Who or what that is monitored is being watched.
Photographer: D. Gordon E. Robertson; licensed under GNU Free Documentation License
And a thing that is attenuated is being reduced, becoming less in size, quality or amount.
For cases in which there is no immediate risk to public health or the environment, or in cases where removal (cleanup, remediation) of the contaminants is not practical for reasons of costs or lack of proper technologies—such cases may resort to leaving the contamination in place to “rot” under watchful eyes.
We call this Monitored Natural Attenuation or MNA for short.
In opting for MNA, one should look carefully into the planned time span and project the cost of monitoring along the way. MNA may stretch into decades with potential impediments on transactions with the land.
With careful consideration of all options and wise planning, MNA can be employed to enable transactions with and redevelopment of contaminated land.
Go to the EPA’s Citizen’s Guide to Monitored Natural Attenuation http://www.clu-in.org/download/Citizens/a_citizens_guide_to_monitored_natural_attenuation.pdf for the rest. It is simple and fun to read.