Laura
The segmentation tools within ArcGIS should be able to build a reasonable polygon around the plume. You'll have to tweak the parameters to optimize the complexity of the resulting polygon (e.g. I presume you don't need to get every tendril of the plume) but you should be able to get a repeatable 2D extent from image to image.
If you can determine an approximate pixel resolution at the plume, you can estimate the size of the plume at least in the 2 dimensions you can see using the segmentation output.
it appears from your photos that you're shooting horizontally over the ground, is that correct? Do you want to put this data onto a map, or is your objective ONLY to estimate the volume and perhaps velocity?
If you want the data on a map, you may want to consider summarizing the volume as a function of time & xy(z?) location as a single point (centroid) with attributes, rather than try to plot the extents of the plume on a map (although you could assume the shape is uniform, convert a horizontally-viewed polygon into a polygon that would have been observed from above, and put that onto the map).
That opens up more questions about how to project horizontally from view point to plume centroid etc. but I wanted to be sure you know about the segmentation tools to measure the plume. I hope this is helpful
Cody B.