A Mathematical Model of the Rainwater Flows in a Green Roof

Catherine C Adley, Mark J Cooker, Gemma L Fay, Ian Hewitt, Andrew A Lacey, Niklas Mellgren, Marguerite Robinson, Michael Vynnycky


A model is presented for the gravity-driven flow of rainwater
descending through the soil layer of a green roof, treated as a
porous medium on a flat permeable surface representing an
efficient drainage layer. A fully saturated zone is shown to
occur. It is typically a thin layer, relative to the total soil
thickness, and lies at the bottom of the soil layer. This provides
a bottom boundary condition for the partially saturated upper
zone. It is shown that after the onset of rainfall, well-defined
fronts of water can descend through the soil layer. Also the
rainwater flow is relatively quick compared with the moisture
uptake by the roots of the plants in the roof. In separate models
the exchanges of water are described between the (smaller-scale)
porous granules of soil, the roots and the rainwater in the
inter-granule pores.

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