Learn Farsi: مدلای هواشناسی میگن که فردا بارون می‌باره. - The meteorology models say that it will rain tomorrow.

This sentence is very casual, which is why it uses the simple میگن که (migan ke - they say that). The phrases مبنی بر اینکه (mabnâ bar in ke) and حاکی از اینکه (hâki az in ke) are quite formal and usually modify nouns, not verbs. To use them here, you would need to change the sentence into a formal news style, for example: 'There are predictions indicating that...' (پیش‌بینی‌هایی مبنی بر اینکه... - pish-bini-hâyi mabnâ bar in ke...).

This sentence feels very conversational. What are the formal equivalents of the colloquial words used here?

Yes, it is highly colloquial. مدلای (model-â-ye) is the spoken plural of مدل‌های (model-hâ-ye). میگن (migan) is the spoken form of می‌گویند (mi-guyand). بارون (bârun) is باران (bârân), and می‌باره (mi-bâre) is می‌بارد (mi-bârad).

The subject is non-human ('meteorology models'), so why is the verb میگن (they say) in the plural form?

You probably remember that non-human plurals usually take a singular verb in Farsi. However, when a non-human subject is personified—like 'models' doing a human action such as 'saying' or 'predicting'—native speakers often use a plural verb, especially in colloquial speech. Using the singular میگه (mige) would also be completely correct here.

Why do we use the present tense می‌باره (it rains) when the sentence is talking about tomorrow?