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Article(id=1200450367885537800, tenantId=1146029695717560320, journalId=1149651085930835976, issueId=1200450365842903349, articleNumber=null, orderNo=null, doi=10.12284/hyxb2024049, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1708531200000, receivedDateStr=2024-02-22, revisedDate=1715270400000, revisedDateStr=2024-05-10, acceptedDate=null, acceptedDateStr=null, onlineDate=1764139270993, onlineDateStr=2025-11-26, pubDate=1719676800000, pubDateStr=2024-06-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1764139270993, onlineIssueDateStr=2025-11-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1764139270993, creator=13701087609, updateTime=1764139270993, updator=13701087609, issue=Issue{id=1200450365842903349, tenantId=1146029695717560320, journalId=1149651085930835976, year='2024', volume='46', issue='6', pageStart='1', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=0, articleOrder=1, issueType=-1, specialIssue=null, createTime=1764139270505, creator=13701087609, updateTime=1764139468823, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1200451197711806771, tenantId=1146029695717560320, journalId=1149651085930835976, issueId=1200450365842903349, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1200451197711806772, tenantId=1146029695717560320, journalId=1149651085930835976, issueId=1200450365842903349, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=14, endPage=25, ext={EN=ArticleExt(id=1200450368162361877, articleId=1200450367885537800, tenantId=1146029695717560320, journalId=1149651085930835976, language=EN, title=A multivariate wave forecasting model for the Zhoushan archipelago using Long Short-Term Memory deep neural networks, columnId=1194652705852465724, journalTitle=Haiyang Xuebao, columnName=Article, runingTitle=null, highlight=null, articleAbstract=

This study is based on the meteorological, oceanic, terrain and other physical quantity data covered by the observation points in the southern Zhoushan Islands from January 1, 2019 to December 31, 2021, and uses long short-term memory neural network (LSTM) to build deep learning wave forecast model. We explore the impact of the input-output sequence ratio and the number of input elements on the prediction performance of the model, realize the short-term forecast of the three elements of waves in the Zhoushan sea area, that is the significant wave height, the significant wave period and the propagation direction, and use the data during the 2022 typhoons “Hinnamnor” and “Muifa” to test the model’s prediction ability for extreme sea conditions. The research results show that the multi-element deep learning wave forecast model trained based on measured data has good prediction accuracy and stability, and can realize the prediction of extreme sea conditions. When the input-output sequence ratio is 1∶1, the model accuracy is higher. In non-extreme sea conditions, the three-element model with a prediction time of 1 hour accurately predicts significant wave height, significant wave period and direction, with Root Mean Squared Errors (RMSE) of 0.116 m, 0.569 s, and 24.583° respectively. In extreme sea conditions, the prediction RMSE for the significant wave height is 0.191 m. The increase in the number of input elements can further improve the model accuracy but also increase the training cost when the prediction time is long.

, correspAuthors=Yefei Bai, authorNote=null, correspAuthorsNote=null, copyrightStatement=Haiyang Xuebao, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Sangjun Zhou, Xiaoran Wei, Xinzhe Xie, Honghuan Zhi, Yifan Zhou, Zhengtao Zhu, Peiliang Li, Yefei Bai), CN=ArticleExt(id=1200450370439869071, articleId=1200450367885537800, tenantId=1146029695717560320, journalId=1149651085930835976, language=CN, title=基于长短时记忆神经网络的舟山海域多要素海浪预报模型, columnId=1149698756456657529, journalTitle=海洋学报, columnName=论文, runingTitle=null, highlight=null, articleAbstract=

本文以2019年1月1日至2021年12月31日舟山群岛南部外海观测点所涵盖的气象、海洋、地形等多种物理量数据为数据基础，使用长短时记忆（Long Short Term Memory，LSTM）神经网络搭建深度学习海浪预报模型，探讨输入输出序列比和输入要素数量对模型预测性能的影响，在舟山海域实现波浪三要素，即有效波高、有效波周期、传播方向的短时预报，并用2022年台风“轩岚诺”和“梅花”期间的数据检验模型对极端海况的预测能力。研究结果表明，根据实测数据所训练的多要素海浪预报模型具有较好的预测准确度和稳定性，能较好地实现对极端海况的预测，当输入输出序列比为1∶1时模型准确度较高，预报时长为1 h的三要素模型对于日常海况中有效波高、有效波周期和波向的预测均方根误差（Root Mean Squared Error，RMSE）分别为0.116 m、0.569 s和24.583°，对于极端海况中有效波高的预测RMSE为0.191 m，输入要素数量的增加可进一步提升模型准确度，但在预测时长较长时也会增加训练成本。

