# R code to plot latitudinal profiles of mean elevation, along with both

# RMSE and correlation coefficients comparing fused layers with both the

# raw ASTER and with the Canada DEM

#

# Jim Regetz

# NCEAS

# Created on 08-Jun-2011

library(raster)

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

# load elevation rasters

d.aster <- raster(file.path(datadir, "aster_300straddle.tif"))

d.srtm <- raster(file.path(datadir, "srtm_150below.tif"))

d.uncor <- raster(file.path(datadir, "fused_300straddle.tif"))

d.enblend <- raster(file.path(datadir, "fused_300straddle_enblend.tif"))

d.bg <- raster(file.path(datadir, "fused_300straddle_blendgau.tif"))

d.can <- raster(file.path(datadir, "cdem_300straddle.tif"))

# extract raster latitudes for later

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

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

#

# plot latitudinal profiles of mean elevation

#

# initialize output pdf device driver

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

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

ylim <- c(540, 575)

plot(lats300, rowMeans(as.matrix(d.can), na.rm=TRUE), type="l",

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

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

lines(lats300, rowMeans(as.matrix(d.aster), na.rm=TRUE), col="blue")

lines(lats150, rowMeans(as.matrix(d.srtm), na.rm=TRUE), col="red")

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

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

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

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

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

plot(lats300, rowMeans(as.matrix(d.uncor), na.rm=TRUE), type="l",

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

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

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

plot(lats300, rowMeans(as.matrix(d.enblend), na.rm=TRUE), type="l",

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

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

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

plot(lats300, rowMeans(as.matrix(d.bg), na.rm=TRUE), type="l",

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

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

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

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

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

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

}

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

ylim <- c(0, 35)

# ...with respect to ASTER

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

    ylab="RMSE", ylim=ylim)

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

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

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

text(min(lats300), max(ylim)-1, pos=4, font=3, labels="simple fuse")

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

mtext(expression(paste(

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

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

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

    ylab="RMSE", ylim=ylim)

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

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

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

text(min(lats300), max(ylim)-1, pos=4, font=3, labels="multires spline")

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

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

    ylab="RMSE", ylim=ylim)

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

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

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

text(min(lats300), max(ylim)-1, pos=4, font=3, labels="gaussian blend")

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

# ...with respect to CDEM

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

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-1, pos=4, font=3, labels="simple fuse")

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

mtext(expression(paste(

    "Elevation discrepancies with respect to Canada DEM (",

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

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

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-1, pos=4, font=3, labels="multires spline")

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

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

    ylab="RMSE", ylim=ylim)

text(min(lats300), max(ylim)-1, 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 correlation coefficients

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

    if (missing(rows)) {

        rows <- 1:nrow(r1)

    }

    m1 <- as.matrix(r1)

    m2 <- as.matrix(r2)

    sapply(rows, function(row) cor(m1[row,], m2[row,],

        use="pairwise.complete.obs"))

}

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

ylim <- c(0.99, 1)

# ...with respect to ASTER

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

    ylab="Correlation", ylim=ylim)

lines(lats150, corByLat(crop(d.uncor, extent(d.srtm)), d.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 fuse")

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

mtext(expression(paste(

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

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

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

    ylab="Correlation", ylim=ylim)

lines(lats150, corByLat(crop(d.enblend, extent(d.srtm)), d.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(d.bg, d.aster), type="l", xlab="Latitude",

    ylab="Correlation", ylim=ylim)

lines(lats150, corByLat(crop(d.bg, extent(d.srtm)), d.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(d.uncor, d.can), type="l", xlab="Latitude",

    ylab="Correlation", ylim=ylim)

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

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

mtext(expression(paste(

    "Elevation correlations with respect to Canada DEM (",

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

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

    ylab="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(d.bg, d.can), type="l", xlab="Latitude",

    ylab="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()

