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  • View in gallery

    Plots of (a) storm track, (b) maximum 10-m wind speed as a function of forecast time, and (c) minimum sea level pressure as a function of forecast time from five sensitivity experiments of Hurricane Earl (2010) varying Lh. Each line color represents each experiment, and the experiment name contains the value of Lh (m) used in the experiment. The control experiment (CTL) used Lh = 1900 m.

  • View in gallery

    Plots of (a) the maximum intensity in terms of maximum surface wind speed and (b) the mean 24-h intensity change as a function of Lh for the 5-day forecasts of Hurricane Earl (2010) initialized at 1800 UTC 26 Aug 2010. The black dashed line represents observed values. Note that Lh = 1900 m was used in the control run.

  • View in gallery

    Radius–height plots of the azimuthally averaged total wind speed over 72–78 h of the 5-day forecasts of Hurricane Earl (2010) initialized at 1800 UTC 26 Aug 2010, from (a) Doppler radar observations, (b) the control experiment (Lh = 1900 m), and the (c) L375, (d) L750, (e) L1500, and (f) L1500 experiments. The contour interval is 5 m s−1, and the black contour has the value of 64 kt (33 m s−1).

  • View in gallery

    Plots of the 2-km RMW as a function of Lh averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). The blue crosses are from the HWRF forecasts. The solid line is an estimate of the parameters based on Doppler radar observations.

  • View in gallery

    Plots of the vertical mean profiles of (a),(b) Vt and (c),(d) Vr at the RMW from the Hurricane Earl (2010) forecasts averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). Comparisons at (left) the RMW and (right) 2 × RMW. The black solid and dashed lines, respectively, in each plot show the mean and 95% confidence interval of the wind profiles from dropsonde observations. Note that Lh = 1900 m was used in the control run.

  • View in gallery

    Plots of the boundary layer height as a function of Lh averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). The blue color represents the inflow layer depth at the RMW, the green color represents the inflow layer depth at 2 × RMW, and the red color represents the height of the maximum tangential wind speed. The solid lines are estimates of the parameters based on dropsonde observations. Note that Lh = 1900 m was used in the control run.

  • View in gallery

    As in Fig. 4, but for the slope of the RMW as a function of Lh.

  • View in gallery

    As in Fig. 4, but for the (a) maximum warm-core anomaly and (b) height of the maximum warm-core anomaly as a function of Lh The solid line in each panel is an estimate of the parameters based on dropsonde observations.

  • View in gallery

    As in Fig. 4, but for the vortex tilt as a function of Lh.

  • View in gallery

    Plots of the (a) absolute track error, (b) along-track error, and (c) cross-track error in HWRF retrospective forecasts with two different setups for the parameterization of horizontal diffusion in terms of Lh. In the control experiment (referred to as HOAC), Lh = 800 m as in H216, while the other experiment (COAC) used Lh =1900 m and the same coac value as in H215 but with the H216 model. The error bar represents the 95% confidence interval. FY16 means year 2016 in the legend.

  • View in gallery

    As in Fig. 10, but for the absolute error for intensity.

  • View in gallery

    As in Fig .10, but for the FSP for intensity error relative to the 2014 version of HWRF.

  • View in gallery

    As in Fig. 10, but for the biases in intensity.

  • View in gallery

    As in Fig .10, but for the bias in the RMW.

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Evaluating the Impact of Improvement in the Horizontal Diffusion Parameterization on Hurricane Prediction in the Operational Hurricane Weather Research and Forecast (HWRF) Model

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  • 1 NOAA/AOML/Hurricane Research Division, and University of Miami/Cooperative Institute for Marine and Atmospheric Studies, Miami, Florida
  • | 2 NOAA/AOML/Hurricane Research Division, Miami, Florida
  • | 3 NOAA/AOML/Hurricane Research Division, and University of Miami/Cooperative Institute for Marine and Atmospheric Studies, Miami, Florida
  • | 4 NOAA/AOML/Hurricane Research Division, Miami, Florida
  • | 5 NOAA/NCEP/Environmental Modeling Center, College Park, Maryland
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Abstract

Improving physical parameterizations in forecast models is essential for hurricane prediction. This study documents the upgrade of horizontal diffusion parameterization in the Hurricane Weather Research and Forecasting (HWRF) Model and evaluates the impact of this upgrade on hurricane forecasts. The horizontal mixing length Lh was modified based on aircraft observations and extensive idealized and real-case numerical experiments. Following an earlier work by the first two authors, who focused on understanding how the horizontal diffusion parameterization worked in HWRF and its dynamical influence on hurricane intensification using idealized simulations, a series of sensitivity experiments was conducted to simulate Hurricane Earl (2010) in which only Lh was varied. Results from the Earl forecasts confirmed the findings from previous theoretical and idealized numerical studies, in that both the simulated maximum intensity and intensity change rate are dependent on Lh. Comparisons between the modeled and observed structure of Hurricane Earl, such as storm size, boundary layer heights, warm-core height and temperature anomaly, and eyewall slope, suggested that the Lh used in the HWRF Model should be decreased. Lowering Lh in HWRF has a positive impact on hurricane prediction based on over 200 retrospective forecasts of 10 Atlantic storms. Biases in both storm intensity and storm size are significantly reduced with the modified Lh.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Jun Zhang, jun.zhang@noaa.gov