, correspAuthors=白晔斐, authorNote=null, correspAuthorsNote=
*白晔斐（1980—），男，内蒙古自治区呼和浩特市人，研究员，博士，主要从事海洋环境与海洋灾害领域的研究。E-mail：
, copyrightStatement=版权所有©《海洋学报》编辑部 2024
周桑君，魏笑然，谢歆哲，等. 基于长短时记忆神经网络的舟山海域多要素海浪预报模型[J]. 海洋学报，2024，46(6)：14–25Zhou Sangjun，Wei Xiaoran，Xie Xinzhe, et al. A multivariate wave forecasting model for the Zhoushan archipelago using Long Short-Term Memory deep neural networks[J]. Haiyang Xuebao，2024, 46(6)：14–25
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周桑君（1999—），女，浙江省东阳市人，主要从事海洋预报工作。E-mail：

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ArticleFig(id=1200860900505809667, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=EN, label=Table 1, caption=

Statistical table of each element information of buoy station in the southern waters of Zhoushan from 2019 to 2021, (with a data sampling interval of 1 hour)

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观测要素单位最大值平均值标准差
有效波高米(m)7.000.980.49
有效波周期秒(s)15.106.001.48
波向度(°)360.00113.1560.46
1 h内最大10 min平均风速米/秒(m/s)20.506.173.07
1 h内最大10 min平均风向度(°)360.00171.29122.52
分钟内瞬时风速米/秒(m/s)25.006.583.44
分钟内瞬时风向度(°)360.00174.51123.57
平均波高米(m)3.000.560.25
平均周期秒(s)10.64.670.79
波数个/千米（km−1）325.00209.4835.48
谱有效波高米(m)7.601.180.54
谱平均波周期秒(s)9.904.960.85
峰值波周期秒(s)24.9011.357.57
峰值能量焦耳(J)91.500.852.40
ADCP流量立方米/秒(m3/s)41.285.162.36
流深米(m)27.9025.291.11
), ArticleFig(id=1200860900627444488, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=CN, label=表1, caption=

2019−2021年舟山南部海域浮标站各要素信息统计表（各数据采样间隔均为1 h）

, figureFileSmall=null, figureFileBig=null, tableContent=
观测要素单位最大值平均值标准差
有效波高米(m)7.000.980.49
有效波周期秒(s)15.106.001.48
波向度(°)360.00113.1560.46
1 h内最大10 min平均风速米/秒(m/s)20.506.173.07
1 h内最大10 min平均风向度(°)360.00171.29122.52
分钟内瞬时风速米/秒(m/s)25.006.583.44
分钟内瞬时风向度(°)360.00174.51123.57
平均波高米(m)3.000.560.25
平均周期秒(s)10.64.670.79
波数个/千米（km−1）325.00209.4835.48
谱有效波高米(m)7.601.180.54
谱平均波周期秒(s)9.904.960.85
峰值波周期秒(s)24.9011.357.57
峰值能量焦耳(J)91.500.852.40
ADCP流量立方米/秒(m3/s)41.285.162.36
流深米(m)27.9025.291.11
), ArticleFig(id=1200860900740690699, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=EN, label=Table 2, caption=

Table of training schemes for neural network models with different input-output sequence ratios

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方案编号输入序列长度/步比例输出序列长度（步）/预报时长（h）
M0111∶11
M0233∶1
M0355∶1
M0477∶1
M0531∶13
M0693∶1
M07155∶1
M08217∶1
M0961∶16
M10183∶1
M11305∶1
M12427∶1
M13121∶112
M14363∶1
M15485∶1
M16747∶1
M17181∶118
M18543∶1
M19705∶1
M20987∶1
M21241∶124
M22723∶1
M231205∶1
M241687∶1
M25481∶148
M261443∶1
M272405∶1
M283267∶1
), ArticleFig(id=1200860901927678732, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=CN, label=表2, caption=

