1. Introduction
On average, 13 tropical cyclones (TCs) occur in the Australian region per year (Dare and Davidson 2004). The threat to human life and the destructive power of these weather systems have been extensively documented over numerous TC basins around the globe [e.g., McTaggart-Cowan et al. (2007) for Katrina in the Gulf of Mexico and Yamada et al. (2010) for Nargis in the Bay of Bengal]. In the Australian region, Tropical Cyclone Tracy, which made landfall at Darwin with tragic loss of life and property on Christmas Eve 1974 (Davidson 2010), is another example. Since then, numerous storms [e.g., Ramsay et al. (2009) and Otto (2012) for Larry 2006 and, more recently, Yasi (2011)] have caused serious property loss, with thankfully much less loss of life. The potential destructive power of these systems over a large area has been a major world-wide motivation for the development of dedicated numerical weather prediction (NWP) systems, specifically focused on TC forecasting (e.g., Kurihara et al. 1995; Davidson and Weber 2000; Cha and Wang 2013). However, precise prediction of hurricane track, structure, and intensity requires realistic representation of the vortex in the initial conditions and therein lies part of the TC prediction problem. Tropical cyclones often originate over tropical oceans where meteorological observations are generally insufficient to accurately define vortex location and structure, particularly of the inner core. Without aircraft reconnaissance, and sometimes even with reconnaissance observations, initialized vortices from state-of-the-art assimilation systems are often “ill-defined, weak and misplaced” (Zou and Xiao 2000). There have been successful and encouraging attempts to use ground-based and airborne Doppler radar data to initialize the inner cores of TCs. This has recently been described by Zhao and Jin (2008), Zhang et al. (2009), Xiao et al. (2009), Aksoy et al. (2012), and Weng and Zhang (2012). Indeed, using a large sample of cases with airborne Doppler radar observations, Zhang et al. (2011) clearly demonstrated the need for high-resolution inner-core observations for tropical cyclones from either in situ or remotely sensed observations. Another promising source of observations is the Doppler radar from the Global Hawk. As discussed in Sippel et al. (2013), the benefits from this new observational source are potentially large for hurricane analysis and prediction. But such data are not yet universally available, and so, acknowledging the importance of inner-core observations, alternative possibly complementary approaches are required. We note as well that the assimilation techniques and initialization experiences described herein are also applicable as in situ or remotely sensed observations become available. This flexibility is important for ongoing upgrades to our TC initialization and prediction system.
Without reconnaissance, some prediction centers have still achieved great success at TC forecasting [e.g., the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Met Office (Heming 2009)] using new observational technologies [e.g., data from the Tropical Rainfall Measuring Mission (TRMM)] and advanced four-dimensional variational data assimilation (4DVAR) techniques. However, initial vortex structure, intensity, and position still remain problems for many poorly observed or weak and small storms. To attempt to make useful intensity and structure forecasts, as well as skillful track forecasts, we describe a validated technique for initializing realistic vortex structures. Encouraging attempts to use the 4DVAR method with synthetic vortex observations are reported, for example, by first Zou and Xiao (2000), Pu and Braun (2001), Park and Zou (2004), and Zhao et al. (2012), and references therein. The study described here extends these works using 1) physically based initial synthetic vortex structures, 2) high resolution, 3) validation of structures initialized by the 4DVAR, and 4) verification for a large number of storms.
The objectives of the project described here are to develop an operational TC NWP system with (i) a resolution sufficient to define, to some extent, an inner-core structure; (ii) a vortex specification scheme, validated against estimated and observed TC structures, to define the initial inner-core circulation; (iii) a state-of-the-art assimilation scheme to define the large-scale environment (LSE) of storms; (iv) a vortex initialization scheme capable of initializing the primary and secondary circulations of TCs; and (v) a numerical forecast model with advanced numerics and sophisticated physical parameterizations. To achieve these goals, the Australian Community Climate and Earth System Simulator (ACCESS; Puri et al. 2010, 2013) has been configured for operational and research applications on tropical cyclones. ACCESS is an implementation at the Australian Bureau of Meteorology of the full Met Office Numerical Modeling System (e.g., Gregory and Rowntree 1990; Wilson and Ballard 1999; Webster et al. 2003; Davies et al. 2005; Rawlins et al. 2007). As of 2011–12, the ACCESS-TC system runs at a resolution of 0.11° and 50 levels. The domain is relocatable and nested in coarser-resolution forecasts. Initialization consists of five cycles of 4DVAR over 24 h and forecasts to 72 h are made. Without vortex specification, initial conditions usually contain a weak and misplaced circulation pattern. This makes it necessary to incorporate a synthetic TC vortex at the observed location in the initial conditions during the data assimilation. Based on estimates of central pressure and storm size, vortex specification is used to filter the analyzed circulation from the original analysis, construct an inner core of the storm, relocate it to the observed position, and merge it with the large-scale analysis at outer radii. Since TC reconnaissance is not conducted in the Australian region, significant effort has been devoted to building physically based, synthetic inner-core structures, validated using historical dropsonde archives from the Atlantic and northeast Pacific. We will demonstrate that the versatility of the 4DVAR is capable of building up realistic horizontal and vertical structures using only synthetic mean sea level pressure observations from an idealized vortex.
This study describes the ACCESS-TC system and documents the vortex specification, the application of 4DVAR to TC NWP, the encouraging verification statistics that have been obtained so far, and some interesting, preliminary structure diagnostics that provide further dynamical validation of the initialization and forecast procedures.
2. ACCESS-TC system configuration
The system configuration is summarized as follows with further details in subsequent sections:
Resolution—A relocatable grid with 0.11° × 50 level dimensions, with the TC near the center of the domain, but offset based on the past motion of the storm, with an option for higher-resolution forecasts.
Vortex specification
Structure is based on observed location, central pressure, and size, as defined by the radius of outer closed isobar (roci) and tuned and validated using ~6000 dropsonde observations from the Atlantic.
Only synthetic MSLP observations are used in the 4DVAR to
relocate the storm to the observed location,
define to some extent the inner-core circulation, and
impose steering flow asymmetries consistent with the past motion (Davidson and Weber 2000).