Abstract

Improving physical parameterizations in forecast models is essential for hurricane prediction. This study documents the upgrade of horizontal diffusion parameterization in the Hurricane Weather Research and Forecasting (HWRF) Model and evaluates the impact of this upgrade on hurricane forecasts. The horizontal mixing length Lh was modified based on aircraft observations and extensive idealized and real-case numerical experiments. Following an earlier work by the first two authors, who focused on understanding how the horizontal diffusion parameterization worked in HWRF and its dynamical influence on hurricane intensification using idealized simulations, a series of sensitivity experiments was conducted to simulate Hurricane Earl (2010) in which only Lh was varied. Results from the Earl forecasts confirmed the findings from previous theoretical and idealized numerical studies, in that both the simulated maximum intensity and intensity change rate are dependent on Lh. Comparisons between the modeled and observed structure of Hurricane Earl, such as storm size, boundary layer heights, warm-core height and temperature anomaly, and eyewall slope, suggested that the Lh used in the HWRF Model should be decreased. Lowering Lh in HWRF has a positive impact on hurricane prediction based on over 200 retrospective forecasts of 10 Atlantic storms. Biases in both storm intensity and storm size are significantly reduced with the modified Lh.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Jun Zhang, jun.zhang@noaa.gov

1. Introduction

As the horizontal resolution of operational hurricane models becomes smaller, improving physical parameterizations of subgrid-scale physical processes such as turbulent mixing becomes more important for hurricane prediction. Turbulent mixing in the vertical direction, especially in the atmospheric boundary layer, is well known to be critical in simulations and forecasts of hurricane intensity and structure (Braun and Tao 2000; Foster 2009; Smith and Thomsen 2010; Kepert 2012; Bao et al. 2012; Gopalakrishnan et al. 2013; Zhu et al. 2014; Zhang et al. 2015, 2017). As part of the Hurricane Forecast Improvement Project (HFIP), recent advances in the parameterization of vertical turbulent mixing (i.e., vertical eddy diffusivity) in the operational Hurricane Weather Research and Forecasting (HWRF) Model, based on aircraft observations reported by Zhang et al. (2011a) and Zhang and Drennan (2012), have led to significant improvements in intensity and track forecasts (Tallapragada et al. 2014). The abovementioned physics improvement in HWRF followed the developmental framework proposed by Zhang et al. (2012), which consisted of four components: model diagnostics, physics development, physics implementation, and further evaluation. Building on the success of this approach, here we adapt the same framework to improve the parameterization of horizontal turbulent mixing (i.e., horizontal diffusion) in HWRF.

Previous studies have demonstrated that horizontal diffusion is an important aspect of the model physics for hurricane simulations. Bryan and Rotunno (2009, hereafter BR09) used an axisymmetric numerical cloud model [Cloud Model 1 (CM1)] to point out that numerical simulations of hurricane maximum potential intensity (MPI) are sensitive to horizontal diffusion in terms of horizontal mixing length Lh. Bryan et al. (2010) confirmed the findings of BR09 by using the three-dimensional CM1 simulations. Bryan (2012) showed that the impact of Lh on MPI can be as significant as the ratio of the surface exchange coefficient that was emphasized in the MPI theory of Emanuel (1995). Rotunno and Bryan (2012, hereafter BR12) further investigated the effects of both vertical and horizontal diffusion on hurricane MPI and structure, offering interpretations of why horizontal diffusion is an important element of hurricane dynamics related to intensity.

Motivated by BR09 and RB12, Zhang and Marks (2015, hereafter ZM15) studied the effect of Lh on hurricane intensity change and structure in idealized 3D simulations using the HWRF Model. They presented a series of 5-day simulations within the context of operational forecasts, instead of simulations with longer periods (i.e., ≥12 days) as used by BR09 and RB12. Nonetheless, the results of ZM15 supported the conclusions of BR09 and RB12 that larger values of Lh were associated with smaller maximum intensity. These studies (i.e., BR09, RB12, and ZM15) all agreed that the main impact of larger Lh on the intensification of a hurricane is to smooth the radial gradient of angular momentum and equivalent potential temperature in the eyewall region. In the simulations with smaller Lh, both the radial inflow and radial gradient of angular momentum are larger than in simulations with larger Lh, which leads to a larger radial advection of the angular momentum and, in turn, more rapid hurricane intensity change, consistent with the spinup dynamics as discussed in Ooyama (1969), Smith et al. (2009), and Smith and Montgomery (2015). ZM15 also suggested that the extent of the sensitivity of maximum intensity and intensity change rate to Lh became smaller when the model horizontal resolution (i.e., grid spacing) was smaller than Lh.

