>He is **under** the water.

<img src="https://i.ytimg.com/vi/dHcn4ZXK450/maxresdefault.jpg" width="400" />


>He is **below** the water.

can be understood to use "*water*" as a layer which something is underneath

<img src="https://i.sstatic.net/Zx0y7.jpg" width="400" />
>The Abyssal Plain and Oceanic Crust is **below** the ocean

<!--- --->
>He is **in** the water.



has the meaning of being surrounded, in part or in whole by water. If you are **under** the water, you are also **in** the water.  If part of you is *above* the water's surface, you are **in** the water.

<img src="https://0.s3.envato.com/files/106305101/2637.jpg" width="400" />

Of your prepositons, one can only "Splash **in** the water".

>**on** the water.

is usually used to describe a boat during an *activity*, since it is "on the *surface* of the water"

<img src="https://i.sstatic.net/7D9Z6.jpg" width="300" />

>The boats are sailing **on** the water.

whereas
>**in** the water

is usually used to describe a *static* position of a boat

<img src="https://i.ytimg.com/vi/VtAxrQGww9k/hqdefault.jpg" width="300" />
>We took the boat from dry dock and put it **in** the water.  
We launched the boat **into** the water.