Why Are the High Frequency Structures of the Sea Surface Temperature in the Brazil–Malvinas Confluence Area Difficult to Predict? An Explanation Based on Multiscale Imagery and Fractal Geometry

Abstract

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.