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Fixing the current cyclone position is the first step in making a track forecast. Since the forecast quality is dependant on the accuracy of the initial fix considerable care is warranted in this analysis stage. Highly accurate positioning is especially important for short range forecasts in critical situations, such as near landfall, but large position errors have resulted in major forecast failures at all times.
Table 3.1: Operational tropical cyclone forecast errors stratified by initial position error. The numbers in parentheses are those derived from Eq. 3.1.
| TIME (h) | 0-25 km | 25-100 km | >100 km |
|---|---|---|---|
| 00 | 15 | 55 | 150 |
| 12 | 91 (91) | 131 (131) | 222 (226) |
| 24 | 178 (166) | 217 (206) | 286 (301) |
| 48 | 382 (317) | 392 (357) | 442 (452) |
An example of the importance of accurate initial cyclone locations is shown by Table 3.1 (Woodcock, personal communication, 1993). By comparing forecast errors for tropical cyclones with good, fair and poor initial position location, Woodcock found the following relationship:
FE= IE + 6.3 
(3.1)
where FE is the forecast error after hours, and IE is the initial location error. As
indicated by the numbers in parentheses in Table 3.1, Eq. 3.1 accurately reproduces the
observed error growth. This growth is equivalent to a mean speed error of 6.3 kmh-1,
which is independent of initial forecast error. Thus, on average an initially bad
position location will be carried through the whole forecast period.
The survey by McBride and Holland (1987) indicated that cyclone position analysis depends primarily on surface observations, satellites and land-based radar. Whilst most centres would prefer aircraft reconnaissance, this is now only available in the North Atlantic. This section is based on these survey results. First we examine some analysis pitfalls, then we discuss methods of analysis using different observing systems.
Figure 3.1. Aircraft reconnaissance observations and related satellite imagery for developing Tropical Cyclone Irving showing the presence of multiple centres (data obtained during the TCM-92 experiment in the western North Pacific).
There is no such thing as a "true" position of a tropical cyclone. The centre, or location is a function both of how we choose to define it and of the type of observing equipment used. For example, satellite and radar are used to locate the geometric centre of a circular region of cloud or rainfall encompassing the eye. Unless there is an exposed surface centre, satellite imagery tends to show the location of the mid-level circulation, which can be quite different to that at the surface in a weakly organised or sheared cyclone. Similarly, radar observations first locate the upper rain features at a distance, then progressively sample lower levels as the cyclone approaches.
The surface pressure and wind centres are rarely collocated with the geometric centres shown by radar or satellite, or with each other. A simple calculation using a symmetric wind and pressure field defined by the tropical cyclone profile of Holland (1980) indicates that the pressure and wind centres may be displaced by half the radius of maximum winds for a moderate cyclone moving at 5-10 ms-1.
Weak systems are a particular analysis problem as they may be strongly sheared or contain multiple centres. The aircraft observations for developing tropical cyclone Irving in Fig. 3.1 provide one example of multiple centres. Which centre to select to represent the actual cyclone is a moot point. During development, one centre may tend to dominate for a period, but then be displaced by a separate centre. Several cases have been found where sharp changes in best tracks have been associated with this changing dominance of multiple centres. Further, some major and near catastrophic forecast errors have been made by analysts following an incorrect feature, or local circulation centre during satellite analysis.
Figure 3.2. Track of tropical cyclone Tracy (1974) showing the trochoidal oscillation observed on radar (from Bureau of Meteorology, 1977).
A common analysis difficulty arises from the presence of small-scale oscillations in tropical cyclone tracks (Fig. 3.2). When accurate, high frequency observations, such as from land-based radar, are available these oscillations can be resolved and are included in the final track. However, on most occasions the data are insufficient for such detailed analysis, the track is smoothed to some extent, and may be biased by the available ad hoc observations. In making an operational fix, it is often nearly impossible to tell whether an analysed position to one side of the previous track is due to poor data, a real oscillation, or a long term change in direction. This can lead to major forecast errors if the wrong interpretation is made.
