This question isn't referring to the general use of umbrella to provide protection from rain rather it concerns the optical effects of the color on lower and upper portion of umbrella.
Umbrella are also used to provide protection from sunlight (at least in regions below tropic of cancer in India) and usually they come in black color on the upper side and silvery on the lower side. What advantage does this provide? Is it just for fashion (I don't think so)? Currently I believe white is more advantageous due to:
white being a poor absorber of heat (via radiation) I it would cause the clothe to get less warm (than dark colors) and transmitt less radiation and hence providing higher protection.
white being a good reflector would be beneficial in night (considering that somethimes rain occurs at night) as it would be more visible than dark colors.