Objective Detection of Tropical Cyclones in High-Resolution Analyses (original) (raw)
1. Introduction
Tropical cyclones are intense disturbances whose peak wind velocities are reached over a relatively small area close to their centers (e.g., Frank 1977). Thus they pose a difficult simulation problem for general circulation models (GCMs) because of the limited horizontal resolution of such models. Also, the representation of convective processes in GCMs used for climate studies is fairly crude compared to processes in the real atmosphere. This is so because of the need for GCMs to run economically in order to achieve the lengthy simulations required for reliable climate averages to be obtained; additionally, scientific understanding of convective processes remains inadequate. Several attempts have nevertheless been made to assess the ability of climate models to simulate tropical low pressure systems whose physical characteristics resemble those of tropical cyclones. The early work of Broccoli and Manabe (1990), Wu and Lau (1992), and Haarsma et al. (1993) employed climate models of fairly low horizontal resolution (about a few hundred kilometers). Examination of observed intense tropical cyclone structure (Frank 1977) suggests that at this resolution intense tropical cyclones may not be reliably differentiated from other less intense tropical or subtropical cyclones. The more recent study of Bengtsson et al. (1995, hereafter B95) was performed at a much higher resolution (T106, roughly equivalent to a grid spacing of 120 km). At this resolution, observations suggest that there may be some hope of simulating several of the features of a tropical cyclone. Whether the tropical vortices generated by a similar high-resolution GCM can then be reliably identified as tropical cyclones is one of the subjects of this study.
One aspect of the previous studies that is crucial to the climatology of simulated tropical vortices is the detection criteria used to identify low pressure systems as tropical cyclone–like vortices. These criteria are typically well-defined, physically based quantities that are determined from examination of typical tropical cyclone characteristics: for example, high low-level vorticity, low mean sea level pressure (MSLP), and the propensity of tropical cyclones to exhibit positive midtropospheric temperature anomalies and tropospheric wind speed maxima at low levels. In the studies mentioned above, a candidate low pressure system was declared to have the characteristics of a tropical cyclone if it satisfied certain minimum values of the specified criteria. In this way, other low pressure systems that did not have several of the observed characteristics of tropical cyclones were excluded from consideration.
Considerable work has also been performed on the detection of tropical cyclones in forecasts made using numerical weather prediction models. The cyclone tracking procedure of Lord (1991) and Lord and Petersen (1993) uses six different parameters (minimum wind speed, maximum relative vorticity, and minimum geopotential heights at both 850 and 1000 hPa) to determine the locations of storm centers in a forecast. In the U.K. Meteorological Office (UKMO) model, tropical storms (tropical cyclones with observed 10-m wind speeds of at least 17 m s−1) are identified as such when a relative vorticity maximum at 850 hPa above the critical value of 5.5 × 10−5 s−1 is found with a specified search area based upon the previous observed location and movement of the storm (Radford 1994; Heming et al. 1995). Fiorino et al. (1993) used the maximum relative vorticity at 925 hPa to identify storm centers within a search area. In all of these models, the quality of the forecasts depends crucially upon the initialization of the model simulation with a synthetic tropical cyclone of similar location, strength, and motion to observed, a technique known as “bogusing” (Hall 1987; Anderson and Hollingsworth 1988; Ueno 1989; Serrano and Unden 1994).
Several of the analyses available for use by the meteorological community include such bogus observations of observed tropical cyclones (e.g., the UKMO analyses, Heming et al. 1995; the U.S. National Meteorological Center, Lord 1991; and the Australian Tropical Analysis and Prediction System (TAPS), Puri et al. 1992, Davidson et al. 1992). In contrast, the analyses produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) do not contain bogusing (Goerss and Petko 1995). Nonetheless, they are used widely for many studies, so it is important to determine their ability to depict observed tropical cyclones. Molinari et al. (1992) examined the ability of the ECMWF analyses to represent aspects of the structure of two tropical cyclones. They found that caution must be exercised in using these analyses to study tropical cyclones in areas far from rawinsonde data, that is, over the open oceans. Over these regions, a priori checks on the accuracy of storm position and intensity would be required, but they found that the representation of storm structure in the analyses was reasonable in regions of good data coverage. Miller (1993) showed that useful representations of tropical cyclone structure were much more likely in the northwest Pacific than the east Pacific and ascribed this result to data voids in the analyses in the eastern Pacific.
