Explanation:

Correct Answer is (b).The original sentence is incorrect.
Reason: There are two errors in the bold part.
Firstly, the phrasal verb ‘stand by’ which means ‘adhere to or abide by (something promised, stated, or decided)’ has been written incorrectly. Therefore, ‘stood up’ must be replaced by ‘stood by’ in order to make the sentence correct.
Secondly, usage of plural case of possessive pronoun ‘their’ is also erroneous. Here the writer refers to the weather office which is a single institution. Therefore, ‘their’ should be replaced by ‘its’ to make it a grammatically correct sentence.
Among the choices available, option B replaces the bold part most appropriately.
The sentence after replacement becomes:
The weather office has stood by its initial forecast of monsoon rainfall being 96% of average in the June-September season.Option B is hence the correct answer.