Learn Farsi: آنها پیامی مبنی بر اینکه وقوع سیل نزدیک است برای ما فرستادند. - They sent a message for us indicating that the occurrence of a flood is near.

The word پیام (message) has the indefinite ی attached, making it پیامی (a message). When a noun takes this indefinite ی, it doesn't need an ezâfe before descriptive phrases like مبنی بر اینکه. The phrase simply attaches directly, translating naturally to 'a message indicating that...'.

Why use وقوع (occurrence) here? Couldn't we just say the flood is near (سیل نزدیک است)?

You definitely could in everyday conversation! However, مبنی بر اینکه sets a formal, journalistic tone. In formal Farsi, natural disasters and events are frequently paired with وقوع (occurrence or happening). Therefore, وقوع سیل sounds much more natural in an official warning or news report than just سیل.

Why is the core action پیامی ... برای ما فرستادند split up by such a long clause?

In Farsi, heavy modifier clauses like the one starting with مبنی بر اینکه need to stay right next to the noun they modify, which is پیامی in this case. If you grouped the main verb and preposition (برای ما فرستادند) together right after the noun, the reporting clause would be orphaned at the end of the sentence. Splitting the main sentence components to accommodate a long descriptive block is standard practice.

Could we swap مبنی بر اینکه for حاکی از اینکه in this sentence?