Proceedings of The National Conference
On Undergraduate Research (NCUR) 2011
Ithaca College, New York
March 31 - April 2, 2011
Using the Rossby Radius of Deformation as a Forecasting Tool for Tropical
Cyclogenesis
Philippe Papin
Atmospheric Sciences
The University of North Carolina Asheville
One University Heights
Asheville, North Carolina 28804 USA
Faculty Advisor: Dr. Christopher Hennon
Abstract
Tropical cloud clusters (TCCs) are large areas of deep convection in the tropics that can develop into tropical
cyclones, a process called “tropical cyclogenesis”. Theoretically, the Rossby Radius of Deformation (RROD) can be
a useful parameter in predicting when this will happen. RROD is defined as the critical radius where latent heat is
unable to be dispersed away from the TCC by gravity waves. Beyond this threshold value, gravity waves disperse
the latent heat too far away to support the intensification of a vortex. In this study, RROD is used in conjunction
with a new TCC dataset to investigate if RROD is a useful parameter in forecasting tropical cyclogenesis. The
RROD was calculated from model analysis fields for Atlantic Basin TCCs that formed during the 2004-2008
hurricane seasons. The resultant RROD was divided by the radius of the TCC to yield the Rossby Radius Ratio
(RRR). Results show that there is a significant difference in RRR between developing and non-developing TCCs,
with roughly 95% of all developing TCCs becoming tropical cyclones with a RRR value of 47 or less. A RRR value
of 47 or less was found in 60% of all non-developing cases. Additionally, using a threshold RRR value of 17
produces the highest Heidke Skill Score. Inputting this predictor into other studies using discriminate analysis could
further improve the prediction of TCG.
Keywords: tropical cyclone, Rossby Radius of Deformation, cloud cluster, tropical cyclogenesis
1. Introduction
The formation of tropical cyclones continues to be a subject of intense research within the meteorological
community. Tropical cyclogenesis (TCG) is a process where deep organized thunderstorm activity, generally within
the tropics, helps to generate enough latent heat to initiate both horizontal and vertical motion necessary to sustain
an intense circulation4. The term tropical cloud cluster (TCC) is used to signify a grouping of thunderstorms in the
tropics that form a unified cirrus shield12. These TCCs form from a variety of sources, such as easterly waves,
monsoonal circulations, and interactions of these features within broader atmospheric disturbances such as the
Madden-Julian Oscillation (MJO)9.
Despite the ability to identify TCCs visually using satellite imagery and passive microwave imagers, correctly
forecasting TCG continues to be a challenge. In the Atlantic basin, less than one in five TCCs go on to become
tropical cyclones1, 5. In addition, the lack of in-situ observations near the location of TCCs makes it difficult to
properly assess the region3, 5. Previous studies suggested that there are mesoscale processes that occur within TCCs
that are not yet fully understood, nor able to be modeled properly due to insufficient model resolution 5, 6, 3. Thus,
much research has been conducted in order to improve forecasting TCG. Oftentimes studies use datasets of TCCs in
order to discriminate between non-developing and developing cases. McBride and Zehr examined TCCs in both the
Atlantic and Pacific basins, finding that there was twice as much low-level vorticity in the vicinity of developing
clusters than in non-developing cases. Additional work with TCCs was conducted in Perrone and Lowe14. Low level
vorticity (defined at 950 hPa) was found to be one of the best predictors for TCG. The researchers also concluded
that it was possible to make tropical cyclone formation forecasts based upon fields derived from observational data.
DeMaria et al. developed a genesis parameter for TCG based upon zonal shear, instability, and mid-level moisture
for the Atlantic basin2. While this parameter was useful in describing the limiting factors necessary for tropical
cyclone development, it is not a sufficient condition. Thus, the study concluded it may be possible to develop a
disturbance-centered parameter to better evaluate the genesis potential of individual TCCs2. Hennon and Hobgood
and Hennon et al. used rigid methods for the identification of TCCs through satellite imagery5, 6. Results showed that
the daily genesis potential (DGP), the different in relative vorticity between 900 and 200 hPa, was the most
significant predictor for TCG, although other predictors were shown to be significant as well. Kerns and Zipser used
vorticity maxima (VM) in tracking tropical disturbances, since the location of tropical disturbances such as easterly
waves do not always have a direct correlation with the convection observed on satellite imagery8. Despite the
difference in tropical disturbance identification, low-level vorticity at 925 hPa proved to be the best predictor of
TCG in both the Atlantic and Pacific basin. Thus, in the studies noted above, the unifying theme is that vorticity
plays a pivotal role in forecasting the development of a tropical cyclone from a TCC.
