# Visualization

### Tanaka contours – a MATLAB solution

Today, I read about the Tanaka method, an approach to depicting relief. The method relies on filled contours and coloring contour lines according to their direction and light origin. I have seen solutions in QGIS (here and here) which made me thinking whether the Tanaka method can also be implemented in MATLAB.

One difficulty with Tanaka’s method is that coloring of contour lines requires knowledge about whether higher values are found to the left or the right of a contour line. GDAL’s contouring algorithm has consistent behavior in this respect. However, MATLAB’s algorithm doesn’t. My trick is to calculate surface normals and their angle to the light source, and then interpolate the gridded directions to the vertex locations of the contour lines.

Now here is my approach which uses some undocumented features of the HG2 graphics. An excellent resource for undocumented features in MATLAB is Yair Altman’s blog.

function tanakacontour(DEM,nlevels) %TANAKACONTOUR Relief depiction using Tanaka contours % % Syntax % % tanakacontour(DEM,nlevels) % % See also: contourf, hillshade % % Author: Wolfgang Schwanghart (w.schwanghart[at]geo.uni-potsdam.de) % Date: 8. December, 2017 if nargin == 1; nlevels = 10; end % calculate solar vector azimuth = 315; azid = azimuth-90; azisource = azid/180*pi; [sx,sy,~] = sph2cart(azisource,0.1,1); % get coordinate matrices and z values [Z,X,Y] = GRIDobj2mat(DEM); % calculate surface normals [Nx,Ny] = surfnorm(Z); N = hypot(Nx,Ny); Nx = Nx./N; Ny = Ny./N; H = GRIDobj(DEM); H.Z = Nx*sx + Ny*sy; % Get coordinate matrices and Z [~,h] = contourf(X,Y,Z,nlevels); axis image drawnow % colormap cmap = gray(255)*255; cval = linspace(0,1,size(cmap,1))'; % the undocumented part for r = 1:numel(h.EdgePrims) % the EdgePrims property contains vertex data x = h.EdgePrims(r).VertexData(1,:); y = h.EdgePrims(r).VertexData(2,:); % interpolate hillshade grayscale values to contour vertices c = interp(H,double(x(:)),double(y(:))); % interpolate to colormap clr = interp1(cval,cmap,c); % adjust color data to conform with EdgePrims ColorData property clr = clr'; clr = uint8([clr;repmat(255,1,size(clr,2))]); % set all properties at once set(h.EdgePrims(r),'ColorBinding','interpolated','ColorData',clr,'LineWidth',1.2); end

Ok, now let’s try this on some data. In this code, I have used GRIDobj, the class for gridded, georeferenced data.

[X,Y,Z] = peaks(500); tanakacontour(GRIDobj(X,Y,Z),10)

And now for the Big Tujunga DEM:

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif'); tanakacontour(DEM,5)

Now that looks ok, but I am not totally convinced by these unrealistic terraces, to be honest. Moreover, my approach so far doesn’t include changing line widths. Contour lines should actually be thicker for slopes that face both towards and away from the light source. However, I didn’t figure out how to do this so far. Any ideas?

### An alternative to along-river swath profiles

Today, I want to show another application of TopoToolbox’s new smoothing suite that Dirk and I have recently released together with our discussion paper in ESURF. I will demonstrate that using different methods associated with STREAMobj enable you to create plots that are quite similar to swath profiles calculated along rivers. Let’s see how it works.

Swath profiles require a straight or curved path defined by a number of nodes. Each node has a certain orientation defined by one or two of its neighboring nodes. Creating swath profiles then involves mapping values from locations that are perpendicular to that orientation and within a specified distance. We will use a simplified version of mapping values lateral to the stream network which is implemented in the function maplateral. maplateral uses the function bwdist that returns a distance transform from all pixels (the target pixels) to a number of seed pixels in a binary image. In our case, seed pixels are the pixels of the stream network and bwdist identifies the target pixels from which it calculates the euclidean distance to the stream pixels. Usually, there are several target pixels for each seed pixel so that we require an aggregation function that calculates a scalar based on the vector of values that are associated with each seed pixel. Unlike swath profiles, however, this approach entails that some seed pixels may not have target pixels up to the maximum distance. We can thus be pretty sure that some pixels may be missing some of the information that we want to extract. While we cannot avoid this problem using this approach, we can at least reduce its impact using the nonparametric quantile regression implemented in the crs function.