神经网络模型不同输入输出序列比的训练方案表

, figureFileSmall=null, figureFileBig=null, tableContent=
方案编号输入序列长度/步比例输出序列长度（步）/预报时长（h）
M0111∶11
M0233∶1
M0355∶1
M0477∶1
M0531∶13
M0693∶1
M07155∶1
M08217∶1
M0961∶16
M10183∶1
M11305∶1
M12427∶1
M13121∶112
M14363∶1
M15485∶1
M16747∶1
M17181∶118
M18543∶1
M19705∶1
M20987∶1
M21241∶124
M22723∶1
M231205∶1
M241687∶1
M25481∶148
M261443∶1
M272405∶1
M283267∶1
), ArticleFig(id=1200860902078673680, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=EN, label=Table 3, caption=

Dataset segmentation

, figureFileSmall=null, figureFileBig=null, tableContent=
数据周期极端海况名称
2019年1月1日至2021年9月27日丹娜丝、利马奇、玲玲、米娜、黑格比、美莎克、烟花、灿都训练集
2021年9月28日至2021年12月31日无非极端海况测试集
2022年8月30日至2022年9月30日轩岚诺、梅花极端海况测试集
), ArticleFig(id=1200860902191919890, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=CN, label=表3, caption=

数据集划分

, figureFileSmall=null, figureFileBig=null, tableContent=
数据周期极端海况名称
2019年1月1日至2021年9月27日丹娜丝、利马奇、玲玲、米娜、黑格比、美莎克、烟花、灿都训练集
2021年9月28日至2021年12月31日无非极端海况测试集
2022年8月30日至2022年9月30日轩岚诺、梅花极端海况测试集
), ArticleFig(id=1200860902451966741, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=EN, label=Table 4, caption=

RMSE comparison of two types of models

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方案编号预报时长/h比例有效波高/m有效波周期/s波向/（°）
三要素七要素三要素七要素三要素七要素
M0111∶10.1160.1160.5690.56424.58324.296
M023∶10.1160.1130.5610.54824.87524.571
M035∶10.1140.1120.5640.54824.56824.882
M047∶10.1140.1140.5660.55024.97524.746
M0531∶10.1490.1460.7040.67831.56532.424
M063∶10.1500.1470.7010.67832.40932.086
M075∶10.1490.1470.7020.67632.86133.492
M087∶10.1490.1470.6990.68032.68232.526
M0961∶10.1810.1740.8500.81845.58144.824
M103∶10.1870.1730.8460.81147.46744.643
M115∶10.1860.1730.8360.81648.32045.477
M127∶10.1820.1730.8300.81847.83745.824
M13121∶10.2320.2230.9540.94348.26046.127
M143∶10.2310.2240.9440.93847.52146.212
M155∶10.2360.2300.9450.95148.18447.818
M167∶10.2350.2190.9410.93847.98249.797
M17181∶10.2550.2441.0221.02050.16851.799
M183∶10.2570.2541.0071.00549.48850.330
M195∶10.2580.2531.0011.00549.44251.580
M207∶10.2640.2601.0101.02651.35850.763
M21241∶10.2950.2961.1071.12054.43050.218
M223∶10.3080.2941.1051.07755.24752.649
M235∶10.3020.3031.0851.07854.85452.503
M247∶10.2920.3001.0951.08053.82352.248
M25481∶10.3720.3661.2181.21858.14353.154
M263∶10.3810.3731.2081.17057.36153.212
M275∶10.4080.3891.2841.24158.14554.375
M287∶10.3880.3621.2581.27857.73654.693
), ArticleFig(id=1200860902581990171, tenantId=1146029695717560320, journalId=1149651085930835976, articleId=1200450367885537800, language=CN, label=表4, caption=

