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  • View in gallery

    Time series of (a) minimum central sea level pressure (hPa) and (b) maximum surface wind speed (m s−1) of Hurricane Earl from different experiments (see Table 1) against best-track data for the period 0600–1800 UTC 30 Aug 2010.

  • View in gallery

    As in Fig. 1, but for the period 0600 UTC 30 Aug–0000 UTC 3 Sep 2010. The data assimilation cycles are separated by the dashed lines.

  • View in gallery

    Vortex structure of Hurricane Earl as revealed by wind fields. (a)–(f) Wind speeds (shaded; m s−1) and vectors at 10-m height from (a)–(c) experiment GSI-G and (d)–(f) experiment GSI-R at 0000 UTC (analysis time), 0300 UTC (3-h forecast), and 0900 UTC (9-h forecast) 31 Aug 2010. (h),(i) West–east cross section of wind speed through the hurricane center at 0000 UTC 31 Aug 2010 [(h) is from GSI-G and (i) from GSI-R], compared with (g) the wind analysis from TDR at 0015 UTC 31 Aug 2010.

  • View in gallery

    Ensemble spreads of (a),(e) temperature (K); (b),(f) u (m s−1) and (c),(g) υ (m s−1) wind components; and (d),(h) relative humidity (%) at 0000 UTC 31 Aug 2010. (a)–(d) From 80 members of global ensemble forecasting and (e)–(h) from 21 members of HWRF ensemble.

  • View in gallery

    Hourly rainfall rate (in. h−1) at 0500 UTC 31 Aug 2010 from (a),(b) HWRF forecasts compared with (c) NASA TRMM satellite-derived hourly rainfall rate at 0439 UTC 31 Aug 2010 (courtesy of Naval Research Laboratory tropical cyclone website). (a) From experiment GSI-G and (b) from experiment GSI-R. The color scales in (a),(b), and (c) are slightly different.

  • View in gallery

    The time series of forecasts of (a) track, (b) minimum central sea level pressure (hPa), (c) track errors (km), and (d) maximum surface wind speed (m s−1) against the best-track data for Hurricane Edouard (2014) from 0600 UTC 15 Sep to 1800 UTC 18 Sep 2014. The data assimilation cycles are separated by the dashed lines.

  • View in gallery

    Radius–height cross sections of the isopleths of the net radial force per unit mass for (a) GSI-G analysis at 0600 UTC 30 Aug 2010, (b) GSI-R analysis minus GSI-G analysis at 0600 UTC 30 Aug 2010, (c) GSI-G 3-h forecast at 0900 UTC 30 Aug 2010, and (d) GSI-R 3-h forecast at 0900 UTC 30 Aug 2010. The contour interval for (a), (c), and (d) is 10 m s−1 h−1 and (b) is 5 m s−1 h−1 with dashed lines indicating negative values. The zero contour is not plotted. The red lines indicate the radius of maximum wind.

  • View in gallery

    As in Fig. 7, but for (a) GFS and (b) vortex initialization (before data assimilation) at 0600 UTC 30 Aug 2010.

  • View in gallery

    As in Fig. 7a, but for (a) vortex initialization, (b) GSI-G without TDR data assimilation, and (c) GSI-G with TDR data assimilation at 1200 UTC 30 Aug 2010.

  • View in gallery

    Distribution of TDR observations at (a) 1200 and (b) 0000 UTC 31 Aug 2010.

  • View in gallery

    Analysis increments of wind fields at 850 hPa at 1200 UTC 30 Aug 2010 from (a),(d) NO-TDR, (b),(e) GSI-G, and (c),(f) GSI-R. Shaded contours are increments of (a)–(c) the u component and (d)–(f) the υ component. The vectors are the wind field increments (Δu, Δυ). The hurricane signs denote the centers of simulated Hurricane Earl.

  • View in gallery

    (a) Storm-relative individual sweeps of radar reflectivity from NOAA P3 aircraft radars during the period of 1202:28–1202:57 UTC 30 Aug 2010 (available on HRD website at http://www.aoml.noaa.gov/hrd/Storm_pages/earl2010/radar.html). Relative vorticity (shaded; 10−3 s−1) and wind (vectors; m s−1) at 850 hPa, vertical velocity averaged from 700 to 300 hPa (magenta contours; only 1, 3, and 5 m s−1 plotted) in the storm-relative coordinate for (b) radar analysis at 1156 UTC 30 Aug 2010 and (c) NO-TDR, (d) GSI-G, and (e) GSI-R at 1200 UTC 30 Aug 2010.

  • View in gallery

    As in Fig. 11, but at 0000 UTC 31 Aug 2010.

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Influence of the Self-Consistent Regional Ensemble Background Error Covariance on Hurricane Inner-Core Data Assimilation with the GSI-Based Hybrid System for HWRF

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  • 1 Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah
  • | 2 Environmental Modeling Center, National Centers for Environmental Prediction, College Park, Maryland
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Abstract

An initial vortex spindown, or strong adjustment to the structure and intensity of a hurricane’s initial vortex, presents a significant problem in hurricane forecasting, as with the NCEP Hurricane Weather Research and Forecasting Model (HWRF), because it can cause significantly degraded intensity forecasts. In this study, the influence of the self-consistent regional ensemble background error covariance on assimilating hurricane inner-core tail Doppler radar (TDR) observations in HWRF is examined with the NCEP gridpoint statistical interpolation (GSI)-based ensemble–three-dimensional variational (3DVAR) hybrid data assimilation system. It is found that the resolution of the background error covariance term, coming from the ensemble forecasts, has notable influence on the assimilation of hurricane inner-core observations and subsequent forecasting results. Specifically, the use of ensemble forecasting at high-resolution native grids results in significant reduction of the vortex spindown problem and thus leads to improved hurricane intensity forecasting.

