690 WEATHER AND FORECASTING VOLUME 26

Estimating Tropical Intensity from Infrared Image Data

MIGUEL F. PIN˜ EROS College of Optical Sciences, The University of Arizona, Tucson, Arizona

ELIZABETH A. RITCHIE Department of Atmospheric Sciences, The University of Arizona, Tucson, Arizona

J. SCOTT TYO College of Optical Sciences, The University of Arizona, Tucson, Arizona

(Manuscript received 20 December 2010, in final form 28 February 2011)

ABSTRACT

This paper describes results from a near-real-time objective technique for estimating the intensity of tropical from satellite infrared imagery in the North basin. The technique quantifies the level of organization or axisymmetry of the infrared cloud signature of a as an indirect measurement of its maximum wind speed. The final maximum wind speed calculated by the technique is an independent estimate of tropical cyclone intensity. Seventy-eight tropical cyclones from the 2004–09 seasons are used both to train and to test independently the intensity estimation technique. Two independent tests are performed to test the ability of the technique to estimate tropical cyclone intensity accurately. The best results from these tests have a root-mean-square intensity error of between 13 and 15 kt (where 1 kt ’ 0.5 m s21) for the two test sets.

1. Introduction estimate the intensity of tropical cyclones was developed by V. Dvorak in the 1970s during the early years of Tropical cyclones (TC) form over the warm waters of satellites (Dvorak 1975). In this technique, an analyst the tropical oceans where direct measurements of their classifies the cloud scene types in visible and infrared intensity (among other factors) are scarce (Gray 1979; satellite imagery and applies a set of rules to calculate McBride 1995). In general, the primary sources of ob- the intensity estimate. The original is servations for these intense vortical weather systems are subjective, is time intensive, and relies on the expertise from satelliteborne instruments (e.g., Ritchie et al. 2003; of the analyst, but it is still used as the primary intensity Velden et al. 2006b). Although these instruments provide forecasting tool in many tropical cyclone forecasting many observations, including winds at various levels of centers around the world (e.g., Velden et al. 1998, 2006b; the atmosphere and temperature and humidity sound- Knaff et al. 2010). Velden et al. (1998) introduced the ings, among others, none of these include direct measure- difference of temperature between 1) the warmest pixel ments of the maximum wind speed or minimum sea level temperature near the of the tropical cyclone and 2) pressure intensity of a tropical cyclone. the coldest of the warmest pixel temperatures found on Because of the lack of direct in situ measurements of concentric rings around the center. This modification is tropical cyclone intensity, several techniques have been known as the objective Dvorak technique, and, although developed to estimate the intensity based on indirect the intensity is objectively calculated, the location of the factors. The most-used technique in operation to eye of the tropical cyclone must still be determined by an expert or by using external sources. Olander and Velden (2007) developed the advanced Dvorak technique (ADT), Corresponding author address: Miguel F. Pin˜ eros, PAS Bldg., Rm. 542, P.O. Box 210081, The University of Arizona, Tucson, AZ which introduces new procedures in making an intensity 85721-0081. estimate from satellite-based imagery rather than sim- E-mail: [email protected] ulating the original Dvorak technique. One of the most

