Bathtub Model Research Articles

Evaluating the Enhanced Bathtub Model for Coastal Flood Risk Assessment in Table Bay, South Africa

ABSTRACTCoastal zones are susceptible to increasing pressures from urban development and natural hazards, such as storm events, climate change, and rising sea levels. The GIS‐based enhanced bathtub model (eBTM) enables the identification of areas at risk of flooding as a baseline for disaster management and coastal adaptation. This study aims to establish the methodological robustness of the eBTM for coastal flood modeling, by analyzing eight sites flooded during a recent storm event in Table Bay, Cape Town by comparing eBTM outputs with observed flood extent data collected after the storm. The validation showed that for 74% of the 332 validation points the spatial modeling error was < 6 m and for 56% below 3 m. The root mean square error for the model was 4.88 m, indicating an acceptable level of accuracy of the eBTM outputs for coastal risk assessments where more sophisticated models are unavailable.

Using Spatial Literacy for Disaster Management in Coastal Communities of Small Island Developing States (SIDS): A Case Study from Lavongai, Papua New Guinea

This study investigates the use of participatory geographic information systems (PGIS) for hazard assessment in small island developing states (SIDS), with a focus on spatial literacy and community-based disaster management. By partnering with the Lavongai community on Papua New Guinea, this research aimed to empower community members through skill development in geodata processing. The program leveraged local knowledge and the global positioning system to create participatory maps, enhancing both community capacity and researcher data quality. Workshops and focus group discussions (FGDs) were conducted to assess the community’s understanding of spatial concepts related to disaster risks. The core objective was a preliminary assessment of the community’s social and economic vulnerability to coastal disasters, using household data and GIS analysis. The results showed varied vulnerability levels within the community, highlighting the need for targeted disaster mitigation training and nature-based solutions. High-resolution satellite imagery and a simple bathtub model simulated sea level rise, identifying land-uses at risk. The program concluded with a community presentation of thematic maps, fostering collaboration and transparency. Future projects will address environmental challenges identified by local leaders and prioritize skill development, social data collection, and water resource mapping.

Hypercongestion, Autonomous Vehicles, and Urban Spatial Structure

This paper examines the effects of hypercongestion mitigation by perimeter control and the introduction of autonomous vehicles on the spatial structures of cities. By incorporating a bathtub model, we develop a land use model where hypercongestion occurs in the downtown area and interacts with land use. We show that hypercongestion mitigation by perimeter control decreases the commuting cost in the short run and results in a less dense urban spatial structure in the long run. Furthermore, we reveal that the impact of autonomous vehicles depends on the presence of hypercongestion. The introduction of autonomous vehicles may increase the commuting cost in the presence of hypercongestion and may cause a decrease in the suburban population; however, it may make cities spatially expand outward. This result contradicts that of the standard bottleneck model. When perimeter control is implemented, the introduction of autonomous vehicles decreases the commuting cost and results in a less dense urban spatial structure. These results show that hypercongestion is a key factor that can change urban spatial structures. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This work was supported by ACT-X [Grant JPMJAX21AE], Fusion Oriented REsearch for disruptive Science and Technology [Grant JPMJFR215M], the Japan Society for the Promotion of Science [Grants 23K13422 and 22H01610], and the Council for Science, Technology and Innovation [Grant JPJ012187]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0519 .

A bathtub model with nonlinear velocity–density relation

The bathtub model is an applicable and effective tool for simulating the characteristics of traffic dynamics in downtown areas during morning rush hour, especially the characteristics of hypercongested traffic. In order to reduce the complexity of the research, previous studies have adopted a linear velocity–density relationship. This has limitations in analyzing the cost and duration of hypercongestion in traffic dynamics. In this paper, we develop a bathtub model with one kind of nonlinear velocity–density Relation, i.e., Pipes–Munjal Relation, based on continuous scheduling preferences and analyze its solutions in both no-toll user equilibrium and social optimum states. Due to the intractability in solving this bathtub model, there exists local analytical solutions, but for a complete solution of the model, only numerical solutions are available. The results indicate that as the value of n increases, the model can simulate traffic dynamics with higher cost and longer duration of hypercongestion under equilibrium, and can simulate traffic states with lower system cost under social optimum. We also explore the results of implementing optimal time-varying toll to realize social optimum. This study expands the relevant theories of bathtub models and provides a new perspective for traffic congestion.

