Introduction:
This assignment was designed to familiarize us with the ideas of mean centers, standard distances and z-scores. We were put into a scenario where we were hired by an independent research consortium to study tornados in Kansas and in Oklahoma. We were provided with tornado data for the study area for two different time periods, and county level shapefiles which included the total number of tornadoes that occurred in each county. We were assigned to think spatially and study the tornadoes' patterns over time, and explore how they might relate to building shelters. We explored questions like whether some areas get larger tornadoes than others, and whether these patterns have changed over time. We used various geostatistical techniques to assist in answering these questions.
Methods:
The first step was to calculate mean center, and weighted mean center. These figures essentially yield the geographic center of the tornado points dataset. I used the Spatial Statistics -- Mean Center tool to calculate the mean center both for the tornadoes from 1995 to 2006 and then from 2007 to 2012. Then, I repeated this process, but weighted the calculation on tornado width. This means that the mean center is more affected by the wider tornadoes. (Note- this assumes that wider tornadoes mean more powerful ones). I created maps for each time period, and a third showing both on the same map. These maps are included below in the results section.
Next, I had to create standard distances. Standard distance measures the degree to which points are concentrated around the mean center I just calculated. I used the Standard Distance tool to do this, and weighted by width once again. This yielded a large circular polygon as shown in the below maps: one for 1995- 2006, one for 2007-2014 and a third that had both time periods.
Finally, I had to create a standard deviation map, and use the associated statistics to calculate z score values for three counties: Russell County, KS, Caddo County, OK, and Alfalfa County, OK. The equations used are shown below.
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| This image shows the equation for calculating Z values. |
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| This image shows the calculation for Alfalfa county, OK. Note the mean value of 4 and the standard deviation value of 4.3 are consistent in the following equations as they are from the same dataset. |
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| Calculation for Caddo County, OK Z-Score |
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| Calculation from Russel County, KS |
Next, I had to calculate the number of tornadoes that would be exceeded 70% of the time, and 20% of the time. These calculations are shown below as well using the same equation as above, but solving for a different variable.
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| This is the calculation for the number of tornadoes that will be exceeded 70% of the time. The answer was 1.764. |
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| This is the calculation for the number of tornadoes that will be exceeded just 20% of the time. It came to 7.612 |
Results:
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| This map shows mean centers and weighted mean centers for Kansas and Oklahoma tornado occurrences |
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| This map shows weighted standard distances by width for Kansas and Oklahoma tornado occurrences |
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| This map shows standard deviation for Kansas and Oklahoma tornado occurrences by county |
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Conclusion:
These statistical processes and spatial mapping helps to answer some of the questions introduced in the introduction. The mean center maps and standard distance maps were helpful in demonstrating that the trends between the 1995-2006 dataset and the 2007-2012 dataset in fact did not change very much. The concentration is quite obviously in the middle of the states, but the distribution is not concentrated enough in my opinion, to merit concentrating the building of new shelters. In addition, I think that the calculations for the number of tornadoes that will be exceeded 70% and 20% solidify the idea that shelters should be built in each county. The figure that I calculated: 1.764 means that 70% of the time, there will be about 2 tornadoes that will occur in a given county. This number is very high, and I think that because of this, shelters should be built pretty uniformly throughout this study area.
