The type of roof chosen can be based on a number of factors, such as tank diameter,Construction costs, product stored, tank operating pressures, sensitivity of the product to internal corrosion etc.
Using the diameter criteria eg: For tanks up to 10m a self supported cone could be used, 20-30m a supported cone roof and a 40m plus dia a dome roof (probably a geodesic dome) may be considered.
At the end of the day its an engineering judgment call or based on client requirements.
To a certain extent, the roof type is also determined by government regulations.
Generally, a light product (gasoline, for example) is going to require either an internal or external floating roof or some type of inerting/ vapor recovery system. The exception being smaller tanks.
Generally, a heavy product (diesel, fuel oil) can be stored in a fixed-roof tank wtih no floater.
For a small tank, a self-supportign roof is easiest, for a large tank, a structuraly supported cone roof.
For domed roofs specifically (as opposed to umbrellas), the main motivation that would require their use would be relatively high pressures. Such tanks are not common.
In most cases where an umbrella is used, a self-supporting cone could also be used. The choice between the two involves owner preference and cosmetics more than anything. At the upper limits of size, a self-supporting cone will be very steep.
For mid range diameter tanks ( 15-25m where a self sup cone wont work) another reason for using umbrella roofs is when internal cleanliness or corrosion is an issue. eg in a caustic tank or similar where corrosion on supporting members could discolor the product.
