1. Introduction
Tropical cyclones (TCs) are one of the costliest and deadliest weather hazards, responsible for more than 50% of total costs and 45% of total deaths of all billion-dollar weather and climate disasters from 1980 to 2020 (NCDC 2020). One of the most significant events in recent years is Hurricane Harvey of 2017. Harvey made its landfall as a category 4 hurricane in Texas on 26 August 2017 shortly after reaching its peak intensity (Blake and Zelinsky 2018). With a record-breaking rainfall of 60.58 in. (1539 mm) from 25 August to 1 September, Harvey is associated with an estimated cost of $125 billion (U.S. dollars), making it the second-costliest TC impacting the United States after adjusted for consumer price index (CPI), just after Hurricane Katrina of 2005 (NCDC 2020). Accurate predictions of TCs and their hazards are important to public safety and economic stability.
It is well known that the accuracy of the official track forecast of the TCs by the NHC has been constantly improving for the past 40 years (e.g., Cangialosi et al. 2020). This is primarily credited to improvements in NWP models, observation platforms, and associated data assimilation techniques that provide more accurate predictions of the large-scale synoptic conditions that steer the TCs. On the other hand, there was virtually no reduction in NHC’s intensity forecast errors before NOAA established the Hurricane Forecast Improvement Project (HFIP) in 2008, although a 15%–30% reduction has been achieved since then (Cangialosi et al. 2020). Aside from the utilization of high-resolution, convection-permitting NWP models that can better resolve the convective structure of the TCs, it is believed that the incorporation of high-resolution observations covering the inner-core region of the TCs [especially radial winds from the tail Doppler radars (TDRs) of the hurricane reconnaissance aircraft] using ensemble-based data assimilation techniques [such as the ensemble Kalman filter (EnKF)] have played a major role (e.g., Zhang et al. 2011; Aksoy et al. 2012, 2013; Aberson et al. 2015; Zhang and Weng 2015; Tong et al. 2018).
Ensemble-based data assimilation (EnDA) techniques, including EnKF, use short-term ensemble forecasts to estimate background error covariances (BECs). This online estimation of BECs makes them flow-dependent and time-variant, unlike the isotropic, homogeneous, time-invariant climatology BECs that pure variational data assimilation techniques usually use. The ensemble-based BECs also allow EnDA techniques to update model state variables that are not explicitly included in the observation operators that produce model predicted equivalents of the observations. This enables EnDA techniques to outperform pure variational techniques for TC applications (e.g., Schwartz et al. 2013; Poterjoy and Zhang 2014a). Previous studies proved that EnKF can improve TC intensity forecasts by assimilating TC inner-core observations, including dropsondes (Poterjoy and Zhang 2014b; Poterjoy et al. 2014; Feng and Wang 2019) and ground-based (Zhang et al. 2009; Zhu et al. 2016) or airborne Doppler radars (Zhang et al. 2011; Weng and Zhang 2012; Sippel et al. 2013, 2014; Zhang and Weng 2015; Tong et al. 2018).
One of the major disadvantages of these inner-core observations is that they are either collected during reconnaissance flights and field campaigns, or only available when the TCs are already very close to the land. However, there has been significant progress recently in our ability to assimilate satellite all-sky (i.e., both clear-sky and cloud-affected) observations for TC predictions. Several studies suggested that TC analyses and predictions can be improved with the assimilation of all-sky infrared (IR) observations from the imagers onboard geostationary satellites (Zhang et al. 2016; Honda et al. 2018; Minamide and Zhang 2018), including the track and the intensity of Hurricane Harvey (Zhang et al. 2019; Minamide et al. 2020). Microwave (MW) observations also show great potential for improving the TC structure forecast (Wu et al. 2019; Sieron 2020). IR observations can provide knowledge about the environmental thermodynamics, the height of the clouds, and can infer synoptic-scale motions implicitly through their temporal evolutions. MW observations can provide information about the hydrometeors in addition to moisture. Therefore, they provide complementary information on different aspects of the TCs. However, both IR and MW observations are underutilized in operational models of major operational weather forecasting centers: all-sky IR observations are not operationally assimilated in any global or regional models, and all-sky MW observations are only operationally assimilated at ECMWF and NCEP as of 2018 (Geer et al. 2018).
With the operational GFS changing to the finite-volume cubed-sphere (FV3; Lin and Rood 1997; Lin 1997, 2004) dynamical core in 2019 and the development of the Hurricane Analysis and Forecast System (HAFS) as a collaborative project under HFIP, we have been building an FV3-based EnKF data assimilation system for TC analyses and predictions based on the Pennsylvania State University (PSU) Weather Research and Forecasting (WRF)-based EnKF data assimilation system (the PSU WRF-EnKF system; Zhang et al. 2009; Weng and Zhang 2012), focusing on assimilating all-sky IR and MW observations. Parallel to the construction of the data assimilation system, this study seeks to explore how assimilating satellite all-sky IR and MW observations might influence TC analyses. We examine the ensemble correlations using a convection-permitting ensemble forecast of Hurricane Harvey generated by a global-to-regional nested FV3-based model. This study complements Poterjoy and Zhang (2011), which examined the structure of covariances of Hurricane Katrina (2005), and Zhang et al. (2016), which briefly examined the structure of the correlations between simulated IR brightness temperatures (BTs) from the Advanced Baseline Imager (ABI) with sea level pressure and zonal wind speed. This is also the first detailed study that examines the length scales of the correlations between all-sky IR/MW BTs and model states in TCs at a convection-permitting resolution. Previously, only two studies have briefly examined correlations between all-sky IR/MW BTs and model states: Bonavita et al. (2020), which examined the length scales of the ensemble correlations between MW BTs and model states in a coarse-resolution global model perspective, and Zhang et al. (2021), which examined the correlation length scale for all-sky IR BTs for continental severe thunderstorms.
This paper is constructed as follows. Section 2 provides an overview of the numerical model, the ensemble forecast of Hurricane Harvey, and the radiative transfer model that we use to produce simulated satellite BTs. After examining the impacts of hurricane position observations in sections 3 and 4 focuses on the correlations between satellite all-sky observations and model states. Section 4 also presents results of single observation EnKF experiments. Conclusions are provided in section 5.
