Using the Rossby Radius of Deformation as a Forecasting Tool for Tropical Cyclogenesis
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- Conclusion and Future Work
- Acknowledgements
- References Avila, L. A., R. J. Pasch, and J.-G. Jiing, 2000: Atlantic tropical systems of 1996 and 1997: Years of contrasts. Mon. Wea. Rev., 128
| After obtaining all the grid points of calculated RROD within a TCC, an average RROD value is assigned for the given six hour interval based upon the total RROD calculated, divided by the total number of grid spaces contained within the TCC. The RROD value is calculated for both the mean radius and max radius of each TCC. The max radius represents the furthest extent horizontally that a TCC cloud shield extends as defined in Hennon et al.4. The mean radius represents the average value between the maximum and minimum extent of the cloud shield. This is an important distinction because TCCs are never completely circular in shape, and contain many indentations and extensions of cloud cover within a general elliptical shape. Mean and max radius will be discussed further in the results section to determine which is more effective at producing significant RROD separation between developing and non-developing clusters.
Results rossby radius ratio and standard deviation In order to make an assessment on how effective the RROD is at helping a TCC maintain energy within the cloud shield radius, a simple variable termed the rossby radius ratio (RRR) is created. RRR is the RROD divided by the actual radius of the TCC. In theory, the lower the RRR value for a TCC, the better the environment is for TCG, since the ratio between the RROD and the radius of the TCC is reduced, allowing for more energy to be contained within the TCC. This variable is then compared in both non-developing and developing TCCs to see if there is a significant difference. Developing TCCs were previously separated from non-developing TCCs before using the RROD algorithm, with developing cases defined as occurring up to 48 hours before a TCC becomes a tropical cyclone. Table 2. RROD Algorithm average values of RRRmax and RRRmean for developing and non-developing TCCs.
Table 2 highlights the different values of RROD and RRR for both non-developing and developing clusters. Results show that despite the small differences in radius between non-developing and developing cases, there is a large difference in RROD and RRR between the two categories. In addition, this table highlights the increased usefulness of using the mean radius for TCCs rather than the max radius. While RRR is lower for cases using the max radius, the smaller value is mainly due to the increased size of the radius, rather than a reduced RROD value. In addition, there is a larger difference in RRR using the mean radius between developing and non-developing clusters. 
Figure 2. Graph comparing RRR values of developing and non-developing TCCs. Blue lines represent RRR mean, while red lines represent RRRmax. Solid lines denote developing TCCs while dotted lines denote non-developing TCCs. The colored vertical lines represent the difference in RRR between developing and non-developing TCCs Figure 2 highlights the increased separation in peak RRR values between developing and non-developing cases using the mean radius of TCC. Thus, it seems that using the mean radius when calculating RROD and RRR is a more useful parameter to evaluate in the prediction of TCG. In addition to radius size, standard deviation in RRR was also calculated for each cluster to see if it could add additional skill to the RRR value. This is based on the hypothesis is that non-developing TCCs do not remain in a consistently favorable environment. This prevents further convective organization necessary for the TCCs to become tropical cyclones. Thus, a higher variance in the RRR value may signal an environment less conductive for TCG, and would more typically be found in non-developing TCCs. Results were analyzed in two scatter plots (not pictured) comparing RRR and the standard deviation of RRR in both developing and non-developing cases. Based upon the distribution on the scatter plots, there is no distinct trend that non-developing cases have a higher standard-deviation of RRR than developing TCCs. If anything, higher standard deviation seems to be better correlated with higher RRR values. Non-developing cases with lower RRR values still have lower standard deviation values similar to developing TCCs with similar RRR values. Thus, standard deviation of RRR was not considered as an important predictor to be used with RRR and the initial hypothesis is rejected. statistical measures of skill When investigating a large dataset that includes hundreds of data points, it is important to not merely focus on the mean of data, but also where the vast majority of the dataset lies. In some cases, the mean can be misleading when there is a large distribution of data. Thus, it becomes necessary to use statistical means such as the cumulative distribution function (CDF) to discover where the vast majority of cases occur within the entire data range.  
