University of Oklahoma

Norman, OK

tajones@ou.edu

Research into the correspondence between tornado strength and WSR-88D algorithm numerical output is presented in this work. A 23 tornado case dependent data set and five tornado case independent data set were formed using a tornado's Fujita scale ranking as a bases for tornado strength. These cases were then studied using archived Level II radar data run on the WSR-88D Algorithm Testing and Display System (WATADS). The WSR-88D algorithm used for the determination of the mesocyclone attributes was the Mesocyclone Detection Algorithm (MDA). The MDA has been developed recently by the National Severe Storms Laboratory (NSSL) as an enhancement to the operational WSR-88D mesocyclone algorithm. MDA derived mesocyclone attributes were analyzed for the period 15 to 20 minutes prior to tornado formation. The MDA derived mesocyclone attributes were then used as predictors in linear regression models that attempted to predict the strength of a future tornado using the Fujita scale as the response variable. However, since many of the mesocyclone attributes produced by the MDA are highly correlated, Principal Component Analysis was undertaken on the attributes in order to form non-correlated predictors. Using the new uncorrelated predictors, seven linear regression models were formed using different temporal combinations of the radar data. The best linear model was able to account for over 50% of the variability in tornado strength using the MDA derived mesocyclone attributes one volume scan prior to tornado formation. In addition, nonlinear models were created that slightly improved effectiveness. Still, this result is somewhat misleading as the models made during this research assume a tornado will form in every case. Thus, performance of the models at predicting whether or not a tornado would form was rather poor.

A mesocyclone is formed when a severe thunderstorm begins to rotate due to wind shear and instability present in its environment. A mesocyclone is often approximated by a rotating column of air in the vertical where the velocity in a horizontal plane increases linearly outward from a point to a ring of maximum velocity and then decreases exponentially outward from that ring (Desrochers and Donaldson 1992). Approximately 30% (possibly fewer) of Doppler radar detected mesocyclones produced tornadoes and less than 1% of those were violent tornadoes (Burgess and Lemon 1991; Burgess and Doswell 1993). During the past decade, the number and variety of mesocyclone detections has increased significantly with the nationwide deployment of the WSR-88D NEXRAD Doppler radar. With the availability of WSR-88D radial velocity data, various algorithms have evolved that are able to detect mesocyclones and are able to calculate many of their associated attributes. These algorithms have provided a wealth of data concerning mesocyclones and tornadoes allowing for greater insight into the process of tornado formation and to aid in tornado forecasting.

Beginning in the early 1990s, the National Severe Storms Laboratory (NSSL) initiated work on enhanced algorithms using archived WSR-88D data from the entire country. One of the algorithms produced by this research was the Mesocyclone Detection Algorithm (MDA) (Stumpf et al. 1998). Early Doppler radar algorithms had difficulties in detecting circulations associated with weak mesocyclones because of beam bending (atmospheric effects on the radar beam) and broadening (the radar beam increasing in width) as range from the radar increased (Mitchell et al. 1998, Stumpf et al. 1998). The NSSL MDA was designed to overcome these difficulties by including range dependent thresholds for the detection of a mesocyclone. Thus, a weak velocity difference at great ranges (>100 km) would cause the MDA to detect a mesocyclone while earlier

algorithms could not make such a detection. This feature increases the probability that a mesocyclone will be detected no matter what its range from the radar (Stumpf et al. 1998). It is hoped that the MDA output will allow the forecaster to determine the strength of a future tornado based on radar algorithm derived mesocyclone attributes. To achieve this predictive capability, the MDA derived mesocyclone attributes will be statistically analyzed in association with the Fujita scale ranking of a corresponding tornado in an attempt to find commonality between various mesocyclone attributes and the impending strength of a tornado.