2. The NWP model and the ensemble forecast of Hurricane Harvey
This section describes the NWP model used in this study, the observation operator used to generate simulated IR and MW BTs from model outputs, and the ensemble forecast of Hurricane Harvey.
a. The FV3-based numerical model
The ensemble forecast of Hurricane Harvey is generated using the numerical model combining the FV3 dynamical core and physical parameterization schemes from the GFS and the WRF models, including the 6-class single-moment GFDL scheme for microphysics processes (Chen and Lin 2013), scale-aware GFS cumulus convective parameterization scheme (Han et al. 2017), the YSU scheme for PBL processes (Hong et al. 2006), and the RRTMG scheme for longwave and shortwave radiation (Iacono et al. 2008). This FV3-based model consists of a global mesh with 6 tiles and a one-way nested regional mesh (Fig. 1a). Each of the global tiles contains 768 × 768 horizontal grid points with a quasi-uniform 13-km grid spacing, the same as the operational GFS. The high-resolution convection-permitting regional mesh contains 2944 × 1536 horizontal grid points with a quasi-uniform 3-km grid spacing. This 3-km domain is situated farther to the west compared to the proposed HAFS domain (e.g., Hazelton et al. 2020, 2021). This was done to keep the domain centered around the track of Hurricane Harvey. There are 63 vertical levels, and the highest level is located at 1 hPa (about 50 km above mean sea level). Note that the vertical size of each grid volume in the FV3 core evolves with time; therefore, the heights of a given grid point at different times or in a different member are different. All ensemble members are vertically interpolated to common height levels before calculating ensemble-based metrics.
(a) FV3GFS model domain setting used in this study with black solid lines outlining the six tiles of the 13-km global domain and the red solid lines outlining the 3-km nested domain, (b) track, and (c) maximum surface wind speed in the ensemble forecast in the 3-km domain with black solid lines representing the best track analysis, green solid lines representing the ensemble mean, and red solid lines representing ensemble members.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
b. The simulated satellite observations
Simulated IR and MW BTs are generated from the 3-km resolution ensemble for all the members that will be introduced in section 2c using the Community Radiative Transfer Model (CRTM; Han et al. 2006), version 2.3.0. For IR, simulated ABI observations are generated. ABI is the newest-generation imager. It flies on GOES-16 and GOES-17 and produces full-disk images every 10 min operationally (Schmit et al. 2017). It has ten IR channels ranging from 3.9 to 13.28 μm, among which three are water vapor channels ranging from 6.19 to 7.34 μm with a nadir resolution of 2 km. Numerous studies show that assimilating real ABI water vapor channel observations can improve predictions of various kinds of severe weather, such as TCs (Zhang et al. 2019) and severe thunderstorms (Zhang et al. 2018; Jones et al. 2020).
For MW, simulated Global Precipitation Measurement (GPM; Hou et al. 2014; Skofronick-Jackson et al. 2017) Microwave Imager (GMI) observations are generated. GMI has 13 channels ranging from 10.65 to 183.31 GHz with two polarizations, including channels similar to those of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI; Kummerow et al. 1998), with nadir footprint sizes ranging from 19.4 km × 32.2 km for the lowest-frequency channel to 4.4 km × 7.3 km for the highest frequency channel (Hou et al. 2014). We have updated CRTM hydrometer scattering look-up tables to increase the accuracy of MW observation simulations following Sieron et al. (2018). These tables are generated specifically for the GFDL microphysics schemes using particle size distribution assumptions that are consistent with the scheme and realistic nonspherical particle scattering properties for snow. For simplicity, azimuth angles of the GMI scans are ignored.
c. The ensemble forecast of Hurricane Harvey
A 60-member ensemble forecast of Hurricane Harvey is carried out using the FV3-based model from 1200 UTC 24 August to 0000 UTC 27 August 2017 (the landfall of Harvey occurred shortly after 0000 UTC 26 August 2017). The initial conditions (ICs) for the ensemble forecast are generated by combining the inner-core structure of the hurricane from the 60-member ensemble analyses of the PSU WRF-EnKF system and the environmental conditions of the GFS analysis. The 60-member PSU WRF-EnKF system assimilates conventional surface, radiosonde, and dropsonde observations and satellite-derived atmospheric motion vectors from the Global Telecommunication System (GTS), all-sky GOES-16 ABI channel 8 (upper-tropospheric water vapor channel) IR observations, and hurricane intensity estimates (center pressure) every hour from 1200 UTC 23 August to 1200 UTC 24 August (Zhang et al. 2019). The EnKF analysis of each member at 1200 UTC 24 August is combined with the GFS analysis by retaining the original EnKF analysis within 250 km from the center position of Harvey and linearly relaxing toward GFS analysis between 250 and 400 km. The ICs of all the members are identical to the GFS analysis beyond 400 km from the center position of Harvey.
Figures 1b and 1c show the ensemble track and maximum surface 10-m wind forecasts of Harvey in the 3-km domain. Only a few members in the 13-km forecast reach a lower-end category 3 intensity (50–58 m s−1), suggesting that this resolution is not capable of resolving essential convective activities of major hurricanes and not suitable for their intensity predictions. Therefore, we only use the 3-km region forecasts in this study. A significant fraction of the 3-km forecasts reach category 5 intensity (>70 m s−1), which is noticeably stronger than the observations, especially after 1200 UTC 25 August 2017. The overprediction of surface maximum wind speed could result from several potential model error sources, including inaccurate PBL scheme and surface exchange processes, which could be improved through simultaneous state and parameter estimation of EnKF (e.g., Nystrom et al. 2020), and the lack of feedbacks from the sea, which could be alleviated through air–sea strongly coupled data assimilation and prediction (e.g., Chen and Zhang 2019; Chen et al. 2020).
