the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2024
An Improvement of the One-dimensional Ocean Wave Description based on SWIM Observations
Abstract. The one-dimensional ocean wave spectra (1D spectra) describing the total energy of the ocean waves are vital for providing ocean surface roughness information in remote sensing simulations. Most existing wave spectrum models deviate from real ocean surface descriptions due to limitations of observation methods and approximation in theories applied to generating them. In this research, the widely applied Goda and Elfouhaily spectra in their 1-D form are compared with the remote sensing products from the Surface Waves Investigation and Monitoring instrument (SWIM) on-board the China France Oceanography Satellite (CFOSAT). Differences between models and the measurements are addressed, then the causes are analyzed and concluded in terms of sea states. Then, a Combined spectrum (C spectrum) considering varied sea states is proposed as a closer model to the observations of the real sea, where parameterization of the spectral peak enhancement factor (γ) is achieved by the inverse wave age and wave steepness for multiple sea states. Then the specific values of the all-state sea are obtained from SWIM observations. The validation of the C spectrum is achieved by comparisons with SWIM measurements not utilized during the model establishment, and with buoy measurements. The difference index (DI) and the R-squared (R2), are calculated for evaluation of the results, indicating that the C spectrum demonstrates closer fitting to the SWIM and buoy measurements than both Goda and Elfouhaily spectra. The DI and R2 for the C spectrum are compared to the Goda spectrum, which is closer to SWIM measurements than E spectrum, and values are 0.780 and 0.909 respectively. Results suggest the C spectrum is suitable for providing information required for remote sensing applications. Further research would be focusing on implementing description in different azimuthal directions.
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CC1: 'Comment on amt-2024-75', Wenming Lin, 07 Jul 2024
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This paper combines the widely used Goda and Elfouhaily spectra in order to improve the one-dimensional wave spectrum. The SWIM data are used for both model development and result verification. The NDBC buoy data is used for validation as well. Based on the evaluation of DI and R2 parameters, it shows that the proposed spectrum (C spectrum) generally performs better than G/E spectrum in term of characterizing the wave energy distribution. The contents of this paper are clear, and the steps of the methodologies are well described. The manuscript is generally well written, though the English is not native and needs polishing.
- Title: “An Improved One-dimensional Ocean Wave Description based on SWIM Observations” may be more concise
- Structure:
a). Keep concise on the description of G/E spectra, and highlight the C spectrum. Particularly, please clarify how you fit the (23)-(24) and (26) – (28).
b). in the result section, you may present the case study (3.4.2) firstly and then illustrate the general verifications.
- Regarding the combination of C spectrum, it’s not a surprise that C spectrum generally agrees better with G spectrum than E spectrum. Is there any case showing that the old G/E spectra may be superior to C spectrum? Why?
Minor comments:
- Do you fit the model using SWIM data, and then calculate R2 and DI for the same wavelength bin as SWIM? Please clarify the effective range of SWIM wavelength in the text, as well the range of integration in Eqs. (21) – (23).
- Page 1, lines 15-16: two “then” appears in the two sentences.
- Page 1, lines 22-23: “The DI and R2 for the C …. 0.909 respectively”. It is not necessary to introduce the detailed numbers here. Lines 24-25, “Further research would … directions.” Remove this sentence.
- Introduction, there are many other wave spectra not reviewed in this section, such as Huang’s model.
- Page 2, lines 57-58, “validation of the C spectrum … of the sea surface.” Conclusion should go to the conclusion section.
- Page 3, lines 73-74: “… describing the inverted transfer of wave …”. This sentence is vague, please rephrase.
- Page 5, lines 127-132. “In comparsion …. observations well.” Are the descriptions the results of this manuscript or previous studies?
- Page 7, line 185, “the Surface Waves Investigation and Monitoring (SWIM) carried”. Not necessary to write abbreviation again here. BTW, which version of SWIM data is used in this study.
- Page 8, lines 200 – 201, informal numbers in the text.
- You may use SWH instead of H1/3 in the text.
- Page 11, figure 4, I don’t see the variation of H1/3 in the caption or in this figure. Please clarify.
- Remove “This is” in the captions of Figures 7-10.
- Page 15, line 325, this sentence is vague, please rephrase.
Citation: https://doi.org/10.5194/amt-2024-75-CC1 -
AC1: 'Reply on CC1', Xingou Xu, 13 Aug 2024
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Thanks for the comments and suggestions!
Please see the attached file for the replies. The revised manuscript will be provided later, following the revision procedures.
