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# R code to plot latitudinal profiles of (circular) mean flow direction,
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# along with both RMSE and (circular) correlation coefficients comparing
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# fused layers with both the raw ASTER and with the Canada DEM
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#
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# Jim Regetz
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# NCEAS
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library(raster)
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library(circular)
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datadir <- "/home/regetz/media/temp/terrain/flow"
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# create function to recode terraflow SFD values into degrees, with
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# 0=North and proceeding clockwise (this matches gdaldem's default
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# azimuth output for aspect calculation)
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recode <- function(r) {
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v <- values(r)
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v[v==0] <- NA
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v[v==1] <- 90 ## east
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v[v==2] <- 135
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v[v==4] <- 180 ## south
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v[v==8] <- 225
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v[v==16] <- 270 ## west
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v[v==32] <- 315
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v[v==64] <- 0 ## north
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v[v==128] <- 45
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r[] <- v
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return(r)
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}
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# load flow direction rasters, recoding on the fly
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sfd.aster <- recode(raster(file.path(datadir, "aster_300straddle_sfd.tif")))
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sfd.srtm <- recode(raster(file.path(datadir, "srtm_150below_sfd.tif")))
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sfd.uncor <- recode(raster(file.path(datadir, "fused_300straddle_sfd.tif")))
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sfd.enblend <- recode(raster(file.path(datadir, "fused_300straddle_enblend_sfd.tif")))
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sfd.bg <- recode(raster(file.path(datadir, "fused_300straddle_blendgau_sfd.tif")))
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sfd.can <- recode(raster(file.path(datadir, "cdem_300straddle_sfd.tif")))
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# extract raster latitudes for later
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lats300 <- yFromRow(sfd.aster, 1:nrow(sfd.aster))
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lats150 <- yFromRow(sfd.srtm, 1:nrow(sfd.srtm))
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# initialize output pdf device driver
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pdf("flowdir-assessment.pdf", height=8, width=11.5)
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#
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# plot latitudinal profiles of mean flow direction
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#
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# simple helper function to calculate row-wise means using circular
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# mean, patterned after circ.mean in the CircStats package
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rowMeansC <- function(r1, na.rm=TRUE) {
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m1 <- as.matrix(r1)
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m1[] <- (m1 * pi)/180
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sinr <- rowSums(sin(m1), na.rm=na.rm)
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cosr <- rowSums(cos(m1), na.rm=na.rm)
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cmeans <- atan2(sinr, cosr)
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(cmeans * 180)/pi
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}
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par(mfrow=c(2,2), omi=c(1,1,1,1))
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ylim <- c(-180, 180)
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plot(lats300, rowMeansC(sfd.can), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean flow direction", ylim=ylim)
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axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))
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text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="Original DEMs")
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lines(lats300, rowMeansC(sfd.aster), col="blue")
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lines(lats150, rowMeansC(sfd.srtm), col="red")
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legend("bottomright", legend=c("ASTER", "SRTM", "CDED"), col=c("blue",
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"red", "black"), lty=c(1, 1), bty="n")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste("Latitudinal profiles of mean flow direction (",
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125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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#plot(lats300, rowMeans(as.matrix(sfd.uncor), na.rm=TRUE), type="l",
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# xlab="Latitude", ylab="Mean flow direction", ylim=ylim)
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#text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="uncorrected")
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#abline(v=60, col="red", lty=2)
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#mtext(expression(paste("Latitudinal profiles of mean flow direction (",
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# 125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rowMeansC(sfd.uncor), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean flow direction", ylim=ylim)
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axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))
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text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="simple fused")
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abline(v=60, col="red", lty=2)
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plot(lats300, rowMeansC(sfd.enblend), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean flow direction", ylim=ylim)
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axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))
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text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="multires spline")
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abline(v=60, col="red", lty=2)
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plot(lats300, rowMeansC(sfd.bg), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean flow direction", ylim=ylim)
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axis(2, at=c(-180, -90, 0, 90, 180), labels=c("S", "W", "N", "E", "S"))
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text(min(lats300), min(ylim)+0.5, pos=4, font=3, labels="gaussian blend")