Initialization using 4DVAR—Five cycles of 4DVAR are run over 24 h prior to the base time of the forecast. All standard observational data are used: surface stations, ships, drifting buoys, aircraft, radiosondes in addition to pilot and profiler winds, as well as data from the Advanced Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (ATOVS), the High Resolution Infrared Radiation Sounder (HIRS), the Advanced Microwave Sounding Unit (AMSU-A and AMSU-B), the Atmospheric Infrared Sounder (AIRS), atmospheric motion vector winds derived from geostationary satellite data, scatterometer winds (Advanced Scatterometer, ASCAT), and synthetic MSLP observations from the vortex specification (no upper-air synthetic observations).
Numerical forecast model—the Met Office’s Unified Model from ACCESS (Puri et al. 2013).
The high-resolution nest does not move with the storm, so we thought it prudent to initially limit the forecast duration to 72 h. However, given the rather large size of the domain, it is very rare for a storm to reach a boundary within 72 h. We are thus planning to extend the forecast duration to 96 and possibly 120 h with just a modest increase in domain size.
3. Vortex specification and validation
Because of the lack of observational data required to consistently and accurately define the location and inner-core structure of most storms, it is necessary to develop techniques for vortex initialization. In summary, the vortex specification is based on an idealized, three-parameter profile similar to that of Chan and Williams (1987), tuned on observed structures for the North Atlantic and eastern Pacific where reconnaissance is frequently used to define vortex structure. The vortex specification uses large-scale analyses and estimates of storm location, central pressure, and the radius of the outer closed isobar to complete the vortex structure parameter set [latitude, longitude, central pressure (cp), maximum wind speed (υm), radius of maximum wind speed (rm), radius of gale-force winds (r34), and roci]. Due to differences in wind-averaging periods from basin to basin (e.g., 1-min over the Atlantic and 10 min over the Australian basin), there will be differences in the estimated central pressures. Note that in the current vortex specification, we have taken whatever central pressure values are provided by the forecast center with responsibility for the storm in question. In this way we retain some consistency within the various basins. From the idealized vortex, synthetic mean sea level pressure observations are extracted and passed to the 4DVAR assimilation. The density and radial extent of synthetic observations is sufficient to define υm at rm and to allow smooth merging of the vortex at outer radii. Details of the technique are given here. The vortex specification has the flexibility to include additional parameters (e.g., rm, r34, and υm) as they become available. We plan to investigate the use of additional vortex parameters (e.g., r34) after comprehensive validation of our estimates.
a. The vortex specification method
The method
The insertion of a realistic synthetic vortex into the numerical model consists of the following steps: (i) the input fields of the vortex specification method are meteorological fields (horizontal wind components, mean sea level pressure, temperature, geopotential height, and relative humidity) produced by a global numerical model. In consequence of insufficient global model resolution in relation to data representing a tropical storm, these fields may contain a model storm that often is weaker than the corresponding real storm and situated at a different location. Hence, in the first step the vortex specification method has to remove these spurious vortices smoothly from the global data, while trying to retain the surrounding larger-scale fields (the so-called environmental fields) intact. Details of this procedure are discussed in Davidson and Weber (2000). (ii) In the second step, a three-dimensional axisymmetric vortex is constructed from available operational estimates of vortex size and strength. This method has been modified and will be discussed in detail below. (iii) The third step consists of a three-dimensional closure at model pressure levels below 500 hPa, specifying wavenumber one flow asymmetries relative to the vortex center such that the sum of the environmental and wavenumber one current through the vortex center matches the vortex drift speed. This procedure has also not been altered and is addressed in Davidson and Weber (2000). (iv) In the final step, the artificial vortex fields are blended smoothly into the corresponding environmental fields and handed to the model initialization procedure. This procedure is discussed also in Davidson and Weber (2000).
The current AVSM is set up to process the following six parameter combinations:
- If φc, dpc, and roci (and therewith also poci and pe) are known (this is the current default in response to the operationally provided storm information used by ACCESS-TC), Eqs. (3.4) and (3.6) are solved for υm to giveandrespectively. Note that for the root the plus sign (+) is used, because no physically meaningful solution can be obtained for the minus sign (−, υm2 < 0). For given roci, the function resulting from the subtraction of Eq. (3.9) from Eq. (3.8) depends only on rm, that is, F(rm) = υm1 – υm2 = 0, and the values of rm represent the zeroes of F. Once rm is determined, υm [needed for Eq. (3.1)] can be computed by evaluation of the right-hand side of Eq. (3.8), and r34 represents the zero of the functionwhere s34 = r34/rm. The quantity υ34 = 17.5 m s−1 represents the wind speed at r34.
- If φc, dpc, r34, poci, and pe are known, the function F(rm) is constructed from the difference of Eq. (3.8) andderived from Eq. (3.1) and solved for υm. Again, the zeroes of F(rm) = υm1 – υm2 = 0 represent the values of rm, from which υm can be computed using Eq. (3.8). In the last step, roci is determined by locating the zero of the functionfor given rm, υm, and dpoci.
For given φc, dpc, rm, poci, and pe, the maximum wind speed υm, r34, and roci can be computed directly by evaluation of Eqs. (3.8), (3.10), and (3.12), respectively;
For given φc, υm, roci, poci, and pe, the difference function for the determination of rm is given by F(rm) = υm2 – υm, using υm2 of Eq. (3.9). After rm has been found, r34 is computed using Eq. (3.10) and dpc can be calculated using Eq. (3.4).
For known φc, υm, r34, the quantity rm results from evaluation of Eq. (3.10), roci from Eq. (3.12), and dpc from Eq. (3.4).
Finally, for known φc, υm, and rm, the values of r34, roci, and dpc can be calculated from Eqs. (3.10), (3.12), and (3.4), respectively.
The final axisymmetric wind field near the surface is subject to the following restrictions:
If more than one zero of the above function class F(rm) exists, the smaller value of rm is used.
The value of rm and the other vortex parameters computed there from are used to calculate radial profiles of the tangential wind υ(s) and the relative-vorticity ζ(s) = d[sυ(s)]/(rmsds), which are then tested for inertial stability, requiring that Λ(s) =[ζ(s) + f]{f +[2υ(s)]/( rms)} > 0. If the profiles are found to be inertially unstable, the parameter α (for s > 1) is decremented from its original value given in Eq. (3.2) by a value of 0.01 and the procedure described above is repeated until an inertially stable vortex profile has been found. Finally, α is reduced further to a value of 0.2 (4α + 0.4) to ensure that the resulting profiles are not near the limit of inertial stability. If no inertially stable profiles can be found for α ≥ 0.4, AVSM stops execution.