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CC2: 'Comment on amt-2024-75', Ping Chen, 24 Mar 2025
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- On page 22, in the third step, what is the specific process of data screening based on the gamma parameter? How are Hs and kp in the empirical spectrum obtained? Are they directly calculated from the SWIM spectrum data?
The Hs data of the SWIM spectrum is derived from the Hs at the nadir point.
The SWIM spectrum data exhibits obvious spurious peaks and the surfbeat effect under low to medium sea states. Note that these are two different non - linear effects. Therefore, the spectrum data under such sea states is incorrect and cannot be used as reference spectrum data. Or the wave parameters kp and other conclusions obtained using these spectra as reference data are unreliable. - On page 33, in Figure 3 - 9, is the SWIM spectrum the average of multiple samples?
Due to the statistical fluctuations of the SWIM spectrum, even under the same sea surface conditions, the kp corresponding to the SWIM - measured spectrum still varies. Directly averaging the spectra will lead to a decrease in the spectral peak and an increase in the spectral width. Therefore, the common practice is to perform wavenumber - normalized spectral averaging. A detailed description of this method can be found in Ref. [52]. - Because the SWIM spectrum data has its own problems under low to medium sea states, it is not suitable to use SWIM data as reference data to establish an empirical spectrum model.
Citation: https://doi.org/10.5194/amt-2024-75-CC2 - On page 22, in the third step, what is the specific process of data screening based on the gamma parameter? How are Hs and kp in the empirical spectrum obtained? Are they directly calculated from the SWIM spectrum data?
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RC1: 'Comment on amt-2024-75', Anonymous Referee #1, 04 Apr 2025
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The manuscript proposes a combined one-dimensional spectrum of ocean surface waves, with wavelengths ranging from swell to wind wave scales, to improve measurement predictions compared to existing models. The model is built using SWIM satellite measurements as input data, and validation is performed using buoy data and a separate set of SWIM measurements. Some parameters and comparison results should be revised.
- Page 5, lines 115 through 125: The authors compare G spectrum and E spectrum predictions of SWIM measurements and define specific wavenumber intervals where each estimation is in agreement with the observed data. Additional to that information, a visual inspection of the predictions against measurements would be helpful. While the method section describes the SWIM dataset (lines 185 - 200), it is unclear how the wavenumbers ranging from 31 m to 209 m were resolved. Providing a time series of SWIM measurements, along with sampling rate and Nyquist wavenumber and frequency, would clarify the analysis. Note that in the section 3.1.2 (line 205), the SWIM measurement range is stated as 0.01–0.2 rad/m⁻¹, but this comes much after than the initial description of the SWIM dataset.
- Equation 20: It can be either written as H1/3 or Hs, it is redundant to use both.
- Equation 23 and 24: The coefficient fit formulas do not match with their corresponding graphs on Figure 2; are those reversed?
- Line 234: Wave steepness range should be 0.0115, not 0.015.
- Line 249: The variable should be denoted as kp, not kp.
- Line 252: What is the exact definition of a height spectrum? Is it wave height spectrum or wave elevation spectrum which is H/2?
- Line 256 with relation to the Figure 4: It is written that “the trend of change is almost identical to the G spectrum, with the spectral peak in the C spectrum slightly smaller than that in the G spectrum” but the G spectrum results are not demonstrated.
- The Figure 4 caption describes spectrum results at different significant wave heights, while the figure legends display wave steepness values and wave age. Although wave steepness is directly related to wave height, the caption and legend should use the same parameter for clarity. Additionally, since wave age remains constant throughout Figure 4, it does not need repetition in each legend entry.
- Figure 5: The previous comment applies to this figure as well. Both wave age and wave steepness change here due to variations in peak wavenumber, not wind speed. For clarity, the legend should show only the varying parameter (peak wavenumber or wave steepness) rather than listing all dependent variables such as wave age.
- Figure 6: The only varying parameter is wind speed yet the legend does not indicate any wind speed variation. Unlike Figure 5, where wave ages vary due to peak wavenumber changes, here they vary due to wind speed changes. The figure should clearly indicate which parameter is being varied.
- Figure 8a: It is hard to see the probability density variations. the colorbar for all plots of figure 8 should be in similar range so that we can better see the comparison.
- The headings of Table 1: “The C spectrum better than the G/E spectrum” is unclear. What does DI and R values for C spectrum better than E spectrum mean?
- Table 2: The previous comment applies to this table as well.
- Figure 11: Height spectra (Elevation spectra?) y label units are missing. Is it normalized?
Citation: https://doi.org/10.5194/amt-2024-75-RC1
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