A basic scenario mode has been added in v0.12.0 - simply click 'Scenarios' on the main menu and choose the one you want to play. Currently the only one available right now is the May 3rd 1999 Bridge Creek Moore tornado.
If you want to edit the scenario or create your own, go to the game directory (right click the game in Steam -> Manage -> Browse local files), then navigate to TRR_Rebuild/Tornado Research and Rescue_Data/StreamingAssets/Scenarios
Each scenario lives in a directory inside of the Scenarios folder, and each scenario must have a scenario.json - this gives basic information like where the player spawns, the name and description of the scenario, start date and time etc. In addition it must have a csv file (referenced in the scenario.json file) which describes the tornado's heading, ground speed, wind speed, width, shape and an option note to display in-game.
Take a look at the bridge-creek json and csv to see how scenarios are structured.
You also have the option to play back the scenario with time compression, rather than speeding up the ground speed of the tornado, the ground path is compressed. So if you're short on time you can run through a scenario at 2.5x speed.