The lower limit of the parameter α is chosen such that the radial integral of the relative angular momentum rυ(r)from zero to infinity with υ(r) given by Eq. (3.1) remains bounded.
As mentioned above, none of the other parts of the method to implant an artificial but realistic vortex in the initial model fields has so far been modified; see Davidson and Weber (2000) for a description of the process. From the artificial vortex constructed in the way described above, only synthetic mean sea level pressure observations are extracted for use in the 4DVAR simulations. Therefore, the initialized vortex does not have an arbitrary vertical structure, but is determined using 4DVAR during initialization. The next section illustrates that the minimal form of vortex specification allows 4DVAR to build the storm’s primary and secondary circulations as well as the vertical structure. This further allows the initialized structure to respond to aspects of the LSE [e.g., the vertical wind shear without imposing constraints on the tilt of the vortex or its interaction with environmental features like neighboring troughs (Hanley et al. 2001)]. Gradient wind balance is not fully valid in the boundary layer (Montgomery and Smith 2008). However, rather than apply empirical adjustments, we have chosen to use the balance as a first approximation in the vortex specification. Because we only provide 4DVAR with synthetic MSLP observations, there is no implied balance seen by the initialization. Gradient wind balance is only used to build the vortex structure during the vortex specification. The dynamics implicit in 4DVAR provides the balance during initialization in accordance with the synthetic surface pressure observations. By using only synthetic surface pressure observations, the boundary layer structure and balance can be built in an unconstrained fashion. Given the importance of the hurricane boundary layer, we believe that this is a very attractive feature. Work is under way to define the secondary circulation and boundary layer flow for a given primary circulation (H. C. Weber 2013, unpublished manuscript). When results from this study become available, we will be able to explore important vortex initialization and balance issues.
We also foreshadow here that a second vortex specification algorithm has been developed, based on three input vortex parameters: storm intensity (either υm or pc) and two size parameters from rm, r34, and roci. This will provide greater variability in the specification of the initial vortex structure. The set of equations of the three-parameter model is similar to that discussed here.
b. Verification of structures
The following datasets were used for the development and verification of the AVSM: 1) the Hurricane Research Division’s (HRD) archive of postseason processed hurricane flight-level data (Willoughby and Chelmow 1982), resulting from aircraft surveillance, and H*Wind datasets (Powell and Houston 1996; Powell et al. 1998), compiled from aircraft–satellite–radar surveillance, of numerous Atlantic and eastern Pacific storms between 1995 and 2007, providing a total of 1349 individual events, and 2) the corresponding Automated Tropical Cyclone Forecast (ATCF) best-track files (so-called B decks), containing storm structure information at 6-hourly intervals (Miller et al. 1990; Sampson and Schrader 2000). The values of the storm parameters in the working and postprocessed B decks do not differ much (say, up to 10% in the case of rm). Operationally, we do not use the B decks but rather the advisories. Because of the small percentage of change and inherent uncertainties, we would not expect a significant mean change in performance quality to result from changing the storm structure information source. The base dates and times of these datasets are correlated with the base dates and times of the flight-level and H*Wind data. (Knaff et al. 2011; DiNapoli et al. 2012).
Two sets of experiments have been carried out to assess the quality of the results of AVSM. In the first, henceforth denoted as the benchmark experiment, the analyzed υm and rm of the H*Wind–flight-level datasets have been used directly as input into AVSM, while in the second (henceforth denoted as the best-track experiment), the best-track estimates of υm and rm have been used as input. As the best-track estimates correspond largely with those produced during the daily routine at the operational forecast centers, they represent the values that would have to be used during a routine numerical model prediction of a given tropical cyclone.
With regard to B-deck data used in the best-track experiment, it should be noted that the best-track information represents only approximate estimates whose accuracy may vary (e.g., Uhlhorn and Nolan 2012). This is documented in Table 1 for the case of υm and rm, showing that there are biases in the best-track estimates relative to the observations. The values of υm are overestimated by about 1 m s−1 if compared with the total wind maximum and by about 8 m s−1 relative to the axisymmetric wind maximum. The smaller bias in the former case is expected because operational forecasters estimate the local rather than the axisymmetric wind speed maximum. In compensation, for the operational practice discussed above, the bias of the best-track estimates from the axisymmetric υm can be reduced considerably (from 8 to about 3 m s−1) if the best-track storm translation speed c is subtracted from the best-track υm. The B-deck values of rm appear to be systematically underestimated relative to the observations. The RMS deviations of the best-track estimates are rather large and amount to over 4 m s−1 in the case of υm and to about 25 km in the case of rm. However, as discussed in Vigh (2010) and somewhat refined by J. L. Vigh (2013, personal communication), “Since there is normally a large radial range in RMW observations due to the limited sampling in the azimuth and time domains, taking an average of the fluctuating values may not necessarily give a representative picture of the RMW in the real storm, which can be very asymmetric, have multiple wind radii, and have broad wind profiles where the RMW jumps around. The statistics may make it look like the best track values are an underestimate, but the best track RMW may actually be quite representative of the time-trended ‘best’ picture view of the RMW in the storm.”
Comparison of best-track (index B) and H*Wind–flight-level υm and rm. The index H refers to the total observed υm and rm, the index HSYM to the corresponding values of the axisymmetric vortex in the H*Wind–flight-level data. The top part of this table shows the biases, and the bottom the RMS errors. Additionally, the third line of each section shows the corresponding biases and RMS errors if the best-track drift speed is subtracted from the best-track υm.
