the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
An EMD-PSO-LSSVM hybrid model for significant wave height prediction
Abstract. Accurate and significant wave height prediction with a couple of hours of warning time should offer major safety improvements for coastal and ocean engineering applications. However, significant wave height phenomenon is nonlinear and nonstationary, which makes any prediction simulation a non straightforward task. The aim of the research presented in this paper is to improve predicted significant wave height via a hybrid algorithm. Firstly, empirical mode decomposition (EMD) is used to preprocess the nonlinear data, which are decomposed into several simple signals. Then, least square support vector machine (LSSVM) with nonlinear learning ability is used to predict the significant wave height, and particle swarm optimization (PSO) is implemented to automatically perform the parameter selection in LSSVM modeling. The EMD-PSO-LSSVM model is used to predict the significant wave height for 1, 3 and 6 hours leading times of two stations in the offshore and deep-sea areas of the North Atlantic Ocean. The results show that the EMD-PSO-LSSVM model can remove the lag in the prediction timing of the single prediction models. Furthermore, the prediction accuracy of the EMD-LSSVM model that has not been optimized in the deep-sea area has been greatly improved, an improvement of the prediction accuracy of Coefficient of determination (R2) from 0.991, 0.982 and 0.959 to 0.993, 0.987 and 0.965, respectively, has been observed. The proposed new hybrid model shows good accuracy and provides an effective way to predict the significant wave height for the deep-sea area.
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Interactive discussion
Status: closed
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RC1: 'Comment on os-2021-2', Anonymous Referee #1, 01 Mar 2021
This manuscript presents the use of a hybrid machine learning model to predict significant wave height. While the results of this study can be of importance, the paper in its current form needs to be significantly improved. The language does not meet the quality standards of scientific publications. There are several grammatical errors, incorrect use of words, vague statements, etc. In addition, I have some concerns about the methodology (see below). My recommendation is major revision.
Some examples of grammatical errors or format issues: (this is not meant to be exhaustive, please revise carefully the whole text)
Lines 21-23. “Furthermore..” please rephrase this sentence as it does not read well.
Line 103: “Ocean wave time series is a kind of complicated nonlinear…” “kind of” is usually not used in scientific writing
Line 117 “kind of natural oscillatory mode”
Line 159: “can be got by” this is incorrect
Line 239 “human experts have performed this task” human experts??
Line 245 “As can be seen”
Other technical issues:
Line 73: “Significant wave height is a complicated, nonlinear, dynamic system” This is not accurate. Significant wave height is not a system but a variable or parameter to characterize ocean waves, among others. Please correct.
There are two Table 3 (page 7 and 9)
How many hidden layers are used in the configurations of the three single models?
Line 170: “The lag is a type of prediction error that can also be found in other work on wave forecasting using single models” Please add corresponding reference.
Figure captions need to be improved. E.g. Figure 5: No need to repeat 41025 twice. Specify what one hour and three hours means. No need to discuss results in figure caption
Line 196: “The time series of ocean waves is” This is vague. Time series of what? Need to specify the parameter used to describe ocean waves. If significant wave height is used often, the authors might want to use Hs or SWH to not have to repeat it all the time.
Figure 7: time axis label missing
In terms of the methodology I am concerned about applying EMD to significant wave height time series, as it is not an oscillatory signal around zero like sea surface height would be. Significant wave height is a parameter obtained from a sea surface height time series by averaging the 1/3 largest waves or calculating the integral over the wave spectra. I wonder if it is appropriate to decompose significant wave height in IMF, which are oscillatory signals with zero-crossings, while significant wave height has no zero-crossing and it is, by definition, non-negative.
My understanding is that the model only considers 5 h of data to predict the following 1 to 3 h. physically speaking the evolution of waves very much depend on surface winds. Shouldn’t the model also consider information about surface winds as an input parameter?
Citation: https://doi.org/10.5194/os-2021-2-RC1 -
AC1: 'Reply on RC1', Haohao Du, 06 Mar 2021
Thank you very much for your comments. We will correct the grammar issue in the next version of the manuscript. Next, we will answer a few questions you raised.
How many hidden layers are used in the configurations of the three single models?
Reply: For this question, we have shown in Table 3. Parameter of three single models. The number of hidden layers is all 10.
In terms of the methodology I am concerned about applying EMD to significant wave height time series, as it is not an oscillatory signal around zero like sea surface height would be. Significant wave height is a parameter obtained from a sea surface height time series by averaging the 1/3 largest waves or calculating the integral over the wave spectra. I wonder if it is appropriate to decompose significant wave height in IMF, which are oscillatory signals with zero-crossings, while significant wave height has no zerocrossing and it is, by definition, non-negative.