Assessing the impact of sea level rise on the Indus delta in Pakistan: A comprehensive analysis of flooded areas and future vulnerabilities

This research investigates the impact of sea level rise (SLR) on the Indus Delta, a vital ecosystem increasingly vulnerable to climate change repercussions. The objective of this study is to comprehensively assess the flooded areas under various shared socioeconomic pathway (SSP) scenarios based on the Intergovernmental Panel on Climate Change's (IPCC) 6th Assessment Report. The study employs a GIS-based bathtub model, utilizing historical (1995–2014) and IPCC-projected (2020–2150) tide gauge data from Karachi, Kandla, and Okha stations to identify potential inundated areas threatened by coastal flooding. Additionally, it analyzes LANDSAT-derived multispectral images to identify coastal erosion hotspots and changes in the landscape. A supervised random forest classifier is used to classify major landforms and understand alterations in land cover. Furthermore, neural network-based cellular automata simulations are applied to predict future land cover for 2050, 2100, and 2150 at risk of inundation. The results indicate that under different SSP scenarios, the estimated inundated land area varies from 307.36 km2 (5 % confidence on SSP1-1.9) to 7150.8 km2 (95 % confidence on SSP5-8.5). By 2150, the region will lose over 550 km2 of agricultural land and 535 km2 of mangroves (mean SLR projection). This work emphasizes identifying sensitive land cover for SLR-induced coastal flooding. It might fuel future policy and modeling endeavors to reduce SLR uncertainty and build effective coastal inundation mitigation methods.

Demonstration-guided deep reinforcement learning for coordinated ramp metering and perimeter control in large scale networks

Effective traffic control methods have great potential in alleviating network congestion. Particularly, in an urban network consisting of heterogeneous roads (e.g., freeways and urban roads), how to integrate and coordinate control policies on different roads is a critical issue in large-scale networks. This study addresses this question from two aspects: modeling and control. From the modeling aspect, we formulate the hybrid traffic modeling in heterogeneous networks with the Asymmetric Cell Transmission Model (ACTM) for freeways and the generalized bathtub model for urban roads. For the control aspect, this study considers two representative control approaches: ramp metering for freeways and perimeter control for urban roads, and we aim to develop a deep reinforcement learning (DRL)-based coordinated control framework for large-scale networks. However, there are two significant challenges in the coordinated control in large-scale networks with DRL methods: non-stationary environment and large search space. To address both issues, we incorporate the demonstration to guide the DRL method for better convergence by introducing the concept of “teacher” and “student” models. The teacher models are traditional controllers that provide control demonstrations. For instance, ALINEA and Gating are two representative feedback controllers for ramp metering and perimeter control which can be “teacher” models. The student models are DRL methods, which learn from teachers and aim to surpass the teachers’ performance. Additionally, we develop a parallel training scheme to accelerate the proposed DRL method. To validate the proposed framework, we conduct two case studies in a small-scale network and a real-world large-scale traffic network in Hong Kong. Numerical results show that the proposed DRL method outperforms demonstrators as well as DRL methods, and the coordinated control is more effective than just controlling ramps or perimeters respectively. The research outcome reveals the great potential of combining traditional controllers with DRL for coordinated control in large-scale networks.

Flow-tub model: A modified bathtub flood model with hydraulic connectivity and path-based attenuation

Global climate change and sea level rise are increasing the risks of flooding for coastal communities. Probabilistic coastal flood risk analysis at regional or global scales requires flood models with relatively low data requirements and low computational costs. Bathtub inundation models, which compute flood depth as the difference between water level and ground elevation, are well-suited for large-scale flood risk analysis. However, these models may overestimate floods because they do not capture some of the relevant underlying hydrodynamic processes that govern flood propagation on land.We present Flow-Tub, a modified bathtub inundation model that integrates two hydrodynamic processes to improve the accuracy of the bathtub inundation model while retaining computational efficiency: hydraulic connectivity and path-based attenuation.1.Hydraulic connectivity ensures that inundation is restricted to areas connected to the water source.2.Path-based attenuation ensures that the modeled flood water depths are reduced along the flow paths to represent the effects of surface friction and the temporary nature of storm surges.We validate the Flow-tub model against a hydrodynamic model. We also compare results of the bathtub model and the Flow-Tub model, highlighting the improved accuracy in the estimation of flood depths in the latter.