Most previous work in algorithm detections of mesocyclones involved the modifying the adaptable input parameters on the various WSR-88D algorithms to detect the parent circulations of relatively weak (F0, F1) tornadoes (Tipton et al. 1998, Stumpf et al. 1998). However, little work has been done using algorithm output in predicting the future strength of tornadoes. Desrochers and Donaldson (1992) did determine that excess rotational kinetic energy (ERKE) was a good predictor of tornado strength. They also determined that other attributes, such as maximum velocity difference and maximum shear, were also useful as predictors of tornado strength. However, the radar data used in that study were pre-WSR-88D and the number of tornado cases tested was severely limited (fewer than ten). No similar work relating tornado strength with mesocyclone attributes derived using WSR-88D algorithm output has been done. During the last ten years, WSR-88D radars have recorded on the order of 1,000 mesocyclones that were associated with tornadoes, giving a large and diverse database of recorded mesocyclones to use as a basis for this work.

The primary purpose of this work is to determine which MDA derived WSR-88D mesocyclone attributes are good predictors of the impending strength of a tornado assuming a mesocyclone was to produce a tornado. Since less than half of detected mesocyclones are

associated with tornadoes, the results of this work could give the forecaster an idea to the future strength of a tornado only if a tornado were to form. This work will not attempt to identify whether or not a mesocyclone will actually produce a tornado. Several previous works (Stumpf et al. 1998, Mitchell et al. 1998, Marzban and Stumpf 1998, Marzban et al.1999) have investigated this question. Results from their investigations included a neural network probability product embedded in the MDA that can give the probability of whether a particular mesocyclone is producing a tornado.

The results of this work would not allow a forecaster to predict whether or not a mesocyclone will produce a tornado. Still, if the results show that certain types of mesocyclones produce certain strengths of tornadoes, it could aid a future forecaster in issuing more appropriate warnings. Any possible predictor of the future strength of a tornado could be quite valuable. If good predictors cannot be found, it is hoped that this work can determine which attributes are bad predictors of tornadoes. This is significant operationally since a forecaster during a tornado outbreak is presented with an overload of information, including a multitude of algorithm products. Knowing what products to disregard would allow the forecaster to focus more time and effort on algorithm attributes that may have a significant link to the future strength of a tornado.

The following discussion presents the methodology used for this work in five sections which include determination of data set and radar data processing, algorithm attributes, and attributes analysis. This is followed by a discussion of the results provided by the MDA output and ensuing statistical analysis. Finally, conclusions will include a discussion on the relevance to tornado forecasting of the statistical results.

One of the most difficult aspects of this work was to determine a ground truth data set because of the many verification issues and inherent inaccuracies in Storm Data (Witt et al. 1998). Tornado cases used for this study are taken from Storm Data between the years of 1994 and 1999. Other more accurate sources for ground truth tornado data, such as the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX) and/or the Doppler On Wheels (DOW) reports, were considered but not included due to the small number of tornadoes being observed in this fashion (Rasmussen et al. 1994, Wurman et al. 1996).

Every tornado case listed in Storm Data with was examined to see if it met the following well observed criteria: 1) a tornado that damaged at least 100 substantial and permanent structures, 2) at least one injury occurred (for electronic search purposes), and 3) the tornado originated from a classical Central Plains type supercell. The above criteria were made to ensure an accurate Fujita scale ranking of the tornado as well as accurate temporal and spatial data for a given tornado. The first criteria is important since a greater number of buildings damaged allows for a more accurate damage survey than if just a few buildings were damaged. For example, a tornado may be classified as a violent tornado if it destroyed only one house on a farm; however, the construction and general condition of that house could cause the structure to fail at less than violent tornado winds. Conversely, the same tornado maybe classified as an F1 if fails to hit any substantial structures at all. Information on nearby structures of similar and dissimilar construction would be required to increase the confidence of a tornado ranking using the Fujita scale. The second criteria is mainly for electronic search purposes using the rationale that tornadoes that produce injuries are more likely to be near areas of denser population, hence more

structures to damage. Finally, the third criteria is used because most tornadoes are produced by supercells and MDA is designed to detect mesocyclonic circulations associated with the types found in supercell thunderstorms (Stumpf et al. 1998).

