A Mathematical Model of the Rainwater Flows in a Green Roof

A model is presented for the gravity-driven flow of rainwater descendingthrough the soil layer of a green roof, treated as a porous medium on a flatpermeable surface representing an efficient drainage layer. A fully saturatedzone is shown to occur. It is typically a thin layer, relative to the total soilthickness, and lies at the bottom of the soil layer. This provides a bottomboundary condition for the partially saturated upper zone. It is shown thatafter the onset of rainfall, well-defined fronts of water can descend throughthe soil layer. Also the rainwater flow is relatively quick compared with themoisture uptake by the roots of the plants in the roof. In separate models theexchanges of water are described between the (smaller-scale) porous granulesof soil, the roots and the rainwater in the inter-granule pores.