MuSRFM: Multiple scale resolution fusion based precise and robust satellite derived bathymetry model for island nearshore shallow water regions using sentinel-2 multi-spectral imagery

The multi-spectral imagery based Satellite Derived Bathymetry (SDB) provides an efficient and cost-effective approach for acquiring bathymetry data of nearshore shallow water regions. Compared with conventional pixelwise inversion models, Deep Learning (DL) models have the theoretical capability to encompass a broader receptive field, automatically extracting comprehensive spatial features. However, enhancing spatial features by increasing the input size escalates computational complexity and model scale, challenging the hardware. To address this issue, we propose the Multiple Scale Resolution Fusion Model (MuSRFM), a novel DL-based SDB model, to integrate information of varying scales by utilizing temporally fused Sentinel-2 L2A multi-spectral imagery. The MuSRFM uses a Multi-scale Center-aligned Hierarchical Resampler (MCHR) to composite largescale multi-spectral imagery into hierarchical scale resolution representations since the receptive field gradually narrows its focus as the spatial resolution decreases. Through this strategy, the MuSRFM gains access to rich spatial information while maintaining efficiency by progressively aggregating features of different scales through the Cropped Aligned Fusion Module (CAFM). We select St. Croix (Virgin Islands) as the training/testing dataset source, and the Root Mean Square Error (RMSE) obtained by the MuSRFM on the testing dataset is 0.8131 m (with a bathymetric range of 0-25 m), surpassing the machine learning based models and traditional semi- empirical models used as the baselines by over 35 % and 60 %, respectively. Additionally, multiple island areas worldwide, including Vieques, Oahu, Kauai, Saipan and Tinian, which exhibit distinct characteristics, are utilized to construct a real-world dataset for assessing the generalizability and transferability of the proposed MuSRFM. While the MuSRFM experiences a degradation in accuracy when applied to the diverse real-world dataset, it outperforms other baseline models considerably. Across various study areas in the real-world data- set, its RMSE lead over the second-ranked model ranges from 6.8 % to 38.1 %, indicating its accuracy and generalizability; in the Kauai area, where the performance is not ideal, a significant improvement in accuracy is achieved through fine-tuning on limited in-situ data. The code of MuSRFM is available at https://github.com/ qxm1995716/musrfm.