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Evaluating the Impact of Improvement in the Horizontal Diffusion FEBRUARY 2018 Z H A N G E T A L . 317 Evaluating the Impact of Improvement in the Horizontal Diffusion Parameterization on Hurricane Prediction in the Operational Hurricane Weather Research and Forecast (HWRF) Model JUN A. ZHANG NOAA/AOML/Hurricane Research Division, and University of Miami/Cooperative Institute for Marine and Atmospheric Studies, Miami, Florida FRANK D. MARKS,JASON A. SIPPEL, AND ROBERT F. ROGERS NOAA/AOML/Hurricane Research Division, Miami, Florida XUEJIN ZHANG NOAA/AOML/Hurricane Research Division, and University of Miami/Cooperative Institute for Marine and Atmospheric Studies, Miami, Florida SUNDARARAMAN G. GOPALAKRISHNAN NOAA/AOML/Hurricane Research Division, Miami, Florida ZHAN ZHANG AND VIJAY TALLAPRAGADA NOAA/NCEP/Environmental Modeling Center, College Park, Maryland (Manuscript received 11 July 2017, in final form 21 December 2017) 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 wasmodifiedbasedonaircraft 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. 1. Introduction parameterizations of subgrid-scale physical processes such as turbulent mixing becomes more important for As the horizontal resolution of operational hur- hurricane prediction. Turbulent mixing in the vertical ricane models becomes smaller, improving physical direction, especially in the atmospheric boundary layer, is well known to be critical in simulations and forecasts Denotes content that is immediately available upon publica- of hurricane intensity and structure (Braun and Tao tion as open access. 2000; Foster 2009; Smith and Thomsen 2010; Kepert 2012; Bao et al. 2012; Gopalakrishnan et al. 2013; Corresponding author: Dr. Jun Zhang, [email protected] Zhu et al. 2014; Zhang et al. 2015, 2017). As part of the DOI: 10.1175/WAF-D-17-0097.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 318 WEATHER AND FORECASTING VOLUME 33 Hurricane Forecast Improvement Project (HFIP), re- which leads to a larger radial advection of the angular cent advances in the parameterization of vertical tur- momentum and, in turn, more rapid hurricane intensity bulent mixing (i.e., vertical eddy diffusivity) in the change, consistent with the spinup dynamics as discussed operational Hurricane Weather Research and Fore- in Ooyama (1969), Smith et al. (2009), and Smith and casting (HWRF) Model, based on aircraft observations Montgomery (2015). ZM15 also suggested that the ex- reported by Zhang et al. (2011a) and Zhang and tent of the sensitivity of maximum intensity and in- Drennan (2012), have led to significant improvements in tensity change rate to Lh became smaller when the intensity and track forecasts (Tallapragada et al. 2014). model horizontal resolution (i.e., grid spacing) was The abovementioned physics improvement in HWRF smaller than Lh. followed the developmental framework proposed by Observational studies on the horizontal diffusion in Zhang et al. (2012), which consisted of four components: hurricane conditions have been limited. Zhang and model diagnostics, physics development, physics im- Montgomery (2012) presented the first observational plementation, and further evaluation. Building on the analysis of horizontal momentum flux, horizontal eddy success of this approach, here we adapt the same diffusivity, and Lh using flight-level data collected during framework to improve the parameterization of hori- four hurricanes (Allen, 1980; David, 1986; Hugo, 1989; zontal turbulent mixing (i.e., horizontal diffusion) and Frances, 2004) at an altitude of ;500 m. Their esti- in HWRF. mates of Lh were conducted within the framework of a Previous studies have demonstrated that horizontal simple K theory that assumed the stationarity and ho- diffusion is an important aspect of the model physics mogeneity of turbulent flow in the intense eyewall, while for hurricane simulations. Bryan and Rotunno (2009, momentum was assumed to be transferred downgradient hereafter BR09) used an axisymmetric numerical cloud of the mean flow. On average, Zhang and Montgomery model [Cloud Model 1 (CM1)] to point out that nu- (2012) found that Lh is approximately 750 m in the hur- merical simulations of hurricane maximum potential ricane eyewall. They also found that while there is a weak intensity (MPI) are sensitive to horizontal diffusion in tendency for Lh to increase with the wind speed, this in- terms of horizontal mixing length Lh. Bryan