两类模型的RMSE对比

, figureFileSmall=null, figureFileBig=null, tableContent=
方案编号预报时长/h比例有效波高/m有效波周期/s波向/（°）
三要素七要素三要素七要素三要素七要素
M0111∶10.1160.1160.5690.56424.58324.296
M023∶10.1160.1130.5610.54824.87524.571
M035∶10.1140.1120.5640.54824.56824.882
M047∶10.1140.1140.5660.55024.97524.746
M0531∶10.1490.1460.7040.67831.56532.424
M063∶10.1500.1470.7010.67832.40932.086
M075∶10.1490.1470.7020.67632.86133.492
M087∶10.1490.1470.6990.68032.68232.526
M0961∶10.1810.1740.8500.81845.58144.824
M103∶10.1870.1730.8460.81147.46744.643
M115∶10.1860.1730.8360.81648.32045.477
M127∶10.1820.1730.8300.81847.83745.824
M13121∶10.2320.2230.9540.94348.26046.127
M143∶10.2310.2240.9440.93847.52146.212
M155∶10.2360.2300.9450.95148.18447.818
M167∶10.2350.2190.9410.93847.98249.797
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基于长短时记忆神经网络的舟山海域多要素海浪预报模型
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周桑君 1, 2 , 魏笑然 1 , 谢歆哲 1, 2 , 支泓欢 1 , 周一帆 1 , 朱正涛 3 , 李培良 1, 2 , 白晔斐 1, 2, *
海洋学报 | 论文 2024,46(6): 14-25
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海洋学报 | 论文 2024, 46(6): 14-25
基于长短时记忆神经网络的舟山海域多要素海浪预报模型
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周桑君1, 2 , 魏笑然1, 谢歆哲1, 2, 支泓欢1, 周一帆1, 朱正涛3, 李培良1, 2, 白晔斐1, 2, *
作者信息
  • 1.浙江大学 海洋学院，浙江 舟山 316021
  • 2.浙江大学 海南研究院，海南 三亚 572025
  • 3.中国空气动力研究与发展中心 空天技术研究所，四川 绵阳 621000

    • 周桑君（1999—），女，浙江省东阳市人，主要从事海洋预报工作。E-mail：

通讯作者:

*白晔斐（1980—），男，内蒙古自治区呼和浩特市人，研究员，博士，主要从事海洋环境与海洋灾害领域的研究。E-mail：
A multivariate wave forecasting model for the Zhoushan archipelago using Long Short-Term Memory deep neural networks
Sangjun Zhou1, 2 , Xiaoran Wei1, Xinzhe Xie1, 2, Honghuan Zhi1, Yifan Zhou1, Zhengtao Zhu3, Peiliang Li1, 2, Yefei Bai1, 2, *
Affiliations
  • 1. Ocean College, Zhejiang University, Zhoushan 316021, China
  • 2. Hainan Institute of Zhejiang University, Zhejiang University, Sanya 572025, China
  • 3. Institute of Space Technology, China Aerodynamics Research and Development Center, Mianyang 621000, China
出版时间: 2024-06-30 doi: 10.12284/hyxb2024049
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摘要
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本文以2019年1月1日至2021年12月31日舟山群岛南部外海观测点所涵盖的气象、海洋、地形等多种物理量数据为数据基础，使用长短时记忆（Long Short Term Memory，LSTM）神经网络搭建深度学习海浪预报模型，探讨输入输出序列比和输入要素数量对模型预测性能的影响，在舟山海域实现波浪三要素，即有效波高、有效波周期、传播方向的短时预报，并用2022年台风“轩岚诺”和“梅花”期间的数据检验模型对极端海况的预测能力。研究结果表明，根据实测数据所训练的多要素海浪预报模型具有较好的预测准确度和稳定性，能较好地实现对极端海况的预测，当输入输出序列比为1∶1时模型准确度较高，预报时长为1 h的三要素模型对于日常海况中有效波高、有效波周期和波向的预测均方根误差（Root Mean Squared Error，RMSE）分别为0.116 m、0.569 s和24.583°，对于极端海况中有效波高的预测RMSE为0.191 m，输入要素数量的增加可进一步提升模型准确度，但在预测时长较长时也会增加训练成本。

深度学习  /  LSTM  /  海浪预报  /  舟山

This study is based on the meteorological, oceanic, terrain and other physical quantity data covered by the observation points in the southern Zhoushan Islands from January 1, 2019 to December 31, 2021, and uses long short-term memory neural network (LSTM) to build deep learning wave forecast model. We explore the impact of the input-output sequence ratio and the number of input elements on the prediction performance of the model, realize the short-term forecast of the three elements of waves in the Zhoushan sea area, that is the significant wave height, the significant wave period and the propagation direction, and use the data during the 2022 typhoons “Hinnamnor” and “Muifa” to test the model’s prediction ability for extreme sea conditions. The research results show that the multi-element deep learning wave forecast model trained based on measured data has good prediction accuracy and stability, and can realize the prediction of extreme sea conditions. When the input-output sequence ratio is 1∶1, the model accuracy is higher. In non-extreme sea conditions, the three-element model with a prediction time of 1 hour accurately predicts significant wave height, significant wave period and direction, with Root Mean Squared Errors (RMSE) of 0.116 m, 0.569 s, and 24.583° respectively. In extreme sea conditions, the prediction RMSE for the significant wave height is 0.191 m. The increase in the number of input elements can further improve the model accuracy but also increase the training cost when the prediction time is long.

