Modify your stream network

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One of the functions that I frequently use but which probably only few people know is the function STREAMobj/modify. As the name implies, the function modify lets you manipulate stream network data stored as a STREAMobj. The function allows you to make a number of choices among automated and manual editing procedures. Here is an overview:

Given one or more STREAMobj, you can
– extract streams with a given streamorder. The syntax for extracting all streams with Strahler streamorder less than 5 would be

Sm = modify(S,'streamorder','<5');

– extract a part of the network defined by the distance from the outlet. An example to extract the streams located between 50 and 100 km away from the outlet would be

Sm = modify(S,'distance',[50000 100000]);

– extract a part of the network that is upstream or downstream to regions specified in a GRIDobj. E.g., the syntax for extracting the stream networks above 1500 m is

Sm = modify(S,'upstreamto',DEM>1500);

– extract a part of the network that is tributary to another network. E.g., to extract the streams that are tributary to the trunk stream simply call

Sm = modify(S,'tributaryto',trunk(S));

Finally, there is the parameter ‘interactive’ which may take two options: ‘reachselect’ or ‘polyselect’. Check the two gif movies below how these work. Make following call if you want to manually select a reach

Sm = modify(S,'interactive','reachselect');
modify_reachselect
STREAMobj/modify with the option ‘interactive’ – ‘reachselect’

 

Or call the function modify in this way to select a stream network based on a polygon outline.

Sm = modify(S,'interactive','polyselect');
modify_polyselect
STREAMobj/modify with the option ‘interactive’ – ‘polyselect’

Do you think the modify function is useful. Are you missing something? Let me know.

Find your way through steep terrain

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One of my favorite functions in the Image Processing Toolbox is graydist. Actually, it was by my request that Mathwork’s Image Processing development team included this function together with bwdistgeodesic in release 2011b (Thanks for this!). The function help says:

graydist(A,mask) computes the gray-weighted distance transform of the grayscale image A. Locations where mask is true are seed locations.

I am using this function frequently, e.g., when routing through flat areas or topographic depressions when calculating a FLOWobj. However, there is a lot more to do with graydist. One nice application is to find a least cost path over a surface. In this post, I will show how to use TopoToolbox to find a way through steep terrain that minimizes the cumulated gradient (up and down) along the path. Thus, this function will be indispensible for planning your next hiking trip into the wild.

Ok, let’s see how to calculate least cost paths using Matlab and TopoToolbox 2. First, load the DEM shipped with TopoToolbox.

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif');
imageschs(DEM)

ex3_graydist_01

Then calculate a gradient grid which we will later use as weights into the distance calculation.

G = gradient8(DEM);

Create a GRIDobj with same spatial referencing as G that we will then use to store the distance grid.

D = GRIDobj(G);

Calculate the gray-weighted distance transform seeded at the lower left corner of the DEM

D.Z = graydist(G.Z,DEM.size(1));
imagesc(D); colorbar

ex3_graydist_02

Use the distance grid as input into the FLOWobj constructor function

FD = FLOWobj(D);

Calculate the influencemap seeded at the upper right corner

I  = influencemap(FD,prod(DEM.size)-DEM.size(1)+1);

Take this influencemap as stream grid for deriving a STREAMobj

S  = STREAMobj(FD,I);

and plot it

imageschs(DEM);
hold on
plot(S,'w','LineWidth',2)

ex3_graydist_03

Ok, that would be a nice walk along the river. Do you have applications in which you need least cost paths? Let me know.

The difference between carving and filling (3)

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In my last posts I wrote about carving and filling. As noted, both algorithms are implemented in the constructor function FLOWobj and thus are primarily used to derive flow directions through topographic depressions. These options, thus, don’t change the DEM itself. In this post, I will show how you will carve and fill the DEM.

Filling is easy and implemented in most terrain analysis software. A number of different algorithms exist that perform flood-fill operations; in our paper, Dirk and I compared processing speeds to fill an image. We found that the speed at which one and the same DEM is filled varies widely between different software. The Matlab’s image processing toolbox’s function imfill (the function that is called by TopoToolbox function fillsinks) outperforms other software by 8-10 times faster processing speed. However, I like to stress that speed is not the only indicator of performance and that other software may have better ways to manage memory. However, I don’t want to go into detail here…

Here is how to fill a DEM (the Big Tujunga DEM is included in the distribution of TopoToolbox 2)

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif');
DEMf = fillsinks(DEM);

One way to judge whether filling is a good option is to calculate the “energy” required to modify the DEM. When we fill the DEM, the energy is the total volume added to the DEM.

sum(DEMf.Z(:)-DEM.Z(:))*(DEM.cellsize)^2

ans =

18801000

A volume of ~19×106 m3 is required to force all flow towards the DEM edges. So how about carving? This requires us to calculate a FLOWobj and use it subsequently in a function called imposemin. Imposemin takes a FLOWobj and a GRIDobj and calculates a downstream minimum operator, i.e., it lets minima flow downstream.

FD = FLOWobj(DEM,'preprocess','carve');
DEMc = imposemin(FD,DEM);
sum(DEM.Z(:)-DEMc.Z(:))*(DEM.cellsize)^2

ans =

7848000

Carving the DEM requires removing a volume of ~8×106 m3 only. This is less than 1/2 of the energy that filling needs.

Based on these results, I would better carve the DEM to make it hydrologically correct. And, as John Lindsay pointed out in his comment on a previous post, carving is probably the better method in most situations. There may be, however, situations where filling might prove better, e.g., when the DEM has erroneously low valued, single scattered pixels. I had this problem once when working on a DEM in the Himalayas. This is why you find another function in TopoToolbox called elevateminima. This one allows you to raise single pixels to the height of their surrounding pixels.

