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### code chunk number 20: Cs5_code
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# GCDF FUNCTION
# This function converts units of degrees lat/lon to miles,
# nautical miles, or kilometers
###############################################################
GCDF <- function(lon1, lon2, lat1, lat2, degrees=TRUE, units="miles") {
# This is the function for the Great Circle Distance Formula
# using decimal degrees or radians
# Calculations at: http://www.nhc.noaa.gov/gccalc.shtml
# This first component is only dependent on degrees or radians
temp = ifelse(degrees==FALSE, acos(sin(lat1) *
sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1)),
acos(sin(lat1/57.2958) * sin(lat2/57.2958) + cos(lat1/57.2958)
* cos(lat2/57.2958) * cos(lon2/57.2958 -lon1/57.2958)))
r=3963.0 # (statute miles) , default
if("units"=="nm") r=3437.74677 # (nautical miles)
if("units"=="km") r=6378.7 # (kilometers)
return (r * temp)
}
library(maps) # must be installed from CRAN
# our noisy data (with no missing values)
turtles = levels(loggerheadNoisy$turtle)
levels(loggerheadNoisy$turtle)
##############SPECIFY THE TURTLE NAME HERE
turtlename="BigMama"
dat = loggerheadNoisy[which(loggerheadNoisy$turtle==turtlename),5:6]
dat = t(dat)
# Set up the MSSM model
# We are going to make a big approximation:
# We are going to pretend that 1 deg longitude
# change is equal to about the same distance (miles)
# over the range of latitudes that the turtles are moving
# That's not true. There is about a 10% difference across
# their range of latitude movement.
Q.model="diagonal and unequal"
R.model="diagonal and unequal"
U.model="unequal"
Z.model="identity"
# Fit a random walk model for lon/lat to the lon/lat data
kem = MARSS(dat, model=list(Z = Z.model,
Q = Q.model, R = R.model, U = U.model))
pred.lon = kem$states[1,]
pred.lat = kem$states[2,]
##########################################
# Plot the results
##########################################
op = par(mai = c(0,0,0,0))
map('state', region = c('florida', 'georgia',
'south carolina', 'north carolina', 'virginia',
'delaware','new jersey','maryland'),xlim=c(-85,-65))
points(loggerheadNoisy$lon[which(loggerheadNoisy$turtle==turtlename)],
loggerheadNoisy$lat[which(loggerheadNoisy$turtle==turtlename)],
col="blue",pch=21, cex=0.7)
lines(pred.lon, pred.lat,col="red", lwd=2)
# add the good location data
goodturtles = loggerhead
gooddat = goodturtles[which(goodturtles$turtle==turtlename),5:6]
points(gooddat[,1], gooddat[,2],col="black", lwd=2, pch=3, cex=1.1)
legend("bottomright",c("bad locations", "estimated true location", "good location data"),pch=c(1,-1,3),lty=c(-1,1,-1),col=c("blue","red","black"),bty=F)
# add the proposed fishery areas
lines(c(-77,-78,-78,-77,-77),c(33.5,33.5,32.5,32.5,33.5),
col="red",lwd=2)
lines(c(-75,-76,-76,-75,-75),c(38,38,37,37,38),
col="red",lwd=2)
###########################################
# Calculate the average miles traveled each day using
# the function GCDF defined above
# You must select and run the GCDF code first
###########################################
distance = array(NA, dim=c(dim(dat)[2]-1,1))
for(i in 2:dim(dat)[2])
distance[i-1]=GCDF(pred.lon[i-1],pred.lon[i],
pred.lat[i-1],pred.lat[i])
par(op) #reset plotting pars back to normal
par(mfrow=c(1,2)) #make a 2 panel graph
hist(distance) #make a histogram of distance traveled per day
print(paste("KalmanEM estimate of ave. mile per day for ",
turtlename," = ", mean(distance) ))
# Compare to the distance traveled per day if you used the raw data
distance = array(NA, dim=c(dim(dat)[2]-1,1))
for(i in 2:dim(dat)[2])
distance[i-1]=GCDF(dat[1,i-1],dat[1,i],dat[2,i-1],dat[2,i])
hist(distance) #make a histogram of distance traveled per day
mean(distance)
print(paste("Raw estimate of ave. mile per day for ",
turtlename," = ", mean(distance) ))
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