Reply: The purpose of EMD is to continuously extract the components of various scales that make up the original signal from high frequency to low frequency. Then the order of the characteristic mode functions obtained by decomposition is arranged in order of frequency from high to low, that is, the highest frequency component is obtained first. Then it is the sub-high frequency, and finally a residual component with a frequency close to 0 is obtained. In this article, we only use EMD to simplify the input, so as to better improve the prediction accuracy.
My understanding is that the model only considers 5 h of data to predict the following 1 to 3 h. physically speaking the evolution of waves very much depend on surface winds. Shouldn’t the model also consider information about surface winds as an input parameter?
Reply: Many researchers have proposed many methods for predicting the significant wave height, and the data input is also different, but most of them use the historical significant wave height as the input. Of course, your suggestion is very helpful to us. The next thing we have to do is to consider more inputs to further improve the prediction accuracy.
Finally, thank you again for your suggestions.
Citation: https://doi.org/10.5194/os-2021-2-AC1
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AC1: 'Reply on RC1', Haohao Du, 06 Mar 2021
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RC2: '关于 os-2021-2 的评论', Anonymous Referee #2, 29 Mar 2021
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å¼å¾æ³¨æçæ¯ï¼æ¬æéè¦æä¸é¨ææ¯è±è¯ç¼è¾ç人ç¼è¾ï¼ç¹å«æ³¨æè±è¯è¯æ³ãæ¼ååå¥åç»æãæ¤å¤ï¼æäºå¥åçæ ç¹ç¬¦å·è¢«æ»¥ç¨ã"å°EMDåå·100ä¸LSSVM模åéææ¯å¢å¼ºæ³¢ç´è°è¯çéè¦æ¹æ³ã"ï¼ç¬¬2页第101è¡ï¼
Citation: https://doi.org/10.5194/os-2021-2-RC2 -
AC3: 'Reply on RC2', Haohao Du, 21 Apr 2021
Thank you very much for your comment.
Citation: https://doi.org/10.5194/os-2021-2-AC3
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AC3: 'Reply on RC2', Haohao Du, 21 Apr 2021
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RC3: 'Comment on os-2021-2', Anonymous Referee #2, 30 Mar 2021
This paper presents a hybrid algorithm to improve predicted significant wave height, and provides an effective way to predict the significant wave height for the deep-sea area. The conclusion is very attractive and constructive. I think this paper could be published after technical corrections.
It is noted that this paper needs editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure. In addition, the punctuation of some sentences is misused. “Integrating an EMD model 100 with an LSSVM model is an important way for enhancing the wave hright prediciton..”(Line 101 on page 2)
Citation: https://doi.org/10.5194/os-2021-2-RC3 -
AC2: 'Reply on RC3', Haohao Du, 30 Mar 2021
Thank you very much for your comment. We will carefully check English grammar, spelling, sentence structure and punctuation again.
Citation: https://doi.org/10.5194/os-2021-2-AC2
-
AC2: 'Reply on RC3', Haohao Du, 30 Mar 2021
Interactive discussion
Status: closed
-
RC1: 'Comment on os-2021-2', Anonymous Referee #1, 01 Mar 2021
This manuscript presents the use of a hybrid machine learning model to predict significant wave height. While the results of this study can be of importance, the paper in its current form needs to be significantly improved. The language does not meet the quality standards of scientific publications. There are several grammatical errors, incorrect use of words, vague statements, etc. In addition, I have some concerns about the methodology (see below). My recommendation is major revision.
Some examples of grammatical errors or format issues: (this is not meant to be exhaustive, please revise carefully the whole text)
Lines 21-23. “Furthermore..” please rephrase this sentence as it does not read well.
Line 103: “Ocean wave time series is a kind of complicated nonlinear…” “kind of” is usually not used in scientific writing
Line 117 “kind of natural oscillatory mode”
Line 159: “can be got by” this is incorrect
Line 239 “human experts have performed this task” human experts??
Line 245 “As can be seen”
Other technical issues:
Line 73: “Significant wave height is a complicated, nonlinear, dynamic system” This is not accurate. Significant wave height is not a system but a variable or parameter to characterize ocean waves, among others. Please correct.
There are two Table 3 (page 7 and 9)
How many hidden layers are used in the configurations of the three single models?
Line 170: “The lag is a type of prediction error that can also be found in other work on wave forecasting using single models” Please add corresponding reference.
Figure captions need to be improved. E.g. Figure 5: No need to repeat 41025 twice. Specify what one hour and three hours means. No need to discuss results in figure caption
Line 196: “The time series of ocean waves is” This is vague. Time series of what? Need to specify the parameter used to describe ocean waves. If significant wave height is used often, the authors might want to use Hs or SWH to not have to repeat it all the time.
