### Smoothing the planform geometry of river networks

In previous posts (here, here, here), I have covered some of the tools and applications of smoothing in the analysis of river networks. Thereby, I have focused on the analysis of river profiles (see also our paper here). However, these tools can also be used to smooth and analyse the planform patterns of river networks.

Here is how:

```
DEM = GRIDobj('srtm_bigtujunga30m_utm11.tif');
FD = FLOWobj(DEM,'preprocess','carve');
S = STREAMobj(FD,'minarea',1000);
S = klargestconncomps(S);
y = smooth(S,S.y,'k',500,'nstribs',true);
x = smooth(S,S.x,'k',500,'nstribs',true);
[~,~,xs,ys] = STREAMobj2XY(S,x,y);
subplot(2,1,1)
plot(S)
subplot(2,1,2)
plot(xs,ys)
```

Now what is this good for? First, simplification by smoothing might help in visualization. Second, the smoothed river coordinates can be used to derive metrics such as planform curvature of river networks. These metrics are strongly affected by the circumstance that river networks derived from digital elevation models are forced to follow the diagonal and cardinal directions of the grid. This results in local flow directions in steps of multiples of 45°. Changes in flow direction thus occur in jumps, and accordingly planform curvature of river networks are highly erratic. These erratic values may hide some of the larger-scale curvature patterns that we might be interested in.

The STREAMobj/curvature function features an example that shows how to accentuate larger-scale curvature patterns using smoothing. Following up on the code above, deriving curvature from smoothed planform coordinates can be done as follows:

```
y = smooth(S,S.y,'k',100,'nstribs',true);
x = smooth(S,S.x,'k',100,'nstribs',true);
c = curvature(S,x,y);
plotc(S,c)
box on
% center 0-value in colormap
caxis([-1 1]*max(abs(caxis)))
colormap(ttscm('vik'))
h = colorbar;
h.Label.String = 'Curvature';
```

Clearly, the amount of smoothing determines the spatial scale of curvature. Here, the chosen smoothing parameter (K=100) accentuates the bends at a scale of a few hundred meters.

There are a number of applications for this kind of analysis. Lateral erosion of rivers may undercut slopes and it may be interesting to investigate if planform curvature metrics help to detect and predict locations of landsliding. Just an idea…