Listening for rain: Principal component analysis and linear discriminant analysis for broadband acoustic rainfall detection

Rain falling on the ocean creates acoustic signals. Ma and Nystuen [(2005). J. Atmos. Oceanic Technol. 22, 1225–1248] described an algorithm that compares three narrowband “discriminant” frequencies to detect rain. In 2022, Trucco, Bozzano, Fava, Pensieri, Verri, and Barla [(2022). IEEE J. Oceanic Eng. 47(1), 213–225] investigated rain detection algorithms that use broadband spectral data averaged over 1 h. This paper implements a rainfall detector that uses broadband acoustic data at 3-min time resolution. Principal Component Analysis (PCA) reduces the dimensionality of the broadband data. Rainfall is then detected via a Linear Discriminant Analysis (LDA) on the data's principal component projections. This PCA/LDA algorithm was trained and tested on 5 months of data recorded by hydrophones in a shallow noisy cove, where it was not feasible to average spectral data over 1 h. The PCA/LDA algorithm successfully detected 78 ± 5% of all rain events over 1 mm/h, and 73 ± 5% of all rain events over 0.1 mm/h, for a false alarm rate of $≈$ 1% in both cases. By contrast, the Ma and Nystuen algorithm detected 32 ± 5% of the rain events over 1.0 mm/h when run on the same data, for a comparable false alarm rate.