I live in a desert where seasonal hard rains occur 5-10 times per year. We have an automated door with a multitrack slide that it lets quite a bit of water in when it rains hard. The door is an architectural feature and very good looking, but the random rains create quite a mess. The patio is not under deep cover, which might prevent the problem. My question is what can I do to stop the rain from coming in under the doors? I don't want to lose the function of the doors, so caulking shut is unfortunately not a solution. One solution might be something that I can place in front of the door before a rain, but I don't know exactly what that could be.
Here is a picture of a similar door:

