Transformation of urban areas satisfies hydraulic invariance (HI) if the maximum flow rate outgoing the area stays unchanged. The HI can be respected by dimensioning appropriate water storage volumes or low impact developments (LID) to balance the soil sealing and ground levelling effects. In order to comply with HI, some Italian regional legislation and river basin authority provide for the creation of storage tanks whose volume must be estimated through simple conceptual rainfallrunoff models. In this work a physically based approach for evaluating HI is proposed. It is based on interpolating the results from a large number of hydraulic simulations conducted using FullSWOF, which is an open source code developed by the University of Orleans. In this software the shallow water equations are solved using a finite volume scheme and friction laws and infiltration models are included. Simulations have been carried out considering the effect of three properties of the area, that is: the saturated hydraulic conductivity of soil, the slope of ground surface and the standard deviation of ground elevation around the mean level. Using the results, interpolating laws for the peak discharge and the critical rainfall duration as function of the three basin parameters have been derived. A parametric hydrograph as a function of the basin parameters and rainfall duration is defined and a HI evaluation method based on routing the parametric hydrograph is proposed. The results from this approach have been compared with those from non-physically based methods currently used, such as the direct rainfall approach and the linear reservoir approach. The comparison shows that the difference between these conceptual methods with that one proposed here is strongly dependent on the runoff coefficient value. It is also not possible to predict whether they are conservative or not.
