A changing wave climate in the Mediterranean Sea during 58-years using UERRA-MESCAN-SURFEX high-resolution wind fields

This study unravels 58-years (1961-2018) of wind-waves in the Mediterranean Sea (MS). A wave dataset was developed using the wave model WAVEWATCH III forced with the high-resolution (5.5 km) UERRA-MESCAN-SURFEX downscaled wind fields which better contain the imprint of the local geomorphology compared to other, coarser wind datasets used in previous studies. Thus, improving the reliability and characterization of the wind-wave climate in the basin. Validation results revealed a higher performance than previous datasets, particularly on the wave direction (θm), with a bias<1º. Climate variability at seasonal and interannual scales, wind-seas and swells distribution, and long-term trends in storminess and in the mean and extreme regimes were analysed. Results show a slight swell influence over the wind-sea in the hourly spectra at a large portion of the basin, excluding the wave generation areas. We detected that the western MS is the most storminess region with an average of three storms/year. Moreover, the anomalies of the seasonal mean wave direction relative to θm are large (~60º), with opposing behaviours between the winter and summer. Finally, the long-term trends in the mean and extreme conditions and in storminess are mild with values reaching 6 cm/decade and less than 2% in the absolute value, respectively

Forma en planta de equilibrio en playas encajadas: influencia de la variabilidad direccional del oleaje

Los autores agradecen al apoyo del Ministerio de Economía y Competitividad bajo la subvención BIA2014-59643-R. El proyecto de MUSCLE-Beach

Forma en planta de equilibrio estático y dinámico en playas encajadas: nuevos avances e influencia del clima marítimo direccional

ABSTRACT: The main objectives of this study were to: (i) investigate the influence of the directional variability of the wave climate on the shape of the equilibrium planform of embayed beaches, (ii) to determine the representative direction of wave energy flux that dictates the orientation of beaches in static equilibrium conditions, and (iii) to model and fit the dynamic equilibrium planform of headland bay beaches characterized by net littoral drift rates. Most of the work presented in this thesis is based on the analysis of directional wave climates impacting prototype beach cases in equilibrium conditions. The study employed field date from several beaches in Spain and Latin America and utilized vertical aerial images of the selected beaches. Moreover, the Coastal Modeling System (SMC) was used as a helpful tool for different purposes within this thesis such as the modeling of wave transformation in the lee of headland breakwaters, estimation of net sediment transport rates and plotting the equilibrium planform shape of the beaches over vertical images. An extensive review of the research topic was addressed in Chapter 2. Next, the effect of beach sediment size and the Shape of the Directional Distribution (SDD) of the energy flux of the wave climate on the direction that dictates the static equilibrium beach orientation was investigated in Chapter 3. Field data from 32 beaches along the Spanish coast and available long-term databases of directional wave climates were employed. Moreover, initiation of sediment motion due to wave action was taken into account in order to filter the directional wave climate to consider only waves that are capable of moving the sediment. The results indicated that the direction of the mean energy flux of filtered waves is more appropriate for the determination of the (SEBO) than that of whole waves. This direction was identified as the morphologically representative direction of the wave energy flux. Chapter 4 investigated the methodology for locating the down-coast control point (Po) point of the SEP of embayed beaches, exploring the role of wave climate directional spreading and employing 44 HBBs in Spain and Latin America. It correlated the planform shape in the long term with the directional variability of the wave climate at the diffraction point. Additionally, an extensive series of numerical simulations using a spectral wave model was carried out to model the combined effects of refraction-diffraction in the lee of a breakwater, defining the part affected by the coastal structure under different wave conditions. The results clarified the importance of wave directional spreading in locating the (Po) point. Additionally, a new formula was derived to locate the down-coast control point (Po) of the parabolic part of the shoreline as a function of the directional variance of the wave climate and the location of the diffraction point with relation to the straight shoreline. The planform shape of embayed beaches in dynamic equilibrium conditions was explored in Chapter 5, proposing a new derived formula to obtain the DEP of (HBBs). The model represents a general form of the Parabolic Bay Shape Equation (PBSE) with modified C coefficients as a function of both the wave obliquity (β) and the net littoral drift rate that is passing through the bay. The angular difference (γd) between the direction of the mean wave energy flux at the diffraction point of the headland and the beach orientation down-coast is utilized in the proposed model as the driver of the net longshore sediment transport rate. The model was verified against natural HBBs in dynamic equilibrium characterized by various net littoral drift rates along the Brazilian coast, producing good results. Furthermore, a design procedure was presented in Chapter 6 to be used for stability studies and design of pocket beaches in dynamic equilibrium conditions. The proposed methodology employs the net sediment transport rate passing through the bay together with the time series of the wave climate impinging on the beach in order to compute the angle (γd) in order to plot and identify the DEP. Furthermore, the design methodology can be employed in coastal management and in the assessment of shoreline changes in situations where the sediment supply rate changes or is reduced from its originating source (e.g. fluvial discharges, sand bypassing, or from an updrift source).RESUMEN: Los objetivos principales de este estudio son: (i) investigar la influencia de la variabilidad direccional del clima marítimo en la forma en planta de equilibrio en las playas encajadas, (ii) determinar la dirección representativa del flujo de energía del oleaje que determina la orientación de las playas en condiciones de equilibrio estático, y (iii) modelar y ajustar la forma en planta de equilibrio dinámico en las playas encajadas caracterizadas por tasas netas de transporte de sedimento. Gran parte del trabajo presentado en esta tesis se basa en el análisis de los climas marítimos direccionales que afectan a casos prototipos de playas en condiciones de equilibrio. En el estudio se emplearon datos de varias playas en España y América Latina y se utilizaron imágenes aéreas verticales de las playas seleccionadas. Por otra parte, se utilizó el Sistema Modelado Costero (SMC) como una herramienta útil para diferentes propósitos en esta tesis, como el modelado de la transformación del oleaje detrás de los diques, la estimación del transporte neto de sedimentos y el ajuste de la forma en planta de equilibrio en playas sobre imágenes verticales. En el capítulo 2, se analizó ampliamente el estado del arte del tema de esta tesis. El capítulo 3 se presentó el efecto del tamaño de los sedimentos de las playas y la forma de la distribución direccional, Shape of Directional Distribution (SDD), del flujo de energía del clima marítimo en la dirección que determina la orientación de playas en equilibrio. Se emplearon datos de 32 playas a lo largo de la costa española y bases de datos de los climas marítimos direccionales disponibles Por otro lado, el inicio del movimiento del sedimento debido a la acción del oleaje se tuvo en cuenta a fin de filtrar el clima marítimo direccional para considerar sólo las olas capaces de mover el sedimento. Los resultados indicaron que la dirección del flujo medio de energía de las olas filtradas es más apropiada para la determinación de la Static Equilibrium Beach Orientation (SEBO) que la de toda la serie del oleaje. Esta dirección se identificó como la dirección representativa morfológicamente del flujo de energía del oleaje. En el capítulo 4, se investigó la metodología de la localización del punto de inicio de la forma en planta de equilibrio estático en las playas encajadas, explorando la influencia de la dispersión direccional del clima marítimo y empleando 44 playas en España y América Latina. Se correlacionó la forma en planta en el largo plazo con la variabilidad direccional del clima marítimo en el punto de difracción. Además, se realizó una serie de simulaciones numéricas utilizando un modelo espectral del oleaje para modelar los efectos combinados de la refracción-difracción detrás de los diques, definiendo la parte afectada por la estructura costera en diferentes condiciones del oleaje. Los resultados aclararon la importancia de la dispersión direccional de las olas en la localización de punto (Po). Además, se derivó una fórmula nueva para localizar el punto de inicio (Po) de la parte parabólica de la costa en función de la varianza direccional del clima marítimo y la ubicación del punto de difracción desde el tramo recto de la línea costa. En el capítulo 5, se exploró la forma en planta en las playas encajadas en condiciones de equilibrio dinámico, proponiendo una fórmula nueva derivada para obtener la Dynamic Equilibrium Planform (DEP) de esas playas. El modelo representa una forma general de la ecuación parabólica (PBSE) Parabolic Bay Shape Equation, con coeficientes modificados como una función de la oblicuidad del oleaje (β) y de la tasa neta del transporte de sedimento que está pasando a través de la bahía. La diferencia angular (γd) entre la dirección del flujo medio de energía de las olas cerca del el punto de difracción y la orientación del tramo recto de la playa se utiliza en el modelo propuesto como el impulsor de la tasa neta de transporte de sedimentos litorales. El modelo se verificó con algunas playas naturales en equilibrio dinámico caracterizado por varias tasas netas del transporte de sedimento a lo largo de la costa brasileña, produciendo buenos resultados. Además, en el capítulo 6 se presentó un procedimiento de diseño que se utilizará para estudios de estabilidad y diseño de las playas encajadas en condiciones de equilibrio dinámico. La metodología propuesta emplea la tasa neta de transporte de sedimentos que pasa a través de la bahía junto con la serie temporal del clima marítimo que incide en la playa para calcular el ángulo (γd) para identificar la forma en plante de equilibrio dinámico (DEP). Además, la metodología de diseño puede emplearse en la gestión costera y en la evaluación de los cambios en la línea costa en las situaciones en que la tasa de suministro de sedimentos cambia o se reduce de su fuente de origen (por ejemplo, los caudales fluviales y el bypassing de la arena)

