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.
A critical challenge of predicting tropical cyclones (TCs) with numerical models is providing the model an accurate and balanced set of initial conditions. The accuracy depends on the density and quality of the observations of the TC, while the balance consists of both dynamical and thermodynamic balances. Since most TCs exist over open oceans with few observations (especially in the inner core), often the main source of information comes from estimates of the maximum sustained surface wind and minimum central pressure issued by operational warning centers [e.g., the National Hurricane Center (NHC) or Joint Typhoon Warning Center (JTWC)]. The intensity is often inferred from satellite imagery; however, routine aircraft reconnaissance missions in the North Atlantic provide in situ measurements as well when a storm is closer to the coast. A TC prediction model which runs in real time needs to have the intensity and position of the vortex as close to the official estimates as possible in the initial conditions, but would not necessarily have all structural details due to the paucity of observations. With regard to the balance, it is critical to initialize the TC vortex in proper balance so that rapid adjustments do not occur in the early stages of the integration, during which the vortex deviates significantly from its initial conditions, and generates spurious gravity waves.
Broadly speaking, there are three main methods of initializing TCs in numerical prediction systems. In the first method, an analytically or empirically constructed vortex is inserted into the model analyses, after the existing vortex is removed, which may be at the wrong intensity or location (Holland 1980; Mathur 1991; Leslie and Holland 1995; Davidson and Weber 2000; Kwon and Cheong 2010). The inserted vortex is designed to match the intensity and structure estimates from the warning centers. The second method is to construct the initial vortex using a variational data assimilation system with synthetic observations, often called the bogus data assimilation method (Goerss and Jeffries 1994; Serrano and Undén 1994; Zou and Xiao 2000; Pu and Braun 2001; Xiao et al. 2006; Wu et al. 2006; Liou and Sashegyi 2011). The third method is dynamic initialization, where the TC vortex (and perhaps the forecast model) is initialized using Newtonian relaxation to some prescribed state (Hoke and Anthes 1976, 1977; Fiorino and Warner 1981; Krishnamurti et al. 1988; Kurihara et al. 1993; Davidson and Puri 1992; Bender et al. 1993; Peng et al. 1993; Peng and Chang 1996, 1997; Hendricks et al. 2011; Nguyen and Chen 2011; Zhang et al. 2012; Cha and Wang 2013). Dynamic initialization (DI) methods have two primary benefits. First, imbalances can be removed through model integration with the addition of relaxation terms, improving both the spinup of the vortex and the initial balance so that rapid adjustments do not occur in the early part of the forecast. Second, they allow for model physics spinup (including the boundary layer and microphysics), which should lead to improved forecasts.
There are multiple ways dynamic initialization schemes can be implemented, encompassing both the TC vortex and the forecast model. Kurihara et al. (1993) demonstrated the benefits of a TC dynamic initialization scheme using an axisymmetric version of the forecast model for spinup to the desired structure and intensity. Hendricks et al. (2011) further demonstrated the utility of the TC dynamic initialization scheme using an independent three-dimensional primitive equation model for vortex spinup. However, there are weaknesses in both schemes because inconsistencies between the forecast model environment and the inserted vortex can manifest themselves in spurious gravity wave activity after the forecast integration begins. Recently, Cha and Wang (2013) and Nguyen and Chen (2011) have developed DI schemes that are designed to improve upon this issue. In their studies, the TC vortex is spun up using short cycle runs of the forecast model starting prior to the initial time, rather than being spun up offline and inserted. A positive impact on TC track and intensity performance was found. Recently, there has been renewed interest in using dynamic initialization schemes with high-resolution regional TC prediction models.
In this paper, three different dynamic initialization schemes that can be applied to a numerical weather prediction model are described and evaluated. The first scheme is a tropical cyclone dynamic initialization (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 in an environment with no mean flow, and relaxed to the observed surface pressure. This vortex is then inserted into the forecast model initial conditions after three-dimensional variational data assimilation (3DVAR) and the removal of the existing TC vortex. The second scheme is a forward dynamic initialization scheme where the forecast model is integrated to reach a balance between the TC vortex and the environment. In the DI scheme, the forecast model is integrated with full-physics processes for a period of 12 h and relaxed to the analyses horizontal momentum. The third scheme combines the TCDI and DI schemes, and is called a two-stage scheme since it involves two separate stages of dynamic initialization: the TC component first, followed by the forecast model. Each dynamic initialization scheme is evaluated in comparison to a control scheme (CNTL), which constructs the initial conditions using a 3DVAR scheme with synthetic TC observations. The evaluation is based on a large sample of TCs in the North Atlantic and western North Pacific basins during 2010–11 (120 cases at the initial lead time). The outline of the rest of the paper is as follows. In section 2, the mesoscale numerical prediction model used for testing is described. In section 3, the four initialization schemes are described. In section 4, a structure evaluation is presented for the different initialization schemes for three cases, representing weak to strong TCs. Analysis of average intensity and track errors for the entire sample of cases is given in section 5. Further structural, track, and intensity forecast analyses of TCDI/DI in comparison to the CNTL scheme are given in section 6. The conclusions are given in section 7.
