Our local airport is regularly visited by Cessna caravans flying cargo. This week I saw one parked outside the FBO building that had its exhaust stack bent down to lead under the cowling, where it was connected to a duct suspended from the underside of the fuselage. The duct was perhaps a foot in diameter and ran all the way back to where the tailcone began. Every other Caravan I have ever seen has the exhaust stack exiting the cowling on one side and then terminating. What's up with the ducted exhaust?
The reason for the long exhaust stack is simply to keep exhaust gasses from interfering with the sensors on board. As I write this, the aircraft is flying over New Orleans, likely assessing damage from Hurricane Ida:
Source: flightaware.com; Sep 5th, 2021
The mission is similar, though not identical, to the Bell 412s operated by the Dept of State, equipped with sensors to measure radiation- baselines are established for cities and these helicopters can be deployed in the unlikely scenario that radiological material is stolen or a nuclear/radiological weapon is suspected to be nearby. Hope this helps!
Update: per StephenS, this is also common on aerial survey aircraft, but since it has been identified as the ASPECT aircraft, the above remains true.