Wednesday, February 25, 2015

Tornado Alley-Showcase of how to use Z-scores, Mean Center, and Standard Distance.


Introduction:

                I have been hired by Tornado Valley Research Institute to study the geography of Tornadoes in Kansas and Oklahoma. Recently there has been some arguments over the distribution of Tornados and if locals should be required to build storm shelters. Proponents of the storm shelters argue that spatial patterns of Tornadoes have not changed that much over the last twenty years and because of that, they should build more shelters in areas that receive more tornadoes. Others argue that shelters are a waste of money and not every “place” ever sees tornadoes.

                So the focus of my study will be to analyze the placement of Tornadoes over two separate time periods (1995-2006 and 2007-2012).  I will look at the varied placement of these Tornadoes and how large they were when recorded (Not the Fujita Scale but rather width in feet). This will give me a good idea of specific locations that have received not only a large amount of tornadoes but also those that were rather large in size and therefore pose more of a threat. Additionally I will look at the placement of tornadoes at the county level of these two states.

 

Methodology:

                To do this study I used ArcGIS to map out these tornadoes how we can best understand them spatially. I was given data of both Kansas and Oklahoma and how many tornadoes each of their counties recorded from 2007-2012. I also have the individual data of each Tornado and its width in feet from 1995-2012. Those dates have been broken up into 1995-2006 and 2007-2012.

                To help me better understanding how the spatial pattern of Tornadoes has changed over time I will be looking at the mean center of the Tornadoes over those two time periods. The mean center gives me the geographic middle of all the data that was collected. By looking at the mean center over the two time periods we can see if and how the pattern has moved over time. I also looked at the weighted mean center of the Tornadoes width. This is the same function as above but this time I add another parameter to the tool so that it weights the wider tornadoes more than the smaller ones. This is especially important as it shows how the pattern has changed over time with respect to the larger, more damaging tornadoes.


Figure one


Another measure I took to study the pattern of tornadoes was the Standard Distance of the Tornadoes. In its most simple form, standard distance draws a circle around the mean center up to the first standard deviation so that theoretically 68% of the tornadoes will lie within that circle. If I were to go up another standard deviation it would draw a circle around 95% of the tornadoes. The standard distance is a good indicator of where in our study area we have the most data associated with our area. In this study I based the standard distance upon the weighted mean center and not the mean center to give more of a priority to the larger tornadoes.

Figure two


The last item I looked at was the standard deviation of the tornadoes at the county level. This was the most basic map I created and shows which counties from 2007-2012 had the most tornadoes and how they deviated from the mean. You can clearly see the counties that drove the mean up as they are indicated by dark blue.


Results:

                After running all the tools in Arc, these are the various maps that I created.

Map one


Map one shows the location of Tornadoes from 1995-2006. I also showed the Mean Center and the Weighted Mean Center of this dataset. You can see that once the mean center is weighted, it shifts to the South due to the abundance of large tornadoes further south. Some patterns that stick out to me are the cluster of tornadoes in the northern central region of Oklahoma. This cluster however doesn’t draw my eye as much as the absence of tornadoes in the Southeastern region of Kansas. From this data set I pick out 7 counties that recorded zero tornadoes in this timespan of roughly 10 years and all 7 of those are in that absent region of Kansas.

Map two


In map two we see the same components as in map one but this data is from the tornadoes recorded from 2007-2012. What we can decipher from looking at this map compared to the last map is that the areas of clustered tornadoes have shifted elsewhere. I now see two separate areas of larger tornadoes, one lateral stretch though the middle of Oklahoma and another cluster in the central region of Kansas. I also infer from this map that the severity of Tornadoes has relatively dropped from the first map to the second. This is peculiar because you always hear how nowadays with climate change that we will see bigger storms than in the past, which is not the case here. I call attention to the Eastern region of Kansas where in the first map we saw a lack of tornadoes. We still don’t see many tornadoes there but the ones we do see are those that are larger than 280 feet in diameter.

Map three


Map 3 illustrates both sets of data put together. If you can look past the busyness of the map you will see that in the past 20 years there has been tornadoes all over Kansas and Oklahoma and every single county has experienced at least one. You can tell that there have been more tornadoes recorded in the central region of the bi-state area but relatively less in that eastern region of Kansas.

 
Map four
 
Map five
 
Map six




Maps 4 and 5 both show us the standard distance of both data sets while Map 6 shows us both overlaid onto one another. If I may so dub each of the regions covered by the standard distance in these maps the disaster zone, you can see the disaster zone over time has shifted slightly to the northeast. I believe this is due to the large increase of tornadoes in southern Kansas versus Northern Oklahoma and to the presence of tornadoes in the once absent region of Eastern Kansas.

Map seven


In my final map (Map 7) I have showed the standard deviation for all the counties in the bi-state area. This data is only for the 2007-2012 data set and you can see those blue counties in southern Kansas as deviating from the mean in a drastic way. This map further reinforces the abundance of tornadoes in the central regions and the lack of them in eastern Kansas. From receiving the standard deviations of the counties I also calculated the Z scores for three of those counties. Caddo County, OK, Alfalfa County, OK, and Russell County, KS were the three. I found that over the recorded period of time we can say that Caddo County will have 13 tornadoes 1.83% of the time, Alfalfa County will have 5 tornadoes 40.9% of the time, and Russell County will have 25 tornadoes less than 1% of the time. Pretty much this is saying that Russell County is likely to not record that many tornadoes in 5 years ever again while Alfalfa County is somewhat likely at 40.9% to record 5 tornadoes again in that time span.

 

 Conclusion:

                My findings have led me to believe that even though some areas of the bi-state region experience a dramatically lower rate of tornadoes, you cannot ever be sure that another tornado will or won’t strike the same general location again. It is my suggestion to these areas will high frequencies of tornadoes that they immediately build shelters that can withstand a substantial amount of people and a substantial tornado as those areas that experience the higher frequency general experience larger tornadoes as well. To those areas with low frequencies, I understand that you don’t record as many tornadoes as other areas do but you cannot ever say for certain that one won’t hit your hometown, your farmhouse, or your family. It is my recommendation that you too build shelters, however, they do not have to be to the standard of the more prone areas shelters, but should still be functioning in the event of a freak storm. If I were you, personally, I would build the best shelter possible no matter where I lived to protect my family in case of an emergency because when the time comes, it will be too late to build one when it is actually needed and too many good people have lost their lives to this beast of mother nature and having said that, we should give these tornadoes the respect they deserve and take the appropriate measures needed to keep our families safe.

I hope you find this study useful in making your final decisions and I would like to thank the Tornado Valley Research Institute for allowing me to conduct this study in the hopes that I could help you all make the best economic decision and the safest one.