Tornado cases determined using these procedures were then checked for WSR-88D Level II tape availability for the appropriate date and time. Level II tapes used were borrowed from the NSSL archive in Norman, OK and availability was determined against Level II tapes they had available. This process eliminated several possible tornado cases since Level II tapes were not made (or were lost) for the specified time and place. Also, tornado cases that were greater than 150 km from a radar were removed due to issues concerning the size of the range bin and diluted data return which would affect the algorithm output (Stumpf et. al 1998, NSSL 1998). This left a tornado data set comprised of 28 tornado cases of various Fujita scale rankings for which mesocyclone attribute analysis would be undertaken (Appendix A). Five random tornado cases in the 28 case data set were held out in order to have an independent data set which was used to verify the results of the attribute analysis on the other 23 cases. Thus, the final data set consisted of a 23 case dependent data set and a five case independent data set. Each data set was subdivided into the separate volume scans of data for later processing giving four subsets of data for each large data set. Hereafter, each sub-data set is defined as the mesocyclone attributes that occur during the time of a particular volume scan before tornado formation (e.g. the data from the volume scan 15 min before tornado formation is defined as T-15, the data from the volume scan 10 min before tornado formation is defined as T-10, etc.).

Level II tape data analyses were performed using the WSR-88D Algorithm Testing And Display System (WATADS) version 10.0 (NSSL 1998). WATADS is a program designed to

read in archived Level II 8 mm tape data and display output using the many algorithms available for the WSR-88D radar including the MDA. It should be noted that there are some minor differences in the algorithms between actual WSR-88D products and WATADS products (NSSL 1998). A full explanation of WATADS including differences in products with respect to actual WSR-88D products is given NSSLs WATADS Reference Guide (1998). The output of the NSSL MDA algorithm is displayed in the Radar Analysis and Display System (RADS) which is a part of WATADS (Fig. 1). Also, this information is provided in somewhat greater detail in text form by the algorithm. Both outputs will be used for the determination of mesocyclone attributes in this work.

Each data set case was processed separately in WATADS using the default set of adaptable parameters with two exceptions. First, in order to save hard drive space, algorithms unnecessary for this work were not processed (e.g. precipitation algorithms). Second, the sounding data (wind profiles) necessary for velocity dealiasing (the determination of velocity magnitudes outside the radars Nyquist frequency) were from actual soundings not statistical averages. This ensured a greater accuracy in the wind fields which in turn provide a greater accuracy for the algorithm output based on those wind fields.

Sounding data were taken from various resources including the National Climate Date Center and NSSLs database specifically compiled for their Level II tapes. A sounding was chosen that was the closest available to the radar site and was closest in time to the studied tornado event. Soundings were downloaded in Forecast Systems Laboratory format, but due to the quality of some sets of sounding data, the values required for WATADS to create the storm relative wind profile were entered by hand.

The Level II WSR-88D data that were used for this study included the three volume scans previous to the touchdown of a tornado as defined by Storm Data, and the one volume scan during tornado touchdown. Since each volume scan takes between five and six minutes depending on radar mode, this accounts for the time window of radar data of 20 to 24 minutes prior to and during the formation of the tornado associated with the mesocyclone being analyzed.

Burgess et al. (1979) showed that the average lead time for the detection of a mesocyclone signature prior to producing a tornado was 21 minutes which is still consistent with current findings though in some extreme cases, the lead time can be much greater (Witt et al. 1998, Stumpf et al. 1998). The time window chosen here and its validity in algorithm research are discussed further in Witt et al. (1998).

