What svg filters could make this noise look more like water?

I am experimenting with svg to generate an impression of water waves.

Here's my initial attempt:

<filter id='water' x='0%' y='0%' width='100%' height='100%'><feTurbulence baseFrequency="0.01 0.1" result="NOISE"/> <feColorMatrix type="matrix" values="0  0  0  0  0                                       0  0  0  0  0                                       0  0  1  0  0                                       0  0  0  1  0" /></filter><rect x="0" y="0" width="100%" height="100%" filter="url(#water)"></rect></svg>

I'm not going for realism here, this sort of thing is actually okay as a basis. I'd appreciate some advice on how I can use other filters to improve the result.

I would like to

• include noise at multiple scales
• sharpen the gradient a bit
• remap the colours
• • make the blue parts slightly lighter, more like cyan
• • make the grey patches also be a kind of blue, a different kind
• • make the white patches also be another kind of blue