We propose to examine further the representation of tropical cyclones in these analyses. We wish to answer three questions.
- Can the ECMWF T106 analyses be used to establish realistic threshold criteria for the detection of tropical cyclone–like vortices in the output of other models?
This issue is important because the quality of the simulation of these systems in climate models is limited by horizontal resolution. It can be argued that the characteristics of such model-generated vortices are best compared to observations that have been smoothed to the resolution of the model, rather than observations of much finer resolution. Since the ECMWF analyses are a representation of observations, the question then becomes how well the features of observed tropical cyclones are represented in these analyses at a chosen resolution. To address this issue, we compare the T106 analyses to observed tropical cyclone track data, and apply an objective cyclone detection technique similar to that of B95 to detect observed tropical cyclones in the analyses. This study differs substantially from previous work in that this methodology enables a direct comparison of the ability of such analyses to represent a large number of real tropical cyclones. - How well do the analyses discriminate between the different intensities of observed tropical cyclones?
Since variations in intensities are one of the most important characteristics of tropical cyclones, the representation of their intensities in the analyses is important as an indication of the ability of a high-resolution GCM to simulate the observed intensities of tropical cyclones. - Is there any sensitivity of numbers of detected tropical lows in the analyses to small variations in the values of the detection parameters?
Any substantial sensitivity would lead to some uncertainty in the numbers of tropical vortices identified if a similar detection technique was applied to a climate model. For comparison of climate model results with observations, unambiguous methods of detection and comparison are required.
Section 2 describes the methodology of the study further. Section 3 details the results, section 4 compares the representation in the analyses of two contrasting tropical cyclones, while the last section discusses and summarizes the work.
2. Methodology
In this study, observed tropical cyclone positions and intensities are taken from the track data supplied in the Global Tropical and Extratropical Cyclone Climatic Atlas (GTECCA), supplied on CD-ROM by the U.S. National Climatic Data Center. The ECMWF analyses were evaluated at a resolution of 1.125°, which is equivalent to the gridpoint spacing of the T106 spectral model used by B95; snapshots were taken at 0000 UTC each day. The ECMWF analyses are produced by four-dimensional data assimilation (Bengtsson et al. 1982). A first guess is provided by a 6-h forecast from a numerical weather prediction model. This is then combined with observations using optimum interpolation procedures (Shaw et al. 1987) and followed by initialization procedures designed to achieve dynamical balance in the resulting fields. These analyses have been widely used in both modeling work and data analysis (e.g., Puri and Miller 1990; Molinari et al. 1992).
Because of the high cost of obtaining the ECMWF data, only two months of analyses were evaluated here: September 1989 and August 1992. Nevertheless, both months have numerous tropical cyclones. A total of 29 cyclones of tropical storm strength or greater was examined, providing a total of 143 cyclone days, which should be enough to provide a basic test of the method. The two months chosen also provide two contrasting storms in the North Atlantic basin: Hurricane Hugo in 1989 and Hurricane Andrew in 1992. Hugo had a large horizontal extent in its mature stage, with a radius of several hundred kilometers. Andrew was a small storm, with most of its circulation at landfall contained within a radius of about 200 km, but it was also one of the most intense ever to strike the United States mainland (Mayfield et al. 1994). Because of its small size, Andrew in particular serves as a rigorous test of the detection technique.
Several detection criteria were established so that an automated procedure could search the analyses at the observed tropical cyclone locations and determine whether the physical fields as represented in the analyses possessed the characteristics of observed tropical cyclones. A number of physical parameters were selected for these criteria, largely based upon those chosen by B95, but with some differences. As in B95, a detection threshold value of the 850-hPa relative vorticity was first established. Observations of tropical cyclones (e.g., Riehl 1979) suggest that at this resolution a minimum vorticity of about 3 × 10−5 s−1 may be typical; as mentioned earlier, Radford (1994) used a threshold value of 5.5 × 10−5 s−1 for tropical storms. We designate the 850-hPa vorticity threshold as VORTMIN.