One potential predictor with a vorticity component is the rossby radius of deformation (RROD). RROD is defined
as the radius at which rotation becomes as important for maintenance of a circulation as buoyancy 18. The basic
premise is that small circulations are typically dominated by buoyancy forcing, which results in gravity waves
quickly dispersing energy in a stable environment. Thus, most of the energy is released as kinetic energy. Larger
circulations are more rotational in character, and are dominated by rossby wave dynamics, allowing for additional
persistence. In this scenario, potential energy is stored within the circulation. Simply put, if a disturbance is larger
(smaller) than the environmentally derived RROD, it will persist (dissipate), all other forcings being equal.
Some literature has noted the potential usefulness of using RROD for TCG. Vitart et al. discussed how increased
low-level vorticity helps to reduce the RROD, with a smaller RROD implying more favorable conditions for TCG 19.
Yeh et al. mentioned the RROD being reduced in the vicinity of a mei-yu front, which is largely enhanced by latent
heat release in a mesoscale convective system (MCS)21. This same study is mentioned by Lee et al.; they implied
that reduced RROD is a result of the increased latent heat release13. The authors also mention that such a process
should be investigated further. In the following paper, RROD will be used in conjunction with a TCC dataset in
order to determine the usefulness of incorporating such a value into a TCG prediction scheme.
Recent advances in unifying the global network of satellite imagery into the development of a global, gridded
infrared (IR) dataset (GridSat) along with the unification of a global tropical cyclone best-track dataset (IBTrACS)
have allowed for the objective automated identification of TCCs11, 10. Such a system has been devised by Hennon et
al., where a global dataset of TCCs have been created to aid in the prediction of TCG4. The following study will use
this dataset of TCCs to test how effective RROD is as a tool to forecast TCG. Section two of this paper will describe
the methodology used to calculate the RROD value for each individual cluster, along with a brief description on how
TCC cases were determined via Hennon et al.4. Section three will present the results of the study, while section four
will provide concluding remarks discussing the usefulness of the results and future work that can be done to further
improve the RROD dataset, including incorporation into other algorithms.
2. Data and Methodology
2.1 TCC database
As mentioned in the introduction, a dataset of TCCs was created by Hennon et al. using a simple automated
algorithm4. This algorithm is described in Hennon et al.4. It is important to note that the following definitions and
assumptions that were made in that study also apply to the TCCs used within this study. These definitions are now
given below.
i.
Clusters are identified as areas of brightness temperature that meet or exceeds the top 2% threshold of
brightness temperature (T b) for each respective basin. As an example, this threshold is 224 K in the
North Atlantic basin.
ii.
A minimum radius of 1o is required for a cluster to be identified in the dataset. The threshold area of
pixels must make an area of at least 34,800 km2 and be generally circular to be considered in the study.
iii.
TCCs that exist beyond 30o north or south were not identified in the dataset. This is because many
baroclinic systems may also inhabit latitudes beyond 30 o and produce clusters that are not tropical in
origin.
iv.
Cluster independence was conducted in the algorithm. Any cluster that is further than 1200 km away
from another cluster is considered to be independent.
v.
A given TCC must persist for at least 24 hours before it is considered a TCC.
vi.
TCCs that are found must not already be a tropical cyclone.
For this particular study TCCs were obtained for a five year period from 2004-2008 in the Atlantic basin. The
TCC dataset contains three-hour temporal resolution tracks with a multitude of characteristics such as latitude,
longitude, size, brightness temperature, radius, and cloud top height. TCC data providing info on TCG is also given,
allowing for the discrimination between developing and non-developing TCCs. Developing TCCs are defined as
clusters that go on to become tropical cyclones, while non-developing TCCs do not. Developing and non-developing
TCCs were separated at this point in order to better determine differences in RROD between each group. Table one
shows yearly data of TCCs used in this study, including the number of TCCs in each given year, the number of
developing cases, and the TCG ratio. It should be noted that some developing TCCs were not found by the
algorithm, since some clusters existed above 30 degrees north, beyond the meridional range of the algorithm.
