Evaluation of Multiple Dynamic Initialization Schemes for Tropical Cyclone Prediction

4028 MONTHLY WEATHER REVIEW VOLUME 141

ERIC A. HENDRICKS AND MELINDA S. PENG Marine Meteorology Division, Naval Research Laboratory, Monterey, California

TIM LI University of Hawai’i at Manoa, and International Paciﬁc Research Center, Honolulu, Hawaii

(Manuscript received 15 November 2012, in ﬁnal form 24 April 2013)

ABSTRACT

Three different dynamic initialization schemes for tropical cyclone (TC) prediction in numerical prediction systems are described and evaluated. The first scheme involves the removal of the analyzed vortex, followed by the insertion of a dynamically initialized vortex into the model analyses. This scheme is referred to as the tropical cyclone dynamic initialization scheme (TCDI) because the TC component is nudged to the observed surface pressure in an independent three-dimensional primitive equation model prior to insertion. The second scheme is a 12-h relaxation to the analyses’ horizontal momentum before the forecast integration begins, and is called the dynamic initialization (DI) scheme. The third scheme is a combination of the previous two schemes, and is called the two-stage dynamic initialization scheme (TCDI/DI). In the first stage, TCDI is implemented in order to improve the representation of the TC vortex. In the second stage, DI is invoked in order to improve the balance between the inserted TC vortex and its environment. All three dynamic initialization schemes are compared with a control (CNTL) scheme, which creates the initial vortex using synthetic TC observations that match the observed intensity and structure in a three-dimensional variational data assimilation (3DVAR) system. The four schemes are tested on 120 cases in the North Atlantic and western North Pacific basins during 2010 and 2011 using the Naval Research Laboratory’s TC prediction model: Coupled Ocean–Atmosphere Mesoscale Prediction System-Tropical Cyclones (COAMPS-TC). It is demonstrated that TCDI/DI performed the best overall with regard to intensity forecasts, reducing the average minimum central pressure error for all lead times by 24.4% compared to the CNTL scheme.

1. Introduction Atlantic provide in situ measurements as well when a storm is closer to the coast. A TC prediction model which A critical challenge of predicting tropical cyclones runs in real time needs to have the intensity and position of (TCs) with numerical models is providing the model an the vortex as close to the official estimates as possible in accurate and balanced set of initial conditions. The ac- the initial conditions, but would not necessarily have all curacy depends on the density and quality of the ob- structural details due to the paucity of observations. With servations of the TC, while the balance consists of both regard to the balance, it is critical to initialize the TC vortex dynamical and thermodynamic balances. Since most TCs in proper balance so that rapid adjustments do not occur in exist over open oceans with few observations (especially in the early stages of the integration, during which the vortex the inner core), often the main source of information deviates significantly from its initial conditions, and gen- comes from estimates of the maximum sustained surface erates spurious gravity waves. wind and minimum central pressure issued by operational Broadly speaking, there are three main methods of warning centers [e.g., the National Hurricane Center initializing TCs in numerical prediction systems. In the (NHC) or Joint Typhoon Warning Center (JTWC)]. The first method, an analytically or empirically constructed intensity is often inferred from satellite imagery; however, vortex is inserted into the model analyses, after the routine aircraft reconnaissance missions in the North existing vortex is removed, which may be at the wrong intensity or location (Holland 1980; Mathur 1991; Leslie Corresponding author address: Eric A. Hendricks, Naval Re- and Holland 1995; Davidson and Weber 2000; Kwon and search Laboratory, Monterey, CA 93943. Cheong 2010). The inserted vortex is designed to match E-mail: [email protected] the intensity and structure estimates from the warning

