1. Introduction
As one of its highest priorities, the Australian Bureau of Meteorology (BoM) issues tropical cyclone (TC) forecasts over its region of responsibility. On average, 10 TCs per year occur in the area, mostly between December and March. Further, in its capacity as a Regional Specialised Meteorological Centre (RSMC), the Darwin Forecast Office’s analysis domain extends into the northwest Pacific, where the frequency of tropical cyclogenesis is much higher at around 26 per year. To assist with the difficult task of analyzing and forecasting these often poorly observed, small-scale, but important weather systems, the new high-resolution, full physics numerical prediction system, the Tropical Cyclone Limited-Area Prediction System (TC-LAPS), with sophisticated vortex specification and initialization, has been developed for real-time operation. This paper describes the new forecasting system and evaluates its performance for a number of TC events in the Australian region.
The paucity of observational data over the tropical oceans often results in severe deficiencies in the analysis of TCs. Indeed without satellite cloud imagery, many TCs would likely go undetected. An example of the data network in the Australian region is illustrated in Fig. 1, which shows the observational network of mean sea level pressure, 500-hPa winds, and 500-hPa temperatures at 2300 UTC 15 March 1997. At this time TC Justin was located near 12°S and 156°E (black dot). The “holes” in the standard observing network to the southeast of New Guinea and to the south of Indonesia—areas often frequented by TCs (Neumann 1993)—are quite evident. We note, but do not illustrate, that at observing times 6, 12, and 18 h prior to that shown in Fig. 1, the distributions of surface pressure and wind observations were similar but sparser, and the only additional data available were satellite soundings at 0500 and 1700 UTC over the southwestern Pacific Ocean.1 Of particular concern for the quality of the objective analyses is the area east of New Guinea where the wind observation from Honiara (near 10°S, 160°E) was and is often the only wind observation available in this area and at this level for a 24-h period. Hence Fig. 1 highlights not only the data paucity, but also the critical importance of data assimilation procedures in preserving what information there is, and in defining the environment of the storm.
The introduction of satellite soundings, cloud drift winds, and scatterometer data have had positive impact on the analysis of the outer structure and environment of some tropical cyclones (e.g., LeMarshall et al. 1996). However, details of the inner core and vertical structure of tropical cyclones have so far not been usefully depicted by these data. The observational network cannot routinely define the location, intensity, and horizontal and vertical structure of the circulations—features that are necessary for consistent, skillful predictions. To improve real-time numerical forecasts, it is thus still necessary to insert synthetic circulations into initial conditions.
During the last 10 years, four developments in numerical forecast systems have resulted in large improvements in the real-time prediction of tropical cyclones: (i) increases in computing power have allowed the resolution of numerical forecast models to increase to a point where most TC circulations (and surrounding mesoscale weather features) can be reasonably well resolved, provided they are depicted in initial conditions;(ii) improvements in the depiction of the large-scale flow have resulted from advances in objective analysis techniques, particularly from the use of satellite soundings and cloud drift winds; (iii) improved parameterizations of physical processes such as convection, have reduced biases in track prediction; and (iv) results from observational and theoretical research have increased our understanding of the structure and motion of tropical cyclones and led to an improvement of vortex specification techniques (cf. Kurihara et al. 1993; Weber and Smith 1995). Through these developments, many operational centers are now successfully using routine vortex specification and reporting significant track prediction skill: for example, the United Kingdom Meteorological Office, Heming and Radford (1998); the Japan Meteorological Agency (JMA), Ueno (1989); the National Centers for Environmental Prediction, Surgi et al. (1998) and Kurihara et al. (1993, 1995, 1998); and BoM, Davidson et al. (1993). Interestingly, local verification based on manual interpretation of surface pressure charts suggests that even without vortex specification, the European Centre for Medium-Range Weather Forecasts (ECMWF) provides good-quality forecast guidance during tropical cyclone events beyond 36 h in the Australian region. However, the most significant improvements in recent years in tropical cyclone forecasting have undoubtedly come from the prediction system developed at the Geophysical Fluid Dynamics Laboratory (GFDL), described in Kurihara et al. (1993, 1995, 1998) and Bender et al. (1993). The demonstrated, large improvement in skill is evidence of the quality of the initialization procedures used in the GFDL system.
For the construction of TC-LAPS, we have tried to utilize each of the aspects listed under (i)–(iv) in the last paragraph. The major components of TC-LAPS may be summarized as follows: 1) data assimilation to define the environment and outer structure of the storm; 2) vortex enhancement to construct a synthetic vortex consistent with the observed location, size, intensity, and past motion of a TC; 3) high-resolution objective analysis to create an initial condition that includes the synthetic vortex; 4) diabatic, dynamic initialization to improve mass-wind balance of the vortex while incorporating satellite-observed convective asymmetries; and 5) numerical prediction of the storm with a high-resolution version of the operational limited-area model of the Australian Bureau of Meteorology.
The techniques used in the current work are similar to those of the GFDL, but they differ in four important ways: (i) the symmetric component is generated via a modified version of the typhoon enhancement scheme described in Davidson et al. (1993); (ii) the asymmetric flow is constructed such that the observed drift speed of the vortex equals the sum of the environmental and asymmetric flows2; (iii) synthetic observations, extracted from the idealized vortex, are merged with the standard observations and an optimum interpolation objective analysis is used to form the initial condition; and (iv) initialization, vortex balancing, and spin up is achieved via the diabatic, dynamical nudging scheme of Davidson and Puri (1992), which allows the vortex to adjust to the model resolution, dynamics, and physics, while incorporating information on the distribution of cloudiness.
The paper is organized as follows. Section 2 summarizes the data processing and numerical systems used. Section 3 describes the method of vortex specification. Section 4 presents detailed results for an individual case study; illustrates the performance for a number of interesting, difficult events; and benchmarks the skill level of the system against the official forecasts and against climatology-persistence forecasts [Australian region CLIPER, Morison and Woodcock (1998)]. Finally, section 5 presents a summary and conclusions and outlines possible future developments.
2. Data processing and numerical systems
The experiments described here have been carried out in a mode to simulate real-time conditions that could be expected if the forecasts were run at the Australian National Meteorological Operations Center (NMOC) of the BoM. In practice, the sequence of processing for a high-resolution, real-time prediction can be summarized as follows (note that details of individual components are described later in the section, following the overview).
Coarse-resolution data assimilation. Because the global analysis is not available at the base time of a forecast and is needed for the generation of synthetic TC data, an unbogussed, limited-area, coarse-resolution (0.75° long × 0.75° lat, 19 levels), 12-h data assimilation is performed over a large domain to obtain the outer structure and environment of the storm in question. The analyses generated in this way are interpolated onto the corresponding global (forecast) grid to produce essentially a “global” analysis.
Coarse-resolution vortex enhancement. Since the resolution of the global dataset (currently 2.5° lat × 2.5° long) is insufficient to define TCs on the grid, the vortex specification is run to generate synthetic observational data to be used by the objective analysis scheme, rather than to implant the vortex directly into the global analysis. The synthetic data extends out to large radii and on pressure levels corresponding with analysis sigma levels. With regard to subsequent objective analyses, this ensures a more accurate representation of the symmetric vortex, a preservation of the imposed asymmetries, a precise definition of vertical structure, and a cleaner merging of the vortex into its environment by the regional objective analysis. For the coarse mesh, vertical profiles of synthetic data are extracted over circles at radii every 200 km from the center, with eight observations per circle, out to a maximum radius of 1000 km.