For the two experiments mentioned above, Tables 2 and 3 show examples of the mean biases and RMS errors over all radii of the axisymmetric wind speed profiles generated by AVSM in comparison with the corresponding H*Wind–flight-level profiles for AVSM input parameters υm and rm. The statistical results of all other possible input parameter combinations are similar. Statistics are shown for radial intervals inside (r < υm) and outside (r ≥ rm) the radius of maximum wind speed. The mean biases are positive and smaller than 1 m s−1 in both experiments, indicating that both under- and overestimations may occur. The relative biases (shown in brackets) have values of only about 5%–7%, demonstrating that AVSM reproduces the analyzed symmetric profiles rather well. Both absolute and (in parentheses) relative RMS errors are in the range of measurement errors of satellite-derived wind speeds (about 3.5 m s−1), with 2–3 m s−1 and 26% deviation in the case of the benchmark experiment and about 4 m s−1 and the same percentage of deviation in the case of the best-track experiment. Figure 1 shows the corresponding distribution of RMS errors over all radial grid points, computed for the benchmark (Fig. 1a) and best-track (Fig. 1b) experiments, respectively. Both experiments produce large mean errors over 6 m s−1 in less than 15% of all cases and the majority of the errors lie below 4 m s−1 in 74% of all benchmark experiment cases and in 64% of all best-track experiment cases.
Benchmark experiment: biases and RMS deviations over all radial grid points of the axisymmetric wind speed profiles produced by AVSM vs the corresponding H*Wind–flight-level profiles. The radial domain is divided into regions inside and outside of rm. The values of υm and rm used to construct the artificial axisymmetric vortex represent the values observed in the H*Wind–flight-level data. The envelope (bottom part of the table) is defined by the minimum and maximum wind speeds at all gridded radial distances from the vortex center, and an artificial radial profile is said to lie inside the envelope if it lies inside the envelope in at least 80% of the total radial domain.
As in Table 2, but showing the statistics of the best-track experiment: the values of υm and rm used to construct the artificial axisymmetric vortex correspond with the best-track values, but with subtracted storm translation speed removed from υm.
RMS errors of AVSM computed over all radial grid points of all cases of the (a) benchmark and (b) best-track experiments.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
A further method to assess the quality of AVSM is to count the numbers of cases where the artificial profiles lie between the extrema of the wind speed measurements, defining an envelope about the mean axisymmetric analyzed profile. At each radial grid point, the envelope roughly defines the total range of possible wind speed values of an axisymmetric storm if it is assumed that the H*Wind–flight-level data are inexact due to measurement uncertainties and/or data-postprocessing effects. Two examples of artificial and observed mean profiles and envelopes (compiled from flight-level data) as a function of radius are shown in Fig. 2 for the cases of Hurricanes Fran (1996) and Floyd (1999). Figures 2a and 2b show the artificial and observed mean axisymmetric wind profiles (thick lines) and the corresponding envelopes (minimum and maximum wind speed of all passes at each radial grid point; thin lines) as a function of radius of the benchmark experiment. Figures 2c and 2d show the results for AVSM input parameters roci and υm taken directly from the best-track values. In this case, the artificial profiles lie outside the envelope in response to the overestimation of υm relative to the observations in the best-track data discussed earlier in this section. In Figs. 2e,f, the same input parameters as before have been used, but this time the best-track storm translation speed c has been subtracted from the best-track υm to obtain a better approximation of the axisymmetric υm needed in AVSM. It should also be noted that in contrast to Figs. 2a,b, the values of rm of the artificial profiles differ from the analyzed values as a consequence of the AVSM input parameter roci instead of rm.
Tangential wind υm in m s−1 as a function of radius in km of (left) Hurricane Fran on 29 Sep 1996 and (right) Hurricane Floyd on 19 Sep 1999. Thick lines represent the average υm of all flight passes and the AVSM output υm (smoother curve). The thin lines define an envelope given by the minimum and maximum υm of all flight passes at each radial grid point. The input parameters of AVSM are (a),(b) rm and υm of the average υm of all flight passes, (c),(d) the operational estimates of roci and υm, and (e),(f) the operational estimates of roci and υm – c.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
Table 2 shows that in the benchmark experiment the artificial profiles lie inside the envelope (defined, e.g., in Fig. 2 by the two thin lines) in about 97% and 89% of all cases for r < rm and r > rm, respectively. Note that an artificial profile is said to lie inside the envelope if at least 80% of its functional values in the radial domain lie inside this envelope. In the best-track experiment shown in Table 3, the corresponding percentages are still 88 and 83%, again documenting the high quality of the results produced by AVSM, with a percentage of only about 10%–20% where AVSM cannot recover the observations satisfactorily within the bandwidth of possible wind speed values given by the envelope.
Validation of the idealized structures is also presented in Fig. 3, which shows the comparison between values of r34 and rm from subjective estimates obtained from an extended best-track dataset (Demuth et al. 2006) and from the vortex specification. Both subjective and objective estimates are consistent and show that generally stronger storms have larger r34 and smaller rm. However, the variability in estimates for a given intensity is similar from both methods and so small intense and large weak storms are represented reasonably well. The mean absolute differences between the objective and subjective estimates for rm and r34 for all storms are 29.3 and 73.8 km, respectively. For category 3–5 storms these values reduce to 12.6 and 67.4 km. The differences are likely within the observational errors for these parameters and so we suggest that the vortex structures used in ACCESS-TC are the best that can be achieved within the current limitations of the observational network being used. We are working toward the use of new observational types from new observing platforms. We hope that eventually the use of such observations will supersede the need for synthetic observations.
Scatterplot comparison between values of (a) r34 and (b) rm from subjective best-track estimates (abscissa) and from the vortex specification (ordinate) based only on central pressure and radius of outer closed isobar estimates. Units are km. Color key follows the Saffir–Simpson hurricane scale: tropical storm, and categories 1–2, 3–4, and 5.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
To summarize, the axisymmetric vortex specification method AVSM allows a dynamically consistent, ocean-basin-independent computation of complete sets of storm parameters from a pair of subjective and independent operational estimates of storm size and storm intensity. Furthermore, it produces inertially stable, analytic tangential wind profiles in gradient-wind balance with finite angular momentum. Verification versus 1349 cases of observed storms shows that AVSM is a valid and useful approach for generating realistic axisymmetric synthetic storms. Moreover, a large number of equivalent tests using mathematical–statistical methods to fit a variety of wind profiles to observations have been carried out during the development of AVSM. None of these alternative approaches was able to reproduce the quality of the results of the current vortex specification method.