Coastal Inundation Hazard Assessment in Australian Tropical Cyclone Prone Regions

One of the hazards associated with tropical cyclones (TCs) is a storm surge, which leads to coastal inundation and often results in loss of life and damage to infrastructure. In this study, we used GIS-based bathtub models and tide-gauge-derived water levels to assess coastal inundation scenarios for the landfall region of TC Debbie. The three scenarios modelled what could have happened if the TC’s maximum storm surge had coincided with the maximum storm tide for that day, month, or TC season, where the water levels were determined through analysis of tide gauge data, using a new method called the variable enhanced Bathtub Model. Additionally, this study analysed the impact of excluding the correction of water levels with the Australian Height Datum. Our study found that between the least and most severe scenarios, with the input water-level difference for the model along the coastline being 0.43 m, the observed inundation depth of the analysed populated region increased from 0.25 m to 1 m. Ultimately, it was found that in the worst-case scenario, the study region could have experienced coastal inundation 0.63 m higher than it did, inundating 72.53 km2 of the coast. The results of this study support the consensus that coastal inundation is highly dependent on the characteristics of the terrain, and that coastal inundation modelling, such as that completed in this study, needs to be performed to better inform decision makers and communities of the potential impacts of TC-induced storm surges.

Assessing potential coastal flood exposure along the Port-Bouët Bay in Côte d’Ivoire using the enhanced bathtub model

Coastal flooding is a growing concern for many communities worldwide due to climate change. This study focuses on the Port-Bouët Bay, located in Abidjan, Côte d’Ivoire. A coastal flood model based on the enhanced bathtub model was used to map the present and future flood extent and assess exposure to quantify the likely affected populations, buildings, and land uses for different scenarios. The model incorporated a digital elevation model, surface roughness, flood water source, and the once a century extreme sea-level scenarios. Validation was conducted against GPS coordinates of recently flooded zones. The analysis revealed that, under current conditions, around 21.58 hectares are vulnerable to flooding, and approximately 2465 people and 544 buildings are exposed to flooding today. Based on future projections, the extent of flooding is anticipated to increase by different ranges depending on the time period and the climate change conditions. By the end of the century, the increase in flooding extent could reach a percentage of 27%, 37%, and 90% under SSP1-2.6, SSP2-4.5, and SSP5-8.5, respectively. The impacts would consequently be worsened with greater number of people and assets exposed to future coastal flood hazard. The land use analysis showed that informal settlements are the occupation most exposed, followed by residential settlements, commercial and industrial land, in that order. The spatial disaggregation of this exposure across neighborhoods indicates that Sogefiha is the most exposed, followed by Petit-Bassam and Vridi. However, a substantial increase in coastal flooding in Vridi by 2100 under the SSP5-8.5 scenario could lead to significant exposure level change for this scenario. This information is critical for evaluating and managing present and future coastal flood risks in the Port-Bouët Bay area and for informing decision-making processes.

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

AbstractIn this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

Assessing coastal vulnerability and land use to sea level rise in Jeddah province, Kingdom of Saudi Arabia

Sea level rise is one of the most serious outcomes of increasing temperatures, leading to coastal flooding, beach erosion, freshwater contamination, loss of coastal habitats, increased soil salinity, and risk of damage to coastal infrastructures. This study estimates the vulnerability to inundation for 2100 in coastal zones in Jeddah Province, Kingdom of Saudi Arabia, under various sea level rise (SLR) scenarios of 1, 2, 5, and 10 m. The predicted flooding was estimated using a combination of factors, including SLR, the bathtub model, digital elevation model, climate scenarios, and land use and land cover. The climate scenarios used were Representative Concentration Pathway (RCP) scenarios 1.9, 2.6, 4.5, and 8.5. The results of the SLR scenarios of 1, 2, 5, and 10 m revealed that 1.6, 4.7, 14.9, and 30.6% (or 88, 214, 679, 1398 km2) of the study area's coast could be classified as inundated areas. The various SLR scenarios can inundate 3.3 to 34% of the road area/length. The inundated built-up and road areas were estimated to range between 0.31 and 0.79 km2, accounting respectively for 1.18 to 3.01% of the total class areas for 1-meter and 2-meter SLR scenarios. In contrast, the inundated area will be significant in the situation of 5 and 10 m SLR scenarios. Regarding the case of a 10-meter SLR scenario, the inundation will negatively impact the built-up and road infrastructure areas, inundating 8.9 km2, with industrial infrastructures affected by inundation estimated at 0.21 km2, followed by green space infrastructures at 0.013 km2. The spatial information based on various SLR scenario impact mapping for Jeddah Province can be highly valuable for decision-makers to better plan future civil engineering structures within the framework of sustainable development.