deep learning  /  Long Short-Term Memory model  /  wave forecasting  /  Zhoushan
周桑君, 魏笑然, 谢歆哲, 支泓欢, 周一帆, 朱正涛, 李培良, 白晔斐. 基于长短时记忆神经网络的舟山海域多要素海浪预报模型. 海洋学报, 2024 , 46 (6) : 14 -25 . DOI: 10.12284/hyxb2024049
Sangjun Zhou, Xiaoran Wei, Xinzhe Xie, Honghuan Zhi, Yifan Zhou, Zhengtao Zhu, Peiliang Li, Yefei Bai. A multivariate wave forecasting model for the Zhoushan archipelago using Long Short-Term Memory deep neural networks[J]. Haiyang Xuebao, 2024 , 46 (6) : 14 -25 . DOI: 10.12284/hyxb2024049
正文
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1 研究简介
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随着可获取的海洋气象数据的增多和机器学习的发展，多种机器学习技术已广泛应用于海洋领域[1]，如支持向量机（Support Vector Machine，SVM）[2-3]、决策树（Decision Tree，DT）[4-5]、人工神经网络（Artificial Neural Network，ANN）[6-7]等。用机器学习方法构建数据模型相对简单，计算效率更高，不仅减小了对使用者的水平限制，还可以节省大量的计算资源[8]。凭借优于传统方法或物理模型的多变量处理能力[9]，神经网络技术发展迅速，已广泛应用于海浪预测并展现出强大的建模与预测能力[10–13]。
在众多神经网络模型中，长短时记忆（Long Short Term Memory，LSTM）神经网络[14]可有效捕捉序列数据中的长期依赖关系，因而在海浪预测中应用较多。赵勇等[15]基于某岛礁地形模型的波浪演化试验数据，分别使用 LSTM神经网络、反向传播（Back Propagation，BP）神经网络、SVM训练能预测畸形波波高的模型，在3类模型的预测结果中，LSTM模型的准确度最高。高丽斌[16]使用时长为两年的第3代浅海海浪数值模式（Simulating WAves Nearshore，SWAN）的输出结果训练了一种带有卷积LSTM网络层的深度学习模型并在台湾海峡海域进行单要素波高预测，所需运行时间相比传统的数值模式可减少98.59%。Fan等[17]通过对比6种不同的机器学习方法在有效波高预测任务上的表现，选择了LSTM神经网络与物理模型SWAN结合，构建SWAN-LSTM模型进行单点波高预测，发现该模型准确率比SWAN模型高约65%。Minuzzi和Farina[18]使用LSTM神经网络实现了对巴西海岸波浪高度的单要素预测，在针对200 m水深海域的6 h有效波高预测中，他们取得了12.96%的平均绝对百分比误差，低于ERA5再分析结果的13.31%。
上述研究表明，LSTM神经网络是进行海浪预报的首选方法，但我们也注意到，多数研究的预测目标以波高为主，而对海上作业同样重要的波周期和波向较少被关注，此外，前人工作的研究区域大多集中在开放大洋，较少涉及中国近岸海域。海浪从远海传播至近岸时易受水深和地形的影响，对近岸海上活动的影响较大且在台风期间更显著，因此，近岸海浪预报对提升近岸港口运输的效率和安全性有重要意义。舟山群岛是我国最大的群岛，其地处东部沿海，岛屿众多，岸线曲折，多深水良港，是多条国际航线的必经之地，位于该海域的宁波舟山港更是我国的重要枢纽港[19]。以舟山近岸的浮标实测数据为基础的海浪预报更能反映海浪在地形复杂的近岸的传播特点，富有代表性。鉴于上述情况，我们将综合考虑风、浪、流3种影响波浪传播的重要因素，使用LSTM神经网络，针对涵盖了台风信息的多要素单点浮标实测气象水文数据（2019−2021年），构建并训练能预报该站点的未来有效波高、有效波周期及传播方向这3个目标要素的多要素海浪预报模型，同时探讨输入输出序列比和输入要素数量对模型预测性能的影响。该研究能为舟山海域的海浪预报提供技术支持，同时为其他近岸海域的海浪预报工作提供参考。