#

# plot pattern of ASTER-SRTM deltas as a function of ASTER elevation

#

plotMeanDeltaByElev <- function(delta.vals, elev, ...) {

    mean.by.elev <- tapply(delta.vals, elev, mean)

    sd.by.elev <- tapply(delta.vals, elev, sd)

    n.by.elev <- tapply(delta.vals, elev, length)

    se.by.elev <- sd.by.elev/sqrt(n.by.elev)

    na.se.points <- mean.by.elev[is.na(se.by.elev)]

    se.by.elev[is.na(se.by.elev)] <- 0

    elev <- as.numeric(names(mean.by.elev))

    plot(elev, mean.by.elev, pch=16,

        xlim=c(0, max(elev)), ylim=c(min(mean.by.elev -

        se.by.elev), max(mean.by.elev + se.by.elev)), type="n", ...)

    segments(elev, mean.by.elev-se.by.elev,

        as.numeric(names(mean.by.elev)), mean.by.elev+se.by.elev,

        col="grey")

    points(elev, mean.by.elev, pch=".")

    points(as.numeric(names(na.se.points)), na.se.points, pch=4,

        col="red", cex=0.5)

}

d.aster.crop.vals <- values(crop(d.aster, extent(d.srtm)))

d.srtm.vals <- values(d.srtm)

delta.vals <- d.aster.crop.vals - d.srtm.vals

plotMeanDeltaByElev(delta.vals, d.aster.crop.vals,

    xlab="ASTER elevation (m)", ylab="ASTER-SRTM difference (m)")

plotDeltaBins <- function(delta.vals, elev, bin.min, bin.width, bin.max=1500,

    outline=FALSE, ...) {

    breaks <- seq(bin.min, bin.max, by=bin.width)

    midpts <- c(

        paste("<", bin.min, sep=""),

        head(breaks, -1) + bin.width/2,

        paste(">", bin.max, sep=""))

    elev <- cut(elev, breaks=c(0, breaks, Inf), labels=midpts)

    bp <- boxplot(delta.vals ~ elev, outline=outline, col="lightgray",

        frame=FALSE, ...)

    text(1:length(bp$n), bp$stats[5,], labels=round(bp$n/1000),

        pos=3, cex=0.5, offset=0.2, font=3, col="gray")

    #axis(3, at=seq_along(bp$n), labels=paste(round(bp$n/1000), "k", sep=""),

    #    cex.axis=0.7, tick=FALSE, font=3, line=-1)

    #mtext("n =", side=3, adj=0, font=3, cex=0.7)

    abline(h=median(delta.vals), col="red", lty=2)

    invisible(bp)

}

d.aster.crop.vals <- values(crop(d.aster, extent(d.srtm)))

d.srtm.vals <- values(d.srtm)

delta.vals <- d.aster.crop.vals - d.srtm.vals

#  d.aster.crop.vals <- d.aster.crop.vals[d.srtm.vals>0]

#  d.srtm.vals <- d.srtm.vals[d.srtm.vals>0]

png("aster-srtm-bins.png", height=5, width=8, units="in", res=300)

plotDeltaBins(delta.vals, d.srtm.vals, 150, 50, 1500, las=2,

    cex.axis=0.8, xlab="Midpoints of SRTM elevation bins (m)",

    ylab="ASTER - SRTM difference (m)")

dev.off()

# plot scatter of aster vs srtm

png("aster-srtm-scatter.png", height=5, width=8, units="in", res=300)

plot(jitter(d.srtm.vals), jitter(d.aster.crop.vals), pch=".",

    xlab="SRTM elevation (m)", ylab="ASTER elevation (m)", cex=0.5)

abline(median(delta.vals), 1, col="red", cex=0.5)

abline(0, 1, col="blue", lty=2, cex=0.5)

# add inset histogram of differences

opar <- par(fig=c(0.55, 0.95, 0.1, 0.6), new=TRUE)

h <- hist(delta.vals[abs(delta.vals)<60], breaks=48, xlab=NA, main=NULL,

    col=grey(0.8), border=grey(0.3), yaxt="n", ylab=NA, cex.axis=0.5,

    cex.lab=0.5, tcl=-0.25, mgp=c(3,0,0))

text(10, 0.4*max(h$counts), labels=paste("Entire range:\n(",

    min(delta.vals), ", ", max(delta.vals), ")", sep=""), cex=0.6,

    adj=c(0,0))

mtext("ASTER - SRTM (m)", side=1, cex=0.5, line=0.6)

dev.off()