2. Mesoscale TC prediction model
The mesoscale model used here is the Coupled Ocean–Atmosphere Mesoscale Prediction System-Tropical Cyclones (COAMPS-TC). COAMPS-TC is a special version of COAMPS,1 which is the navy's operational mesoscale prediction system. A description of the COAMPS model is provided by Hodur (1997) and more details can also be found in Chen et al. (2003). The model uses a terrain-following sigma-height coordinate and the nonhydrostatic compressible equations of motion (Klemp and Wilhelmson 1978). The microphysics scheme is based on Rutledge and Hobbs (1983), with prognostic equations for mixing ratios of cloud droplets, ice particles, rain, snow, graupel, and drizzle. The model also includes a short- and longwave radiation scheme (Harshvardhan et al. 1987), and a planetary boundary layer scheme with a 1.5-order turbulence closure (Mellor and Yamada 1982).
The tropical cyclone prediction version of COAMPS-TC includes the following enhancements: (i) synthetic wind and mass observations of the TC based on the official warning message, (ii) relocation of the first-guess field to the observed TC position, (iii) TC-following nested inner grids using an automatic TC tracker, (iv) dissipative heating (Jin et al. 2007), and (v) a surface drag coefficient that approaches 2.5 × 10−3 for wind speeds exceeding 35 m s−1 (Donelan et al. 2004). COAMPS-TC has been tested in real-time runs and used to support several field experiments (Doyle et al. 2011). The forecast system also has a capability for ocean coupling; however, for this study the model was run in stand-alone atmosphere mode.
For the experiments conducted here, three nested grids were used, with horizontal resolutions of 45, 15, and 5 km, respectively. The 15- and 5-km grids automatically move following the TC circulation with two-way interactive nesting, while the outer 45-km grid was held fixed. The setup of all three domains for COAMPS-TC in the North Atlantic basin is shown in Fig. 1. The model was run with 40 sigma levels in the vertical with a top at 31 km. While the microphysics scheme was used for all three nests, the Kain–Fritsch cumulus scheme was activated in the 45- and 15-km domains to help resolve subgrid-scale convection.
For the first forecast of a TC, the global analysis from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) is used as the first guess, defined here as a cold start. Subsequent runs of the same storm then use the previous COAMPS-TC forecast as the first guess, identified here as warm starts. The lateral boundary conditions for the 45-km horizontal resolution outer mesh are also obtained from the GFS forecast data. In either case, a 3DVAR system (the Naval Research Laboratory Atmospheric Variational Data Assimilation System, NAVDAS; Daley and Barker 2001) is used to optimally blend the observations with the first guess, creating the analysis. For the data assimilation, an update cycle of 6 h was used.
3. Initialization schemes
Four different initialization schemes are described in this section: the control initialization, which uses the 3DVAR system with TC synthetic observations (CNTL), the TC dynamic initialization scheme (TCDI), a dynamic initialization for the forecast model (DI), and a two-stage dynamic initialization scheme which is a combination of TCDI and DI (TCDI/DI). While dynamic initialization is typically used to describe a combination of backward and forward integrations in order to remove the unbalanced components (e.g., Ghil et al. 1982; Daley 1991; Peng and Chang 1996), all three dynamic initializations used here (TCDI, DI, and TCDI/DI) only involve forward model integrations. A schematic of how these schemes can be applied to a numerical prediction model is given in Fig. 2, and more details of each scheme are given below.
a. Control initialization scheme: CNTL
In the control initialization method, the construction of the TC structure and intensity is implemented in the data assimilation using synthetic observations based on the official TC warning message. On warm starts, first the first-guess vortex is removed from the environment and relocated to the observed TC location, using the methods of Kurihara et al. (1995). Next, a vortex is constructed with a modified Rankine wind profile that fits the observed TC intensity and size parameters of the maximum wind, and the radii of 34- and 50-kt (1 kt = 0.5144 m s−1) winds. From these parameters, the radius of maximum wind and modified Rankine vortex decay parameter are uniquely determined (Liou and Sashegyi 2011). Next, the geopotential and temperature field is determined by enforcing gradient and hydrostatic balance constraints on the winds. Zonal and meridional velocity, geopotential height, and temperature synthetic observations are then created at eight azimuthal segments, and at radii of 0.5°, 1°, 2°, 4°, and 6°.2 The synthetic observations are constructed at the vertical levels of 1000, 965, 925, 850, 775, 700, 600, 500, and 400 hPa, with prescribed vertical decay factors of 1.000, 0.996, 0.992, 0.983, 0.970, 0.950, 0.920, 0.870, and 0.720, respectively. Then, the environmental flow is added to the synthetic observations. The environmental flow is obtained from the spectrally truncated global wind analysis, retaining components of the large-scale flow. Within 3° of the vortex center, the environmental wind is adjusted in order to match the motion as given by the operational warning center. Finally, the 3DVAR system is used to optimally blend the TC synthetic observations and all the other observations [including conventional and aircraft observations, geostationary satellite winds, Special Sensor Microwave Imager (SSM/I) wind speeds, total precipitable water retrievals, passive-microwave-derived surface marine winds, and satellite temperature retrievals] with the first guess to obtain the initial fields of the model. In the 3DVAR system, the geostrophic balance constraint is relaxed in the tropics to help produce a more gradient-balanced vortex. More details on the control initialization procedure can be found in Liou and Sashegyi (2011). Note that the CNTL scheme is used in the current real-time version of COAMPS-TC.