Here is the approach. We’ll load a DEM, derive flow directions and a stream network which is in this case just one trunk river. We use the function maplateral to map elevations in a distance of 2 km to the stream network. Our mapping uses the maximum function to aggregate the values. Hence, we will have for each pixel along the stream network the maximum elevation in its 2 km nearest-neighborhood. The swath is plotted using the function imageschs and the second output of maplateral. Then we plot the maximum values along with a profile of the stream network.

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif'); FD = FLOWobj(DEM); S = STREAMobj(FD,'minarea',1e6,'unit','map'); S = klargestconncomps(S); S = trunk(S); z = getnal(S,DEM); [zmax,mask] = maplateral(S,DEM,2000,@max); subplot(2,1,1) imageschs(DEM,mask,'truecolor',[1 0 0],... 'colorbar',false,... 'ticklabels','nice'); subplot(2,1,2) plotdz(S,z) hold on plotdz(S,zmax) legend('River profile','maximum heights in 2 km distance')

This looks quite ok, but the topographic profile has a lot of scatter and a large number of values seem not to be representative. Most likely, those are the pixels whose closest pixels fail to extend to the maximum distance of 2 km. Rather, I’d expect a profile that runs along the maximum values of the zigzag line. How can we obtain this line? Well, the crs function could handle this. Though it was originally intended to be applied to longitudinal river profiles, it can also handle other data measured or calculated along stream networks. The only thing we need to “switch off” is the downstream minimum gradient that the function uses by default to create smooth profiles that monotoneously decrease in downstream direction. This is simply done by setting the ‘mingradient’-option to nan. I use a smoothing parameter value K=5 and set tau=0.99 which forces the profile to run along the 99th percentile of the data. You can experiment with different values of K and tau, if you like.

figure zmaxs = crs(S,zmax,'mingradient',nan,'K',5,'tau',0.99,'split',0); plotdz(S,z); hold on plotdzshaded(S,[zmaxs z],'FaceColor',[.6 .6 .6]) hold off

This looks much better and gives an impression on the steepness of the terrain adjacent to the stream network. Let’s finally compare this to a SWATHobj as obtained by the function STREAMobj2SWATHobj.

figure SW = STREAMobj2SWATHobj(S,DEM,'width',4000); plotdz(SW) xlabel('Distance upstream [m]'); ylabel('Elevation [m]');

Our previous results should be similar to the maximum line shown in the SWATHobj derived profile. And I think they are. In fact, the SWATHobj derived profiles also shows some scatter that is likely due to the sharp changes of orientation of the swath centerline. While we can remove some of this scatter by smoothing the SWATHobj centerline, I think that the combination of maplateral and the CRS algorithm provides a convenient approach to sketch along-river swath profiles.

### Orientation of stream segments

*Today’s guest post comes from Philippe Steer, assistant professor at the University of Rennes. Philippe contributed two new functions and I asked him to describe them here to show potential applications. Thanks, Philippe, for this contribution!
*

I recently needed to compute river network orientation. Indeed river network orientation can reveal distributed tectonics deformation at the vicinity of strike-slip faults (e.g. Castelltort et al., 2012) or can enable to identify developing vs paleo river networks. One way to obtain orientation is first to extract the river segments that are linking confluences to outlets or confluences to channel heads and then to compute the orientation of the resulting segments. The streampoi function allows to extract these feature points of the network such as channel heads, confluences, b-confluences (the points just upstream any confluence) and outlets. To connect these feature points into segment, one can use the propriety that each segment belongs to a unique watershed that is given by the function drainagebasins using as outlets the true river outlets and the b-confluences. By definition, each segment also corresponds to a unique value of strahler order.

Once the river segments are identified, segment orientation is easily obtained. What is interesting is that defining these segments also paves the way to compute several other geometric metrics averaged over the river segment such as segment direct or flowpath length, sinuosity, direct or flowpath slope, mean drainage area and even steepness index (if assuming a value of concavity).

