I agree with Frank, the PAHS system is genius!! You don't have to worry so about the soil being wet for a while. it will still do it's job to capture and retain heat through the summer months and release it through the winter. You don't want water running thur the soil. This washes away heat with every rain. The umbrella serves to isolate the soil so it can store heat. You don't need all the fancy heat sinks and to turn flips to store the heat inside the house. The heat will transfer into the soil via the earth tubes and natural convection, so the temperature in the house is warm in the winter and cool in the summer. This system eliminates the need to insulate the house from the soil. In fact , you want to facilitate the heat exchange from house to soil to maximize the amount of heat you can store. However, you do need to use that insulation in the umbrella. to keep the heat trapped in the soil as well as keeping the water from running through this soil. This system is so simple , but elegant. And very inexpensive. I am planning to build a walipini, using the PAHS methods. Facing south,I'm in Virginia, Dirt walls slanting out or stepping up bermed on the northside. The north berm will allow a gentle slope down into a trench 20 feet out from the base. Add 4 inch pvc tubing snaking through this soil entering at the front base and exiting near the roof for natural ventilation; covering all around with a layer of plastic and insulation 20 feet out from all sides. And a layer of soil on top of the umbrella to protect it and add to the insulation. I haven't got the roof down yet, since the angle for the roof must be 52 degrees here. It will be rather steep, mostly glass or polycarbonate.
It will take one summer to capture the heat it needs for the winter. Planning to put an aquaponics system inside, with an in ground fish tank , that will serve to hold heat also.
If it does well, I may move in with my plants and fish.