There also is a natural tendency for analysts who have carefully considered all aspects and available data to overestimate the accuracy of the derived location. As noted in the introduction, Bell (1979) found a mean difference between "best track" analyses for the same storms of 40 km, or roughly one eye diameter. These results were for combined aircraft and satellite fixes, and for offices that had access to each other's position analyses in making the best track. It is of interest that the mean operational errors for one of the centres, the JTWC, were found to be 35 km by Curry et al. (1985), slightly less than the differences between best tracks.
The often confusing claim and counter claim on accuracy of cyclone centre fixes should be treated with caution. A study by Holland (1981c) indicated both the changing quality of the historical record in Australia and the potentially major analysis errors arising from use of surface observations, even those of good quality and coverage. In particular, studies that provide error statistics for satellite fixes made in conjunction with aircraft should not be transferred directly to regions with only satellite data. For example, Curry et al. (1985) found mean satellite position errors for the JTWC in the western North Pacific to vary from 20-55 km during a period when aircraft reconnaissance also was available. But in the Australian region, where there was no aircraft reconnaissance available, Keenan (1981) found a 76 km mean difference between the operational satellite fixes by JTWC and the Australian Tropical Cyclone Warning Centres.
The best method of locating a tropical cyclone is by direct observation from aircraft. Unfortunately, the expense of current aircraft operations means that they are now routinely available only in the North Atlantic Ocean. New initiatives within the United Nations International Decade for Natural Disaster Reduction indicate the possibility for widespread use of small, inexpensive aircraft, such as those proposed by Holland et al. (1992). Special analysis techniques will need to be developed to fully utilise the data from such new platforms.
Because of their extremely accurate centre location (usually within half of the radius of maximum winds for a cyclone with a well developed eye), aircraft locations suffer from the problems with resolution of trochoidal oscillations described in Section 3.2.1. Sheets (1985) proposed a "mass-field envelope" approach in which pressure heights outside the radius of maximum winds are used to provide a conservative centre location that is relatively unaffected by trochoidal oscillations. However, no evidence has been presented to show that this method produces a more accurate forecast and it is likely that the analysis errors are similar to those arising from trochoidal oscillations.
Satellite imagery provide the most universal source of data for locating tropical cyclones. Except for some parts of the Indian Ocean, all tropical cyclone warning centres have access to data from both polar orbiting and geostationary satellites, although not all centres have a sophisticated display and analysis capacity (McBride and Holland, 1987). Particularly useful for satellite analyses are graphical workstations that provide a capacity for colour enhancement and looping of imagery.
Figure 3.3: Six common cloud patterns associated with tropical cyclones (from Elsberry, 1987).
Three basic types of sensors are contained on weather satellites, two passive and one active. First is a television system capable of taking "photographs" of the atmosphere, which provided the only observations in the early satellites and can still provide extremely high resolution images. Second are sophisticated radiometers that collect the upwelling radiation from the atmosphere and earth, and are usually set to sample in a range of wavelengths suitable for observing different atmospheric features. Particularly useful for locating tropical cyclones are sensors in the visible, near infrared and microwave regions. The infrared sensors provide indications of the temperature of the emitting body and thus directly differentiate cloud at different levels. The microwave radiation cuts through cloud with little attenuation, and thus can be used to remotely sense the cyclone warm core. The third type of instruments are active in that they send out a pulse of energy and measure its backscattered component, and include microwave radars and lasers. Microwave radars provide observations of the liquid water in clouds and can be interpreted using similar techniques to those described for ground-based radars in Section 3.3.4
The most common satellite fix method is to use the Dvorak technique (Dvorak, 1984) in combination with spiral overlays and subjective interpretations (McBride and Holland, 1987). This is done by locating the appropriate Cloud System Centre (CSC), as illustrated by example in Fig. 3.3.
For a system that has reached tropical cyclone intensity (maximum winds exceeding 17 ms-1, Chapter 1) use the following procedure:
| TC1. |
|
|
| TC2. | When the CSC is not obvious, but cloud bands are present, draw a line along the "curved band axis" through the most dense (coldest) portion of the band. This axis should parallel the concave (inner) overcast boundary of the band. The CSC is located near the inner (concave) edge of the cyclonically curved portion of the band, using any tightly curved lines, merging lines or the CDO if present and greater than 1.5o lat in diameter. For large CDOs, the centre may be defined by an arc of overshooting cloud tops or an isolated cluster of convective tops. | |
| TC3. | When the above features are not visible, or the curved band is not apparent, use the circle method: first draw lines following the cloud line curvature or any curved boundaries that fall within the band; then fit circles to the lines with tightest curvature; the CSC is placed at the centre of the area common to the circles. For relatively circular embedded centre patterns of >T3.5 intensity, fit a 10o logarithmic spiral overlay to the curved band axis to locate the centre. | |
| TC4. | When a wedge of little, or no cloud is visible on the concave side of the band near its middle, the CSC is located at the midpoint of a line drawn between the sharp end of this wedge and the cyclonic extremity of the curved band axis. This method is frequently used with Enhanced IR (EIR) pictures in which the CSC is often located in the tight gradient near the coldest part of the pattern. | |
| TC5. | When the location of the CSC is unclear, or could be placed at different locations, use all the methods above along with an extrapolation from the past track position. Such circumstances have lead to major analysis errors and great care needs to be taken to utilise all other sources of information in making the analysis decision. | |
| TC6. | When more than one well-defined CSC is apparent, use the one that best fits the past track of the storm, that is defined by the best low level cloud lines, or that provides the best fit with other available observations.. When strong vertical shear is apparent, remember that the upper-level (dense) clouds will not be centred directly over the low-level centre, but will be displaced on, or beyond the sharp boundary, upshear side of the dense cloud pattern. |
For weak systems, not yet at tropical cyclone intensity, the CSC can be analysed from the following procedure:
| W1. | Curved band, a dense overcast band that shows some curvature around a relatively warm (cloud minimum) area. It should curve at least one-fifth the distance around a 10o logarithmic spiral. Cirrus, when visible, will indicate anticyclonic shear across the expected CSC. Locate the CSC as described in TC2 above. |
| W2. | Curved cirrus lines indicating a centre of curvature within or near a dense, cold overcast. Locate the CSC at the centre of curvature. |
| W3. | Curved low cloud lines showing a centre of curvature within 2o lat of a cold cloud mass. Locate CSC at the centre of curvature. |
Considerable care needs to be taken with interpreting weak and sheared systems. Unless there are clearly defined low-level clouds, the cloud system centre will provide an indication of the middle-level centre, which may be substantially displaced from that at the surface. Some of the largest errors result from incorrect analysis where the mid-level circulation is mistaken for the surface centre. The presence of multiple centres also has caused major errors (Fig. 3.1). Some of these are later identified as analysing the "incorrect" cloud feature, on other occasions a sharp change of "track" is used to accommodate the changing dominance of different centres. Use of visible satellite imagery to identify low-level cloud spirals or circulation centres is strongly recommended, wherever possible.
The use of loops of satellite imagery is strongly recommended as a method of locating the centre. In this way movement of spiral bands and individual echoes provide a natural method for the eye to locate centres. Errors of judgment and incorrect interpretation of anomalous patterns in the satellite imagery also are less likely than with static imagery. Considerable care and experimentation also is recommended for choosing the most appropriate colour or grey shading for differentiating the important components. This choice is often a personal one and reflects individual tastes in scales and colours.
Whilst navigation of satellite imagery is much better now than in the past, substantial errors are still possible. In particular the viewing angle of geostationary satellites well away from the sub-point can cause unacceptably large errors if uncorrected. Care should be taken to use coastlines or other visible geographical features to check navigation accuracy.