Perimeter control in a mixed bimodal bathtub model

Perimeter control involves monitoring network-wide traffic and regulating traffic inflow to alleviate hypercongestion. Implementation of transit priority with perimeter control measures, which allow transit into a controlled area without queuing at the perimeter boundary, is an effective strategy in bimodal transportation systems. However, travelers’ behavior changes in response to perimeter control strategies, such as shifts in their departure times and transportation modes, have not been fully investigated. Therefore, important questions remain, such as the use of transit during perimeter control with transit priority. This paper examines the travelers’ behavior changes in response to perimeter control with transit priority in a mixed bimodal transportation system with cars and flexible route transit (FRT) vehicles. We model departure time and transportation mode choices in such a transportation system with hypercongestion and discomfort in FRT (called the mixed bimodal bathtub model). Initially, we investigate the properties of dynamic user equilibrium without perimeter control. Then, we study the equilibrium patterns during perimeter control with transit priority. Unlike existing works, we find that the number of FRT passengers decreases with time toward the desired arrival time and that FRT may not be used around the peak of rush hour. Furthermore, transit priority may not be sufficient to promote the use of FRT, and additional incentive such as subsidy for lower fares may be required to encourage FRT use during perimeter control. Finally, we show that operating many FRT vehicles does not always decrease the equilibrium cost, even under perimeter control with transit priority.

From entrepreneurial leadership to new product development performance: A study of the Coleman bathtub model

PurposeThis study aims to examine the relationship between entrepreneurial leadership (EL) and new product development performance (NPDP) at the firm level (level 2) of analysis and employee’s creativity (EC) at the cross level (level 1) of analysis. It also examines the serial mediations of (1) intrinsic motivation (IM)-EC and (2) creative self-efficacy (CSE)-EC on the relationship between EL and NPDP.Design/methodology/approachA systematic random sampling technique was used to collect data through self-administered surveys from leaders and employees of small and medium-sized enterprises (SMEs) in Pakistan’s IT sector. Analysis was conducted on net responses from 114 leaders and 476 employees.FindingsThe results revealed significant positive associations between EL and NPDP at the firm level of analysis and EC at the cross level of analysis. The results of the cross-level serial mediations show that (1) IM and EC, and (2) CSE and EC serially mediate the relationship between EL and NPDP.Originality/valueThis study is among the few to use the Coleman bathtub model to show top-down and bottom-up relationships. The study extends and complements the multilevel perspective on leadership and new product development research by simultaneously examining the relationships between EL and NPDP at the individual and firm levels.

Dynamic tradable credit scheme for multimodal urban networks

A Tradable Credit Scheme (TCS) is a demand management policy aiming for more sustainable travel behavior. The regulator defines the total credit cap and the credit distribution; it also determines the credit charges for each travel alternative at different times of the day, which modifies the perceived users’ costs. The credit price is determined by trading of credits between travelers. Defining the credit scheme at the urban level and estimating its impacts on user travel decisions and the network congestion dynamics is challenging. We propose a framework wherein travelers change their departure times and choose between solo car driving, Public Transportation (PT), and carpooling to complete their trips under a dynamic TCS, meaning the credit charge is time-dependent. A multimodal macroscopic traffic simulator based on a generalized bathtub model captures the congestion dynamics for the different transport modes. Additionally, we consider different values of time, trip lengths, and desired arrival times for the demand profile.The proposed TCS minimizes the total travel cost, (the sum of all travelers’ travel costs) and the carbon emissions by solving an optimization problem through an iterative method, including an inner loop that updates the users’ choices and credit price under the stochastic user equilibrium principle; and an outer loop that updates the credit charge profile. The methodology is implemented and applied to a realistic test case in Lyon (France). The dynamic TCS profiles result in 36% fewer carbon emissions than static TCS for a total travel cost reduction of 19%. Besides, 94% of the travelers benefit from the TCS as their user costs decrease in the case study. The final results are compared with a more advanced simulation framework, which is too computationally expensive to find the optimal TCS. The proposed TCS is effective with refined traffic dynamics representation.