b. TC dynamic initialization scheme: TCDI
TCDI (Hendricks et al. 2011) involves the removal of the analyzed vortex from the initial field after the 3DVAR data assimilation, followed by the insertion of a new vortex, which is dynamically initialized to the observed surface pressure. The purpose of using TCDI after 3DVAR is to improve the TC initial dynamic and thermodynamic balances. This is necessary because the 3DVAR system used (NAVDAS) has a geostrophic 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 cyclostrophic term in 3DVAR systems (Barker et al. 2004). The removal of the analyzed vortex is done by using a Tukey window spatial low-pass filter. The filter cutoff wavelength was set to 5 × 105 m for zonal and meridional velocity fields and to 3 × 105 m for the temperature, geopotential height, and moisture fields. Note that while the TCDI scheme here is invoked after 3DVAR, it may also be invoked before 3DVAR to improve the TC representation in the first guess prior to data assimilation (Zhang et al. 2012).
For the specific experiments performed here, we use the three-dimensional Tropical Cyclone Model (TCM3; Wang 2001) to spin up the vortices in idealized environmental conditions. The model is hydrostatic and uses a terrain-following sigma-pressure coordinate. An initial weak vortex is first specified in the model, and then the vortex is nudged during integration to the observed surface pressure at the center of the model domain as ∂ps/∂t = −γ(ps − pobs), where γ is the relaxation coefficient, ps is the prognostic in the model surface pressure, and pobs is the estimated surface pressure from the best-track data. It can be readily seen that in the absence of other forcing to the surface pressure, ps will exponentially decay to pobs with a 1/e-damping time of 1/γ. For the experiments here, γ was set to 4.4 × 10−5 s−1, corresponding to a 1/e-damping time of 6.25 h. This rather small coefficient is used in order to gently relax the vortex to the prescribed pressure over a 48-h integration period. Since nudging is done at one point at the center of the model domain, the radial profiles of tangential velocity and pressure arise from the model integration. The insertion of the dynamically initialized vortex into the model environment is accomplished as follows. In the radial direction, the ideal vortex is used for r < 300 km, followed by a blending zone into the environment using linear weighting from 300 < r < 400 km. The analysis outside this blending zone is obtained from the 3DVAR system, which includes the synthetics observations based on the observed TC wind profile. Thus, TCDI helps improve the inner-core representation and balance of the vortex, while the 3DVAR analysis will help capture the outer wind field properly (especially for TCs with large outer winds fields). In the vertical, the ideal vortex is used from 1013 to 500 hPa, followed by a linear decay function to zero from 500 to 10 hPa. In this manner, TCDI is used to improve the representation of the TC vortex at low to middle levels while retaining more of the environment at upper levels. Currently, observational uncertainty in the best-track-estimated minimum pressure is not accounted for; the best-track value is assumed to be the truth. However, it should be noted that there is greater certainty in the estimated pressure in the North Atlantic basin, where routine aircraft reconnaissance missions are conducted, than in the western North Pacific basin.
The TCDI scheme operates through using a vortex library of varying intensities. The vortex library is built consisting of vortices with central pressures ranging from 1010 to 910 hPa at 1-hPa increments. The vortex that most closely matches the observed intensity estimate is chosen for the real TC forecast. While variances in size have not been explicitly built into this vortex library yet, a comparison of the wind–pressure relationship of the vortex library versus the empirical wind–pressure relationships of Atkinson–Holliday (Atkinson and Holliday 1977, hereafter AH1977) and Knaff and Zehr (2007, hereafter KZ2007) are shown in Fig. 3. The KZ2007 pressure was determined using an environmental pressure of 1010 hPa, an average latitude of 20°, zero translation speed, and a size parameter of unity. As shown, the wind–pressure relationship of the TCDI vortex library compares favorably with other empirical examples. Notably, however, the peak winds are slightly too weak for the pressure for intense vortices. This is a result of the 15-km horizontal resolution used to spin up the vortices. TCDI is expected to perform best for observed TCs with average sizes that more closely match the TCDI wind–pressure relationship.