Further diagnoses are conducted to examine the spindown problem with a gradient wind balance. It is found that artificial vortex initialization, performed before data assimilation, can cause strong supergradient winds or imbalance in the vortex inner-core region. Assimilation of hurricane inner-core TDR data can significantly mitigate this imbalance by reducing the supergradient effects. Compared with the use of a global ensemble background error term, application of the self-consistent regional ensemble background covariance to inner-core data assimilation leads to better representation of the mesoscale hurricane inner-core structures. It can also result in more realistic vortex structures in data assimilation even when the observational data are unevenly distributed.

Corresponding author address: Prof. Zhaoxia Pu, Department of Atmospheric Sciences, University of Utah, 135 S 1460 E, Rm. 819, Salt Lake City, UT 84112. E-mail: zhaoxia.pu@utah.edu

Abstract

An initial vortex spindown, or strong adjustment to the structure and intensity of a hurricane’s initial vortex, presents a significant problem in hurricane forecasting, as with the NCEP Hurricane Weather Research and Forecasting Model (HWRF), because it can cause significantly degraded intensity forecasts. In this study, the influence of the self-consistent regional ensemble background error covariance on assimilating hurricane inner-core tail Doppler radar (TDR) observations in HWRF is examined with the NCEP gridpoint statistical interpolation (GSI)-based ensemble–three-dimensional variational (3DVAR) hybrid data assimilation system. It is found that the resolution of the background error covariance term, coming from the ensemble forecasts, has notable influence on the assimilation of hurricane inner-core observations and subsequent forecasting results. Specifically, the use of ensemble forecasting at high-resolution native grids results in significant reduction of the vortex spindown problem and thus leads to improved hurricane intensity forecasting.

Further diagnoses are conducted to examine the spindown problem with a gradient wind balance. It is found that artificial vortex initialization, performed before data assimilation, can cause strong supergradient winds or imbalance in the vortex inner-core region. Assimilation of hurricane inner-core TDR data can significantly mitigate this imbalance by reducing the supergradient effects. Compared with the use of a global ensemble background error term, application of the self-consistent regional ensemble background covariance to inner-core data assimilation leads to better representation of the mesoscale hurricane inner-core structures. It can also result in more realistic vortex structures in data assimilation even when the observational data are unevenly distributed.

Corresponding author address: Prof. Zhaoxia Pu, Department of Atmospheric Sciences, University of Utah, 135 S 1460 E, Rm. 819, Salt Lake City, UT 84112. E-mail: zhaoxia.pu@utah.edu

1. Introduction

Improving hurricane intensity prediction is a major challenge in operational weather forecasting. According to Rogers et al. (2013) and the National Hurricane Center (NHC; www.nhc.noaa.gov/verification/verify5.shtml), the NHC official 48-h track forecast error has decreased by about 50% between 2000 and 2010, but the intensity forecast error over the same period has remained virtually unchanged. To improve hurricane intensity forecasting, much effort has been dedicated to develop operational numerical models, including approaching cloud-permitting resolution (e.g., Gopalakrishnan et al. 2011; Tallapragada et al. 2014), new techniques for assimilating inner-core observations into numerical models (Zhao and Jin 2008; Zhang et al. 2011; Aksoy et al. 2012; Zhang et al. 2013), methods for optimizing ensemble forecasts of tropical cyclone (TC) intensity, and refinement of statistical and dynamical models for predicting TC intensity change and rapid intensification (RI; Kaplan and DeMaria 2003; Kaplan et al. 2010). Despite this progress, there are still uncertainties in hurricane intensity forecasting, among which hurricane initialization is a notable problem owing to the lack of vortex inner-core observations and the inability of coarser-resolution analysis to resolve both hurricane center position and vortex intensity and structure. Previous studies have proven that accurate inner-core structure is vital for hurricane intensity forecasts (Pu et al. 2009; Zhang et al. 2011).

At the National Centers for Environmental Prediction (NCEP), the Hurricane Weather Research and Forecasting Model (HWRF) (Tallapragada et al. 2014) has provided regional mesoscale hurricane intensity and track forecasts since 2007. It has provided real-time TC forecasts to the NHC for the Atlantic and eastern North Pacific basins since it became operational at NCEP in the 2007 hurricane season and then extended to all global oceanic basins in 2014. A vortex initialization scheme (Liu et al. 2006) and a GSI-based hybrid data assimilation system (Tallapragada et al. 2014) were implemented with HWRF to provide initial conditions for hurricane forecasts. In the current operational setup, HWRF initialization undergoes two steps: A vortex initialization scheme first relocates the vortex to its observed location, followed by a size and intensity correction process with adjustments to the wind, pressure, and thermodynamics fields. After that, data assimilation is performed using a GSI-based hybrid system with available conventional, radar, and satellite data. To achieve flow-dependent background errors, a hybrid three-dimensional variational (3DVAR) assimilation system with global ensemble is currently used in the operational environment (Tallapragada et al. 2014). During the hurricane season, the NOAA Hurricane Research Division (HRD) has been using airborne tail Doppler radar (TDR) to collect observations in hurricane core regions. These inner-core observations have proven to be significant for improving numerical prediction of TCs through data assimilation (Zhang et al. 2011). However, the vortex spindown problem in operational HWRF, especially in forecasts of major hurricanes (Tallapragada et al. 2014; M. Tong et al. 2016, personal communication), is notable in many cases. Specifically, vortex spindown here refers the significant adjustment of hurricane vortex intensity [e.g., a 10–20-knot (kt; 1 kt = 0.51 m s−1) drop in the maximum surface wind] in the first few hours of a forecast, which leads to a significant degradation of the hurricane intensity forecast. To improve these forecasts, it is essential to mitigate the influence of the spindown problem in the operational environment and also to gain better understanding of the possible reason for the spindown.

