In oceanography, there’s a very important characteristic of the ocean that we refer to as “Mixed Layer Depth”, or MLD. It’s the depth of the surface layer of the ocean that is well mixed by surface forcing, such as wind and waves. It essentially defines how much of the ocean is in direct contact with the atmosphere and directly affected by atmospheric processes.
It’s also a complete pain to deal with.
The image below shows a temperature profile, that is, how temperature changes with depth. By glancing at this graph, you can see that the temperature is constant for about the first 200 or so meters near the surface. Thus, the mixed layer depth here is about 200 meters. If the graph had been of salinity or density instead, the same reasoning would apply – the mixed layer is the portion at the surface that is well mixed.
Picking out a mixed layer depth is quite simple visually, but it gets complicated analytically. How do you define the bottom of the mixed layer? Currently there are several methods which are more or less accurate depending on location and season.
The first basic method is known as the “threshold” method. It’s defined as the depth at which a parameter (temperature, salinity, or density), differs from the value at the surface by a set threshold amount. Given that not all mixed layers are 100% well mixed, the appropriate value of the threshold can differ between research studies, making it difficult to compare mixed layer depths.
The second basic method is the “gradient” method. It’s defined as the depth at which the gradient (or change over depth) of a parameter exceeds a certain amount (or, alternately, reaches a maximum). This method is meant to take into consideration those cases where the mixed layer isn’t 100% mixed, but it too has its limitations.
Other methods have been developed to further refine the analytical definition of mixed layer depth, making the whole issue even more complicated. Often, it is hard to distinguish which method would be the best choice, especially when different methods give very different answers for the same data set.
I found one very rigorous method for calculating mixed layer depth, which was actually a combination of five other methods that were then analyzed to see which overlapped, and modeled to give a final mixed layer depth. This 5 part method may be the best I’ve seen, but it is not at all practical. The calculation takes several days at least!
And so, in my search for the best way to calculate mixed layer depth, I’ve defaulted to what others have used before me. In most other studies conducted in the same part of the ocean I am looking at, the threshold method is most commonly used, with a small twist. Now I calculate mixed layer depth with a threshold for temperature, and for density, and take the shallowest of the two to be the “real” mixed layer depth.
It may not be the simplest, or even the best, way. But it is reasonable, consistent with past work, and enables me to make progress in my research. Although, if I start looking at a different part of the world, I’m sure I’ll have to go through the whole process of deciding how to calculate mixed layer depth again.