Figure 2 shows observed and simulated IR and MW BTs at 1200 UTC 25 August 2017. One ensemble member that is overall closest to the observed track and maximum surface wind speed is subjectively selected and shown here together with the storm-relative ensemble mean that all ensemble members have been aligned based on their respective minimum sea level pressure centers. Three channels from two satellite instruments that are inspected in this study are shown here. The first channel is the 6.19-μm channel 8 of ABI (Fig. 2a), which is sensitive to the moisture in the upper troposphere. The second channel is the 18.7-GHz vertically polarized channel 3 of GMI (Fig. 2d), which is sensitive to land surface temperature, liquid particles, and moisture. In channel 3 of GMI, warmer BTs are associated with more liquid particles and moisture, although the influence of moisture is much smaller than that of liquid particles. The third channel is the 183 ± 7-GHz vertically polarized channel 13 of GMI (Fig. 2g), which is sensitive to snow and graupel. For channel 13 of GMI, more snow and graupel are associated with colder BTs due to scattering. Comparing observations to the simulated BTs interpolated from the original convection-permitting model grid to the observation grids, it is clear that the general feature of Harvey, including eye, eyewall, and rainbands, are reasonably replicated in simulated BTs from the FV3 forecasts. Despite this, some detailed differences exist. For example, at this time the simulated TC is smaller and is missing a rainband to the north of the TC near the Texas coastline (Figs. 2b,e,h). The primary TC structures are also clearly revealed in the storm-relative ensemble mean of the BTs (Figs. 2c,f,i) with reduced horizontal variability.
(a),(d),(g) Observed and simulated brightness temperature from (b),(e),(h) an ensemble member and (c),(f),(i) the ensemble mean in the 3-km domain at 1200 UTC 25 Aug 2017 for (a)–(c) ABI channel 8, (d)–(f) GMI channel 3, and (g)–(i) GMI channel 13. Simulated brightness temperatures in (d)–(i) are interpolated to grids of the observations, and no beam convolutions are applied for the two GMI channels.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
3. Impacts of hurricane position observations
One common practice to correct the TC surface locations (or reduce the displacements) and keep the simulated TC from drifting away using EnKF is by assimilating the estimated positions (Wu et al. 2010). In this section, we briefly examine how assimilating surface position observations can change the structure of the hurricane and provide a TC vortex that is better aligned with the observed location for subsequent assimilation of remote sensing observations in the FV3-based model.
Figure 3 shows the zonal cross sections of correlations and covariances between the longitude of the surface TC center (defined as the location of the minimum sea level pressure) and temperature (T), water vapor mixing ratio (Qv), and horizontal wind components (U and V) in the original geographical coordinate, averaged every 6 h from 1800 UTC 24 August to 0600 UTC 26 August. The structures of the correlations and covariances between the latitude of the surface TC center and model variables are similar. The correlations between center longitude and T show a dipole structure symmetric about the ensemble-mean TC center at the same heights where the warm core is located (Fig. 3a). The positive (negative) correlations to the east (west) of the TC center indicate that a positive increment of center longitude (i.e., an eastward displacement of the observed center relative to the simulated center) will increase (decrease) T to the east (west) of the ensemble-mean TC center, and the opposite behavior of T will occur when the center longitude displacement is negative/westward. This means the warm core will be moved toward the direction where the observed TC center is located relative to the simulated ensemble-mean center. There is also a thin layer near the surface with correlations that have opposite signs compared to the correlations aloft in the upper troposphere, which results from the intense rainfall and cold pool near the eye and the eyewall. The correlations between center longitude and Qv (Fig. 3b) are similar to those for T, suggesting similar shifts of the eye—where Qv is higher—when a center longitude observation is assimilated.
Zonal cross sections across the mean center of the simulated TCs of (a)–(d) correlations and (e)–(h) covariances between center longitude of the simulated TCs and (a),(e) temperature; (b),(f) water vapor mixing ratio, (c),(g) zonal wind; and (d),(h) meridional wind (representing tangential wind) averaged from 1800 UTC 24 Aug to 0600 UTC 26 Aug every 6 h. Contours in (a) and (e) are ensemble-mean perturbation temperature relative to the environment every 1 K from 1 K; contours in (b) and (f) are ensemble-mean water vapor mixing ratio every 1 g kg−1 from 1 g kg−1; contours in (c) and (g) are ensemble-mean zonal wind speed every 4 m s−1 with solid lines representing 0 and positive values and dashed lines representing negative values; and contours in (d) and (h) are ensemble-mean meridional wind speed every 8 m s−1 with solid lines representing 0 and positive values and dashed lines representing negative values.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
The correlations between the center longitude and U/V also show consistent shifts (Figs. 3c,d). For example, with a positive innovation (eastward displacement) of the “observed” center longitude, positive increments in the U-component of wind will increase the easterly near-ground inflow to the east of the TC center and decrease the westerly inflow to the west of the TC center, and the positive–negative–positive correlation pattern associated with the V-component essentially shifts the primary circulation of the hurricane toward the direction where the TC center is observed.
Compared with correlation, the ensemble covariance acts as a direct estimation of potential updates to model fields when a certain observation is assimilated. This is because covariance determines the magnitude of the analysis increments in EnKF. The comparison of correlation and covariance can also reveal regions with greater uncertainty (larger standard deviation). This is revealed when comparing correlations between center longitude and model states (Figs. 3a–d) with corresponding covariances (Figs. 3e–h). Covariance between center longitude and T peaks around regions of the greatest temperature perturbations in the upper troposphere (warm cores; Fig. 3e), covariances between center longitude and Qv peak in the mid- to lower troposphere (Fig. 3f), and covariances between center longitude and U/V peak around the eye and eyewall in the mid- to lower troposphere (Figs. 3g,h). The distributions of larger covariances suggest that these regions have larger uncertainties and the increments will be greater in these regions.
It is apparent from the above analysis that the assimilation of surface position observations will change the position of the TC by modifying the structure and better align the position of the TC with the observed position. This improved alignment of simulated and observed TC centers will not only improve subsequent track forecasts but also benefit the assimilation of high-resolution observations due to an improved juxtaposition of the simulated TC with the observations (e.g., Aksoy 2013). Therefore, we will switch to a storm-relative coordinate in the following section to examine the covariances between satellite observations and model states.