Coarse-resolution data assimilation with synthetic vortex. The 12-h data assimilation is rerun with the synthetic data merged with the standard observational data, and a coarse-resolution forecast is made to 48 h.
High-resolution vortex enhancement. The vortex enhancement is rerun to generate high-resolution synthetic TC data, which are merged with the standard observational data. To define the large gradients in the mass field and winds in the vicinity of the radius of maximum wind, synthetic observations are extracted over circles at radii every 25 km from the center, with eight observations per circle, out to a maximum radius of 1000 km.
High-resolution objective analysis. Using the assimilated coarse-resolution, bogused analysis as first guess (to reduce the occurrence of data rejection by the quality control), a high-resolution analysis (the initial condition) is generated using univariate statistical interpolation. Similar procedures are used to generate analyses every 6 h over a 24-h period prior to the base time of the forecast.
Model initialization. The diabatic, dynamical nudging commences, with relaxation toward each analysis over the 24 h prior to the forecast base time. Satellite imagery, used to define the distribution of cloudiness, is updated every 6 h.
High-resolution prediction. A 48-h high-resolution forecast is carried out.
The global datasets used in this study are from the BoM’s operational Global Assimilation and Prediction System (Seaman et al. 1995; Bourke et al. 1995). The data assimilation is a standard, 6-h analysis–forecast cycle. The analysis method is multivariate statistical interpolation, the convective parameterization is the ECMWF’s mass flux scheme of Tiedtke (1989) and the boundary layer parameterization is based on an early version of the Louis scheme from the ECMWF. The parameterizations are documented in Hart et al. (1990).
The new prediction system TC-LAPS is based on the current operational limited-area assimilation and prediction system (LAPS) of the BoM, which is described in detail in Puri et al. (1998). Because of its close relationship with LAPS, we have adopted the acronym TC-LAPS for the forecast system described in this paper. Even with its early data cutoff and update of the boundaries from an earlier global forecast, objective verification indicates a skill level for operational LAPS very close to that of all major global forecast systems (NMOC Melbourne 1997). The assimilation component of LAPS and TC-LAPS is a standard 6-h analysis–forecast cycle. The analysis method is multivariate statistical interpolation. At high resolution, the analysis is made univariate (i.e., no coupling between the mass and wind increments) and is tuned with appropriate length scales and quality control tolerances to retain as much as possible the structure of the artificial vortex. To force the vortex into the objective analysis, it was found necessary to have two passes through the statistical interpolation. The output from the first pass is used as first guess for a second pass, which includes reduced length scale parameters to reproduce the observed intensity. The digital filter of Lynch and Huang (1992) is used for initialization. LAPS uses high-order numerics and advanced parameterizations of physical processes, including the mass flux convection scheme of Tiedtke (1989). For the experiments described here, analyses and forecasts have been doubly nested. The outer coarse-grid configuration is for the Australian Region domain 65°S–15°N, 65°–184°E with a resolution of 0.75° lat × 0.75° long and with 19 σ levels (σ = pressure/surface pressure). Global forecasts are used to provide boundary conditions for this outer grid. The inner domain is relocatable with 180 × 180 grid points, at a resolution of 0.15° lat × 0.15° long (approximately 15 km), and with 19 σ levels. The integration uses a time step of 20 s and the physical processes are computed every 3 min. Forecasts from the coarse, outer grid are used to provide boundary conditions for the inner grid. The nesting is one-way interactive. The boundaries are updated by linear interpolation in time from 6-hourly datasets. The topography is defined by a high-resolution (0.1°) dataset. For the present study, real-time sea surface temperature (SST) analyses, based on weekly collections of ship and satellite data (Smith 1995), and climatological soil moistures are used by the physical parameterizations.
A diabatic, dynamical nudging scheme (following Davidson and Puri 1992) is used for initialization of the forecast model. The method uses cloud imagery from Japan’s Geostationary Meteorological Satellite (GMS) to redefine the vertical motion field at the initial time of the forecast to be consistent with the observed distribution of cloudiness, while at the same time it preserves the analyzed vorticity and surface pressure field (by nudging). At the high resolution used here, only moderate nudging is required to retain these reliable components of the initial analysis. Relaxation coefficients are 0.75 × 107 m2 s−1 for vorticity and and 0.4 × 10−3 s−1 for surface pressure. As a simplistic interpretation, these coefficients correspond to approximately one part analysis to nine parts forecast. During nudging the parameterized convective heating is switched off, and at grid points where the cloud imagery indicates deep convection, a vertical heating profile is imposed. The strength and vertical extent of this heating is defined from satellite-observed cloud-top temperatures [see Davidson and Puri (1992) for details]. As a compensation for the forced heating, the model responds with cooling that is associated with adiabatic ascent. In this way, the vertical motion field is redefined to be consistent with the cloud imagery. The imposed vertical profile of heating (which defines the profile of vertical motion) is based upon budget studies (e.g., Frank and McBride 1989) from the Global Atlantic Tropical Experiment (GATE) and the Australian Monsoon Experiment (AMEX). The effectiveness of the technique in initializing the vortex and reducing erratic behavior during the early hours of the forecast is described in Davidson et al. (1993) and will be further illustrated in a later section. It is also worth noting here that at times, the initialization can modify the net steering flow imposed by the vortex enhancement procedure. Although this may seem to be undesirable, it can be particularly important during situations of recurvature, when the steering flow is possibly changing rapidly and the specified steering may be only representative for a very short time. As described in Davidson et al. (1993) and later here in section 4 for tropical cyclones Beti and Rewa, the initialization and forecast components seem capable of adjusting the vortex structure during these rapidly evolving events to alter the steering flow and allow the recurvature to proceed. However, determination of the reasons for this behavior requires further investigation.
The standard observational database used here, obtained in real time from the Global Telecommunications System, is the conventional data (surface synoptic and upper-air observations), plus satellite sounding retrievals, cloud drift winds from the JMA and aircraft reports. Because of the early run times of the regional prediction systems at the BoM, importance is placed on the use of local readout satellite temperature retrievals and cloud drift winds (Le Marshall et al. 1994a; Le Marshall et al. 1994b). Note that the former observation type are the high-density data illustrated in the bottom panel of Fig. 1. Synthetic moisture profiles obtained from GMS infrared imagery (Mills and Davidson 1987) have also been used to enhance the moisture analysis and provide some additional information on the asymmetries in cloudiness.
3. Vortex specification
The vortex-specification algorithm used for the forecast experiments described here is based on the methodology discussed in detail by Weber and Smith (1995). Since January 1996, the algorithm has been used with some success for track forecasting in the BoM’s operational LAPS at coarser resolution. It derived from an earlier modified version of the typhoon bogus scheme of the JMA, described in Ueno (1989) and Davidson et al. (1993).
