Analysis of DEMs in R+ILWIS/SAGA

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he science of quantitative analysis of land surface or surfaces in general is refer to as geomorphometry. One of the main objectives of geomorphometry is the (automated) extraction of land-surface parameters and objects, and assessment of their properties. Analysis of DEMs can be today easily automated by combining open source packages R+ILWIS/SAGA (read more on how to obtain and install these packages). This allows us to run series of same operations on DEMs coming from various sources (or on their simulations) and compare the outputs using sound statistical procedures. The complete script used to generate graphs and maps shown below is available here. Note that you can try running the same script using any of the four DEMs attached. These are the DEMs of the same area, but generated using elevation measurements from various data sources (National Elevation Dataset, SRTM DEMs). See also an ArcGIS script to measure drumlin attributes from a DEM. An updated version of this article can be followed in Hengl (2009; ch.9).

Sample script to extract land-surface parameters and landform classes.
  • Icon R.png Analysis_DEMs.R : R script for automated analysis of DEMs.
  • Icon zip.png : Four DEMs prepared for the Palmyra region, NY (0.95 MB).


Import of DEMs and extraction of land surface parameters

We start by reading a DEM into R:

> gridmaps <- readGDAL("NED1.asc")  # this scripts uses only one DEM; to compare analysis, change the input!
> names(gridmaps)[1] <- "DEM"
> proj4string(gridmaps) <- CRS("+init=epsg:32618")
> spplot(gridmaps)

Next, we want to extract Topographic Wetness Index, altitude above channel network and solar insolation. All this can be extracted using the SAGA GIS. We start by converting the DEM (ArcInfo ASCII) to SAGA grid format:

>"NED1.asc", out.sgrds="NED1.sgrd", in.path=getwd())

# derive catchment area:
> rsaga.geoprocessor(lib="ta_hydrology", module=15, param=list(DEM="NED1.sgrd", C="catharea.sgrd", 
+      GN="catchslope.sgrd", CS="modcatharea.sgrd", SB="twi.sgrd", T=10))

# filter the spurious sinks:
> rsaga.geoprocessor(lib="ta_preprocessor", module=2, param=list(DEM="NED1.sgrd", RESULT="NED1_f.sgrd"))

# extract channel network:
> rsaga.geoprocessor(lib="ta_channels", module=0, param=list(ELEVATION="NED1_f.sgrd", 
+      CHNLNTWRK="chnlntwrk.sgrd", CHNLROUTE="channel_route.sgrd", SHAPES="channels.shp", 
+      INIT_GRID="NED1_f.sgrd", DIV_CELLS=round(sqrt(length(gridmaps@data[[1]]))/100, 0), 
+      MINLEN=round(sqrt(length(gridmaps@data[[1]]))/10, 0)))

# derive altitude above channel network:
> rsaga.geoprocessor(lib="ta_channels", module=3, param=list(ELEVATION="NED1_f.sgrd", 
+      CHANNELS="chnlntwrk.sgrd", ALTITUDE="achan.sgrd", THRESHOLD=0.1, NOUNDERGROUND=TRUE))

# derive incoming solar radiation:
> rsaga.geoprocessor(lib="ta_lighting", module=2, param=list(ELEVATION="NED1.sgrd", 
+      INSOLAT="insolat.sgrd", DURATION="durat.sgrd", LATITUDE=43, HOUR_STEP=4, TIMESPAN=2, DAY_STEP=10))
# ! this can take time; modify latitude accordingly;
Figure: Extracted land-surface parameters visualized in SAGA GIS.