Commonly, the spindown problem is related to the unrealistic initial conditions. The background error covariance is one of the important factors that controls the spatial and structure of the analysis increments. In current GSI-based ensemble–3DVAR hybrid data assimilation system for HWRF, 80 members of 6-h ensemble forecasts from the NCEP Global Forecast System (GFS) ensemble Kalman filter (EnKF)–3DVAR system (Wang et al. 2013) are used to achieve the flow-dependent background error covariance. Since the resolution of the GFS EnKF ensemble forecast is at a resolution of T254 (~55 km), which is much coarser than the resolution of HWRF innermost domains (~3 km), it is necessary to evaluate the influence of the resolution of the background error covariance term on hurricane inner-core data assimilation.

In this study, we first present a set of numerical results that demonstrates the significant influence of the self-consistent high-resolution HWRF ensemble on hurricane initialization with HWRF and the GSI-based hybrid system. Then, diagnoses of the results will be used to reveal the possible causes for the spindown and why data assimilation in different configurations can result in an improved initial vortex and hurricane forecasting. Section 2 describes the model and GSI hybrid data assimilation system. Section 3 presents numerical results to demonstrate the benefits of including self-consistent HWRF regional ensemble in GSI ensemble–3DVAR to HWRF hurricane forecasting. Sections 4 and 5 interpret the benefits by examining the spindown problem from the perspective of a gradient wind imbalance in the hurricane inner-core region and also by evaluating the effects of the use of a regional ensemble background error term on inner-core data assimilation in terms of representing hurricane inner-core structures. Additional discussion and some concluding remarks are made in section 6.

2. Description of HWRF and the GSI-based hybrid data assimilation system

HWRF (Gopalakrishnan et al. 2011; Bao et al. 2012; Tallapragada et al. 2014), version 3.6, was used. The model grid setup and physics options were configured as closely as possible to the operational HWRF system in late 2014 (Tallapragada et al. 2014). HWRF uses the same dynamical core as NCEP’s WRF-Nonhydrostatic Mesoscale Model (NMM; Janjić et al. 2010). The major features of HWRF include the following: a two-way interactive, movable, triply nested-grid procedure with three nested-grid domains—D1, D2, and D3—with (x, y) areas of 8559 km × 8343 km, 1566 km × 1521 km, and 1131 km × 903 km, and grid resolutions of 27, 9, and 3 km, respectively; the simplified Arakawa–Schubert cumulus scheme and the Ferrier cloud microphysics scheme for the 27- and 9-km-resolution domains, but only the latter for the 3-km-resolution domain, the Eta Geophysical Fluid Dynamics Laboratory (GFDL) longwave and shortwave radiation schemes, and the GFDL surface layer and PBL schemes [see details in Gopalakrishnan et al. (2011)].

A GSI-based ensemble–3DVAR hybrid data assimilation system was used for data assimilation for HWRF. In this system, the analysis increment is obtained by minimizing the following hybrid cost function:
e1
where the first term on the right-hand side is the background term with hybrid covariance . Namely, the background error covariance information is a combination of two sources: a static, pregenerated matrix 1, and a flow-dependent matrix 2 derived from the NCEP GFS global hybrid EnKF–3DVAR system (Wang et al. 2013) 6-h ensemble forecasts. The second term is the observational term, which is the same as in a traditional 3DVAR system except that x is the total analysis that is associated with both static and ensemble covariances. Observations are represented by , H is a forward model or transferring operator, and is an observational error covariance matrix. To achieve hybrid data assimilation, the two weighting factors and satisfy . The current system sets and equal to 0.2 and 0.8, respectively, meaning more weight was given to the ensemble background term. The ensemble background term was generated from the 80 members of the GFS EnKF system at a resolution of T254. Because the HWRF ensemble–3DVAR system uses the GFS ensemble but does not update the ensemble members through EnKF, this procedure is termed “one-way hybrid.”

To achieve accurate track and intensity forecasts, a vortex initialization scheme [Liu et al. 2006; also see details in Tallapragada et al. (2014)] was first used to relocate the hurricane vortex at the location determined by the NHC tropical cyclone vital statistics (TCVitals); this was then followed by a procedure of intensity correction, which corrects the size and intensity of hurricane vortex with dynamic and thermodynamic adjustments for consistency. Then, data assimilation was performed to assimilate conventional, satellite, and available TDR radial velocity data into the ghost domain 2 (9-km grid spacing) and conventional and available TDR radial velocity data into ghost domain 3 (3-km grid spacing) to refine the structure of the initial vortex. Note that each ghost domain covers the corresponding model domain, but it is larger than the corresponding model domain. Operational evaluation based on the 2008–12 hurricane seasons showed that the vortex initialization and TDR inner-core data assimilation led to significant improvement in hurricane forecasts at NCEP. However, in many cases, especially for forecasts that began at the mature phase of a hurricane, the vortex spindown, and sometimes spinup, was very obvious. The spinup and/or spindown caused significantly degraded hurricane forecasts, which were more serious in the first several hours of forecasts.

