# Estimating tidal constituents in shallow waters from satellite altimetry using a 2D hydrodynamic model with nonlinear tide-surge interactions

## TL;DR

A new method improves tidal estimates in shallow waters by using a 2D model that accounts for nonlinear tide-surge interactions, reducing water level variability.

## Contribution

A novel method for estimating tidal constituents in shallow waters using a 2D hydrodynamic model with nonlinear tide-surge interactions.

## Key findings

- The method reduced residual water level standard deviations in shallow waters from 11 cm to 5 cm.
- The method outperformed existing models in shallow waters but performed slightly worse in deep waters.
- The estimated total tidal error at satellite crossovers was about 1.5 cm.

## Abstract

Tidal models that incorporate satellite altimeter data have historically shown discrepancies in accuracy between shallow and deep marine environments. A recent study suggests that these differences may partly stem from neglecting the nonlinear tide-surge interactions in tidal analyses. In this study, we introduce a novel method for estimating tidal constituents from satellite altimeter data in shallow waters, leveraging a 2D hydrodynamic model that accounts for these nonlinear interactions. This approach substantially reduces the variance of unaccounted water level variability, thereby benefiting the estimation. A distinctive feature of our method is the treatment of prior model tidal constituents as stochastic, which helps manage the low temporal resolution of altimeter data by ensuring that unresolved tidal constituents are not updated. We tested our method in the data-rich northwest European continental shelf region, using the high-resolution 2D Dutch Continental Shelf Model version 7 (DCSM). Results show a substantial reduction in the standard deviations of residual water level time series in the shallow waters around Great Britain and in the German Bight, from 11 cm to 5 cm. In deep waters (>200 m), the median standard deviation decreased from 6.8 cm to 6.2 cm. When compared to state-of-the-art ocean tide and surge corrections from publicly available models, our method outperformed them in shallow waters (median standard deviation of 6.0 cm versus 7.5 cm), though the alternative products performed better in deep waters (median standard deviation of 5.5 cm versus 6.2 cm). An estimate of the accuracy at satellite crossovers resulted in an estimated total tidal error of about 1.5 cm (RSS VD). We acknowledge that comparisons in shallow waters are complicated, as alternative products do not account for nonlinear tide-surge interactions. Overall, the demonstration along-track tidal product developed in this study shows potential for improving the tidal representation in the DCSM model. In data-poor regions, the number of tidal constituents that can be reliably estimated using the method may be limited, and alternative strategies might be needed to evaluate the model’s uncertainty in representing tides.