For Exercise 1, I investigated autocorrelation in patterns of cross-sectional change across and along stream reaches.

For Exercise 2, I wanted to know whether these patterns of change were related to channel geometry.

Specifically, I wanted to know if erosion or deposition happened more frequently close to cut banks than further away from them.

I was originally going to investigate change in both the along-channel and across-channel directions, but after consulting with my classmates, I decided that I would not be able to draw as many conclusions in the along-channel direction because I don’t have good information about the spacing and orientation of my cross sections.

Methods:

To find cross-sectional change, I paired sequential years and calculated change along each cross section for each pair of years as I did in exercise #1.

I wanted to compare the change to the location of the steepest bank, but I couldn’t figure out how to identify what parts of a cross section counted as a “bank” using a computer. Instead, I looked at the spatial pattern of change in relationship to the point of steepest slope in the across-channel direction.

I used the original cross section profiles to identify the point of steepest across-channel slope. Since the point of steepest slope may move from year to year, I used the steepest slope from the first year in every year pair. I used the loess function in R to lightly smooth each cross-sectional profile before extracting slope in hopes of reducing the effects of some small bed features. This worked well in most cross sections, but in some cross sections, especially those with prominent midchannel features, the point of steepest slope occurred in the middle of the channel.

Once I had identified the steepest point in each of the cross section for each year pair, I calculated how far every other point in the cross section was from the steep point. Then, within each reach, I aggregated the data by distance, rounding to the nearest decimeter, and calculated the mean absolute elevation change (that is, counting both erosion and deposition as positive values). I wanted to see broad patterns overall, so the aggregate combines data for every cross section and every pair of sample years.

I plotted the resulting data from each reach. In the figure below, the colors represent how many horizontal centimeters of reach are aggregated into each point on the line graph. Bigger numbers and more blue colors represent averages from more cross sections and years while smaller numbers and more yellow colors represent distances where fewer cross sections or fewer years had data at that distance from the steep point.

Results:

The figure implies that perhaps a lot of channel change tends to happen very close to the steepest point, but then stabilizes. Far from the point, the average vertical change values become very unsteady, perhaps because fewer data points are integrated into the average.

Critique:

I thought that this was an interesting and fairly straightforward analysis to conduct, but I am not sure how physically meaningful the results are, since the steepest points are not placed in the same location in each cross section. The results figure looks a bit like a channel cross section itself, which I thought was very interesting! I wonder if this is because the averaging falls apart at a distance roughly equal to the average channel width or if there really is more change happening near channel banks on average in these streams.