Locating, tracing, characterizing, quantifying soil erosion, sediment deposits, and correlating in one or more ways with ecosystem stability suggest there may or may not be reason to expect to use statistics, depending on your sampling design, replications if needed, questions or hypotheses to address, etc. Ecosystem stability over a century can be complex, droughts, floods, fires, land use changes, etc., vegetation and ground cover change, stream morphology adjustment, deposits of soil due to surface erosion, stream bank erosion, possibly periods od channel degradation and/or aggradation, etc. In conducting research, you design your sampling based on the question or hypothesis being tested, and the statistical design is developed then, before sampling is conducted. If you were to collect a bunch of data, then ask what statistics do I want to use to present it, the point of research design has been bypassed. Most universities have both statistical courses and a Statistician or qualifying professor to help with statistical design, or at least review study design. Best to get this direct input up front, raher than after work is done.