Some satellites now have sensors in the water vapor channel and provide imagery of integrated water vapor throughout the atmosphere. Use of these imagery, with animation, provides a valuable adjunct to the analysis of visible and IR data, especially for weak and developing systems (Velden, 1987).
Microwave instruments on polar orbiting satellites provide a means of seeing through cloud cover. Temperature soundings made in this manner can help to locate the cyclone warm core and assist in operational fixes, though the resolution is poor. Scatterometers and direct sounding devices, such as the SSM/I (Special Sensor Microwave/Imager), borne on the US DMSP series of polar-orbiting satellites, provide an indication of surface winds and waves, which also can help with locating the surface centre. The SSM/I and future spaceborne radars, such as is planned for the US/Japan TRMM (Tropical Rainfall Measuring Mission) satellite, can provide detailed mapping of the rainfall distribution, and thus accurate centre location, regardless of the degree of cirrus overcast. For example, Velden et al. (1989) showed that rainband observations from SSM/I provided useful information for locating the centre of tropical cyclones, especially when the eye region is obscured by cirrus. Unfortunately, such observations will not be commonly available for some time and will only sample cyclones occasionally.
Radar is an acronym that stands for RAdio Direction And Ranging. The heart of the system is a conical beam of pulsed electromagnetic energy in the microwave range transmitted outward from a rotating antenna. Backscattered energy from hydrometeors and other atmospheric scatterers is collected by the same antenna and displayed either as a horizontal Plan Position Indicator (PPI) plot, or a vertical Range Height Indicator (RHI) slice. Some radar display systems also have the capacity integrate volumetric data collected from several scans at different beam elevations.
Doppler radar also measures the change in frequency between the original and backscattered beam. Because of the Doppler effect, backscattering particles moving towards the radar will cause a change to higher frequency, particles moving away change to lower frequency. Thus the mean motion of the scatterers towards or away from the radar can be determined. Two Doppler radars in close proximity can provide full three dimensional winds in regions where their beams overlap at an appropriate angle. An airborne Doppler radar can also obtain a full wind field by appropriate manouvering to sample the same volume from different directions. Since Doppler radars only have limited use in tropical cyclone diagnosis at this stage, no further description of methodologies will be provided here.
Because of the conical nature of a radar beam, and the earth curvature, considerable resolution and information is lost as the distance from the radar increases. The diameter (m) of the expanding cone can be estimated from:
(3.2)
where, 
(o) is the beam width and R (m) is the distance from the
radar. Thus, a 2o beam width radar samples a 7 km diameter conical section at
200 km range. The earth curvature also causes the straight radar beam to sample higher
levels of the atmosphere with increasing radius, so that a PPI display is actually a huge
bowl (Fig. 3.4a). For a zero degree elevation the height of the centre of the beam above
the earth is given by (Battan, 1973):
(3.3)
where: z is the height above the earth surface (km), a is the earth radius (approximately 6320 km), and the 4/3 factor corrects for the refraction of the radar beam by the stratified atmosphere. One method of correcting for this fishbowl PPI view is to step the radar through several elevations to obtain a volumetric scan, then transform the data to a series of Constant Altitude PPIs (CAPPIs), as shown in Fig. 3.4a.
Figure 3.4. a) Illustration of the bowl shaped PPI and straight CAPPI relative to the curved earth surface, b) Tropical Cyclone Joan (1975) off the Australian west coast, showing the loss of signal at large radii from the combined effects of the bowl shaped PPI and attenuation by heavy rainfall. All terms are defined in the text.
Figure 3.5. a) Radar echo PPI for Trixie (1975) off the Australian west coast, together with, b) a schematic showing an earlier incorrectly analysed centre, c) the correct centre after reformation of the eye wall, and d) corrections to the operational track made by following the conservative features of the eye wall (adapted from Meighen, 1987, and Bureau of Meteorology, 1978).