Tropical cyclones also are characterized by a closed low pressure field near the surface. The detection program therefore searched for the minimum MSLP in an area 2.25° (i.e., two grid points) around the 850-hPa vorticity maximum. A further condition was applied that this minimum pressure must also be lower than any of its surrounding points, in order to ensure that the circulation was closed. If a grid point with a minimum of MSLP was found that satisfied these conditions, it was taken as the center of a possible tropical cyclone (see Fig. 1). We also define a threshold 10-m wind speed for detection (W10MIN), as the intensities of observed tropical cyclones are defined by the strength of their near-surface winds. The same area searched for the minimum MSLP was searched for 10-m wind speed maximum, which was then compared to the W10MIN threshold.
Molinari et al. (1992) showed that, for the two tropical cyclones they examined in the ECMWF analyses, the 850-hPa relative vorticity was a more reliable detection criterion than the 1000-hPa height, which was often poorly represented in the analyses. A similar conclusion might also be made about the MSLP fields used here. Accordingly, an alternative detection method was evaluated in which the center of the storm was defined using 850-hPa vorticity instead of MSLP. Unfortunately, the results were not as good as those using the method presented in this paper. The reason was related to the use of a threshold 10-m wind speed criterion as part of the detection procedure. The detection method using 850-hPa vorticity to define the center of the storm sometimes missed a 10-m wind maximum, which was found when the storm center was defined using MSLP, since low-level wind speed is strongly correlated with MSLP gradients and less strongly correlated with 850-hPa vorticity.
In addition to the use of W10MIN, another criterion was based upon the observation that tropical cyclones typically have maximum wind speeds in the lower troposphere, near the top of the boundary layer (Frank 1977). A criterion comparing the wind speeds at 850 and 300 hPa was therefore applied, with the requirement that the wind speed at the lower level be greater than that at the higher level. It was found that the sensitivity of the detection routine was best if wind speeds at each level used for this comparison were averaged over several grid points around the center.
A temperature criterion was also specified. Tropical cyclones typically have tropospheric warm cores, and thus the tropospheric temperature anomaly at the center of the storm was calculated. The total tropospheric temperature anomaly criterion (TTOT) was determined by first calculating a mean reference temperature at 700, 500, and 300 hPa over a band 2 grid points north and south of the pressure minimum and 13 grid points east and west (Fig. 1). There is some sensitivity to the specification of the area over which the reference temperature is calculated. It was found that 13 grid points on either side in the east–west direction was the best compromise between economy and sensitivity. This was a significant difference from the criteria of B95. Smaller values tended to make the anomaly test less sensitive, while larger values were more time consuming while not significantly increasing the sensitivity of the test. Specifying a larger extent in the north–south direction tended to make the test prone to biases caused by north–south temperature gradients. TTOT was taken to be the sum of the temperature anomalies relative to the reference temperature at each of the above levels, when calculated at the center of the storm. Since tropical cyclones also typically have higher temperature anomalies at 300 hPa than lower in the atmosphere (Frank 1977), it was additionally required that the anomaly at this height be greater than that at 850 hPa. This was found to be useful in improving the sensitivity of the method through the reduction of false detections, particularly in the midlatitudes.
By applying the detection method to the analyses and comparing the detected cyclones to the observed track data, we find storms that are both observed in the track data and detected in the analyses (successfully detected cyclones), those that are observed but not detected (missing cyclones), and those that are detected but not observed (false cyclones). The sensitivity of these quantities to various values of the detection criteria is examined, and the best values of the criteria are thereby determined.
Despite reasonable choices of detection criteria, at the relatively coarse resolution of the analyses, real tropical storms or hurricanes could be missed by the detection routine because of their small size or low intensity. False detections could also occur for the same reason, in that at this resolution a tropical low that is not a tropical storm could satisfy all of the criteria, unless they were so stringent that many real tropical storms were also missed. Note here that, apart from deciding which physical parameters it is logical to evaluate in order to detect tropical cyclones in the analyses, and also making some decision about appropriate starting values for the testing procedure, no a priori assumption about the best values of the criteria is made. These are determined by performing many sensitivity tests in which VORTMIN, W10MIN, and TTOT are varied to establish optimal values of these quantities. Thus we are using the ECMWF analyses in an attempt to “tune” the chosen values of the detection criteria.
