Wave spectrum analysis for southern Caspian Sea

The general form of spectrum S(ω)=Aω−pexp(−Bω−q) was used in the present study to mathematically describe the spectrum of the Caspian Sea waves, and its fit to observations was obtained by assigning different values to pair (p,q). For this purpose, five spectral models, including Donelan, Pierson-Moskowitz (PM), Krylov, Davidan, and Neumann were considered corresponding to (4,4), (5,4), (7,4), (6.5,5.5), and (6,2). In the first step, the default coefficients were found to lack the required accuracy, therefore, they were optimized. The performance comparison of these five models showed that the spectral width index (ν) provides a good insight into the performance of the models such that the Krylov model exhibited the highest accuracy for narrow spectra (ν < 0.4). For broad (ν > 0.45) and medium-width spectra (0.4 < ν < 0.45), the Donelan model and PM model yielded the best result, respectively. The highest rate of error was related to the Davidan model; therefore, it was excluded from the study. The Neumann model had similar performance to the Donelan model. Additionally, it was observed that the models are sometimes incapable of accurately estimating the spectrum in high frequency band. In validation of Philips (∼ω−5) and Toba (∼ω−4) theories, the frequency dependence of spectrum in the equilibrium range was found to take the form of ω−7, ω−4, and ω−5 in narrow, broad and medium-width spectra, respectively.