Using the Poisson Distribution to Determine the Probability of Tornado Strike in Bolivar County, MS

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Using the Poisson Distribution to Determine the
Probability of Tornado Strike in Bolivar County,
MS

• Talbot Brooks, Director
• Center for Interdisciplinary Geospatial
  Information Technologies
• Delta State University

This work supported by USGS Cooperative Agreement
07ERAG0083 and contributions from Breandán Ó
hUallacháin, Dept. of Geography, Arizona State
University
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Problem 1 Amnesia and Wishful Thinking

• Cleveland is the county seat and most populous
  place in Bolivar County, Mississippi.
• Cleveland has not suffered a direct strike from a
  tornado in recent memory, though many surrounding
  areas have.
• Local lore has it that geographic features, such
  as the Mississippi River, serve to split storms
  and prevent tornadoes from smashing Cleveland
  into itty-bitty pieces.

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Problem 2 Scale

• The National Weather Service, Storm Prediction
  Center (Norman, OK) collects storm data to a
  spatial resolution of 0.01 decimal degrees
  (question to class what does this mean in terms
  of an on-the-ground measurement)
• Provide analysis, but using small scale (large
  geographic region) techniques as indicated on the
  next slides
• Each grid square on the following slides is at
  least 30km x 30km!!!

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Severe Thunderstorms 1950-2002
Bolivar County
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Tornados 1950-2002
Bolivar County
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Problem 3 Lack of Observation Power

• Bolivar County lies at the edge of the coverage
  areas for 3 weather radar sites
• NWS Jackson is the responsible forecast office,
  even though they have the worst radar picture
  (orange circle represents maximum range of the
  radar)
• Note the difference among these images all were
  taken at the same time

NWS Memphis
NWS Jackson
NWS Little Rock
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Lack of Observation Power

• While a wonderful place to live, residents are
  pretty sparse as the total population is about
  38,000 spread out over 930 square miles.
• It is highly probable that the number of tornados
  and associated severe weather events are
  underestimated for this geographic region.

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Basic Issue

• Very few (lt 1) of all residents have a basement
  or storm shelter.
• Less than half of Bolivar Countys population
  live with the effective range of a storm siren
  system
• A third of tornados in this area occur at dusk or
  night and the majority are shrouded by rain.
• Of a total of 78 injured by tornados between 1950
  and 2007, 62 were injured at night

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• We must raise awareness about the threat of
  tornado such that both people and government take
  appropriate mitigating actions such as
• Improving radar coverage for better detection of
  severe storms and potential tornados
• Improving/expanding storm warning systems
• Encouraging individuals to take personal
  responsibility and actions such as purchasing
  weather alert radios, installing storm shelters,
  and enacting better storm-proof building codes
• To make a convincing argument, we must perform a
  fair and accurate assessment of risk

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Methodology

• Capture historical data from the National Storm
  Prediction Center and save it into a spreadsheet
• Transfer data to ArcGIS to make a map an assess
  data quality
• Plot and analyze tornado touchdowns in the area
  of interest
• Plot and analyze tornado tracks in the area of
  interest

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Storm Prediction Center

• Stores data in text format for each mode of
  severe weather
• Tornado http//www.spc.noaa.gov/wcm/ONETOR5006.tx
  t
• Hail http//www.spc.noaa.gov/wcm/FHAIL5506.txt
• Thunderstorm Winds http//www.spc.noaa.gov/wcm/FWI
  ND5506.txt
• Metadata for tornado file structure is at
  http//www.spc.noaa.gov/wcm/torforma.doc
• Note longitude is presented as a positive
  number and MUST be converted to a negative for
  correct mapping by ArcGIS

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• Open the web site as indicated on the previous
  page and wait for all the data to load
• Use the mouse or Select All function to copy
  all of the data on the page note that it may
  take some time for all of the data to copy to the
  clipboard
• Open Excel and paste the data into cell A2

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Convert Text to Columns by Selecting Column A
and then Text To Columns
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Choose Delimited
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And then Comma with being a text qualifier
choose Finish
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Label The Columns As Specified In The Metadata
Table (back up a few slides)
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Convert Longitude To A Negative By First
Inserting A Column Next To Stlon
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Calculate Values For New Column As A Relative
Path Formula (with cursor in cell Q2, type
P2-1)
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Copy The Formula Into The Entire Column

• Hit ltCtrlgt and c on the keyboard to copy the
  formula
• Select all of column Q
• Hit ltCtrlgt and p to paste the formula into the
  entire column
• Move the cursor to the first zero in column Q
  after the last row of data (see picture next
  slide)