As a tropical cyclone approaches a radar the first evidence is usually bands of heavy precipitation, called precursor rainbands, which move ahead of and at roughly the same speed and direction as the cyclone. Accurate location is not possible at this stage. Once significant lengths of spiral band are observed, fitting logarithmic curves with a constant crossing angle of 10-20o can provide an initial indication of the cyclone centre (Senn and Heiser, 1959). The basic method is to make up an overlay with several logarithmic curves, then to find the best fit to the observed spiral bands. The spiral centre then provides the approximate cyclone fix.
Once an eye, or distinct circulation centre appears, radar can provide high frequency locations with errors generally equivalent to those from aircraft reconnaissance (of the order of half the radius of maximum winds). The basic technique is to simply find the geometric centre of the eye (which may be elliptic). However significant analysis errors may occur when the eye is ragged or only formed on one side (Meighen, 1987, Fig. 3.5). In these circumstances, considerable care needs to be taken to find the conservative eye wall feature (Fig. 3.5b). This can best be done by looping the radar PPIs, and by maintaining a conservative size and shape of the eye over periods of several hours.
Surface observations used in conjunction with other observing methods provide a valuable analysis aid in fixing a tropical cyclone. For example, when satellite data indicate a loosely organised developing system, surface observations of an overall circulation, especially with westerly winds on the equatorward side, can help considerably with the satellite interpretation. Two major analysis methods may be used (Bureau of Meteorology, 1978). In the first, the analyst draws lines normal to the frictionally adjusted wind observations. The area enclosed by the intersecting radials then provides an estimate of the centre location. The second method involves fitting a predetermined pressure or wind profile (Holland, 1980) to surrounding observations. This can be done manually by drawing concentric circles inwards from the available surface observations. Such methods can help to locate the approximate centre location when an independent method of estimating the cyclone intensity is available, but they are of little use by themselves (eg, Holland, 1981c).
The importance that forecasters place on the use of surface observations is indicated by the survey of McBride and Holland (1987), in which such data were nominated by the majority of forecast offices as being the most important and useful. However, we strongly caution that care be taken with using surface observations as the major means of locating a tropical cyclone. Holland (1981c) showed the errors in location of the early tropical cyclone data for the Australian region, despite a careful reanalysis of these data using all available surface observations. Holland also reported on an experiment where a large number of experienced analysts estimated the location and intensity of a tropical cyclone using surface data alone. Although the data were extremely good by normal standards, errors of over 100 km in location were common, and the intensity estimates were of little use.
Several non-standard methods of locating tropical cyclones have been developed. Some of these, such as the use of microseisms transmitted from breaking waves (Bureau of Meteorology, 1978) and the appearance of storm swell at the coast, have been made redundant by the use of satellites. Two methods that do have some merit are the use of spherics and data from over-the-horizon radar (OHR).
Spherics use an array of instruments to locate the timing and direction of the radio "crackle" associated with lightning discharges in the atmosphere. They were traditionally used to locate regions of intense storms and have recently been re-established with modern, personal-computer based analysis and display. These offer a potentially useful means of locating tropical cyclone bands, and perhaps the core over oceanic areas. At this stage insufficient analysis has been completed, but those offices with spherics networks should experiment with analysis methods for tropical cyclones.
OHR is a phased array radar which sends out and receives beams of electromagnetic energy over very long distance by using reflection from the ionosphere. When properly processed, the signals that are backscattered from ocean waves can provide a good indication of the local wind direction and a fair to poor indication of the wind-speed (Keenan and Anderson, 1987). With only one radar an ambiguity exists in wind direction, which can only be resolved by hand analysis, or by comparison with other observations in the region. With available resolution of less than 25 km the resulting surface wind field can be used to accurately locate cyclone centres. The major advantage of such OHR observations is their incredible range which can extend several thousands of kilometres from the radar site. Some testing has been conducted in Australia, but the full operational potential has not yet been achieved.