The WSR-88D has four VCPs available, two of which are applicable to this work. The first, VCP 11, contains 14 unique elevations in a five-minute scan. The second, VCP 21, contains nine unique elevations in a six-minute scan (Brown et al. 1998). The VCP recommended for operation in severe weather is VCP 11 due to is greater resolution especially at higher levels and its slightly faster update speed. According to Brown et al. (1998), values of all algorithm output will sometimes be higher when using VCP 11 rather than VCP 21 due to the greater resolution available. Unfortunately, in several cases included in the 28 case data set, the radar was set to VCP 21. Fortunately, algorithm output, though affected by the radar setting to VCP 21 in this case, is usually not underestimated by such a magnitude as to make it incomparable to cases in which the radar was in VCP 11 (Brown et al. 1998).

Several previous works have noted problems in associating a specific mesocyclone circulation with a specific tornado case (Desrochers and Donaldson 1992, Mitchell et al. 1998, Stumpf et al. 1998). The ability of the MDA algorithm to detect many different circulations in close proximity to each other causes uncertainty as to which circulation is producing a tornado. Combined with time errors common in Storm Data, significant error in time and location can result leading to an incorrect determination of a tornado's parent circulation. Fortunately, much of this verification work has already been done with the NSSL’s Level II database. Listings are available that give times, range, and azimuth for every severe weather event recorded on that tape. Using this information makes the process of determining the parent circulation of a particular tornado much simpler and more reliable.

The MDA uses a centroid-relative method to associated vertically adjacent 2D circulation detections (Mitchell 1999). This means that once a 2D circulation is detected, the MDA then searches the radar from the scan angle above and below that circulation for a corresponding 2D circulation within a certain search radii. Unfortunately, this technique breaks down when many 2D circulations are detected in a small region. In this case, the algorithm attempts to define the most appropriate 2D circulation to correspond to an already detected 2D circulation above of below. If the algorithm is wrong in defining the appropriate circulation, the final 3D circulation output will be incorrect and often a single mesocyclone would be split up into two or more detections. When this problem occurred during the course of research, a manual correction of the 3D mesocyclone attributes (Appendix B) was attempted using the data form the two or more detections that should have made up a single detection.

3. Attribute Analysis

Eleven MDA derived mesocyclone attributes (Appendix B) were statistically analyzed in conjunction with the dependent data set (Appendix A) in order to from regression models with which one could predict the future strength of a tornado based on those mesocyclone attributes up to 15 minutes before a tornado's formation. In addition to each volume scan of data being analyzed separately e.g. (T-15; T-10; T-5; T-0), the data set was also analyzed using the combination volume scans including volumes (T-15 + T-10; T-15 + T-10 + T-5; T-15 + T-10 + T-5 + T-0) in order to take in to account temporal trends in the mesocyclone data. Since many of the attributes are highly dependent on each other, Principal Component Analysis (PCA) was performed on each volume scan of data in order to quantitatively define the various dependencies. Another possible solution to the dependency problem was to analyze each attribute separately in conjunction with the Fujita scale and ignore an attribute if it was highly correlated with another. Marzban et al. (1999) have showed that this method can provide useful results, but a significant amount of unique information was lost using the single attribute method.

Principal Component Analysis involves finding the similarities between different attributes in the data set. PCA uses specific loadings (amount of similarity) of each attribute to produce a new data set comprised of a smaller number of new variables. Each new variable may be physically interpreted as a combination of correlated mesocyclone attributes if the groupings of attributes fall into logical clusters. The interpretation can be enhanced with a rotation of the axis such that these correlations (or non-correlations) become more apparent without reducing the amount of variance explained by the new variables. At this point, the number of variables was reduced using the most significant loading variables. This number is set by the number of

variables required to explain roughly 80% of the variance of the original data set. The final number of variables consisted of between three and six variables. Scores will then be defined using Eq. 1 where F is the score, Z represents the normalized attribute values, and A represents the principal component loadings of the various attributes. The scores were then used as the new, uncorrelated predictor variables for use in the linear regression analysis.

