Managing coastal environments under climate change: Pathways to adaptation

Review of the Impacts of Climate Change on Ports and Harbours and Their Adaptation in Spain

Climate change is one of the issues of greatest concern to today’s society. The increase in temperatures has affected sea levels, polar masses and extreme events, among others. There are many scientific studies that analyze the impacts of climate change on coastal communities, but most of them focus on beach erosion and coastal recession. Scientific literature on the effects of climate change on ports and harbors and their adaptation is much less abundant. Ports are essential for the economy and society of their cities, so studying the impact of climate change on them is an urgent need. The Mediterranean and the Spanish Mediterranean coast is one of the areas that will be most affected by climate change in the future. In addition, the Spanish economy depends a lot on its tourism and, thus, on its coastal cities. Therefore, the study of the impact of climate change on Spanish ports and coastal communities is essential. This article presents a review of the studies carried out until now on the effects of climate change on Spanish ports, and it identifies research gaps and weaknesses and suggests new research lines.

A methodological framework for selecting an optimal sediment source within a littoral cell

One of the most used measures to counteract coastal erosion is beach nourishment. It has advantages with respect to the use of rigid structures that sometimes entail non desired impacts on the surrounding areas. However, beach nourishments are often unsuccessful, requiring frequent refills due to the use of sediments that are not suitable. In this paper, a methodological framework for increasing the probability of success of beach nourishment projects is presented. First, this framework consists of detecting potential borrowing areas, by analysing shoreline evolution and selecting the stretch that shows a more accretive character. Once the borrowing area has been identified, several sand extraction options are defined. The beach response (in terms of erosion and flooding) to each sand extraction alternative is analysed by using two numerical models, which simulate the hydro-morphodynamic patterns in the studied area. The numerical model results allow to find the best extraction alternative, which is that producing the least impact in the borrow area. As an example, the methodology is applied to a stretch of the Catalan coast (NW Mediterranean) to illustrate its potential. The proposed methodology shows to be a useful tool for helping coastal managers to optimize their available resources.

Nonstationary Extreme Value Analysis of Nearshore Sea-State Parameters under the Effects of Climate Change: Application to the Greek Coastal Zone and Port Structures

In the present work, a methodological framework, based on nonstationary extreme value analysis of nearshore sea-state parameters, is proposed for the identification of climate change impacts on coastal zone and port defense structures. The applications refer to the estimation of coastal hazards on characteristic Mediterranean microtidal littoral zones and the calculation of failure probabilities of typical rubble mound breakwaters in Greek ports. The proposed methodology hinges on the extraction of extreme wave characteristics and sea levels due to storm events affecting the coast, a nonstationary extreme value analysis of sea-state parameters and coastal responses using moving time windows, a fitting of parametric trends to nonstationary parameter estimates of the extreme value models, and an assessment of nonstationary failure probabilities on engineered port protection. The analysis includes estimation of extreme total water level (TWL) on several Greek coasts to approximate the projected coastal flooding hazard under climate change conditions in the 21st century. The TWL calculation considers the wave characteristics, sea level height due to storm surges, mean sea level (MSL) rise, and astronomical tidal ranges of the study areas. Moreover, the failure probabilities of a typical coastal defense structure are assessed for several failure mechanisms, considering variations in MSL, extreme wave climates, and storm surges in the vicinity of ports, within the framework of reliability analysis based on the nonstationary generalized extreme value (GEV) distribution. The methodology supports the investigation of future safety levels and possible periods of increased vulnerability of the studied structure to different ultimate limit states under extreme marine weather conditions associated with climate change, aiming at the development of appropriate upgrading solutions. The analysis suggests that the assumption of stationarity might underestimate the total failure probability of coastal structures under future extreme marine conditions.

The Use of News Information Published in Newspapers to Estimate the Impact of Coastal Storms at a Regional Scale

The evaluation of coastal damage caused by storms is not straightforward and different approaches can be applied. In this study, damage caused by extreme storms is evaluated at a regional scale based on news information published in regional newspapers. The data derived from the news are compared with hydrodynamic parameters to check the reliability of this methodology as a preliminary” fast approach” to evaluate storm damage and to identify hotspots along the coast. This methodology was applied to the two most extreme storms ever recorded along the Spanish Mediterranean coast, which occurred in January 2017 and January 2020, severely impacting the coast and causing significant community concerns. The news information from different media sources was processed and weighted to describe the resulting erosion, inundation, sand accumulation, and destruction of infrastructures. Moreover, an accuracy index for scoring the quality of the information was proposed. In spite of some limitations of the method, the resulting regional coastal hazard landscape of damage provides a rapid overview of the intensity and distribution of the damage and enables one to identify the location of potential hotspots for the analyzed extreme storm events. The results show that estimated damage intensity is better related to maximum wave energy than cumulative wave energy during a storm, and that beach characteristics should also be included for understanding the distribution of coastal damage.