Figure 3. CDF graphs showing the differences in developing and non-developing TCCs Figure 3 shows the CDF of RRR mean for both non-developing and developing clusters. The results show that 95% of all developing TCC cases have an RRR value of 47 or less. This value is only consistent with roughly 60% of all non-developing cases. These results can help give guidance for the creation of a “threshold value” for RRR, allowing the identification of a value useful in forecasting TCG. A contingency table can then be created, which allows the testing of skill scores that give an objective numerical value for testing the forecast ability of that threshold. Contingency tables take on the common form found below in figure 4. 
Figure 4. A typical format of a contingency table. This same letter format is used in the equations below. where the one row stands for a forecasted occurrence of a developing TCC, while the one column represents the actual occurrence of developing TCC. The zero row is the forecast of a non-developing TCC, while the zero column represents the actual occurrence of a non-developing TCC. Three such skill scores were then derived from the contingency table above. Probability of detection (POD) represents the likelihood a developing TCC will be classified correctly using the given threshold20. False alarm rate (FAR) gives the ratio of false alarms to the total number of non-occurrences20. The equations for both of these values are given below. POD  (3)
FAR = The use of both of these scores individually might not prove that useful since TCG is a rare event to forecast, and applying typical probabilistic variables to a threshold’s ability to forecast TCG may be misleading15. A better skill score to use is the Heidke skill score (HSS) which is a combination of both the POD and FAR. The equation for calculating HSS is given below. HSS =  (5)
For a perfect forecast, the HSS would be 1, while a random forecast lacking skill would be equal to 0. HSS is considered to be a useful skill score for rare events such as TCG15. Using these three measures of skill on the threshold value of 47 RRR we discover that a very high POD (.95) is attainable. This makes sense, because this threshold samples roughly 95% of all the developing TCCs in our dataset. However, using the same threshold value also produces a pretty high FAR (.60) and a very low HSS (.05). 
Figure 5. Development probability of a TCC given a specific RRR value. Best fit line is dotted. Figure 5 highlights another method for determining a threshold RRR value for developing TCCs. Here, a histogram shows the total percentage of TCG based upon a RRR value. Note that up until around 21 RRR units, the percentage of TCG is generally at or above 10%. This is a rather significant statistic considering the rarity of TCG. This result also suggests a threshold value of 21 RRR might be a better predictor of developing TCCs. In order to objectively decide the most effective value to use as a threshold for developing TCCs, the POD, FAR, and HSS was calculated for all RRR values from 0 to 50. 
Figure 6. Skill scores based upon a given RRR value Figure 6 presents this information in graphical form. The highest HSS value was found using a RRR threshold of 17 (.17). Such a value maximizes the POD (.42) while limiting the FAR (.13). Previous studies have used HSS as an objective way to identify the best decision threshold for a parameter6, 8. Hennon et al. broke down HSS at six hour intervals, while also discriminating between decision thresholds6. HSS is higher in Hennon et al. at most time intervals, ranging from .26 at 48 hours to .41 at 12 hours6. However, this is largely due to the fact that eight different predictors were involved in enhancing the forecast ability of TCG through linear discriminant analysis. Kerns and Zipser investigated the HSS of non-developing vorticity maxima containing convection compared to developing vorticity maxima that persisted between 6-48 hours before genesis8. The latter temporal definition of developing systems is similar to the definition of developing TCCs defined in this study. Similar to Hennon et al., a multitude of different predictors (14) were selected to perform linear discriminant analysis to aid in the correct prediction of developing cases8. When using all parameters the max HSS obtained