2 数据与方法
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2.1 数据介绍
本研究选取2019年1月1日至2021年12月31日时间段内舟山南部海域一浮标站点的实测气象与水文数据以训练能够预测有效波高、有效波周期、波向的LSTM模型。我们首先对获取的原始数据进行异常值检测和清洗，插值填充单条缺失数据，剔除连续缺失数据，从而最大程度的保存数据的真实性。经处理获得与风、浪、流相关的共计16项要素数据，其单位、采样间隔、最大值等统计信息如下（表1）。表中波向表示波浪来向，来自正北方的波浪方向被定义为0°，其余方向以此为基准顺时针递增；ADCP流量为声学多普勒流速剖面仪（Acoustic Doppler Current Profilers，ADCP）测得的数据积分后所得。我们将使用该实测数据集训练两套LSTM模型：一套为包括3个输入要素和3个输出要素的三要素模型；另一套为含有7个输入要素和3个输出要素的七要素模型。三要素模型的输入与输出一致，具体包括有效波高、有效周期和主要传播方向；七要素的输入参数通过相关分析筛选得到。
2.2 数据相关性分析
皮尔逊相关系数可有效度量两组数据间的线性相关程度，多用于剔除与目标要素相关性低的无关要素，删减与目标要素重复度过高的冗余要素，其数学表达式定义为[20]：
$ {\mathrm{Pearson}}=\frac{\displaystyle\sum _{i=1}^{n}\left({x}_{i}-\bar{x}\right)\left({y}_{i}-\bar{y}\right)}{\sqrt{\displaystyle\sum _{i=1}^{n}{\left({x}_{i}-\bar{x}\right)}^{2}}\sqrt{\displaystyle\sum _{i=1}^{n}{\left({y}_{i}-\bar{y}\right)}^{2}}} ,$
其中$ n $为样本数量，$ i $为索引值，$ {x}_{i} $、$ {y}_{i} $均为单一变量，$ \bar{x} $与$ \bar{y} $是相应变量的平均值。皮尔逊系数的取值在 [−1，1] 范围内，用于刻画x与y之间的关系度[21]。相关性强弱的度量标准为：0.8～1.0 属极度相关，0.6～0.8为强相关，0.4～0.6为中等程度相关，0.2～0.4表示弱相关，0.0～0.2则为极弱相关或无相关；该系数的正负号分别代表两者为正相关或负相关。
从图1的皮尔逊相关系数矩阵图中我们发现1 h内最大10 min平均风向、分钟内瞬时风向、峰值波周期、ADCP流量、流深（流深H = ζ + d，其中ζ为海表自由面高度，d为水深，海表自由面高度的基准为平均海平面，主要包含潮汐信息）为无关要素，平均波高、平均周期、谱有效波高、谱有效波周期为冗余要素，1 h内最大10 min平均风速和分钟内瞬时风速两者之间互有重复，且分钟内瞬时风速与目标要素相关性更高，因此1 h内最大10 min平均风速也归为冗余要素。我们希望模型能在不同站点中表现出较好的泛化性能，所以保留具备测站地理信息的流深要素，删除其余所有的无关要素、冗余要素，最终确定七要素模型的输入数据为有效波高、有效波周期、波向、分钟内瞬时风速、波数、峰值能量及流深。图2展示了各要素的时间序列，从中我们可以看到各要素的数值范围差异较大，变化杂乱，无浅显规律，因此本研究利用深度学习技术以分析挖掘不同要素间的复杂联动关系。
2.3 训练方案
鉴于短时预报（12 h及以下）有助于即时决策和灾害管理，长时预报（12 h以上）可为中长期规划提供参考，本研究在训练方案中共考虑1 h、3 h、6 h、12 h、18 h、24 h、48 h7个预报时长；同时因现有人工智能海浪预报中最佳输入输出时间序列比对模型性能的影响尚不清楚，故额外考虑4种不同比例（1∶1、3∶1、5∶1、7∶1）进行试验。两套LSTM模型（三要素模型、七要素模型）均按表2中的28套方案进行训练，再根据评价指标分析预报时长和输入输出序列比对模型预测性能的影响，从而确定最终的海浪预报模型的重要配置参数。本研究中所有训练过程都在Intel(R) Core(TM) i7-8750H CPU @ 2.20GH处理器上实现。