Two independent datasets are used during the vortex-specification process: the first dataset contains “global” analyses (as defined in the previous section) of zonal and meridional wind, mean sea level pressure, geopotential height, temperature, and mixing ratio. The data is on 15 pressure levels (1000, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, and 10 hPa) in a geographical coordinate system with 2.5° horizontal resolution. The second dataset (a TC advisory produced in real time by the Darwin Regional Forecasting Centre) provides information on the structure and past motion of the TC in question. It includes estimates of (i) the current location of the storm and its position 6 and 12 h earlier—used to define the current drift speed of the vortex and its position at the initial time, (ii) the central sea level pressure as estimated from the Dvorak technique (Dvorak 1975)—used to specify the intensity, and (iii) the radius of the outermost closed isobar that is assumed to coincide approximately with the radius of gale-force winds—used to define the size of the storm. The second dataset is used for the construction of the synthetic vortex that is subsequently to be included in the initial high-resolution fields used in TC-LAPS. Note that in all experiments shown in the present study, actual real-time advisories—and not best-track information—have been used to construct the initial vortex. Note also that one further and important free parameter, the radius of maximum wind (RMW), is needed for the vortex specification. As this parameter is difficult to estimate, we have set the RMW constant and equal to 125 km. This is much larger than might be expected from observations. Shea and Gray (1973) indicate radii of maximum winds of near 40 km. However, it was found necessary to use the above value to maintain the observed central pressure at the 0.15° horizontal resolution. We anticipate that as we increase the horizontal resolution, a more realistic RMW can be used.
The objective analysis at any time is obtained using a series of 6-h forecasts and successive adjustments to the observed meteorological data (four-dimensional data assimilation), leading up to the base time of the forecast. Existence, size, and strength of a TC in the global data fields depend to a large extent on the representation of the TC in the observations provided by the meteorological station network. However, once a TC is represented by the observations, its misplacement in the global dataset is an artifact of the short-range forecasts performed during the assimilation, because the vortex starts to move away from its observed position in the course of a time integration of the forecast model. On many occasions, the global fields provided by the objective analysis thus contain a not necessarily weak but often misplaced atmospheric vortex. The vortex-specification procedure is designed to locate these mispositioned vortices, to eliminate them in a circular region of twice the radius of the outermost closed isobar and to retain as much as possible of their structure at larger radii. In this way, the vortex specification method guarantees a minimum of contamination of the initial fields used by the regional forecast in the vicinity of a TC and a maximum preservation of information in its farther environment. The elimination of spurious vortices is carried out using the fields of all meteorological variables provided by the objective analysis. Fields on pressure levels without a distinct vortex or fields on pressure levels at higher altitudes than the last level where a distinct vortex is found remain unchanged. It should also be noted that for each meteorological variable and each level, vortex specification is carried out independently, as the vortex center3 may vary with the variable and the level. The present vortex specification algorithm is capable of handling an arbitrary number of storms at any analysis time.
In the following paragraphs, the separate steps of the vortex specification procedure are discussed only briefly and exemplified by Figs. 2 and 3, showing the fields of geopotential height on the 850-hPa surface for the case of TC Beti on 25 March 1996 2300 UTC. A detailed description of the vortex specification method is given in the appendix.
The general concept of the method is based on an arbitrary partitioning of all global meteorological fields F provided by the objective analysis on all mandatory pressure levels (cf. Weber and Smith 1995; see also Kurihara et al. 1993). An example of a global field is shown in Fig. 2a. In view of the discussion earlier in this section it should be noted that the vortex center is displaced from the satellite-observed location (indicated by the crosshairs). Each field F is partitioned into an environmental component FE and a vortex component FV such that F = FE + FV (see Table 1 for all definitions used in this section). The environmental and vortex components are further subpartitioned into FE = FEL + FES and FV = FVS + FVA, where FEL represents features of larger horizontal scale than the horizontal scale of the TC (defined by the radius of the outermost closed isobar in the TC advisory), FES represents features of approximately the same or smaller horizontal scale than the scale of the TC, FVS represents the mispositioned radially symmetric vortex, and FVA the azimuthal asymmetric contributions4 relative to the mispositioned vortex center. The above partitioning approach for FV is applied only to the wind components, the mean sea level pressure and the geopotential height. An extraction of temperature and mixing ratio asymmetries is not necessary, because the thermodynamic fields are strongly modified by dynamical nudging during the further initialization of TC-LAPS.
The large-scale environment FEL is extracted using a modified Barnes’ scheme in combination with a low-pass filter (Barnes 1964; Weber and Smith 1995, pp. 637f). An example of FEL is shown in Fig. 2b. Subtraction of FEL from the original field yields the residual field FR (Fig. 2c; cf. also Kurihara et al. 1993). After an accurate location of the mispositioned vortex center in FR, the residual field is subjected to an azimuthal Fourier analysis about this center and the mispositioned symmetric vortex FVS and its asymmetric contribution FVA (illustrated in Figs. 2d and 2e, respectively) are processed. Subtraction of FVS and FVA from FR results in the field FES, which is added subsequently to FEL to form the total environment FE as shown in the example of Fig. 2f. Note that FE includes also features of the same or smaller horizontal scale than the scale of the symmetric vortex. In an effort to retain a maximum amount of the original information present in the global analysis and based on the assumption that the storm is well resolved in the global analysis at large radii, FVS is stored for a later combination with the synthetic symmetric vortex constructed from the TC advisory. In contrast, FVA is regarded as being mainly a numerical artifact produced by a moving vortex during the short-range forecasts of the assimilation process and therefore not saved for further use.
The construction of the symmetric synthetic vortex FBS uses the information provided by the operational TC advisory and is based originally on the vortex enhancement scheme of the JMA used in the earlier version of LAPS (Davidson et al. 1993). To retain as much information as possible in the fields used for the initialization of TC-LAPS, FBS is merged smoothly with FVS at radii greater than the radius of maximum tangential wind speed on each pressure level. Figure 3a shows an example of the final synthetic symmetric vortex FBO resulting from the combination of FBS and FVS and should be compared with FVS shown in Fig. 2d. The azimuthal wavenumber one vorticity5 asymmetry ζBA is constructed by application of the lowest-order analytical theory of vortex motion of Smith and Ulrich (1990), Smith (1991), and Smith and Weber (1993) to FBO on each mandatory pressure level. The computation and adjustment of ζBA is based on the assumption that the “vortex-induced” cross-vortex flow cBA, computed by radial integration of the wavenumber one contributions to ζBA, matches the vector difference between the observed drift speed c and the environmental flow across the vortex center cE. The latter is interpolated from the total environmental zonal and meridional wind components. In contrast to Ross and Kurihara (1992) and Kurihara et al. (1993), ζBA resembles a β gyre of barotropic theory (see, e.g., Fiorino and Elsberry 1989) only in the cases where the vector difference c − cE has a northwestward/southwestward orientation in the Northern/Southern Hemisphere. In all other cases, the vorticity asymmetries are used exclusively for an adjustment of the initial motion of the model storm to the observed drift of a storm in question. Note that unlike Mathur and Shapiro (1992), the flow asymmetries are computed separately for each particular symmetric vortex profile FBO on any given mandatory pressure level by radial integration of the wavenumber one contributions to relative vorticity (cf. also Kurihara et al. 1993, pp. 2035f). Geopotential height asymmetries, as shown for example in Fig. 3b (cf. Fig. 2e), are produced by the solution of a wavenumber truncated divergence equation with zero tendency.
In the final step of vortex specification, an output field FO is combined from FE, FBO, and FBA on each pressure level and the original global objective analysis F is replaced by FO. An example of FO is shown in Fig. 3c and should be compared with the original field of Fig. 2a. Note that, as well as relocating and smoothly implanting a more intense circulation, the structure of the field at large radii is mostly conserved. The output field FO is also used to generate a high-resolution dataset with artificial observations in a cylindrical coordinate system to ensure that the finescale structure of the fields produced by the vortex specification scheme is well represented in the high-resolution fields used for the initialization of the regional forecast model.
