# Multitemporal SAR Data and 2D Hydrodynamic Model Flood Scenario Dynamics Assessment
## 3 Method
### Hydraulic Model Calibration Framework Using SAR- and DEM-Derived Flood Maps  
Several studies have pointed to hydraulic roughness as a dominant factor for relatively shallow inundation ([10; 49; 50; 51]) in particular for 2D hydraulic models ([25; 52]), as it can affect flood extent, timing of flood waves, and localized processes such as location of hydraulic leaps. Moreover, recent research has highlighted that roughness parameters are the chief factors in deciding the rate of flooding and receding, and thus their calibration heavily depends on the timing of the SAR images ([15; 53]) during model calibration as in the proposed study. Hence, we decided to restrict FLORA-2D model calibration to Manning coefficients considered the most important parameters, but also the main source of uncertainty ([43; 54]), especially in an area with a gentle and flat topography where we can consider that friction and ground slope in a gravity wave have the same order of magnitude within the energy equation, controlling flow characteristics even though it is acknowledged that several parameters (e.g., related to roughness, channel cross-section dimensions, initial condition) can influence model results. In particular, the Manning (roughness) coefficient is a spatio-temporally-distributed parameter that changes over space (e.g., bed channel versus vegetated floodplains) and time (e.g., seasonal changes of vegetation or temporal resistance variation due to vegetation). However, variable spatio-temporal Manning coefficients of this kind cannot be measured in real world applications [15]. Moreover, this parameter is generally determined under uniform flow conditions rarely observed in an area characterized by flat and complex topography. Thus, Manning coefficient values are regarded in literature as parameters that may vary widely. Classes of coefficient have been drawn up for the different land use categories to be used as parameters, which are estimated using model calibration. For this purpose, a set of model runs corresponding to a set of plausible Manning coefficient values was carried out, assuming that the Manning roughness values may lie between 0.04 and 0.1. A low roughness coefficient of 0.04 represents quite a clean channel, i.e., covered by grassland, whereas a high roughness coefficient of 0.1 would represent a channel with very thick vegetation. We therefore performed three simulations with roughness coefficients, respectively, of 0.04, 0.08, and 0.1 for the whole area. Later, we distinguished between the Manning coefficients in the main channel and floodplain assuming they were temporally and spatially constant. When considering that the Manning coefficient for the channel was higher than in the floodplain, we performed another two simulations that has, respectively, (i) a Manning coefficient value of 0.033 in the channel and 0.06 elsewhere, representing a wet season; and, (ii) 0.025 in the main channel and 0.04 in the floodplains, representing a dry season in which vegetation is quite sparse and low. In this way, Manning coefficient values in the floodplain, which can be considered the area of greatest influence due to its sheer extension, varied in regular steps of 0.02 in these five simulations (i.e., 0.04, 0.06, 0.08, 0.1). Finally, for the last hydraulic simulation, we used variable spatio-temporal Manning coefficients that can take into consideration the dynamic effects of vegetation: cell roughness varies with floodwater depth according to a low that depends on the type of vegetation, as in [45]. In particular, Manning coefficient n is calculated according to [55] when vegetation is rigid, and [56] in the case of flexible vegetation. The step size for the Manning coefficient was explored over a fixed grid of 10 m cell resolution for all of the model runs. To emphasize the integration of SAR-derived datasets instead of traditional calibration data, e.g., hydrographs, a two-step approach was adopted.