Another note: Hybrid methods exist that partially fill and breach. I have not implemented these algorithms until now but perhaps I’ll do so in the future.

The difference between carving and filling (2)

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In my last post, I wrote about the algorithm that FLOWobj uses to derive flow directions in flat areas when choosing the option ‘fill’. This option ensures that flow paths run along centerlines of flat areas – an effect that may be desirable when there are large lakes in the DEM. The other option available is ‘carve’. So what does this option make different?

The preprocess option ‘carve’ works similarly to the ‘fill’ option. The difference, however, is that FLOWobj won’t seek the best path along the centerlines of flat sections. Instead it tries to find the path through sinks that runs along the deepest path, e.g. the valley bottom.

The algorithm works as follows: First, all sinks are identified. The sinks are filled by a flood fill operation (function fillsinks) and the difference between the filled and the original DEM is calculated. Then, the complement (e.g. max(z)-z) is calculated within each sink so that we have a raster where in each sink the smallest values are found in the valley bottoms. Then, this grid is used as weight in a gray-weighted distance transform (function graydist) with the sills of the sinks are used as distance seeds.

Understood? Well, following code and figures might help:

First, let’s load an example DEM and extract a subset that includes a sink in the channel network

DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif');
DEM = filter(DEM,'mean',[13 13]);
Z = crop(DEM,[352089 370106]);
imagesc(Z);
title('DEM')

ex2_carve_01

Identify sink and sill

[I,SI] = identifyflats(fillsinks(Z));
imagesc(I+2.*SI);
title('Sill and sink')

ex2_carve_02

Create the cost matrix for the gray-weighted distance transform

C = fillsinks(Z)-Z;
C = max(C)-C;
C.Z(~I.Z & ~SI.Z) = inf;
imagesc(C);
title('Complement of sink depth')

ex2_carve_03

Calculate the gray-weighted distance transform

D = GRIDobj(C);
D.Z = graydist(C.Z,SI.Z);
imagesc(D);
title('Gray-weighted distance transform')

ex2_carve_04

The code snippets above are implemented in similar form in the constructor function FLOWobj. Let’s look at a stream network derived for above DEM (Z).

FD = FLOWobj(Z,'preprocess','carve');
imagesc(Z);
S = STREAMobj(FD,'minarea',5);
hold on
plot(S,'k')
hold off
title('DEM and stream network')

ex2_carve_05

In the last figure, you will notice that the streams tend to run along the deepest cells of the DEM. This is exactly what we wanted to have and what we will need to carve the DEM with a minimum of energy, e.g., with a minimum modification of the DEM. In the next post, I will show how to use the FLOWobj derived with the ‘carve’-option to carve the DEM.

By the way, I have published a paper in ESPL in which I explain carving in more detail (e.g., gray-weighted distance transforms) and how you can use this approach to derive flow patterns in lowland, agricultural landscapes. If you are interested, please read on here.

The difference between carving and filling (1)

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People using TopoToolbox asked me quite frequently about the difference between the two preprocessing options when calculating a flow direction object (FLOWobj): ‘carve’ and ‘fill’.

First and most important: These options do not alter the DEM, they only control how FLOWobj internally preprocesses the DEM to optimize how flow is routed through topographic depressions.

In this first post I’ll describe how the option ‘fill’ works.

Option ‘fill’: The constructor function FLOWobj fills all topographic depressions (function fillsinks). It then identifies all flat sections (function identifyflats) and calculates an euclidean distance transform (function bwdist) within each flat section seeded at their outer rim. Subsequently, the complement of the distance transform is calculated in each flat area. The complement grid is subsequently used as weights in a gray-weighted distance transform (function graydist). This generates an auxiliary surface in each flat area. The surface has the nice property that flow will run through the centerline of flat areas.

map
D8 flow networks in flat areas derived with different terrain analysis software.

So how does this approach to derive flow directions in flat areas compare to other software. Above figure shows how other software handle flow directions in the flat areas. It seems that only TauDEM uses a similar approach as TopoToolbox 2. Other software seem to handle the problem differently and produce linear, somewhat unelegant flowpaths through flat sections.

Welcome

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Hi,

this is my first post and I want to quickly provide an overview on what you can expect from my posts. I am geoscientist with a major background in geomorphology, GIS, geostatistics and numerical modeling. In the last couple of months Dirk Scherler (Caltech) and I have developed TopoToolbox, a function library for Digital Elevation Model (DEM) analysis in MATLAB. This toolbox has been applied in research topics such as pedometrics, glaciology, landscape evolution modeling and hydrology by researchers and practitioners around the globe. TopoToolbox is also interesting for those amongst you, who study geomorphology, geomorphometry and hydrology and who seek to develop their own models and experimenting with DEMs.

The key to understanding how TopoToolbox works requires some knowledge about mathematics and image processing. I will try my best to cover these topics in posts that should be understood with only little background in these disciplines. Since my interests also go beyond the technical issues I will cover other topics related to DEM analysis as well.

So, hope you enjoy reading. Please leave comments.

References

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Schwanghart, W., Scherler, D. (2014): TopoToolbox 2 – MATLAB-based software for topographic analysis and modeling in Earth surface sciences. Earth Surface Dynamics, 2, 1-7. [DOI: 10.5194/esurf-2-1-2014, Discussion paper: 10.5194/esurfd-1-261-2013]. open access and software available here [DOI: 10.1594/IEDA/100175].

Schwanghart, W., Kuhn, N. J. (2010): TopoToolbox: a set of Matlab functions for topographic analysis. Environmental Modelling & Software, 25, 770-781. [DOI: 10.1016/j.envsoft.2009.12.002]