An umbrella? Cabriolet cars by design can't have roof gutters. Rain falling on the roof runs off down the sides into the car when any window is open. The carpets, leather seats and passengers usually complain. But if you drove fast enough with the top down for more fresh air and didn't stop except under a bridge or in a tunnel, you might stay dry?
My EOS has V.W Climatronic controls to select the level of comfort for driver or passenger, if that's insufficient, just put on the heated seats. More fresh air is number 4 on the blower with the face vents pointing at your face. But if you open the sunroof and pop up the wind deflector whilst driving fast the rain may(?) go over the top. You can test this out with a wind tunnel. Otherwise, remotely set off a smoke test cartridge safely fixed on the front grill with a camera mounted somewhere to monitor the smoke at different road speeds, then post the result on YouTube. But don't make a hazard for other road users or set fire to your car.
When I look at my parked EOS roof during a heavy storm, rivers of water can pour off it and down the side windows. It would need some very deep gutter channels and the car parked absolutely level for them to hold back this amount of water. But I can see they might help the aerodynamics whilst moving and keep roof water on the roof and not over the side windows. But it wouldn't work for the EOS because the semi open back gutter under the rear window wouldn't take the extra water volume now only pouring off the back.