3. Impact of inner-core TDR data assimilation: Global versus regional ensemble background error terms

We first examine the spindown/spinup problem and then propose numerical experiments to seek a way to mitigate it. Because of the notable spindown problem observed in HWRF, Hurricane Earl (2010; see NHC report at http://www.nhc.noaa.gov/data/tcr/AL072010_Earl.pdf) at its mature phase is used as a sample case. The initial time was chosen at 0600 UTC 30 August 2010, when Earl was a mature hurricane with a minimum central sea level pressure (MCSLP) of 967 hPa and a maximum surface wind (MSW) of 95 kt. Following the vortex relocation and intensity correction, the conventional and satellite observations were assimilated at 0600 UTC 30 August 2010. The first group of experiments (see Table 1 for detailed configuration) includes 1) no data assimilation (NO-DA), 2) GSI 3DVAR data assimilation [viz., in Eq. (1); GSI-3DVAR], and 3) GSI-based ensemble–3DVAR hybrid data assimilation (GSI-G0). Figures 1a and 1b show that a strong vortex spindown/spinup problem is apparent during the first 2 h of forecasts. The spindown/spinup changes the intensity of the initial vortex significantly in the first 2 h, and then the model starts to adjust the vortex again by a spinup process in the next few hours. Significant adjustments during these spindown and spinup periods seem to be artificial. The mass and wind balance also fail to maintain during these periods, as both MCSLP and MSW decrease at the beginning of the forecasts. The experiment with GSI-based hybrid data assimilation outperforms the other two experiments in terms of the intensity forecast for Earl. However, the spindown/spinup problem is still significant.

Table 1.

List of the configurations of numerical experiment. Data assimilation is performed on Ghost d02 (20° × 20°, ~9-km horizontal resolution) and Ghost d03 (10° × 10°, ~3-km horizontal resolution). Satellite data are only assimilated in the Ghost d02.

Table 1.
Fig. 1.
Fig. 1.

Time series of (a) minimum central sea level pressure (hPa) and (b) maximum surface wind speed (m s−1) of Hurricane Earl from different experiments (see Table 1) against best-track data for the period 0600–1800 UTC 30 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Cycled data assimilation (experiment GSI-G) is then performed during 0600 UTC 30 August–0000 UTC 31 August 2010 using the GSI-based hybrid system with inner-core TDR observations assimilated in 6-hourly data assimilation cycles. Figures 2a and 2b indicate that the vortex spindown/spinup problem becomes even more serious in the cycled data assimilation, thus harming the forecasts. The analysis increments and vortex structures, before and after data assimilation experiments and during the vortex spindown periods, have been examined in detail (see section 5). Notable vortex structural changes (in terms of vortex size, structural features, and distribution of wind, warm core, etc.) were found during the vortex spindown period. For instance, Figs. 3a–c shows the wind speed and vectors at 10-m height at the analysis time of 0000 UTC 31 August 2010 and for 3- and 9-h forecasts after the data assimilation. Adjustments in vortex structure are notably large during the spindown period. In addition, compared with the radar-derived wind field across the center of the hurricane (Fig. 3g), GSI-G analysis at 0000 UTC 31 August 2010 overestimates the maximum wind speed in the inner-core region (Fig. 3h).

Fig. 2.
Fig. 2.

As in Fig. 1, but for the period 0600 UTC 30 Aug–0000 UTC 3 Sep 2010. The data assimilation cycles are separated by the dashed lines.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Fig. 3.
Fig. 3.

Vortex structure of Hurricane Earl as revealed by wind fields. (a)–(f) Wind speeds (shaded; m s−1) and vectors at 10-m height from (a)–(c) experiment GSI-G and (d)–(f) experiment GSI-R at 0000 UTC (analysis time), 0300 UTC (3-h forecast), and 0900 UTC (9-h forecast) 31 Aug 2010. (h),(i) West–east cross section of wind speed through the hurricane center at 0000 UTC 31 Aug 2010 [(h) is from GSI-G and (i) from GSI-R], compared with (g) the wind analysis from TDR at 0015 UTC 31 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

To examine the impact of the ensemble background on the analysis and forecasts, a set of self-consistent HWRF regional ensemble forecasts, downscaled from the 21 ensemble members of the NCEP global ensemble forecasting system (GEFS), was generated. The regional HWRF ensemble members use initial and boundary conditions derived from the GFS analysis and GEFS members and forecasts forwarded inside the 6-hourly analysis cycle. Figures 4e–h shows the HWRF regional ensemble spreads at 0000 UTC 31 August 2010 (corresponding to Figs. 4a–d). Apparently, the spreads from 21 HWRF ensemble members provide many detailed storm-scale structural features for wind, temperature, and moisture. Compared with global ensemble forecasts, regional ensemble forecasts in HWRF native model domains should offer much more realistic (storm scale) correlation structures among these variables.

Fig. 4.
Fig. 4.