DOI: 10.1175/MWR-D-12-00329.1

Ó 2013 American Meteorological Society NOVEMBER 2013 H E N D R I C K S E T A L . 4029 centers. The second method is to construct the initial observed surface pressure. This vortex is then inserted vortex using a variational data assimilation system with into the forecast model initial conditions after three- synthetic observations, often called the bogus data as- dimensional variational data assimilation (3DVAR) and similation method (Goerss and Jeffries 1994; Serrano the removal of the existing TC vortex. The second scheme and Unden 1994; Zou and Xiao 2000; Pu and Braun is a forward dynamic initialization scheme where the 2001; Xiao et al. 2006; Wu et al. 2006; Liou and Sashegyi forecast model is integrated to reach a balance between 2011). The third method is dynamic initialization, where the TC vortex and the environment. In the DI scheme, the TC vortex (and perhaps the forecast model) is ini- the forecast model is integrated with full-physics pro- tialized using Newtonian relaxation to some prescribed cesses for a period of 12 h and relaxed to the analyses state (Hoke and Anthes 1976, 1977; Fiorino and Warner horizontal momentum. The third scheme combines the 1981; Krishnamurti et al. 1988; Kurihara et al. 1993; TCDI and DI schemes, and is called a two-stage scheme Davidson and Puri 1992; Bender et al. 1993; Peng et al. since it involves two separate stages of dynamic initial- 1993; Peng and Chang 1996, 1997; Hendricks et al. 2011; ization: the TC component first, followed by the forecast Nguyen and Chen 2011; Zhang et al. 2012; Cha and model. Each dynamic initialization scheme is evalu- Wang 2013). Dynamic initialization (DI) methods have ated in comparison to a control scheme (CNTL), which two primary benefits. First, imbalances can be removed constructs the initial conditions using a 3DVAR scheme through model integration with the addition of relax- with synthetic TC observations. The evaluation is based on ation terms, improving both the spinup of the vortex and a large sample of TCs in the North Atlantic and western the initial balance so that rapid adjustments do not occur North Pacific basins during 2010–11 (120 cases at the initial in the early part of the forecast. Second, they allow for lead time). The outline of the rest of the paper is as follows. model physics spinup (including the boundary layer and In section 2, the mesoscale numerical prediction model microphysics), which should lead to improved forecasts. used for testing is described. In section 3, the four initiali- There are multiple ways dynamic initialization schemes zation schemes are described. In section 4, a structure can be implemented, encompassing both the TC vortex evaluation is presented for the different initialization and the forecast model. Kurihara et al. (1993) demon- schemes for three cases, representing weak to strong strated the benefits of a TC dynamic initialization TCs. Analysis of average intensity and track errors for scheme using an axisymmetric version of the forecast the entire sample of cases is given in section 5. Further model for spinup to the desired structure and intensity. structural, track, and intensity forecast analyses of Hendricks et al. (2011) further demonstrated the utility TCDI/DI in comparison to the CNTL scheme are given of the TC dynamic initialization scheme using an in- in section 6. The conclusions are given in section 7. dependent three-dimensional primitive equation model for vortex spinup. However, there are weaknesses in 2. Mesoscale TC prediction model both schemes because inconsistencies between the forecast model environment and the inserted vortex can The mesoscale model used here is the Coupled manifest themselves in spurious gravity wave activity Ocean–Atmosphere Mesoscale Prediction System- after the forecast integration begins. Recently, Cha and Tropical Cyclones (COAMPS-TC). COAMPS-TC is a Wang (2013) and Nguyen and Chen (2011) have de- special version of COAMPS,1 which is the navy’s op- veloped DI schemes that are designed to improve upon erational mesoscale prediction system. A description this issue. In their studies, the TC vortex is spun up using of the COAMPS model is provided by Hodur (1997) and short cycle runs of the forecast model starting prior to more details can also be found in Chen et al. (2003). The the initial time, rather than being spun up offline and model uses a terrain-following sigma-height coordinate inserted. A positive impact on TC track and intensity and the nonhydrostatic compressible equations of motion performance was found. Recently, there has been re- (Klemp and Wilhelmson 1978). The microphysics scheme newed interest in using dynamic initialization schemes is based on Rutledge and Hobbs (1983), with prognostic with high-resolution regional TC prediction models. equations for mixing ratios of cloud droplets, ice particles, In this paper, three different dynamic initialization rain, snow, graupel, and drizzle. The model also includes a schemes that can be applied to a numerical weather short- and longwave radiation scheme (Harshvardhan prediction model are described and evaluated. The first et al. 1987), and a planetary boundary layer scheme with a scheme is a tropical cyclone dynamic initialization 1.5-order turbulence closure (Mellor and Yamada 1982). (TCDI) scheme (Hendricks et al. 2011) that constructs a balanced vortex based upon the officially estimated TC intensity. Here, a tropical cyclone vortex is spun up 1 COAMPS is a registered trademark of the Naval Research in an environment with no mean flow, and relaxed to the Laboratory. 4030 MONTHLY WEATHER REVIEW VOLUME 141

FIG. 1. COAMPS-TC grid setup in the North Atlantic basin. The inner two meshes (15- and 5-km horizontal resolutions, respectively) move with the TC.

The tropical cyclone prediction version of COAMPS- of the same storm then use the previous COAMPS-TC TC includes the following enhancements: (i) synthetic forecast as the first guess, identified here as warm starts. wind and mass observations of the TC based on the of- The lateral boundary conditions for the 45-km hori- ficial warning message, (ii) relocation of the first-guess zontal resolution outer mesh are also obtained from the field to the observed TC position, (iii) TC-following GFS forecast data. In either case, a 3DVAR system (the nested inner grids using an automatic TC tracker, (iv) Naval Research Laboratory Atmospheric Variational dissipative heating (Jin et al. 2007), and (v) a sur- Data Assimilation System, NAVDAS; Daley and Barker 2 face drag coefficient that approaches 2.5 3 10 3 for 2001) is used to optimally blend the observations with the 2 wind speeds exceeding 35 m s 1 (Donelan et al. 2004). first guess, creating the analysis. For the data assimilation, COAMPS-TC has been tested in real-time runs and an update cycle of 6 h was used. used to support several field experiments (Doyle et al. 2011). The forecast system also has a capability for 3. Initialization schemes ocean coupling; however, for this study the model was run in stand-alone atmosphere mode. Four different initialization schemes are described in For the experiments conducted here, three nested grids this section: the control initialization, which uses the were used, with horizontal resolutions of 45, 15, and 5 km, 3DVAR system with TC synthetic observations (CNTL), respectively. The 15- and 5-km grids automatically move the TC dynamic initialization scheme (TCDI), a dy- following the TC circulation with two-way interactive namic initialization for the forecast model (DI), and nesting, while the outer 45-km grid was held fixed. The a two-stage dynamic initialization scheme which is a setup of all three domains for COAMPS-TC in the North combination of TCDI and DI (TCDI/DI). While dynamic Atlantic basin is shown in Fig. 1. The model was run with initialization is typically used to describe a combination 40 sigma levels in the vertical with a top at 31 km. While of backward and forward integrations in order to remove the microphysics scheme was used for all three nests, the the unbalanced components (e.g., Ghil et al. 1982; Daley Kain–Fritsch cumulus scheme was activated in the 45- and 1991; Peng and Chang 1996), all three dynamic initiali- 15-km domains to help resolve subgrid-scale convection. zations used here (TCDI, DI, and TCDI/DI) only involve For the first forecast of a TC, the global analysis from forward model integrations. A schematic of how these the National Centers for Environmental Prediction schemes can be applied to a numerical prediction model (NCEP) Global Forecast System (GFS) is used as the is given in Fig. 2, and more details of each scheme are first guess, defined here as a cold start. Subsequent runs given below. NOVEMBER 2013 H E N D R I C K S E T A L . 4031