Observational studies on the horizontal diffusion in hurricane conditions have been limited. Zhang and Montgomery (2012) presented the first observational analysis of horizontal momentum flux, horizontal eddy diffusivity, and Lh using flight-level data collected during four hurricanes (Allen, 1980; David, 1986; Hugo, 1989; and Frances, 2004) at an altitude of ~500 m. Their estimates of Lh were conducted within the framework of a simple K theory that assumed the stationarity and homogeneity of turbulent flow in the intense eyewall, while momentum was assumed to be transferred downgradient of the mean flow. On average, Zhang and Montgomery (2012) found that Lh is approximately 750 m in the hurricane eyewall. They also found that while there is a weak tendency for Lh to increase with the wind speed, this increase was not statistically significant. Note also that the optimal value of Lh recommended by Bryan et al. (2010) for hurricane model prediction is 1000 m, a result based on a large number of 3D CM1 simulations. This value of Lh is much closer to the observational estimate of Zhang and Montgomery (2012) than the value of Lh recommended by BR09 (1500 m) based on 2D simulations. The abovementioned theoretical, numerical, and observational studies provided guidance for improving Lh in the operational HWRF model.

As pointed out by ZM15, the value of Lh used in the 2015 version of the operational HWRF model (H215) was 1900 m, and Lh was >2000 m in earlier versions of HWRF because of the larger horizontal model resolution. Following the recommendation of ZM15 and real-case HWRF simulations presented in section 3, Lh was reduced in the 2016 version of the operational HWRF model (H216). The value of Lh used in H216 is 800 m, which is much closer to the observational estimate of Zhang and Montgomery (2012) and the value recommended by Bryan et al. (2010), than that used in H215. The present study documents the model upgrade process for the horizontal diffusion parameterization in HWRF and evaluates the impact of this improvement in Lh on HWRF’s ability to predict track, intensity, and structure using extensive retrospective forecasts. For the first time, the effects of Lh on hurricane intensity and structure are evaluated in real-case hurricane forecasts and simulations.

2. Horizontal diffusion parameterization in HWRF

The description of the horizontal diffusion parameterization in the HWRF Model given below parallels that given by ZM15. Details of other aspects of the HWRF Model physics can be found in Tallapragada et al. (2014) and Zhang et al. (2015). The horizontal diffusion scheme in HWRF is essentially the typical second-order nonlinear Smagorinsky-type parameterization as detailed by Janjić (1990). Horizontal eddy diffusivity Kh is used to parameterize the horizontal turbulent momentum flux1 Fh in the form of
e1
where Sh is the horizontal strain rate of the mean flow (e.g., Stevens et al. 1999), which has the form of
e2
where x and y are the distances in the longitudinal and latitudinal directions, respectively, and u and υ are the velocity components in the longitudinal and latitudinal directions, respectively. In addition, Kh is parameterized as a function of Lh and the horizontal deformation Dh in the form of
e3
where Dh has the form of
e4

In HWRF’s dynamical core (the so-called NMM) Kh is set to be proportional to the sum of the deformation and another term related to turbulent kinetic energy (TKE). Because the planetary boundary layer (PBL) parameterization scheme in HWRF is based on a K-profile method, which is not a TKE-type scheme, the term related to TKE is set to a very small value that is close to zero and is thus not shown in Eq. (3). Furthermore, Lh is tuned through a parameter “coac” in HWRF that was named as the Smagorinsky constant in Janjić (1990). Note that Lh is a function of both coac and horizontal spacing dx in HWRF in the form of Lh2 = coac dx, following Janjić (1990) and Janjić et al. (2010). Values of coac are set to be different for the three domains to reflect the dependence of Kh on model grid spacing.

Without TKE, the parameterization of Kh in HWRF was essentially the same as that used in the CM1 model as well as in NCAR’s Weather Research and Forecasting (WRF) Model (Janjić 2003), except that the method of tuning the Smagorinsky constant is slightly different. A similar horizontal diffusion parameterization was also used in the Tropical Cyclone Model version 4 (TCM4; Wang 2007). We also note that the equations used by Zhang and Montgomery (2012) for observational estimates of Kh and Lh follow the same concept of momentum-flux parameterization as those used in the abovementioned numerical models, except that there is no scale dependence in the Lh estimation in that study, because a constant cutoff frequency was used in their momentum flux calculation. Nonetheless, the observational data reported by Zhang and Montgomery (2012) would provide useful guidance for the range of values of Lh to be tuned in HWRF, being aware of the relatively large uncertainty (~50%) of Lh in their estimates. Developing a new horizontal diffusion parameterization using observational data including a TKE term would be ideal for a hurricane model that uses a TKE-type boundary layer scheme, but this is beyond the scope of the present study.