c. Dynamic initialization scheme: DI
The dynamic initialization scheme is a 12-h forward relaxation to the analyzed momentum fields in model space as ∂u/∂t = −α(u − ua), where u = (u, υ) is the prognostic horizontal momentum vector (where u is the zonal momentum per unit mass and υ is the meridional momentum per unit mass), ua is the analyses horizontal momentum vector, and α = 0.001 s−1 (1/e-damping time of 0.26 h). Note that ua is the same analyzed field as is generated in the control scheme. The rather strong Newtonian damping is used to ensure the relaxation tendency is sufficient to nudge the momentum to the analyzed fields during the initialization period. This also ensures that the TC vortex is anchored (not moving) during DI. Since the 3DVAR analysis is created using the synthetic TC observations that match the best-track-estimated wind structure, the DI scheme will preserve this structure through the horizontal momentum nudging.
In the DI scheme, COAMPS-TC is integrated with full physics, but is relaxed to the analyses' horizontal momentum. During the DI period, the mass field is allowed to adjust. The purpose of DI is to remove imbalances introduced during the interpolation and analyses procedures, to allow for the mass field of the TC to be in a nonlinear balance with the momentum, and to allow for the generation of the secondary circulation associated with the TC vortex. (Also note that the TCDI scheme also accomplishes the latter two objectives.) The DI scheme is applied to all three nests, and two-way interactive nesting is turned off during this procedure. In addition, the lateral boundary tendencies of the outer mesh (45-km horizontal resolution) are set to zero for each prognostic variable since the interior relaxation is set to the initial state.
d. Two-stage dynamic initialization scheme: TCDI/DI
The fourth TC initialization scheme is a two-stage dynamic initialization scheme that combines the latter two schemes. First, the TCDI scheme is invoked to improve the representation of the TC, and then the DI scheme is invoked to help remove imbalances. Since this scheme involves two separate stages of dynamic initialization (the TC component first and then the full model), it is hereafter called a two-stage dynamic initialization scheme (TCDI/DI). In this procedure, however, the analyses vector ua is the modified analyses after insertion of the TCDI vortex. This is the major difference between TCDI/DI and DI.
4. Case studies
Example studies of the four initialization schemes are illustrated for three cases—moderate, intense, and weak initializations, respectively: (i) Hurricane Irene (2011), 1200 UTC 25 August, Vmax = 95 kt, pmin = 955 hPa, category 2 strength; (ii) Typhoon Ma-On (2011), 0000 UTC 15 July, Vmax = 110 kt, pmin = 940 hPa, category 3 strength; and (iii) Tropical Storm Maria (2011), 1200 UTC 11 September, Vmax = 50 kt, pmin = 1004 hPa. This section gives structural details concerning how the schemes perform on initializing and predicting TCs of varying intensities. All of the COAMPS-TC forecast plots here are shown for the innermost domain simulations with a horizontal gridpoint spacing of 5 km.
a. Hurricane Irene (2011)
Irene (2011) is chosen as a case study because it was a high-impact event along the U.S. southeast coast, causing widespread damage. Tropical Storm Irene formed to the east of the Lesser Antilles on 0000 UTC 21 August. It crossed Puerto Rico and became a category 3 hurricane near the Bahamas on 1200 UTC 24 August. After that, Irene moved northward up the southeast coast of the United States, making landfall as a tropical storm near Cape Hatteras, North Carolina, and then moved north making another landfall near New York, New York. After decaying, widespread flooding also occurred in Vermont. Hurricane Irene was noteworthy because many numerical and statistical model predictions as well as the official guidance predicted that it would intensify or maintain its intensity during the critical period prior to landfall, while it actually weakened. It was also noteworthy for its unusually large size. More details can be found in Avila and Cangiolosi (2012). During the real-time forecast of Irene, COAMPS-TC had the best intensity forecast among all dynamic models (Doyle et al. 2011). The average intensity error for all lead times up to 120 h was approximately 7 kt, significantly lower than other operational dynamical models. Therefore, a stringent test of the new initialization schemes is to see whether or not they will degrade the good structural and intensity performance of the real-time CNTL simulation.
