Using the Rossby Radius of Deformation as a Forecasting Tool for Tropical Cyclogenesis

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
   

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 cyclones^{1, 5}. In addition, the lack of in-situ observations near the location of TCCs makes it difficult to properly assess the region^{3, 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 imagery^{5, 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 buoyancy¹⁸. 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 TCG¹⁹. 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 TCCs^{11, 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
   

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.

1. 
   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.
   
2. 
   A minimum radius of 1^o 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.
   
3. 
   TCCs that exist beyond 30^o 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.
   
4. 
   Cluster independence was conducted in the algorithm. Any cluster that is further than 1200 km away from another cluster is considered to be independent.
   
5. 
   A given TCC must persist for at least 24 hours before it is considered a TCC.
   
6. 
   TCCs that are found must not already be a tropical cyclone.
   

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 1^o by 1^o 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 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.