Seeking advice about brown stains on rocks in pond please

My Guess... Probably Iron... if you wait for a dry spell (sorry about
the drought) and run a magnet through the sediment in your roof gutters
you'll normally find lots of Iron dust..

I've heard lots of differtent explanations as to the source of this
Iron .. from outer space through industrial polution, in any case it is
certainly there when I checked years ago.

I don't have a solution but maybe a settleing chamber to condition the
run off before it gets into your pond... water softening salts work if
your have iron in well water but I don't know if they would work in
this instance..