Coastal infrastructure operativity against flooding - A methodology

The operativity of the transport infrastructures and urban developments protected by coastal structures is conditioned by flooding events and the resulting wave overtopping. This work presents a methodology to assess the operational conditions of infrastructures located in coastal areas based on the combination of advanced statistical techniques, laboratory experiments and state-of-the-art numerical models properly validated. It is applied to a case study in the SW coast of England, the railway seawall at Dawlish, which was subjected to recurrent wave overtopping until its dramatic collapse in February 2014. To quantify the increase in overtopping discharges with wave height and water level, we define an ad hoc variable, the effective overtopping forcing, which explains 98% of the variability of the overtopping discharge. The return periods associated to the operational thresholds for coastal structures protecting people and railways are also obtained. The proposed methodology enables the assessment of the overtopping discharge induced by a given sea state and, thus, check if a coastal infrastructure will be or not operational under any expected marine condition. This innovative methodology can also be used to analyse the flooding event consequences on urban areas protected by coastal infrastructures.

The Costs of Sea-Level Rise: Coastal Adaptation Investments vs. Inaction in Iberian Coastal Cities

Iberian coastal cities are subject to significant risks in the next decades due to climate change-induced sea-level rise. These risks are quite uncertain depending on several factors. In this article, we estimate potential economic damage in 62 Iberian coastal cities from 2020 to 2100 using regional relative sea-level rise data under three representative concentration pathways (RCP 8.5, RCP 4.5 and RCP 2.6). We analyze the expected accumulated damage costs if no adaptation actions take place and compare this scenario to the investment cost of some adaptation strategies being implemented. The results show that some adaptation strategies are less costly than the potential damage under inaction. In other words, it is economically rational to invest in adaptation even in a context of high uncertainty. These calculations are very relevant to inform climate change adaptation decisions and to better manage the risk posed by sea-level rise. Moreover, our findings show the importance of a good understanding of the shape of the sea-level rise and damage cost distributions to calculate the expected damage. We show that using the 50th percentile for these calculations is not adequate as it leads to a serious underestimation of expected damage and coastal risk.

Modeling of Future Extreme Storm Surges at the NW Mediterranean Coast (Spain)

Storm surges are one of the main drivers for extreme flooding at the coastal areas. Such events can be characterized with the maximum level in an extreme storm surge event (surge peak), as well as the duration of the event. Surge projections come from a barotropic model for the 1950–2100 period, under a severe climate change scenario (RCP 8.5) at the northeastern Spanish coast. The relationship of extreme storm surges to three large-scale climate patterns was assessed: North Atlantic Oscillation ( N A O ), East Atlantic Pattern ( E A W R ), and Scandinavian Pattern ( S C ). The statistical model was built using two different strategies. In Strategy #1, the joint probability density was characterized by a moving-average series of stationary Archimedean copula, whereas in Strategy #2, the joint probability density was characterized by a non-stationary probit copula. The parameters of the marginal distribution and the copula were defined with generalized additive models. The analysis showed that the mean values of surge peak and event duration were constant and were independent of the proposed climate patterns. However, the values of N A O and S C influenced the threshold and the storminess of extreme events. According to Strategy #1, the variance of the surge peak and event duration increased with a fast shift of negative S C and a positive N A O , respectively. Alternatively, Strategy #2 showed that the variance of the surge peak increased with a positive E A W R . Both strategies coincided in that the joint dependence of the maximum surge level and the duration of extreme surges ranged from low to medium degree. Its mean value was stationary, and its variability was linked to the geographical location. Finally, Strategy #2 helped determine that this dependence increased with negative N A O .