3. Case study on the sensitivity of Hurricane Earl (2010) forecasts to Lh

To confirm the findings of ZM15, we conducted a series of sensitivity experiments to simulate Hurricane Earl (2010). We chose the Earl case because excellent aircraft observations were gathered during this storm (e.g., Montgomery et al. 2014; Rogers et al. 2015) that provided the ground truth for evaluating the modeled hurricane structure. The same model configuration as in the idealized simulations of ZM15 was used in the Earl forecasts. The brief description of the model and numerical experiments below parallels that in ZM15. The HWRF model used here is triply nested, with the parent domain covering 50° × 50°, while the two inner nests cover ~15° × 15° and ~5° × 5°, respectively. The grid spacings of the three domains are 27, 9, and 3 km, respectively. Two-way interactions are configured for the inner two domains. The model has 61 hybrid vertical levels in total and more than 10 vertical levels below 850 hPa. Details of the model configuration and other aspects of the physics can be found in ZM15.

Five HWRF forecasts of Earl were run by varying Lh only while keeping other physics options the same. Hurricane Earl originated from a tropical wave off the west coast of Africa on 23 August 2010 and underwent rapid intensification between 28 and 30 August. The forecasts were initialized at 1800 UTC 26 August 2010. This cycle was chosen because of the excellent observational data available for model evaluation after the 24-h forecast. In the control simulation, Lh was set to 1900 m, which is the same as in H215. In the four other simulations, we set Lh to 375, 750, 1500, and 3000 m, respectively (referred to as L375, L750, L1500, and L3000 hereafter). The observational data used for model evaluation were collected by multiple research aircraft during Earl (Montgomery et al. 2014; Rogers et al. 2015). Doppler radar data were used to evaluate the vortex-scale structure. High-altitude dropsonde data from NASA’s DC-8 aircraft were used to verify the warm-core structure. Dropsonde data at low levels collected by both the NASA DC-8 and NOAA WP-3D aircraft were used to evaluate the boundary layer structure. Note that Chen and Gopalakrishnan (2015) and Smith et al. (2017) used the same observational dataset to verify their Earl forecast of the same cycle that was run using an earlier version of the HWRF model (H212).

The simulated track and intensity for these five Earl forecasts are shown in Fig. 1. There is not much difference in the track forecasts (Fig. 1a), while the intensity forecast in terms of both maximum 10-m wind speed (Fig. 1b) and minimum sea level pressure (Fig. 1b) shows strong sensitivity to Lh. Figure 1 indicates that smaller values of Lh are associated with stronger storms. Additionally, the maximum hurricane intensity of the 5-day forecast is found to increase with decreasing Lh (Fig. 2a). The mean 24-h intensity change of the 5-day forecast also increases with decreasing Lh (Fig. 2b). This result indicates that storms simulated with smaller Lh tended to intensify faster than those with larger Lh, supporting the results of ZM15 and BR09. It is evident from Figs. 1 and 2 that both the maximum intensity and the mean intensification rate in L750 better match the observed values from the National Hurricane Center’s (NHC) best-track data than those in the other experiments. This value of Lh is close to the observational estimates of Zhang and Montgomery (2012) and the numerical recommendation of Bryan et al. (2010), but is much smaller than that used in H215 (i.e., 1900 m). In the control experiment, where Lh as in H215 was used, both the maximum intensity and intensity change rate are underestimated compared to the best track. Below, we evaluate the simulated structure from these five experiments using observations.2

Fig. 1.
Fig. 1.

Plots of (a) storm track, (b) maximum 10-m wind speed as a function of forecast time, and (c) minimum sea level pressure as a function of forecast time from five sensitivity experiments of Hurricane Earl (2010) varying Lh. Each line color represents each experiment, and the experiment name contains the value of Lh (m) used in the experiment. The control experiment (CTL) used Lh = 1900 m.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

Fig. 2.
Fig. 2.

Plots of (a) the maximum intensity in terms of maximum surface wind speed and (b) the mean 24-h intensity change as a function of Lh for the 5-day forecasts of Hurricane Earl (2010) initialized at 1800 UTC 26 Aug 2010. The black dashed line represents observed values. Note that Lh = 1900 m was used in the control run.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

The observed radius–height structure of the azimuthal wind speed is compared to that averaged between 72 and 78 h in the five Earl forecasts (Fig. 3). During this period (1800 UTC 29 August–0000 UTC 30 August), a total of four aircraft [i.e., NOAA WP-3D and Gulfstream-IV (G-IV), U.S. Air Force C-130, and NASA DC-8] were flown into Earl simultaneously, collecting Doppler radar and dropsonde data with extensive coverage. Here, the quality-controlled Doppler radar data from the NOAA WP-3D aircraft are used to validate the vortex-scale structure in the Earl forecasts (Fig. 3a). The depth and strength of the hurricane vortex increase with decreasing Lh. For instance, the contour of 64 kt (~33 m s−1) extends to 12-km altitude and 130-km radius in L375 (Fig. 3c), while the same contour in L3000 only extends to 2-km altitude and 100-km radius (Fig. 3f). The maximum azimuthally averaged wind speeds for these two forecasts are 54 and 33 m s−1, respectively, differing by as much as 21 m s−1. The experiment with Lh = 750 m (Fig. 3d) has a contour of 64 kt (~33 m s−1) up to 10-km altitude and 150-km radius, which is close to that in the observed vortex. The Earl forecasts in L750 and L1500 match the observed wind structure in terms of both the maximum wind speed and the depth of the vortex, which is much better than that in other experiments. This result suggests the control experiment used too large a value of Lh to obtain the correct vortex structure.