2.4 评价指标
在本项研究中使用均方根误差（Root Mean Square Error，RMSE）和平均绝对百分比误差（Mean Absolute Percentage Error，MAPE）评估模型预测的准确性，具体定义如下：
$ {\mathrm{RMSE}}=\sqrt{\left(\frac{1}{n}\right)\sum _{i=1}^{n}{\left({y}_{i}-{f}_{i}\right)}^{2}} ,$
$ {\mathrm{MAPE}}=100\frac{1}{n}\sum _{i=1}^{n}\frac{\left|\left({y}_{i}-{f}_{i}\right)\right|}{{|y}_{i}|} ,$
其中，$ {y}_{i} $是真实观测值，$ {f}_{i} $是预测值，$ n $为样本数量，$ i $为索引值。RMSE表示预测值与真实值的偏差程度，数值越小表示预测越准确；MAPE以百分比表示，其值越小，预测越准确。
3 模型框架
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3.1 模型结构
本研究以TensorFlow框架[22]和Keras框架[23]为基础，采用LSTM神经网络结构，开发用于海浪预测的神经网络模型。如图3所示，本研究所使用的神经网络模型结构包括输入层、4个隐藏层以及输出层。模型的输入层接收形状为(N，step_in，k)的三维时间序列数据，其中N表示训练数据的样本数量，step_in为每个样本包含的时间步数，k为每个时间步的要素个数。第一个隐藏层为LSTM层，使用sigmoid作为激活函数，添加L2正则化以防止过拟合，该层用来学习输入数据中的时序依赖关系。第二个隐藏层为Repeat Vector层，为实现对3个目标要素的预测，需将上一个LSTM层的输出重复3次，以匹配目标输出序列的形状。第三个隐藏层仍为LSTM层，该层进一步处理在第一个LSTM层上学习到的特征信息，进行最终的多步预测，并以序列形式返回数据。第四个隐藏层为使用了Time Distributed操作的全连接层，通过保留输入序列的顺序以增强模型的时序预测能力。最后，根据实际运行的输出序列长度step_out设置输出层的形状，完成模型构建。
3.2 数据集构建
由于该模型的输入同时考虑了处于不同数量级的风、浪、流多个要素，因此需要通过标准化将所有数据放缩到同一尺度上以稳定模型收敛过程。本研究所采用的标准化方法为：
$ Z=\frac{X-u}{s} ,$
其中，X为样本，u为样本的平均值，s为标准差，Z为标准化样本。将放缩后的数据集（2019−2021年）按表3划分为用于模型训练的训练集和在模型训练完成后用于指标分析的测试集，其中训练集内包含了8次台风信息，测试集内没有直接影响该海域的台风数据，因此再添加2022年9月台风“轩岚诺”和“梅花”过境时的数据检验模型对极端海况的预测能力。
我们通过滑动窗口将完整数据样本按照时间顺序划分为多个子样本，构建符合模型训练要求的监督学习数据集，在划分某一子样本的过程中若遇到时间上缺失的数据段，将立即停止当前子样本的划分，并向后移动至缺失数据段之后的新时间点重新开始划分下一条子样本，其中子样本序列长度由模型的预报时长和输入输出序列比确定。以使用过去15 h数据对未来3 h海浪要素进行预测的七要素模型为例，图4a为训练集子样本的划分方式，图4b为测试集的划分方式。每个子样本由输入序列（深蓝色块）和相应的标注标签（浅蓝色块）组成，模型将根据大量子样本中的输入序列及其标注的目标序列，学习输入到输出的映射关系。需要注意的是，此处的输入包含了7个要素的历史时间序列，输出包括3个目标要素（有效波高、有效波周期、波向）的预测时间序列。训练集的滑动窗口每次移动步长为1，以充分学习各要素间的关系，测试集滑动窗口的移动步长与模型输出序列长度（即预报时长）一致，以避免输出的预测数据发生重叠，本例中输出序列长度为3，因此移动步长也设置为3。
4 结果分析