The initial conditions of the 10-m wind speed for Hurricane Irene at 1330 UTC 25 August for the four different initialization schemes in comparison to the H*Wind analysis are given in Fig. 4. The H*Wind product is obtained from the National Oceanic and Atmospheric Administration/Atlantic Oceanographic and Marine Laboratories/Hurricane Research Division (NOAA/AOML/HRD) (Powell et al. 1998; Powell and Houston 1998). Due to the limited availability of H*Wind, instead of the true initial conditions, the COAMPS-TC t = 1.5 h forecasts are used and shown here (and subsequent diagrams) for the comparison at the time of the H*Wind analysis. As shown, all four schemes do a reasonable job of capturing the observed surface wind field of Irene, in terms of both structure and magnitude. In Fig. 4b, the CNTL scheme has more small-scale structure. The TCDI scheme (Fig. 4b) is smoother and more axisymmetric, which is a consequence of the insertion of a quasi-axisymmetric TCDI vortex into the environment. The DI scheme (Fig. 4d) is a smoother representation of the CNTL scheme, since relaxation is performed on the CNTL horizontal momentum. Finally, the TCDI/DI scheme (Fig. 4e) is similar to TCDI, but compares more favorably to H*Wind in terms of size.
In Fig. 5, the surface wind field forecasts at t = 49.5 h are shown for all initialization schemes in comparison to H*Wind, valid at 1330 UTC 27 August. All initialization schemes produce a hurricane-like vortex; however it is slightly too large in comparison to the H*Wind analysis. The size error may partially be due to the fact that the actual storm was interacting with land at this time, while the simulated TC vortices in the model were still over water. While all COAMPS-TC forecasts move slightly too slowly, each initialization scheme produces a similar surface wind field, demonstrating that the effects of model physics may be dominating the initialization at this later time. The intensity performance of TCDI/DI in comparison to the CNTL scheme and NHC best track is further discussed in section 6.
b. Typhoon Ma-On (2011)
As an example for initializing an intense storm, a case study of Typhoon Ma-On is given here. Typhoon Ma-On was a powerful typhoon that affected southern Japan in 2011. On 11 July 2011 a tropical depression formed in the western North Pacific basin near Wake Island and became Tropical Storm Ma-On shortly thereafter. Ma-On gradually intensified and became a typhoon on 14 July due to favorable environmental conditions. The peak intensity of 110 kt occurred at 0000 UTC 15 July.
In Fig. 6, the initial conditions and t = 48 h forecasts for the surface pressure of Ma-On are given for the different initialization schemes. The JTWC best-track estimate of the pressure at 0000 UTC 15 July and 0000 UTC 17 July was 941 hPa, indicated at the bottom of Fig. 6. As shown in the left panel of Fig. 6a, the CNTL initialization produces a vortex that is too weak (966 hPa) and the DI scheme is also too weak (958 hPa; left panel of Fig. 6c). The higher pressure in the CNTL scheme is a result of 3DVAR not being able to produce a vortex pressure in gradient balance with the winds. The DI scheme helps this somewhat as the mass field adjusts, but the pressure still remains too high. The TCDI and TCDI/DI schemes produce more intense vortices initially (939 and 934 hPa, respectively; left panels of Figs. 6b and 6d), more consistent with the JTWC best-track estimate. Moving to the t = 48 h forecast (right panel of Fig. 6a), the CNTL scheme produces a 929-hPa vortex, slightly deeper than the JTWC best-track estimate of 941 hPa. The TCDI scheme produces too intense of a vortex (909 hPa; right panel of Fig. 6b). The DI and TCDI/DI schemes produce vortices closer to the JTWC best-track estimate (930 and 925 hPa, respectively; right panels of Figs. 6c and 6d). Here, the TCDI scheme overdeepened Ma-On, although it started closer to the JTWC best-track estimate. The TCDI/DI scheme performed the best, as it had initial and t = 48 h intensities that were most consistent with the JTWC best-track estimates.
c. Tropical Storm Maria (2011)
Finally, as an example of the initialization of a weak storm, the schemes are tested on Tropical Storm Maria (2011). Maria spent most of its life cycle as a tropical depression and tropical storm, although it briefly became a weak hurricane prior to making landfall in Newfoundland, Canada. Maria became a tropical depression at 1800 UTC 5 September, approximately 1300 km west-southwest of the Cape Verde Islands. From that point, Maria experienced large vertical wind shear for much of its life and often had little deep convection in its core (Brennan 2012).
The t = 1.5 h COAMPS-TC forecasts are shown for the different initialization schemes in comparison to H*Wind in Fig. 7 for Tropical Storm Maria at 1330 UTC 11 September. As in Fig. 4, the t = 1.5 h forecast is used as a proxy for the initial conditions so that it matches the H*Wind analysis time. Here, all initialization schemes produce too large of an outer wind field in comparison to H*Wind. The CNTL scheme has the most accurate inner-core wind structure, with the TCDI, DI, and TCDI/DI schemes having too large of an inner-core wind structure. All schemes obtain the wavenumber-1 asymmetry due to TC motion. Further examination of the intensity forecasts of the TCDI/DI scheme in comparison to the CNTL scheme and NHC best track for Maria are given in section 6.