The MDA was able to detect mesocyclones associated with every tornado case in the dependent and independent data set for all times in the time window. In some cases, several different circulations were defined by the MDA over a small area of interest. In these cases, the strongest circulation in a specific area was defined as the parent mesocyclone and its attributes used for the statistical analysis. In other cases, the multiple circulations where a sign of a split mesocyclone detection (Fig. 2). The problem with vertical association feature of the MDA algorithm had been noted previously, but the degree of its occurrence seemed to be significantly underestimated in the initial study of the subject (Mitchell 1999). To alleviate that problem in this work, 3-D derived mesocyclone attributes (Appendix B) were calculated manually by adding together the attributes of the split detections. While not a perfect solution, this manual correction to the MDA numerical data seemed to be the only reasonable way to account for split mesocyclones detections without ignoring them altogether. The solution of just choosing the

strongest circulation out of a mesocyclone detection that is split would have adverse effects of the statistical analysis as the true features of a particular mesocyclone would be lost. Also, dropping tornado cases from the data set where this split mesocyclone detection occurred is not an option as split mesocyclone detections occurred in over half of the cases in the complete data set.

In order to get a better model for further interpretation, the temporal effects of mesocyclone attributes needed to be taken into account. Thus, models combing data from two, three, or four volume scans of data were then made. The new models included data from times

T-15 + T-10, T-15 + T-10 + T-5, and one for all times. The model with only two volume scans of data had three predictors plus a constant while the other two models had five predictors

(Table 1). The longer the time window, the more data that must be looked at in order to get a useful model. This was not unexpected as longer time windows would allow attribute trends to make a greater impact on the model. As in the single volume scan model the first predictor was a combination of several velocity attributes while the others vary depending on the model. Also, these models showed the same nonlinearity problems as with the single volume scan models (Fig. 3). The effectiveness of these models was somewhat better than the single volume scan models as expected (Table 1). Interestingly, the model with the best performance was not the one that included the most data. The model T-15 + T-10 + T-5 proved significantly more effective than the model with all four volume scans of data. One possible reason was that the final volume scan of data occurs when the tornado forms; thus, dynamical characteristics of the mesocyclone detection may change so that they do not correlate well with the data from previous volume scan. Also, the five to six minute length of volume scans means that the volume scan during tornado formation probably encompass the entire life cycle of several weaker tornado cases.

Since it appeared that nonlinear interactions were present in all models including the best linear model, a nonlinear model was created using the same three volume scans of data as the best linear model. In order to take into account the nonlinearites present in the data, an arbitrary function was applied to the data set in order to nonlinearize it. Also, since it appears that the nonlinearities were mostly present in the velocity attributes, only those attributes (MXGTG, MXROTV, MSI, etc.) were nonlinearized while attributes such as Depth and LLDia were left alone. Also the attributes MSI*Depth and Core Depth were removed from the data set for use in this model. MSI*Depth was removed because the PCA procedure make this a redundant

showed a less of a trend, indicating that at least some of the nonlinearities were taken into account by the nonlinear model. However, the small magnitude of decrease in the trend line suggests that higher order nonlinearities may exist. Also, this suggests that the Constant term (C) in the regression model may be the most important term as all models overestimate tornado strength for cases which were below the value of C and underestimated the strength of those with a greater value than C. Finally, the nonlinear model appeared to be not as precise as the linear model due to the greater number of errors greater than ±1 Fujita scale.

Testing of the independent data set on this model gave mixed results. The results, shown in Table 8, show that the model fails to predict the F0 and F2 tornadoes correctly. The failure to predict the F0 tornado was common to all the linear models, but the significant overestimation of the F2 tornado is unique to this model. One possible cause is the nonlinear function used to nonlinearize the data set could have the incorrect profile for moderate strength tornadoes. A model based on a different nonlinearization function could perform much better with this case. Still, the model accurately predicts a difference between weak and violent tornadoes which was considered highly significant.

The linear and nonlinear models in the previous section were also tested against a small data set of mesocyclones that did not produce a tornado. Since the models were not designed with null cases taken into account, the models were not expected to be able to predict negative Fujita scale numbers that would be defined as a prediction of no tornado. The results of the testing with the null cases in fact showed that the models could not make a prediction of no-tornado. The focus of this work was not the predict whether or not a mesocyclone would produce a tornado, thus the models produced by this work fails in that test. However, other algorithm

features such as the neural network for tornado probability and TVS signatures themselves can be used to predict a tornadic circulation at which time the model used in this work would be applied.

