# Simulation Model of Wind and Wave-Induced Doppler Shifts for Multi-Band Radars and Its Application in SAR-Based Ocean Current Inversion

## TL;DR

This paper introduces a new model to simulate Doppler shifts caused by wind and waves in multi-band radars, improving the accuracy of ocean current measurements using SAR data.

## Contribution

A multi-band Doppler shift simulation model is developed and validated across C-, Ka-, and Ku-bands for improved ocean current inversion.

## Key findings

- The model shows high correlation (0.97, 0.93, 0.98) with existing CDOP, KaDOP, and KuMOD models.
- Ocean current retrieval using the model achieves a mean absolute error of 0.26 m/s against HF radar measurements.
- The model is applicable across multiple radar bands and improves inversion accuracy for SAR-based ocean current retrieval.

## Abstract

What are the main findings?
Developed a multi-band applicable simulation model for wind and wave-induced Doppler shift, which shows correlation coefficients of 0.97, 0.93, and 0.98 relative to the CDOP, KaDOP and KuMOD models, respectively.Using the proposed model, ocean currents retrieved based on Sentinel-1 ocean (OCN) data achieve a mean deviation (MD) of −0.04 m/s, a mean absolute error (MAE) of 0.26 m/s, and a root-mean-square error (RMSE) of 0.32 m/s against high-frequency (HF) radar measurements.

Developed a multi-band applicable simulation model for wind and wave-induced Doppler shift, which shows correlation coefficients of 0.97, 0.93, and 0.98 relative to the CDOP, KaDOP and KuMOD models, respectively.

Using the proposed model, ocean currents retrieved based on Sentinel-1 ocean (OCN) data achieve a mean deviation (MD) of −0.04 m/s, a mean absolute error (MAE) of 0.26 m/s, and a root-mean-square error (RMSE) of 0.32 m/s against high-frequency (HF) radar measurements.

What are the implications of the main findings?
The proposed model can be further applied to retrieve ocean currents based on radar data of different frequency bands, providing an effective approach for removing the wind and wave-induced Doppler shift across varying bands.

The proposed model can be further applied to retrieve ocean currents based on radar data of different frequency bands, providing an effective approach for removing the wind and wave-induced Doppler shift across varying bands.

The wind and wave-induced Doppler shift (WDS) significantly affects the accuracy of ocean surface current fields retrieved from synthetic aperture radar (SAR). Understanding how different factors affect WDS is therefore essential for improving current inversion accuracy. Existing studies have predominantly focused on single-band WDS, mainly in the C-band, while investigations across other radar bands remain limited. In this study, we simulate the dynamic ocean surface height field and velocity field, and the radar backscatter from the ocean surface that includes the effect of breaking waves. Based on the Doppler shift theory of ocean surface motion proposed by Chapron, we develop a WDS simulation model with potential applicability to multiple radar bands. The performance of the model is verified by comparing its results with those from the CDOP, KaDOP and KuMOD models. The correlation coefficient between the proposed model and the CDOP model reaches 0.97, with mean deviation (MD), mean absolute error (MAE), and root-mean-square error (RMSE) not exceeding −2.07 Hz, 3.35 Hz, and 4.49 Hz, respectively. For comparisons with the KaDOP model, the correlation coefficient is 0.93, and the MD, MAE, and RMSE are within −21.23 Hz, 42.37 Hz, and 52.20 Hz. For comparisons with the KuMOD model, the correlation coefficient is 0.98, and the MD, MAE, and RMSE are within −2.60 Hz, 7.13 Hz, and 9.08 Hz. These results demonstrate that the proposed model can effectively predict the WDS for both C-, Ka-, and Ku-band radar returns. Furthermore, we investigate the impacts of radar parameters, including frequency band, polarization, and incidence angle, as well as wind field forcing on WDS, showing the model’s applicability across multiple radar bands. Finally, the proposed model is applied to current retrieval using Sentinel-1 ocean (OCN) data, and the inversion accuracy is assessed against collocated high-frequency (HF) radar observations. The MD, MAE, and RMSE of the current retrieval using the proposed model are −0.04 m/s, 0.26 m/s, and 0.32 m/s, which are close to those from the CDOP-based retrieval (MD, MAE, and RMSE of −0.02 m/s, 0.25 m/s, and 0.30 m/s). These results demonstrate that the proposed model performs well in ocean surface current inversion and shows potential for further application to ocean current retrieval based on radar data across different frequency bands.