FIG. 2. Flowchart depicting the application of all four initialization schemes (CNTL, TCDI, DI, and TCDI/DI) to a numerical TC prediction model. a. Control initialization scheme: CNTL analysis, retaining components of the large-scale flow. Within 38 of the vortex center, the environmental wind is In the control initialization method, the construction adjusted in order to match the motion as given by the of the TC structure and intensity is implemented in the operational warning center. Finally, the 3DVAR system data assimilation using synthetic observations based on is used to optimally blend the TC synthetic observations the official TC warning message. On warm starts, first and all the other observations [including conventional the first-guess vortex is removed from the environment and aircraft observations, geostationary satellite winds, and relocated to the observed TC location, using the Special Sensor Microwave Imager (SSM/I) wind speeds, methods of Kurihara et al. (1995). Next, a vortex is total precipitable water retrievals, passive-microwave- constructed with a modified Rankine wind profile that derived surface marine winds, and satellite temperature fits the observed TC intensity and size parameters of the retrievals] with the first guess to obtain the initial fields maximum wind, and the radii of 34- and 50-kt (1 kt 5 2 of the model. In the 3DVAR system, the geostrophic 0.5144 m s 1) winds. From these parameters, the radius balance constraint is relaxed in the tropics to help pro- of maximum wind and modified Rankine vortex decay duce a more gradient-balanced vortex. More details on parameter are uniquely determined (Liou and Sashegyi the control initialization procedure can be found in Liou 2011). Next, the geopotential and temperature field is and Sashegyi (2011). Note that the CNTL scheme is used determined by enforcing gradient and hydrostatic bal- in the current real-time version of COAMPS-TC. ance constraints on the winds. Zonal and meridional velocity, geopotential height, and temperature synthetic b. TC dynamic initialization scheme: TCDI observations are then created at eight azimuthal TCDI (Hendricks et al. 2011) involves the removal of segments, and at radii of 0.58,18,28,48, and 68.2 The the analyzed vortex from the initial field after the synthetic observations are constructed at the vertical 3DVAR data assimilation, followed by the insertion of levels of 1000, 965, 925, 850, 775, 700, 600, 500, and a new vortex, which is dynamically initialized to the 400 hPa, with prescribed vertical decay factors of 1.000, observed surface pressure. The purpose of using TCDI 0.996, 0.992, 0.983, 0.970, 0.950, 0.920, 0.870, and 0.720, after 3DVAR is to improve the TC initial dynamic and respectively. Then, the environmental flow is added thermodynamic balances. This is necessary because the to the synthetic observations. The environmental flow 3DVAR system used (NAVDAS) has a geostrophic is obtained from the spectrally truncated global wind balance constraint rather than a gradient balance constraint. Note that it is possible to improve the mass–wind balance in areas of high curvature by the inclusion of the 2 2 For TCs with a maximum sustained wind ,23 m s 1, the 68 cyclostrophic term in 3DVAR systems (Barker et al. synthetic observations are not included. 2004). The removal of the analyzed vortex is done by 4032 MONTHLY WEATHER REVIEW VOLUME 141 using a Tukey window spatial low-pass filter. The filter The TCDI scheme operates through using a vortex cutoff wavelength was set to 5 3 105 m for zonal and library of varying intensities. The vortex library is built meridional velocity fields and to 3 3 105 m for the consisting of vortices with central pressures ranging temperature, geopotential height, and moisture fields. from 1010 to 910 hPa at 1-hPa increments. The vortex Note that while the TCDI scheme here is invoked after that most closely matches the observed intensity esti- 3DVAR, it may also be invoked before 3DVAR to mate is chosen for the real TC forecast. While variances improve the TC representation in the first guess prior in size have not been explicitly built into this vortex to data assimilation (Zhang et al. 2012). library yet, a comparison of the wind–pressure rela- For the specific experiments performed here, we use tionship of the vortex library versus the empirical wind– the three-dimensional Tropical Cyclone Model (TCM3; pressure relationships of Atkinson–Holliday (Atkinson Wang 2001) to spin up the vortices in idealized envi- and Holliday 1977, hereafter AH1977) and Knaff and ronmental conditions. The model is hydrostatic and uses Zehr (2007, hereafter KZ2007) are shown in Fig. 3. The a terrain-following sigma-pressure coordinate. An initial KZ2007 pressure was determined using an environ- weak vortex is first specified in the model, and then the mental pressure of 1010 hPa, an average latitude of 208, vortex is nudged during integration to the observed zero translation speed, and a size parameter of unity. As surface pressure at the center of the model domain as shown, the wind–pressure relationship of the TCDI

›ps/›t 52g(ps 2 pobs), where g is the relaxation co- vortex library compares favorably with other empirical efficient, ps is the prognostic in the model surface pres- examples. Notably, however, the peak winds are slightly sure, and pobs is the estimated surface pressure from the too weak for the pressure for intense vortices. This is best-track data. It can be readily seen that in the absence a result of the 15-km horizontal resolution used to spin of other forcing to the surface pressure, ps will expo- up the vortices. TCDI is expected to perform best for nentially decay to pobs with a 1/e-damping time of 1/g. observed TCs with average sizes that more closely 2 2 For the experiments here, g was set to 4.4 3 10 5 s 1, match the TCDI wind–pressure relationship. corresponding to a 1/e-damping time of 6.25 h. This c. Dynamic initialization scheme: DI rather small coefficient is used in order to gently relax the vortex to the prescribed pressure over a 48-h in- The dynamic initialization scheme is a 12-h forward tegration period. Since nudging is done at one point at relaxation to the analyzed momentum fields in model the center of the model domain, the radial profiles of space as ›u/›t 52a(u 2 ua), where u 5 (u, y) is the tangential velocity and pressure arise from the model prognostic horizontal momentum vector (where u is the integration. The insertion of the dynamically initialized zonal momentum per unit mass and y is the meridional vortex into the model environment is accomplished as momentum per unit mass), ua is the analyses horizontal 2 follows. In the radial direction, the ideal vortex is used momentum vector, and a 5 0.001 s 1 (1/e-damping time for r , 300 km, followed by a blending zone into the of 0.26 h). Note that ua is the same analyzed field as is environment using linear weighting from 300 , r , generated in the control scheme. The rather strong 400 km. The analysis outside this blending zone is ob- Newtonian damping is used to ensure the relaxation tained from the 3DVAR system, which includes the tendency is sufficient to nudge the momentum to the synthetics observations based on the observed TC wind analyzed fields during the initialization period. This also profile. Thus, TCDI helps improve the inner-core repre- ensures that the TC vortex is anchored (not moving) sentation and balance of the vortex, while the 3DVAR during DI. Since the 3DVAR analysis is created using analysis will help capture the outer wind field properly the synthetic TC observations that match the best-track- (especially for TCs with large outer winds fields). In the estimated wind structure, the DI scheme will preserve this vertical, the ideal vortex is used from 1013 to 500 hPa, structure through the horizontal momentum nudging. followed by a linear decay function to zero from 500 to In the DI scheme, COAMPS-TC is integrated with 10 hPa. In this manner, TCDI is used to improve the full physics, but is relaxed to the analyses’ horizontal representation of the TC vortex at low to middle levels momentum. During the DI period, the mass field is al- while retaining more of the environment at upper levels. lowed to adjust. The purpose of DI is to remove imbal- Currently, observational uncertainty in the best-track- ances introduced during the interpolation and analyses estimated minimum pressure is not accounted for; the procedures, to allow for the mass field of the TC to be in best-track value is assumed to be the truth. However, it a nonlinear balance with the momentum, and to allow should be noted that there is greater certainty in the es- for the generation of the secondary circulation associ- timated pressure in the North Atlantic basin, where ated with the TC vortex. (Also note that the TCDI routine aircraft reconnaissance missions are conducted, scheme also accomplishes the latter two objectives.) The than in the western North Pacific basin. DI scheme is applied to all three nests, and two-way NOVEMBER 2013 H E N D R I C K S E T A L . 4033

