Treeseeker, halt. First get out your survey and look on it for an indication of " SWIM buffer". SWIM is an acronym for Storm Water I____ Management. EPA federally required of all states.

EPA nationally has required all states and municipalities to require these buffers be untouched to protect the water quality of stormwater flowing to lakes, rivers etc.

Your municipal (county) property tax records on line will have this information.

If these trees are within your property line, it makes no difference. SWIM buffers average 20 to 30 feet from waters edge.

Even if there were no stream nearby as an issue, you would need to do good research on plant choices because every part of black walnut contains juglone, a toxic substance that kills off a great many other plants, shrubs and trees. The root system is the most persistent cause of dead trees shortly after planting.

You also have to factor for position of pool filtration system so it is outside the buffer zone and not discharging during backwash and affecting the stream water quality.