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• Hold down Shift End and the Down Arrow to
  select all the zeros all the way to the bottom of
  the page
• After they are selected, delete them
• Hit Ctrl and the Home keys to return to the
  top of the spreadsheet
• Select (right click) Column Q and copy the values

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Right Click A Second Time on Column Q and Choose
Paste Special Choose Values and hit OK
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• Enter Stlon into cell Q1
• Delete Column P
• Repeat this process for Splon column S
• For our purposes, there is a lot of extra data in
  this file go ahead and delete columns B, C,
  H-N, W, AB-AE, and AG-AI (Hold down the Ctrl key
  and select these columns all at once if you
  delete them one at a time, they column letters
  will re-number and confuse you)

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Save your work!!!

• Save this Excel file in a location youll be able
  to easily locate!!!

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Tune Up ArcGIS

• Before proceeding, youll need to do the
  following
• Download and install a copy of Hawths Analysis
  Tools for ArcGIS from http//www.spatialecology.co
  m/htools/download.php
• Download and extract the appropriate US National
  Grid Polygon layer(s) for your geographic area
  from http//mississippi.deltastate.edu
• Download and extract boundary and roadway data
  layers appropriate for your geographic region

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Four More Things To Do In ArcMap

• First, well import the table and convert it to a
  geographic layer
• The resulting layer has some bad data well
  have to edit it out
• Well perform a Poisson analysis for tornado
  touchdowns
• Well then edit the data a second time and use
  Hawths Tools to plot tornado tracks and repeat
  the analysis

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Start ArcCatalog and Create A New Personal
Geodatabase
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Import Your Tornado Spreadsheet Into This New
Geodatabase (right click on the geodatabase)
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Start ArcMap And Add Your Table From The
Geodatabase (click on the black plus with a
yellow background)
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Choose Add X/Y Data From The Tools Menu
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Choose Your Table And REMEMBER X is Longitude and
Y is Latitude!!!
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Click the Edit Button To Choose A Coordinate
System When the chooser opens, hit the
Select button and then navigate Geographic
Coordinate Systems World WGS 1984.prj
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OK Your Way Back Out The Final Dialogue Should
Appear As Follows
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You Should Now Have A Map Like This
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Now Export The Data To Your Geodatabase By Right
Clicking On The Tornado Table Events Layer
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• Allow ArcMap to add the exported data to the map
• Right click on Tornado_TableEvents and choose
  Remove
• Right click on Tornado_Table and choose Remove

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Open The Table For The Remaining Layer (I called
mine US Tornados) Right Click On The Layer
Name
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Right Click On The Stlon Field and Sort This
Column In Descending Order
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Blank/Zero Values

• Note that the first many values for latitude and
  longitude are either 0, blank, or labeled ltNullgt
• Are we interested in these values?
• Create a backup of your data by exporting the
  US_Tornados layer back to the geodatabase as
  US_Tornados_Backup (DO NOT add it to the map
  this is your backup in case you mess up)

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Open The Editor Toolbar
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Choose Start Editing
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Select All Rows For Which Stlon is 0, ltNullgt, or
blank and hit Delete
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Check Your Work

• Re-sort Stlon and make sure no 0, null, or blank
  remains
• Do the same for Stlat
• Close the attribute table
• Save your edits
• Re-export the US_Tornado layer as TornadoTracks
  for use later DO NOT add it to the map at this
  time

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Theory

• Tornados are discreet events (you cannot have ½ a
  tornado)
• Tornados are fairly rare events
• Our objective is to predict the probability of a
  tornado strike
• Now that we have the data, lets take a few
  minutes to review probability theory in geography
  and how it will apply to this problem

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Probability distributions

• establishing link between probability theory and
  statistical judgments
• probability distribution graph showing the
  potential values of a variable and their
  corresponding probabilities

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• frequency histogram
• probability distribution

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Discrete variables

• only certain values (e.g. integers) can be
  values of the variable
• the sum of the heights of the bars is
• 1.0

• the expected value of a discrete variable
• E(X)

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Two theoretical discrete probability distributions

• 1 discrete uniform probability of each
  discrete outcome (of k outcomes) is equal.

a discreet uniform

• P(x) 1/k

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The Uniform Distribution

• A little simplistic and perhaps useless
• But actually well applied in two situations
• 1. The probability of each outcome is truly equal
  (e.g. the coin toss, card pick)
• 2. No prior knowledge of how a variable is
  distributed (i.e. complete uncertainty), the
  first distribution we should use is uniform (no
  assumptions about the distribution)

