Wave Force Near Mussels

A series of experiments in which I look at whether hiding at the base of a mussel bed provides organisms with a protected microhabitat. If, indeed, such protections exist, I am testing how far away from a mussel bed such protection might extend.

Background & Methods

On wave-swept shores, hydrodynamic forces can play a role in determining where organisms can live. The basic premise of these experiments is to measure the wave forces experienced by plastic balls inside and outside of mussel beds. If the physical structure of the mussels are conferring some protection from the waves, forces within the bed ought to be reduced.

Mussels can form thick beds, to the exclusion of other organisms... understanding their distributions is important to understanding intertidal communities

The fake mussel bed is assembled in rings, 5cm wide, that can be removed separately. This allows me to test how far from the edge of the mussels an objects needs to be in order to receive protection (assuming any protection is measurable).

flat plate, 60cm on side mounted on rock
mussel plate 5 ring

Same plate with 5 rings of mussels around ball

To measure wave forces, I used small nylon balls. Within the bed, the ball was 9.54mm in diameter (referred to as "small" ball"). The ball outside the bed was a 4.1cm practice golf ball. The larger ball was chosen so that it would be of the same size order as the mussels that formed the roughness array. Both of the balls were connected, by a pieces of low-stretch string, to a bending-beam load cell mounted beneath the plate. This technique simplified the experiment, in that force on the ball in any direction (lift or drag) is translated through the spring into pure bending on the beam. It adds the confounding problem, however, of impulses as the ball reaches the end of its string (probably small) as well as leverage effects that are dependent on the length of the string (potentially problematic).

Additionally, a pressure transducer mounted just below the plate recorded the height of each wave as it approached the plate.

To extract the interesting data from the files, I use a routine which looks for valleys in the pressure record. It then extracts the force records from the large and small force transducers. Both transducers are filtered to avoid resonant effects, using an FIR lowpass filter. I record the maximum force experienced during the time of the wave.

Analysis

After all of this, I'm left with lots and lots of individual wave records.
For each one, I have:
- time
- maximum force on the large and the small balls
- height of the individual wave that hit the plate
- tide height (every 6 minutes)
- offshore wave climate (every 6 hours)

I have these data for various treatments...
Flat plate (no mussels near the small ball)
3-rings (mussels 15 cm from ball)
5-rings (mussels 5 cm from ball)

I also have some data for 4 and 6 rings, but I am working on the 3 and 5 cases first.

I performed this experiment on two separate occasions, December 2004 and March 2005. In between these experiments, the small ball was changed, resulting in a different length of string and potentially different force behavior.

These figures are for three different treatments during the 2 experiments.

My initial thought was that I'd be able to look at a regression of force on large ball to force on small ball... if mussels are providing any protection, I thought that would lower the slope of the regression line.

Unfortunately, that turns out not to be a valid assumption. Basically, the relationship between the forces on the large and small balls is pretty tenuous, which shouldn't really be surprising given the level of turbulence. There are a number of physical factors involved, including air entrainment, wave size, and turbulence which mean that any individual wave is a crap shoot in terms of the forces it imposes on an object.

It is likely that the distributions of the forces on the small ball at a given-sized force on the large ball might be shifted towards higher forces, but I can't see this because I am data-limited at the high end.

Again, this makes sense because larger forces are more rare, so even with thousands of waves, I am only measuring a few of the largest ones -- not enough to actually see the shape of the distribution of large forces.

So what am I trying to measure anyway?

Given that there is only a probabilistic relationship between the force experienced by the large ball and the force experienced by the small ball, there isn't going to be a wave-by-wave reduction in force when the ball is near the mussel bed. Instead, I would expect that, for a given force on the large ball, having mussels nearby would just reduce the likelihood that the small ball would get creamed by a large force.

To explore this, I need some way to compare the relative distributions between the forces experienced by the large and small balls through different mussel-array treatments.

How about QQ Plots?

Someone suggested to me that comparing distributions was what QQ plots were all about. QQ plots are a scatter plot of a given quantile (for instance percentile) of one variable versus the same quantile of another variable. As far as I've seen in the ecology literature, they seem to be primarily used to check whether data satisfy requirements of normality.

QQ plots certainly sound like a useful tool for my analysis... Here, I've plotted my data from the March experiment:

So far, so good... this certainly seems to show exactly what I would expect: over the whole data collection period (generally a day), the ratio of the distributions of the large to the small seems to shift by the presence of mussel rings around the plate. And, as expected, the closer the mussels get to the small ball, the more dramatic the effect.

So Far, So Good

Visually, I can see the effect. My data from December show a similar trend, although slightly different due to different offshore waves.

But now I need a way to determine whether the differences I can see are actually significant. In other words, maybe the difference between the flat plate and 6-rings is meaningful, but is the Flat plate truly different from the 3-ring plate?

The more I think about this, the trickier it gets. All the statistics I know require knowing something about the distribution of points in order to test whether differences are significant. In this case, I seem to have used all of my information to create this plot, so I don't know anything about any variability. I have looked through as much literature as I can find about QQ plots, but I haven't seen anyone assign significance to differences between lines.

If anyone reading this can offer me insight, I'd greatly appreciate it. I can be reached at mooseo@stanford.edu