Here optimal values of criteria are defined as those that minimize both type I and type II errors; in other words, the detection routine should detect more cyclones than it misses and should also have fewer false detections than real detections. Both these signal-to-noise ratios should be high if the detection method is successful. The magnitude of the signal-to-noise ratios at these optimal values is a test of whether tropical cyclones are well represented in the analyses. Ideally, the best possible values of the detection criteria should find all tropical storms and hurricanes and no other systems. This may not be physically possible at a resolution of T106 for the reasons mentioned above. Because some cyclones may be missed at this resolution, for best results the numbers of false detections and missed cyclones should be roughly equal, in order that the total number of cyclones detected by the routine, even including false detections, should be about the same as that observed. It was also found in the course of this work that the ECMWF analyses often represented the center of a cyclone as being a few degrees away from the position specified in the track data (e.g., Molinari et al. 1992). Thus a geographical tolerance limit for detection was imposed in the routine so that it searched some distance on either side of the observed cyclone location for a point in the analyses matching the imposed criteria. In addition, the detection routine only searches points over the oceans.
To sum up the detection criteria, it is assumed that tropical cyclones must satisfy these conditions (after B95):
- a minimum vorticity of VORTMIN;
- there must be a closed pressure minimum within a user-specified distance of a point satisfying condition 1; this minimum pressure is taken as the center of the storm;
- a minimum 10-m wind speed of W10MIN;
- a minimum total tropospheric temperature anomaly of TTOT;
- mean wind speed around the center of the storm at 850 hPa must be higher than at 300 hPa;
- the temperature anomaly at 300 hPa must be greater than at 850 hPa at the center of the storm; and
- a geographical tolerance limit for detection was imposed.
3. Results
This section describes the ability of the detection technique to find tropical storms and hurricanes in the analyses.
a. Detection of hurricanes in analyses
It is logical to assume that intense tropical cyclones might be better detected using this technique than weaker storms, since the threshold values of detection criteria can then be set high enough to eliminate many false detections. This is what has been found, and results are first presented for storms of hurricane, typhoon, and severe tropical cyclone intensity only (minimum observed sustained 10-m wind speed of 33 m s−1). Hereafter, these storms are designated as “hurricanes.” Figures 2–4 depict the sensitivity of the numbers of hurricanes detected, falsely detected, or missed to the specification of various criteria. The results are given as totals of hurricanes at all latitudes, but results poleward of 40° are not compiled in the bar charts because of the low number of tropical cyclones observed at those latitudes in the chosen months.
When all hurricanes are considered, best results appear to be obtained for a minimum vorticity (VORTMIN) of 11 × 10−5 s−1 and a minimum 10-m wind speed (W10MIN) of 14 m s−1. Note that two passes are made through the data to compile the statistics: in the first pass, detected vortices in the analyses are compared to track data to determine successfully detected and false storms, while in the second pass, the track data are compared to the list of detected vortices to determine any tropical cyclones missing from the observed record. Thus the skill of the technique may be assessed by comparing the number of storms successfully detected to the number of either false detections or missing storms, not the sum of the two. In addition, the observed number of tropical cyclones is in all cases the sum of the number of successfully detected and missing storms. Many sensitivity tests showed that, for lower values of vorticity and wind speed, there were too many false detections, particularly at lower latitudes. Note that this minimum wind speed is far below the accepted definition of a hurricane, as given above. This is partly caused by the relatively coarse resolution of the analyses compared to that necessary to detect the sharp gradient of wind speed that occurs in hurricanes close to their centers (Frank 1977).
Figure 2 shows the sensitivity at these optimal values of VORTMIN and W10MIN to the specification of TTOT. Optimal results (as defined earlier) are obtained with TTOT of 2°C. Given the relatively small size of the sample, some scatter in the exact proportion of the various quantities at an optimum choice of values is to be expected. Nevertheless, at lower values of TTOT than the optimum of 2°C the number of false detections is larger as a proportion of the number of successful detections, with no substantial compensating increase in successful detections. It must be said, however, that the signal-to-noise ratios shown in Fig. 2 are not high.