4. 4DVAR initialization
The 4DVAR used for vortex initialization is described in Rawlins et al. (2007). In very simple terms, the 4DVAR approach used here iterates back and forth over a time window (in this case 6 h) and attempts to fit both the observations and the model trajectory, taking into account (i) the quality of the observations, defined via observational errors, and (ii) the quality of the model forecast, defined via background covariances. To avoid rejection by the quality control, observational errors for synthetic observations are set to small values. The approximate ratio of the observational error of the standard observations to the background error near latitude 20° is around 2.0.
The effect of using the synthetic observations in the 4DVAR is to
define the horizontal structure of the inner-core circulation at the observed location (cp, υm, rm, r34);
build the vertical structure of the circulation from MSLP observations;
construct the secondary circulation without constraining the secondary circulation with synthetic wind observations;
create a balanced TC circulation at the observed location, with structure and intensity consistent with estimates; and
create a structure that is responsive to environmental wind shear without imposing constraints on the vertical stacking or tilt of the circulation. These are important for vortex dynamics (e.g., Jones 1995; DeMaria 1996; Frank and Ritchie 1999) and in building cloud asymmetries (e.g., Corbosiero and Molinari 2002), which, in a general sense, are consistent with observed asymmetries.
The synthetic observations used in the 4DVAR contain a value at the storm center that is the central pressure estimate. Since we start from a t = −24 h initial guess that can differ greatly from the actual intensity and structure of the storm, but is still given some weight in the 4DVAR, the initialization tends not to exactly fit the central pressure estimate. Additional issues are the resolution and the covariance modeling used in the 4DVAR. The synthetic observations also have an assigned observational error and even though this may be less than the background error, the 4DVAR will not exactly fit the observations. Another possible issue is whether the use of surface pressure observations only is reducing the information content of the synthetic observations via poor wind to mass adjustments during initialization for strong storms. We provide evidence later that the winds are adjusting to the forced surface pressure, resulting in a reasonably well-balanced set of initial conditions. However, the balanced adjustment could be slow and inefficient, which we believe may be one reason we have an intensity bias in the initial conditions, particularly for strong storms. We plan to investigate this issue further since it is a general problem for TC initialization and independent of the use of synthetic observations.
a. Impact of vortex specification and construction of vertical structure
The impact of the synthetic observations used by the 4DVAR is illustrated in Fig. 4, which shows first the forecasts without and with vortex specification, and second the building of the vertical structure based only on the use of synthetic surface pressure observations. Note the impact of the vortex specification on 1) the initial location of the storm and 2) the prediction of the track. Use of the synthetic observations reduces the initial position error from about 270 km to around 40 km. We note here that the 4DVAR does not result in extremely small initial position errors. The same applies for intensity and even less so. It relocates the vortex based not only on the synthetic data but also on other available observational data, short-term forecasts of the storm, and the skill of these short-term forecasts; and does so in a way that is consistent with the LSE of the storm. In addition, estimates of TC location, which may be dependent on intensity, also contain errors, and so it is believed that it is not desirable to force the 4DVAR to position the storm more accurately. It will be shown later that the mean initial position error for a large number of forecasts is about 30 km. This is within the estimation errors for location.
TC Anthony (top) observed and forecast track (with errors, km) and central pressure (hPa) intensities (left) without and (right) with vortex specification. (bottom) Initial conditions for 500-hPa wind (left) without and (right) with vortex specification (synthetic MSLP observations only); contour interval is 10 m s−1 and winds >10 m s−1 are shaded yellow.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
Note from Fig. 4 the construction of the 3D structure (500-hPa cyclonic circulation) from the 4DVAR based only on the use of synthetic MSLP observations. The cyclonic circulation over the Tasman Sea at 500 hPa is represented in the initial conditions using synthetic observations. No such circulation exists in the analysis without vortex specification. The 4DVAR uses the synthetic MSLP observations to define the horizontal structure, vertical depth, and tilt of the system in the presence of environmental wind shear; these are all important for the evolution of the vortex. The technique defines the primary circulation and vertical structure in a way that is consistent with the LSE of the storm.
b. Primary and secondary circulations
It is also important that the initialization (i) builds the primary circulation to be consistent with estimates of vortex structure parameters and (ii) builds the secondary circulation to be in quasi balance with the primary circulation [see the quasi-balanced constraint implied via the Sawyer–Eliassen equation in, e.g., Holton (1992)]. We illustrate the construction by 4DVAR of the primary and secondary circulations using a case study of TC Yasi from the Australian region. Figure 5 shows (i) observed and forecast tracks and intensities for TC Yasi from a base time of 0000 UTC 31 January 2011, and (ii) north–south cross sections of the zonal and meridional wind and vertical motion at the initial time of the forecast following the application of 4DVAR over 24 h in five cycles. Note first that the forecast skill levels for both track and intensity are rather encouraging. The 60-h track error near landfall is around 100 km and the forecast has skill in predicting the intensification but does not forecast the rapid intensification just prior to landfall. Initialization of the primary circulation can be seen in the zonal wind cross section, which reveals an inner core with a low-level azimuthal-mean υm of approximately 35 m s−1 at an rm of approximately 50 km on the equatorward side of the storm. The initialized secondary circulation can be seen in the north–south cross sections of meridional wind and vertical motion, with (i) radial inflow (outflow) concentrated mostly in the boundary layer (upper troposphere) and extending to at least 1000 km from the center of the storm and (ii) ascent focused at small radii on Yasi’s equatorward side. Note that at this time, Yasi was being influenced by southeasterly environmental wind shear and so we might expect convection to be mostly located to the north of the circulation. We illustrate this in Fig. 6, which shows 85-GHz imagery (left) and the ACCESS-TC 500-hPa vertical motion field at t = 6 h (initialized with 4DVAR) for Yasi from a base time of 0000 UTC 31 January 2011. There is quite reasonable correspondence between the regions of observed active inner rainbands and eyewall convection, and regions of strong and weak ascent obtained after initialization. The 4DVAR has built the vertical motion field, which is quite consistent with the observed structure. Note as well that the inner-core circulation has been built during the 24 h of assimilation and that the central pressure (illustrated in the time series of Fig. 5) evolves smoothly after initialization. This suggests that the primary and secondary circulations are in a quasi-balanced state at t = 0, even though the storm is forecast to intensify. We note that Pu and Braun (2001) found that ascent was stronger when only pressure observations were assimilated. Our result is consistent with theirs. We suggest that the use of synthetic wind observations may unnecessarily constrain the secondary circulation, something we have limited knowledge on for specific cases.