FIG. 3. Wind–pressure relationship of the TCDI vortex library in comparison to other empirical wind–pressure relationships (AH1977 and KZ2007).

interactive nesting is turned off during this procedure. In 11 September, Vmax 5 50 kt, pmin 5 1004 hPa. This sec- addition, the lateral boundary tendencies of the outer tion gives structural details concerning how the schemes mesh (45-km horizontal resolution) are set to zero for perform on initializing and predicting TCs of varying in- each prognostic variable since the interior relaxation is tensities. All of the COAMPS-TC forecast plots here are set to the initial state. shown for the innermost domain simulations with a horizontal gridpoint spacing of 5 km. d. Two-stage dynamic initialization scheme: TCDI/DI a. Hurricane Irene (2011) The fourth TC initialization scheme is a two-stage dynamic initialization scheme that combines the latter Irene (2011) is chosen as a case study because it was a two schemes. First, the TCDI scheme is invoked to im- high-impact event along the U.S. southeast coast, caus- prove the representation of the TC, and then the DI ing widespread damage. Tropical Storm Irene formed to scheme is invoked to help remove imbalances. Since this the east of the Lesser Antilles on 0000 UTC 21 August. scheme involves two separate stages of dynamic initial- It crossed Puerto Rico and became a category 3 hurri- ization (the TC component first and then the full model), cane near the Bahamas on 1200 UTC 24 August. After it is hereafter called a two-stage dynamic initialization that, Irene moved northward up the southeast coast of scheme (TCDI/DI). In this procedure, however, the the United States, making landfall as a tropical storm analyses vector ua is the modified analyses after inser- near Cape Hatteras, North Carolina, and then moved tion of the TCDI vortex. This is the major difference north making another landfall near New York, New between TCDI/DI and DI. York. After decaying, widespread flooding also occurred in Vermont. Hurricane Irene was noteworthy because many numerical and statistical model predictions as 4. Case studies well as the official guidance predicted that it would Example studies of the four initialization schemes are intensify or maintain its intensity during the critical illustrated for three cases—moderate, intense, and weak period prior to landfall, while it actually weakened. It initializations, respectively: (i) Hurricane Irene (2011), was also noteworthy for its unusually large size. More

1200 UTC 25 August, Vmax 5 95 kt, pmin 5 955 hPa, cate- details can be found in Avila and Cangiolosi (2012). gory 2 strength; (ii) Typhoon Ma-On (2011), 0000 UTC During the real-time forecast of Irene, COAMPS-TC had

