The Extremal Value Analysis of Sea Level in the Gulf of Cádiz and Alborán Sea: A New Methodology and the Resilience of Critical Infrastructures

Rising sea levels and increasing storm wave heights are two clear indicators of climate change affecting coastal environments worldwide. Coastal cities and infrastructure are particularly vulnerable to these hazards, highlighting the need for accurate predictions and effective adaptation and resilience strategies to protect human lives and economic activities. This study focuses on the Andalusia coast of southern Spain, from Cádiz to Almería, analyzing twelve years of sea level and wave height records using an Extreme Value Analysis. A key challenge lies in selecting the most suitable statistical distribution for long-term predictions. To address this, we propose a modified application of the Cramér–Rao Lower Bound and compare it with the Akaike Information Criteria and the Bayesian Information Criteria. Our results indicate that sea level extremes generally follow a Gumbel distribution, while wave height extremes align more closely with the Fisher–Tippett I distribution. Additionally, a high-resolution digital elevation model of the Navantia Puerto Real shipyard, generated with LiDAR scanning, was used to identify flood-prone areas and assess potential operational impacts. This approach allows for the development of practical recommendations for enhancing infrastructure resilience. The main contribution of this work includes the estimation of extreme regimes for sea level and wave stations, a novel and more efficient application of the Cramér–Rao Lower Bound, a comparative analysis with Bayesian criteria, and providing recommendations to improve the resilience of shipyard operations.