Now, if it could be dirt simply being washed off the leaves or some other run off, then this would cause the water's murkiness and this would be removed from a fines mechanical filter, such as quilt batting or some other fines filtration.
Major water changes is also an option to reduce the tannins, but be careful with this since it can cause major temperature fluctuations and potentially harmful pH fluctations. If you are confident in the quality of your source water, then doing
slow major water changes (around 40%) spread out over a period of 8~12 hours is an option, might be cheaper, and be sure to use a water conditioner (before, periodically throughout it, and at the end of the change) if you are using city water that has chlorine or chloramines. (( if wanting a cheap dechlorinator that lasts at least 24~36 hours in the water, look into
sodium thiosulphate))
If you are positive it is a compound, such as tannins, then I don't think any particulate mechanical filtration will have an impact on the colored water.
To remove something that is not a particulate, such as microscopic algae or dust or soil or other solid waste, then you will have to use an appropriate medium that attracts the appropriate chemical compound by essentially magnetically pulling the chemical compound from the water that is absorbed and bound into another medium. These mediums involve polymers or granular activate carbon (GAC) materials.
There are many different formulations of granular activated carbon (GAC) materials, where one particular formulation is better at absorbing and binding different compounds.
A proper 3-5 stage Reverse Osmosis system actually involves a special formulation of carbon filter, but this route would be incredibly slow and expensive. If the water is not properly filtered for sediment and other very fine particulates prior to entering this carbon filter, then the dirty water will significantly reduce the effectiveness of the special carbon filters since RO carbon absorbs pretty much everything, not just the metals and chemical compounds. I would
not go this route.
You
can build your self a type of RO carbon chamber, such as a
DIY source water filter that you fill with granular activated carbon, but this will add a significant amount of head pressure causing your flow rate to go down. You could have another pump, such as an emergency backup pump, that is only connected to this filter to
periodically filter the water through the carbon material. If you do not have an emergency backup pump, then I highly recommend looking into getting one.
You could also build your self a type of quite small sand & gravel (S&G) type of filter where there are thick layers of carbon, but the carbon product would have to be removed eventually. So, the S&G is
not a viable option.
As Mmathis described, a Skippy, with the carbon in mesh bags,
works fine, or even puting a layer of it where there is moving water but effectiveness will significantly increase if you can push, or squeeze, the water through the mesh bags of carbon rather than the water going around it so there is more water in contact with more surface area of the carbon. This is why I like the filter setup in the afformentioned hyperlink.
Keep in mind.
You do have to eventually remove the old GAC material, trash it, and put in new carbon. This is due to the fact that the contanimants are absorbed into the carbon. If you keep the carbon in the water too long, then the carbon will eventually decompose causing the absorbed compounds to be released back into the water. I have no idea how often the carbon needs to be changed out, but I know eventually it will have to be removed and replaced with fresh material.
I have only dabbled with GAC materials. Some can get real expensive and some is quite cheap. Some absorb "X" better whiel others absorb "Y" better. So, you might want to start out with the cheap regular koi freshwater pond grade stuff while you do more research.
Reef hobby,
is all GAC created eqally?, is the one arena that use all sorts of different GAC formulations, but their context is on a very small scale and might be too specialized for simply absorbing tannins and likely might be too expensive when applied in a larger scale.
Again, I have only dabbled with GAC materials since I never had a real need to use them...
But... I do know that GAC materials absorb tannin issues quite well, but properly implemented water changes
might be the cheaper route.