Natural calamities can be controlled only by the ALMIGHTY. Here are some chants/incantations/prayers from our scriptures
1) History has proved that, when a natural calamity (incessant thunder and rain by Indra) wanted to blow the Brijwasis(people of Gokulam), Lord krishna pleased by their prayer and saved them. The following sloka relates to that incident. This sloka is from the Narayaneeyam (Govardhana Uddarana)
कृष्ण कृष्ण महाभाग त्व्न्नाथं गोकुलम प्रभो |
त्रातु मर्हसी देवाण कुपिताद भक्वत्सल ||
This can be prayed whenever there is a problem to living beings from natural calamities like floods,tsunami,earthquakes, etc.
2) Below is a Tamil poem sung by Shaivaite saint Sri Sundaramoorthy Nayanmar in Tirupungur temple to stop rains.
The Prayer in this temple can be done even to stop the heavy rains as well.
4) In the below image, please find the Sloka from Durga Saptashati to stop natural calamities
Sloka from Durga Saptashathi to stop rains
Also please check the below where Sri Sri Bharathi Tirtha MahaSwamiji made a special Prayer to reduce the heavy rains in Tamilnadu in December, 2015 to Sage RishyaSringa
Bharathi Tirtha Swamiji Prayer to Stop rains
Related Article: Mantras,prayers and chants for rain