Equilibrium planform of pocket beaches behind breakwater gaps: On the shape of the equilibrium shoreline

ABSTRACT: Bay beaches are common coastal landforms along the world’s coastlines and have frequently been used as equilibrium coastal systems to mitigate erosion problems and stabilize coasts. Throughout the literature, several formulae can be found to obtain the static equilibrium planform (SEP) of such beaches on the leeward sides of single protruding headland structures. However, equations used to define SEP behind breakwater gaps are rare and based on a limited number of studies, especially when the obliquity angle (β) is large. This paper proposes a new formula for modelling the SEP of bay beaches that includes cases with planform shapes characterized by large obliquity angles (β > 75°) for which the SEP is almost quasi-semicircular. The formula represents a general form of the parabolic bay shape equation (PBSE) with modified coefficients to alter the planform’s curvature to be quasi-semicircular, mimicking the behavior of such bays in nature. The coefficients are expressed as functions of both the obliquity angle (β) and the curvature-adjustment angle (�), which was determined based on field observations of the best-fitting SEP of 26 bay beaches with (β > 75°) along the coasts of Spain, Portugal and Brazil. Additionally, 32 beach cases characterized by smaller obliquity angles (β < 70°) were included in the derivation of the curvature adjustment angle, which was expressed as a function of (β). The model showed good results in modelling the SEP, with an RMSE of 0.90° obtained when estimating the planform’s curvature-adjustment angle (�) to obtain quasi-semicircular planform shapes for the prototype cases, confirming its utility as a valuable tool for engineering applications.The authors would like to acknowledge the support of the Spanish Ministry of Economy, Industry, and Competitiveness under Grant BIA2017–89491-R (Beach-Art Project)