4. Results
The new prediction system has been tested on 17 base date-times for 13 different TCs. In consultation with operational forecasters, events have been selected on the basis of degree of difficulty, documented forecast failures, and events of particular meteorological significance. The events represent a broad spectrum of TCs with different characteristics, including small and large storms, intensifying and weakening storms, slow- and fast-moving systems, and recurving storms. We note here that for two of the earlier storms (Rewa and Bobby), global forecasts were not available so global analyses were used to nest the outer coarse-mesh forecasts. Because of the very large size of the coarse-resolution domain, we believe that this only very marginally improves the results from the numerical system for these storms. We will first present a case study of TC Beti to illustrate some structural details and forecast sensitivities, then show selected examples of a number of other interesting and difficult cases. Finally, we present general statistics on track and central pressure errors, and benchmark the skill level of the new prediction system against the official forecasts and CLIPER. Unfortunately, formal verifications of other numerical forecasts are not yet routinely performed at BoM. For this reason, model intercomparisons are not available.
a. Case study of TC Beti
Beti developed in the southwest Pacific and tracked west-southwest to be located north of New Caledonia at 2300 UTC, 25 March 1996. Just prior to this time it abruptly changed direction and began moving to the south-southeast. Numerical guidance available at the time was generally conflicting (see LeMarshall et al. 1996), with some forecasts maintaining the westward movement and others suggesting recurvature. Observed and forecast tracks and central pressure information obtained from TC-LAPS are shown in Fig. 4. Although the prediction began to deteriorate by 48 h, the forecast shows substantial skill in predicting the track and useful skill for central pressure. The official forecast was also skillful and maintained the direction change in the track. However, it did not adequately account for the observed southeastward acceleration. CLIPER, which can be a little slow to respond to changes in direction of movement, forecast the storm to move to the southwest at constant speed. An encouraging aspect of the new numerical forecast is the behavior of central pressure, which, besides being smoothly varying (see later discussion), is also in reasonable agreement with the estimated pressures, at least during the early part of the forecast. However, it should be kept in mind that considerable uncertainty exists regarding the actual central pressure, which affects both the initial condition and the verification. Central pressure is essentially estimated by interpretation of satellite cloud imagery and based on the Dvorak technique (Dvorak 1975), which, besides being difficult to apply when the eye is not clearly identifiable, may be quite inappropriate for the Australian region.
Figure 5 shows mean sea level pressure fields of the initial condition, and the 24- and 48-h forecasts. First, we note that the TC advisory at this base time for Beti, obtained via Darwin RSMC, indicated a central pressure of 960 hPa and a radius of outer closed isobar of 400 km. Note that after the initialization these estimates are extremely well preserved. For other storms, this was generally but not always the case. There were two cases where the initialization was not able to maintain the observed central pressure estimates, although the size was always conserved (see, e.g., the later discussion on TC Chloe). Second, it can be seen that the size and intensity are preserved during the forecast even though the forecast central pressure decreased to approximately 950 hPa. Finally, the forecasts of the surface pressure field display very little short wavelength noise and highlight the very stable character of the initialization and forecast modules, even for high wind speeds at high resolution.
Figure 6a shows time series of observed and forecast central pressures, and forecast maximum low-level winds, obtained from the forecast data at 3-hourly intervals. Note first that the forecast minimum central pressure is about 950 hPa, which occurs about 6 h after the winds peak at around 60 m s−1. Even though Beti was an intense storm, the behavior of the forecast central pressure is quite smoothly varying—even during the early hours of the forecast—suggesting that the diabatic, dynamical nudging is adequately initializing the vortex. There is reasonable consistency between the estimates and forecasts of intensity, particularly during the first 18 h, although there are clearly timing and magnitude differences in the later period. Figure 6b is similar to Fig. 6a but for a “cold start” forecast with no diabatic, dynamical nudging and using the digital filter for initialization. The erratic behavior, indicated by the sharp increase in central pressure during the early hours of the forecast, is clearly evident. In this case, the impact on the forecast track (not illustrated) was not significant;however, there have been other instances when the track forecast was also seriously degraded without the nudging initialization. To further illustrate the impact of the initialization, Fig. 7 shows 400-hPa vertical motion fields (a) after nudging and (b) after initialization of the base time objective analysis by the digital filter. The differences are large, with virtually no vertical motion in (b), and significant ascent in rainbands in (a). The adjustment as the vertical motion develops from a cold start forecast is one reason for the erratic behavior of the surface pressure field shown in Fig. 6b. Other factors are described below.
Figure 8 shows north–south cross-sections of zonal wind and temperature through the storm center after nudging, and difference fields between the initialized and uninitialized analyses of zonal wind and temperature. Note first that the wind field after initialization still displays the characteristic structure of a TC, with maximum winds at low levels in agreement with the warm core structure, and an anticyclone aloft. The characteristic structure of a tropical cyclone is also evident in the temperature field. This indicates that the nudging makes only moderate adjustments to these key features and preserves the essential structure of the vortex. The smooth merging of the vortex into the large-scale flow is also clearly evident. The changes in the wind field produced by the initialization (Fig. 8c) are of the order of 5 m s−1 at low levels and certainly within the error limits of the synthetic data and objective analysis. At high levels the changes are much larger and consistent with the temperature adjustments (Fig. 8d), which are also substantial.
The erratic behavior of the central pressure and the adjustments that the model makes to the bogused vortex structure during the early hours of a forecast without careful initialization indicate that the balance implied by the vortex enhancement (essentially gradient wind balance) is not the balanced state that the model prefers. One aspect is that the divergent circulations are initially nonexistent (Fig. 7b). Moreover, in an environment with a boundary layer, heating and momentum mixing by convection, this structure is unrealistic and exacerbates the spinup problem. As we do not know exactly what balance is required, we allow the model to define its own balance within certain constraints. During nudging, the rotational flows and the surface pressure (which we think are more reliably known) are constrained to the analyzed values, while the divergent circulations are allowed to develop in a manner consistent with the resolution and physics. Even though the vortex specification creates a circulation in gradient wind balance, no attempt is made to preserve this during initialization. The model’s dynamics and physics are used to define the balance (or imbalance). The changes illustrated here emphasize the importance of the initialization in balancing the vortex prior to the start of the forecast. Without this, the adjustments would necessarily occur during the forecast, with subsequent negative effects on the ensuing prediction. Further, although the imposed convective heating is empirically based, it never reaches an amplitude where the hydrostatic approximation is breached.
The imposed RMW of 125 km is clearly evident in Fig. 8. As suggested by an anonymous reviewer, the use of a relatively large RMW at the 0.15° resolution allows useful prediction of the central pressure despite the limitations of this resolution. Interestingly, the use of a relatively large RMW does not adversely affect the predicted storm size.
b. Case studies of significant events
Figure 9 shows forecast and observed tracks and central pressures for six events in the Australian region. Except for TC Justin, observed characteristics (central pressure, size, location) are all real-time estimates, which may of course differ significantly from postanalysis estimates. However, since the specification of TCs is based on operational locations and intensities, it is reasonable to verify on the same data. The cases shown include both very skillful and poor forecasts and have been chosen to illustrate some of the idiosyncrasies of the system.
1) Tropical Cyclone Rachel
Rachel (upper-left panel of Fig. 9) was a small, moderately intense storm that was moving west-southwest at the base time of the forecast. Real-time numerical guidance was suggesting that the storm would maintain this direction of motion and not make landfall. Indeed this tendency was reflected in the official forecast. Instead, Rachel changed course to the south-southwest and made landfall some 30 h after the base time of the forecast. The forecast failure is documented in Foley (1997), who shows examples of the forecast guidance and describes the difficulties of this and the TC Bobby event.6 The CLIPER forecast for TC Rachel provided very useful guidance and indicated landfall close to the observed location but some 12 h later than it actually occurred.
