 1995).The WDSS-II software can be obtained from (Lakshmanan et al., 2007).The HWRF & GSI software can be found from (Biswas et al., 2018).

Figure 1 .
Figure 1.Plan views of reflectivity analysis for (a, c) control experiment and (b, d) DBZ experiments near (a, b) 6 km and (c, d) 5 km heights, and north-south vertical cross-section of tangential wind (shaded; kts) and vertical wind (contour; 2-kts, positive contours are solid, negative contours are dashed) for the DBZ experiment at 17 UTC.The right-up panels in (e) show the corresponding plan view of the tangential wind at 1 km height within a 150 km radius circle from Matthew's center (dashed contour; 50-km).(f) Plan views of assimilated observed reflectivity at 17 UTC.The black arrow in (f) indicates the direction of the 850-200-hPa vertical wind shear, associated with downshear left quadrant and downshear right quadrant.

Figure 2 .
Figure 2. (a-d) Radius-height cross sections of azimuthally averaged radial wind (shaded; m s 1 ) and tangential wind (contour; 10-m s 1 ) for the forecast in the control experiment at 1800, 1820, 1840, and 1900 UTC 06 October.(e-h) As in (a-d), but in the DBZ experiment.

Figure 3 .
Figure 3. Time-radius diagram of axisymmetric composite reflectivity from 1900 UTC 6 October to 0400 UTC 7 October for the forecast in the (a) control and (b) DBZ experiments, and the azimuthal angle and time evolution of averaged vertical wind from 72 to 108 km radii and below 5 km height for the forecast in the (c) CTL and (d) DBZ experiments.

Figure 4 .
Figure 4. Radius-height cross sections of azimuthally averaged angular momentum budget at hour 18. Actual changes of angular momentum for the (a) control (CTL) and (b) DBZ experiments, integrated changes of angular momentum for the (c) CTL and (d) DBZ experiments, and vertical advections by mean vertical velocity for the (e) CTL and (f) DBZ experiments.