et al. crease was not statistically significant. Note also that the (2010) confirmed the findings of BR09 by using the optimal value of Lh recommended by Bryan et al. (2010) three-dimensional CM1 simulations. Bryan (2012) for hurricane model prediction is 1000 m, a result based showed that the impact of Lh on MPI can be as signif- on a large number of 3D CM1 simulations. This value of icant as the ratio of the surface exchange coefficient Lh is much closer to the observational estimate of Zhang that was emphasized in the MPI theory of Emanuel and Montgomery (2012) than the value of Lh recom- (1995). Rotunno and Bryan (2012, hereafter BR12) mended by BR09 (1500 m) based on 2D simulations. The further investigated the effects of both vertical and abovementioned theoretical, numerical, and observa- horizontal diffusion on hurricane MPI and structure, tional studies provided guidance for improving Lh in the offering interpretations of why horizontal diffusion is operational HWRF model. an important element of hurricane dynamics related to As pointed out by ZM15, the value of Lh used in the intensity. 2015 version of the operational HWRF model (H215) Motivated by BR09 and RB12, Zhang and Marks was 1900 m, and Lh was .2000 m in earlier versions of (2015, hereafter ZM15) studied the effect of Lh on HWRF because of the larger horizontal model resolu- hurricane intensity change and structure in idealized 3D tion. Following the recommendation of ZM15 and real- simulations using the HWRF Model. They presented a case HWRF simulations presented in section 3, Lh was series of 5-day simulations within the context of opera- reduced in the 2016 version of the operational HWRF tional forecasts, instead of simulations with longer pe- model (H216). The value of Lh used in H216 is 800 m, riods (i.e., $12 days) as used by BR09 and RB12. which is much closer to the observational estimate of Nonetheless, the results of ZM15 supported the con- Zhang and Montgomery (2012) and the value recom- clusions of BR09 and RB12 that larger values of Lh were mended by Bryan et al. (2010), than that used in H215. associated with smaller maximum intensity. These The present study documents the model upgrade pro- studies (i.e., BR09, RB12, and ZM15) all agreed that the cess for the horizontal diffusion parameterization in main impact of larger Lh on the intensification of a HWRF and evaluates the impact of this improvement in hurricane is to smooth the radial gradient of angular Lh on HWRF’s ability to predict track, intensity, and momentum and equivalent potential temperature in the structure using extensive retrospective forecasts. For the eyewall region. In the simulations with smaller Lh, both first time, the effects of Lh on hurricane intensity and the radial inflow and radial gradient of angular mo- structure are evaluated in real-case hurricane forecasts mentum are larger than in simulations with larger Lh, and simulations. FEBRUARY 2018 Z H A N G E T A L . 319 2. Horizontal diffusion parameterization in HWRF domains to reflect the dependence of Kh on model grid spacing. The description of the horizontal diffusion parame- Without TKE, the parameterization of K in HWRF terization in the HWRF Model given below parallels h was essentially the same as that used in the CM1 model that given by ZM15. Details of other aspects of the as well as in NCAR’s Weather Research and Fore- HWRF Model physics can be found in Tallapragada casting (WRF) Model (Janjic´ 2003), except that the et al. (2014) and Zhang et al. (2015). The horizontal method of tuning the Smagorinsky constant is slightly diffusion scheme in HWRF is essentially the typical different. A similar horizontal diffusion parameteriza- second-order nonlinear Smagorinsky-type parameteri- tion was also used in the Tropical Cyclone Model ver- zation as detailed by Janjic´ (1990). Horizontal eddy sion 4 (TCM4; Wang 2007). We also note that the diffusivity Kh is used to parameterize the horizontal 1 equations used by Zhang and Montgomery (2012) for turbulent momentum flux Fh in the form of observational estimates of Kh and Lh follow the same concept of momentum-flux parameterization as those F 5 rK S , (1) h h h used in the abovementioned numerical models, except that there is no scale dependence in the L estimation in where S is the horizontal strain rate of the mean flow h h that study, because a constant cutoff frequency was used (e.g., Stevens et al.
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