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# R code to plot latitudinal profiles of (circular) mean aspect, along
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# with both RMSE and (circular) correlation coefficients comparing fused
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# layers with both the raw ASTER and with the Canada DEM
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#
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# Aspect layers were generated from the respect DEMs in this way:
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# $ gdaldem aspect -s 111120 <layer>.tif <layer>_a.tif
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# ...where the default azimuthal behavior produces output values ranging
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# from 0-360 where 0 is north, and proceeding clockwise
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#
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# For exploratory plotting, note the following (uses 'circular'
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# package):
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# > cx <- circular(as.matrix(a.bg)[151,], units="degrees",
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# rotation="clock", zero=pi/2)
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# > rose.diag(cx, bins=8)
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# > points(mean.circular(cx, na.rm=TRUE), col="red")
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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/aspect"
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# load aspect rasters
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a.aster <- raster(file.path(datadir, "aster_300straddle_a.tif"))
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a.srtm <- raster(file.path(datadir, "srtm_150below_a.tif"))
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a.uncor <- raster(file.path(datadir, "fused_300straddle_a.tif"))
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a.enblend <- raster(file.path(datadir, "fused_300straddle_enblend_a.tif"))
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a.bg <- raster(file.path(datadir, "fused_300straddle_blendgau_a.tif"))
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a.can <- raster(file.path(datadir, "cdem_300straddle_a.tif"))
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# extract raster latitudes for later
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lats300 <- yFromRow(a.aster, 1:nrow(a.aster))
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lats150 <- yFromRow(a.srtm, 1:nrow(a.srtm))
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# initialize output pdf device driver
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pdf("aspect-assessment.pdf", height=8, width=11.5)
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#
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# plot latitudinal profiles of mean aspect
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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(a.can), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean aspect", 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(a.aster), col="blue")
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lines(lats150, rowMeansC(a.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 aspect (",
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136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rowMeansC(a.uncor), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean aspect", 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(a.enblend), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean aspect", 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(a.bg), type="l", yaxt="n",
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xlab="Latitude", ylab="Mean aspect", 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 aspect 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(a.uncor, a.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(a.uncor, extent(a.srtm)), a.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="simple fused")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Aspect discrepancies with respect to separate ASTER/SRTM components (",
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136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rmse(a.enblend, a.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(a.enblend, extent(a.srtm)), a.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="multires spline")
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abline(v=60, col="red", lty=2)
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plot(lats300, rmse(a.bg, a.aster), type="l", xlab="Latitude",
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ylab="RMSE", ylim=ylim)
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lines(lats150, rmse(crop(a.bg, extent(a.srtm)), a.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(a.uncor, a.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="simple fused")
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abline(v=60, col="red", lty=2)
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mtext(expression(paste(
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"Aspect discrepancies with respect to Canada DEM (",
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136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, rmse(a.enblend, a.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="multires spline")
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abline(v=60, col="red", lty=2)
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plot(lats300, rmse(a.bg, a.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(a.uncor, a.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(a.uncor, extent(a.srtm)), a.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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"Aspect correlations with respect to separate ASTER/SRTM components (",
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136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, corByLat(a.enblend, a.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(a.enblend, extent(a.srtm)), a.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(a.bg, a.aster), type="l", xlab="Latitude",
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ylab="Circular correlation", ylim=ylim)
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lines(lats150, corByLat(crop(a.bg, extent(a.srtm)), a.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(a.uncor, a.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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"Aspect correlations with respect to Canada DEM (",
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136*degree, "W to ", 96*degree, "W)")), adj=0, line=2, font=2)
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plot(lats300, corByLat(a.enblend, a.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(a.bg, a.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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