Point Patterns of New Brunswick Forest Fires
Point patterns created from yearly records, provided by the New Brunswick Department of Natural Resources, of all fires falling under their jurisdiction for the years 1987 to 2003 inclusive (with the year 1988 omitted until further notice).
The coordinates of the fire locations were provided in terms of
latitude and longitude, to the nearest minute of arc. These were converted
to New Brunswick stereographic projection coordinates (Thomson,
Mephan and Steeves, 1977) which was the coordinate system in which
the map of New Brunswick --- which constitutes the observation
window for the pattern --- was obtained. The conversion was done
C program kindly provided by Jonathan Beaudoin of
the Department of Geodesy and Geomatics, University of New Brunswick.
Finally the data and window were rescaled since the use of the New Brunswick stereographic projection coordinate system resulted in having to deal with coordinates which are expressed as very large integers with a bewildering number of digits. Amongst other things, these huge numbers tended to create very untidy axis labels on graphs. The width of the bounding box of the window was made equal to 1000 (nameless) units. In addition the lower left hand corner of this bounding box was shifted to the origin. The height of the bounding box was changed proportionately, resulting in a value of approximately 959.
The window for the fire patterns comprises 6 polygonal components, consisting of mainland New Brunswick and the 5 largest islands. Some lakes which should form holes in the mainland component are currently missing; this problem will be remedied in future releases. The window was formed by ``simplifying'' the map that was originally obtained. The simplification consisted in reducing (using an interactive visual technique) the number of polygon edges in each component. For instance the number of edges in the mainland component was reduced from over 138,000 to 500.
For some purposes it is probably better to use a discretized (mask type) window. See ``Examples''.
Because of the coarseness of the coordinates of the original data (1 minute of longitude is approximately 1 kilometer at the latitude of New Brunswick), data entry errors, and the simplification of the observation window, many of the original fire locations appeared to be outside of the window. This problem was addressed by shifting the location of the ``outsider'' points slightly, or deleting them, as seemed appropriate.
The columns of the data frames comprising
Dateand have the format
data(nbfires) creates three objects:
nbfires is a marked point pattern (an object
"ppp") consisting of all of the fires in the years
1987 to 2003 inclusive, with the omission of 1988. The marks
consist of the last two digits of the years, with the string
nbfires. prepended. Patterns for individual years can
be extracted using the function
nbextras is a list of data frames, with
extras.03. The columns
of these data frames provide ``extra'' information about the
fires. (See ``Details''.)
nbw.rect is a rectangular window which covers
central New Brunswick. It is provided for use in illustrative and
``practice'' calculations inasmuch as the use of a rectangular
window simplifies some computations considerably.
The data were kindly provided by the New Brunswick Department of Natural Resources. Special thanks are due to Jefferey Betts for a great deal of assistance.
Turner, Rolf (2007) Point patterns of forest fire locations. To appear in Environmental and Ecological Statistics.
Thomson, D. B., Mephan, M. P., and Steeves, R. R. (1977)
The stereographic double projection.
Technical Report 46, University of New Brunswick,
Fredericton, N. B., Canada
data(nbfires) X <- split(nbfires) # Create a list of yearly point patterns. attach(X) # Make the individual point patterns accessible. attach(nbextras) # Make the individual `extras' accessible. ftyp <- extras.00$fire.type Y.00 <- nbfires.00[ftyp==1 | ftyp==2] # Pick out forest and grass fires. stt <- extras.00$dis.julian[ftyp==1 | ftyp==2] fin <- extras.00$out.julian[ftyp==1 | ftyp==2] Y.00 <- setmarks(Y.00,fin-stt) # Mark the pattern with fire duration. plot(Y.00) # nbw.mask <- as.mask(nbfires$window, dimyx=500) plot(nbw.mask, col=c("green", "white")) plot(nbfires$window, border="red", add=TRUE) # plot(unmark(Y.00)[nbw.rect], add=TRUE) plot(nbw.rect,add=TRUE,border="blue") # K.00 <- Kest(Y.00) plot(K.00)