The geographical distribution of all successfully detected, false, and missing cyclones, for TTOT = 2°C and the same VORTMIN and W10MIN values used in Fig. 2, is shown in Fig. 3. A number of conclusions can be drawn from these maps. The geographical distribution of false detections (Fig. 3b) shows five midlatitude systems, apparently unrelated to tropical cyclones, in the general region of the Aleutian and Icelandic lows, respectively. Nevertheless, of the 31 systems detected at all latitudes in Fig. 3b, 18 were tropical storms, with low-level wind maxima less than that of hurricane strength. Three were tropical depressions that either became or had been tropical storms. Three were extratropical systems that had previously been tropical storms or hurricanes, while two remain unidentified from the available data. Thus, 24 of the 31 falsely detected storms (77%) were in some way associated with tropical cyclones of varying intensities. The addition of a minimum lifetime criterion as imposed by B95 may help remove the spurious midlatitude detections.
The geographical pattern of missing storms is shown in Fig. 3c. When compared to the pattern of successfully detected storms, one clear difference is seen: the missing storms are generally farther away from the continents. An exception is the eastern North Pacific, which as previously mentioned is a region of sparse data (Miller 1993). This behavior strongly suggests that the analyses are missing at least some storms because of lack of data. This is a nonphysical cause that would affect the determination of optimal criteria in the sense that storms would be classified as missing solely because of a lack of observational data and not because of their actual size or intensity. For this reason, it is likely that the current methodology overestimates the number of missing storms. One could overcome this problem by examining the data sources of the analyses to determine data-sparse regions, which could then be excluded from consideration. The net effect on the results of this study is that the real optimal values of the criteria are probably somewhat higher than determined here. One could illustrate the possible impact of this effect by examining Fig. 2 for the case where (for example) seven of the missing storms located far from the major land masses were caused by poor data rather than by small size or low intensity. If this was the case, the optimal value of TTOT for the test shown in Fig. 2 would increase to about 3°C. Similar increases in the real optimum values of VORTMIN and W10MIN might also be expected.
Missing storms occurred at the values used in Fig. 2 mostly because they failed to exceed either the vorticity or the wind speed threshold or both. Temperature criteria were satisfied more often, while most of the missing storms also had recognizable pressure minima. Several did not, however. If (ideally) the grid spacing of the data used to initialize the ECMWF analyses was identical to the T106 Gaussian grid used in this study, then even the smallest cyclones should have some circulation as represented in the analyses. The fact that several storms are missing from the analyses strengthens the argument that their omission is the result of sparse data. Because the data coverage in the analyses is less than optimal, their representation of real tropical cyclones is inherently uncertain; even in data-rich regions, some essential data may be missing from the analyses, which could then make their depiction of tropical cyclones less than optimal. The presence of data-sparse regions in the analyses negatively affects the ability of the sensitivity tests to define reliable threshold values of the detection criteria. The low signal-to-noise ratios shown in Fig. 2 imply that it is unlikely that the analyses could be used for this purpose.
Tests were conducted to examine whether a specification of a higher minimum value of TTOT would be sufficient to eliminate many false detections while permitting more real cyclones to be retained through a less restrictive specification of other criteria. It was found that too many false detections were made compared to the optimal values shown in Fig. 2. Similar results were found for lower VORTMIN and W10MIN values. Tests with higher values of W10MIN, however, suggest that results of only slightly lower quality could be obtained with VORTMIN = 11 × 10−5 s−1, W10MIN = 15 m s−1, and TTOT = 0°C. Similar tests for higher values of W10MIN show that a test based on W10MIN is apparently more sensitive than one based on VORTMIN, as the number of storms detected falls dramatically if W10MIN is increased.
Figure 4a shows the variation with VORTMIN of the probability of detection (POD) and false-alarm rate (FAR) (e.g., Wilks 1995) for fixed TTOT and W10MIN. In the context of the current study, the POD is defined as
while the FAR is defined as
The solid line is POD, while the dashed line is FAR. While the POD remains fairly constant and then declines as VORTMIN increases, the FAR decreases fairly rapidly when VORTMIN is increased. Likewise, Fig. 4b shows that below a certain threshold the POD remains relatively constant with varying W10MIN and does not increase as VORTMIN is decreased, as might be expected. As mentioned earlier, this problem of “persistent” missing storms is most likely associated with inadequate data in certain regions of the globe, whereby no matter how low VORTMIN or W10MIN are set, the POD does not increase because the storms are not adequately represented in the analyses.