5. Average intensity and track errors
To better understand the performance of each initialization scheme, testing was performed on a large sample of TCs from the 2010 and 2011 seasons in the North Atlantic and western North Pacific basins. Eleven storms were tested, comprising a total of 120 cases from the homogeneous sample at the initial lead time. The homogeneous samples were obtained at each lead time in order to compute the errors. The TCs and date ranges are listed in Table 1. To reduce correlated forecasts, only COAMPS-TC forecasts that are 12 h apart were used in the sample, even though the model runs with an update cycle of 6 h (four forecasts per day). An unequal variance two-tailed t test was performed for the intensity and track errors in order to assess whether or not the differences were statistically significant. The null hypothesis for the tests was that there is no difference between the average value of the given dynamic initialization scheme (either TCDI, DI, or TCDI/DI) and the CNTL scheme. A 95% confidence interval was used with a p value of 0.05 for the tests. In Figs. 8 and 9, an open black diamond at a given lead time indicates that there was a rejection of the null hypothesis, indicating a statistically significant difference at the 95% confidence level for the given lead time. Similarly, the lack of an open black diamond indicates that there was a failure to reject the null hypothesis, and therefore it cannot be said that there is any difference between either the dynamic initialization scheme or the CNTL scheme.
a. Track errors
The average track errors for each initialization scheme are given in Fig. 8. In Fig. 8a, the average track errors for the entire sample are presented. In Figs. 8b and 8c, respectively, the average track errors for intense and weak initializations are shown. In each plot, the solid line represents the total track error, the dotted line represents the along-track error, and the dashed line represents the cross-track error. For physical interpretation, along-track errors denote errors in TC translation velocity (either movement too slow or too fast), while cross-track errors denote errors in the perpendicular direction of the storm trajectory (such as recurvature too early). As shown in Fig. 8a, the track errors are similar at each lead time for each initialization scheme for the entire sample. At the later lead times, the TCDI scheme is shown to perform slightly better than the others, while at earlier lead times, the TCDI/DI scheme performs the best. Moving to the group of intense storms (Fig. 8b), the TCDI and TCDI/DI schemes perform slightly better, while for weak storms (Fig. 8c), the variance is not as significant between the different schemes. It should be noted here, however, that there are no statistically significant differences between each dynamic initialization scheme and the CNTL scheme with regard to the average track error. Therefore, in a statistical sense, all initialization schemes produce similar track errors. With regard to the along- and cross-track components, the TCDI scheme tends to generally produce smaller cross-track errors than the other groups, while both the TCDI/DI and TCDI schemes produced smaller along-track errors.
b. Intensity errors
The average intensity errors are given in Fig. 9. The intensity errors are given by both the maximum sustained surface wind (Fig. 9; left panels) and minimum central pressure (Fig. 9; right panels). In Fig. 9a, the average intensity errors are shown for the entire sample. In Figs. 9b and 9c, the average intensity errors are given for intense and weak initializations, respectively. In each panel, the solid lines denote the mean absolute intensity errors, and the dotted lines denote the biases (or mean error). In the wind plots (left panels), a positive bias signifies that on average the simulated TC was too intense (and vice versa). In the pressure plots (right panels), a positive bias signifies that on average the simulated TC was too weak (and vice versa). The zero line is marked in green.
In the left panel of Fig. 9a, it can be seen that by maximum sustained surface wind both the TCDI/DI and DI schemes have lower errors at the later lead times, while there is not as significant of a difference at the earlier lead times. In terms of biases, the TCDI/DI scheme has the best bias overall (closest to zero). In the right panel of Fig. 9b, the TCDI/DI scheme is shown to have the lowest errors at each lead time by minimum central pressure, with statistical significance at the earlier lead times (t = 0–30 h). The TCDI scheme has the lowest error in the early lead times, while the DI scheme has a lower error in the later lead times. The two-stage scheme (TCDI/DI) combines the benefits of each individual scheme and produces the lowest errors at each lead time. With regard to the initialization of intense storms (Fig. 9b), similar results are shown; however, the TCDI/DI scheme has further reduced errors over the CNTL scheme, with statistical significance at both the early and later lead times (t = 0–96 h). The differences are especially significant in the pressure plots (left panel of Fig. 9b). The TCDI/DI scheme has the best bias overall (left panel of Fig. 9b). For weak initializations (Fig. 9c), there are no statistically significant differences between each of the dynamic initialization schemes (TCDI, TCDI/DI, and DI) and the CNTL scheme. While not statistically significant, the CNTL scheme actually has lower errors than the others for weak storms.
c. Percent differences
In addition to the average mean absolute errors plotted versus lead time, the errors were also averaged over all lead times and percent differences were computed between each dynamic initialization scheme (TCDI, DI, and TCDI/DI) and the CNTL. The purpose of this is to determine the net effect of each dynamic initialization on either improving or degrading the CNTL performance. The percent differences in the mean absolute errors for maximum sustained wind, minimum central pressure, and track are given in Table 2, stratified by the initial intensity (as before; all cases, intense initializations, and weak initializations).