Ensemble spreads of (a),(e) temperature (K); (b),(f) u (m s−1) and (c),(g) υ (m s−1) wind components; and (d),(h) relative humidity (%) at 0000 UTC 31 Aug 2010. (a)–(d) From 80 members of global ensemble forecasting and (e)–(h) from 21 members of HWRF ensemble.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Data assimilation experiments (Table 1) are then performed with the GSI-based ensemble–3DVAR hybrid system, using aforementioned regional ensemble forecasts in HWRF native domains, instead of GFS EnKF global ensemble forecasts, to form the ensemble background term for the GSI hybrid data assimilation system. As indicated in Figs. 2a and 2b, the use of regional ensemble forecasts mitigates the vortex spindown problem substantially, thus improving the intensity forecasts of Earl significantly, with an error reduction of about 70% (50%) in MCSLP (MSW). In addition, compared with Figs. 3a–c, Figs. 3d–f reveal that the vortex spindown problem has really been mitigated to a great degree, as the intensity and structure of the mature hurricane (Earl) are maintained during the first several hours of forecasts after the data assimilation. Moreover, while GSI-G analysis overestimates the maximum wind speed in the inner-core region (Fig. 3h) at 0000 UTC 31 August 2010, GSI-R reproduces a more reasonable magnitude of maximum wind speed (Fig. 3i).

Furthermore, Fig. 5 compares the hourly rainfall rate near 0500 UTC 31 August 2010 from HWRF forecasts (Figs. 5a,b) with the NASA Tropical Rainfall Measuring Mission (TRMM) satellite-derived hourly rainfall rate (Fig. 5c). Compared with GSI-G (Fig. 5a), the figure illustrates a clear improvement in the convective structures and precipitation patterns in GSI-R (Fig. 5b) regardless of all details, proving that the forecasts of hurricane intensity and structures are indeed improved.

Fig. 5.
Fig. 5.

Hourly rainfall rate (in. h−1) at 0500 UTC 31 Aug 2010 from (a),(b) HWRF forecasts compared with (c) NASA TRMM satellite-derived hourly rainfall rate at 0439 UTC 31 Aug 2010 (courtesy of Naval Research Laboratory tropical cyclone website). (a) From experiment GSI-G and (b) from experiment GSI-R. The color scales in (a),(b), and (c) are slightly different.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

To refine this conclusion, another case has been tested in the same way. Cycled data assimilation is performed for the period of 0600–1800 UTC 15 September 2014 with inner-core TDR data assimilated (see Table 1) for Hurricane Edouard (2014; http://www.nhc.noaa.gov/data/tcr/AL062014_Edouard.pdf) in its mature phase. Figure 6 shows that the experiment with the HWRF regional ensemble background indeed outperforms the experiment that uses the GFS global ensemble background. Specifically, the track errors in 72-h forecasts are reduced. For the intensity forecast, the spindown of MCSLP is significantly mitigated with the HWRF regional ensemble background (GSI-R) during the data assimilation cycles (the time periods are separated by the dashed lines), as the variations in MCSLP in GSI-R nearly match the variations in MCSLP in the best track. During the forecast period, the vortex spindown problem is significantly mitigated and intensity errors are reduced within 24-h forecasts, with a nearly 70% (30%) error reduction for hurricane MCSLP (MSW), although a smaller impact of data assimilation on 2- and 3-day forecasts is found, either positive or mixed.

Fig. 6.
Fig. 6.

The time series of forecasts of (a) track, (b) minimum central sea level pressure (hPa), (c) track errors (km), and (d) maximum surface wind speed (m s−1) against the best-track data for Hurricane Edouard (2014) from 0600 UTC 15 Sep to 1800 UTC 18 Sep 2014. The data assimilation cycles are separated by the dashed lines.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Overall, compared with the experiments using the global ensemble background error covariance term, the experiments with the HWRF regional ensemble background covariance term mitigate the vortex spindown and also lead to significant improvement in intensity forecasts. The above differences between GSI-R and GSI-G in terms of initial vortex adjustments could be attributed to the use of global versus regional ensemble background error terms in the GSI-based hybrid data assimilation system. For instance, Figs. 4a–d show the ensemble spreads from 80 GFS EnKF members at 850 hPa for u and υ wind components, temperature, and moisture fields at 0000 UTC 31 August 2010. Clearly, the overall structure of these spreads is much too smooth, with large-scale features, and does not correspond well to the realistic hurricane vortex structures. Since GSI ensemble–3DVAR hybrid data assimilation accounts largely for the background term from the ensemble forecasting, the spindown problem could be attributed (at least partly) to the mismatch of the resolution between the HWRF inner domain and ensemble background.

Results in this section also provide robust evidence that the spindown problem is associated with vortex initialization, inner-core TDR data assimilation, and the use of different background error covariances in the data assimilation system. It can be alleviated by using a self-consistent HWRF EnKF ensemble background with the same resolution as the HWRF forecast domains. Thus, in the following two sections, we will use Hurricane Earl as a case study to investigate how and why inner-core data assimilation and the use of a self-consistent HWRF EnKF ensemble background term can mitigate the spindown problem and result in improved intensity forecasts.

