Brandon's Light.R Homework (08/31/2012)

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Code

require(fields)
require(plyr)

PLOTS!!!!!!!

Plot #1

This is the plot of PAR with time

plot(sun_time, PAR, type = "o")

Plot #2

This is the color contour plot modelers use to wow the rest of us.

image.plot(sun_time, z, uI.field, ylab = "Depth", xlab = "Time")

Plot #3

Contour with depth truncated for emphasis on detail

contour(sun_time, z, uI.field, yaxt = "n", nlevels = 10, ylab = "Depth", 
    xlab = "Time", ylim = c(-20, 0))
axis(2, at = seq(0, -20, -5), labels = seq(0, 20, 5), las = 1)

Questions

1. How is the depth of the Ik light level changing over these 120 hours? How does it change daily? How does it change across days?

   • As can be seen in Plot #2, the the diurnal pattern of pentration increasing to its deepest after midday and returning to 0 near sunset. Over the 120 hour time span the max penetration appears to be increasing.

2. By how many meters (approximately) does the 1 W m^-2 isolume change when there is a does a doubling of the attenuation coeffiecient? What about tripling?

########### Double k
uI.field.2 <- NULL
k = 0.15 * 2
for (x in 1:length(PAR)) {
    uI <- PAR[x] * exp(k * z)
    uI.field.2 <- rbind(uI.field.2, uI)
}
########### Triple k
uI.field.3 <- NULL
k = 0.15 * 3
for (x in 1:length(PAR)) {
    uI <- PAR[x] * exp(k * z)
    uI.field.3 <- rbind(uI.field.3, uI)
}
contour(sun_time, z, uI.field, levels = c(1), yaxt = "n", lwd = 1.8, 
    ylab = "Depth", xlab = "Time", ylim = c(-40, 0))
axis(2, at = seq(0, -40, -5), labels = seq(0, 40, 5), las = 1)
contour(sun_time, z, uI.field.2, levels = c(1), add = T, col = "red", 
    lwd = 1.8)
contour(sun_time, z, uI.field.3, levels = c(1), add = T, col = "blue", 
    lwd = 1.8)
legend("bottom", legend = c("k", "k*2", "k*3"), col = c("black", 
    "red", "blue"), pch = NA, lwd = 1.8, horiz = T)

• The differences in the 1 W m^-2 isolume is about 20 m from k to k*2 and 25 m from k to k*3 at max daily PAR. The light is more quickly attenuated with depth at higher k values as can been seen by k being an expontential term. When the PAR term is low in the morning and evening the exponential term doesn't change the penetration as much.