Fig. 3.
Fig. 3.

Radius–height plots of the azimuthally averaged total wind speed over 72–78 h of the 5-day forecasts of Hurricane Earl (2010) initialized at 1800 UTC 26 Aug 2010, from (a) Doppler radar observations, (b) the control experiment (Lh = 1900 m), and the (c) L375, (d) L750, (e) L1500, and (f) L1500 experiments. The contour interval is 5 m s−1, and the black contour has the value of 64 kt (33 m s−1).

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

The storm size in terms of the radius of the maximum wind speed (RMW) in L375 and L750 is found to be closer to the radar-observed value than the other experiments (Fig. 4). It is also evident from Fig. 4 that the RMW averaged during the same period as in Fig. 3 increases with Lh. This result again supports ZM15. This increase in RMW is likely due to the weaker inflow in the boundary layer in simulations with larger Lh, as shown in Fig. 5, following the dynamical argument of Kilroy et al. (2016). Less horizontal diffusion yields stronger radial pressure gradients and stronger inflow in the boundary layer. With stronger inflow, air parcels travel closer to the storm center before being lifted in the eyewall region, favoring the contraction of the storm.

Fig. 4.
Fig. 4.

Plots of the 2-km RMW as a function of Lh averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). The blue crosses are from the HWRF forecasts. The solid line is an estimate of the parameters based on Doppler radar observations.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

Fig. 5.
Fig. 5.

Plots of the vertical mean profiles of (a),(b) Vt and (c),(d) Vr at the RMW from the Hurricane Earl (2010) forecasts averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). Comparisons at (left) the RMW and (right) 2 × RMW. The black solid and dashed lines, respectively, in each plot show the mean and 95% confidence interval of the wind profiles from dropsonde observations. Note that Lh = 1900 m was used in the control run.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

Vertical profiles of tangential Vt and radial Vr velocity averaged at the RMW and 2 × RMW are compared to averaged dropsonde3 data and are shown in Fig. 5 for the same period as in Fig. 3. It is evident from Fig. 5 that the simulated vertical Vt and Vr profiles from L750 and L1500 are mostly within the error bar (i.e., 95% confidence interval calculated based on raw sample statistics) of the observations, while those in the other forecasts, including the control experiment, are outside of the error bar. These two forecasts also better captured the observed peak values of Vt and Vr. In the control experiment, the vertical profile of Vt lies at the edge of the error bar in the eyewall region (i.e., RMW), but the values of Vt in the boundary layer at the outer radii (2 × RMW) are significantly lower than those in the dropsonde wind profiles, again implying that Lh used in H215 is too large.

The height of the maximum Vt and the inflow layer depth4 in L750 and L1500 are closer to the dropsonde observations than those in the other experiments (Fig. 5). This result is corroborated by Fig. 6, where the boundary layer heights are plotted as a function of Lh at the RMW. Both the height of the maximum Vt and the inflow layer depth are found to slowly increase with increasing Lh in the eyewall region for Lh < 2000 m, then increase much faster with Lh for larger Lh. Note that we also studied the thermodynamic mixed-layer depth that is taken as the height where the vertical gradient of the virtual potential temperature is higher than 3 K km−1 (Zeng et al. 2004; Zhang et al. 2011b) and found that the thermodynamic mixed-layer depth is generally independent of Lh (result not shown), in agreement with ZM15.

Fig. 6.
Fig. 6.

Plots of the boundary layer height as a function of Lh averaged between 72 and 78 h (1800 UTC 29 Aug–0000 UTC 30 Aug). The blue color represents the inflow layer depth at the RMW, the green color represents the inflow layer depth at 2 × RMW, and the red color represents the height of the maximum tangential wind speed. The solid lines are estimates of the parameters based on dropsonde observations. Note that Lh = 1900 m was used in the control run.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

ZM15 also evaluated the vertical structure of the hurricane vortex in terms of eyewall slope, which is computed by linearly fitting the RMW at each level between 2 and 8 km, following Stern and Nolan (2009). According to balanced dynamics, the eyewall slopes outward because of the warm core that is maximized in the middle and upper troposphere (Shapiro and Willoughby 1982). When the eyewall slope is larger, the wind speed tends to decay faster with height. Thus, the eyewall slope can be a useful structural metric for evaluating the model depiction of the TC warm core and the subsequent response of the wind field. Figure 7 shows that the slope of the RMW gets larger with larger Lh, which again supports the finding of ZM15. Figures 4 and 7 together indicate that the eyewall slope increases with the RMW as the RMW also increases with Lh, which agrees with the observations documented by Stern and Nolan (2009) and Stern et al. (2014). It is also evident from Fig. 7 that the eyewall slope simulated in L750 is closest to that estimated based on the Doppler radar data.