in the Atlantic basin was slightly more than double (.38) the max HSS value obtained from RRR in this study (.17). Once again the additional skill can be attributed to the fact that the discriminant function produced can differentiate between developing and non-developing cases more effectively than an individual predictor alone. Despite the observation that max HSS score in this reading is lower than both of the studies highlighted above, it is worth noting that our result stems from the use of one single predictor, RRR. Given that the HSS is still relatively comparable to other studies involving multiple variables gives increased confidence that the RRR value derived from RROD does contain skill in forecasting TCG. While this skill is not quite as impressive as the derived discriminant functions found in Hennon et al. and Kerns and Zipser, potential inclusion as a new parameter in these already robust functions may help to further improve TCG forecasts6, 8. The next section will highlight this potential application in future work. Conclusion and Future Work Thanks in large part to a new TCC dataset generated from Hennon et al. and the incorporation of data from GFS analysis files, an objective RROD algorithm is created in order to assign six hour RROD values to each given TCC identified within this study4. From this variable a ratio value between the RROD and the actual radius of each TCC is calculated, called the rossby radius ratio. This value is used to test its potential usefulness in forecasting TCG between developing and non-developing TCCs. Results showed that using the mean radius for TCCs proved to be a better descrimiant between developing and non-developing clusters. This is highlighted by the CDF of both types of clusters, where 95% of developing clusters contain a RRR value that was only comparable in 60% of the non-developing cases. Using a contingency table, skill scores of POD, FAR, and HSS were conducted for RRR values from 0 to 50 units. These results showed that the maximum HSS possible based on an optimal RRR value is .17. While this compares unfavorably to higher HSSs found in other studies, it is not quite fair to assess TCG predictability of just one variable against the discriminant functions of many variables used in other studies, a method that is expected to produce higher HSS scores than any one predictor of TCG6, 8. Considering that RRR is nearly half of the magnitude of HSS found in other studies, one can hypothesize that RRR could have a significant impact to these discriminant functions if included as a predictor. There are several aspects to the predictive qualities of using the RROD that need to be researched further. The first of which, is inclusion of a predictor using RROD within studies that have already employed a discriminant function using multiple predictors. Hennon et al. highlight in their future work that more predictors would be desirable in order to improve upon the discriminant analysis6. The RRR variable in this study could provide one such predictor that provides a significant contribution to the skill of forecasting TCG. In addition to possible incorporation into other studies, increased resolution in modeling data of the GRIB GFS dataset is desirable to obtain better calculations of vorticity and temperature within a TCC. Current RROD and RRR assessments likely contain a high bias due to the fact that the highest vorticity and temperature at 600 hPa within a TCC is not properly sampled due to low modeling resolution. Increased resolution will likely be more effective at capturing the mesoscale features common in all TCCs that increase vorticity. Finally, increasing the number of TCCs, by adding additional years of data will increase the number of developing cases within the dataset; likely improving on the accuracy of the RRR threshold. RROD is also not only relegated to the Atlantic basin; other oceanic basins such as the Pacific and Indian can be tested to see if RROD is also effective as a TCG predictor. It is promising to see the basic theory of RROD have some usefulness operationally in a significant fashion. With the incorporation of RROD into other prediction methods used in previous studies, RROD could prove to become one of the more important predictors in assessing potential for a TCC to undergo TCG.