15 July, Vmax 5 110 kt, pmin 5 940 hPa, category 3 strength; the best intensity forecast among all dynamic models and (iii) Tropical Storm Maria (2011), 1200 UTC (Doyle et al. 2011). The average intensity error for all 4034 MONTHLY WEATHER REVIEW VOLUME 141 lead times up to 120 h was approximately 7 kt, signifi- Tropical Storm Ma-On shortly thereafter. Ma-On gradu- cantly lower than other operational dynamical models. ally intensified and became a typhoon on 14 July due to Therefore, a stringent test of the new initialization favorable environmental conditions. The peak intensity of schemes is to see whether or not they will degrade the 110 kt occurred at 0000 UTC 15 July. good structural and intensity performance of the real- In Fig. 6, the initial conditions and t 5 48 h forecasts time CNTL simulation. for the surface pressure of Ma-On are given for the The initial conditions of the 10-m wind speed for different initialization schemes. The JTWC best-track Hurricane Irene at 1330 UTC 25 August for the four estimate of the pressure at 0000 UTC 15 July and different initialization schemes in comparison to the 0000 UTC 17 July was 941 hPa, indicated at the bottom H*Wind analysis are given in Fig. 4. The H*Wind of Fig. 6. As shown in the left panel of Fig. 6a, the CNTL product is obtained from the National Oceanic and initialization produces a vortex that is too weak Atmospheric Administration/Atlantic Oceanographic (966 hPa) and the DI scheme is also too weak (958 hPa; and Marine Laboratories/Hurricane Research Division left panel of Fig. 6c). The higher pressure in the CNTL (NOAA/AOML/HRD) (Powell et al. 1998; Powell scheme is a result of 3DVAR not being able to produce and Houston 1998). Due to the limited availability of a vortex pressure in gradient balance with the winds. H*Wind, instead of the true initial conditions, the The DI scheme helps this somewhat as the mass field COAMPS-TC t 5 1.5 h forecasts are used and shown adjusts, but the pressure still remains too high. The here (and subsequent diagrams) for the comparison at TCDI and TCDI/DI schemes produce more intense the time of the H*Wind analysis. As shown, all four vortices initially (939 and 934 hPa, respectively; left schemes do a reasonable job of capturing the observed panels of Figs. 6b and 6d), more consistent with the surface wind field of Irene, in terms of both structure and JTWC best-track estimate. Moving to the t 5 48 h fore- magnitude. In Fig. 4b, the CNTL scheme has more cast (right panel of Fig. 6a), the CNTL scheme produces small-scale structure. The TCDI scheme (Fig. 4b) is a 929-hPa vortex, slightly deeper than the JTWC best- smoother and more axisymmetric, which is a conse- track estimate of 941 hPa. The TCDI scheme produces quence of the insertion of a quasi-axisymmetric TCDI too intense of a vortex (909 hPa; right panel of Fig. 6b). vortex into the environment. The DI scheme (Fig. 4d) is The DI and TCDI/DI schemes produce vortices closer a smoother representation of the CNTL scheme, since to the JTWC best-track estimate (930 and 925 hPa, re- relaxation is performed on the CNTL horizontal mo- spectively; right panels of Figs. 6c and 6d). Here, the mentum. Finally, the TCDI/DI scheme (Fig. 4e) is sim- TCDI scheme overdeepened Ma-On, although it started ilar to TCDI, but compares more favorably to H*Wind closer to the JTWC best-track estimate. The TCDI/DI in terms of size. scheme performed the best, as it had initial and t 5 48 h In Fig. 5, the surface wind field forecasts at t 5 49.5 h intensities that were most consistent with the JTWC are shown for all initialization schemes in comparison best-track estimates. to H*Wind, valid at 1330 UTC 27 August. All initiali- c. Tropical Storm Maria (2011) zation schemes produce a hurricane-like vortex; however it is slightly too large in comparison to the H*Wind Finally, as an example of the initialization of a weak analysis. The size error may partially be due to the fact storm, the schemes are tested on Tropical Storm Maria that the actual storm was interacting with land at this (2011). Maria spent most of its life cycle as a tropical time, while the simulated TC vortices in the model were depression and tropical storm, although it briefly be- still over water. While all COAMPS-TC forecasts move came a weak hurricane prior to making landfall in slightly too slowly, each initialization scheme produces Newfoundland, Canada. Maria became a tropical de- a similar surface wind field, demonstrating that the ef- pression at 1800 UTC 5 September, approximately fects of model physics may be dominating the initiali- 1300 km west-southwest of the Cape Verde Islands. zation at this later time. The intensity performance of From that point, Maria experienced large vertical wind TCDI/DI in comparison to the CNTL scheme and NHC shear for much of its life and often had little deep con- best track is further discussed in section 6. vection in its core (Brennan 2012). The t 5 1.5 h COAMPS-TC forecasts are shown for b. Typhoon Ma-On (2011) the different initialization schemes in comparison to As an example for initializing an intense storm, a case H*Wind in Fig. 7 for Tropical Storm Maria at 1330 UTC study of Typhoon Ma-On is given here. Typhoon Ma-On 11 September. As in Fig. 4, the t 5 1.5 h forecast is used was a powerful typhoon that affected southern Japan in as a proxy for the initial conditions so that it matches the 2011. On 11 July 2011 a tropical depression formed in the H*Wind analysis time. Here, all initialization schemes western North Pacific basin near Wake Island and became produce too large of an outer wind field in comparison to NOVEMBER 2013 H E N D R I C K S E T A L . 4035

21 FIG. 4. The initial conditions of the 10-m winds (m s ) for Hurricane Irene using the different initialization schemes in comparison to H*Wind: (a) H*Wind analysis valid 1330 UTC 25 Aug, (b) CNTL initialization, (c) TCDI, (d) DI, and (e) TCDI/DI, where (b)–(e) are given at t 5 1.5 h to match the time of the H*Wind analysis. 4036 MONTHLY WEATHER REVIEW VOLUME 141

21 FIG. 5. The COAMPS-TC t 5 49.5 h forecasts of the 10-m winds (m s ) of Hurricane Irene using different initializations in comparison to H*Wind: (a) H*Wind analysis valid 1330 UTC 25 Aug, (b) CNTL initialization, (c) TCDI, (d) DI, and (e) TCDI/DI. NOVEMBER 2013 H E N D R I C K S E T A L . 4037

FIG. 6. (left) The initial sea level pressure (hPa) and (right) forecast pressure at t 5 48 h for Typhoon Ma-On using the different initializations: (a) CNTL, (b) TCDI, (c) DI, and (d) TCDI/DI. The left panels are valid at 0000 UTC 15 Jul 2011 and the right panels are valid at 0000 UTC 17 Jul 2011. The COAMPS-TC minimum central pressure is given in each plot, and the JTWC best-track minimum central pressure is also given at the bottom of the ﬁgure. 4038 MONTHLY WEATHER REVIEW VOLUME 141

FIG. 7. As in Fig. 4, but for Tropical Storm Maria. NOVEMBER 2013 H E N D R I C K S E T A L . 4039

