No standing water = nothing to freeze. Greywater is warm enough that it will
melt a film of ice in distribution plumbing each time it drains, without buildup.
Branched drain systems are a distribution system with continuous downhill slope.
At least six inches of fall from the greywater outlet to the surface the water lands on will prevent the outlet from plugging with ice. The ground should slope away steeply from the outlet at first, then may gradually flattentransitioning from say, 4% slope to 1-2% within the four feet of the outlet.
Continuously downhill sloping pipes may not require any insulation. However,
burying them in the soil and covering them with mulch will certainly provide
some.
Mulch basins generally will stay unfrozen well above frost line, because of
heat from applied greywater and composting, held in by insulating mulch and
snow above.
The composting heat can be cranked up by adding plenty of carbonaceous yard
waste in the fall (leaves, for example) then adding nitrogen throughout the
winter via the greywater (by peeing in the shower, for example).
On the south and west side of a house, within a windbreak to the north, the climate will be significantly less frosty.
A passive solar greywater greenhouse is the ultimate in favorable microclimates.
The treatment capacity per square foot in a greenhouse can easily be many multiples
of the capacity outdoors. (Each 10 degree Celsius increase in temperature doubles
the rate of most biological reactions.)
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