I have data on the percent of organic matter in lake sediments from 0 cm (i.e., the sediment - water interface) down to 9 cm for approximately 25 lakes. In each lake 2 cores were taken from each location so I have 2 replicate measures of organic matter percentage at each sediment depth for each lake.
I am interested in comparing how lakes differ in the relationship between percent organic matter and sediment depth (i.e., slope). In some lakes the relationship between percent organic matter and sediment depth appears linear but in other cases the relationship is more complex (see examples below).
My initial thoughts were to fit linear relationships where appropriate either to the whole curve or to a subset of the curve if it was "mainly" linear and only compare those lakes where a significant linear relationship was found. However I am unhappy with this approach in that it requires eliminating data for no other reason than they do not fit the linear model and it ignores potentially interesting information about the relationship between percent organic matter and sediment depth.
What would be a good way to summarize and compare the curves from different lakes?
Example curves: In all cases the y-axis is the percent organic matter in the sediment and the x-axis is the sediment depth where 0 = the sedi ment-water interface.
A nice linear example:
2 non-linear examples:
An example with no obvious relationship: