One way to do this would be still focusing on organic traffic in aggregate, but having access to the granularity of which keywords have lead to these increases, and the specific initiative behind it. Pretty reasonable expectation.
Here is data on organic click through rates within search engine result pages you can use to estimate increases in traffic for a keyword based on an increase in ranking position (or decrease 
). You can use freemium tools like Moz to estimate search volume for the keyword.