Fig. 7.
Fig. 7.

As in Fig. 4, but for the slope of the RMW as a function of Lh.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

With observations from the high-altitude NASA DC-8 aircraft, additional structures such as the warm-core anomaly can be evaluated. Following the same method as Stern and Nolan (2012), we calculated the warm-core anomaly as the difference between the mean potential temperature within the 15-km radius of the storm center and that in an annulus 200–300 km away from the storm center. Figure 8a compares the peak warm-core anomaly as a function of Lh with the observed warm-core anomaly obtained from high-altitude dropsonde data from the same period (1800 UTC 29 August–0000 UTC 30 August). A similar calculation of the warm-core anomaly using dropsonde data was documented by Durden (2013). It is evident from Fig. 8 that the peak warm-core anomaly, which is also correlated with storm intensity (cf. Fig. 1), decreases with Lh. The warm-core anomaly simulated in L750 and L1500 is found to be closer to the observed value than that in the other experiments.

Fig. 8.
Fig. 8.

As in Fig. 4, but for the (a) maximum warm-core anomaly and (b) height of the maximum warm-core anomaly as a function of Lh The solid line in each panel is an estimate of the parameters based on dropsonde observations.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

The warm-core height, defined as the height of the peak warm-core anomaly, is shown in Fig. 8b as a function of Lh. Here, the warm-core height slowly increases with Lh and is only weakly correlated with the storm intensity. This is consistent with Durden (2013) based on a large number of high-altitude dropsonde data in the eye and ambient regions of multiple hurricanes. For the warm-core height forecast, once again L750 and L1500 performed better than the other experiments.

As previous studies have suggested, vortex tilt is an important aspect of sheared storms (Jones 1995; Reasor et al. 2000), and we evaluated how vortex tilt may be linked to Lh. Here, the tilt is computed as the displacement of the circulation center between 1- and 8-km altitude, where the circulation center is defined as the location of minimum horizontal wind speed. Figure 9 shows that the vortex tilt increases with Lh. The observed tilt during the period of interest (1800 UTC 29 August–0000 UTC 30 August) was obtained from Doppler radar data. Once again, L750 and L1500 captured the tilt magnitude better than the other experiments. Previous theoretical and observational studies (Reasor et al. 2004; Reasor and Eastin 2012) have suggested that a stronger, deeper vortex tends to be more resilient against the environmental wind shear and from being tilted. Our results are consistent with this, as the hurricane vortex is much stronger and deeper in the Earl forecasts with smaller Lh than those in the Earl forecasts with larger Lh, as discussed earlier (cf. Fig. 3). This result thus suggests that as the vortex-scale structure is sensitive to Lh, the vortex response to environmental shear may also be sensitive to Lh. It would be of interest to understand the underlying dynamics for the tilt reduction when Lh is small, which may be related to vortex Rossby waves and deep convection. However, this topic is beyond the scope of the present study.

Fig. 9.
Fig. 9.

As in Fig. 4, but for the vortex tilt as a function of Lh.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

4. Verification of retrospective HWRF forecasts of multiple storms

The sensitivity experiments for Hurricane Earl shown above and the idealized simulations of ZM15 suggest that the Lh used in the operational H215 was too large and should be reduced to values between 750 and 1500 m. During the model upgrade in 2016, Lh was lowered from 1900 to 800 m by tuning the coac parameter in HWRF. The value of Lh (800 m) used is close to the median value of the observationally estimated Lh reported by Zhang and Montgomery (2012) and is also consistent with the recommendations of Bryan et al. (2010) based on extensive CM1 simulations and comparisons of the modeled MPI and storm structure to climatology and observational composites.

To further evaluate the impact of the modification of Lh in H216, we ran two sets of retrospective forecasts: one using the operational H216 HWRF in which Lh was set to 800 m (referred to as HOAC hereafter) and the other using H216 but with Lh set to 1900 m (i.e., the value as in H215, referred to as COAC hereafter) for 10 Atlantic tropical cyclones. These included all eight storms in the 2014 season (Arthur, Bertha, Cristobal, Dolly, Edouard, Fay, Gonzalo, and Hanna) and two storms in the 2016 season (Earl and Matthew). Note that the data assimilation system was turned on in these retrospective forecasts in a similar manner as previous studies on model physics upgrades, such as in the European Centre for Medium-Range Weather Forecasts model (Rodwell and Palmer 2007; Rodwell and Jung 2008; Klocke and Rodwell 2014), and the WRF Model (Cavallo et al. 2016). Data assimilated into HWRF included observations from radiosondes, aircraft, surface ships and buoys, surface land stations, pilot balloons, wind profilers, scatterometers, aircraft-released dropsondes, satellites recording radiances and winds, and the tail Doppler radar on the NOAA WP-3D (Tallapragada et al. 2014).