Coastal Flooding and Erosion under a Changing Climate: Implications at a Low-Lying Coast (Ebro Delta)

Episodic coastal hazards associated to sea storms are responsible for sudden and intense changes in coastal morphology. Climate change and local anthropogenic activities such as river regulation and urban growth are raising risk levels in coastal hotspots, like low-lying areas of river deltas. This urges to revise present management strategies to guarantee their future sustainability, demanding a detailed diagnostic of the hazard evolution. In this paper, flooding and erosion under current and future conditions have been assessed at local scale at the urban area of Riumar, a touristic enclave placed at the Ebro Delta (Spain). Process-based models have been used to address the interaction between beach morphology and storm waves, as well as the influence of coastal environment complexity. Storm waves have been propagated with SWAN wave model and have provided the forcings for XBeach, a 2DH hydro-morphodynamic model. Results show that future trends in sea level rise and wave forcing produce non-linear variations of the flooded area and the volume of mobilized sediment resulting from marine storms. In particular, the balance between flooding and sediment transport will shift depending on the relative sea level. Wave induced flooding and long-shore sand transport seem to be diminished in the future, whereas static sea level flooding and cross-shore sediment transport are exacerbated. Therefore, the characterization of tipping points in the coastal response can help to develop robust and adaptive plans to manage climate change impact in sandy wave dominated coasts with a low-lying hinterland and a complex shoreline morphology.

Defining Coastal Resilience

The concept of resilience has taken root in the discourse of environmental management, especially regarding Building with Nature strategies for embedding natural physical and ecological dynamics into engineered interventions in developed coastal zones. Resilience is seen as a desirable quality, and coastal management policy and practice are increasingly aimed at maximising it. Despite its ubiquity, resilience remains ambiguous and poorly defined in management contexts. What is coastal resilience? And what does it mean in settings where natural environmental dynamics have been supplanted by human-dominated systems? Here, we revisit the complexities of coastal resilience as a concept, a term, and a prospective goal for environmental management. We consider examples of resilience in natural and built coastal environments, and offer a revised, formal definition of coastal resilience with a holistic scope and emphasis on systemic functionality: “Coastal resilience is the capacity of the socioeconomic and natural systems in the coastal environment to cope with disturbances, induced by factors such as sea level rise, extreme events and human impacts, by adapting whilst maintaining their essential functions.” Against a backdrop of climate change impacts, achieving both socioeconomic and natural resilience in coastal environments in the long-term (>50 years) is very costly. Cost trade-offs among management aims and objectives mean that enhancement of socioeconomic resilience typically comes at the expense of natural resilience, and vice versa. We suggest that for practical purposes, optimising resilience might be a more realistic goal of coastal zone management.

Temporal (1948–2012) and Dynamic Evolution of the Wouri Estuary Coastline within the Gulf of Guinea

The Wouri estuary is located in the Gulf of Guinea on the Atlantic coast of Cameroon’s coastline plain (3°49′ and 4°04′ north latitude and 9°20′ to 9°40′ east longitude), and is strongly influenced by coastal dynamics that have remained unquantified over a long period of time. This study analyzed the historical evolution of the Wouri estuarine coastline between 1948 and 2012. Variations in the estuarine evolution of the Wouri were studied from (i) minute topographic extracts from 1948, (ii) 1996–1999 nautical charts, and (iii) 2012 spatial map vectors. The net temporal spatial variation rates were calculated using the statistical methods of the Digital Shoreline Analysis System (DSAS). These change rates were also calculated over two time intervals (1948–1996 and 1996–2012) and over a 64-year period (1948–2012). The study reveals highly disparate results. Indeed, kinematics show that the Wouri estuary was dominated by erosion in its downstream section, with 262.83 ha for –3.2 m/year and 110.56 ha for –5.8 m/year between 1948–1996 and 1996–2012 respectively, and by accretion on the other hand in its upstream section, with 239.17 ha for 4.3 m/year in zone 5 between 1948–1996 and 150.82 ha for 12.6 m/year in zone 4 between 1996–2012. Thus, over the 64-year period (1948–2012), we have a dominance of variation by erosion downstream and conversely by accretion upstream, marked by the presence of amplifying factors (anthropogenic pressure and climate change) of the rate of variation of morphological evolution at the beginning of the 21st century, as compared to the middle-20th century. The observed development of sediment loss and accumulation, both influences and will influence, the sediment regime along the Wouri estuarine coastline. There is a need to develop a systematic sub-regional coastal surveillance activity to effectively manage Cameroon’s coastline system.