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

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 a proposed formula for the variance might be universal, and (iii) the system exhibits critical behavior near the capacity state where the accumulation variance diverges. This indicates that the tools from critical phenomena and phase transitions might be useful to understand congestion in cities.

Investigating the effects of inflow river water quality on lake nutrient-concentration variations: a case study in Gehu Lake, China

Context Controlling the inputs of nutrients, one of the main sources of lake pollution from inflow rivers, is an important way to protect lakes. Aims To obtain a whole picture of spatiotemporal variation of water quality in Gehu lake and its main inflow rivers from 2011 to 2018, and to study relationship of water quality between lake and inflow rivers. Methods We analysed the relationship by using correlation analysis and BATHTUB model and discussed the goal of collaborative control by setting up different scenarios. Key results The concentrations of total nitrogen (ρ(TN)) and total phosphorus (ρ(TP)) are the main water pollutants in Gehu Lake and it continues to maintain the middle-eutropher state. ρ(TN) and ρ(TP) in the lake have a significant negative correlation with the quantity of water inflow and a significant positive correlation with ρ(TN) and ρ(TP) in inflow rivers. Conclusions It showed that when ρ(TN) and ρ(TP) in inflow rivers decreased by 25%, ρ(TN) and ρ(TP) in Gehu Lake decreased by 21.01 and 22.64%. Furthermore, when ρ(TN) and ρ(TP) in inflow rivers decreased by 50%, they correspondingly decreased by 40 and 36.91% in the lake. Implications Our findings provide effective control of water quality in Gehu Lake and give a guide for environmental governance and water-quality improvement measures.

Improving Risk Projection and Mapping of Coastal Flood Hazards Caused by Typhoon-Induced Storm Surges and Extreme Sea Levels

Seawater inundation mapping plays a crucial role in climate change adaptation and flooding risk reduction for coastal low-lying areas. This study presents a new elevation model called the digital impermeable surface model (DISM) based on the topographical data acquired by unmanned aerial vehicle (UAVs) for improving seawater inundation mapping. The proposed DISM model, along with the bathtub model, was used to assess coastal vulnerability to flooding in significant tropical cyclone events in a low-lying region of Victoria Harbor in Hong Kong. The inundation simulations were evaluated based on the typhoon news and reports which indicated the actual storm surge flooding conditions. Our findings revealed that the proposed DISM obtains a higher accuracy than the existing digital elevation model (DEM) and the digital surface model (DSM) with a RMSE of 0.035 m. The DISM demonstrated a higher skill than the DEM and the DSM by better accounting for the water-repellent functionality of each geospatial feature and the water inflow under real-life conditions. The inundation simulations affirmed that at least 88.3% of the inundated areas could be recognized successfully in this newly-designed model. Our findings also revealed that accelerating sea level rise in Victoria Harbor may pose a flooding threat comparable to those induced by super typhoons by the end of the 21st century under two representative emission scenarios (RCP4.5 and RCP8.5). The seawater may overtop the existing protective measures and facilities, making it susceptible to flood-related hazards.

Projections of coastal flooding under different RCP scenarios over the 21st century: A case study of China's coastal zone

