# R code to plot latitudinal profiles of (circular) mean aspect, along

# with both RMSE and (circular) correlation coefficients comparing fused

# layers with both the raw ASTER and with the Canada DEM

#

# Aspect layers were generated from the respect DEMs in this way:

#   $ gdaldem aspect -s 111120 <layer>.tif <layer>_a.tif

# ...where the default azimuthal behavior produces output values ranging

# from 0-360 where 0 is north, and proceeding clockwise

#

# For exploratory plotting, note the following (uses 'circular'

# package):

#  > cx <- circular(as.matrix(a.bg)[151,], units="degrees",

#      rotation="clock", zero=pi/2)

#  > rose.diag(cx, bins=8)

#  > points(mean.circular(cx, na.rm=TRUE), col="red")

#

# Jim Regetz

# NCEAS

library(raster)

library(circular)

datadir <- "/home/regetz/media/temp/terrain/aspect"

# load aspect rasters

a.aster <- raster(file.path(datadir, "aster_300straddle_a.tif"))

a.srtm <- raster(file.path(datadir, "srtm_150below_a.tif"))

a.uncor <- raster(file.path(datadir, "fused_300straddle_a.tif"))

a.enblend <- raster(file.path(datadir, "fused_300straddle_enblend_a.tif"))

a.bg <- raster(file.path(datadir, "fused_300straddle_blendgau_a.tif"))

a.can <- raster(file.path(datadir, "cdem_300straddle_a.tif"))

# extract raster latitudes for later

lats300 <- yFromRow(a.aster, 1:nrow(a.aster))

lats150 <- yFromRow(a.srtm, 1:nrow(a.srtm))

# initialize output pdf device driver

pdf("aspect-assessment.pdf", height=8, width=11.5)

#

# plot latitudinal profiles of mean aspect

#

# simple helper function to calculate row-wise means using circular

# mean, patterned after circ.mean in the CircStats package

rowMeansC <- function(r1, na.rm=TRUE) {

    m1 <- as.matrix(r1)

    m1[] <- (m1 * pi)/180

    sinr <- rowSums(sin(m1), na.rm=na.rm)

    cosr <- rowSums(cos(m1), na.rm=na.rm)

    cmeans <- atan2(sinr, cosr)

    (cmeans * 180)/pi

}

par(mfrow=c(2,2), omi=c(1,1,1,1))

ylim <- c(-180, 180)

plot(lats300, rowMeansC(a.can), type="l", yaxt="n",

    xlab="Latitude", ylab="Mean aspect", ylim=ylim)

axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))

text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="Original DEMs")

lines(lats300, rowMeansC(a.aster), col="blue")

lines(lats150, rowMeansC(a.srtm), col="red")

legend("bottomright", legend=c("ASTER", "SRTM", "CDED"), col=c("blue",

    "red", "black"), lty=c(1, 1), bty="n")

abline(v=60, col="red", lty=2)

mtext(expression(paste("Latitudinal profiles of mean aspect (",

    136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)

plot(lats300, rowMeansC(a.uncor), type="l", yaxt="n",

    xlab="Latitude", ylab="Mean aspect", ylim=ylim)

axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))

text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="simple fused")

abline(v=60, col="red", lty=2)

plot(lats300, rowMeansC(a.enblend), type="l", yaxt="n",

    xlab="Latitude", ylab="Mean aspect", ylim=ylim)

axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))

text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="multires spline")

abline(v=60, col="red", lty=2)

plot(lats300, rowMeansC(a.bg), type="l", yaxt="n",

    xlab="Latitude", ylab="Mean aspect", ylim=ylim)

axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))

text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="gaussian blend")

abline(v=60, col="red", lty=2)

#

# plot latitudinal profiles of RMSE

#

# simple helper function to calculate row-wise RMSEs, accounting for the

# fact that aspect values are circular (0-360), so the difference

# between e.g. 5 and 355 should only be 10

rmse <- function(r1, r2, na.rm=TRUE, use) {

    diffs <- abs(as.matrix(r1) - as.matrix(r2))

    if (!missing(use)) diffs[!use] <- NA

    diffs[] <- ifelse(diffs>180, 360-diffs, diffs)

    sqrt(rowMeans(diffs^2, na.rm=na.rm))