Wave farm impacts on coastal flooding under sea-level rise: A case study in southern Spain

Coastal flooding, already an acute problem in many parts of the world, will be exacerbated in the near future by the sea level rise induced by climate change. The influence of wave farms, i.e., arrays of wave energy converters, on coastal processes, in particular sediment transport patterns, has been analysed in recent works; however, their influence on coastal flooding has not been addressed so far. The objective of this work is to investigate whether a wave farm can provide some protection from flooding on the coast in its lee through a case study: a gravel-dominated beach in southern Spain (Playa Granada). We consider three sea-level rise (SLR) scenarios: the present situation (SLR0), an optimistic projection (SLR1) and a pessimistic projection (SLR2). Two state-of-the-art numerical models, SWAN and XBeach-G, are applied to determine the wave propagation patterns, total run-up and flooded dry beach area. The results indicate that the absorption of wave power by the wave farm affects wave propagation in its lee and, in particular, wave heights, with alongshore-averaged reductions in breaking wave heights about 10% (25%) under westerly (easterly) storms. These lower significant wave heights, in turn, result in alongshore-averaged run-up reductions for the three scenarios, which decreases with increasing SLR values from 5.9% (6.8%) to 1.5% (5.1%) for western (eastern) storms. Importantly, the dry beach area flooded under westerly (easterly) storms is also reduced by 5.7% (3.2%), 3.3% (4.9%) and 1.99% (4.5%) in scenarios SLR0, SLR1 and SLR2, respectively. These findings prove that a wave farm can actually reduce coastal flooding on its leeward coast.

Dual wave farms and coastline dynamics: The role of inter-device spacing

In dual wave farms, i.e., arrays of wave energy converters (WECs) with a dual function - generation of renewable power and mitigation of coastal erosion - the spacing between the WECs is a fundamental design parameter. The present research has the objective of establishing how this parameter affects the shoreline evolution behind the array and, on this basis, to propose and apply a method to determine the optimum spacing for coastal protection. The method is demonstrated on a beach subjected to severe erosion. Five case studies are considered: four with different inter-WEC spacings, and one without the wave farm (baseline). A spectral wave propagation model is applied to analyse the variations in significant wave height behind the WEC array. Longshore sediment transport rates are calculated, and a shoreline model is applied. We find that in all the case studies the dry beach area is greater than in the baseline (no farm) case study, which proves the capacity of the dual WEC array to mitigate the erosive trends of the system. Importantly, we obtain that the inter-WEC spacing plays a fundamental role in the evolution of the shoreline and, consequently, in the effectiveness of the WEC array for coastal protection. The case studies with intermediate spacings yield the best performance in terms of dry beach area. More generally, the benefits of dual wave farms in terms of protection of coastal properties and infrastructure, and the ensuing savings in conventional coastal defence measures (coastal structures, beach nourishment, etc.) contribute to the development of wave energy by enhancing its economic viability. The methodology presented in this paper can be used to optimize the design of dual wave farms elsewhere.

Wave farm effects on the coast: The alongshore position

For wave energy to become a fully-fledged renewable and thus contribute to the much-needed decarbonisation of the energy mix, the effects of wave farms (arrays of wave energy converters) on coastal systems must be addressed. The objective of this work is to investigate the effects of wave farms on the longshore sediment transport and shoreline evolution of a gravel-dominated beach and, in particular, its sensitivity to the longshore position of the farm based on eight scenarios. Nearshore wave propagation patterns are computed by means of a spectral wave propagation model (SWAN), variations in sediment transport rates induced by the farm are calculated, and a one-line model is applied to determine the shoreline position and dry beach area. The significant wave height at breaking is reduced in the lee of the wave farm, dampening sediment transport. We find that changes in the dry beach area induced by the wave farm are highly sensitive to its alongshore position, and may result in: (i) erosion relative to the baseline scenario (without wave farm) in three of the eight scenarios, (ii) accretion in three other scenarios, and (iii) negligible effects in the remaining two. These results prove that the alongshore position of the wave farm controls the response of the beach to the extent that it may shift from accretionary to erosionary, and provide evidence of its effectiveness in countering erosion if appropriately positioned. This effectiveness opens up the possibility of using wave farms not only to generate carbon-free energy but also to manage coastal erosion, thus strengthening the case for the development of wave energy.

