Prediction uncertainty of wind-generated noise spectra from wind speed

The prediction of wind-generated noise spectral levels at one frequency is typically based on a linear regression function, which is defined over the logarithm of the 10-m wind speed. However, despite its widespread success, the linear regression model does not pay attention to its prediction uncertainty because it makes point predictions. The main reasons for the uncertainty in the predicted value of the wind-generated noise level are that it cannot be uniquely determined by 10-m wind speed and its measurements may be corrupted by other sources of ambient noise. To quantify the uncertainty in predictions in this scenario, a Bayesian treatment of linear regression models and its associated predictive distribution are applied, making distribution predictions instead of point predictions. Once the predictive distribution for one frequency has been fixed, its linear variants are used to obtain predictive distributions for other frequencies. The data for the ocean ambient noise and 10-m wind speed are collected from two deep-water experiments, conducted in the South China Sea, and reanalysis data sets of the European Centre For Medium-Range Weather Forecasts, respectively. Empirical expressions for the predictive distribution of noise spectra (0.5-10 kHz) at wind speeds from 3.3 to 14 m/s have been developed. The results indicate decreasing uncertainties with an increasing wind speed.