The TC-LAPS forecast for Rachel is remarkably skillful, particularly with regard to timing and location of the landfall, and to some extent also with the intensity. More investigations are required to diagnose the cause of the differences between all numerical forecasts discussed above. However, it seems that large pressure falls and development of a secondary low pressure system were occurring near the westernmost tip of Western Australia, in association with an approaching upper trough. We speculate that without the necessary intensity and balance of the circulation of the TC in the initial condition and without the resolution needed to maintain the Rachel circulation, the secondary development would have dominated the forecast and led to an apparent forecast movement to the west-southwest in the coarser-resolution forecasts. Indeed the limited-area, coarse-resolution forecast in which the high-resolution prediction is nested produced similar behavior to this.
2) Tropical Cyclone Justin
The complete life history of TC Justin is documented by Callaghan (1998). It underwent numerous track and intensity changes during its life and had periods when it became extremely difficult to forecast. The top-right panel in Fig. 9 shows the observed and forecast tracks and central pressures from a base time of 1100 UTC 14 March 1997. From this base time and of the four global forecast systems available in real time, one was indicating acceleration to the west, one was suggesting acceleration to the east, and the remaining two were forecasting steady motion to the south (see Callaghan 1998). What happened instead was initially a very slow movement to the eastnortheast and then a sharp recurvature back to the southwest. These trends in speed and direction were quite well captured by CLIPER, which predicted motion to the east and later to the southeast. Despite the conflicting guidance, the official forecast also displayed some skill and suggested very slow movement to the south. The forecast of TC-LAPS displays very encouraging skill at foreshadowing the observed changes, and in absolute terms is vastly superior to all numerical guidance that was available in real time.
Callaghan (1998) indicates that TC Justin at this time was located in the monsoon trough with strong westerlies on its equatorward side and strong easterlies to the south. In such an environment, it is perhaps not surprising that there would be considerable variance in the forecast behavior, depending on the analyzed structure and strength of the surrounding flow. The reason for the improved forecast from TC-LAPS appears to lie in the ability of the vortex specification to accurately locate the circulation within the large-scale environment, and to adjust the net steering (environment plus asymmetries) to be consistent with the observed (in this case slow) movement. The initialization was also found to be important in reducing erratic track behavior during the early hours of the forecast (not illustrated).
3) Tropical Cyclone Ethel
At the base time of the forecast, TC Ethel (middle-left panel in Fig. 9) was located in the Gulf of Carpentaria, which is nearly an inland sea between New Guinea (and its high mountains) to the north and the (heated) Australian continent to the south. It is our experience that because Gulf storms exist at low latitudes, can be small, and are influenced by local topographic effects, they are often difficult to forecast. At the base time considered here, most real-time guidance was indicating that Ethel would move rapidly to the east. In fact the storm moved at a steady speed to the east and then began a sharp 180° turn to the west. In the diagram, this turn has just commenced at the final 48-h verification time. The official forecast showed considerable skill but did not indicate the turn toward the south after about 24 h. On the other hand, CLIPER, which also provided useful forecast guidance, began the turn to the south too soon and indicated movement that was a little slower than observed.
The numerical forecast displays outstanding skill in predicting both track and intensity of TC Ethel. Although the storm was of minimal strength, it is encouraging that the prediction did not produce excessive or spurious intensification or weakening.
4) Tropical Cyclone Rewa
Prior to and at the base time of the forecast, TC Rewa (middle-right panel of Fig. 9) was moving steadily westward toward the Queensland coast. It had given no indication of slowing or weakening. Indeed the operational forecasts reflected these tendencies and incorrectly maintained the westward movement. In contrast to that, the storm recurved rapidly to the eastsoutheast from this base time and did not make landfall. The degree of difficulty of this forecast is naturally very high.
The forecast of TC-LAPS gives strong indications of the recurvature but does not adequately capture the severity of the turn. Because the prediction is for landfall by 36 h, the intensity forecasts are, of course, not useful in this case. For this situation, CLIPER predicted the recurvature much too slowly, and the forecast was for landfall at 24 h.
5) Tropical Cyclone Chloe
Chloe (bottom-left panel in Fig. 9) was a small, intense storm located off the northwest coast of Australia. During the forecast period it intensified rapidly just prior to landfall. Although its track was not particularly unusual, the challenge was to not only forecast the track accurately, but to maintain the intensity, and possibly forecast the intensity changes, of the small storm during the forecast.
Forecasts of the track and intensity are encouraging. There are clearly amplitude and phase errors between the observed and forecast intensities, but given the uncertainty in the estimates of intensity, the forecasted trends seem acceptable. Interestingly, the intensification near landfall is similar to that discussed in Li et al. (1997). They describe the development of a coastal outer cloud band that is associated with frictional changes, as the outer circulation of a typhoon impinges on a coastline. As the cloud band wraps into the center, the central pressure deepens.
This case illustrates two interrelated deficiencies in the prediction system. First, at the resolution used in TC-LAPS, the model does not seem capable of retaining the intensity of small and intense storms. Estimates and initialized values of central pressure at the base time of the forecast were 955 and 970 hPa. The radius of the outer closed isobar, which is generally preserved during initialization, was 300 km. It is planned to use higher resolutions to alleviate these problems. Second, a deficiency in this and two other forecasts is the slight increase in size of the circulation during the prediction, which seems a common feature of many high-resolution simulations and forecasts (Ooyama 1969). The size appears to not only affect the motion via the β effect, but also the intensity change through the timing of interactions with surrounding weather systems (e.g., midlatitude troughs). The origin of the size-intensity issue in the forecasts is currently under investigation.
6) Tropical Cyclone Celeste
The worst forecast we have obtained so far is for TC Celeste, which was a very small storm that developed close to the northeast coast of Australia and then moved eastward. Figure 9 (bottom-right panel) illustrates these characteristics and the poor forecast produced by TC-LAPS. The official forecast and CLIPER were a little more skillful, moving the system slowly to the southeast, but still had very significant errors by 48 h. The reasons for the large errors is the subject of ongoing investigations. However, we note the following factors contributing to the errors: at the base time of the forecast, Celeste was of minimal strength (only 17 m s−1) and just named. Its location and intensity at forecast time and during the previous 12 h was difficult to estimate. Since it developed near to coastal observations, unbogused analyses may be expected to be quite reliable and they indicate structures (particularly in the vertical) that were not consistent with the synthetically specified structures. Further investigations suggest that the storm was not particularly well-developed in the vertical at this time, and that secondary development may have occurred to its east, in which the initial circulation at low levels dissipated and a new circulation became dominant. The lack of vertical alignment, and redevelopment of a low-level circulation below regions of upper-level forcing or a midlevel vortex during the early stages of formation is not an uncommon problem for forecasters (M. M. Williams 1998, personal communication; Davidson et al. 1990). For Celeste, it would suggest eastward movement. Under these circumstances, insertion of a synthetic vortex may have been wrong and may have caused a degradation in the forecast. Indeed forecasts from an “unbogused” initial condition, although inadequate for intensity, show improved skill for track.