Examining all of the cases, the TCDI scheme slightly degrades the overall intensity error (+3.9% by wind and +5.7% by pressure) and reduces the overall track error (−7.8%). The DI scheme improves the overall intensity error (−5.0% by wind and −18.7% by pressure), and is neutral with regard to track (+0.8%). Finally, the TCDI/DI scheme improves the overall track and intensity (−13.5% by wind, −24.4% by pressure, and −5.6% by track). For intense initializations, the results are similar; however, the improvements in intensity by the TCDI/DI (−25.3% by wind and −39.0% by pressure) and DI (−7.0% by wind and −27.7% by pressure) schemes are more substantial. Finally, moving to the weak initializations, all of the dynamic initialization schemes perform slightly worse than the CNTL scheme with regard to track and intensity. One exception to this is TCDI, which even for weak initializations improved the track (−5.2%). The results in Table 2, along with the results presented in Figs. 8 and 9, demonstrate that TCDI/DI performed the best overall.
6. Further comparison of the CNTL and TCDI/DI schemes
Since the TCDI/DI scheme was shown to perform better than the other initialization schemes on average, further comparisons of this scheme with the CNTL scheme are given in this section in order to better understand the differences in the initial structure and track and intensity forecasts.
a. Azimuthal mean structure
In Fig. 10, side-by-side comparisons of the CNTL and TCDI/DI schemes are given for the initial conditions of Typhoon Ma-On (08W) at 0000 UTC 15 July. In Figs. 10a–c, the azimuthal mean tangential velocity, radial velocity, and perturbation temperature (deviation from the environment) are given, respectively. Recall from Fig. 6 that the CNTL scheme produced a vortex that was too weak for this case, while TCDI/DI was more consistent with the JTWC best-track estimate. This is further illustrated in the azimuthal mean structure at the initial time. Examining Fig. 10a, the TCDI/DI scheme produces a larger area of stronger tangential winds, with more significant vertical penetration to upper levels. Examining Fig. 10b, the region of maximum upper-level outflow is closer to the TC center for the TCDI/DI scheme in comparison to the CNTL scheme, there exists more radial inflow at middle levels (at approximately p = 400 hPa and r = 70 km), the boundary layer radial inflow is stronger (consistent with a more intense vortex), and the boundary layer thickness is smaller. In Fig. 10c, the level of the upper-level warm core is also significantly different between the two schemes. In the CNTL scheme, the upper-level warm-core maximum is at approximately p = 400 hPa, while in the TCDI/DI scheme, the maximum is at approximately p = 300 hPa and the magnitude is slightly larger than in the CNTL scheme. In each scheme, the location of the warm core is consistent with expectations from enforcing the vortex thermal wind balance upon the mean tangential velocity (Fig. 10a). The level of the maximum vertical gradient in the azimuthal mean tangential velocity is lower in the CNTL scheme than in the TCDI/DI scheme. While it is not possible to verify which azimuthal mean structure is closest to the observations, clearly the TCDI/DI scheme produces a more intense vortex consistent with the JTWC best-track estimate.
b. Intensity and track forecast comparisons
Comparisons of the forecasted COAMPS-TC intensity using the TCDI/DI scheme versus the CNTL scheme are given in Fig. 11. In Figs. 11a–d, comparisons are given for Typhoon Ma-On, Hurricane Katia (2011, 12L), Tropical Storm Maria (2011, 14L), and Hurricane Irene (2011, 09L), respectively. In each plot, the colored curves are individual COAMPS-TC forecasts, and the black curve is either the NHC or JTWC best-track estimate of the maximum sustained wind. For each curve, time is plotted relative to the time at the top of the figure, so that the colored and black curves can be directly compared at each time. For a set of perfect simulations, the colored curves would exactly overlap the black curve. In Fig. 11a, which is an example of TC with high intensity, the CNTL simulation suffers from significant spindown effects in the early part of many forecasts, while the TCDI/DI scheme does not. The spindowns in the CNTL scheme are most likely a result of the 3DVAR system not producing a TC in proper balance nor with a consistent secondary circulation. The TCDI/DI scheme does not suffer as much from the imbalance issue and, therefore, maintains the initial strong intensity, yielding more accurate intensity forecasts. In Fig. 11b, similar plots are shown for Hurricane Katia. Katia was generally a weak TC, but had a rapid intensification event. Here, both the CNTL and TCDI/DI schemes produce similar results. However, the TCDI/DI scheme is slightly better overall and better captures the rapid intensification event. In Fig. 11c, a comparison is shown for Tropical Storm Maria. Maria was a weak storm due to unfavorable environmental conditions (as stated earlier). Here, the CNTL scheme performs better than the TCDI/DI scheme overall, as the TCDI/DI scheme tends to overintensify Maria in many forecasts. This is likely a result of inserting a vertically aligned bogus vortex with TCDI, which is more primed to intensify. Clearly, the initialization of weaker TCs that may not be vertically aligned due to vertical shear or other unfavorable environmental conditions is a significant challenge. Finally, the comparison of the CNTL and TCDI/DI schemes for Hurricane Irene is given in Fig. 11d. While both series of forecasts are good, capturing the general weakening of Irene after 0000 UTC 25 August, the TCDI/DI scheme has less scatter and performs slightly better.