DOI: 10.1175/WAF-D-10-05062.1

Ó 2011 American Meteorological Society Unauthenticated | Downloaded 09/25/21 03:36 PM UTC OCTOBER 2011 P I N˜ EROS ET AL. 691 important improvements of the ADT consists of the in- These images are cropped to cover an area from 48 to troduction of regression equations to estimate the tropical 348N and from 1058 to 288W over the northern Atlantic cyclone intensity. Kossin et al. (2007) recently described basin and are resampled to a spatial resolution of 10 km a new satellite-based technique in which the radius of per pixel. Although the period of interest is from 2004 to maximum wind, the critical wind radii, and the two- 2009, tropical cyclones that had the majority of their dimensional surface wind field are estimated from in- trajectory outside the footprint of the cropped satel- frared (IR) imagery. This technique uses 12-h mean IR lite image were excluded from the study. This included imagery and best-track position data to estimate the Hurricane Vincent (2005) and Tropical Storms Beryl two-dimensional wind fields, which are compared with (2006), Chantal (2007), Ten (2008), and Grace (2009). aircraft wind profiles. In addition to visible and infrared As a result, a total of 15 147 half-hourly images from imagery, techniques for estimating the intensity of a tropi- 2004 to 2009 were analyzed, covering the life cycle of 36 cal cyclone have also been developed on the basis of mea- tropical storms and 42 hurricanes. surements from the Advanced Microwave Sounding Unit All samples that were located over land (center (AMSU; Spencer and Braswell 2001; Demuth et al. passed over continents and large islands) were removed 2004). Some of these techniques have been combined to from the database for consistency. Observations show enhance the TC intensity estimation (e.g., Velden et al. that tropical cyclones that make landfall rapidly decay at 2006a). a rate that is inconsistent for overocean tropical cy- A different approach for characterizing the dynamics clones. Thus, a different set of parametric curves will be of tropical cyclones was described in Pin˜ eros et al. required for landfalling TCs and is a topic of future (2008). In that study, a method to quantify the axisym- work. For now, all overland samples are simply removed metry of a tropical cyclone from remote-sensing data from the training set. was introduced. Using 30-min-resolution geostationary The original technique to determine the axisymmetry infrared imagery, the gradient of the brightness tem- of a cloud cluster using the deviation angle is illustrated in peratures was calculated, and the departure of that Fig. 1 (Pin˜eros et al. 2008). First the gradient of the IR gradient from a perfectly axisymmetric hurricane was image at every pixel (in vector form) is calculated. Figure determined. A single value that quantified that depar- 1a shows the pseudo-IR image for an idealized hurricane. ture from asymmetry was calculated, and a time series The associated IR gradient field is shown in Fig. 1b. Next, was built and correlated with the best-track intensity choosing a reference or center pixel, the deviation of the estimates from the National Hurricane Center (NHC). IR gradient vector in a pixel from a radial extending from The technique proved to be quite successful because the the center pixel is determined and stored. This calculation organization of the clouds about the vortex, including of the deviation angle is repeated for every pixel within the cirrus shield, is directly tied to the kinematic orga- 350-km radius of the center pixel. Next, the distribution nization of the vortex, including the organization of the of the deviation angles is plotted (Fig. 1c) and the vari- eyewall, , and tangential winds. ance of that distribution (the deviation-angle variance or In this paper, an improvement of the tropical cyclone DAV) is determined. The higher the variance of the an- intensity estimation technique described in Pin˜ eros et al. gle distribution is, the more disorganized is the cloud. (2008) is presented. In the next section, a brief review of The lower the variance is, the closer to pure axisymme- the method is presented and the improvement of the try is the cloud pattern. Figures 1d and 1e show the same technique is introduced. Results are shown in section 3. sequence as in Figs. 1a–c but for a single snapshot of Conclusions are discussed in section 4. (2005). The calculation is repeated using every pixel in turn as the reference center. The variance values are then plotted back into the reference pixel lo- 2. Method cation to create a ‘‘map of DAVs’’ (Pin˜eros et al. 2010) The study incorporates the 2004–09 North Atlantic that corresponds to the original IR image. In Pin˜eros et al. Ocean hurricane seasons (Franklin et al. 2006; Beven (2010), the map of variances was used to detect tropical et al. 2008; Franklin and Brown 2008; Brennan et al. cyclogenesis. In this study, the map of variances is used to 2009; Brown et al. 2010). The data used in this study are estimate the tropical cyclone intensity by developing longwave (10.7 mm) IR satellite imagery from the Geo- a parameterized curve fitting that relates the DAV values stationary Operational Environmental Satellite-12 with a parameterized function. (GOES-12). The data are available at ;4-km spatial The original DAV technique used a fixed 350-km ra- resolution, but we found previously that reducing the dius for calculation. Here, we improve the system by resolution does not particularly influence the results but using eight different maps for each image in the training does decrease the computational time considerably. set at radii varying from 150 to 500 km in steps of 50 km.

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FIG. 1. (a) Brightness temperature image of an ideal vortex. (b) Gradient vectors of the central section in (a). (c) Distribution of deviation angles for the ideal vortex in (a). (d) Hurricane Rita, 1415 UTC 21 Sep 2005 (intensity: 130 kt and 932 hPa). (e) Distribution of deviation angles in (d), with variance 5 593 deg2.