Protection of gravel-dominated coasts through wave farms: Layout and shoreline evolution

The impacts of wave farms (arrays of wave energy converters, or WECs) on the nearshore must be fully understood for wave technology to develop and thus contribute to a sustainable, carbon-free energy mix in the near future. The objective of this work is to investigate the role played by the farm layout on the wave propagation patterns leewards and the implications for longshore sediment transport (LST) and shoreline evolution on a gravel-dominated deltaic coast. Changes in wave propagation in four scenarios, corresponding to as many wave farm layouts, are computed by means of a spectral numerical model (Delft3D-WAVE) under (i) low-energy and storm conditions, and (ii) westerly and easterly waves - the two prevailing wave directions. On this basis, sediment transport rates are computed and changes in the shoreline position assessed using a one-line model. To quantify the impact of the wave farm on the nearshore wave conditions, sediment transport and shoreline, we define three ad hoc indicators: the non-dimensional wave height reduction, the non-dimensional LST rate reduction and the non-dimensional shoreline advance. Significant wave heights decrease in the lee of the wave farm, with the consequent reduction in LST rates. As a result, the dry beach area increases in every scenario under both westerly and easterly waves. We find that case studies with the WECs arranged on fewer rows but covering a greater stretch of coastline provide better coastal protection. These results confirm that wave farms can be used not only to generate carbon-free energy but also to protect gravel-dominated coasts.

Optimized Reliability Based Upgrading of Rubble Mound Breakwaters in a Changing Climate

The present work aims at presenting an approach on implementing appropriate mitigation measures for the upgrade of rubble mound breakwaters protecting harbors and/or marinas against increasing future marine hazards and related escalating exposure to downtime risks. This approach is based on the reliability analysis of the studied structure coupled with economic optimization techniques. It includes the construction of probability distribution functions for all the stochastic variables of the marine climate (waves, storm surges, and sea level rise) for present and future conditions, the suggestion of different mitigation options for upgrading, the construction of a fault tree providing a logical succession of all events that lead to port downtime for each alternative mitigation option, and conclusively, the testing of a large number of possible alternative geometries for each option. A single solution is selected from the total sample of acceptable geometries for each upgrading concept that satisfy a probabilistic constraint in order to minimize the total costs of protection. The upgrading options considered in the present work include the construction or enhancement of a crown wall on the breakwater crest, the addition of the third layer of rocks above the primary armor layer of the breakwater (combined with crest elements), the attachment of a berm on the primary armor layer, and the construction of a detached low-crested structure in front of the breakwater. The proposed methodology is applied to an indicative rubble mound breakwater with an existing superstructure. The construction of a berm on the existing primary armor layer of the studied breakwater (port of Deauville, France), seems to be advantageous in terms of optimized total costs compared to other mitigation options.

Integrating complex numerical approaches into a user-friendly application for the management of coastal environments

This paper presents a software platform to compute the total water level, one of the key variables for the environmental management of coastal zones. The platform integrates six modules: (1) simulation of deep-water wave variables, storm surge and river flow; (2) wave downscaling; (3) wave propagation; (4) contribution of the river discharge; (5) astronomical tide; and (6) total water level. It was applied to three case studies in southern Spain. The first case study consisted of designing the extension of a fluvial marina in a highly dynamic area (Guadalete estuary, Cádiz), and the maximum number of floating docks to avoid flooding events was obtained. The second case study involved calculating the operation conditions for navigation purposes in an inlet with sedimentation problems (Punta Umbría, Huelva), and a relationship between the percentage of operation hours and the dredged volume was obtained. The third case study consisted of estimating the number of overwash events as a function of the height of the berm on a deltaic beach with erosion issues (Guadalfeo, Granada), and a simple design curve to help managers during the decision-making process of artificial nourishment projects was provided. These results highlight the potential of the developed software, whose methodology is feasibly extensible to other coastal areas worldwide, to help managers handle a wide range of environmental problems related to the total water level. This is especially relevant due to the expected sea level rise in the coming years.

An integrated methodology to forecast the efficiency of nourishment strategies in eroding deltas

Many deltas across the globe are retreating, and nearby beaches are undergoing strong erosion as a result. Among soft and prompt solutions, nourishments are the most heavily used. This paper presents an integrated methodology to forecast the efficiency of nourishment strategies by means of wave climate simulations, wave propagations with downscaling techniques, computation of longshore sediment transport rates and application of the one-line model. It was applied to an eroding deltaic beach (Guadalfeo, southern Spain), where different scenarios as a function of the nourished coastline morphology, input volume and grain size were tested. For that, the evolution of six scenarios of coastline geometry over a two-year period (lifetime of nourishment projects at the study site) was modelled and the uncertainty of the predictions was also quantified through Monte Carlo techniques. For the most efficient coastline shape in terms of gained dry beach area, eight sub-scenarios with different nourished volumes were defined and modelled. The results indicate that an input volume around 460,000m³ is the best strategy since nourished morphologies with higher volumes are more exposed to the prevailing storm directions, inducing less efficient responses. After setting the optimum coastline morphology and input sediment volume, eleven different nourished grain sizes were modelled; the most efficient coastline responses were obtained for sediment sizes greater than 0.01m. The availability of these sizes in the sediment accumulated upstream of a dam in the Guadalfeo River basin allows for the conclusion that this alternative would not only mitigate coastal erosion problems but also sedimentation issues in the reservoir. The methodology proposed in this work is extensible to other coastal areas across the world and can be helpful to support the decision-making process of artificial nourishment projects and other environmental management strategies.

