I'd like to say that there is a law and weather changes by following this law.
I mean the law determines how weather changes in future.
Is it possible to say "there is a law, by following which weather changes"?
I'd like to say that there is a law and weather changes by following this law.
I mean the law determines how weather changes in future.
Is it possible to say "there is a law, by following which weather changes"?
First, you need to decide on the head of your sentence - will it be the law or the weather? Second, you should use terms that are consistent with the less-than-precise nature of weather. Here are two examples:
Changes in weather tend to follow this law.
This law predicts changes in weather.
As Tom pointed out, weather doesn't follow any laws that we know of. If you still insist on creating your sentence, it could look like this:
Weather changes following a (certain/specific) law.
This might be grammatically OK, but from a scientific point of view it isn't. Use at your own risk.
Your sentence could be broken up as you intend:
There is a law,
by following which
[,] weather changes
but that is very difficult to read without the hints I've given!
Ignoring the scientific argument, in English you should avoid structuring your sentence that makes it ambiguous. Instead, I'd say
Weather follows a law that makes it change.
Weather follows laws that make it change.
Or, if you have to structure it like that, I'd say
there is a law, which by following thereof weather changes
You do have to make it clear what you mean by law, as law is typically understood as a written word people must follow, but you do have common sayings such as "laws of physics," "law of gravity."
To fix that, say:
A law of physics, by following which weather changes ...
Which is not used properly here. The way it is used, you are making it sound like there is more than one weather, and you mean the weather which changes over time.
A law of physics by following which changes the weather.
This still has a big problem, the main subject in this sentence should really be the weather, but you have it completely "flipped" around.
The weather changes by following a law of physics.
This is much clearer, because it follows more standard patterns of specifying X, then how X is changed or modified.
You still left the reader/listener hanging here ... this is still going to sound incomplete because most people are not familiar with all the laws of physics, so the immediate question brought up will be "Which law of physics?" If you are answering that in subsequent sentences then this is OK.
If you mean all the laws of physics could possibly change the weather - and definitely at least one of them will, then it is OK to say:
The weather changes by following the laws of physics.
It's fine to abstract the entire system of the laws of physics into those words.
One final problem - people follow laws, but things like the weather are not people. So in my opinion it would be slightly better if you said:
The weather changes in accordance with the laws of physics.
In this way it makes it seem less that the weather is a volitional thing with a mind and more just something that exists in a greater system.