TABLE 1. North Atlantic (NA) and western North Pacific (WNP) with a p value of 0.05 for the tests. In Figs. 8 and 9, an tropical cyclones used for the evaluation. open black diamond at a given lead time indicates that Basin Year TC Time period there was a rejection of the null hypothesis, indicating a statistically significant difference at the 95% con- NA 2010 Danielle (06L) 0000 UTC 22 Aug–0000 UTC 31 Aug fidence level for the given lead time. Similarly, the lack NA 2010 Earl (07L) 1200 UTC 25 Aug–0000 of an open black diamond indicates that there was UTC 2 Sep a failure to reject the null hypothesis, and therefore it NA 2010 Igor (11L) 0000 UTC 11 Sep–1200 cannot be said that there is any difference between UTC 16 Sep either the dynamic initialization scheme or the CNTL NA 2010 Julia (12L) 1200 UTC 12 Sep–1200 UTC 20 Sep scheme. NA 2011 Irene (09L) 1200 UTC 22 Aug–0000 a. Track errors UTC 27 Aug NA 2011 Katia (12L) 0000 UTC 30 Aug–0000 The average track errors for each initialization UTC Sep 6 scheme are given in Fig. 8. In Fig. 8a, the average track NA 2011 Maria (14L) 1200 UTC 7 Sep–1200 UTC 14 Sep errors for the entire sample are presented. In Figs. 8b NA 2011 Rina (18L) 0000 UTC 24 Oct–1200 and 8c, respectively, the average track errors for intense UTC 27 Oct and weak initializations are shown. In each plot, the WNP 2010 Fanapi (12W) 0000 UTC 15 Sep–1200 solid line represents the total track error, the dotted line UTC 20 Sep represents the along-track error, and the dashed line WNP 2010 Chaba (16W) 0000 UTC 23 Oct–1200 UTC 27 Oct represents the cross-track error. For physical interpre- WNP 2011 Ma-On (08W) 0000 UTC 12 Jul–0000 tation, along-track errors denote errors in TC trans- UTC 21 Jul lation velocity (either movement too slow or too fast), while cross-track errors denote errors in the perpen- dicular direction of the storm trajectory (such as recur- H*Wind. The CNTL scheme has the most accurate vature too early). As shown in Fig. 8a, the track errors inner-core wind structure, with the TCDI, DI, and are similar at each lead time for each initialization TCDI/DI schemes having too large of an inner-core scheme for the entire sample. At the later lead times, the wind structure. All schemes obtain the wavenumber-1 TCDI scheme is shown to perform slightly better than asymmetry due to TC motion. Further examination of the others, while at earlier lead times, the TCDI/DI the intensity forecasts of the TCDI/DI scheme in com- scheme performs the best. Moving to the group of in- parison to the CNTL scheme and NHC best track for tense storms (Fig. 8b), the TCDI and TCDI/DI schemes Maria are given in section 6. perform slightly better, while for weak storms (Fig. 8c), the variance is not as significant between the different 5. Average intensity and track errors schemes. It should be noted here, however, that there To better understand the performance of each ini- are no statistically significant differences between each tialization scheme, testing was performed on a large dynamic initialization scheme and the CNTL scheme sample of TCs from the 2010 and 2011 seasons in the with regard to the average track error. Therefore, in North Atlantic and western North Pacific basins. Eleven a statistical sense, all initialization schemes produce storms were tested, comprising a total of 120 cases from similar track errors. With regard to the along- and cross- the homogeneous sample at the initial lead time. The track components, the TCDI scheme tends to generally homogeneous samples were obtained at each lead time produce smaller cross-track errors than the other in order to compute the errors. The TCs and date ranges groups, while both the TCDI/DI and TCDI schemes are listed in Table 1. To reduce correlated forecasts, only produced smaller along-track errors. COAMPS-TC forecasts that are 12 h apart were used in b. Intensity errors the sample, even though the model runs with an update cycle of 6 h (four forecasts per day). An unequal vari- The average intensity errors are given in Fig. 9. The ance two-tailed t test was performed for the intensity intensity errors are given by both the maximum sus- and track errors in order to assess whether or not the tained surface wind (Fig. 9; left panels) and minimum differences were statistically significant. The null hy- central pressure (Fig. 9; right panels). In Fig. 9a, the pothesis for the tests was that there is no difference average intensity errors are shown for the entire sample. between the average value of the given dynamic ini- In Figs. 9b and 9c, the average intensity errors are given tialization scheme (either TCDI, DI, or TCDI/DI) and for intense and weak initializations, respectively. In each the CNTL scheme. A 95% confidence interval was used panel, the solid lines denote the mean absolute intensity 4040 MONTHLY WEATHER REVIEW VOLUME 141

FIG. 8. Average total track errors and along- and cross-track components for (a) all cases, (b) intense initializations (initial best-track-estimated intensity # 990 hPa), and (c) weak initializations (initial best-track-estimated intensity . 990 hPa) for CNTL, TCDI, TCDI/DI, and DI. The number of cases at each lead time is given at the bottom of each panel in blue parentheses. NOVEMBER 2013 H E N D R I C K S E T A L . 4041

FIG. 9. Average mean absolute errors in intensity for (a) all cases, (b) intense initializations (initial best-track-estimated intensity # 990 hPa), and (c) weak initializations (initial best-track-estimated intensity .990 hPa) for CNTL, TCDI, TCDI/DI, and DI. The first column is the error in maximum sustained surface wind and the second column is the error in minimum sea level pressure. The number of cases at each lead time is given at the bottom of each panel in blue parentheses. errors, and the dotted lines denote the biases (or mean In the left panel of Fig. 9a, it can be seen that by error). In the wind plots (left panels), a positive bias maximum sustained surface wind both the TCDI/DI and signifies that on average the simulated TC was too in- DI schemes have lower errors at the later lead times, tense (and vice versa). In the pressure plots (right while there is not as significant of a difference at the panels), a positive bias signifies that on average the earlier lead times. In terms of biases, the TCDI/DI simulated TC was too weak (and vice versa). The zero scheme has the best bias overall (closest to zero). In the line is marked in green. right panel of Fig. 9b, the TCDI/DI scheme is shown to 4042 MONTHLY WEATHER REVIEW VOLUME 141

