Given the scary situation in the Arctic, I would apportion parts of the $10 million to methods that promise immediate results:
- Testing of SRM such as sulfur aerosols, bright water and marine cloud brightening.
- Testing ways to ignite or break down methane from the sky, i.e. from airplanes or satellites. Laser beams spring to mind. Short, amplified pulses of light could be focused on hydrogen peroxide or ozone, in efforts to produce hydroxyl and oxidize as much methane as possible.
- Building on the outcome of 2., equipping small aircraft with such technology, as well as autopilot software, GPS, LiPo batteries and with solar thin film mounted both on top of and underneath the wings.
At first, two such planes could navigate to the north of Canada and Alaska at the start of summer.
In subsequent years, numerous such planes could follow, also going to other parts of the Arctic. At the end of summer, the planes could return home for a check-up and possible upgrade of the technology, to be launched again early summer the next year.
There are many self-financed clubs where members build and fly remote controlled aircraft, as discussed in comments underneath this post. Even a small financial incentive would give them a goal, while the publicity would make people more aware of the problems we face in the Arctic.
Such airplanes could navigate the Arctic, guided by satellite detection of methane concentrations (image left) and equipment carried onboard, such as small versions of these analyzers.
Measuring from different vantage points can pinpoint the most suitable location to cross-aim multiple laser beams at, to minimize the energy needed to heat up methane to its point of auto-ignition (image below).
Methane can be ignited where present in concentrations of 5 to 15 %. In concentrations of around 9%, methane could be ignited with as little as 0.3 mj of energy (see image, adapted from Zabetakis).
At well over 500 degrees Celcius, methane's minimum auto-ignition temperature is rather high. Other volatile hydrocarbons in the vicinity may ignite at lower temperatures (with less energy), in turn igniting the methane.