(top) Observed and 72-h forecast (left) tracks and central pressure (with errors, km), and (right) central pressures (hPa) and forecast maximum wind (kts) for TC Yasi from base time at 0000 UTC 31 Jan 2011. (bottom) South–north vertical cross sections of (left) zonal wind, (middle) meridional wind, and (right) vertical motion (contour intervals are 5 m s−1, 5 m s−1, and 2 Pa s−1, respectively) through the initialized center of TC Yasi (indicated by Y) at 0000 UTC 31 Jan 2011.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
(left) The 85-GHz brightness temperature (from <230 to >270 K) imagery and (right) ACCESS-TC forecast 500-hPa vertical motion field at t = 6 h (initialized with 4DVAR) for Yasi from base time at 0000 UTC 31 Jan 2011. Contour interval for vertical motion is 1 Pa s−1. Red shading indicates regions of ascent >2 Pa s−1. Yellow shading indicates regions of ascent >0 but <2 Pa s−1.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
The structures illustrated here are examples of how the 4DVAR (i) initializes the primary and secondary circulations (horizontal and vertical branches), using only synthetic surface pressure observations, and (ii) how the initialization does not constrain the vortex dynamics from evolving naturally, and allowing it to respond to the LSE. The initialization cannot represent unique inner-core structures like eyewall mesovortices or secondary eyewall structures.
5. Forecast verification
a. Comparison with other equivalent forecast guidance and impact of vortex specification
The single base time example of the impact of the vortex specification is shown above in Fig. 4 for TC Anthony. This one example indicates the potential impact of the vortex specification in the Australian region, where observational data to accurately define the location and structure of TCs are not generally available. Table 4 shows a comparison of forecast verifications for a homogeneous sample of two important TCs, Iggy and Lua, during the 2011–12 season over the Australian region from ACCESS-A (Puri et al. 2013) and ACCESS-TC. Limited computing power and the expense of running numerous comprehensive parallel experiments prevented us from running comparative tests with and without vortex specification. However, ACCESS-A runs operationally over a larger domain but at the same resolution and with the same physics settings as in ACCESS-TC, but without vortex specification. It thus seems reasonable to assess the quality of the forecast guidance and the impact of the vortex specification by comparison of the same set of forecasts from both systems. We also suggest that ACCESS-A forecasts are representative of the forecast skill of the operational guidance that is available from other forecast systems. Table 4 shows the very major impact that dedicated ACCESS-TC and the vortex specification can have on forecasts. Mean initial position and 48-h forecast errors for 22 forecasts are, respectively, 30 and 137 km for ACCESS-TC and 117 and 243 km for ACCESS-A. Initialized and forecast intensity errors from ACCESS-TC are also smaller. Some interesting examples of differences in the two systems are illustrated in Fig. 7, which shows observed and forecast tracks and intensities from ACCESS-TC (left) and ACCESS-A (right). The top panels in Fig. 7 are for TC Iggy. ACCESS-A has the TC nearly on the Western Australian coast at 48 h, while ACCESS-TC has slowed the storm and began to recurve it back toward the west. The middle panels in Fig. 7 are also for Iggy and demonstrate the impact of initializing the storm in the correct location. This produces an improvement in the t = 0 and 48 h forecasts of approximately 100 and 150 km The bottom panels in Fig. 7 are for TC Lua when it at first was moving toward the northwest and then made a hairpin turn back toward the southeast. ACCESS-TC captures the track quite well, while ACCESS-A is a little fast in making the motion change and accelerating the storm toward the southeast. Further diagnostics are required to understand the nature of the impact of vortex specification on the track and this should be the subject of future research. We have cases when the position error without vortex specification is quite accurate, but the forecast is still inferior to the forecast with vortex specification. We suggest that vortex structure sometimes plays an important role in the forecast (Davidson and Ma 2012). We note but do not illustrate here that the ACCESS-A forecasts from these times were rather similar to forecasts from other international forecast centers, including the ECMWF, which quite rightly is the most favored guidance used by forecasters. There are other examples of forecasts that demonstrate the importance of the vortex specification.
Mean track and mean absolute central pressure (intensity) errors (TERR, IERR) from 0 to 48 h for ACCESS-TC and ACCESS-A for 22 forecasts for TCs Iggy and Lua.
Observed and forecast tracks (with errors, km) and central pressure (hPa) intensities from (left) ACCESS-TC and (right) ACCESS-A for TCs (top two rows) Iggy and (bottom) Lua.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
We rather hope that in the future, with new and better uses of observations, we will be able to eliminate the need for vortex specification. There are a small number of cases when vortex specification has a negative impact, but overwhelmingly, its use has been positive, suggesting it is still necessary to apply these techniques to generally improve prediction.
b. Mean verification statistics and illustrative case studies of forecasts
The system was implemented at the Australian National Meteorological and Oceanographic Centre (NMOC) and was run in real time commencing with the 2011 tropical cyclone season over the northwest Pacific. Due to (i) differences in wind-averaging periods (1 min over the Atlantic, 10 min over the Australian basin) and (ii) previous systematic errors in boundary layer winds, historically we have used central pressure to verify intensity. The systematic wind errors in ACCESS-TC are much smaller and so we plan to evolve to verification of Vmax and RMW soon. Verification statistics for the 2011 tropical cyclone season over this basin are shown in Fig. 8. The track and intensity forecasts for around 100 forecasts are quite encouraging. For example, the mean track error at 48 h is about 150 km and seems competitive with errors produced by other NWP systems (http://www.metoffice.gov.uk/weather/tropicalcyclone/verification). Intensity errors show promise but further improvement will need higher resolution, additional work on improving initial vortex structures, assimilation of new observational and satellite data, and improved physical parameterizations.