The case of TC Celeste emphasizes the difficulties with minimal strength and recently named storms. We are currently working on assimilating the satellite cloud imagery to try to alleviate these sorts of problems.
c. Systematic behavior of predictions
Although our sample of predictions is not large, it is still instructive to describe the systematic behavior for track and intensity forecasts. Errors from TC-LAPS have been compared with the official forecasts and with those from CLIPER. Issue times of official forecasts sometimes differed from the base times for TC-LAPS by up to 2 h and thus some time interpolation was required. Also lead times of official forecasts only extend to the time of forecast landfall, and so in three forecasts we have taken the liberty of extrapolating the trend in official forecasts. However, we have attempted to bias the forecast track toward the observed track in these cases in an effort to avoid any subjective degradation in the official forecasts. The Australian version of CLIPER is described in Morison and Woodcock (1998). This system requires the track of a tropical cyclone for the 24 h preceding the base time of the forecast. For Celeste and Warren the track was only available for the preceding 12 h and so we have subjectively extrapolated the track backward using persistence and trends in the observed track for these two cases. Again, in these cases, we have attempted to produce an optimum forecast from CLIPER by tuning the observed, preforecast track.
For all tropical cyclones investigated, Fig. 10 shows the track errors from TC-LAPS between 0 and 48 h at 12-hourly intervals. The highlighted curve defines the mean errors at each time. The diagram should be viewed as a scatterplot and shows that most of the forecasts are extremely skillful and there are only a few poor forecasts that adversely affect the verification statistics. In absolute terms, the skill in track prediction is clearly evident and even with the large errors associated with Celeste and one of the Justin forecasts, mean errors at each validity time of 16, 80, 115, 163, and 259 km are very promising. As indicated previously, these cases represent a broad spectrum of difficult and significant situations, and thus a particularly encouraging aspect of the forecasts is the consistent performance for a variety of storms with different characteristics. However, the large errors in 3 of 17 forecasts are reminders that poor forecasts are possible, should be expected, and that further work is needed to analyze and understand the forecast failures.
Mean track errors in the official forecasts, from the CLIPER system and from TC-LAPS, verified against real-time locations, are shown in Table 2. Track predictions from TC-LAPS are clearly superior to both CLIPER and the official forecasts. The degree of difficulty of the sample of chosen forecasts is evident from the CLIPER performance, which indicates mean errors approximately 20% larger than those described in Morison and Woodcock (1998) for tests on independent data. Verification of TC-LAPS against best tracks after postanalysis indicates only small differences from the statistics in the table. Interestingly, the errors are slightly smaller at all times except t = 0 and t = 48 h. Furthermore, it is important to note that the results from TC-LAPS are retrospective and, for a variety of reasons (e.g., the use of late observations in the analysis), actual real-time forecasts tend to be not as good. However, since the cases selected for testing were specifically chosen for their high degree of difficulty, we are confident that the high standard of prediction will be maintained during operational running.
Figure 11 shows, for the 17 forecasts, absolute central pressure errors every 12 h out to 48 h. Also shown are the mean (observation-forecast) errors, the rms errors, and the rms errors for persistence forecasts. We repeat that there are considerable uncertainties in central pressure estimates that affect both the initial intensity of the specified vortex and the verification. However, even with these uncertainties, the forecasts of central pressure are encouraging. The mean error is close to zero at each verification time, indicating that there is no bias in the predictions to overintensify or weaken the circulations. However, the spread of errors is rather large and a larger sample of forecasts is required to confirm the above finding. The rms errors at each time are approximately 10 hPa and thus within the error bars of the estimates. Individual differences can, however, be of the order of 20 hPa. For these relatively few cases, TC-LAPS forecasts of central pressure show a skill level comparable to persistence out to 24 h, and small improvements over persistence beyond that time. This represents useful forecast guidance on intensity change.
5. Summary and conclusions
A high-resolution prediction system for tropical cyclones has been described. The vortex-specification, assimilation, initialization, and prediction components can be summarized as follows:
Based on observational and theoretical studies of the structure and motion of TCs, synthetic data are generated at any desired resolution to define a storm’s circulation. The method uses the storm’s observed location, intensity, size, and past motion to construct a synthetic vortex and involves the definition of an environmental flow by filtering of the symmetric and wavenumber one components of the TC circulation in the (old) objective analysis, the generation of a new symmetric vortex that is merged with the old symmetric vortex at outer radii, and the construction of vortex asymmetries by requiring that the observed motion equals the environmental plus the asymmetric flow.
At first a 12-h collection of the standard observational data (satellite and conventional), is assimilated at coarse resolution without the synthetic data, using multivariate statistical interpolation and a 6-h analysis–forecast cycle. The analyses thus formed define the environment and outer structure of the misplaced storm, and are used in the generation of the synthetic observations. The 12-h assimilation, using the synthetic plus standard observational data, is then rerun and a 48-h forecast is made at coarse resolution, providing the lateral boundary conditions for the high-resolution prediction.
Objective analyses from the data assimilation are used as first guesses for the high-resolution analyses of a given storm and its environment. The database for these analyses include the standard observational network and sufficient synthetic data to define the storm’s “core” and asymmetric flow. Initialization for fine-mesh prediction consists of 24 h of diabatic, dynamical nudging through 6-hourly, high-resolution objective analyses. During this phase, the vertical component of vorticity and surface pressure fields are preserved, while infrared satellite cloud imagery is used to reconstruct the moisture and vertical motion field in accordance with the observed distribution of cloudiness. This procedure initializes and balances the vortex. It has been demonstrated here and elsewhere (Davidson et al. 1993; Kurihara et al. 1993) that a careful initialization is required to reduce erratic track, intensity, and structure behavior during the early hours of the forecast.
The prediction model is a high-resolution version of the operational limited-area model of the Australian Bureau of Meteorology and utilizes high-order numerics and advanced physical parameterizations including a mass flux convection scheme. The fine-mesh forecast is one-way nested in the coarse mesh prediction.
A number of unresolved issues and ongoing research projects remain. Presently, efforts are being made to improve the general performance of the operational vortex enhancement procedure. The objective is to develop an expert system based on the performance in various experimental situations, with special attention on major forecast failures. The modifications include, inter alia, a more rigorous algorithm to test for vortex existence on each mandatory pressure level of the global datasets, the use of the extended analytical theory of Smith and Weber (1993) to generate wavenumber one vorticity asymmetries, and further restrictions on the depth and extent of the implanted asymmetries. Furthermore, it is planned that, in cases of slowly or erratically moving storms or in cases where the environmentally induced flow at the satellite-fixed center matches approximately the observed drift speed, no synthetic asymmetries are included. Additionally, if the asymmetry is directed to the northwest/southwest in the case of a TC in the Northern/Southern Hemisphere, β gyres will be implanted instead of the asymmetries used in the present study. Some of these refinements to the construction of the idealized vortex are currently being tested with some success on some of the forecast failures described above.
