How could I present this spatial data simply?

Dear all, I have several maps of an estuary, with two variables noted for each year: position of salt marsh edge and position of the main water channel.

I want to know if there's a relationship between change in channel position and change of the marsh edge over time. My H1 is that "the marsh edge moves away from the tidal channel at a threshold proximity" (Because the closer a water channel is to the marsh edge, the more erosion there is, although the channel has to be close enough to start the erosion process, hence the threshold proximity).

This simple model is analogous to that of a magnet - two magnets with opposite poles facing each other, lie on a table. As you start to move magnet A closer to magnet B, Magnet B does not start moving until Magnet A is close enough to overcome the friction between magnet B and the table, causing it to move. Magnet A is the water channel and magnet B is the salt marsh.

So, my problem. How would I graphically demonstrate this relationship, and furthermore, prove statistically a relationship between channel position and marsh edge erosion?

Thank you in advance for any advice you can offer.

All the best, Cai

Answer 1

[Chad Greene]

As I understand your question, the salt marsh edge is a curvy line which can be approximated by many x,y points that moves over time. I'd first convert position of salt marsh edge to a 1D variable as a function of time. This conversion may mean considering only a key point along the curvy line that moves over time, whereby you could consider how many number of meters of advance/retreat happened when. Or if you want to consider more than a single point along the line, use the curvy line to calculate an area of marsh or non-marsh. You don't have to calculate the area of the entire marsh--you can focus on just one section and talk about local change in marsh area over time.

Do something similar to get water channel as a 1D variable, then you can simply make a scatter plot of salt marsh position versus water channel position. If you think the relationship is linear, try plotting a linear regression to see how well that fits the data.

Determining a correlation coefficient and statistical significance is easy using the P output of corrcoef, but note that the strength of the correlation will depend on how you scale the data. And the P value assumes all of your measurements are independent. That is, if you're looking at changes on the annual timescale and some of your measurements are taken a few minutes apart, those two closely-spaced measurements are not fully independent.

[Cai Ladd]

Hi Chad, Excellent, thanks for your reply.

Your interpretation is spot on. Thanks for your suggestion on how to treat the data. I started thinking about an alternative way to tackle the problem - by dropping the function of time (or at least incorporate it into the spatial element of my data).

I'd split the estuary up into x number of 1D profiles (as you suggested). Along each segment, I'd measure the distance between marsh edge and nearest channel point neighbor, giving proximal distance. If the shorter the proximal distance is, the more likely the marsh is to erode, I'd then need a measure of proximal distance on marsh edge dynamics (erosion or accretion). A measure for marsh erosion/accretion would be change from, a standard position, say the mean position of the marsh edge over my sample period (here, incorporating the temporal element). To a final graph would look like this:

Does this sound sensible to you? I believe it addresses the hypothesis!

[Chad Greene]

Looks good. If your data are sufficiently sampled in time, you could also get a sense of phase lag (how long it takes A to cause B) by calculating correlation coefficients for many time offsets. That is, if you think it takes seven days for A to cause B, correlation of A(t0) with B(t0) may be pretty good, but correlation of A(t0) with B(t7) should be higher. Calculate the correlation coefficient for many different time offsets and then plot correlation coefficient as a function of time offset. The peak of that curve will indicate how long it takes A to cause B. But again, phase lag analysis requires that time between measurements is less than half the time it takes A to cause B.