During operations cyclone fixes are derived at odd times from a variety of observing platforms. Analysis inaccuracies, inherently different locations provided by different observing systems and real high-frequency oscillations of the cyclone centre combine to produce a scatter of potential cyclone positions from which an operational track must be derived. Most cyclone warning centres do this by using some form of curve fitting or smoothing based on a reliability-weighted average of the available fixes. Surface analyses are used to check for gross errors and to fine tune the final position estimate (McBride and Holland, 1987).
A good, conservative method of deriving the operational track is to plot all available fixes with a code that indicates their source (aircraft, satellite, radar, etc). Where possible this should be done on both a computer and a large chart. The chart provides an opportunity for independent hand analysis, a ready reference for later cross checking, and a fail-safe recourse in the case of a computer failure. The computer provides a capacity for use of objective curve fitting or smoothing routines and ease of direct comparison of tracks derived from different sources.
The next step is to make a forecast of the current analysis position using past data. This forecast may be derived from the previous official forecast, application of a simple persistence and climatology technique, or use of some curve fitting method. The forecast period used depends on the required detail in the operational track. A smooth track for long-period forecasts should use 6-12 hours and a low-order curve fitting method. Tracks needed to resolve short period oscillations should use a few hours and high-order techniques. It should be noted that the sensitivity to noise increases as smaller scales are resolved and only radar or regular aircraft fixes are really capable of resolving the details of a trochoidal oscillation.
The forecast position is the first guess for fixing the cyclone. This provides a conservative method, especially when using satellite data with poorly defined systems, but great care needs to be taken to ensure that the wrong cloud feature is not being followed. For hand analysis, the next step is to carefully consider all fixes over the past 24 hours, or so, and indicate those that should be given the highest weighting. Such weighting can be generic to the observation type (eg radar would rate higher than satellite), or it can be from immediate past experience for the current cyclone. Next redraw the track for at least the past 24 hours using a degree of smoothing appropriate to the situation, as described in the previous paragraph. Go back further in the track if needed to overcome an obvious analysis error.
On a computer, several objective methods for developing and maintaining an operational track may be utilised. A curve of suitable order may be applied to the past fixes using a least-squares fit with each fix weighted according to the perceived accuracy. Holland and Lander (1992) provide an indication of the impact of fitting curves of various orders to cyclone tracks and Willoughby (personal communication, 1989) has utilised a least-squares approach to smoothing aircraft tracks for NHC. Such curves also provide a short term forecast method, but care needs to be taken as higher order curves can provide very unstable extrapolations. A better alternative, is to fit a curve through both the past fixes and short-term forecasts. For example, Curry et al. (1985) use a simple climatology and persistence technique to forecast the short-term track, then fit a smooth curve to derive the current warning position. Applied weighting factors give most emphasis to recent fixes in addition to observation type. Titus and Jarrell (1985) use a Kalmen filter approach in which the relevant parameters change in time based on the "errors" of previous fixes along the current storm track. This is an objective equivalent to the subjective forecaster judgement of fix accuracy. The above techniques provide warning positions that are of similar accuracy to those derived by forecasters.
The next step is to carefully consider the possible errors in the track, particularly those that might significantly change the direction or speed of the immediate past motion, which is of considerable importance for the first 24 hour forecast. It is a good idea to consider all outlying fixes individually. Many can be ruled out as inaccurate, but some may indicate a real change in direction. The basic rule to be applied in such cases is to be conservative and to maintain the current track in uncertain situations. A good rule also is to selectively remove certain fixes of doubtful quality from the track and all computer based systems should have this capacity as a requirement.
Occasionally a major analysis error occurs and new information indicates that the cyclone position needs to be substantially modified. In this case, it is a good idea to go back and redraw the track for a substantial period, re-interpreting the observations and their inherent errors in light of the new information. Considerable care should be taken to understand the reasons for the erroneous track interpretation, especially so that it will not be repeated.
Once the analysis position has been decided, it should be given a confidence indicator for the benefit of other users. For example: radar, good 20 km, fair 40 km, or poor 100km. The associated errors should be derived from known analysis errors using the particular observing platform or analysis technique.
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