4. Impacts of all-sky satellite observations
All calculations in this section are performed in storm-relative coordinates. We will first examine how the magnitude of the ensemble correlations between BTs and model states vary with respect to height and distance between BT and model states, then take a look at how a satellite observation at specific locations influences the dynamical and thermodynamical structure of the TC. Last, the impact of assimilating IR/MW BTs on the structure of TCs will be analyzed through single observation EnKF experiments with synthetic observations.
a. Height and distance dependencies of correlations
To examine how ensemble correlations vary with height and distance, we first need to define different regions for the channels we plan to examine. For ABI channel 8, we subset the “clear-sky” and “deep-cloud” regions based on cloud-top pressure diagnosed by the model: the clear-sky region has no clouds (undefined cloud top pressure) across all members, and the deep-cloud region consists of grid points where the cloud top pressures of all ensemble members are unanimously smaller than 300 hPa, similar to the definitions in Zhang et al. (2021). Since GMI channel 3 is strongly sensitive to surface emissivity, which contains extremely large uncertainties, we only examine the grid points where all ensemble members are over the sea surface. Within that part of the domain, we further subset the “with-liquid” and “no-liquid” regions if the column-maximum total liquid mixing ratios (cloud liquid and rain) of all ensemble members are unanimously greater or smaller than 10−6 kg kg−1, respectively. For GMI Channel 13, “with-ice” and “no-ice” regions are defined if the column-maximum total ice mixing ratios (cloud ice, snow, and graupel) of all the ensemble members are unanimously greater or smaller than 10−6 kg kg−1, respectively. The threshold of 10−6 kg kg−1 is also used by Kerr et al. (2015), Hayatbini et al. (2019), and Zhang et al. (2021) to identify clouds. Different thresholds for region separation are also tested and they do not qualitatively change the structures presented below.
Figure 4 shows how the mean correlations between IR/MW BTs and hydrometeors vary with respect to the horizontal distances between the IR/MW BTs and hydrometeors and the height of the hydrometeors. Model outputs every 6 h from 1800 UTC 24 August to 0600 UTC 26 August 2017 are used for the calculation. It is apparent that different IR or MW channels are sensitive to different hydrometeor types at different heights. Over cloudy regions, ABI channel 8 is mostly correlated with ice particles, especially cloud ice and snow [Figs. 4a(2),a(4)], that significantly contribute to the deep clouds; since more hydrometeors are indicative of potentially higher and colder cloud tops, and colder BT, the correlations are generally negative. GMI channel 3 is most strongly correlated with rain in the lower troposphere [Fig. 4b(3)] and relatively less correlated with other hydrometers. The correlation is positive because more liquid particles increase the radiation at this MW band. For GMI channel 13, strong correlations exist with all ice particles [Figs. 4d(2),d(4),d(5)]. Meanwhile, the correlations are slightly weaker with rain [Fig. 4d(3)]. These correlations extend deeper compared with those of ABI channel 8 due to its capability to penetrate cloud tops. BTs of this channel are negatively correlated with hydrometeors because the hydrometeors scatter and reduce the outgoing radiation. Correlations between the MW channels and hydrometeors in the no-liquid or the no-ice region are generally weak (Figs. 4c,e) because there are not many hydrometeors in these regions. The strong correlations between IR/MW channels and the hydrometeors indicate potential influences on these hydrometeors when BTs from these three channels are assimilated.
Changes of correlations between BTs and hydrometeors with respect to the height of the hydrometeors and the distance between BTs and hydrometeors. BTs come from (a) ABI channel 8 in the deep-cloud region, GMI channel 3 in (b) the with-liquid region and (c) the no-liquid region, and GMI channel 13 in (d) the with-ice region and (e) the no-ice region. Hydrometeors include (top to bottom) cloud liquid, cloud ice, rain, snow, and graupel, respectively.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
The correlations between these IR/MW channels and temperature/moisture are shown in Fig. 5. Correlations between IR BTs and temperature are generally positive [Figs. 5a(1) and 5b(1)], and correlations between IR BTs and moisture are generally negative [Figs. 5a(2) and 5b(2)]. This is likely because a higher temperature acts to increase outgoing longwave radiation, while more moisture leads to stronger absorption of radiation in the clear-sky region. In cloudy regions, lower BTs are associated with tall clouds that have higher and colder cloud tops. The low-frequency MW BTs are positively correlated with Qv [Figs. 5c(2) and 5d(2)], which might be resulting from the strong positive correlations between moisture and liquid hydrometeors and the increase of radiation at this band when moisture or liquid water content increases. The correlations between this channel and T, on the other hand, are negative in the lower troposphere [Figs. 5c(1) and 5d(1)]. This is probably associated with enhanced evaporation and, therefore, reduced liquid particles in the lower troposphere when the temperature becomes warmer (remember that the influence of moisture is much smaller than liquid particles at this spectral band). This is also consistent with the relationship between temperature and liquid particles in this region. The average gridpoint-wise correlation between temperature and the mixing ratio of total liquid water in the lowest 1 km of the troposphere is about −0.39, suggesting that high temperatures are associated with less liquid particles in this part of the region. Correlations between the high-frequency MW channel BTs and Qv [Figs. 5e(2) and 5f(2)] show similar signs to those of the IR BTs; however, its correlations with T [Figs. 5e(1) and 5f(1)] are negative in the upper troposphere, probably due to the heating profile associated with the stratiform regions of TCs. Stronger stratiform regions tend to generate stronger latent heating (cooling) above (below) the melting level and also more ice particles above the melting level (Didlake and Houze 2013).
Changes of correlations between BTs and model states with respect to the height of the model states and the distance between BTs and model states. BTs come from ABI channel 8 in (a) the clear-sky region and (b) the deep-cloud region, GMI channel 3 in (c) the with-liquid region and (d) the no-liquid region, and GMI channel 13 in (e) the with-ice region and (f) the no-ice region. Model states include (top) temperature and (bottom) water vapor mixing ratio.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
It is also apparent from Fig. 5 that BTs from different channels are correlated to different layers of the troposphere, and they are consistent with the characteristics of these channels. ABI channel 8 is most sensitive to the moisture in the upper troposphere, and the strongest correlations between BTs from this channel and Qv in the clear-sky region appear at around a height of 10 km [Fig. 5a(2)]; on the other hand, for the deep-cloud region, the strongest correlations appear at around 13 km [Fig. 5b(2)], which corresponds to the height of the cloud tops. For GMI channel 3, the strongest correlation in regions with liquid particles occurs at roughly 7 km [Fig. 5c(2)], while in the no-liquid region the strongest correlation occurs in the near-surface lower troposphere [Fig. 5d(2)]. Due to the sensitivity to ice particles, GMI channel 13 has the strongest correlation with Qv at around 12 km [Fig. 5e(2)], where Qi is the most abundant, while in the no-ice region it is strongly correlated with moisture in the midtroposphere around 6–7 km [Fig. 5f(2)]. The distinctions of the vertical structure of the correlations with Qv suggest that BTs from different IR/MW channels can provide complementary information about different parts of the troposphere.
