If you leave analyze and go back to Select Area, it keeps the dataset and the time range but not the variable , smoothing, or transformation (or probably summary statistic). If possible make those sticky as well.
[x] Persist all of the properties from #18 in the client side store
[x] Clear these properties when the dataset, study area, or variable changes
[x] Include properties in download archive as a metadata file that can be uploaded again to restore the parameterization #92