Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ocean wave spectrum reconstruction from HF radar data and its application to wave height estimation

Kaede Watanabe, Toshiaki Yachimura, Tsubasa Terada, Hiroshi Kameda, Ryuhei Takahashi, Hiroshi Suito

TL;DR

This work tackles reconstructing the ocean wave spectrum $S(p,q)$ from HF radar–derived second-order Doppler data $\sigma_2$ to enable real-time wave height estimation. It casts the inverse problem as a nonnegative sparse regularization of a Tikhonov functional, derives the Fréchet derivative and gradient, and proves a stability bound $\|u^{\delta}_{\lambda,\alpha}-u^\dagger\|_X \le c\delta^{1/4}$ under suitable parameter choices. Numerical tests using a kataoka2016–based directional spectrum model show accurate recovery of $S(p,q)$ and robust estimation of the significant wave height $H_s$ despite perturbations. A real-data application to NOWPHAS measurements demonstrates potential improvements over Barrick-based methods, indicating practical value for coastal wave-height monitoring.

Abstract

Real-time estimation of ocean wave heights using high-frequency (HF) radar has attracted great attention. This method offers the benefit of easy maintenance by virtue of its ground-based installation. However, it is adversely affected by issues such as low estimation accuracy. As described herein, we propose an algorithm based on the nonnegative sparse regularization method to estimate the energy distribution of the component waves, known as the ocean wave spectrum, from HF radar data. After proving a stability estimate of this algorithm, we perform numerical simulations to verify the proposed method's effectiveness.

Ocean wave spectrum reconstruction from HF radar data and its application to wave height estimation

TL;DR

This work tackles reconstructing the ocean wave spectrum from HF radar–derived second-order Doppler data to enable real-time wave height estimation. It casts the inverse problem as a nonnegative sparse regularization of a Tikhonov functional, derives the Fréchet derivative and gradient, and proves a stability bound under suitable parameter choices. Numerical tests using a kataoka2016–based directional spectrum model show accurate recovery of and robust estimation of the significant wave height despite perturbations. A real-data application to NOWPHAS measurements demonstrates potential improvements over Barrick-based methods, indicating practical value for coastal wave-height monitoring.

Abstract

Real-time estimation of ocean wave heights using high-frequency (HF) radar has attracted great attention. This method offers the benefit of easy maintenance by virtue of its ground-based installation. However, it is adversely affected by issues such as low estimation accuracy. As described herein, we propose an algorithm based on the nonnegative sparse regularization method to estimate the energy distribution of the component waves, known as the ocean wave spectrum, from HF radar data. After proving a stability estimate of this algorithm, we perform numerical simulations to verify the proposed method's effectiveness.
Paper Structure (10 sections, 6 theorems, 66 equations, 11 figures, 1 table, 1 algorithm)

This paper contains 10 sections, 6 theorems, 66 equations, 11 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Elimination of the delta function
  4. Nonnegative sparse regularization
  5. Fréchet derivative of Tikhonov functional and stability estimate
  6. Numerical experiments
  7. Model wave spectrum and algorithm
  8. Validation of the algorithm
  9. Wave height estimation using real data
  10. Conclusions

Key Result

Proposition 1

Assume $S \in H^1(\mathbb{R}^2)$. Then, the operator $A$ can be expressed as Therein, $f_{m_1, m_2}(p, q) :=m_1 \sqrt{gk_1} + m_2 \sqrt{gk_2}$, and $ds$ is the surface measure on $f_{m_1,m_2}^{-1}(\omega)$. Furthermore, $A: H^1(\mathbb{R}^2) \to L^2(K)$.

Figures (11)

  • Figure 1: Example of a Doppler spectrum observed using HF radar. The peaks appearing symmetrically on both sides correspond to the first-order Doppler spectrum, whereas the remaining parts correspond to the second-order Doppler spectrum.
  • Figure 3: Relative error of reconstructed wave spectrum
  • Figure 4: Relative error of significant wave heights
  • Figure 6: Summary of estimated wave heights. The black line represents the true values, whereas the red line represents the wave heights estimated using the proposed method. The other lines correspond to estimations obtained using methods based on the Barrick method.
  • Figure : ($A$) True wave spectrum
  • ...and 6 more figures

Theorems & Definitions (11)

  • Proposition 1
  • proof
  • Theorem 2: Muoi2018
  • Proposition 3
  • proof
  • Corollary 4
  • proof
  • Theorem 5
  • proof
  • Proposition 6
  • ...and 1 more