Brian L. Taylor, P.E., and Drew A. Gangnes, P.E. - Green Roofs for ...

For a freely drained media the discharge is computed from the surface area (A) and the effectiveinfiltration rate (i):(Eqn. A2) O = i * A [L3/T]For porous drained media layers in an eco-roof, the infiltration rate is assumed to be proportional to thetransient storage provided in the media (17). Noting that the maximum storage (Smax) corresponds tothe maximum infiltration rate (imax):(Eqn. A3) O = (S/Smax) * imax * A [L3/T]Using the porosity (neff) corresponding to the transient storage within the media layer of the specifieddepth (D) and volume (Vmedia), the effective storage volume in the media layer is:(Eqn. A4) Smax = Vmedia * neff = D * A * neff [L3]Substituting Equations 3 and 4 into Equation 1 yields:(Eqn. A5) K = D * neff / imax [T]Thus, the storage coefficient is a function of the depth of the soil media layer, the porosity of the layer,and the saturated infiltration rate for the layer. This value is analogous to the time of concentration usedin SBUH models; the routing coefficient is then computed from the storage coefficient.HYDROLOGIC ROUTING EQUATIONUsing the storage coefficient for a basin, the hydrologic routing coefficient that relates the discharge tothe inflow is computed, and the modified Att-Kin routing analysis performed, by using the followingequations (4, 5, 6):(Eqn. A6) O2 = O1 + w (I2 + I1 – 2O1)where: O1 = discharge from previous time intervalO2 = discharge from current time intervalI1 = discharge from previous time intervalI2 = discharge from current time intervalK = storage coefficientw = hydrologic routing coefficient = (timestep) / (2 K + timestep)timestep = time interval used for time series analysis, min.ECO-ROOF MODEL EQUATIONS(Omitted for space)Available upon request from the authors.Method for Quantifying Runoff Reduction of Green RoofsBrian L. Taylor, P.E., and Drew A. Gangnes, P.E.11