Based upon the sensitivity tests performed, an optimal choice of parameters for the detection of hurricanes might be in the range of VORTMIN = 9–13 × 10−5 s−1, W10MIN = 13–15 m s−1, and TTOT = 1°–3°C. It must be reemphasized that these optimal values include a large number of missing storms that fail to be detected for no other reason than they are likely in data-sparse regions of the analyses. Because of this, it is unlikely that these optimal values could be used as reliable threshold values for detection of hurricane-like vortices in a GCM of similar resolution to the ECMWF T106 analyses.
b. Detection of both hurricanes and tropical storms
The results for both hurricanes and tropical storms are less convincing. Although the numbers of storms are greater than for hurricanes alone (and thus the statistics are better), the procedure is less successful in separating tropical storms from weaker lows. Figure 5 shows results for the optimal values for detection of cyclones of at least tropical storm strength. Best results are achieved at TTOT = 0°C. Even so, no sensitivity test was able to detect more of these weaker storms than both false and missing storms considered separately, which was one of the main specifications for a good detection routine. Higher and lower values of VORTMIN and W10MIN produced generally worse results. Given the results shown here, it is unlikely that the use of more months of these analyses would improve the signal-to-noise ratios shown in Figs. 2 and 5. Note that the number of false detections may be reduced somewhat by the inclusion of a minimum lifetime criterion as imposed in B95.
The optimum value of VORTMIN in Fig. 5 is of the same order as that used by Radford (1994) and Heming et al. (1995) for the detection of a tropical storm center in the UKMO prediction scheme. The substantial numbers of false cyclones detected in the ECMWF analyses at this value of 850-hPa vorticity has implications for the skillful prediction of tropical cyclone genesis, where the forecaster has no a priori knowledge of the position of the tropical cyclone.
c. Sensitivity of the total number of detected cyclones to variations in values of the detection parameters
B95 used values of VORTMIN = 3.5 × 10−5 s−1, W10MIN = 15 m s−1, and TTOT = 3°C to detect tropical cyclone–like vortices in their climate model and to establish the model climatology of such lows. We have performed tests that show that the number of detected vortices in the Tropics in the ECMWF analyses is quite sensitive to the exact values of these criteria. Figure 6a shows numbers of detected vortices in the analyses over the latitudes 0°–25°N for various values of W10MIN and the same values of TTOT and VORTMIN used by B95. If W10MIN is raised to 17 m s−1 (the actual defined minimum wind speed of a tropical storm), the number of detected tropical vortices falls by over 30% (from 23 to 16). Similarly, numbers rise if W10MIN is decreased. There is a less pronounced sensitivity to the chosen value of TTOT (Fig. 6b). Little sensitivity was detected to changes in VORTMIN at values close to those used by B95, however.
While such sensitivity has been demonstrated in the analyses, the analogous sensitivity in a climate model might be different. This is because the energetics and structure of tropical cyclones may change as the model is run forward in a forecast mode and as the effect of the initialization data decreases. Detection sensitivity in the analyses is a function both of model quality and of initial data, whereas in a climate model the detection sensitivity depends only upon the ability of the model to generate tropical cyclone–like systems. This question would need to be examined before the sensitivities demonstrated here could be firmly stated to be applicable to a climate model simulation; but these results show that care must be taken in the comparison of a model climatology of tropical vortices to that of observed tropical cyclones. If the choice of a certain threshold is somewhat ambiguous, as shown above, then the entire distribution of intensities of simulated storms should be compared to reality, not just those stronger than a threshold. Nonetheless, studies such as that of B95 can lead to useful comparisons of the ability of climate models to simulate the observed distribution and intensities of tropical cyclones.
d. Composite structure of successfully detected hurricanes as depicted in analyses
To determine the structure of observed tropical cyclones in the analyses, the composite structure of all successfully detected hurricanes in Fig. 3a was calculated. Figure 3a shows that successfully detected storms generally occur closer to the coast than missing storms; in these regions, numbers of successfully detected storms are much greater than those of missing storms. Thus, the composites should be a good description of the hurricane structure as represented in the analyses in regions where data coverage is reasonable. The composites are shown in Fig. 7. Because of the cost of the analyses, only certain variables were obtained, which limits the composite data that can be displayed.