Figure 7: time axis label missing
In terms of the methodology I am concerned about applying EMD to significant wave height time series, as it is not an oscillatory signal around zero like sea surface height would be. Significant wave height is a parameter obtained from a sea surface height time series by averaging the 1/3 largest waves or calculating the integral over the wave spectra. I wonder if it is appropriate to decompose significant wave height in IMF, which are oscillatory signals with zero-crossings, while significant wave height has no zero-crossing and it is, by definition, non-negative.
My understanding is that the model only considers 5 h of data to predict the following 1 to 3 h. physically speaking the evolution of waves very much depend on surface winds. Shouldn’t the model also consider information about surface winds as an input parameter?
Citation: https://doi.org/10.5194/os-2021-2-RC1 -
AC1: 'Reply on RC1', Haohao Du, 06 Mar 2021
Thank you very much for your comments. We will correct the grammar issue in the next version of the manuscript. Next, we will answer a few questions you raised.
How many hidden layers are used in the configurations of the three single models?
Reply: For this question, we have shown in Table 3. Parameter of three single models. The number of hidden layers is all 10.
In terms of the methodology I am concerned about applying EMD to significant wave height time series, as it is not an oscillatory signal around zero like sea surface height would be. Significant wave height is a parameter obtained from a sea surface height time series by averaging the 1/3 largest waves or calculating the integral over the wave spectra. I wonder if it is appropriate to decompose significant wave height in IMF, which are oscillatory signals with zero-crossings, while significant wave height has no zerocrossing and it is, by definition, non-negative.
Reply: The purpose of EMD is to continuously extract the components of various scales that make up the original signal from high frequency to low frequency. Then the order of the characteristic mode functions obtained by decomposition is arranged in order of frequency from high to low, that is, the highest frequency component is obtained first. Then it is the sub-high frequency, and finally a residual component with a frequency close to 0 is obtained. In this article, we only use EMD to simplify the input, so as to better improve the prediction accuracy.
My understanding is that the model only considers 5 h of data to predict the following 1 to 3 h. physically speaking the evolution of waves very much depend on surface winds. Shouldn’t the model also consider information about surface winds as an input parameter?
Reply: Many researchers have proposed many methods for predicting the significant wave height, and the data input is also different, but most of them use the historical significant wave height as the input. Of course, your suggestion is very helpful to us. The next thing we have to do is to consider more inputs to further improve the prediction accuracy.
Finally, thank you again for your suggestions.
Citation: https://doi.org/10.5194/os-2021-2-AC1
-
AC1: 'Reply on RC1', Haohao Du, 06 Mar 2021
-
RC2: '关于 os-2021-2 的评论', Anonymous Referee #2, 29 Mar 2021
æ¬ææåºäºä¸ç§æ··åç®æ³ï¼ç¨äºæé«é¢æµçæ¾èæ³¢é«åº¦ï¼å¹¶ä¸ºé¢æµæ·±æµ·å°åºæ¾èæ³¢é«æä¾äºæææ¹æ³ãè¿ä¸ªç»è®ºé常æå¸å¼åå建设æ§ãæ认为æ¬æå¯ä»¥å¨ææ¯æ´æ£åå表ã
å¼å¾æ³¨æçæ¯ï¼æ¬æéè¦æä¸é¨ææ¯è±è¯ç¼è¾ç人ç¼è¾ï¼ç¹å«æ³¨æè±è¯è¯æ³ãæ¼ååå¥åç»æãæ¤å¤ï¼æäºå¥åçæ ç¹ç¬¦å·è¢«æ»¥ç¨ã"å°EMDåå·100ä¸LSSVM模åéææ¯å¢å¼ºæ³¢ç´è°è¯çéè¦æ¹æ³ã"ï¼ç¬¬2页第101è¡ï¼
Citation: https://doi.org/10.5194/os-2021-2-RC2 -
AC3: 'Reply on RC2', Haohao Du, 21 Apr 2021
Thank you very much for your comment.
Citation: https://doi.org/10.5194/os-2021-2-AC3
-
AC3: 'Reply on RC2', Haohao Du, 21 Apr 2021
-
RC3: 'Comment on os-2021-2', Anonymous Referee #2, 30 Mar 2021
This paper presents a hybrid algorithm to improve predicted significant wave height, and provides an effective way to predict the significant wave height for the deep-sea area. The conclusion is very attractive and constructive. I think this paper could be published after technical corrections.
It is noted that this paper needs editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure. In addition, the punctuation of some sentences is misused. “Integrating an EMD model 100 with an LSSVM model is an important way for enhancing the wave hright prediciton..”(Line 101 on page 2)
Citation: https://doi.org/10.5194/os-2021-2-RC3 -
AC2: 'Reply on RC3', Haohao Du, 30 Mar 2021
Thank you very much for your comment. We will carefully check English grammar, spelling, sentence structure and punctuation again.
Citation: https://doi.org/10.5194/os-2021-2-AC2
-
AC2: 'Reply on RC3', Haohao Du, 30 Mar 2021
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