[HO455]

As posted it"s a common problem. I would wire brush the area and then use a product like POR-15 to cover the existing rust you can see. The rest of the story is the rust behind the sheet metal in the void that makes up the door frame. To stop as much rust as possible in my Burban I drilled some holes the same size as factory plugs and used a flexible wand to spray POR-15 into the void spaces. The idea is to cover all the rust so no oxygen gets to the metal to stop the rusting process . When I finished I pushed a new factory plug in the hole and painted. Only someone really sharp eyed who knows these trucks would notice it.
For more information see my WMB thread below page 1.
Unfortunately when you place a tarp over the truck you also lock the moisture under the tarp as well. If what ever you have the vehicle parked on gets wet then when it starts to dry the moisture evaporates from the soil or concrete and then gets trapped under the tarp.
Moisture in the cab is the biggest cause of this rust. Repairing the drip rail seal will stop the majority of the moisture from getting directly to that area. But if you have other leaks in the cab the moisture will condense in those areas. After it evaporates. So of you have a tarp on the vehicle it is important you take additional steps to control the moisture inside the vehicle