Acknowledgements The author would like to thank Dr. Christopher Hennon of the University of North Carolina Asheville for his invaluable insight, assistance, and overall aid in making this research a success. He assisted and created many of the programs used to create the RROD algorithm. In addition, without the research and work conducted to create the TCC database from Mr. Charles “Chip” Helms while he worked at the National Climatic Data Center, much of the research that is presented here would not be possible. References Avila, L. A., R. J. Pasch, and J.-G. Jiing, 2000: Atlantic tropical systems of 1996 and 1997: Years of contrasts. Mon. Wea. Rev., 128, 3695–3706. DeMaria, J. A. Knaff, B. H. Connell, 2001: A tropical cyclone genesis parameter for the tropical Atlantic. Wea. Forecasting, 16, 219– 233. Frank, W. M., P. E. Roundy, 2006: The Role of Tropical Waves in Tropical Cyclogenesis. Mon. Wea. Rev., 134, 2397–2417. Hennon, C.C., C.N. Helms, K.R. Knapp, and A.R.Bowen, 2011: An objective algorithm for detecting and traking tropical cloud clusters: Implications for tropical cyclogenesis prediction. In Publication, J. Atmos. Ocean. Tech. Hennon, C. C., J. S. Hobgood, 2003: Forecasting Tropical Cyclogenesis over the Atlantic Basin Using Large-Scale Data. Mon. Wea. Rev.,131, 2927–2940. Hennon, C.C., C. Marzban, J. S. Hobgood, 2005: Improving Tropical Cyclogenesis Statistical Model Forecasts through the Application of a Neural Network Classifier. Wea. Forecasting, 20, 1073–1083. Hennon, P.A., 2006: The Role of the Ocean in Convective Burst Initiation: Implications for Tropical Cyclone Intensification. Dissertation, Ohio State University, 162 pp. Kerns, B., E. Zipser, 2009: Four Years of Tropical ERA-40 Vorticity Maxima Tracks. Part II: Differences between Developing and Nondeveloping Disturbances. Mon. Wea. Rev., 137, 2576–2591. Klotzbach, P. J., 2010: On the Madden–Julian Oscillation–Atlantic Hurricane Relationship. J. Climate, 23, 282–293. Knapp, K.R., M.C. Kruk, D.H. Levinson, H.J. Diamond, and C.J. Neumann, 2010a: The International Best Track Archive for climate stewardship (IBTrACS). Bull. Amer. Meteor. Soc., 91, 363-376. Knapp, K.R., and Coauthors, 2010b: Globally gridded satellite (GridSat) observations for climate studies. Submitted to Bull. Amer. Meteor. Soc. (July 2010). Leary, C. A., and R. A. Houze Jr., 1979: The Structure and Evolution of Convection in a Tropical Cloud Cluster. J. Atmos. Sci., 36, 437-457. Lee, C., Y. Lin, K. K. W. Cheung, 2006: Tropical Cyclone Formations in the South China Sea Associated with the Mei-Yu Front. Mon. Wea. Rev., 134, 2670–2687. Lowe, P. R., and T. J. Perrone, 1989: An operational technique for prediction tropical storm formation in the western North Pacific Ocean. Natl. Wea. Dig., 14, 5–13. Marzban, C., 1998: Scalar Measures of Performance in Rare-Event Situations. Wea. Forecasting, 13, 753–763. McBride, J. L., Raymond Zehr, 1981: Observational Analysis of Tropical Cyclone Formation. Part II: Comparison of Non-Developing versus Developing Systems. J. Atmos. Sci., 38, 1132–1151. Stull, R. B., 1995: Meteorology Today for Scientists and Engineers, 385 pp. University Corporation for Atmospheric Research, 2007-2010: Introduction to Tropical Meteorology. http://www.meted.ucar.edu/tropical/textbook/ch10/tropcyclone_10_3_1.html Vitart, F., J. L. Anderson, W. F. Stern, 1999: Impact of Large-Scale Circulation on Tropical Storm Frequency, Intensity, and Location, Simulated by an Ensemble of GCM Integrations. J. Climate, 12, 3237–3254. Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp. Yeh, H., G. T. Chen, W. Timothy Liu, 2002: Kinematic Characteristics of a Mei-yu Front Detected by the QuikSCAT Oceanic Winds. Mon. Wea. Rev., 130, 700–711. Directory: student student -> How to Create a Student Recital Program student -> Tracks, Mixes, Masters, and More!: Analyzing Preservation Priorities for Multitrack Recordings student -> A chronology 1660-1832 The Restoration Settlement student -> Introduction student -> Disaster planning and recovery: post-katrina lessons for mixed media collections student -> Comparing Hurricanes and Hurricane Seasons student -> Storm Surge: a rising Danger student -> Dr. Jeff Masters' WunderBlog student -> April 9, 2008 Hurricanes (Continued) student -> Instructions for Writing Hurricane Term Paper Download 364.18 Kb. Share with your friends:
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