While this comment does not offer a tracking mechanism or a tool, I do believe you can measure and feel when an environment gets better. More subjective than most would like...but you can definitely observe a difference in behaviors.
The UN also thought that this was important. There are more details at liveHappy.com and #HappyActs. There is an upcoming International Happiness Day on March 20th.
In our office we are celebrating the day with everything from team walks, Jenga competitions, popcorn, and managers serving the employees ice cream, as well as building a Happiness Wall.
I can tell you over a year of diligently addressing team morale...it is nothing Big Bang it is consistent small steps and paying attention to the employees and their needs.