Figure 2 shows an example of three images and their signal. The oscillations present in the filtered DAV 400-km maps for (2007). For each signal include diurnal and semidiurnal frequencies, as analysis radius, a time series of the minimum DAV in well as some smaller-scale components, and they make it the sequence of maps associated with a given tropical difficult to relate the DAV to the best-track intensity. cyclone over its life cycle was constructed (the DAV Thus, one intensity value in the best track could have signal). A single-pole low-pass filter (impulse response: several associated DAV values. To overcome this prob- e2kt) with a cutoff frequency of 0.01p radians per sample lem, the median of all DAV values associated with a (filter time constant of 100 h) was applied to smooth the single best-track intensity estimate was used to create signal and provide a better correlation with the best- the data scatterplot. A sigmoid was then fit to the rough track intensity estimates, which are only available every DAV–intensity scatterplot so that the final parametric 6 h but are interpolated to 30 min. curve was described by a continuous equation: Next, the filtered DAV signals were mapped to the NHC best-track intensity records to obtain a parametric 160 f (s2) 5 1 25 (kt), (1) curve between the variance and maximum wind speed 1 1 exp[a(s2 1 b)] for each of eight radii of analysis. Because the filtered DAV signal is created using 30-min imagery but the where a and b are two parameters to fit from the input best-track intensity estimates are available only every data and s2 is the filtered DAV value. Note that the es- 6 h, there is considerably more structure in the DAV timatedwindspeedf(s2) is bounded between 25 and

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FIG. 2. Map of the variances for Hurricane Dean (2007) with a 400-km radius: (a) 1215 UTC 14 Aug—35 kt, 1004 hPa, and a map minimum value (MMV) of 1727 deg2; (b) 0015 UTC 16 Aug—60 kt, 991 hPa, and an MMV of 1548 deg2; (c) at 0015 UTC 18 Oct—125 kt, 944 hPa, and an MMV of 1250 deg2.

185 kt (where 1 kt ’ 0.5 m s21) in Eq. (1). Although we test set. This set included five tropical cyclones from considered several different polynomial functions, the 2004, seven from 2005, two from 2006, and six from sigmoid was chosen for this application because it is 2008. Figure 3 shows the two-dimensional histogram of bounded at both ends of the intensity range, thus avoiding the filtered DAV samples and best-track intensity es- the possibility of obtaining unrealistically high or low timates for this random set. The best-fit sigmoid curve intensity estimates. Last, the parametric curve for the ra- for this set is shown as a solid line and was obtained dius with the minimum sum of squares of error over the training set was chosen as the final intensity estimator parametric curve. The specific optimum radius depends on the training data used, and we typically see values be- tween 300 and 400 km. Once the system is trained, DAV maps are computed for the testing storms with this single optimum value. This process was repeated with two dif- ferent training sets, and the resulting two testing data- sets, to measure its effectiveness as an intensity estimate.

3. Results For the first test, the intensity estimation parametric curve was calculated using a training set of 50 tropical cyclones (70% of the available data) randomly chosen from the period 2004–08. Only samples with intensities above tropical storm strength were considered because of FIG. 3. Two-dimensional histogram of the 300-km filtered DAV samples and best-track intensity estimates using 20 deg2 3 5-kt bins uncertainty in the best-track database at lower intensities for 70% of the tropical cyclones randomly chosen from the period (D. Brown, NHC, 2010, personal communication). The 2004–08. The curved line corresponds to the best-fit sigmoid curve remaining tropical cyclones were used as an independent for the median of the samples.

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FIG. 4. Intensity estimates and best-track intensities for 20 tropical cyclones (30% of the dataset) randomly chosen from 2004 to 2008, and the remaining 70% used to obtain a and b. The RMSE is 14.7 kt. using a radius of 300 km. The root-mean-square error best-track intensity estimates from the NHC that are (RMSE) for the testing set of tropical cyclones was used as the reference are available only every 6 h as com- 14.7 kt (Fig. 4). pared with the 30-min resolution of the DAV estimates. The second test consisted of training the intensity es- For example, Fig. 9 shows the 350-km DAV signal and the timator with all tropical cyclones from the years 2004–08 wind speed for (2004); the open circles and then using the eight tropical cyclones in the dataset indicate a diurnal oscillation (23.5 h apart). These fluc- from 2009 as the independent test set. Figure 5 shows the tuations in the DAV signal in comparison with the lower- two-dimensional histogram and the best-fit parametric temporal-resolution best-track estimates decrease the curve, which was obtained using a radius of calculation correlation with the best-track intensity. Figure 10 shows for the variance of 350 km. The total RMSE for the 2009 the dispersion produced by the DAV–wind speed samples test set was 24.8 kt. The increase in RMSE was entirely of Jeanne in the two-dimensional histogram of Fig. 5. The due to just two cases: Tropical Storms Ana and Erika. open circles shown in Fig. 9 are also plotted in Fig. 10. Although these tropical cyclones were only weak trop- Although we have mitigated this problem to some degree ical storms, the cloud structure associated with each by smoothing the DAV signal and fitting the sigmoid curve showed high levels of axisymmetry (Fig. 6), resulting in to the data to produce our final DAV–intensity relation- a DAV that was very low and thus an estimated intensity ship, this mismatch in the temporal resolution between that was too high. For these two cases the technique over- the DAV signal and the best-track intensity estimate will estimated the intensity by more than 250% (Fig. 7). The always be a limiting factor on the agreement between the likely cause for this overestimate is the dislocation of the DAV and the best track. systems’ centers from the very circular cloud masses by environmental vertical shear. Work is on going to reduce the overestimates of intensity caused by these kinds of very circular, but displaced, systems. Until this is accom- plished in an automated way, it will be necessary to su- pervise the results of the intensity estimator to avoid this particular kind of error. The RMSE for the six tropical cyclones of 2009 excluding Tropical Storms Ana and Erika is 12.9 kt (see Fig. 8). Table 1 summarizes the curve parameters and the radius selected for these results.