It has been found that the quality of the coarse- and fine-resolution objective analyses are of critical importance to the accurate prediction of storm behavior. The development of techniques to enhance the use of satellite radiance data, water vapor and cloud drift winds, scatterometer data, and infrared and visible cloud imagery within the data assimilation system are of high priority. Since these experiments were conducted, the BoM has acquired a significant upgrade to its supercomputing capacity. We hope to increase the horizontal and vertical resolution, the domain size, and the forecast lead time to 72 h in the near future. We expect improvements in intensity forecasts for small, intense storms and possibly increased skill of longer duration predictions, which in the current configuration sometimes have the storm near to a boundary. The experiments described in the present study use SST analyses based on weekly collections of observations, whereas now daily regional SST analyses are available. We anticipate that the use of this data will also have a positive impact on the forecasts of intensity. Upgrades to our derivation of GMS moisture and cloud-top temperature data have recently been implemented (C. W. Tingwell 1998, personal communication). This will allow the use of satellite imagery during the initialization at the horizontal resolution of the model and at a minimum of 1-hourly intervals. As part of the general development of LAPS, improved parameterizations of the planetary boundary layer and the implementation of explicit moist physics are likely new developments that we believe will be beneficial to the forecasting of TCs in the future. The validation of forecasts and simulated structure change from high-quality observational datasets also will have priority. In the longer term, we hope to assess the value of coupling an ocean model to improve intensity forecasting. Even in its current form, the data archive of TC forecasts contains many interesting examples of structure and intensity change that we hope to exploit for clues to the associated physical mechanisms. Indeed, recent prediction studies on TC Katrina (January 1998)—a long-lived storm, which underwent a number of intensity variations—indicate the forecast system has useful skill at predicting such variations. Detailed diagnostic studies are planned. Finally, we hope to test the new system in real time over the northwest Pacific and Australian TC basins during 1999. Results from these trials will be reported on elsewhere.
Acknowledgments
This rather major undertaking could not have been attempted without the excellent work on the base LAPS system by Kamal Puri, Graham Mills, and Peter Steinle of BMRC. Frank Woodcock, also of BMRC, provided much of the motivation and encouragement during the course of the project, and also kindly provided us with the CLIPER forecasts. Thoughtful comments from John LeMarshall of BMRC on an early version of the manuscript clarified many issues. Input and provision of data from the following forecasters was invaluable: Gary Foley (Perth), Jeff Callaghan (Brisbane), Gordon Jackson (Darwin), and Alipate Waqaicelua (Fiji). Jon Gill from the BoM’s Services Policy Branch provided us with expert guidance on selection of cases, TC track data, and operational forecasts. Work on this project by H. C. Weber was funded by the Office of Naval Research through Grant No. N00014-95-1-0394. Finally, we would like to sincerely thank the three anonymous reviewers for their assistance and valuable suggestions.
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APPENDIX
The Vortex-Specification Method
On each mandatory pressure level, any given meteorological variable F is partitioned arbitrarily into an environmental component FE and a vortex component FV such that F = FE + FV. The two contributions to F are further subpartitioned according to FE = FEL + FES and FV = FVS + FVA. All definitions used in the appendix are identical with those used in section 3 and summarized in Table 1.
The large-scale field FEL is computed iteratively on each pressure level, using a modified Barnes scheme (Barnes 1964; Weber and Smith 1995, pp. 637f) in combination with a low-pass filter defined by a one-dimensional fast Fourier transform (Press et al. 1986, pp. 495ff). The filter is designed to extract waves with wavelengths greater than a given truncation wavelength. With regard to the particular filter characteristics and as a consequence of the convergence of the meridians in the geographical coordinate system,7 a new, large domain is defined in an equidistant Cartesian coordinate system within the global geographical grid system. The new domain is centered at the satellite-fixed vortex center and has a horizontal size of 7000 km × 7000 km, with a horizontal grid size of 250 km.
Distances of grid points from the satellite-fixed center in the geographical coordinate system are measured using spherical geometry and the dependent variables are interpolated to the new grid by birational interpolation (Späth 1991) as explained in Weber and Smith (1995, p. 636). The filter is applied alternately to all row and column vectors of F in the Cartesian coordinate system. In practice and with regard to the particular characteristics of the Barnes method, the truncation wavelength is chosen to be 15 times the radius of the outermost closed isobar up to a maximum value of 3500 km, to obtain an FEL that varies smoothly over the area covered by the vortex in question. However, the iterative Barnes algorithm does not sharply eliminate all waves of shorter wavelengths than the truncation wavelength, it rather produces a spectrum of waves of longer and shorter wavelengths that smoothly decrease in magnitude with decreasing wavelength. Therefore, to avoid the occurrence of patterns of smaller wavelengths or even artifacts of the vortex itself in FEL and to improve the performance of the Barnes method, it was found necessary to smooth the fields in a square, vortex-centered domain of 1500-km side length prior to the application of the Barnes method. The final field FEL (cf. Fig. 2b) forms a smooth and slowly varying background and guarantees that, after its subtraction from the original field and its storage for further use, the remaining residual field FR = F − FEL (Fig. 2c) is free of large-scale patterns that would possibly contaminate the azimuthal Fourier analysis of FR described below. After the extraction of FEL, all fields involved in the iteration process are reinterpolated to the geographical grid in the same way as before.
Prior to an azimuthal analysis of FR, the mislocated vortex center must be found in FR with adequate precision. The center-search has to be carried out separately for each dependent variable and on each level in order to avoid the spurious occurrence of an apparent mode of azimuthal wavenumber one (cf. Weber and Smith 1995). On the 1000-hPa level, the procedure to locate the vortex center uses the satellite-fixed center as first guess, while on levels at higher altitudes, the center of the previous lower-altitude level is used as first guess. The center can be located with satisfactory accuracy by the application of birational interpolation to FR in combination with a Downhill method (Bach 1969). As described in Weber and Smith (1993), the Downhill method locates the minimum of a given function by successively changing the values of the independent variables (here latitude and longitude) using a range of walk patterns, until the minimum is reached to within a predefined degree of accuracy (presently set to 500 m). On the 1000-hPa level, a center is declared as being valid only if it lies within a circle of 4° lat × 4° long from the satellite-fixed center, while on all other pressure levels an acceptable center must be located within a circle of 3° lat × 3° long from the center detected on the previous lower-altitude level. If no center is found on a given pressure level, no azimuthal analysis is carried out on this and all levels at higher altitudes and the original fields remain unchanged until the implementation of a synthetic vortex.
Once the center is determined accurately in FR, an azimuthal Fourier analysis of FR relative to this center produces the symmetric vortex FVS and the wavenumber one contribution FVA. Contributions of higher wavenumbers are not processed, because of the limited horizontal resolution of the global dataset. In the case of kinematical fields, the Fourier analysis is applied to the radial and tangential wind components instead of the zonal and meridional wind fields for the following reason: at lowest order of approximation, barotropic vortex motion is governed by the cross-vortex flow of the wavenumber one streamfunction (cf., e.g., Fiorino and Elsberry 1989). Using cylindrical coordinates r (radius, measured on a great circle) and θ (azimuthal angle) relative to the vortex center, streamfunction ψ, relative vorticity ζ, radial and tangential wind (u, υ), and zonal and meridional wind (U, V) can be expressed as f(r, θ, t) = f0(r, t) + f1c(r, t) cos(θ) + f1s(r, t) sin(θ) + f2c(r, t) cos(2θ) + f2s(r, t) sin(2θ) + O(3θ), where the subscripts 0, 1, 2, . . . define the azimuthal wavenumber and c and s the cosine and sine contributions, respectively. Note that in the above formulation, u0 is zero by definition.8 Using the above formulation, it can be shown mathematically that ψij(r, t) ∼ ζij(r, t), υij(r, t) ∼ dψij(r, t)/dr (i = 0, 1, 2, . . . ; j = c, s) and uij(r, t) ∼ ψil(r, t) (i = 1, 2, . . . ; j, l = c, s; j ≠ 1). An equivalent relationship between (U, V) and ψ does not exist, because U(r, θ, t) = u(r, θ, t) cos(θ) − υ(r, θ, t) sin(θ) and V(r, θ, t) = u(r, θ, t) sin(θ) + υ(r, θ, t) cos(θ). The azimuthal analysis processes the symmetric contribution FVS and the wavenumber one contribution FVA (Figs. 2d,e) of each dependent variable except temperature and relative humidity, for which only FVS is computed. The fields FVS and FVA are smoothed such that they tend to zero for large radii, to ascertain a continuous transition in the remaining field FES = FR − FVS − FVA at the outer end of the azimuthal analysis domain. As the objective analysis may resolve the storm in question fairly well farther away from its center, the field FVS is stored for later combination with the synthetic symmetric vortex constructed using the TC advisory. In contrast to FVS, FVA is regarded as a numerical artifact of the data assimilation process and not conserved. Combination of FEL and FES yields the total environment FE (Fig. 2f).
