What you see is a realistic simulation of an effect that you see in real life (caustics).
There are no additional parameters like "caustics intensity", "intensity from distance", "blur from distance", etc, because such things do not exist in real life.
In reality, caustics are sharper or more blurry, more or less intensive, etc, depending on multiple factors such as:
- water brightness
- water clearness
- sun intensity
- environment lighting (e.g. whether clouds scatter sunlight)
You have those controls available in Corona and you can use them to adjust your caustics.
Therefore, in order not to become like the VRay, I suggested these 2 additional options: "Intensity from Distance" and "Blur from Distance" :-)
The effect would be exactly the opposite of what you are saying. Corona is not V-Ray, because it does not feature additional "fake" controls, even if they often mean more artistic freedom, it is more physically accurate, and makes it easier to get realistic-looking results out of the box.
If you really want to break realism to get some extra control over your caustics, you can use rayswitch material/map to use different material for water's direct visibility and water's caustics (GI component). You can for example create water with lower refraction glossiness, and use that to get more blurry caustics.