4. Discussion a. DAV time series Although the filtered DAV signals are negatively cor- related with the best-track intensity estimates (Pin˜eros FIG. 5. Two-dimensional histogram of the 350-km filtered DAV et al. 2008), the oscillations present in the signals produce samples and best-track intensity estimates using 20 deg2 3 5-kt bins some dispersion of DAV–wind speed samples, shown in for tropical cyclones from the period 2004–08. The curved line cor- Figs. 3 and 5. This dispersion is unavoidable because the responds to the best-fit sigmoid curve for the median of the samples.

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FIG. 6. Two weak tropical cyclones in 2009 that were removed from the analysis because of their high level of axisymmetry: (a) Tropical Storm Ana, 0615 UTC 12 Aug (intensity: 30 kt and 1006 hPa), and (b) , 0615 UTC 1 Sep (intensity not reported). b. Intraseasonal and interannual variability investigate whether there is sensitivity to either seasonal or annual variations, the DAV–intensity curves were Previous work by our group (Demirci et al. 2007) has recalculated based on training by year and training by demonstrated that interannual and intraseasonal vari- month over the 5-yr period of 2004–08. The fitted curves ability of the atmospheric circulation patterns can also for individual years and for individual months over be a limitation on how well an automated technique the 5-yr period are very similar to the overall training can estimate or predict tropical cyclone behavior. To curve for the entire period, suggesting that seasonal and

FIG. 7. Intensity estimates of two weak tropical cyclones in 2009 that were removed from the analysis: Tropical Storms (a) Ana and (b) Erika.

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FIG. 8. Intensity estimates and best-track intensities for 2009, using tropical cyclones from the period 2004–08 to obtain a and b. The RMSE is 12.9 kt. interannual variations in the North Atlantic basin do not the filter to reduce the fluctuations of the DAV signal so appear to affect the DAV intensity curve. The greatest as to obtain DAV–wind speed samples that are more con- departure from the general intensity curve for any of the centrated around the curved line in Fig. 5 simultaneously annual curves is less than 10 kt (data not shown). A sim- increases the technique’s error for rapid-intensification ilar result was obtained for the months of July–October, tropical cyclones. The rapid intensification of Hurricane where there are enough samples for the system to be stable Wilma (2005) is an example of how this trade-off can de- (data not shown). Thus, we conclude that there is no sig- crease the DAV performance. In the case of Wilma, the nificant value added in developing different parametric low-pass filter that is applied to smooth the DAV signal curves for individual seasons or for different months. results in a response in the DAV signal that is behind the actual intensification of Wilma (Fig. 11). The rate of in- c. Physical reasons for the overall robustness tensification and final intensity of Wilma are actually very of the method well modeled by the DAV parametric curve. However, Similar to the Dvorak technique that has proven to be the starting time of the rapid-intensification phase is late, so successful for more than 30 years, this technique has and the time difference between the maximum values of a physical foundation for its success. This foundation is both signals is around 35 h. Implementing another fil- based on the premise that the cloud patterns and their ter configuration such as a finite impulse response, which similarity to a perfectly annular pattern are directly re- typically has lower transient responses, or utilizing a higher lated to the organization of the secondary circulation, cutoff frequency for rapid intensification cases might solve which includes the eyewall and patterns. The this problem. This will be a subject for future study. organization (and strength) of the secondary circulation is then directly related to the size and intensity of the e. Real-time implementation tropical cyclone primary wind field. Thus, as a general The first step in the process is to convert the imagery rule, the symmetric organization of the observed cloud from a natural Earth coordinate system to a Cartesian patterns is an indirect indicator of the intensity of the primary wind circulation. d. Rapid intensification The cutoff frequency of the low-pass filter applied to smooth the DAV signal determines its transient response, which in turn increases as the bandwidth decreases (Priemer 1991). Thus, decreasing the cutoff frequency of

TABLE 1. Estimator parameters calculated for two training sets.