Last, Figs. 4 and 5 also reveal the horizontal extension of correlations between the satellite channels and model states. In regions with no cloud or little liquid or ice particles, the correlations between BTs and T and Qv can extend a long distance, especially for ABI channel 8 and GMI channel 13. However, in cloudy or precipitating regions, magnitudes of the correlations between BTs and model states generally reduce to around 0 at the distance of 100–200 km (shorter scales are observed especially between GMI channel 3 and hydrometeors in Fig. 4b). This is longer than the scales of the correlations between cloudy IR BTs and model states for severe thunderstorms (Zhang et al. 2021) and likely represents the scale of the dominant dynamical and thermodynamical processes associated with TCs.
b. Impact of assimilating satellite observations on TC structures
In this subsection, we will show the impact of assimilating a specific satellite observation on the dynamical and thermodynamical structures of a TC through ensemble correlations. The correlations are calculated throughout the ensemble forecast among several model prognostic variables and IR/MW BTs at grid points where the maximum meridional wind speed occurs in the zonal vertical cross section that goes through the TC center at each time. Although the exact location of the BTs that are used to calculate correlations vary throughout the forecast, they always represent observations at the horizontal location of the strongest tangential wind in the cross section; therefore, their physical representation with respect to the TC structure largely remains unchanged (except for Fig. 8, which will be explained later), and most structural changes of the correlations that will be presented are associated with the structural changes of the simulated TC. We only considered prognostic variables to examine what direct model state changes those single-point IR/MW BTs will lead to.
The correlations between BTs and model states are consistent with the relationships between BTs and TC intensity. For the correlations between temperature and ABI channel 8 (Figs. 6a–d and 7a–d), opposite correlations within the center of the TC—coincident with the location of the maximum temperature perturbations—occur persistently throughout the entire forecast. Furthermore, at later forecast times, a positive correlation region emerges at the eyewall region, forming into a tube wrapped around the negative correlation region in the eye (Figs. 6c,d and 7c,d). This suggests that when an observed IR BT colder than modeled BT is assimilated, the correlations will make the warm core warmer and narrower, leading to a stronger TC that better matches the observed BT.
Zonal vertical cross sections across the center of the simulated TCs (marked by the black circles) of correlations between IR/MW BTs at one grid point at the same latitude of the TC center (marked by the black stars) and storm-relative temperature (shading) and ensemble-mean perturbation temperature relative to the environment (contours; every 2 K) for BTs from (a)–(d) ABI channel 8, (e)–(h) GMI channel 3, and (i)–(l) GMI channel 13, at (a),(e),(i) 1800 UTC 24 Aug; (b),(f),(j) 0600 UTC 25 Aug; (c),(g),(k) 1800 UTC 25 Aug; and (d),(h),(l) 0600 UTC 26 Aug.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
As in Fig. 6, but for horizontal cross sections at 9 km above mean sea level of correlations between IR/MW BTs and storm-relative temperature (shading) and ensemble-mean perturbation temperature relative to the environment (contours; every 2 K).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
Similar correlations occur between temperature and GMI channel 13 (Figs. 6i–l and 7i–l). This is because this channel is sensitive to ice particles, and lower BTs at this channel are associated with more ice particles (stronger scattering), which is often associated with stronger updrafts and a stronger TC. On the other hand, the correlations between temperature and GMI channel 3 show opposite signs compared to the correlations with the other two channels before the landfall (Figs. 6e–g and 7e–g), and become similar to the other two channels after the landfall which occurs shortly after 0000 UTC 26 August 2017 (Figs. 6h and 7h). Because the transmissivity of the atmosphere for this channel is high, this channel is heavily modulated by surface emissivity. The surface emissivity over the ocean is low, producing a radiatively cold surface. The liquid particles increase outgoing radiation because they emit more radiation than they absorb and scatter radiation from lower levels. As such, higher BTs are associated with more liquid particles; therefore, the correlations between temperature and this channel are generally positive in the eye when the TC is over the sea surface. On the other hand, the surface emissivity over the land surface is high, providing a radiatively warm background (Fig. 2), and liquid particles act to reduce rather than enhance outgoing radiation under this circumstance; therefore, the correlations between temperature and GMI channel 3 become similar to the correlations with the two other channels after the landfall.
The sensitivities of the correlations with respect to the locations of the simulated BTs are also evaluated. Figure 8 presents examples of correlations between temperature and IR BTs from ABI channel 8 at different locations, including simulated IR BT at TC center (Figs. 8b,f), within the eye (Figs. 8c,g), and farther away from the eye (Figs. 8d,h), in addition to the original locations that are already evaluated in Figs. 6 and 7 (Figs. 8a,e). When the TC is relatively weak, the structures of the correlations with the four evaluated points are similar in the eye region (Figs. 8a–d); however, there is a region of positive correlations at about 12000 m for the IR BT at the TC center (Fig. 8b) whereas correlations with all other three locations are generally negative. This might be associated with the inhomogeneities across the ensemble members that some of the members already have formed a clear eye while the other members have not. The differences of correlations between IR BTs from the eye region versus outside the eye region become more distinct later when clear eyes formed in all the ensemble members (Figs. 8e–h): opposite to the negative correlation in the warm core for correlations with IR BTs at the eyewall (Fig. 8e) or farther away from the TC center (Fig. 8h), IR BTs from within the eye show very strong positive correlations with temperature in this region (Figs. 8f,g). Because no deep convection exists in the eye region at this time, IR BTs directly detect the temperature of the warm core, ergo resulting in a strong positive correlation (>0.6). Similar variabilities of correlations with IR BTs located a short distance apart also occur for other model prognostic variables (figure not shown). This behavior suggests that a compact localization, smaller than Fig. 5 suggests, might be beneficial when assimilating these observations in the eye and the eyewall region. Determining the optimal localization scale for different regions within a TC is beyond the scope of this study.