}

par(mfrow=c(2,3), omi=c(1,1,1,1))

ylim <- c(0, 100)

# ...with respect to ASTER

plot(lats300, rmse(a.uncor, a.aster), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

lines(lats150, rmse(crop(a.uncor, extent(a.srtm)), a.srtm), col="blue")

legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="simple fused")

abline(v=60, col="red", lty=2)

mtext(expression(paste(

    "Aspect discrepancies with respect to separate ASTER/SRTM components (",

    136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)

plot(lats300, rmse(a.enblend, a.aster), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

lines(lats150, rmse(crop(a.enblend, extent(a.srtm)), a.srtm), col="blue")

legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="multires spline")

abline(v=60, col="red", lty=2)

plot(lats300, rmse(a.bg, a.aster), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

lines(lats150, rmse(crop(a.bg, extent(a.srtm)), a.srtm), col="blue")

legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="gaussian blend")

abline(v=60, col="red", lty=2)

# ...with respect to CDEM

plot(lats300, rmse(a.uncor, a.can), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="simple fused")

abline(v=60, col="red", lty=2)

mtext(expression(paste(

    "Aspect discrepancies with respect to Canada DEM (",

    136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)

plot(lats300, rmse(a.enblend, a.can), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="multires spline")

abline(v=60, col="red", lty=2)

plot(lats300, rmse(a.bg, a.can), type="l", xlab="Latitude",

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-5, pos=4, font=3, labels="gaussian blend")

abline(v=60, col="red", lty=2)

#

# plot latitudinal profiles of correlation coefficients

#

# simple helper function to calculate row-wise *circular* correlation

# coefficients

corByLat <- function(r1, r2, rows) {

    if (missing(rows)) {

        rows <- 1:nrow(r1)

    }

    m1 <- circular(as.matrix(r1), units="degrees", rotation="clock")

    m2 <- circular(as.matrix(r2), units="degrees", rotation="clock")

    sapply(rows, function(row) {

        p <- cor.circular(m1[row,], m2[row,])

        if (is.null(p)) NA else p

        })

}

par(mfrow=c(2,3), omi=c(1,1,1,1))

ylim <- c(-1, 1)

# ...with respect to ASTER

plot(lats300, corByLat(a.uncor, a.aster), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

lines(lats150, corByLat(crop(a.uncor, extent(a.srtm)), a.srtm), col="blue")

legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), min(ylim), pos=4, font=3, labels="simple fused")

abline(v=60, col="red", lty=2)

mtext(expression(paste(

    "Aspect correlations with respect to separate ASTER/SRTM components (",

    136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)

plot(lats300, corByLat(a.enblend, a.aster), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

lines(lats150, corByLat(crop(a.enblend, extent(a.srtm)), a.srtm), col="blue")

legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), min(ylim), pos=4, font=3, labels="multires spline")

abline(v=60, col="red", lty=2)

plot(lats300, corByLat(a.bg, a.aster), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

lines(lats150, corByLat(crop(a.bg, extent(a.srtm)), a.srtm), col="blue")

legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),

    lty=c(1, 1), bty="n")

text(min(lats300), min(ylim), pos=4, font=3, labels="gaussian blend")

abline(v=60, col="red", lty=2)

# ...with respect to CDEM

plot(lats300, corByLat(a.uncor, a.can), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

text(min(lats300), min(ylim), pos=4, font=3, labels="simple fused")

abline(v=60, col="red", lty=2)

mtext(expression(paste(

    "Aspect correlations with respect to Canada DEM (",

    136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)

plot(lats300, corByLat(a.enblend, a.can), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

text(min(lats300), min(ylim), pos=4, font=3, labels="multires spline")

abline(v=60, col="red", lty=2)

plot(lats300, corByLat(a.bg, a.can), type="l", xlab="Latitude",

    ylab="Circular correlation", ylim=ylim)

text(min(lats300), min(ylim), pos=4, font=3, labels="gaussian blend")

abline(v=60, col="red", lty=2)

# close pdf device driver

dev.off()