Figure 7a shows the composite tangential wind speed at 850 hPa as a function of radius from the storm center. Maximum values occur near a radius of 2° of latitude and then decline closer to the center, in contrast to the observed behavior, where maximum tangential winds at this level usually occur at radii of less than 1°. This is likely a result of the limited resolution of the model, as tropical cyclone forecasts with global models have indicated a decrease in the radius of maximum winds as horizontal resolution is increased (Krishnamurti and Oosterhof 1989). Maximum tangential wind speeds are about 19 m s−1, compared to the observed value of 20 m s−1 at 850 hPa and a radius of 2° given by Frank (1977). With the exception of the region close to the center of the storm, the tangential wind speed as a function of radius is quite similar to observed.
Figure 7b shows the composite temperature structure versus radius from the storm center. Here the temperature structure is displayed as anomalies from the radial average at a distance of nine grid points from the center (about 10.125° of latitude). The composite structure in the analyses is similar to that derived from observations by Frank (1977). The data analyzed here only included a top level of 300 hPa, and thus it is not possible to say whether this is the level of maximum temperature anomaly. However, temperature anomalies are clearly increasing toward this level and toward the center of the storm, as observed. Thus we conclude that if the analyses are initialized with reasonable data, they provide a representation of hurricane structure, which is similar in certain respects to reality, with the exception of the wind speed structure close to the center of the storms.
4. Case study: Hurricanes Hugo and Andrew as represented in the analyses
The representation of a small but intense storm like Hurricane Andrew in analyses at a resolution of 1.125° is problematical. Figure 8 shows the MSLP field from the analyses at this resolution just before it hit the coast of Florida near Miami. Also included for comparison is the same field for a much larger storm, Hurricane Hugo (Fig. 8b). It is clear from Fig. 8a that a small but intense storm like Andrew is poorly represented in these analyses. The minimum pressure of the hurricane in the analyses just before landfall, as depicted in Fig. 8a, is about 1012 hPa; but observed values at this time were 930 hPa. Miller (1993) suggested that Hurricane Andrew was not captured in the analyses because of inadequate data. The depiction of the circulation of Hugo also suffers at this resolution, although it is clearly much better represented than Andrew. Just before landfall (Fig. 8b), the minimum pressure of Hugo in the analyses is about 991 hPa, compared to an observed value of 935 hPa.
When low-level wind speeds are examined, the comparison becomes more striking. Figure 9 shows 10-m wind speeds in the analyses at the same times as shown in Fig. 8. For Andrew, the maximum wind speed in the analyses is about 12 m s−1, versus 64 m s−1 as observed. This low wind speed would ensure that Hurricane Andrew was not detected with the optimum value of W10MIN determined in the previous section for hurricanes; it would have been detected using values more typical of tropical storms, however. Hurricane Hugo fares better, with an analyzed maximum 10-m wind speed of about 25 m s−1, well above W10MIN but well below the observed value of 61 m s−1. Thus, aspects of the analyses, including resolution and data coverage, need to be greatly improved before any but the broadest criteria based upon intensity could be reliable.
5. Discussion and conclusions
This study makes the following conclusions regarding the representation of tropical cyclones in the ECMWF T106 analyses.
- An objective cyclone detection technique was used to show that these analyses cannot be used to define robust threshold values of criteria for the detection of tropical cyclone–like vortices in GCMs. This is because the presence of data-sparse regions where observed tropical cyclones are poorly represented makes such a determination inherently uncertain. If regions of adequate data coverage could be identified (and if “adequate” could be rigorously defined), this conclusion could then be reevaluated. Hurricanes are more reliably detected in the analyses than weaker systems, although a small hurricane like Hurricane Andrew is very poorly depicted. The results suggest that a resolution of 1.125° is perhaps just barely adequate for the representation of stronger tropical cyclones in such a way as to reliably distinguish them from weaker tropical systems, but only in regions of reasonable data coverage.
- If the analyses are initialized with reasonable data, the structure of tropical cyclone–like vortices in the analyses is similar in many respects to that of observed tropical cyclones but differs for tangential wind speeds close to the center of the storms. This structural difference in the region of observed maximum wind speed should be recognized in any comparison between the distribution of model-simulated and observed intensities of these systems.