Sea level anomaly in the North Atlantic and seas around Europe: Long-term variability and response to North Atlantic teleconnection patterns

Sea level anomaly (SLA), provided globally by satellite altimetry, is considered a valuable proxy for detecting long-term changes of the global ocean, as well as short-term and annual variations. In this manuscript, monthly sea level anomaly grids for the period 1993-2013 are used to characterise the North Atlantic Ocean variability at inter-annual timescales and its response to the North Atlantic main patterns of atmospheric circulation variability (North Atlantic Oscillation, Eastern Atlantic, Eastern Atlantic/Western Russia, Scandinavian and Polar/Eurasia) and main driven factors as sea level pressure, sea surface temperature and wind fields. SLA variability and long-term trends are analysed for the North Atlantic Ocean and several sub-regions (North, Baltic and Mediterranean and Black seas, Bay of Biscay extended to the west coast of the Iberian Peninsula, and the northern North Atlantic Ocean), depicting the SLA fluctuations at basin and sub-basin scales, aiming at representing the regions of maximum sea level variability. A significant correlation between SLA and the different phases of the teleconnection patterns due to the generated winds, sea level pressure and sea surface temperature anomalies, with a strong variability on temporal and spatial scales, has been identified. Long-term analysis reveals the existence of non-stationary inter-annual SLA fluctuations in terms of the temporal scale. Spectral density analysis has shown the existence of long-period signals in the SLA inter-annual component, with periods of ~10, 5, 4 and 2years, depending on the analysed sub-region. Also, a non-uniform increase in sea level since 1993 is identified for all sub-regions, with trend values between 2.05mm/year, for the Bay of Biscay region, and 3.98mm/year for the Baltic Sea (no GIA correction considered). The obtained results demonstrated a strong link between the atmospheric patterns and SLA, as well as strong long-period fluctuations of this variable in spatial and temporal scales.

Measuring geomorphological vulnerability on beaches using a set of indicators (GVI): A tool for management

A system of indicators has been developed to evaluate beach geomorphological vulnerability (GVI) through: intrinsic susceptibility, the agents that model them, and their ability to remain stable over time. The method is applied to 34 beaches on the island of Gran Canaria (Spain) that experience different levels and conditions of human occupation, marine incidence, landforms and sediments, and spatial evolution that have been recorded since 1960. In contrast with other studies, the analysis of these dimensions (and their relationships) allows a diagnosis of the geomorphology of the beaches with an integrated approach. The results illustrate the numerous causes that generate geomorphological vulnerability, such as wave intensity, the presence of dikes or breakwaters, coastline variations, the absence of foredunes and embryonic dunes, the width of the intertidal zone, or the absence of beachrocks or lavic stones outcropping onto the shore. These variables combine and operate differently in five defined groups of beaches with different management needs. The most vulnerable ones were those with strong marine incidence, which require maintenance of their landforms in order to guarantee their stability. The opposite situation is found in beaches with little impact from anthropic and marine components. These beaches are less vulnerable since they have moderate susceptibility and high resilience. Their management requirements consist of soft measures since they have a strong geomorphological robustness. In this context, the proposed indicator system is a potentially relevant contribution to the management of beaches, especially for those that are under threat.

Coastal modification of a scene employing multispectral images and vector operators

Changes in sea level, wind patterns, sea current patterns, and tide patterns have produced morphologic transformations in the coastline area of Tamaulipas Sate in North East Mexico. Such changes generated a modification of the coastline and variations of the texture-relief and texture of the continental area of Tamaulipas. Two high-resolution multispectral satellite Satellites Pour l'Observation de la Terre images were employed to quantify the morphologic change of such continental area. The images cover a time span close to 10 years. A variant of the principal component analysis was used to delineate the modification of the land-water line. To quantify changes in texture-relief and texture, principal component analysis was applied to the multispectral images. The first principal components of each image were modeled as a discrete bidimensional vector field. The divergence and Laplacian vector operators were applied to the discrete vector field. The divergence provided the change of texture, while the Laplacian produced the change of texture-relief in the area of study.