As in Fig. 6, but for zonal vertical cross sections of correlations between ABI channel 8 IR BTs at different locations and temperature (shading) and ensemble-mean perturbation temperature relative to the environment (contours; every 2 K) at (a)–(d) 1800 UTC 24 Aug and (e)–(h) 1800 UTC 25 Aug. The locations of IR BT that are used to calculate the correlations (marked by the stars) in (a) and (e) are as in Figs. 6a and 6c.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
The correlations between IR/MW BTs and water vapor mixing ratios (Qv; Figs. 9 and 10) are consistent with the correlations between BTs and temperature discussed above. During the early intensification stage of the TC, positive correlations with ABI channel 8 and GMI channel 13 (Figs. 9b,j and 10b,j) and negative correlations with GMI channel 3 (Figs. 9f and 10f) at the center of the TC suggest that assimilating observations that are indicative of a stronger TC (i.e., colder BT with negative increments for ABI channel 8 and GMI channel 13, or warmer BT with positive increments for GMI channel 3) are going to reduce the moisture in the center of the TC, thereby helping to establish a clear, open eye. At later stages, the correlations become negative within the eye and positive at the eyewall for ABI channel 8 (Figs. 9c,d and 10c,d) and GMI channel 13 (Figs. 9k,l and 10k,l) with a slight hint of positive correlations at the TC center in the upper troposphere, and positive within the eye and negative at the eyewall for GMI channel 3 (Figs. 9g and 10g). It is also noteworthy that the locations where ensemble mean Qv peak, suggesting the existence of the eyewall, are also the locations where the correlations reverse the sign horizontally. This circular structure of positive and negative correlations between IR/MW BTs and Qv at the TC center at later stages of the TC development is similar to the correlations with the temperature at those times, suggesting that the assimilation of BTs will modify the contraction of the eyewall.
As in Fig. 6, but for zonal vertical cross sections of correlations between IR/MW BTs and water vapor mixing ratio (Qv; shading) and ensemble-mean Qv (contours; every 3 g kg−1).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
As in Fig. 7, but for horizontal cross sections at 9 km above mean sea level of correlations between IR/MW BTs and water vapor mixing ratio (Qv; shading) and ensemble-mean Qv (contours; every 0.5 g kg−1).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
Assimilating IR/MW BTs will also have direct influences on hydrometeors. At 1800 UTC 24 August when the TC is relatively weak and just about to start its rapid intensification, stronger correlations between IR/MW BTs and hydrometeors are generally collocated with regions of greater mixing ratios near the TC center (Fig. 11). For example, for GMI channel 3, which is more sensitive to liquid particles, strong positive correlations occur above the location of the simulated observation in the mid- to lower troposphere where there is more cloud ice (Fig. 11f) and rain (Fig. 11h). On the other hand, ABI channel 8 and GMI channel 13 are more sensitive to ice particles, and strong negative correlations with these two channels occur above the location of the simulated observation in the mid- to upper troposphere where higher mixing ratios of cloud ice (Figs. 11b,l), snow (Figs. 11d,n), and graupel (Figs. 11e,o) occur. Note that although the regions of higher hydrometeor mixing ratios suggest the existence of the potential eyewall to the east and the west of the TC center, stronger positive and negative correlations are generally concentrated in the part of the eyewall to the east of the TC center immediately above the location of the simulated observation, while the correlations are much weaker in the eyewall of the opposite side. Because the horizontal length scales of the correlations between IR/MW BTs and hydrometeors in this region are generally around 100 km (Fig. 4), shorter than the distance between the western part of the eyewall and the location of the simulated observation (about 1° to 1.5°), the correlations at the western part of the eyewall are heavily contaminated by sampling errors and are less reliable. Overall, the correlations at this time suggest that IR/MW BTs associated with deeper convection or more hydrometeors will increase hydrometeor contents, thus helping to build up the eyewall.
As in Fig. 6, but for zonal vertical cross sections at 1800 UTC 24 Aug between BTs from (a)–(e) ABI channel 8, (f)–(j) GMI channel 3, and (k)–(o) GMI channel 13, and (a),(f),(k) cloud liquid (Qc); (b),(g),(l) cloud ice (Qi); (c),(h),(m) rainwater (Qr); (d),(i),(n) snow (Qs); and (e),(j),(o) graupel (Qg). Contours are ensemble-mean mixing ratios of the hydrometeors every 0.1 g kg−1 for Qc and Qi and every 0.3 g kg−1 for Qr, Qs, and Qg.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
Similar to the correlation with temperature and moisture, the structures of correlations between IR/MW BTs and hydrometeors also change at later times when the TC becomes stronger (Fig. 12). Strong negative correlations between ABI channel 8/GMI channel 13 and cloud ice (Figs. 12b,l) and snow (Figs. 12d,n) move inward compared with 24 h earlier (Fig. 11). This also happens with the strong positive correlations between GMI channel 3 and cloud liquid (Fig. 12f) and rain (Fig. 12h). This means that when IR/MW BTs that are associated with more hydrometeors in the eyewall region are assimilated, the increments will contract the eyewall, consistent with the behavior for temperature and moisture (Figs. 6–10).
As in Fig. 11, but at 1800 UTC 25 Aug.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
Temperature, moisture, and hydrometeors directly impact simulated IR/MW BTs through radiative transfer processes. Dynamic variables, on the other hand, are primarily correlated with IR/MW BTs through TC dynamics. An exception to this is surface wind, which can directly impact simulated MW BTs via the surface emissivity. Figure 13 shows the zonal cross section of correlations between IR/MW BTs and V-wind, which serves as a representation of the tangential wind (primary circulation). At the early stage of the TC development, strong correlations are generally correlated with strong winds (Figs. 13a,b,e,f,i,j), and the structures of the correlations will lead to enhanced primary circulation if an ABI channel 8/GMI channel 13 BT colder than the prior mean or a GMI channel 3 BT warmer than the prior mean is assimilated. Later on, when the TC becomes stronger (Figs. 13c,d,g,k,l), the structures of the correlations change in a way that the assimilated IR/MW BTs will change the radius of maximum winds (RMW) of the simulated TC. For example, if an IR/MW BT associated with a stronger TC (higher cloud tops, or more hydrometeors in the eyewall region) is assimilated, the RMW will become smaller. This structural change with respect to TC intensity is also confirmed in the horizontal structure of the correlation between IR/MW BTs and V-wind (Fig. 14). This result is consistent with our previous analysis for the correlations between temperature, moisture, and hydrometeors regarding their influence on the formation and placement of the eyewall.