Verification statistics for operational ACCESS-TC. (left) The 2011–12 Australian region (0°–35°S, 80°E–180°) 6 TCs. (right) The 2012 northwest Pacific 16 TCs up until early October 2012. (top) Number of forecasts (middle) mean track error (km), and (bottom) mean absolute central pressure error (hPa) every 6–72 h. The dashed green curves in the center panel are the approximate long-term mean (last 5 yr) track errors (http://www.metoffice.gov.uk/weather/tropicalcyclone/verification) and in the bottom panel are the mean absolute central pressure error using persistence as the forecast. For the northwest Pacific, forecast central pressures have been bias corrected using the initialized minus observed value at t = 0.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
An example of track and intensity forecasts for one storm, TC Ma-On, is shown in Fig. 9. In this case, forecast maximum wind is the instantaneous, local maximum wind at 10 m at the valid time of the forecast. The track forecasts mostly stay tight on the observed track and the intensity forecasts show some skill but tend to be slow with the intensification and slow with the weakening. These systematic errors are the subject of ongoing experiments. Testing suggests that the errors will be reduced with the next upgrade of ACCESS-TC.
(left) Observed (thick blue curves) and forecast tracks (various colors) and (middle),(right) intensities [central pressure (hPa) and wind speed (m s−1), respectively] for TC Ma-On using the ACCESS-TC model with start at 12 Jul 2011. The sample contains all 9 forecasts at 12-h intervals during the life of the storm.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
Mean track and intensity errors for Australian region storms during 2010–11 and 2011–12 have also been quite encouraging (not illustrated here). The system became fully operational in November 2011. Operational ACCESS-TC provides TC forecast guidance for named storms over the western Pacific and eastern Indian Oceans in both hemispheres. Examples of high quality real-time forecasts over the Bay of Bengal (TC Thane), northwest Pacific (TY Muifa), Australian region (TC Iggy, a particularly difficult forecast of a decelerating storm changing its direction of motion from the southeast to the west), and southwest Pacific (TC Jasmine) are illustrated in Fig. 10.
Observed (red O symbols) and forecast (green F symbols) tracks (with errors, km) and central pressures (hPa) for TCs (top left) Thane, (top right) Muifa, (bottom left) Iggy, and (bottom right) Jasmine from the base times specified. Shown are the valid time of forecast, forecast hours, observed central pressure, forecast central pressure (hPa), and track error (TERR, km).
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
An example of operational forecast quality over the Australian region is shown in Fig. 11 for TC Lua. The diagram shows the observed track and intensity, superimposed with all forecasts made for TC Lua. Points to note are (i) the correct forecast of the hairpin turn following genesis, (ii) the way that nearly all track forecasts stay tight on the observed track, (iii) the high quality of the timing and location of landfall, and (iv) the useful guidance on intensity change, even though the rapid intensification just prior to landfall is not forecast.
(left) Observed (thick blue curves) and forecast tracks and (right) central pressure (hPa) intensities for TC Lua using the ACCESS-TC model with start at 13 Mar 2012. The sample contains all NN forecasts at 12-h intervals during the life of the storm.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
There are now numerous examples of high quality forecasts from ACCESS-TC. Unfortunately, there are still poor forecasts. We suggest that these are mostly associated with errors in the initialization and forecasts of the LSE. With ongoing improvements in observational data coverage and better use of the data, we might expect that the number of poor track forecasts will continue to diminish; a trend that has been evident over at least the last 10 yr. We also hope to further address this issue using ensemble prediction.
c. Validation of initial and forecast cloud structures
Comparison of actual and synthetic cloud imagery from the model (Sun and Rikus 2004) has been used to validate initial conditions and forecasts. An example for TC Yasi from a base time of 1200 UTC 31 January 2011 is shown in Fig. 12, which shows synthetic imagery from the ACCESS-TC forecast and corresponding actual imagery from the Multifunctional Transport Satellite (MTSAT) at t = 0 and 46 h, just prior to landfall. Comparison suggests that the initial conditions contain many of the satellite-observed cloud features, even including some mesoscale features not associated with the TC (over inland Australia, Cape Yorke peninsular, and south of the TC). The synthetic imagery may contain a larger area of cold clouds, but the shape and texture of the synthetic imagery is a further indicator that the 4DVAR is initializing the TC circulation and its vertical motion and moisture fields quite well. The 46-h forecast of the imagery also compares favorably with that observed. Interesting features are the cloud bands to the west of the storm center. Such mesoscale features often produce heavy rain not associated with the TC center. It is encouraging that the model tries to produce its own version of these weather systems.
(left) Synthetic cloud imagery at t = (top) 1 and (bottom) 46 h from the ACCESS-TC forecast for Yasi from a base time at 0000 UTC 31 Jan 2011. (right) Corresponding actual imagery from MTSAT.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
d. Initialized and forecast pressure–wind relationships
Theoretical studies (e.g., Schubert et al. 1980; Shutts 1994) suggest that mass tends to adjust to wind for mesoscale systems. Questions that then arise include the following: 1) Is the wind adjusting to the synthetic surface pressure observations during the 4DVAR? 2) Are the initial structures reasonably well balanced with respect to mass and wind? 3) How efficiently is the 4DVAR using the synthetic surface pressure observations during initialization? To partially address these questions, Fig. 13 shows scatterplots of central pressure versus maximum wind obtained from ACCESS-TC at t = 0 and for all forecast times from 6 to 72 h every 6 h. The sample includes over 100 forecasts for more than 20 storms with different latitudes, intensities, sizes, and movements, run over the northwest Pacific during 2011. In the diagrams we have also included an indication of the operational pressure–wind relationship commonly used over that basin, from which the following can be seen: (i) the pressure–wind (PW) relationship from the initialized structures is rather similar to the operational curve, but differences in latitude, size, and movement likely increase the variability about the mean (Courtney and Knaff 2009); (ii) the winds have adjusted to the surface pressure forcing (note that even for intense storms, the PW values generally lie close to the mean curve); and (iii) the PW relationships at t = 0 and at forecast times are rather similar, suggesting that the initialized structures are generally well balanced.
