Quantitative Methods- Assignment 2

Introduction

     In this assignment, I have been hired by an independent research consortium to study the geography of tornados in Kansas and Oklahoma. This is a topic of interest because tornados are very common in these states. If there is a spatial pattern to where the tornados land and how destructive they are in a given area, safety measures can begin to be implemented in places that need it most.
     This analysis compares two periods of time; 1995-2006 and 2007-2012. Some people argue that tornado patterns have not changed over the years, so places where they have always occurred should be required to build shelters. Others disagree, and say that not every place sees tornados, shelters are a waste of time and money. This project will be looking at if tornados change over time, if there are any reoccurring patterns of touchdowns and size of tornados across the states. This review will provide answers to whether or not storm shelters could be a necessary precaution to be implemented.

Methodology

      Two datasets were received of tornado locations and width for the years 1995-2006 and 2007-2012. A shapefile of the county level for a combined view of Kansas and Oklahoma. The first spatial statistical analysis tool used is the mean center. The mean center is the average spatial point of a given data set. This is calculated from the average of x and y values. A weighted mean center was also used, which is a mean center but take into occasion frequencies of grouped data. The mean center was found for both 1995-2006 and 2007-2008. The weighted mean center was also found for both data sets and was weighted by width of tornados. It is assumed in this study that the width of tornados makes it more destructive.
      The next spatial statistical tool used is standard distance. Standard distance is the spatial equivalent to the standard deviation. Standard distance measures the degree to which features are concentrated or dispersed around the points and expressed by as a radius or circle. It can only be calculated if there is a weighted mean center. Standard distance was found for 1995-2006 and 2007-2012 within 1 standard deviation, both weighted by tornado width.
     Lastly, the standard deviation of tornado occurrences by counties was found. The standard deviation shows how close to the mean a given dataset is. A high standard deviation shows that there is a lot more occurring in an area than the mean, and  a low standard deviation showing there is a lot less than the mean.

Results

The mean center and weighted mean center of 1995-2006 data show that the mean center is farther north than the weighted mean center (Figure 1). This means that there is a tendency for larger tornados in the more southerly locations. For 2007-2012, the weighted mean center also is more southerly and farther east than the mean center(Figure 2). This means that there were larger tornados in the south and east pulling the weighted mean center in that direction compared to just the tornadoes locations in the mean center. Comparing the years 1995-2006 and 2007-2012, both weighted mean centers are the farthest south (Figure 3). The mean center for 2007-2012 is also farther north than all of the weighted and non-weighted mean centers, meaning that there was more frequency of tornados farther north in 2007-2012, but they were not as big.




Figure 1

Figure 2

Figure 3

The standard distance for the two time periods, 1995-2006  (Figure 4) and 2007-2012 (Figure 5). These maps show 1 standard deviation around the mean center weighted by width of tornados. Comparing the two standard distances shows that in 2007-2012 (Figure 6),has a smaller radius than 1995-2007. This means that the 2007-2012 data is more concentrated around the weighted mean center than in 1995-2006. In 2007-2012, the width of tornados and their locations show two concentrations of tornados, one starting north and running through the weight mean center and one running through the south side of the standard distance. These concentrations are both near the weighted mean center, and there is not many tornados outside of the standard distance. In 1995-2006 there is a much higher number of tornados farther away from the mean center, it is much more spread across the states. The standard distance has to be bigger for 1995-2007 to account for the larger number of tornados occurring on the edges of the states.




Figure 4

Figure 5



Figure 6

The standard deviations of the year 2007-2012 was also found (Figure 7). This shows where each county falls within a normal distribution. This map shows where there are patterns by counties that more or less tornados.




Figure 7



    Statistics of the data were also calculated. The Z-scores based on the number of tornadoes per county for Russell County, KS is 4.88, for Caddo County, OK is 2.09, and Alfalfa County is .23. The average number of tornadoes per county is 4 and the standard deviation is 4.3. Russell County has a very high Z-score of 4.88 which means that it is 4.88 standard deviations away from the mean, that county has many more tornados compared to the mean. Afalfa County on the other hand, with a Z-score of .23, is close to an average amount of tornados because it is within 1 standard deviation.
    If the patterns hold true over the next five years in OK and KS, the z-score of tornados that will be exceeded 70% of the time is 1.764. The z-score of tornados that will exceed only 20% of the time is 7.612.

Conclusions

the weighted mean center for both time period shift to the south which means that width plays a role in tornados, it shows that more southern locations have larger tornados. There is a larger standard distance radius for 1995-2006 because there are more tornados spread on the outer edges of the state, where has in 2007-2012 tornados are more concentrated around the weighted mean center. The standard deviations of counties show that there are patterns of more occurrences and less occurrences of tornados by county. The z-scores show that there is a large difference between counties on the frequency of tornados, this shows that some counties would benefit more from shelters than other counties. Both time periods lean towards the south for larger tornados, so if shelters were to be put in, Oklahoma would benefit the most from shelters. Looking at the graduated symbols of tornados across both states, there are a large number of tornados happening almost everywhere, so for safety precautions I would suggest shelters are a necessity, especially around the weighted mean center.