I suppose the word "level" refers to a height of something. But, would there be other alternatives to replace the word "level"?
Answer from a Native speaker
In this case, you could use the word "amount" by saying "the amount of water had increased" or simply "there was more water". However, it is most common to measure large amounts of water using the word "level". This term works for baths, the sea, dams, lakes, and rivers. This is because it's usually in reference to the ground or a lower surface. Ex: The sea level had risen since that morning. They couldn't cross the beach to get back. Ex: There had been a drought for about a year now. The water level at the dam hadn't risen enough. Ex: After the rain, the river had more water flowing in it.