Central pressure (CP, hPa) vs maximum wind (VMAX, m s−1) from ACCESS-TC forecasts for the northwest Pacific for 2011. (left) For t = 0 h with initialized structures. (right) For forecasts every 6 h from t = 6 to 72 h. The red symbols indicate the standard Dvorak PW relationship.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
By successive insertion every 6 h of synthetic surface pressure observations, which are consistent with intensity estimates, it appears that the 4DVAR is initializing realistic structures. But it is possible that the adjustment of the winds to the surface pressures could be inefficient, thus contributing, among other factors (e.g., resolution, moist processes, assumed gradient wind balance), to the intensity bias described above. We plan to explore this issue in ongoing work, since it is likely to be a general problem for TC initialization whether synthetic observations are used or not.
6. An illustrative example of vortex structure change at high resolution: TC Yasi
Historically, track and intensity (as measured by central pressure or maximum wind) have been the main metrics used to verify TC forecasts. However understandably, TC structure, as indicated by, for example, rm and/or r34, is becoming increasingly important (Ma et al. 2012; Davidson and Ma 2012). It is thus interesting to illustrate some structure change features forecast by a sophisticated NWP system like ACCESS-TC for an intensifying, high-impact storm at landfall. This provides additional validation of the system for operational forecasting and research applications. Figure 14 shows estimated and forecast tracks and central pressures from an ACCESS-TC forecast for TC Yasi from a base time of 0000 UTC 31 January 2011. This forecast was run at a higher resolution of 0.04° with 50 levels and initialized from and nested in the standard 0.11°-resolution forecast, as described above for operational ACCESS-TC. The skill of the forecast is rather encouraging. The track error near landfall was less than 50 km, and estimated and forecast central pressures were around 930 and 945 hPa, respectively. Figure 15 shows time series of forecast central pressure, and azimuthal-mean values of υm, rm, r64, r50, and r34 from the ACCESS-TC forecast. The time series show (i) the forecast intensification, (ii) the inward contraction of rm during intensification, and (iii) the growth and expansion of the circulation during intensification, as indicated by the r34 time series, and the development of r50 then r64. During and following intensification the circulation grows in size (Smith et al. 2009), while the inner circulation contracts. Figure 16 shows graphs of azimuthal-mean tangential and radial winds and vertical motion at 12-h intervals during the forecast. Note that at t = 0, as described above, the primary and secondary circulations are already well developed by the 4DVAR. The cyclonic tangential winds and radial inflow extend to at least 1000 km, far beyond what is the size of the TC. This large radial extent of the primary and secondary circulations is maintained during the intensification. At t = 0, there exist multiple cloud bands inside the azimuthal-mean radius of maximum winds. Substantial ascent is occurring inside of rm. As the rate of intensification declines, the large ascent establishes at or outside of rm, with relatively little ascent inside of the well-defined eyewall. Another interesting feature is the apparent decay of the first eyewall, with the development of twin peaks in ascent and the development of a consolidated eyewall at slightly larger radii then existed previously. There is some evidence here of secondary eyewall formation and an eyewall replacement cycle (e.g., Wang et al. 2013 and references therein). Documentation and understanding of the way in which these structure changes occur is the focus of ongoing research.
Observations (estimated) and forecast tracks (with errors, km) and central pressures (hPa) for TC Yasi from base time at 0000 UTC 31 Jan 2011. The red O symbols are the estimated observed locations and the green F symbols are corresponding forecast locations.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
Time series of (top) forecast central pressure (hPa) and (top to bottom) azimuthal-mean values of the maximum wind (m s−1) at 10 m for Vmax and the following radii: rm, r64, r50, and r34 (km) for TC Yasi from base time at 0000 UTC 31 Jan 2011.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
Radius–time Hovmöller diagrams of (left to right) tangential wind, radial wind at 10 m, and vertical motion at 500 hPa during the forecast intensification of TC Yasi from base time at 0000 UTC 31 Jan 2011. Contour intervals for tangential wind, radial wind, and vertical motion are 5 m s−1, 2 m s−1, and 2 hPa s−1. Vertical motion < 0 hPa s−1 (ascent) is contoured in green, and > 0 hPa s−1 (descent) in red. The black contour is 0 hPa s−1. The thick black line in each panel shows the azimuthal-mean RMW.
Citation: Monthly Weather Review 142, 3; 10.1175/MWR-D-13-00062.1
7. Summary and future plans
ACCESS-TC has been developed for operations and research. Unique aspects of the initialization include the following:
use of 4DVAR and comprehensive observational datasets to define the LSE of storms;
application of a physically based, validated vortex specification and use of synthetic MSLP observations (no upper-air synthetic data) to initialize the TC circulation; and
use of 4DVAR assimilation to build balanced horizontal and vertical structures, and the storm’s secondary circulation.
Verification of track, intensity, and structure for the Australian region seasons of 2010–11 and 2011–12 and the northwest Pacific seasons of 2011 and 2012 have been encouraging. Like most operational forecast systems, ACCESS-TC will evolve and be refined. The system has produced very encouraging verification statistics. We believe it provides the infrastructure necessary to accomplish some progress on predictions of the structure and intensity, as well as the track.
Future plans include
upgrades to ACCESS-TC to use more satellite data, higher resolution, improved physics, and data assimilation;
real-time forecasts for pregenesis circulations (TC genesis is a critical forecast problem in the Australian region);
experiments with assimilation of inner-core reconnaissance data using 4DVAR;
further experiments into specification, prediction, and validation of TC structure (CP, Vmax, RMW, r34, roci), which is critical for the prediction of track, intensity, structure, storm surge, and rainfall;
experiments with high-resolution initialization and prediction, and with ensemble prediction, as developed at the Met Office [e.g., hybrid ensemble Kalman filter (ENKF)–4DVAR methods];
experiments with revised and new physics and diagnostics for the TC boundary layer and moist processes; and
NWP and basic research applications from special experimental datasets, including The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (TPARC) and the Tropical Cyclone Structure-2008 (TCS-08) program (Elsberry et al. 2008), and the Pre-Depression Investigation of Cloud-Systems in the Tropics (PREDICT) experiment (Montgomery et al. 2012), as well as genesis and rapid intensification.
Acknowledgments
This research was partially supported by the National Oceanographic Partnership Program (NOPP) and the Office of Naval Research (ONR) under Award N000141010139. Comments from Drs. Jin Lee, Chris Tingwell, Jonathon Vigh, the external reviewers, and the editor clarified many issues and greatly improved the presentation.
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