These are the phrases that create a comic tone in the passage. When we think of an umbrella, we think that its main purpose is to protect us from the rain. The irony in the passage, which creates the comic tone, is that the author talks about the umbrella as primarily designed to make people look more British and behave in a pretentious way. This is supported by the fragments that create a comic tone.
<span>"an enormous ornamental bat", because this is a humorous mental image, and
"as the atmospheric conditions demanded", because this is saying that the atmosphere and weather could make it necessary for someone to look a certain way (that's what is meant by putting on airs) rather than to actually stay dry or warm.</span>