The symmetric synthetic vortex FBS is constructed on all mandatory pressure levels using the operational TC advisory. The present concept of generating FBS does not differ much from the original vortex enhancement scheme of the JMA (Davidson et al. 1993). Modifications to the original scheme include: (a) the option to use the parametric pressure profile of Holland (1980), which produces slightly smaller storms with somewhat stronger inner core winds, compared with the profile of Fujita (1952); (b) the replacement of the former top-hat structure of the synthetic symmetric relative humidity9 profile by a smooth radial distribution; (c) the computation of a synthetic symmetric vortex FBS as perturbation to the background field FE, ensuring a smooth transition between the synthetic vortex and the background field. In the former version, the synthetic vortex (including a constant velocity field representing the actual motion of the storm in question) simply replaced the background field in a circular region about the satellite-fixed vortex center; (d) the smooth blending of FBS and FVS to give FBO (Fig. 3a). Inside the radius of maximum tangential wind speed of the synthetic symmetric vortex FBS, FBO corresponds exactly with FBS, while at radial distances greater than twice the radius of the outer closed isobar of the TC advisory, FBO is identical with FVS. Between these two radii, FBO is represented by a smooth transition from FBS to FVS. Note also that uBO = uVS. The blending of FBS and FVS ensures that the large-scale structure of the symmetric field FVS, possibly containing information of the original objective analysis that is not related to the mispositioned symmetric vortex processed by the analysis, is conserved.
Finally, the output field FO (Fig. 3c) is combined from FE, FBO, and FBA on each pressure level and replaces the original field F of the objective analysis. Moreover, FO is conserved in a second, high-resolution dataset with artificial observations in a cylindrical coordinate system that is used for the initialization of the regional forecast model.
(a) Distribution of observations of mean sea level pressure, (b) 500-hPa wind, and (c) 500-hPa temperature valid at 2300 UTC 15 Mar 1997. At this time TC Justin was located near 12°S, 156°E (marked by a bold dot).
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Fields of 850-hPa geopotential height for TC Beti at 2300 UTC 25 Mar 1996. Units are m. (a) Original input field F, produced by the global objective analysis; (b) large-scale environment FEL; (c) residual field FR after subtraction of FEL; (d) symmetric field FVS (height anomaly) as produced by the azimuthal analysis; (e) wavenumber one contribution FVA resulting from the azimuthal analysis; and (f) total environment FE. The intersection of axes represents the satellite-fixed center. Here “×” marks the center of the mislocated vortex in the global field. Contour intervals are 10 m in (a), (b), (c), and (f), and 1 m in (e).
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
As Fig. 2 but (a) symmetric synthetic vortex FBO (height anomaly), (b) wavenumber one vortex asymmetry FBA, and (c) total output field FO. Contour intervals are 1 m in (b) and 10 m in (c). The intersection of axes represents the satellite-fixed center.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Observed and forecast tracks and central pressures for TC Beti from the base time of 2300 UTC 25 Mar 1996. The OBS and FORC columns in the panel refer to observed and forecast central pressures in hPa, and TERR refers to the forecast track error in km. Observed track is labeled “O,” and forecast track is labeled “F.”
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Initial condition, and 24- and 48-h forecasts of mean sea level pressure (in hPa) for TC Beti from the base time of 2300 UTC 25 Mar 1996. Contour interval is 2 hPa.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Time series of observed and forecast central pressures (hPa), and forecast maximum winds (m s−1) for TC Beti from the base time of 2300 UTC 25 Mar 1996: (a) obtained after initialization with diabatic, dynamical nudging, (b) after initialization by the digital filter.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Diagnosed fields of 400-hPa vertical motion (hPa s−1) for TC Beti at the base time of 2300 UTC 25 Mar 1996. Contour interval is 0.5 hPa s−1 and ascent is negative. Levels of shading are for regions less than 0 hPa s−1 and less than −1.0 hPa s−1: (a) after diabatic, dynamical nudging; (b) after initialization by the digital filter.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
North–south vertical cross sections from 30°S to 7.5°S, averaged from 161.1° to 165.9°E for: (a) zonal wind (m s−1), (b) temperature (K), (c) difference between uninitialized and initialized zonal wind (m s−1), and (d) difference between uninitialized and initialized temperature (K). The ordinate is σ×1000, where σ = pressure/surface pressure. Contour interval for winds is 5 m s−1, with westerly (easterly) winds positive (negative) and indicated by full (dashed) contours. Contour interval for temperatures is 4 K, and for temperature difference 2 K.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Observed (O) and forecast (F) tracks and central pressures for various TCs. The OBS and FORC columns in the panels refer to observed and forecast central pressures in hPa, and TERR refers to the forecast track error in km. Base time of each forecast is shown at the bottom of each panel with the legend yymmddhh UTC, where yy = year, mm = month, dd = day of month, and hh = hours.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Time series of forecast track errors (km) for each TC. The highlighted curve is the mean error for all forecasts.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Time series of forecast central pressure errors (hPa) for each TC. The solid highlighted curve is the mean (observed − forecast) error, the dash-dot highlighted curve is the rms error, and the dashed highlighted curve is the rms persistence error.
Citation: Monthly Weather Review 128, 5; 10.1175/1520-0493(2000)128<1245:TBHRTC>2.0.CO;2
Abbreviations and definitions used in section 3 and in the appendix.
Mean 0–48 h forecast track errors for 17 base date–times for the official forecasts (OFCL), CLIPER, and TC-LAPS. Units are km.
In this context it should also be noted that for storms existing over more open ocean areas, the observational network is likely to be even more sparse.
It should be noted that in consequence of this matching condition, the asymmetries do not necessarily correspond with β-gyres (cf., e.g., Holland 1983; Chan and Williams 1987; Fiorino and Elsberry 1989;Smith and Weber 1993).
It should be noted that we generally define the vortex center (a) separately for each meteorological variable and (b) as the local extremum (e.g., a minimum in case of geopotential height or a maximum of relative vorticity in the Northern Hemisphere) of a monopolar pattern with quasi-circular orientation of isolines.
Azimuthal asymmetric contributions are wavenumber one contributions in the case of geopotential height, mean sea level pressure, and radial and tangential wind. Note that wavenumber one components of radial and tangential wind represent wavenumber zero and two components of zonal and meridional wind.
Henceforth, vorticity refers to the vertical component of relative vorticity.
The TC Bobby event is also part of the database used in the present study, and although not described in detail, TC-LAPS in this case also produced substantially improved guidance over what was available in real time.
The distances between neighboring grid points vary strongly over the the size of the domain.
It should be noted, however, that the symmetric radial wind, resulting from the azimuthal analysis, has finite values and is retained in the final output field used for the initialization of TC-LAPS.
For reasons of consistency with the earlier bogus scheme of the JMA, relative humidity is used during the vortex specification process instead of mixing ratio.