As in Fig. 6, but for zonal vertical cross sections of correlations between IR/MW BTs and V-wind (shading) and ensemble-mean V-wind (contours; every 10 m s−1 with solid lines representing positive values and dashed lines representing negative values).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
As in Fig. 7, but for horizontal cross sections at 1 km above mean sea level of correlations between IR/MW BTs and V-wind (shading) and ensemble-mean V-wind (contours; every 10 m s−1 with solid lines representing positive values and dashed lines representing negative values).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
The secondary circulation of the TC consists of U-wind and W-wind in a zonal cross section. Figures 15 and 16 show their correlations with IR/MW BTs. For U-wind, strong correlations occur near the surface and at the upper troposphere, corresponding to the near-surface inflow and the upper-level outflow of the TC (Fig. 15). For W-wind, strong correlations occur in the eyewall where the strongest updrafts within a TC usually appear (Fig. 16). Additionally, increments (as suggested by the structure of correlations) associated with the secondary circulation resulting from assimilating IR/MW BTs are also consistent with our previous analysis on the primary circulation (Figs. 13 and 14). For example, at 0600 UTC 25 August, if a GMI channel 13 BT located at the eyewall is assimilated with a negative innovation, the negative correlation near the surface to the west of the TC center will enhance the inflow, and the positive correlation aloft in the upper troposphere will enhance the outflow (Fig. 15j). The negative correlation between this observation and W-wind will also enhance the updraft in the eyewall (Fig. 16j). On the other hand, for 1800 UTC 25 August, the horizontal extension of the upper-level outflow (Fig. 15l) and the location of the strongest updrafts associated with the eyewall (Fig. 16l) will also be influenced.
As in Fig. 6, but for zonal vertical cross sections of correlations between IR/MW BTs and U-wind (shading) and ensemble-mean U-wind (contours; every 5 m s−1 with solid lines representing positive values and dashed lines representing negative values).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
As in Fig. 6, but for zonal vertical cross sections of correlations between IR/MW BTs and W-wind (shading) and ensemble-mean W-wind (contours; every 0.5 m s−1).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
c. Single-observation EnKF experiments
Due to the combined effects of observation error, ensemble variance, and localization, structures of the correlations do not reflect the increments of model prognostic states when certain observations are assimilated. Therefore, single-observation EnKF experiments, i.e., only one point observation is assimilated in each experiment, are performed to examine the actual increments resulting from assimilating all-sky IR/MW BTs. For each experiment, one ensemble member is randomly selected among those stronger than the ensemble means in terms of both minimum sea level pressure and maximum surface wind speed (referred to as “the truth member” hereafter). Synthetic IR/MW observations using simulated BTs of the truth member are generated at the same locations that are used in section 4b, facilitating direct comparisons with correlation structures of section 4b. In total, 40 randomly selected members excluding the truth member are used as the EnKF priors. The adaptive observation error inflation (AOEI; Minamide and Zhang 2017) method, with a minimum error of 3 K, is used to help deal with the non-Gaussian observation errors. A 100-km horizontal radius of influence is used for all synthetic IR/MW observations to showcase the increments, which is longer than typically used when assimilating high-resolution all-sky IR observations for TCs (e.g., 30 km in Zhang et al. 2016, 2019; Minamide and Zhang 2017; Minamide et al. 2020). No vertical localization of BTs is applied in these experiments.
The experiment at 1800 UTC 24 August is presented here (experiments at other times show consistent results). Table 1 shows the values of the assimilated observations, EnKF prior means, innovations, observation errors (with AOEI), and ensemble standard deviations. The innovations of the three observations suggest higher cloud tops, more liquid particles, and more ice particles in the truth member than in the ensemble mean, respectively. Large innovations occur for the GMI channel 13 observation resulting from the displacement of the asymmetric eyewall; therefore, its observation error is inflated significantly by AOEI to avoid unrealistically large increments being added to the model states.
Values from the single-observation EnKF experiments.
Figure 17 shows EnKF prior mean and increments of several model prognostic fields in response to the assimilation of the observation. Temperature shows positive increments in the upper troposphere at the location of the assimilated observation (Figs. 17a,e,i), consistent with the negative, positive, and negative innovation of these three observations (Table 1) and the negative, positive, and negative correlations in this region (Figs. 6a,e,i), respectively. The increments also tapered down gradually when the distance to the location of the assimilated observation increases due to the impact of the localization in the horizontal direction (100 km). Similarly, V-wind (as a representation of the primary circulation) is increased throughout the entire troposphere at the RMW and reduced inward of the RMW (Figs. 17b,f,j), consistent with previous analysis based on the structure of the correlations (Figs. 13a,e,i). Contents of the hydrometeors at the eyewall also increase (Figs. 17c,d,g,h,k,l), suggesting a denser, more intense eyewall. Furthermore, with the help of the localization, increments are confined to the eyewall to the east of the TC center, avoiding potential degradation on the eyewall to the west of the TC center due to spurious correlations (Fig. 11). These increments are all beneficial for a stronger TC to develop.
Zonal vertical cross sections across the center of the simulated TCs (black circles) of EnKF increments (shading) and prior mean (contours) of (a),(e),(i) temperature; (b),(f),(j) V wind; (c),(g),(k) cloud liquid (Qc); and (d),(h),(l) snow when an observation from (a)–(d) ABI channel 8, (e)–(h) GMI channel 3, and (i)–(l) GMI channel 13 is assimilated at 1800 UTC 24 Aug. The black stars mark the horizontal location of the assimilated observations. Contours are every 2 K for temperature, 10 m s−1 for V wind with solid lines representing positive values and dashed lines representing negative values, 0.1 g kg−1 for Qc, and 0.3 g kg−1 for Qs.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0369.1
Although single observation EnKF experiments show increments that are consistent with the correlations, it should be pointed out that these results are idealized and simplified, and the nonlinearities associated with all-sky IR/MW BTs will complicate interpretation of the increments when more, dense observations are assimilated.
5. Conclusions
Aiming at assimilating satellite all-sky IR and MW observations for the analysis and prediction of TCs using an FV3-based EnKF data assimilation system, this study examines the structure and dynamics of the correlations between satellite all-sky observations and model states using an ensemble forecast of Hurricane Harvey generated by the FV3-based global model with a nested high-resolution convection-permitting regional domain. Correlations and covariances between model states and center positions of the TC calculated from the nested convection-permitting domain suggest that assimilating center position will make the simulated TCs better align with the observed position, facilitating our analysis on the structures of the correlations in a storm-relative framework.