The results of the regression analyses on the MDA derived mesocyclone attributes have shown that the prediction of tornado strength was at least plausible. Using the best linear model, this work was able to successfully predict over 50% of the variability in the strength of tornadoes using mesocyclone attributes. This number was improved by taking nonlinearities into account in the nonlinear model. Both models were able to reasonably predict the strengths of several tornadoes from an independent data set. Though specific Fujita scale predictions made by the models were not perfectly accurate, they were able to differentiate between mesocyclones that would produce violent vs. weak tornadoes. In both the linear and nonlinear models, the violent tornado case in the independent data set was predicted by the models to be violent and also be much stronger than any of the other cases tested. Given all the problems inherent in even detecting mesocyclones and their associated attributes by the algorithms, the ability of the models to predict to impending strength of a tornado using the MDA derived mesocyclone attributes must be seem as a sign that radar algorithms in general can be useful in tornado forecasting (Stumpf et al. 1998). The implications of these results on tornado forecasting could be far reaching assuming they can be validated. First, given the prediction of a certain strength tornado, appropriate warnings could be issued for that impending tornado that define the proper response one should take in preparing for its arrival. For example, if a violent tornado were to be predicted, warnings that urge people to go below ground and avoid wood framed structures could

be issued. Also, if a violent tornado was predicted, a forecaster could also take that as a sign that a tornado, no matter what its strength, is likely to form thus increasing the likelihood of a warning being issued. Also, during tornadic event, the model output of potential tornado strength could be used to alert appropriate emergency officials to areas that are likely receiving the greatest amount of damage while the damage is occurring. This could decrease the response time required to get to injured in a heavily damaged area and possibly save lives. Finally, in the immediate aftermath of a tornado, the model output could be used as a preliminary damage assessor by giving an estimate of the strength of a tornado. When a damage survey was done that tornado, the predicted strength could be used as a guide as to what kind of damage to look for to verify a certain predicted Fujita scale ranking.

The linear regression model produced in this work is still far from being an operational product. First, MDA's problem with its vertical association feature would prevent the model from having accurate 3D mesocyclone attribute data; thus, the model would fail to give results. Also, the use of Fujita scale rankings as a measure of tornado strength is a questionable assumption at best even given all the precautions this work has taken to ensure that a Fujita scale ranking is indeed related to the strength of a tornado. Variability in radar products from volume scan to volume scan can also cause significant variability in the performance of the model. When that occurs, model reliability and trustworthiness decreases drastically. Finally, the most significant problem is the inability of the model to discriminate between mesocyclones that do and do not produce tornadoes. While many previous works have examined this subject, all of their results were inconclusive at best. Thus, if the ability to even predict whether or not a tornado will form from a given mesocyclone remains dubious; the ability to forecast the strength of that future

tornado using algorithms must also be seen as highly dubious. Until the quality of the radar data itself can be improved, an algorithm's ability to predict whether or not a tornado will form and give its future strength as well cannot be fully tested.

In order to increase the viability of the model, more dependent and independent data sets must be included in order to get a more statistically relevant fit between the mesocyclone attributes and the Fujita scale. To do this, approximately 100 cases should be added to both data sets. In both cases, the new data sets should have a large complement of null cases in them so that non-tornadic events can also be predicted by the model. Also, the testing procedure with the independent data set should cover a much larger time window encompassing the entire life cycle of a particular mesocyclone. This is to ensure a stable model output from volume scan to volume scan which is crucial for allowing forecasters to believe the model output and use it for tornado forecasts. Additional nonlinear models should be created using different nonlinear modifications to the mesocyclone data. If appropriate nonlinear functions are found, regression models made from the modified data could be much more effective than the linear alternatives. In addition, other radar algorithm attributes from the variety of available algorithms could be used in a future analysis to determine if their are other radar derived products, which are not directly associated with a mesocyclone or tornado, that could could be used in predicting tornado strength (e.g storm relative helicity). Since the Fujita scale being a damage scale and the regression models using it as the response signifying tornado wind strength, Doppler On Wheels velocity data could be used to show that the models do indeed correlate to the wind strength a tornado, not just to the damage caused by a tornado. Finally, during the next 10 to 15 years, the radar data for the mesocyclone attributes could be improved dramatically by using the data from the new phased array radar in