4. Source of imbalance and effects of inner-core data assimilation

To examine vortex spindown, it is necessary to diagnose the dynamics of the initial vortex in various experiments. First, imbalance (or inconsistent variation) between the wind and pressure fields, as shown in Fig. 1 and mentioned above, implies that there might be imbalance in the initial vortex for some reason. Meanwhile, as mentioned, the initial hurricane vortex is formed by two steps in the HWRF system: vortex initialization [vortex relocation, intensity, and size correction, as documented by Liu et al. (2006) and Tallapragada et al. (2014)] and inner-core data assimilation. This raises a question about the possible cause of the imbalance embedded in these procedures that could trigger the spindown.

To investigate the imbalance in the initial vortices, we use a gradient wind balance relationship for the diagnosis. Previous studies by Willoughby (1990) and Smith et al. (2009) indicated that the azimuthal-mean tangential circulation of TCs, especially in their inner-core region, is approximately in gradient wind and hydrostatic balance. Thus, we examine here the structure of the net radial force field F which is defined by Smith et al. (2009) as the difference between the local radial pressure gradient and the sum of the centrifugal and Coriolis forces; that is,
e2
where p is the pressure, ρ is the air density, υ is the tangential wind speed, and f0 is the Coriolis parameter at the storm center. In pressure coordinates, Eq. (2) can be rewritten as
e3
where g is gravitational acceleration, z is geopotential height, and other quantities are as defined in Eq. (2). If F = 0, the tangential flow is in exact gradient wind balance; if F < 0, the flow is subgradient; and if F > 0, it is supergradient. Note that all variables in Eqs. (2) and (3) are in azimuthal average framework.

To check whether there is an imbalance in the initial vortex, Figs. 7a and 7b illustrate radius–height cross sections of F isopleths in GSI-G and the differences between GSI-R and GSI-G at 0600 UTC 30 August 2010 (analysis time for Earl), respectively. Figures 7c and 7d show the same radius–height cross sections of F isopleths at 0900 UTC 30 August 2010 (3-h HWRF forecasts) for GSI-G and GSI-R, respectively. Contrasts between Figs. 7a and 7b and Figs. 7c and 7d clearly reveal that very strong supergradient wind fields in the inner-core region of the vortex at analysis time (0600 UTC; Figs. 7a,b) in both GSI-G and GSI-R. While after the 3-h forecast, the gradient wind balance is established in the inner-core region after the vortex spindown (Figs. 7c,d). The subgradient wind is also clearly seen in the lower boundary layer of the vortex (Figs. 7c,d). Specifically, these features depicted by Figs. 7c and 7d are consistent with Smith et al. (2009). Therefore, the results here confirm that the imbalance exists in the HWRF initial vortex. Very strong supergradient winds are the indication of the initial vortex imbalance. In addition, compared with GSI-G (Fig. 7a), GSI-R has reduced supergradient winds (Fig. 7b).

Fig. 7.
Fig. 7.

Radius–height cross sections of the isopleths of the net radial force per unit mass for (a) GSI-G analysis at 0600 UTC 30 Aug 2010, (b) GSI-R analysis minus GSI-G analysis at 0600 UTC 30 Aug 2010, (c) GSI-G 3-h forecast at 0900 UTC 30 Aug 2010, and (d) GSI-R 3-h forecast at 0900 UTC 30 Aug 2010. The contour interval for (a), (c), and (d) is 10 m s−1 h−1 and (b) is 5 m s−1 h−1 with dashed lines indicating negative values. The zero contour is not plotted. The red lines indicate the radius of maximum wind.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

To track the possible cause of the imbalance in the initial vortex, Fig. 8 displays the radius–height cross sections of F isopleths from the initial vortex in the GFS analysis and the vortex generated by HWRF initialization (before data assimilation; namely, the result of vortex relocation, size, and intensity correction) at 0600 UTC 30 August 2010. It is apparent that the vortex in the GFS analysis satisfies the gradient wind balance in its inner core (Fig. 8a). However, significant supergradient winds are present in the inner-core region of the HWRF vortex as a result of its vortex initialization procedure (Fig. 8b). The comparison here indicates that the major imbalance in the initial vortex should come from the HWRF vortex initialization because of the expected artificial specification of the vortex during its relocation, size, and intensity correction. However, a comparison of Fig. 8b with Figs. 7a and 7b shows that HWRF data assimilation (both GSI-G and GSI-R) has reduced this supergradient in the vortex inner-core region, indicating that data assimilation can help reduce the imbalance in the initial vortex. However, because of a lack of TDR inner-core observations at 0600 UTC 30 August 2010, we need further confirm the effects of inner-core data assimilation by diagnosing the results at 1200 UTC 30 August 2010.

Fig. 8.
Fig. 8.

As in Fig. 7, but for (a) GFS and (b) vortex initialization (before data assimilation) at 0600 UTC 30 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

The radius–height cross sections of F isopleths are compared at 1200 UTC 30 August 2010 (Fig. 9) for GSI-G without and with inner-core data assimilation. A significant impact of inner-core TDR data assimilation in the initial vortex structure has been revealed (Fig. 9) as a result of very good coverage of inner-core TDR observations (Fig. 10a). Without TDR data assimilation (Fig. 9b), supergradient winds are still present in the vortex inner-core region although they have been much reduced from the vortex initialization (Fig. 9a). With inner-core TDR data assimilation (Fig. 9c), the supergradient winds are replaced by gradient wind balance and weak subgradient winds appear in the vortex inner-core region. This result evidently indicates that assimilation of TDR data can mitigate the spindown problem in the analysis cycle. Results from GSI-R are similar (figures not shown), although the magnitudes of supergradient winds are slightly smaller than those in Figs. 9b and 9c.