- The number of tropical vortices detected in the analyses is sensitive to the exact threshold values chosen for the detection criteria. This suggests that care should be taken in the comparison of the climatology of model-generated vortices to that of observed tropical cyclones, as substantially different numbers of vortices could be detected in a model simulation for relatively small changes in detection threshold values.
The detection technique would naturally work much better if applied to bogused analyses. However, the use of bogus observations requires some foreknowledge of tropical cyclone structure and position, and is not relevant to the problem of false detections and, thus, of producing skillful predictions of cyclogenesis. The fact that large numbers of false tropical storms were detected in the analyses at reasonable threshold values of the detection criteria (see Fig. 5) implies that a successful prediction technique for cyclogenesis would likely have to use higher threshold values and an improved model. Such predictions would clearly only be useful in regions of good data coverage. It is also of interest to determine whether the representation of tropical cyclones in the analyses is affected by the rejection of good data by the assimilation scheme itself. This might be a concern in data-rich regions traversed by a small, intense tropical cyclone. A typical example is Hurricane Andrew.
It is possible that a similar technique would perform better using analyses produced by a model of substantially finer horizontal resolution or data from one of the reanalysis datasets currently being prepared (Gibson et al. 1994; Kalnay et al. 1996). These results are relevant to recent work, which uses climate model simulations to obtain an estimate of how the climatology of tropical cyclones may change as a result of global warming (e.g., B95). The results suggest that model simulations performed at a resolution similar to 1.125° may have some skill in representing the observed characteristics of intense tropical cyclones, but that higher resolution would be preferable. Similar simulations will certainly be performed in the future. The methodology used in this paper may serve as a guide to such direct estimates of the effects of climate change on the numbers and locations of tropical cyclones.
Acknowledgments
I would like to thank Chris Landsea, Greg Holland, Barrie Pittock, Kevin Hennessy, Brian Ryan, and John McBride for some useful discussions regarding the ideas behind this paper. I also thank Alan Radford and two anonymous reviewers for helpful comments. We gratefully acknowledge the financial support of the governments of the Northern Territory, Western Australia and Queensland, and of the CSIRO. This work is a product of the CSIRO Climate Change Research Program, which is partly funded by the Australian Department of Environment, Sport, and Territories.
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Fig. 1.
Schematic diagram of detection criteria definitions. An analysis grid point exceeding the vorticity threshold VORTMIN is found at point V; an area two grid points on either side is searched to find the associated surface pressure minimum P, which is taken as the center of the storm. The tropospheric temperature anomaly TTOT is calculated over a region 13 grid points east–west and 2 grid points north–south around the storm center.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 2.
Number of cyclone days detected, falsely detected, and missed for the specified values of VORTMIN and W10MIN, as a function of TTOT, for hurricanes only. Units of VORTMIN are 10−5 s−1, of W10MIN meters per second, and of TTOT degrees Celsius.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 3.
Geographical distribution of vortices for TTOT = 2°C and the same VORTMIN and W10MIN values used in Fig. 2, for (a) successfully detected hurricanes; (b) falsely detected hurricanes; and (c) missing hurricanes. Crosses mark vortex locations.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 4.
(a) The variation with VORTMIN of the probability of detection (POD) and the false-alarm rate (FAR) for fixed values of W10MIN and TTOT; (b) the same showing the variation of W10MIN for fixed values of VORTMIN and TTOT. The solid line is the POD, while the dashed line is FAR. Units of VORTMIN are 10−5 s−1, of W10MIN meters per second, and of TTOT degrees Celsius.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 6.
(a) The variation of the number of detected cyclones with W10MIN for fixed values of VORTMIN and TTOT, at values near those used by B95; and (b) the variation of numbers with TTOT for fixed values of VORTMIN and W10MIN. Units are the same as in Fig. 2.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 7.
Composite structure as a function of radius from the storm center of all successfully detected storms shown in Fig. 3a, for (a) mean tangential velocity (m s−1); and (b) temperature anomaly (°C) versus mean temperature at a radius of nine grid points from the storm center.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
Fig. 8.
(a) Mean sea level pressure (hPa) from ECMWF analyses at 1.125° resolution, verifying at 0000 UTC 24 August 1992 and depicting Hurricane Andrew just before landfall; (b) the same but verifying at 0000 UTC 22 September 1989 and depicting Hurricane Hugo.
Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1767:ODOTCI>2.0.CO;2
