Forecast verification of a 3D model of the Mediterranean Sea. The use of discrete wavelet transforms and EOFs in the skill assessment of spatial forecasts

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provençal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The experiment lasts for nine weeks, and at each week sea surface temperature (SST) and sea level anomaly are assimilated. The quality assessment of the surface temperature is done in a spatio-temporal approach, to take into account the high complexity of the SST distribution. We focus on the multi-scale nature of oceanic processes using two powerful tools for spatio-temporal analysis, wavelets and Empirical Orthogonal Functions (EOFs). We apply two-dimensional wavelets to decompose the high-resolution model and observed SST into different spatial scales. The Ligurian Sea model results are compared to observations at each of those spatial scales, with special attention on how the assimilation affects the model behaviour. We also use EOFs to assess the similarities between the Mediterranean Sea model and the observed SST. The results show that the assimilation mainly affects the model large-scale features, whereas the small scales show little or no improvement and sometimes, even a decrease in their skill. The multiresolution analysis reveals the connection between large- and small-scale errors, and how the choice of the maximum correlation length of the assimilation scheme affects the distribution of the model error among the different spatial scales.     

Multicomponent decomposition of a time-varying acoustic Doppler signal generated by a passing railway vehicle using Complex Shifted Morlet Wavelets

Complex Shifted Morlet Wavelets (CSMW) present a number of advantages, since the concept of shifting the Morlet wavelet in the frequency domain allow the simultaneous optimal selection of both the wavelet center frequency and the wavelet bandwidth. According to the proposed method, a cluster of CSMW wavelets is used, covering appropriate ranges in the frequency domain. Then, instead of directly processing the instantaneous frequency of each CSMW, an invariance approach is used to indirectly recover the individual harmonic components of the signal. This invariance approach is based actually on the same rotational approach, using the same matrix properties, which consists the core of the well known ESPRIT algorithm. Moreover, the DESFRI (DEtection of Source Frequencies via Rotational Invariance) approach is introduced to support the proposed CSMW method to semi-automated selection of the center frequency of the applied Morlet window. This approach is based on the singular values that are extracted as an intermediate product of the proposed decomposition process. By the application of the method in a multi-component synthetic signal a way to select the critical parameters of the Morlet wavelet, is investigated. The method is further tested on a time-varying acoustic Doppler signal generated by a passing railway vehicle, indicating promising results for the estimation of the variable instantaneous frequency and the multi-component decomposition of it.