Norman, OK which will give much faster volume scans since it does not have to physically rotate to get a 3D volume scan.

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(UTC) (deg) (km)

F0 KDDC 9 April 1994 22:24 187.6 42.2 KDDC

F0 KDVN 19 April 1996 23:00 204.4 74.5 KDVN

F0 KDDC 20 August 1997 19:46 185.6 45.8 KDDC

F1 KFWS 8 May 1995 3:15 9.7 29.3 KFWD

F1 KSGF 17 May 1995 14:34 305.3 114.9 KSGF

F1 KMPX 22 July 1995 0:58 16.8 85.2 KMPX

F1 KDVN 20 April 1996 0:00 140.0 59.7 KDVN

F1 KIND 20 April 1996 5:24 132.2 81.1 KIND

F1 KFSD 29 March 1998 21:55 72.4 89.2 KFSD

F1 KLSX 13 April 1998 22:35 83.9 22.0 KILX

F2 KLWX 29 May 1995 21:30 38.6 145.6 KPIT

F2 KBMX 6 March 1996 11:20 147.4 110.9 KFFC

F2 KBMX 24 January 1997 23:00 266.4 74.5 KFFC

F2 KOHX 24 January 1997 23:38 106.5 49.5 KBNA

F2 KTLX 14 June 1998 1:12 305.6 28.0 KOUN

F3 KFWS 7 May 1995 21:10 348.4 106.9 KFWD

F3 KMLB 23 February 1998 4:40 291.3 111.8 KXMR

F3 KOHX 16 April 1998 20:30 238.5 37.6 KBNA

F4 KLZK 1 March 1997 20:19 215.9 48.0 KLZK

F4 KFSD 29 March 1998 21:49 68.7 109.1 KFSD

F5 KGRB 19 July 1996 0:04 206.5 97.2 KGRB

F5 KBMX 9 April 1998 0:42 296.5 61.5 KFFC

F5 KTLX 3 May 1999 23:31 252.3 50.7 KOUN

(UTC) (deg) (km)

F0 KEMX 15 August 1996 0:10 321.0 55.2 KTUS

F1 KILX 19 April 1996 2:05 137.2 48.5 KILX

F1 KTBW 12 July 1995 18:15 279.9 29.7 KTBW

F2 KTLX 25 May 1997 22:00 205.1 43.3 KOUN

F4 KTLX 4 May 1999 2:25 344.3 75.1 KOUN

1) Shear (S)

2) Gate To Gate Velocity Difference (GTGVD)

3) Rotational Velocity (ROTV)

4) Mesocyclone Diameter (DIA)

Mesocyclone Diameter is defined as the diameter of the mesocyclone circulation at each 2-D detection. It should be noted that the algorithm assumes a perfectly circular mesocyclone and elliptical features are ignored. A low-level diameter less than four km is considered significant. The diameter value at the lowest elevation scan of a mesocyclone's detection was used for this work.

1) Mesocyclone Depth

Mesocyclone depth is defined as the height above radar level of the vertically associated 2-D circulations. It is calculated by adding the half power beam width to both the top and the base of the 3-D circulation attribute. (The half power beam width is the width of the radar beam in which half of the power is transmitted.) Depth values were disregarded in cases where the mesocyclone is too close to the radar (<30 km) to detect its full height.

2) Core Depth

Core Depth is the depth of the strongest part (e.g. the core) of a mesocyclone detection. The strength is based on 2D rotational attributes.