After dividing the model domain into several subregions, we first examined how correlations between IR/MW BTs and model states vary with respect to distance and height. Naturally, different IR and MW channels are sensitive to different hydrometeors at different layers of the troposphere. ABI channel 8 (upper-tropospheric water vapor channel) and GMI channel 13 (high-frequency ice-sensitive channel) are strongly correlated with ice particles (cloud ice, snow, and graupel) in the mid- to upper troposphere, although GMI channel 13 is also strongly correlated with rainwater in the entire troposphere. GMI channel 3 (low-frequency liquid-sensitive channel) is strongly correlated with rainwater in the lower-troposphere. The correlations between moisture and these three channels are also different: ABI channel 8 is mostly sensitive to moisture in the mid- to upper troposphere, especially around cloud tops in the cloudy region; GMI channel 13 is also strongly correlated with upper-troposphere moisture in the cloudy region, but in the clear-sky region it is sensitive to lower layers of the troposphere compared with ABI channel 8; GMI channel 3 shows strong correlations with lower-troposphere moisture, especially near the surface. The different characteristics in the structure of the correlations between different IR/MW channels and different model states suggest that we can potentially achieve a more accurate estimation of moisture and hydrometeors over the entire troposphere when these channels are assimilated together with proper vertical localization. The correlations reduce to 0 beyond about 100–200 km in the cloudy region, which might be associated with the scales of the dominant dynamical processes of the TC.
We then assessed potential changes in the model states when these observations are assimilated through examinations of the correlations between IR/MW BT at one point (strongest tangential wind) and the model states. In general, the correlations suggest that the model states will adjust the structure of the simulated TC in the model so that it will better fit the “observed” BT. For example, when an ABI channel 8 BT that is colder than the model predicted equivalent comes in (innovation is negative), the correlations suggest an increase of the temperature of the TC warm core, enhancement in both the primary and the secondary circulations, and increase of the amount of moisture and hydrometeors in the eyewall. As a result, the simulated TC will become stronger, leading to stronger, deeper convection in the eyewall region that generates higher, colder cloud tops that better fit the “observed” BT. Similar and consistent adjustments of the model states are also observed based on the correlations between model states and MW BTs. Furthermore, different influences of IR/MW BTs suggested by the correlations at different stages of TC development also surfaced when comparing the structures of the correlations at different times. More specifically, when the simulated TC is relatively weak, these observations will help to build the eyewall, clear the eye, and strengthen the primary and secondary circulations. As the simulated TC becomes stronger, these observations will also contribute to the change of the placement of the eyewall and the radius of maximum winds, eventually altering the size of the eye.
Single-observation EnKF experiments were examined to assess the impact of the correlations when combined with ensemble variance and observation error models. The results of these experiments show that the actual increments are consistent with the structures of the correlations. It should be pointed out that the results obtained from single observation experiments are simplified and idealized. In reality, nonlinearities associated with the assimilation of dense IR/MW BTs as well as the nonlinearities associated with the numerical model may complicate or diminish the benefits that we can acquire from assimilating these observations.
In summary, through examinations of ensemble correlations, we found that assimilating all-sky IR/MW observations can improve the model estimation of the dynamical and thermodynamical structure of the TCs. It should be emphasized that this study only presents the analyses of a single event: Hurricane Harvey was an upright TC undergoing rapid intensification in a favorable environment until landfall, while complexities might emerge for other less organized TCs in a less favorable environment. However, the results show great potential to further improve our ability to accurately predict TC intensity and associated hazards such as torrential rainfalls, especially when they are still far away from land and in regions where hurricane reconnaissance flights are not available. Retrospective forecasts of the entire 2017 hurricane season using the PSU WRF-EnKF system that assimilates all-sky IR BTs from GOES-16 ABI show promising results with more accurate intensity forecasts (including the onset of rapid intensification) compared to the official forecasts from the NHC (Minamide and Posselt 2021).
This study presented the first analysis of the horizontal and vertical scales of correlations between all-sky IR/MW BTs and model prognostic variables for a TC and its environment. These scales are valuable for the design of horizontal and vertical localizations for the ensemble-based assimilation of all-sky IR/MW BTs for TC applications. Furthermore, this study also shows that IR/MW BTs, effectively two-dimensional observations, can impact the entire column of the troposphere from the surface to the upper troposphere in a way that is physically and dynamically consistent with the structure of the TC when 40–60 ensemble members are used. Although how long the benefits of assimilating all-sky IR/MW BTs can persist for TCs remains a question, these results enhance our confidence in the potentials of these underutilized observations.
It should also be pointed out that more complicated situations associated with the nonlinear observation operators and the non-Gaussian observation errors of the real-world IR/MW BTs will occur when they are assimilated. Advanced observation error models, considerations of correlated observation errors, and treatments of the zero-gradient problem associated with cloudy radiances are some of the primary issues associated with all-sky radiance assimilations that are being actively investigated. How best to initialize TC forecasts using all-sky IR/MW BTs to improve not only the track and intensity forecast of the TC but also its associated hazards is still a largely unresolved question that deserves more, in-depth research. An EnKF experiment assimilating real-world GOES-16 ABI observations using the FV3-based model is already underway and will be reported separately in the future.
Acknowledgments
We thank Robert Nystrom (UCAR/NCAR) for providing the PSU WRF-EnKF analysis of Hurricane Harvey, and David Stensrud and Christopher Hartman (the Pennsylvania State University) for helpful discussions. Comments from the three anonymous reviewers improve this work. This work is supported by NOAA NGGPS Grant through University of Michigan Subcontract 3004628721, NOAA Grant NA18NWS4680054, ONR Grant N000141812517, and NASA Grant 80NSSC19K0728. Numerical simulations are performed on the Jet supercomputer of NOAA, and the Stampede 2 supercomputer of the Texas Advanced Computing Center (TACC) through the Extreme Science and Engineering Discovery Environment (XSEDE) program support by the National Science Foundation (NSF). Results of this manuscript are available at http://hfip.psu.edu/yuz31/Zhangetal2021MWR/.
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