Wind Waves Inversion Based on Wind Speeds and Wind Wave Mean Periods

Wind speed and wind fetch are two critical factors influencing the development of wind waves. However, due to the challenges in acquiring accurate wind fetch, most existing empirical models for retrieving significant height of wind waves (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i>) primarily consider wind speed while neglecting the influence of wind fetch, resulting in relatively low inversion accuracy. Given the strong correlation between wind wave mean period and wind fetch, this study indirectly accounted for the impact of wind fetch on wind wave development by incorporating wind wave mean period, and developed two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> inversion models based on the Elfouhaily spectrum and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i>, wind speeds and wind wave mean periods provided by ECMWF, which are defined as Model 1 (M1) and Model 2 (M2), respectively. The two developed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> inversion models were evaluated using multiple datasets, including sea surface data provided by ECMWF and NDBC, GNSS buoy measurements, wind speeds provided by meteorological station, and airborne SAR imagery. The results demonstrate that both models achieve high inversion accuracy for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> in most scenarios, with M2 exhibiting particularly robust stability, and the correlation coefficients between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> retrieved by M2 and the reference <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> are greater than 0.95, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAE</i> are approximately 0.19m and 0.13m, respectively. Furthermore, when developing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i> inversion model, this study enhanced the inversion accuracy by incorporating the wind wave mean period to indirectly account for wind fetch effects on wind wave development, thereby providing a novel research direction for obtaining high-precision <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH_ww</i>.