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abline(v=60, col="red", lty=2)
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#
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# plot latitudinal profiles of RMSE
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#
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# simple helper function to calculate row-wise RMSEs, accounting for the
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# fact that flow dir values are circular (0-360), so the difference
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# between e.g. 5 and 355 should only be 10
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rmse <- function(r1, r2, na.rm=TRUE, use) {
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diffs <- abs(as.matrix(r1) - as.matrix(r2))
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if (!missing(use)) diffs[!use] <- NA
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diffs[] <- ifelse(diffs>180, 360-diffs, diffs)
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sqrt(rowMeans(diffs^2, na.rm=na.rm))
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}
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par(mfrow=c(2,3), omi=c(1,1,1,1))
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ylim <- c(0, 100)
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# ...with respect to ASTER
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plot(lats300, rmse(sfd.uncor, sfd.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(sfd.uncor, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="uncorrected")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Flowdir discrepancies with respect to separate ASTER/SRTM components (",
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125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rmse(sfd.enblend, sfd.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(sfd.enblend, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="exponential ramp")
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abline(v=60, col="red", lty=2)
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plot(lats300, rmse(sfd.bg, sfd.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(sfd.bg, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("topright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="gaussian blend")
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abline(v=60, col="red", lty=2)
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# ...with respect to CDEM
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plot(lats300, rmse(sfd.uncor, sfd.can), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="uncorrected")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Flowdir discrepancies with respect to Canada DEM (",
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125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rmse(sfd.enblend, sfd.can), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="exponential ramp")
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abline(v=60, col="red", lty=2)
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plot(lats300, rmse(sfd.bg, sfd.can), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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text(min(lats300), max(ylim)-5, pos=4, font=3, labels="gaussian blend")
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abline(v=60, col="red", lty=2)
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#
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# plot latitudinal profiles of correlation coefficients
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#
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# simple helper function to calculate row-wise *circular* correlation
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# coefficients
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corByLat <- function(r1, r2, rows) {
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if (missing(rows)) {
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rows <- 1:nrow(r1)
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}
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m1 <- circular(as.matrix(r1), units="degrees", rotation="clock")
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m2 <- circular(as.matrix(r2), units="degrees", rotation="clock")
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sapply(rows, function(row) {
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p <- cor.circular(m1[row,], m2[row,])
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if (is.null(p)) NA else p
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})
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}
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par(mfrow=c(2,3), omi=c(1,1,1,1))
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ylim <- c(-1, 1)
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# ...with respect to ASTER
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plot(lats300, corByLat(sfd.uncor, sfd.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(sfd.uncor, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), min(ylim), pos=4, font=3, labels="simple fused")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Flow direction correlations with respect to separate ASTER/SRTM components (",
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125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, corByLat(sfd.enblend, sfd.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(sfd.enblend, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), min(ylim), pos=4, font=3, labels="multires spline")
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abline(v=60, col="red", lty=2)
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plot(lats300, corByLat(sfd.bg, sfd.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(sfd.bg, extent(sfd.srtm)), sfd.srtm), col="blue")
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legend("bottomright", legend=c("ASTER", "SRTM"), col=c("black", "blue"),
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lty=c(1, 1), bty="n")
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text(min(lats300), min(ylim), pos=4, font=3, labels="gaussian blend")
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abline(v=60, col="red", lty=2)
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# ...with respect to CDEM
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plot(lats300, corByLat(sfd.uncor, sfd.can), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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text(min(lats300), min(ylim), pos=4, font=3, labels="simple fused")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Flow direction correlations with respect to Canada DEM (",
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125*degree, "W to ", 100*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, corByLat(sfd.enblend, sfd.can), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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text(min(lats300), min(ylim), pos=4, font=3, labels="multires spline")
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abline(v=60, col="red", lty=2)
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plot(lats300, corByLat(sfd.bg, sfd.can), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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text(min(lats300), min(ylim), pos=4, font=3, labels="gaussian blend")
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abline(v=60, col="red", lty=2)
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# close pdf device driver
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dev.off()
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