Training set 50 tropical cyclones (70%) randomly chosen from 70 tropical cyclones 2004 to 2008 from 2004 to 2008 a (deg22) 0.002 655 0.002 697 b (deg2) 1008 1110 FIG. 9. Best-track intensity and 350-km DAV signal for Hurricane Radius (km) 300 350 Jeanne (2004). The two open circles are 23.5 h apart.

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FIG. 10. Histogram of Fig. 4. The red points are the 350-km DAV best-track samples for Hurricane Jeanne (2004). The two open circles from Fig. 9 are plotted to pinpoint the dis- persion produced from the DAV oscillations. projection that removes the differences in pixel resolution cyclone with the deviation-angle-variance metric as an that are due to Earth’s curvature. A standard software indirect estimate of the intensity from infrared imagery package developed by the University of Wisconsin— alone. In this paper, a set of parametric curves relating Madison, known as the Man–Computer Interactive Data DAV to maximum wind speed that are the result of the Access System (McIDAS; see online at http://www.ssec. technique were tested on two independent sets of trop- wisc.edu/mcidas/software/about_mcidas.html) was used ical cyclones: one set randomly selected from the 2004– to compute the projection change. Processing the DAV 08 period to be used as the testing set and the other set maps of an IR image takes less than 1 min on a 2.3-GHz comprising eight tropical cyclones from 2009. These Intel Core i7 computer with 8 gigabytes of memory using tests produce an RMSE that is between 13 and 15 kt the Linux CentOS 5.5 operating system and running the after two obviously bad cases are removed from the technique’s program with the software package Matlab testing set. Although part of the remaining 13–15-kt 7.10 (in no-display mode). error is probably due to the DAV signal oscillations that Once the parameterized wind speed estimator is ob- do not occur in the smoothed best-track intensity esti- tained, a shell script can be executed every hour to com- mates, other factors that may help to reduce the overall pute the projection change and calculate the DAV values of the image using the radius chosen in the development of the estimator. The process takes less than 4 min for asingleimage.TheDAVsignalisobtainedbyaddingone sample every time that one image is processed. Although these tasks can be automatically executed at a specific time by programming a Linux script, the user should manually start and stop the job.

5. Conclusions This paper describes improvements to a completely objective technique developed in Pin˜ eros et al. (2008,

2010) to characterize the intensity of a tropical cyclone. FIG. 11. Estimated intensity results for (2005). The technique quantifies the axisymmetry of a tropical The RMSE is 31 kt.

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RMSE include binning cases by environmental factors Demuth, J. L., M. DeMaria, J. A. Knaff, and T. H. Vonder Haar, such as the environmental vertical and sea 2004: Evaluation of Advanced Microwave Sounding Unit surface temperatures; these are the topics of future work. tropical cyclone intensity and size estimation algorithms. J. Appl. Meteor., 43, 282–296. The potential of the DAV technique to quantify the Dvorak, V. F., 1975: Tropical cyclone intensity analysis and axisymmetry of a tropical cyclone (and thus to charac- forecasting from satellite imagery. Mon. Wea. Rev., 103, terize its dynamics) has been demonstrated in this and 420–430. previous papers. This characterization of the tropical cy- Franklin, J. L., and D. P. Brown, 2008: season of clone dynamics with a single parameter is what makes it 2006. Mon. Wea. Rev., 136, 1174–1200. ——, R. J. Pasch, L. A. Avila, J. L. Beven, M. B. Lawrence, S. R. possible to estimate robustly the intensity of the tropical Stewart, and E. S. Blake, 2006: Atlantic hurricane season of cyclone. The testing results presented in this paper sug- 2004. Mon. Wea. Rev., 134, 981–1025. gest that the intensity estimates produced by this tech- Gray, W. M., 1979: Hurricanes: Their formation, structure and nique are reasonably accurate, and, in its current version likely role in the tropical circulation. Meteorology over as an independent estimate of tropical cyclone intensity, Tropical Oceans, D. B. Shaw, Ed., Royal Meteorological So- ciety, 155–218. the DAV technique is a complement to other estimates of Knaff, J. A., D. P. Brown, J. Courtney, G. M. Gallina, and J. L. Beven tropical cyclone intensity. Future work includes running II, 2010: An evaluation of Dvorak technique–based tropical real-case simulations of the life cycle of tropical cyclones cyclone intensity estimates. Wea. Forecasting, 25, 1362–1379. using a full-physics, high-resolution mesoscale model to Kossin, J. P., J. A. Knaff, H. I. Berger, D. C. Herndon, T. A. 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