A green roof is a multilayered vegetated roof covering consisting of a ponding layer, an engineered soil layer, a storage layer and an underdrainage system. The drainage layer forms the underdrain system of the roof, which carries the inﬁltrated runoff away from the plant zone (see the figure below). SCHEMATIC DIAGRAM OF AN GREEN ROOF

The governing equations for the green roof with an underdrain would be:

Ponding layer: (10.49)
where Vol is cumulative ponding volume up to specified depth (m³); d is depth; A is Area at specified depth (m²); t is the last time step.

Then, the amount of water stored in the ponding storage layer is calculated using a continuity equation: (10.50) (10.51) (10.52)
where is volume of water in a ponding layer (m³) during the time step t; is the inﬂow to the pavement (m³/s).). , which is constant (m/s) in both single event and continuous models or or using Green-Ampt Mein-Larson (GAML) equation to calculate infiltration in a continuous model. is the area of green roof area (m²). Surface runoff would be calculated if volume of ponding water ( ) exceeds the ponding storage capacity (Vol(t)).

Engineered Soil: (10.53) (10.54)
where PC is the percolation rate in the engineering soil base to storage layer (m/s);

Storage layer: (10.55)
where is underdrain flow (m³/s) to native soil from storage layer.