To verify the retrospective forecasts, the postprocessed best-track data from NHC were used. These data and the HWRF-generated track outputs are shown in Fig. 10a, which shows the mean track forecast errors for HOAC and COAC for the retrospective forecasts. There is a small improvement in the track forecast for HOAC compared to COAC at a lead time of 36–48 h, although this improvement is not statistically significant at the 95% confidence interval. This small improvement in the track forecast appears in both the along-track (Fig. 10b) and cross-track (Fig. 10c) error verifications during the 36–48-h forecast period. During other periods of the forecast, the performance levels of the along-track and cross-track forecasts are reversed. This result basically suggests that lowering Lh in HWRF did not degrade the hurricane track forecast. Of note, we found that the improvement in the track error by reducing Lh in HWRF is much larger for strong storms than weak storms (not shown).

Fig. 10.
Fig. 10.

Plots of the (a) absolute track error, (b) along-track error, and (c) cross-track error in HWRF retrospective forecasts with two different setups for the parameterization of horizontal diffusion in terms of Lh. In the control experiment (referred to as HOAC), Lh = 800 m as in H216, while the other experiment (COAC) used Lh =1900 m and the same coac value as in H215 but with the H216 model. The error bar represents the 95% confidence interval. FY16 means year 2016 in the legend.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

The mean intensity (VMAX) errors for HOAC and COAC for the retrospective forecasts are shown in Fig. 11, where the error bar represents the 95% confidence interval. It is evident from Fig. 11 that substantial improvements in the intensity error were made when we lowered Lh in the HWRF Model. The overall improvement is 10%–15% for HOAC compared to COAC for almost all of the verification times. Although statistical analysis (t test) showed that the improvement is not statistically significant at the 95% confidence level, this result suggests that lowering Lh in HWRF has a positive impact on the intensity forecasts. Note that this improvement is statistically significant at the 80% confidence interval for lead times of 6–30, 40–60, and 84–120 h.

Fig. 11.
Fig. 11.

As in Fig. 10, but for the absolute error for intensity.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

An alternative way to measure the forecast impact is to examine the frequency of superior performance (FSP), which is a measure (in percent) of how frequently one model yields a better forecast than another. The FSP for the intensity forecasts from HOAC and COAC are compared to the 2014 operational version of the HWRF model (H214) in Fig. 12. The improvement in the intensity forecasts of HOAC compared to COAC is consistent throughout the 120-h forecast period except at 72-h lead time. Figure 12 also indicates that both HOAC and COAC performed much better in terms of intensity forecast compared to H214. The 10%–15% improvement in the intensity forecasts of HOAC compared to COAC is also clearly shown in Fig. 12.

Fig. 12.
Fig. 12.

As in Fig .10, but for the FSP for intensity error relative to the 2014 version of HWRF.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

In addition to the intensity error improvement due to the modification of Lh, the bias in intensity is largely improved in HOAC compared to COAC (Fig. 13). The low bias in the intensity forecast of ~8 kt (after a 12-h lead time; 1 kt = 0.51 m s−1) was reduced to ~3 kt from COAC to HOAC because of the modification of Lh only. This improvement in the hurricane intensity bias forecast is statistically significant at the 95% confidence interval, which is quite encouraging. Our previous work on improving the vertical eddy diffusivity based on aircraft observations (Zhang et al. 2015) also led to improvement in the intensity bias forecast, but the change was not as large as the improvement caused by improving Lh shown here.

Fig. 13.
Fig. 13.

As in Fig. 10, but for the biases in intensity.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

Using NHC data, we also validated the storm size forecasts for COAC versus HOAC. A statistically significant improvement was found in the RMW forecast in HOAC compared to COAC (Fig. 14). The high bias in the RMW forecast of HWRF was reduced by 6 n mi (~10 km) on average (Fig. 14). There is only a small improvement in the forecast of other outer storm size metrics, such as 64- and 34-kt radii, while the improvement is not statistically significant (result not shown). Of note, there is still a relatively large positive bias in the RMW in H216, even after the improvement in Lh (Fig. 14), which is consistent with the continued weak bias. This result suggests that other physics may be required to further reduce the storm size bias in HWRF.

Fig. 14.
Fig. 14.

As in Fig .10, but for the bias in the RMW.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0097.1

5. Conclusions and discussion

This study documents the process of upgrading the horizontal diffusion parameterization in HWRF. Idealized numerical experiments were first conducted to understand the effects of horizontal diffusion on hurricane intensification and the associated dynamics in HWRF in an earlier study (ZM15). We then conducted a real-case study with HWRF using the same setup as in the idealized experiments to verify the findings from the idealized study. In the sensitivity experiments of real-case HWRF forecasts (Hurricane Earl), we compared the modeled hurricane structure to extensive aircraft observations using structural metrics developed in our previous model evaluation studies (i.e., Zhang et al. 2015). Results from the Earl forecasts confirmed that storm intensity decreases with Lh in agreement with the results reported by BR09 and ZM15. In addition, storm structural characteristics including storm size in terms of RMW, kinematic boundary layer heights, warm-core height and temperature anomaly, and eyewall slope are found to be sensitive to Lh. Comparisons between the modeled and observed structures suggest that the experiments with Lh = 750–1500 m performed better than the control experiment. These values of Lh are much smaller than that used in H215, but they are closer to the observational estimates of Zhang and Montgomery (2012) and the numerical estimates of Bryan et al. (2010). Based on the results of our sensitivity experiments of both idealized and real-case simulations, as well as the previous studies on horizontal diffusion mentioned above, a decision was made to reduce Lh to 800 m in H216.