Fig. 9.
Fig. 9.

As in Fig. 7a, but for (a) vortex initialization, (b) GSI-G without TDR data assimilation, and (c) GSI-G with TDR data assimilation at 1200 UTC 30 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Fig. 10.
Fig. 10.

Distribution of TDR observations at (a) 1200 and (b) 0000 UTC 31 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Since both GSI-G and GSI-R mitigate the initial vortex imbalance and also result in improved intensity forecasting, further examination should be conducted to investigate why GSI-R can lead to better forecasts. This motivates us to check the influence of self-consistent regional background error covariance on detailed vortex inner-core structures, as Zhang et al. (2011) and Pu et al. (2009) stated that accurate inner-core structure is vital for hurricane intensity forecasts.

5. Influence of self-consistent background error covariance on inner-core structure

As mentioned in section 3, compared with the HWRF regional ensemble spread, the overall structure of the global ensemble spreads is much too smooth, has large-scale features and does not correspond well to the realistic hurricane vortex structures (e.g., Fig. 3). Since GSI ensemble–3DVAR hybrid data assimilation accounts largely for the background term from the ensemble forecasting, the mismatch of the resolution between the HWRF inner domain and ensemble background could have a strong influence on the initial vortex structure. In this section, we further compare the analysis increments and initial vortex structures between GSI-G and GSI-R.

Figure 11 compares the analysis increments of wind fields at 850 hPa at 1200 UTC 30 August 2010 from NO-TDR, GSI-G, and GSI-R. A significant influence of the assimilation of TDR inner-core data can be clearly seen in both GSI-G and GSI-R compared with NO-TDR, as the adjustments to the vortex core regions are notable. It is noteworthy that corresponding with the ensemble spread structure in GSI-R (similar to that in Fig. 4), increments in GSI-R show more detailed vortex inner-core structure with organized circulation. The increment in GSI-G shows largely the large-scale structure and does not align with the vortex circulation well.

Fig. 11.
Fig. 11.

Analysis increments of wind fields at 850 hPa at 1200 UTC 30 Aug 2010 from (a),(d) NO-TDR, (b),(e) GSI-G, and (c),(f) GSI-R. Shaded contours are increments of (a)–(c) the u component and (d)–(f) the υ component. The vectors are the wind field increments (Δu, Δυ). The hurricane signs denote the centers of simulated Hurricane Earl.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Figure 12 illustrates the radar-observed vortex inner-core convective structures, as revealed by radar reflectivity in Fig. 12a. The averaged vertical velocity between 700 and 300 hPa and flow features, as depicted by radar wind analysis and vorticity at the 850-hPa level (Fig. 12b) around 1200 UTC 30 August 2010, are compared with those from NO-TDR, GSI-G, and GSI-R. Apparently, neither NO-TDR nor GSI-G capture well the observed vortex convective structures and large vorticity in the core region, as both experiments show convective vertical motion only in the south quadrant and relatively weak vorticity in the vortex region. There is also no notable improvement in GSI-G compared with NO-TDR. However, at the same time, GSI-R is able to capture the observed convective features around the vortex with strong vertical motion around the vortex. It also successfully captures the realistic magnitude of the vorticity in the vortex inner core. The realism of the initial vortex as a result of GSI-R could definitely reduce the initial vortex structure adjustment, thus mitigating the initial vortex spindown.

Fig. 12.
Fig. 12.

(a) Storm-relative individual sweeps of radar reflectivity from NOAA P3 aircraft radars during the period of 1202:28–1202:57 UTC 30 Aug 2010 (available on HRD website at http://www.aoml.noaa.gov/hrd/Storm_pages/earl2010/radar.html). Relative vorticity (shaded; 10−3 s−1) and wind (vectors; m s−1) at 850 hPa, vertical velocity averaged from 700 to 300 hPa (magenta contours; only 1, 3, and 5 m s−1 plotted) in the storm-relative coordinate for (b) radar analysis at 1156 UTC 30 Aug 2010 and (c) NO-TDR, (d) GSI-G, and (e) GSI-R at 1200 UTC 30 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

Figure 13 displays the analysis increments at 0000 UTC 31 August 2010, confirming that the analysis increments correspond with the background error terms in data assimilation. The large-scale character of the background errors in GSI-G (e.g., Fig. 3) leads to more large-scale and smoothed analysis increments, and the detailed and more structured background errors in GSI-R result in mesoscale features of analysis increments. More importantly, it should also be noted that the TDR observations are evenly distributed (Fig. 10a) around the vortex of Hurricane Earl at 1200 UTC 30 August 2010 but unevenly distributed at 0000 UTC 31 August 2010 (Fig. 10b), as more data are available on the east side of the vortex compared with the west side. A comparison of the analysis increment in winds from GSI-G and GSI-R and also against NO-TDR at the same time shows that GSI-R made a similar magnitude of analysis increments as GSI-G in terms of the u component. However, for the υ component, GSI-R made a large analysis increment on the west side of the vortex but a smaller analysis increment on the east side, reflecting the influence of both background field and the distribution of observations on the analysis. Meanwhile, GSI-G made a relatively large analysis increment on the east side of the vortex, responding to more observations being available on this side. In addition, large increments of the υ component located near 19°N, 65°W and its surroundings in GSI-G (Fig. 13e) due to the assimilation of TDR data correspond to the unrealistic horizontal wind structure around the inner-core region in the southeast quadrant of the storm center, as shown in Fig. 3a. These unrealistic large increments, however, are mitigated by GSI-R, as shown in Fig. 13f. Combined the results from Figs. 3 and 13, it seems that the GFS global ensemble (self-consistent HWRF regional ensemble) background can lead to unrealistic (realistic) increments around the storm center and produce an unrealistic (realistic) horizontal storm structure in the analysis wind field when the TDR data are unevenly distributed, which leads to a strong (weak) storm-structure adjustment in the first few hours of forecasts. In addition, the results here also imply that a regional, self-consistent HWRF ensemble can lead to realistic vortex structures, even when the observational data are unevenly distributed.