3) Mesocyclone Strength Index (MSI)

MSI is a vertically integrated vortex strength index, which is dimensionless. It relies upon each 2-D strength index calculated for each 2-D circulation in the 3-D vortex. The 2-D strength indices are calculated from various maximum values of shear, GTGVD, and ROTV. In the MSI each 2-D attribute is multiplied by 1000 and then vertically integrated for the whole of the 3-D vortex. Each 2-D attribute is weighted by the average air density at the height of a particular 2-D detection. The value resulting from the integration is divided by the depth to normalize between shallow and deep mesocyclones. Values in excess of 3,600 are considered strong.

4) Mesocyclone Rank

Very similar to MSI, but uses a different integration procedure. Values lower than five define a weak circulation. Values greater than or equal to five define a strong mesocyclone.

5) MSI * Depth

Manually calculated attribute made by unnormalizing MSI with respect to the depth of the mesocyclone. Research has shown that the strength of a mesocyclones is also a function of the mesocyclones depth as well as the rotational attributes.

Figures and Tables

Figure 1. Base reflectivity (left) and radial velocity (right) products from the KTLX radar during the tornado outbreak on May 3, 1999. Note that on the velocity image the yellow circles are MDA detected mesocyclones with the red triangle being a tornado vortex signature detection.

Figure 3. Residual plots for all seven models showing the residual error for each case in the dependent data set. The cases are ordered in ascending order with F0's on the left and F5 on the right. The lines at ± 1 represent ± 1 Fujita scale ranking. Note that all models show the same upward trend in the residuals, which indicates there are nonlinearities in the mesocyclone data that the regression models cannot take into account.

Figure 4. Residual plots for the linear and nonlinear T-15 + T-10 + T-5 models. The lines at ± 1 represent ± 1 Fujita scale ranking and the other line represents a first order fit to the trend of the residuals. Note the upward slope of the trend line in both plots. The slope of the trend line is less for the nonlinear model, but the magnitude of the decrease from the slope of the trend line on the linear model is small. Also, the nonlinear model appears to have a greater number of outliers beyond the ± 1 Fujita scale threshold.

Table 1. Effectiveness of the seven linear regression models produced. Note the total sum of squares including model error is 56.609 for all seven models. The value shown represents the amount explained by the model. Note that the T-15 + T-10 + T-5 model had the highest R2 and sum of squares values which suggests that this model is most effective.

Table 2. Values for the five predictor variables and regression constant from model T-15 + T-10 + T-5. Also given are the P-values for each predictor, which represents the usefulness of each predictor to the overall model.

Table 3. Loadings of each mesocyclone attribute associated with a particular predictor variable for the linear T-15 + T-10 + T-5 model. Loadings greater the 0.5 are highlighted as having a significant contribution to a predictor.

Table 4. Predicted Fujita scale rankings for the tornado cases in the independent data set using the linear T-15 + T-10 + T-5 model. Also shown are the actual rated rankings for each tornado case and the amount of deviation the models predicted rankings were from the actual rankings.

Table 5. Effectiveness of the linear T-15 + T-10 + T-5 model vs. the nonlinear T-15 + T-10 + T-5 model. Note the total sum of squares including model error is 56.609 for both models. Note that the nonlinear model is more effective according to all statistics.

Table 6. Values for the five predictor variables and regression constant from nonlinear model

T-15 + T-10 + T-5. Also given are the P-values for each predictor, which represents the usefulness of each predictor to the overall model.

Table 7. Loadings of each mesocyclone attribute associated with a particular predictor variable for the nonlinear T-15 + T-10 + T-5 model. Loadings greater the 0.5 are highlighted as having a significant contribution to a predictor.

Table 8. Predicted Fujita scale rankings for the tornado cases in the independent data set using the nonlinear T-15 + T-10 + T-5 model. Also shown are the actual rated rankings for each tornado case and the amount of deviation the models predicted rankings were from the actual rankings.