GRIDobj

Jet is dead

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Jet is dead, long live parula! The criticism of MATLAB’s former default colormap is all around. Jet is perceptually non-uniform. Our brains tend to detect changes between particular kinds of colors better than the transition between others. The colormap jet is thus misguiding, it accentuates parts of your data and thus misrepresents it.

I have to admit that I used jet for quite a while. And it was the default colormap of imageschs, one of the core visualization tools in TopoToolbox. These days are over now. The default colormap is now parula which you’ll find in the folder colormaps. In addition, you’ll find other colormaps:

– landcolor
– flowcolor
– magmacolor
– and a whole bunch of terrain coloring maps in ttcmap

And the good thing: Now you can have multiple colormaps in one figure…

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif');
subplot(2,2,1);
imageschs(DEM,[],'colormap','landcolor','ticklabels','nice')
title('DEM - landcolor')
subplot(2,2,2);
G = gradient8(DEM);
imageschs(DEM,G,'colormap',flipud(magmacolor(255)),'ticklabels','nice')
title('Gradient - magmacolor')
subplot(2,2,3);
FD = FLOWobj(DEM);
A  = flowacc(FD);
A  = dilate(A,ones(5));
imageschs(DEM,sqrt(A),'colormap','flowcolor','ticklabels','nice')
title('Flow accumulation - flowcolor')
subplot(2,2,4)
[clr,lims] = ttcmap(DEM,'cmap','gmtglobe');
imageschs(DEM,[],'colormap',clr,'caxis',lims,'ticklabels','nice')
title('DEM - gmtglobe')

 

colormaps.png

Of course, you can use all kinds of colormaps with imageschs such as hot, spring, etc. If you use custom colormaps, remember that

  • imageschs requires colormaps with less than or equal 256 colors or 255 if there are nans in the data.
  • you can easily flip colormaps, e.g. flipud(gray(255)).
  • you can easily build your own colormaps using colormapeditor.

Do you have a favourite colormap that you want to share with others and that should be included in a future release of TopoToolbox. TopoToolbox could need a bipolar colormap for displaying curvature, for example.

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Better maps with TopoToolbox

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I am increasingly using MATLAB to create maps. I simply find the workflow cumbersome that combines TopoToolbox, ArcGIS or QGIS. This is among the reasons why I implemented a new function in TopoToolbox that helps you coloring DEMs, particularly those that include topography and bathymetry. The function is ttcmap and you’ll find it in the colormaps folder.

Here is an example application of this function. I’ll use a DEM that covers one of the world’s steepest topographic gradients from the Andes down to the Peru-Chile deep-sea trench.

Before you run the function, choose a colormap. Calling ttcmap without input arguments displays a table that shows the different colormaps and their respective elevation ranges.

ttcmap

    Colormap_Name    Min_Elevation    Max_Elevation
    _____________    _____________    _____________

    'gmtrelief'       -8000           7000         
    'france'          -5000           4000         
    'mby'             -8000           4000         
    'gmtglobe'       -10000           9500    

Now here are three colormaps that span the elevation range in our DEM. Note that ttcmap outputs the array zlimits which is required as input to imageschs so that the land-sea boundary is exactly at zero. ttcmap is similar to the mapping toolbox function demcmap but more precisely sets the land-sea transition to the zero value.

[cmap,zlimits] = ttcmap(DEM,'cmap','gmtrelief');
imageschs(DEM,[],'caxis',zlimits,'colormap',cmap)
gmtrelief.png
gmtrelief
[cmap,zlimits] = ttcmap(DEM,'cmap','mby');
imageschs(DEM,[],'caxis',zlimits,'colormap',cmap)
mby.png
mby
[cmap,zlimits] = ttcmap(DEM,'cmap','gmtglobe');
imageschs(DEM,[],'caxis',zlimits,'colormap',cmap)
gmtglobe.png
gmtglobe

I downloaded the colormaps from cpt-city, a great resource for colormaps.

Tanaka contours – a MATLAB solution

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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)

tanaka1.png

And now for the Big Tujunga DEM:

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

tanaka2.png
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?

One tool to download them all

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Some changes and additions to TopoToolbox are subtle and may not be visible at first glance. Hence, I report them here. One such addition is part of version 2.2 (which Dirk and I are about to finalize shortly) and is found in the folder IOtools (input/output tools): readopentopo. The function uses opentopography’s RESTful Web service for global raster data access for seamless download of global digital elevation models. readopentopo offers access to SRTM-3, SRTM-1, and ALOS 3D World data at your finger tips. By default, the downloaded *.tif-file is stored in your system’s temporary folder and is deleted as soon as it is read into MATLAB. If you want to permanently save the file on your hard drive make sure to define a file path and to set the ‘deletefile’-option to false. The tif-file comes in geographic coordinates. Hence, don’t forget to reproject the DEM to UTM (see reproject2utm) before you start working with it.

Many thanks to members of the opentopography-team who make the data and service available. Please use these services reasonably and don’t excessively download data!

Orientation of stream segments

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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:

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

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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).

sunpositioneiger_12.gif

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.

eiger_animation

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

Large landslides lie low: Excess topography in the Himalaya-Karakoram ranges

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In a just published article in Geology by Jan Blöthe, Oliver Korup and me, we show that the Himalaya-Karakoram Range exhibits an intriguing vertical stacking of erosional domains driven by mass-wasting and (peri-)glacial activity. We show that large bedrock failures preferably detach below the limit of sporadic alpine permafrost adjusting hillslope inclinations to rapid fluvial incision and postglacial stress fields in oversteepened valley flanks. Intense frost cracking above the permafrost limit in turn may result in high-frequency/low-magnitude rockfalls and avalanches, thus limiting the occurrence of low-frequency/high-magnitude rock-slope failures.

As part of the analysis, we introduced ‘excess topography’ as a new measure to characterize mountain topography. Here is an excerpt taken from the supplementary material that describes excess topography and how it is calculated from a DEM:

Excess topography measures for each grid cell in a digital elevation model (DEM) the rock-column height above an arbitrarily defined threshold slope surface. The threshold slope surface is an idealized surface that we derive from a given DEM. The threshold surface only contains inclinations that are lower or equal than the arbitrarily set threshold inclination. The elevations of the threshold surface are constrained by the DEM elevations and the threshold inclination such that (1) the elevation of the threshold and DEM input surface coincide for a given grid cell if the slopes between this grid cell and all others are less or equal the threshold slope; and (2) elevations of the threshold surface fall below the DEM input surface in grid cells rising above the surrounding topography at angles steeper than the threshold inclination. In case (2), we calculate the threshold surface elevation as the minimum elevation of all surrounding locations plus the maximum allowed topographic rise (threshold inclination) along the distance separating the locations.

A picture is worth a thousand words. Here you go:

Excess topography
Also check the animation below to see how the minimum filter with additional offsets works in 2D.
excesstopography

Excess topography can be calculated using the new function excesstopography in TopoToolbox. The function is quite simple. The most important algorithm that it requires – image morphology with a grayscale structuring element – is made available by the function ordfilt2 in the Image Processing Toolbox. Did you know this function? This function is extremely powerful and I can think of quite a lot of nice applications of DEM analysis. Since I said that graydist is my favorite function, ordfilt2 is my second favorite function.

Reference

Blöthe, J.H., Korup, O., Schwanghart, W. (2015): Large landslides lie low: Excess topography in the Himalaya-Karakorum ranges. Geology, 43, 523-526. [DOI:

** edited on May 23, 2015 to update reference **

** edited on June 23, 2015 to include free pdf download **