We can read the maps back to R:

>"twi.sgrd", "achan.sgrd","chnlntwrk.sgrd", "insolat.sgrd"), 
+      out.grids=c("twi.asc", "achan.asc", "chnlntwrk.asc", "insolat.asc"), prec=1, out.path=getwd())
> gridmaps$twi <- readGDAL("twi.asc")$band1
> gridmaps$achan <- readGDAL("achan.asc")$band1
> gridmaps$insolat <- readGDAL("insolat.asc")$band1
> gridmaps$chnlntwrk <- readGDAL("chnlntwrk.asc")$band1

Some land-surface parameters are very skewed, so you might want to transform them:

hist(gridmaps$DEM); hist(gridmaps$twi); hist(gridmaps$achan)
gridmaps$logachan <- log1p(gridmaps$achan)

Unsupervised extraction of landforms

An objective way to extract landform parameters is to use the kmeans method of the stats package in R. Before we actually extract the landforms, it is a wise idea to reduce multicolinearity of the land-surface parameters by running a Principal Component Analysis:

> pc.dem <- prcomp(~DEM+twi+achan+insolat, scale=TRUE, gridmaps@data)
> biplot(pc.dem, arrow.len=0.1, xlabs=rep(".", length(pc.dem$x[,1])), main="PCA biplot")
Figure: Biplot showing the multicolinearity of land-surface parameters. This plot shows that DEM and achan are highly correlated.

Next, we wish to determine the optimal number of clusters:

> demdata <-$x)
> wss <- (nrow(demdata)-1)*sum(apply(demdata,2,var))
> for (i in 2:12) {wss[i] <- sum(kmeans(demdata, centers=i)$withinss)}
> plot(1:12, wss, type="b", xlab="Number of Clusters", ylab="Within groups sum of squares")
Figure: Selecting the optimal number of clusters for unsupervised classification of landforms.

Unfortunately, the Sum of squares does not converge, so we can at least use the maximum number of clusters (12):

> kmeans.dem <- kmeans(demdata, 12)
> gridmaps$kmeans.dem <- kmeans.dem$cluster
> gridmaps$landform <- as.factor(kmeans.dem$cluster)
> summary(gridmaps$landform)
> spplot(gridmaps["landform"], col.regions=rainbow(12))
# writeAsciiGrid(gridmaps["kmeans12.dem"], "landform.asc")

We can write this landform map to ILWIS GIS and display it so we can edit the legends manually:

> writeGDAL(gridmaps["kmeans.dem"], "landform.mpr", "ILWIS")
# create a domain in ILWIS:
> shell(cmd=paste(ILWIS, " crdom landform.dom -type=group -items=0",sep=""), wait=F)
# add elements to the domain:
> for(i in 1:length(levels(gridmaps$landform))){
   shell(cmd=paste(ILWIS, " additemtodomaingroup landform.dom ", i+.01," cl",i,sep=""), wait=F)
> shell(cmd=paste(ILWIS, "landform_c.mpr = MapSlicing(landform.mpr, landform.dom)"), wait=F)
> shell(cmd=paste(ILWIS, "open landform_c.mpr -noask"), wait=F)
Figure: Map of landforms extracted using unsupervised k-means clustering.

Supervised classification of land-surface objects

If some training data is available, we can also map a belonging of a certain area to what we have visually classified into a certain class (landform). Imagine that a polygon map is available with borders of some landform of interest (in this case drumlins). We want to use this map to specify the position of the class in feature space, and then derive a probability of drumlin using some relevant land surface parameters. We first need to import this map to R:

# import the map showing location of drumlins (training pixels)
> drumlins <- readShapePoly("drumlins.shp")
# spplot(drumlins)
# overlay drumplins and grid maps and create a new grid:
> gridmaps$drumlins <- as.factor(overlay(gridmaps, drumlins))

Next, we need to estimate the class centres and variation around class centers based on the training areas:

# standard deviation:
> drumlin.var <- sd(subset(gridmaps@data, drumlins=="2")[c("DEM","twi","logachan")], na.rm=T)
> drumlin.var
      DEM       twi  logachan 
2.4675426 0.7109454 0.2330179
# mean values:
> drumlin.mean <- mean(subset(gridmaps@data, drumlins=="2")[c("DEM","twi","logachan")], na.rm=T)
> drumlin.mean
       DEM        twi   logachan 
177.565516  11.051724   2.318473
# range of values (most reliable):
> drumlin.range <- data.frame(DEM=range(subset(gridmaps@data, drumlins=="2")["DEM"], na.rm=T), 
+     twi=range(subset(gridmaps@data, drumlins=="2")["twi"], na.rm=T), 
+     logachan=range(subset(gridmaps@data, drumlins=="2")["logachan"], na.rm=T))
> drumlin.range
    DEM  twi logachan
1 174.0  9.8 1.916923
2 182.9 12.5 2.766319

We can now calculate the mean normal density function (probability) that a point belongs to some class in the feature space. In this case, we use the extreme values of DEM, twi and achan, because we assume the class centers are in fact where the elevation is highest; twi is the lowest; and achan is the highest!

> qu <- 2  # adjustment factor!
# average probability:
> gridmaps$ <- (2*pnorm(abs((gridmaps$DEM-drumlin.range[2,"DEM"])/(qu*drumlin.var["DEM"])), lower.tail=F)
+     +2*pnorm(abs((gridmaps$twi-drumlin.range[1,"twi"])/(qu*drumlin.var["twi"])), lower.tail=F)
+     +2*pnorm(abs((gridmaps$logachan-drumlin.range[2,"logachan"])/(qu*drumlin.var["logachan"])), lower.tail=F))/3
# hist(gridmaps$, breaks=30)  
# spplot(gridmaps[""], col.regions=grey(rev(seq(0,1,0.01))))
# writeGDAL(gridmaps[""], "mu_drumlin.mpr", "ILWIS")

which gives the following map:

Figure: Probability of drumlin based on the training areas indicated in the map.

Export of maps to Google Earth

In the last step, we can export the created maps to Google Earth for visual assessment. First, we need to create the grid in the geographic system:

> gridmaps.ll <- spTransform(gridmaps["landform"], CRS("+proj=longlat +datum=WGS84"))
> corrf <- (1+cos((gridmaps.ll@bbox[2,2]+gridmaps.ll@bbox[2,1])/2*pi/180))/2
> geogrd.cell <- corrf*(gridmaps.ll@bbox[1,2]-gridmaps.ll@bbox[1,1])/gridmaps@grid@cells.dim[1]
> geoarc <- spsample(gridmaps.ll, type="regular", cellsize=c(geogrd.cell,geogrd.cell))
> gridded(geoarc) <- TRUE
> gridparameters(geoarc)
   cellcentre.offset     cellsize cells.dim
x1         -77.23152 0.0002932871       283
x2          42.97029 0.0002932871       220

Next, we can resample the map to the new geographic grid (e.g. in ILWIS GIS):

> shell(cmd=paste(ILWIS, " crgrf geoarc.grf ",geoarc@grid@cells.dim[[2]]," 
+     ",geoarc@grid@cells.dim[[1]]," -crdsys=LatlonWGS84 -lowleft=(",geoarc@grid@cellcentre.offset[[1]],",
+     ",geoarc@grid@cellcentre.offset[[2]],") -pixsize=",geoarc@grid@cellsize[[1]],sep=""), wait=F)
> shell(cmd=paste(ILWIS, "landform_ll.mpr = MapResample(landform_c.mpr, geoarc, NearestNeighbour)"), wait=F)
> shell(cmd=paste(ILWIS, "export tiff(landform_ll.mpr, landform_ll.tif)"), wait=F)

Finally, we generate a KML (ground overlay) by using the kmlOverlay method of the maptools package:

> overlay.kml <- GE_SpatialGrid(geoarc)
> kmlOverlay(overlay.kml, "landform.kml", "landform_ll.tif", name="Landform classes")
Figure: Extracted landform classes as shown in GE.

For more details on how to export raster maps to Google Earth, read also this article.

Important references

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