Track and intensity comparisons (by minimum central pressure) of the CNTL and TCDI/DI schemes are also given for Hurricane Earl (2010) and Hurricane Danielle (2010) in Figs. 12 and 13, both compared to the NHC best-track data. Examining Fig. 12, broadly, the track differences are not that significant between the two schemes (as evinced also by the average track errors in the previous section). The CNTL scheme has fewer forecasts that recurve too early for Hurricane Earl. On the other hand, for Hurricane Danielle, the TCDI/DI scheme has less scatter and fewer forecasts that recurve too early. For the intensity forecasts (Fig. 13), the initial central pressure in the CNTL scheme is generally too high in comparison to the NHC best-track estimate, resulting in forecasts that start too weakly. This is especially evident for Hurricane Earl (Fig. 13a), but also evident to some extent for Hurricane Danielle (Fig. 13b). With the TCDI/DI scheme, however, the initial pressure is much closer to the NHC best-track estimate, resulting in overall improved intensity forecasts for both TCs.
While a systematic evaluation of size has not been conducted on this sample, on a different sample of approximately 200 cases, the TCDI/DI scheme was shown to have a lower mean absolute error at the initial time than the CNTL scheme for the radii of 34-, 50-, and 64-kt winds. The TCDI/DI scheme had a larger error in the radius of maximum wind, presumably due to the 15-km horizontal resolution of the TCDI vortex library. At later lead times, the errors were similar, indicating that model physics exerts more control over the size at these later lead times.
Three different dynamic initialization schemes for tropical cyclone prediction in numerical models were designed and evaluated on a sample of real cases. The first scheme is a tropical cyclone dynamic initialization (TCDI) scheme, where the TC component is spun up in an independent three-dimensional primitive equation model and inserted into the forecast model initial conditions. The second scheme is a forward dynamic initialization (DI) scheme, where the forecast model is relaxed to the analyses' momentum in model space for a period of 12 h prior to the beginning of the forecast. The third scheme is a combination of the first two schemes, a two-stage dynamic initialization scheme (TCDI/DI). In the first stage, the TC component is dynamically initialized and inserted into the forecast model initial conditions (TCDI). In the second stage, the DI scheme is used to improve the balance between the TC and its environment. A systematic evaluation of each dynamic initialization scheme was performed versus a control (CNTL) scheme that uses a 3DVAR data assimilation system in conjunction with synthetic TC observations generated based upon intensity and structure estimates from the warning centers (a static initialization scheme). The evaluation was conducted using the Naval Research Laboratory's tropical cyclone prediction model: COAMPS-TC. The dynamic initialization schemes were shown to yield improved initial dynamic and thermodynamic balances over the CNTL scheme, and also to allow for improved model physics spinup prior to the start of the forecast integration.
By testing each initialization scheme on 120 real cases from both the North Atlantic and western North Pacific basins from 2010 to 2011, it was shown that TCDI/DI had the lowest average intensity errors overall, with even greater error reductions for intense storms. Averaging all lead times, the TCDI/DI scheme reduced the average minimum central pressure and maximum sustained wind errors over the CNTL scheme by 24.4% and 13.5%, respectively. When considering intense storms only, the TCDI/DI scheme reduced the average minimum central pressure and maximum sustained wind errors by 38.9% and 25.3%, respectively. For weak storms, the TCDI/DI scheme does not show better performance than the CNTL scheme. The average track errors were found to be similar for all initialization schemes. It was also shown through example cases that the three new dynamic initialization schemes produce realistic TC structures, with favorable comparisons to available wind structure analysis (H*Wind) at the initial time.
The two-stage dynamic initialization scheme can easily be applied to a TC forecast system, yielding improved initial balances of the TC and its environment and, subsequently, improved intensity forecasts. Future work will be devoted to the significant challenge of initializing weak storms, and better representation of vortices that are highly asymmetric due to unfavorable environmental conditions such as strong vertical wind shear. Additionally, work will be devoted to implementing relaxation to satellite-derived heating profiles in the DI step in order to improve the wind structure and asymmetries.
EH and MP acknowledge the support of the Chief of Naval Research through the NRL base program, PE 0601153N. We thank Drs. Jim Doyle and Rich Hodur for helpful discussions. This manuscript was improved by the constructive comments of two anonymous reviewers.
COAMPS is a registered trademark of the Naval Research Laboratory.
For TCs with a maximum sustained wind <23 m s−1, the 6° synthetic observations are not included.