As 2018 draws to a close, one cannot help but look back and think about what a whirlwind the year has been. In memory of the year 2018, I decided to look at the history of real whirlwinds – tornadoes – in the state of South Carolina. Data concerning tornado frequencies were pulled from the database at the National Oceanic and Atmospheric Administration Storm Events database.
Below is a time series plot of the number of tornadoes each year in South Carolina for the years between 1950 and 2018. It seems 2004 experienced an abnormally high amount of tornadoes, but it also looks like there might be a general increasing trend.
The trend for tornadoes over the years by Fujita Scale rating can also be visualized, revealing an apparent trend for weaker tornadoes to increase in frequency.
The distribution of the months in which tornadoes occured is in line with the nationwide trend pictured below (courtesy of Climate Central).
Now let’s look at which counties get the most tornadoes.
Another way to inspect this is a heatmap of the cumulative tornado county over a map of South Carolina. This graph is interactive, so hold your mouse over a county to see its name and tornado count!
Here are some trends for a few counties, two of which I have lived and one event which I experienced a tornado firsthand!
Next, it might be natural to wonder how global climate drives the number of tornadoes experienced each year in South Carolina. To explore this question three variables of interest were be entered into a generalized additive model. The first variable is the global temperature anomaly (globalTemp), which characterizes the change in global temperature over time on a scale relative to the global mean over a 30 year period. This is important because the North Atlantic Oscillation occurs over a roughly 30 year period. Hence, the global temperature anomaly is not driven by normal climate cycles and represents the deviation from average temperature after accounting for normal climate cycles.
The second variable included is the yearly average Oceanic Niño Index (ONI), which records the effects of El Nino (greater than average sea surface temperature) and La Nina (lower than average sea surface temperature). This data was gathered from National Weather Service Climate Prediction Center. It is important to note that the ONI is adjusted for global warming trends, so ONI will not be confounded by globalTemp (see this link for more information ). Last, the number of sunspots recorded in each year were gathered from the Australian Government Space Weather Services because sunspots are known to affect weather patterns. Because of this an interaction term between globalTemp and sunspots was also included in the model.
It is important to note that the generalized additive model is not the same as a generalized linear model. The GAM models non-linear interactions between predictors and an outcome variable. Hence, a simple linear regression would model \(\text{Outcome} \sim \text{Intercept} + \sum_i \text{Predictor}_i \cdot \text{Coefficient}_i\) while the generalized additive model instead models the outcome as a linear combination of potentially non-linear functions of each predictor, ie, \(\text{Outcome} \sim \text{Intercept} +\sum_i f\text{(Predictor)}_i\). Penalized cyclic (appropriate for time series with potentially cyclical patterns) b-splines (cp basis spines in the mgcv R package used to fit the model) were used to find these non-linear functions. Finally, a poisson family with identity link function were used due to the outcome being a count variable (number of tornadoes).
Below is an ANOVA table of the model showing the statistical significance of each predictor and interaction. Also shown are partial dependence plots (pdps) with individual conditional expectation (ice) curves for the main effect of each predictor. The pdp shows the marginal effects of each predictor on the predicted outcome (J. H. Friedman 2001). The prediction function is fixed at the values of the predictor and averaged over the other features. The ice curves visualize the dependence of the predicted response for each observation of a predictor separately, which yields an impression of how sensitive the prediction is to values of the predictor.
| variable | edf | ref.df | chi-squared | p.val | VSMPR |
|---|---|---|---|---|---|
| s(globalTemp) | 2.892 | 3 | 183.774 | 0.000 | ≥ 1000 |
| s(YrlyONI) | 0.000 | 3 | 0.000 | 0.384 | 1 |
| s(Sunspots) | 2.468 | 3 | 74.715 | 0.000 | ≥ 1000 |
| ti(globalTemp,Sunspots) | 4.541 | 9 | 23.273 | 0.000 | ≥ 1000 |
| Note: | |||||
|
The VSMPR is the Vovk-Selke Maximum P-Ratio, which is the maximum Bayes Factor in favor of the hypothesis of an effect existing one could obtain under the most favorable prior distribution. |
Now let’s take a look at the predicted number of tornadoes vs the number actually observed. The Spearman’s correlation between the predicted and observed is .66, which means the non-parametric \(R^2\) is 0.44. In other words, this model explains 44% of the variance in the observed data.
Now for the partial dependence plots.
It seems that there is good evidence to support the hypothesis that global warming is driving the number of tornadoes in South Carolina. El Nino and La Nina are not supported to be related to the number of tornadoes. The main effect of sunspots is weak at best, but there is a significant interaction with the global temperature fluctuations. The interaction plot shows that despite the interaction between sunspots and global temperature, evidenced by a dip in number of tornadoes when the number of sunspots is average (around 100), greater increases in global temperature drive a larger number of tornadoes in a year. An interesting trend is that the predicted number of tornadoes dips during years with a temperature anomaly \(\geq\) .60. This could potentially be due to disruptions in Arctic air currents carrying cold dry air due to years with abnormally high temperature anomalies, or it could be a quirk. Perhaps in the future I will look at tornado data for other states, but for now, this concludes my analysis of the history of tornadoes in South Carolina.
Thank you for reading!