The upwelling cores on the Caribbean Colombian coasts are mainly located at the Peninsula de la Guajira and Cabo de la Aguja. We used monthly averaged Moderate Resolution Imaging Spectroradiometer (MODIS) sea surface temperature as the only information to build up a prediction model for the upwelling events. This comprised two steps: (i) the reduction of the complexity by means of the Karhunen–Loève transform and (ii) a prediction model of time series. Two prediction models were considered: (a) a parametric autoregressive-moving average (ARMA) time series from the Box–Jenkins methodology and (b) a harmonic synthesis model. The harmonic synthesis also comprised of two steps: the maximum entropy spectral analysis and a least-squares harmonic analysis on the set of frequencies. The parametric ARMA time series model failed at the time of prediction with a very narrow range, and it was quite difficult to apply. The harmonic synthesis allowed prediction with a horizon of six months with a correlation of about 0.80. The results can be summarized using the time series of the weights of the different oscillation modes, their spatial structures with the nodal lines, and a high confidence model with a horizon of prediction of about four months.

The development of the mathematical morphology meant a major turn on digital image processing. Among its operators, the skeleton is one of the most difficult to apply. Authors have studied the sensitivity of the fractal dimension of the skeleton of geometrical structures in a digital image when its spatial resolution and threshold level change. The procedure is first tested on a scientific and industrial standard and second carried out on a sea surface temperature (SST) imagery of the Colombian Caribbean. The results can be summarized as (i) the distribution of the variance of the binarized images and of the fractal dimension of the skeleton of the SST respect to the threshold level and losses in resolution, (ii) a criterion to choose the threshold level for binarization and the loss in resolution to compute the skeleton, and (iii) such transformation leads to a fractal dimension of the corresponding skeleton with the minimum standard deviation. The study is completed by analysing the influence of El Niño on the fractal dimension of the skeletons by means of cross-spectral analysis obtaining an average phase lag of about 2.8 months.

The Brazil–Malvinas Confluence (BMC) is one of the most complex oceanic areas in the Earth’s oceans and the prediction of high frequency structures tends to fail. The authors studied the BMC using Multiscale Ultrahigh Resolution (MUR) imagery for the Sea Surface Temperature (SST) to address why the predictions are not as good as expected. The studies were carried out by means of two approaches. The first approach is the non-linear fitting of a harmonic model keeping the frequencies as parameters pixel by pixel. The second approach is from fractal geometry. The three first q-order Rényi dimensions were computed. At the same time, an inverse fractal interpolation was carried out to compute the contraction factor. Both of them are related to the chaotic behavior of nature. This work has three relevant contributions. The correlation between the harmonic models and the SST data is quite poor in general, implying the low harmonicity, and low harmonic predictability, of the pixel-by-pixel time series. It is verified that the quasi-annual and quasi-semiannual waves have periods of about 420 and 210 days, respectively. The second one is the confirmation of the high complexity of the BMC area because the three Rényi dimensions are equal. This has the strong finding of the monofractality of the dynamic of the SST in the BMC. Finally, the contraction factor, one of the parameters of the fractal interpolation, is relatively high, implying the presence of highly complex internal structures in the SST temporal evolution.

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.