TABLE 2. Percent differences between the mean absolute errors neutral with regard to track (10.8%). Finally, the TCDI/ of the dynamic initialization schemes and the CNTL scheme. DI scheme improves the overall track and intensity Negative values denote improvements and positive values denote (213.5% by wind, 224.4% by pressure, and 25.6% by degradations. track). For intense initializations, the results are similar; Group Quantity TCDI DI TCDI/DI however, the improvements in intensity by the TCDI/DI All Wind error 13.9 25.0 213.5 (225.3% by wind and 239.0% by pressure) and DI Pressure error 15.7 218.7 224.4 (27.0% by wind and 227.7% by pressure) schemes are Track error 27.8 10.8 25.6 more substantial. Finally, moving to the weak initiali- # 1 2 2 Intense ( 990 hPa) Wind error 2.2 7.0 25.3 zations, all of the dynamic initialization schemes per- Pressure error 13.4 227.7 239.0 Track error 28.8 10.7 28.2 form slightly worse than the CNTL scheme with regard Weak (.990 hPa) Wind error 18.0 10.0 19.8 to track and intensity. One exception to this is TCDI, Pressure error 110.7 11.1 14.6 which even for weak initializations improved the track Track error 25.2 11.5 10.3 (25.2%). The results in Table 2, along with the results presented in Figs. 8 and 9, demonstrate that TCDI/DI have the lowest errors at each lead time by minimum performed the best overall. central pressure, with statistical significance at the earlier lead times (t 5 0–30 h). The TCDI scheme has the 6. Further comparison of the CNTL and TCDI/DI lowest error in the early lead times, while the DI scheme schemes has a lower error in the later lead times. The two-stage scheme (TCDI/DI) combines the benefits of each in- Since the TCDI/DI scheme was shown to perform dividual scheme and produces the lowest errors at each better than the other initialization schemes on average, lead time. With regard to the initialization of intense further comparisons of this scheme with the CNTL storms (Fig. 9b), similar results are shown; however, the scheme are given in this section in order to better un- TCDI/DI scheme has further reduced errors over the derstand the differences in the initial structure and track CNTL scheme, with statistical significance at both the early and intensity forecasts. and later lead times (t 5 0–96 h). The differences are a. Azimuthal mean structure especially significant in the pressure plots (left panel of Fig. 9b). The TCDI/DI scheme has the best bias overall In Fig. 10, side-by-side comparisons of the CNTL and (left panel of Fig. 9b). For weak initializations (Fig. 9c), TCDI/DI schemes are given for the initial conditions there are no statistically significant differences between of Typhoon Ma-On (08W) at 0000 UTC 15 July. In each of the dynamic initialization schemes (TCDI, Figs. 10a–c, the azimuthal mean tangential velocity, TCDI/DI, and DI) and the CNTL scheme. While not radial velocity, and perturbation temperature (deviation statistically significant, the CNTL scheme actually has from the environment) are given, respectively. Recall lower errors than the others for weak storms. from Fig. 6 that the CNTL scheme produced a vortex that was too weak for this case, while TCDI/DI was c. Percent differences more consistent with the JTWC best-track estimate. In addition to the average mean absolute errors This is further illustrated in the azimuthal mean struc- plotted versus lead time, the errors were also averaged ture at the initial time. Examining Fig. 10a, the TCDI/DI over all lead times and percent differences were com- scheme produces a larger area of stronger tangential puted between each dynamic initialization scheme winds, with more significant vertical penetration to up- (TCDI, DI, and TCDI/DI) and the CNTL. The purpose per levels. Examining Fig. 10b, the region of maximum of this is to determine the net effect of each dynamic upper-level outflow is closer to the TC center for the initialization on either improving or degrading the CNTL TCDI/DI scheme in comparison to the CNTL scheme, performance. The percent differences in the mean abso- there exists more radial inflow at middle levels (at lute errors for maximum sustained wind, minimum cen- approximately p 5 400 hPa and r 5 70 km), the bound- tral pressure, and track are given in Table 2, stratified by ary layer radial inflow is stronger (consistent with a the initial intensity (as before; all cases, intense initiali- more intense vortex), and the boundary layer thick- zations, and weak initializations). ness is smaller. In Fig. 10c, the level of the upper-level Examining all of the cases, the TCDI scheme slightly warm core is also significantly different between the degrades the overall intensity error (13.9% by wind and two schemes. In the CNTL scheme, the upper-level 15.7% by pressure) and reduces the overall track error warm-core maximum is at approximately p 5 400 hPa, (27.8%). The DI scheme improves the overall intensity while in the TCDI/DI scheme, the maximum is at ap- error (25.0% by wind and 218.7% by pressure), and is proximately p 5 300 hPa and the magnitude is slightly NOVEMBER 2013 H E N D R I C K S E T A L . 4043

FIG. 10. Radius–pressure (r2p) cross sections of the (a) azimuthal mean tangential velocity, (b) azimuthal mean radial velocity, and (c) azimuthal mean perturbation temperature. Plots are for the initial conditions of Typhoon Ma- On at 0000 UTC 15 Jul. Shown are the results for the (left) CNTL and (right) TCDI/DI schemes. larger than in the CNTL scheme. In each scheme, the of the maximum vertical gradient in the azimuthal location of the warm core is consistent with expecta- mean tangential velocity is lower in the CNTL scheme tions from enforcing the vortex thermal wind balance than in the TCDI/DI scheme. While it is not possible to upon the mean tangential velocity (Fig. 10a). The level verify which azimuthal mean structure is closest to the 4044 MONTHLY WEATHER REVIEW VOLUME 141

FIG. 11. Intensity forecasts of (left) CNTL and (right) TCDI/DI for (a) Ma-On, (b) Katia, (c) Maria, and (d) Irene. The thick black line is the NHC or JTWC best-track intensity and colored lines represent individual COAMPS-TC forecasts. Time is plotted in days relative to the date–time group at the top of the panel (format is YYYYMMDDHH, where YYYY is the year, MM is the month, DD is the day, and HH is the hour). NOVEMBER 2013 H E N D R I C K S E T A L . 4045