Table 1. TCCs data obtained from 2004-20084
Year
2004
2005
2006
2007
2008
Tropical Cloud Cluster Data for the Atlantic Basin
Clusters
Developing Clusters
TCG Ratio
214
13
6.07%
266
22
8.27%
238
8
3.36%
222
10
4.50%
253
12
4.74%
2.2 GFS analysis field and RROD calculation
The RROD calculation also requires additional atmospheric data. The global forecast system (GFS) model from the
National Center for Environmental Prediction (NCEP) was used for the 2004-2008 period. The GFS is a global
operational atmospheric model that produces a multitude of different variables at 6 hour forecast intervals on a 1o by
1o horizontal grid. This temporal resolution allows for the introduction of key meteorological variables to be used in
conjunction with individual cluster data obtained from the TCC dataset. Within this dataset, temperature, absolute
vorticity, and pressure data at the model analysis time (no forecast fields were used) were obtained for use in the
RROD algorithm.
The TCC and GFS datasets provides the necessary data to calculate the RROD value for each six hour time
interval for each individual TCC. The Rossby radius of deformation ( ) is defined as
(1)
where, N is the Brunt Vaisala frequency, H is the depth of the system, ζ is the relative vorticity and
planetary vorticity. The Brunt Vaisala frequency is calculated as:
is the
(2)
Where g is the local acceleration due to gravity, is potential temperature at 1000 hPa, and z is geometric height.
represents the difference in potential temperature from 600 hPa to 1000 hPa. Brunt Vaisala frequency represents
the frequency at which an air parcel will oscillate when displaced. This is critical since the frequency of internal
gravity waves do not exceed the Brunt-Vaisala frequency within the local environment17. The importance of using
600 hPa as the upper height level of potential temperature is that this represents the general height where the
maximum latent heat release occurs in convection associated with tropical cyclones 7.
The denominator in equation 1 is also known as the absolute vorticity: it simply the sum of both relative and
planetary vorticities. The absolute vorticity was obtained at 10 vertical levels between 925 hPa and 500 hPa and
averaged together to provide a mean absolute vorticity number that could then be applied to the RROD equation.
Simply using one level of vorticity (ie. 925 hPa) will not reveal the entire scope of a circulation within a TCC.
Indeed, many clusters contain absolute vorticity maxima at higher heights than 925 hPa. Using an average value of
absolute vorticity through 10 vertical levels provides a more realistic view of vorticity within a cluster. Vertical
height (H) used to calculate RROD comes directly from the TCC database.
For each TCC time, RROD is calculated globally from the GFS and TCC data. However, the only relevant
information needed is the area within each individual TCC, since the study is attempting to provide a reliable RROD
value associated with each cluster. Thus, the algorithm checks to see if the grid point calculated is within the radius
of the TCC. Figure 1 represents a flow chart used to reason how the algorithm works to obtain a proper RROD value
for each cluster. A visual schematic is provided to show how the algorithm checks to make sure grid points are
contained within a TCC. Each grid point within the cluster is represented by a blue dot and the center of the cluster
is represented by a red x. The area of the cluster is represented as a black circle as defined by the radius.
Figure 1. Flow chart of RROD algorithm.
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.
3. Results
3.1 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.
Cloud Cluster
Select Values From RROD Algorithm
RRODmax (km) RRODmean (km) RADIUSmax (km) RADIUSmean (km) RRRmax RRRmean
Developing
3485.68
2997.58
248.10
149.99
15.63
21.81
Non-Developing
11629.81
11417.74
255.93
147.66
50.79
84.44
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 standarddeviation 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.
3.2 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 =
(4)
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 parameter 6, 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 nondeveloping 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.
4. 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 nondeveloping 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 TCG 6, 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.
5. 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.
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