Wave Analysis in the Mexican Caribbean: Spectral Consistency and Parameter Optimization

Abstract The Caribbean Sea, a semi-enclosed basin, exhibits wave dynamics where the evolution of wave spectra from deep waters to nearshore regions changes slightly, with energy becoming more concentrated around the peak period despite shoaling processes. This study optimizes the JONSWAP formulation to better represent the Mexican Caribbean coast by refining two parameters: the scaling parameter exponent $$\alpha \left( {x_{b} } \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mfenced> </mml:mrow> </mml:math> (adjusted from 0.22 to 0.18) and the empirical exponent of the peak frequency $$f_{p}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> (modified from 0.33 to 0.29). Using NOAA buoy data and wave-wind coherence analysis, the optimized model, JONSWAP-CAR, significantly improved wave parameter estimations, reducing the average error for $$H_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> from 1.01 m to 0.2114 m and for $$T_{p} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> from 4.64 s to 0.87 s. Spectral comparisons showed consistent wave characteristics along the coastline, even in areas influenced by Cozumel Island. These findings highlight the benefits of tailoring global wave models to regional conditions, offering improved tools for wave modeling and coastal management in the Caribbean Sea.