The ability of scientists to provide models of the atmosphere’s complex responses to changing conditions, like seasonal and daily cycles or different planetary conjunctions, have become ever more accurate.(A) The ability of scientists to provide models of the atmosphere’s complex responses to changing conditions, like seasonal and daily cycles or different planetary conjunctions, have become ever more accurate. - Singular subject "ability" and plural verb" have" - wrong. There is also a meaning issue here; even if the verb had been "has," it would not have made the difference, as "ability" can't be more accurate. Either you are able or not able. I can't say you are accurately able or inaccurately able. Doesn't make sense. The usage of like to give examples is wrong. We need to use "such as."
(B) The ability of scientists has become ever more accurate in providing models of the atmosphere’s complex responses to changing conditions, such as seasonal and daily cycles or different planetary conjunctions. - wrong meaning, as explained in A. Also, the more acceptable idiomatic usage is "ability to." E.g., She has shown a remarkable ability to adapt to new situations.
(C) Scientists have become able to provide ever more accurate models of the atmosphere’s complex responses to such changing conditions as seasonal and daily cycles or different planetary conjunctions. - It sounds a little weird, but as such, it is ok.
(D) Scientists have become ever more accurate in their ability for providing models of the atmosphere’s complex responses to changing conditions, like seasonal and daily cycles or different planetary conjunctions. - correct usage is "ability to provide." And use "such as" to share examples.
(E) Scientists’ ability to provide models of the atmosphere’s complex responses to such changing conditions as seasonal and daily cycles or different planetary conjunctions have become ever more accurate. - same subject-verb issues. But even with correct, it doesn't make sense to say that ability has (if we use the correct verb) become more accurate.