# Quantifying magnitude of change in dataset containing base values of 0?

I have a dataset with the low-water and high-water surface area of lakes/ponds within a delta for each year obtained from satellite imagery. These lakes vary substantially in surface area and can experience important changes from year to year, sometimes drying out completely. As such, surface area can have values of 0 during the low-water period. I'm trying to quantify the magnitude of flooding in the spring on the surface areas of these lakes. Given the high inter annual variations in surface area, I need to compare the low-water value from the previous year to the high-water value of the following year to quantify this magnitude; comparing to a mean hasn't shown enough sensitivity to change. However, given the low water surface area of 0 for some lakes, I cannot quantify percent change. Unfortunately we don't have volume and elevation data for the area as it is quite remote, but I'm hoping to interpolate the results using kriging to see flood water influence over the delta.

My current idea is to do an "inverse" of percent change (don't know how else to describe it), where I divide the low-water value by the high-water value. This gives me a scale where large change will equal 0 and little change will equal 1. However, again small changes from a surface area of 0 will be over represented. Any idea how I could accurately compare the magnitude of flooding in such a case? I confess to have little background in statistics so I may be missing something important.

## 1 Answer

From a mathematical/statistical point of view, you can scale the differences any way you want. What scale makes sense/is best really depends on your scientific question. Relative differences often make sense, but as you've noticed that they can have issues.

• Can you say why comparing the absolute change doesn't make sense?
• You could scale the absolute difference by the mean of the two values, ie. $$\frac{\textrm{high}_{t+1} - \textrm{low}_t}{(\textrm{high}_{t+1} + \textrm{low}_{t})/2}$$ which would avoid the problems you've seen so far (the only problem would be lakes that had zero surface for both measurements, but you might be OK with throwing those out). But statistically this would be no more or less correct than any of your other choices ...
• Thanks for your response Ben. I will explore the method you have described, at least its another tool in the box. I want to stay away from absolute values as we want to interpolate the data from year to year to determine the influence of the spring flood on lake levels. Absolute data skews the influence of larger lakes on the interpolation and makes inter-annual comparisons difficult to interpret.
– Nic
Jun 17, 2021 at 2:05