where does this hose connect?

I think that ribbed hose is from the furnace, leading warm air down under to prevent freezing. The pipe going to the water tank is the one going left from the lower winterizing valve. Interesting that there are two valves. Mine just has one that connects the pump to either the tank or the antifreeze jug. But I have no way to let air into the pipe to the tank so the water can fall out of the pipe, while this one does that with both valves open.