Fig. 13.
Fig. 13.

As in Fig. 11, but at 0000 UTC 31 Aug 2010.

Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0017.1

6. Discussion and concluding remarks

Hurricane intensity forecasting is a challenging problem in numerical weather prediction. Accurate specification of hurricane inner-core and environmental conditions plays an essential role in hurricane intensity forecasts. The vortex spindown (i.e., strong vortex intensity and structure adjustments) in operational hurricane forecasting, as presented in the NCEP HWRF, can result in significant errors in hurricane intensity forecasts. Results from this study present a potential way to mitigate the vortex spindown problem. Results show that the use of self-consistent regional ensemble forecasts, generated at the native HWRF grid resolution, instead of the global ensemble in the GSI ensemble–3DVAR hybrid background term, can result in more realistic hurricane initial inner-core structure, thus leading to improved hurricane forecasting. Even with 21 HWRF regional ensemble members, vortex inner-core data assimilation with the GSI-based 3DVAR–ensemble hybrid method and the subsequent hurricane forecasts outperform the experiment with 80 ensemble members that form the global ensemble background term. A significant influence of the resolution of the ensemble background error covariance on vortex inner-core data assimilation and forecasting has been shown.

Further diagnoses show that the vortex spindown comes mainly from the vortex initialization scheme (e.g., vortex relocation, size, and intensity correction that performed before data assimilation) in HWRF, as it leads to large supergradient imbalance in the azimuthal-mean framework. Because of this imbalance, the wind and pressure have to be adjusted as soon as the forecast starts; therefore, strong spindown shows up in the first 1–2-h forecast (1–6-h forecast in some cases) with inconsistent variations in MCSLP and MWS. Neither the regional HWRF background nor the global GFS background can efficiently constrain these imbalances if the inner-core data are sparse or absent. However, with the inner-core TDR data assimilation, this imbalance in the vortex inner-core region can be overcome to a great degree, thus helping to mitigate the initial vortex spindown.

More important, because the self-consistent regional ensemble background covariance can provide detailed mesoscale structures in background error terms, it can thus constrain the whole data assimilation to better represent the vortex inner-core structure. In the case of the rich and even distribution of inner-core observations, the regional ensemble background covariance can lead to a realistic inner-core vortex structure. In the case of uneven distribution of inner-core data, it has the ability to modulate the analysis increments to be less strongly dependent on the observations. Because of the more realistic inner-core structures it produces, the use of the self-consistent regional HWRF ensemble background covariance results in reduced initial vortex structure adjustments (spindown) and improved hurricane intensity forecasts.

The outcomes from this study suggest that the ensemble background term has a significant impact on the analysis and forecasting of hurricanes. It is necessary to use a consistent resolution of ensemble forecasts to form the ensemble background error covariance in ensemble–3DVAR and EnKF–3DVAR hybrid systems. Advancements in computer science and improvements in computer resources will ensure the possibility of this implementation with more sophisticated regional ensemble forecasts (e.g. Zhang et al. 2014) or cycling regional EnKF.

In addition, as shown in this study, the major source of imbalance (part of the reason for spindown) comes from vortex initialization due to vortex relocation, intensity, and size correction before data assimilation. The reason why this vortex initialization causes the imbalance is beyond the scope of this study; thus, it should be pursued in future studies. Owing to following the specific procedures of vortex initialization and data assimilation for HWRF, the findings from this study could be limited by this particular hurricane initialization method. However, results from this study clearly indicate that the assimilation of inner-core observations can overcome the imbalance problem to a great extent. Future work should place more emphasis on the vortex initialization solely using data assimilation instead of the current combination of vortex relocation, intensity correction, and data assimilation, although this will rely to a great degree on the availability of vortex inner-core observations in future observing systems. In addition, this study uses a gradient wind balance relationship to examine the imbalance in the initial vortex. In fact, there could also be physical aspects of the inconsistencies inside the initial vortex that could possibly cause the spindown problem, and these should be addressed in future studies. To the best of our knowledge, this study is the first to diagnose the initial vortex spindown with dynamic imbalance. More work is certainly needed to address the vortex spindown problem in the future in order for us to better understand it and fully overcome it in the numerical prediction of hurricanes.

Acknowledgments

Computer resources from the NOAA TJet supercomputer maintained by NOAA/ESRL and the Center for High-Performance Computing (CHPC) at the University of Utah are acknowledged. Software and data support by the NCAR Development Testbed Center (DTC) is also appreciated. This study is supported by NOAA Grant NA14NWS4680025. The first author (ZP) is also supported by NSF Award AGS-1243027. Review comments from Prof. Chun-Chieh Wu and three anonymous reviewers have been very helpful in improving the manuscript.

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