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P (head) 0.50 P (tail) 0.50
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Two theoretical discrete probability distributions

• 2 Discrete Rare Events --- Poisson
  distribution
• important in point pattern analysis
• forms the basis for models of randomly
  distributed points in an area
• tells the probability that a certain number of
  occurrences or points will fall in a certain unit
  of time or space

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Critical Information To Know

• Average Number of things in a unit
• Lamda or the Greek letter
• l

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Poisson distribution
e-l lx
where l is the average number of things in a unit
(time or area)
P(x)
x!
l 12/4 3
P(5) 2.71828335 / (54321)
0.1008 P(2) 2.71828332 / (21)
0.2240
you can look this up if you dont want to
calculate this! Table A2 in the back of the book
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What is the probability that we get 2 or 3 or 4
dots in a square?

• Probability of 4, plus the probability of 3, plus
  the probability of 2
• .168 .224 .224 .616

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What is the probability that we get 3 or 2 dots
in a square?

• Probability of 3 plus the probability of 2
• .224 .224 .448

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What is the least likely number of dots?

• Answer 12 (all dots in one square)
• Why?
• Probability of 12 is 0.001
• Note that this is smaller than the likelihood of
  no dots (0.0498)

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Analyzing The Data Using The Poisson Distribution
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Add Map Data For Your Area

• Add city/county boundaries and the US National
  Grid Layer for your local area
• Note in my map, Ive edited the US National
  Grid layer to just include squares for my area of
  interest this helps me quickly determine the
  number of squares in the analysis you dont
  have to do this youll just need to add yours up

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Use Select By Location To Determine The Number Of
Tornados That Have Occurred Within Your Area Of
Interest
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Use Poisson

• Lamda equals the average number of events per
  unit or, in the case of Bolivar County, there 78
  tornados occurred and there are 2,424 grid
  squares. Lamda equals 78/2424 0.0322

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Probability Of 1 Tornado Touching Down In Any
Given Grid Cell
P(1) .032
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Hmmm.

• Thats the probability of touchdown, but tornados
  are linear events as the map at right indicates

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Right Now, Our Dataset Includes All Of The USA
Lets Simplify It To Our Area Of Interest

• First, lets select tornados in our area of
  interest using Select by Location

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• Use the boundary layer for your area of interest
  to capture the tornados that have occurred within

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• Note that just tornados falling inside the
  Bolivar County boundary are selected

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• Right-click on the tornados layer to create a
  layer from the selected features.

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• Now export the data to your geodatabase by
  right-clicking on the US_Tornados Selection

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• Click on the file button to determine the save
  to location
• Make sure the drop down save type is SHAPEFILE

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• Allow ArcMap to add this layer well use it as
  the active layer for the remainder of this
  exercise
• Though Poisson is supposed to be used for
  discrete, unrelated events, we can stretch the
  analysis basis a bit and include cells that are
  crossed by a tornado track (though a statistician
  would like choose another method, the results
  will be very similar)
• Revisit the editing technique shown earlier, but
  this time remove 0, null, and blank values for
  Splat and Splong
• Well next use Hawths Analysis Tools to plot
  tornado tracks

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• Start Excel and choose Open
• Navigate to the directory where you saved the
  SHAPEFILE
• Change the File Type listing to All Files
• Open the file with shapefilename.dbf

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• Save the filename.dbf file as an Excel
  Spreadsheet
• Import the spreadsheet into the geodatabase (see
  previous steps)
• Add the table to ArcMap (see previous steps)

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• First, make sure that the Hawths Analysis Tools
  extension is turned on

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• Turn the toolbar on

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• From the Hawths Tools toolbar, select Add XY
  Line Data From Table

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• Setup the dialogue as shown, making sure you save
  the resulting shapefile in a location you can
  find later

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Almost Final Step Project The Output

• Start ArcCatalog and then ArcToolbox
• Select from the Define Projection tool indicated

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• Find the track shapefile output earlier
• Click on the Select button to the right of where
  it says Coordinate System

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• Select the same coordinate system as shown
  earlier(Geographic World WGS 1984.prj)

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• Add your track layer to ArcMap and repeat the
  Poisson Analysis (use the select by location
  function to find how many cells are affected by
  tracks and then add to that number the number of
  tornados for which no tracks are shown)
• Scared? I am were at a 15 probability of
  experiencing a tornado where I live and the
  forecast is for severe thunderstorms tomorrow

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