We then further evaluated the impact of the reduced Lh on track, intensity, and structure forecasts using extensive retrospective forecasts from over 200 cases for 10 Atlantic tropical cyclones. To identify the impact of the improvement in Lh and optimize the model initial conditions, the HWRF data assimilation system was turned on during the retrospective experiments following previous studies of model physics improvement of other forecast models (e.g., Rodwell and Jung 2008; Klocke and Rodwell 2014; Cavallo et al. 2016). Our results show that lowering Lh in HWRF significantly reduced the bias in intensity forecasts. The improvement in the mean intensity error is 10%–15% for almost all lead time for the 5-day forecasts by reducing Lh, and this improvement is statistically significant at 80% for lead times of 6–30, 40–60, and 84–120 h. The track forecast is only slightly improved and the improvement is not statistically significant. Small improvements in both along- and cross-track errors are found at lead times of 24–36-h forecasts. The storm size forecast is found to be significantly improved in H216 using the modified Lh, with the bias in RMW reduced by 6 n mi (~10 km) on average. We also note that the RMW in HWRF is still much larger than the observations based on the best track, indicating further improvement in HWRF’s model physics beyond horizontal diffusion is required.

Our results suggest that the impact of lowering Lh in HWRF is independent of the version of the HWRF used here, as sensitivity experiments using both H215 and H216 showed similar positive impacts on intensity and structure forecasts, when Lh was lowered to values close to previous observational and numerical estimates. Besides the improvement in the vertical eddy diffusivity in HWRF using aircraft data as documented by Zhang et al. (2015), the present study further emphasizes the important role of aircraft observations in model diagnostics and improvement. We demonstrate the utility of the developmental framework as proposed by Zhang et al. (2012) to improve TC model physics. This framework illustrates a process for identifying model deficiencies through a comparison with observations, new model physics development and implementation, and additional validation of the new physics. Here, we show the usefulness of this framework to improve the horizontal diffusion parameterization in the operational HWRF. It should be invaluable for evaluating and advancing other aspects of the model physics beyond horizontal diffusion in the future.

In the end, it is worthwhile to note that the current parameterization of horizontal diffusion in HWRF is far from perfect, given the limited knowledge of Lh and the uncertainty in the tuning method used here. As mentioned earlier, the observation-based estimate of Lh given by Zhang and Montgomery (2012) did not take into account the model resolution associated with subgrid-scale turbulent parameterization in the numerical models. Note also that the value of Lh recommended by Bryan et al. (2010) was based on a different numerical model from HWRF, which utilized different model resolution and physics configurations. This study is only a first attempt to improve the parameterization of subgrid turbulent mixing in NWP models like HWRF, while further proving the importance of horizontal-diffusion parameterization in NWP models for real-case hurricane forecasts. Future work is aimed at developing a new parameterization of Lh that includes the scale-aware feature. Including a TKE component into the horizontal-diffusion parameterization is also recommended, which will benefit a hurricane model that utilizes a TKE-type PBL scheme. Given the limited number of turbulence observations in hurricanes, a field program especially designed for low-level hurricane measurements, likely with unmanned aircraft, is desirable for further calibration of the turbulent parameterizations in hurricane models.

Acknowledgments

This work was mainly supported by NOAA’s Hurricane Forecast Improvement Project (HFIP) with Grant NA14NWS4680028. JZ was also supported by NSF Grant AGS1249732, NOAA Grant NA14NWS4680030, and NASA Grant NNX14AM69G. We thank the HWRF team from EMC and HRD, and the code management team from DTC, for their efforts to improve the model and make it available for the research community. We are grateful to John Kaplan for his comments on an early version of the paper. We also thank Ms. Gail Derr for offering editorial support. We thank Prof. Roger Smith and two anonymous reviewers for their comments that led to a substantial improvement of our paper.

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1

Note that the horizontal eddy diffusivities for heat Kt and moisture Kq are set to be the same as that for momentum (i.e., Kt = Kq = Kh).

2

Note that the remainder of this section describes structural sensitivity that has a basic agreement with stronger storms. For example, stronger storms have smaller RMW values, less tilt, a stronger warm-core anomaly, and less eyewall slope.

3

Dropsondes located within 5 km from the RMW are used for comparison. Nine and 12 dropsondes are averaged at the RMW and 2 × RMW, respectively.

4

The inflow-layer depth is taken as the height of 10% of the maximum inflow strength (Zhang et al. 2011b).

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