In which scenario is an air carrier required to have DME equipment on their airplanes?

DME, or Distance Measuring Equipment, is necessary when VOR (VHF Omnidirectional Range) navigational receivers are required. This is because DME provides pilots with the distance to the ground station, allowing for more precise navigation and situational awareness. When relying on VOR for navigation, utilizing DME alongside it enhances the capability to confirm position and distance, especially during approaches and while en route in congested or complex airspace.

In contrast, the other scenarios listed do not universally require DME. For instance, flying above 10,000 feet, while it introduces certain operational requirements, does not mandate DME use unless specifically required for navigation or approach procedures. Operating in controlled airspace or during night operations also does not inherently necessitate DME equipment; the requirements are situational and depend on the specific procedures in effect rather than a blanket rule tied to those conditions.