This paper presents additional results of the generalized bathtub model for urban networks, including a simpler derivation and exact solutions for uniformly distributed trip lengths. It is shown that in steady state this trip-based model is equivalent to the more parsimonious accumulation-based model, and that the trip-length distribution has merely a transient effect on traffic dynamics, which converge to the same point in the macroscopic fundamental diagram (MFD). To understand the statistical properties of the system, a queueing approximation method is proposed to compute the network accumulation variance. It is found that (i) the accumulation variance is much larger than predicted by traditional queueing models, due to the nonlinear dynamics imposed by the MFD, (ii) the trip-length distribution has no effect on the accumulation variance, indicating that the proposed formula for the variance might be universal, (iii) the system exhibits critical behavior near the capacity state where the variance diverges to infinity. This indicates that the tools from critical phenomena and phase transitions might be useful to understand congestion in cities.

This work assesses sea-level rise using three different models created on Free and Open-Source Software for Geographic Information System (FOSS4GIS). Based on regional projections of Special Report on Climate Change and Oceans and Cryosphere (SROCC) of the Intergovernmental Panel on Climate Change (IPCC), the models were applied to a case of study on Rio Grande do Sul coast – Brazil under different sea-level rise scenarios by the end of this century. The End Point Rate for QGIS (EPR4Q), calculates a shoreline projection using End Point Rate method. The Uncertainty Bathtub Model (uBTM), analyses the sea-level rise impact by the uncertainty of sea-level projec-tions and vertical error of the Digital Elevation/Terrain Model (DEM/DTM). The Bruun Rule for Google Earth Engine Model (BRGM) predicts the shoreline position with sea-level rise, using topographic and bathymetric data from Unmanned Aerial Vehicles (UAV) and Coastal Modelling System (SMC – Brazil), respectively. The results indicated a maximum shoreline retreat for 2100 of -502 m and -1727 m using EPR4Q and BRGM, correspondingly. The uBTM using the land-use of Mapbiomas showed a maximum of 44.57 km2 of urban area impacted by the sea-level flood. This research highlights the possibility of performing coastal management analysis in GIS environ-ment using non-commercial software.

This study assesses coastal flooding extension mapping based on two innovative approaches. The first is based on the coupling of two robust numerical models (SWASH and LISFLOOD), in this case, discharges were extracted from the wave overtopping results from SWASH 1D and set as boundary conditions for LISFLOOD on the crest of an existing seawall where overtopping typically occurs. The second, hereby called the ‘Tilted Bathtub Approach’ (TBTA), is based on wave run-up levels and buffering the affected area of a prior flooding event, adjusting it for expected sea-states according to different return periods. The proposed approaches are applied to a case study on the Northern Portuguese coast, at Furadouro beach, in the municipality of Ovar, which has been facing multiple flooding episodes throughout recent years, including a dramatic storm in February 2014. This event was used as validation for the proposed methods. A 30 years long hourly local wave climate time series was used both to perform an extreme value analysis in order to obtain expected sea-states according to different return periods, and also for performing a sensitivity test for established empirical formulas to estimate wave run-up at this particular case. Results indicate both approaches are valuable: they yield coherent flood extension predictions that align well with the real inundated area from the 2014 storm. The convergence of these findings underscores the potential for these methods in future coastal flood risk assessment and planning.