FIG. 12. COAMPS-TC track forecasts for (a) Hurricane Earl and (b) Hurricane Danielle using the (left) CNTL and (right) TCDI/DI schemes. The thick black line is the NHC best-track position and colored lines represent individual COAMPS-TC forecasts. observations, clearly the TCDI/DI scheme produces scheme does not suffer as much from the imbalance a more intense vortex consistent with the JTWC best- issue and, therefore, maintains the initial strong in- track estimate. tensity, yielding more accurate intensity forecasts. In Fig. 11b, similar plots are shown for Hurricane Katia. b. Intensity and track forecast comparisons Katia was generally a weak TC, but had a rapid in- Comparisons of the forecasted COAMPS-TC intensification event. Here, both the CNTL and TCDI/DI tensity using the TCDI/DI scheme versus the CNTL schemes produce similar results. However, the TCDI/DI scheme are given in Fig. 11. In Figs. 11a–d, comparisons scheme is slightly better overall and better captures the are given for Typhoon Ma-On, Hurricane Katia (2011, rapid intensification event. In Fig. 11c, a comparison is 12L), Tropical Storm Maria (2011, 14L), and Hurricane shown for Tropical Storm Maria. Maria was a weak Irene (2011, 09L), respectively. In each plot, the colored storm due to unfavorable environmental conditions (as curves are individual COAMPS-TC forecasts, and the stated earlier). Here, the CNTL scheme performs better black curve is either the NHC or JTWC best-track es- than the TCDI/DI scheme overall, as the TCDI/DI timate of the maximum sustained wind. For each curve, scheme tends to overintensify Maria in many forecasts. time is plotted relative to the time at the top of the fig- This is likely a result of inserting a vertically aligned ure, so that the colored and black curves can be directly bogus vortex with TCDI, which is more primed to in- compared at each time. For a set of perfect simulations, tensify. Clearly, the initialization of weaker TCs that the colored curves would exactly overlap the black may not be vertically aligned due to vertical shear or curve. In Fig. 11a, which is an example of TC with high other unfavorable environmental conditions is a signifi- intensity, the CNTL simulation suffers from significant cant challenge. Finally, the comparison of the CNTL spindown effects in the early part of many forecasts, and TCDI/DI schemes for Hurricane Irene is given in while the TCDI/DI scheme does not. The spindowns in Fig. 11d. While both series of forecasts are good, cap- theCNTLschemearemostlikelyaresultofthe turing the general weakening of Irene after 0000 UTC 3DVAR system not producing a TC in proper balance nor 25 August, the TCDI/DI scheme has less scatter and per- with a consistent secondary circulation. The TCDI/DI forms slightly better. 4046 MONTHLY WEATHER REVIEW VOLUME 141

FIG. 13. Intensity forecasts by minimum central pressure of (a) Hurricane Earl and (b) Hurricane Danielle using the (left) CNTL and (right) TCDI/DI schemes. The thick black line is the NHC best-track intensity and colored lines represent individual COAMPS-TC forecasts. Time is plotted in days relative to the date–time group at the top of the panel (as in Fig. 11).

Track and intensity comparisons (by minimum central While a systematic evaluation of size has not been pressure) of the CNTL and TCDI/DI schemes are also conducted on this sample, on a different sample of ap- given for Hurricane Earl (2010) and Hurricane Danielle proximately 200 cases, the TCDI/DI scheme was shown (2010) in Figs. 12 and 13, both compared to the NHC to have a lower mean absolute error at the initial time best-track data. Examining Fig. 12, broadly, the track than the CNTL scheme for the radii of 34-, 50-, and 64-kt differences are not that significant between the two winds. The TCDI/DI scheme had a larger error in the schemes (as evinced also by the average track errors in radius of maximum wind, presumably due to the 15-km the previous section). The CNTL scheme has fewer horizontal resolution of the TCDI vortex library. At forecasts that recurve too early for Hurricane Earl. On later lead times, the errors were similar, indicating that the other hand, for Hurricane Danielle, the TCDI/DI model physics exerts more control over the size at these scheme has less scatter and fewer forecasts that recurve later lead times. too early. For the intensity forecasts (Fig. 13), the initial central pressure in the CNTL scheme is generally too 7. Conclusions high in comparison to the NHC best-track estimate, resulting in forecasts that start too weakly. This is espe- Three different dynamic initialization schemes for cially evident for Hurricane Earl (Fig. 13a), but also tropical cyclone prediction in numerical models were evident to some extent for Hurricane Danielle (Fig. 13b). designed and evaluated on a sample of real cases. The With the TCDI/DI scheme, however, the initial pressure first scheme is a tropical cyclone dynamic initialization is much closer to the NHC best-track estimate, resulting (TCDI) scheme, where the TC component is spun up in in overall improved intensity forecasts for both TCs. an independent three-dimensional primitive equation NOVEMBER 2013 H E N D R I C K S E T A L . 4047 model and inserted into the forecast model initial con- in the DI step in order to improve the wind structure and ditions. The second scheme is a forward dynamic ini- asymmetries. tialization (DI) scheme, where the forecast model is relaxed to the analyses’ momentum in model space for Acknowledgments. EH and MP acknowledge the a period of 12 h prior to the beginning of the forecast. support of the Chief of Naval Research through the The third scheme is a combination of the first two NRL base program, PE 0601153N. We thank Drs. Jim schemes, a two-stage dynamic initialization scheme Doyle and Rich Hodur for helpful discussions. This (TCDI/DI). In the first stage, the TC component is dy- manuscript was improved by the constructive comments namically initialized and inserted into the forecast of two anonymous reviewers. model initial conditions (TCDI). In the second stage, the DI scheme is used to improve the balance between the REFERENCES TC and its environment. A systematic evaluation of each Atkinson, G. D., and C. R. Holliday, 1977: Tropical cyclone dynamic initialization scheme was performed versus minimum sea level pressure/maximum sustained wind re- a control (CNTL) scheme that uses a 3DVAR data as- lationship for the western North Pacific. Mon. Wea. Rev., 105, similation system in conjunction with synthetic TC ob- 421–427. Avila, L. A., and J. Cangiolosi, 2012: Hurricane Irene. 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