Among sea level rise (SLR)-induced threats to coastal regions, flooding inundation is considered the most serious, especially in China's coastal zone (CCZ). Previous attempts to simulate the inundation area caused by SLR at the macro spatial scale usually employed the bathtub model based on a large number of historical tide station data. However, these efforts mainly focused on simplifying the calculation of the inundation process at a large scale, but failed to improve the accuracy mainly due to the failure to exclude isolated depressions. Here, based on regional sea level data of the Integrated Climate Data Center (ICDC), the University of Hamburg, a physical ocean model (Finite Volume Coast and Ocean Model, FVCOM) was employed to simulate the maximum possible regional SLR in offshore China from 2021 to 2100 under the representative concentration pathways (RCPs) 2.6, 4.5, and 8.5 scenarios, respectively, and the hydraulic connectivity model was applied based on multi-source data to improve the simulation accuracy of the inundation area. Through these improved methods, the maximum possible inundation characters of CCZ over the 21st century were observed as follows: (1) Under RCP2.6/4.5/8.5 scenarios, the macro spatial patterns of inundation areas are similar, with the inundation area mainly distributing in the coastal areas around the Bo Hai, the coastal areas from Jiangsu to the estuary of the Yangtze River, the Pearl River Delta, and the western coastal areas of Taiwan, and the inundation area gradually expands and spreads over time. (2) Under the three scenarios, the maximum possible inundation area shows a wavelike rising trend, and by 2100, the inundation area is expected to exceed 48.89 × 103 km2 (RCP 2.6) and reach a maximum of 53.50 × 103 km2 (RCP 8.5). (3) There are significant differences in the inundation depth and flood frequency under the three scenarios, with the inundation characters of the high-emission scenario being the most extreme. Overall, our work can provide meaningful information for proper coastal urban planning, disaster prevention, and mitigation measures selection in China. The methodology can also be used for predicting the inundation areas in other coastal countries facing the threat of SLR.

Ecosystem services values at risk in the Atlantic coastal zone due to sea-level rise and socioeconomic development

Uncertainties about the future extent of sea-level rise (SLR) and socioeconomic development will determine the future of coastal ecosystem services and values. This study analyzes the joint impact of flooding and socioeconomic development on the future ecosystem services and values in the Atlantic coastal zone by 2100. To this end, flood probability maps (using the Uncertainty Bathtub Model; uBTM) and local ecosystem service value (ESV) estimates (using meta-analytic based global ecosystem service value functions for Provisioning, Regulating & maintenance, and Cultural ecosystem services across 12 biomes) are derived for a wide combination of Representative Concentration Pathway (RCP) and Shared Socioeconomic Pathways (SSP) scenarios to obtain future values of coastal ecosystem services (ES). Results show that the higher potential of ESV at risk is associated with RCP 8.5 and SSP5, i.e. the scenario associated with a narrative related to fossil-fueled development. For this scenario, by 2100, the coastal zone with the highest probable losses in Provisioning ESV is Europe (∼5.9 € billion/year), for Regulating & maintenance ESV this is North America (∼6.0 € billion/year) and for Cultural ESV this is South America (∼21.3 € billion/year). Countries facing highest relative risk of losing Provisioning ESV are the Netherlands (10.6 %), United States (7.4 %), and Mauritania (5.8 %). For Regulating & maintenance ESV, the top 3 countries impacted are Mauritania (17.6 %), the Netherlands (10.0 %) and Argentina (8.0 %). For Cultural ESV, the countries are Mexico (19.0 %), Denmark (18.1 %) and Sweden (15.6 %). Changes in ESV are exponentially related to flood risk and economic growth, such that small changes in flood or income lead to large changes in ESV. Unlike previous studies, the ESV functions used are dependent on time and local factors, such as population and income. Although population and income growth result in an increase in ESV, it also emphasizes the ecosystem service values at risk. Thus, sea-level rise and socioeconomic changes impact ecosystem services and values – directly affecting the well-being of the world population. The unequal distribution of coastal ecosystem service value losses across continents and countries highlighted in this work is important to identify what values are at risk and for whom. Adaptation measures and strategies can, in turn, be defined.

Geographic information system data considerations in the context of the enhanced bathtub model for coastal inundation

AbstractThis study determines input data appropriateness for geographic information system‐based enhanced bathtub model (eBTM) modeling of coastal inundation in an urban setting. Various tests were conducted concerning digital surface models (DSMs) to determine: (a) the highest appropriate resolution achievable from available LiDAR data and consider variations between derived sub‐meter DSMs; (b) optimal DSM horizontal resolution for coastal inundation modeling based on “out‐the‐box” solutions; and (c) mechanisms to address the challenge presented by DSMs regarding overhanging structures for a study site in False Bay, South Africa. Results showed that while sub‐meter DSMs are achievable, low point cloud densities may result in the misrepresentation of structures, which affects the inundation extents. High horizontal resolution DSMs are required for inundation modeling in an urban setting to account for narrow thoroughfares. Challenges posed by first return LiDAR depicting bridges as solid structures could be circumvented by modifying the input water source for the eBTM processing.