To cleanly do the job, I have written two MATLAB functions:

- networksegment.m: which does the computations
- plotsegmentgeometry.m: which plots the results

Here is a piece of code showing you the use of these functions (assuming you have already loaded the DEM of interest):

%% Flow direction and drainage area DEMf = fillsinks(DEM); FD= FLOWobj(DEMf); A = flowacc(FD); %% Extract rivers % Set the critical drainage area A_river=1e7/(res^2); % m^2 W = A>A_river; % Extract the wanted network S = STREAMobj(FD,W); %% River segments % Extract segment and compute their orientations mnratio=0.5; [segment]=networksegment(S,FD,DEM,A,mnratio); % Plot results plotsegmentgeometry(S,segment)

To illustrate the results, I thought the South Island of New-Zealand was a good example. Indeed, as first suggested by Castelltort et al. (2012) the river catchments at the south of the Alpine fault are tilted, possibly suggesting that they have recorded a distributed shear deformation. This tilting is also quite obvious when looking at the river segments in the following figure. Another interesting feature is that the river segments north of the Alpine fault, facing the tilted rivers, display a higher steepness than their south neighbours. This could be due to a long list of forcings, including active tectonics, orographic precipitation gradient or the transition from glacial to fluvial erosion.

**References:**

Castelltort, S et al. (2012). River drainage patterns in the New Zealand Alps primarily controlled by plate tectonic strain. Nature Geoscience, 5(10), 744-748. [DOI: 10.1038/ngeo1582]

### A sunny day in the Bernese Alps, but not in the Eiger North Face

The Eiger north face (46.34°N, 8.00°E) is one of the most spectacular climbing routes in the Alps. Loose rocks, avalanches and severe weather conditions make it particularly challenging. And, as pertinent to north faces, it is shadowed during most of the daytime.

When and where you can catch a glimpse of sunlight, you can calculate using a sun position calculator, TopoToolbox, and a digital elevation model (DEM). A sun position calculator has been made available by Vincent Roy on the file exchange. The function calculates for a given latitude, longitude, date and time the azimuth and zenith angle of the sun. You can then use this input into the function castshadow which calculates the shadowed areas of a DEM for any azimuth and altitude (90°- zenith angle).

The animation below shows the Eiger north face on September 1, 2015. I looped through the hours from 5:00 to 19:00 and saved the figures as gif movie. Of course, there are edge effects that cause that parts of the DEM close to the DEM borders lack the cast shadow of mountains nearby. But the Eiger north face should be captured quite right.

Do you have any applications for the function castshadow? Let me know and comment!

### Visualization fun

Ok, this doesn’t have a direct value for whatsoever, but it is just an example of how to have fun with the visualization tools in MATLAB. Note that you’ll need to download the function plot3d from github to run this example.

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif'); FD = FLOWobj(DEM,'preprocess','carve'); S = STREAMobj(FD,'minarea',1000); S = klargestconncomps(S); RGB = imageschs(DEM,DEM,'colormap','landcolor'); [x,y] = getcoordinates(DEM); surface('XData',x,'YData',y,... 'ZData',repmat(min(DEM),numel(y),numel(x)),... 'CData',double(RGB)/255,... 'FaceColor','texturemap','EdgeColor','none'); hold on plot3d(S,DEM) axis image exaggerate(gca,2) axis off hold off

### Plotting colored stream networks

Visual exploration of stream networks and channel length profiles is a mandatory first step before advancing towards more sophisticated tools such as slope-area plots or chiplots. Taking a look at both planform river patterns and respective channel length profiles will provide a good impression of the three-dimensional river patterns. Here is a quick guide how to visualize a stream network using different colors for each river system (or drainage basin). An underappreciated function comes in handy here: STREAMobj2cell.

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif'); FD = FLOWobj(DEM,'preprocess','carve'); S = STREAMobj(FD,'minarea',1000); CS = STREAMobj2cell(S); h1 = subplot(1,2,1); hold(h1,'on'); h2 = subplot(1,2,2); hold(h2,'on'); clrs = jet(32); for r=1:numel(CS); axes(h1) plot(CS{r},'color',clrs(r,:)); axes(h2) plotdz(CS{r},DEM,'color',clrs(r,:)); end; hold(h1,'off') hold(h2,'off') axis(h1,'image') box(h1,'on') axis(h2,'image') set(h2,'DataAspectRatio',[1 1/16 1]) box(h2,'on')

I have manually edited the figure to make the figure look nicer. The question, however, is: What is the function STREAMobj2cell doing? This function returns stream networks belonging to an individual drainage basin as separate STREAMobjs in a cell array. Having this cell array, you just need to loop through and index into the cell array to access individual “connected components” of the stream network. Together with other functions for stream network modification such as modify, trunk or klargestconncomps, I think STREAMobj2cell will greatly help you to automate your stream network analysis.