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4.1 模型耗时与误差分析
图5展示了两套模型在28种不同训练方案下的训练耗时，从图中可知三要素模型与七要素模型受输入输出序列比、预报时长影响的结果大致相同：训练耗时随着预报时长的增长而增加，在输入输出序列比为1∶1时，1 h三要素模型的训练耗时为8 min，48 h三要素模型的耗时为32 min；训练耗时也随着输入输出序列比例的增大而增加，且在长时预报中（12 h以上）的增长幅度更大，1 h七要素模型在1∶1和7∶1设定下的耗时为8 min、12 min，48 h七要素模型的耗时则分别为52 min、318 min。此外我们也发现，七要素模型的耗时在短时预报（预报时长为12 h及以下）任务中低于三要素模型，而在长时预报中高于三要素模型。整体而言训练耗时主要由单次数据量决定，输入输出序列比越大、预报时长越长，对应的数据量越多，训练耗时也随之增加。短时预报中七要素模型的耗时少于三要素模型则是因为在数据量增长不多的前提下增加的输入要素提供了更丰富的信息，利于模型学习其中规律，从而加速了训练过程。
我们在非极端海况的测试集上详细评估不同训练方案下的模型，表4给出了经反归一化后的结果与真实值的RMSE，需要注意的是，采集到的原始数据为两位小数，而模型的预测值在数据精度上则具有更大的灵活性，为了更细致地区分不同模型间的性能差异，我们将模型预测结果及其误差值精确到了3位小数。表中显示，随着预测时长从1 h增加到48 h，RMSE也随之增加，有效波高从0.11 m升至0.38 m，有效波周期从0.56 s升至1.25 s，波向从24.00°增至58.00°；输入输出序列比对RMSE影响不大，相同预报时长、不同序列比例设定下的RMSE差值在0.006 m、0.016 s、1.148°左右浮动；引入更多相关要素能在一定程度上提高模型预测精度，如输入输出序列比为1∶1、预报时长6 h时，七要素模型的3项RMSE为0.174 m、0.818 s、44.824°，低于三要素模型的0.181 m、0.850 s、45.581°。此外我们也探索了七要素模型与不包含“流深”的六要素模型在预测误差上的差异，由于我们文中仅在舟山南部站点进行验证，而同一站点的流深变化不大，因此两类模型差距并不明显。
4.2 非极端海况期间模型验证
图6以时间序列形式展示了三要素模型在设定输入输出序列比为1∶1、预报时长分别为1 h、6 h、18 h、48 h下对非极端海况测试集（表3）中三目标要素的预测效果。该测试时间段内的波浪变化相对和缓，有效波高在 10 月11 日前后出现受南海台风“圆规”影响而产生的大浪过程外，波高均低于2 m。通过与实测数据对比我们发现当预报时长较短时（低于 12 h），三要素模型可有效追踪波浪在波高、周期、波向上的演化过程，其中1 h模型在三目标要素的 RMSE值仅为0.117 m、0.563 s、24.861°，而计算所需的时间仅为0.091 s；然而当预报时长较长时（高于12 h），三要素模型重构出的时间序列出现振幅衰减、位相滞后、精度降低等现象，48 h模型的误差增长至 0.372 m、1.218 s、58.143°。
4.3 极端海况期间模型验证
图7展示了输入输出序列比为1∶1，预报时长分别为1 h、3 h、6 h和12 h的三要素模型对台风“轩岚诺”（2022年9月1日至6日）、“梅花” （2022年9月12日至15日）过境前后的3个目标要素的预测结果。图中蓝色阴影表示受台风影响的时间段，红色阴影为出现3 m以上海浪的时间段。测站记录显示，“轩岚诺”期间有效波高从1 m逐渐增至4 m，有效波周期最大达10.10 s。“轩岚诺”过后波浪运动趋向和缓，有效波高低于1 m，有效波周期下降至5 s左右。受“梅花”影响，自9月12日起该测点海域有效波高急速攀升至7 m，并随着台风中心的快速北移而快速下降至1 m，此期间波周期又抬升至10 s左右。这两个台风过程使得局地风场变得异常复杂，同时台风浪中涌浪和风浪此消彼长、相互影响，导致波向呈现出频繁且不定的变换，进而增加了模型预测的难度。对比实测数据可知，三要素模型在极端海况期间仍能在0.06 s内较好地预测台风浪的演化过程，1 h模型在三目标要素的 RMSE值为0.191 m、0.636 s、91.976°。该误差随预报时长的增加而增大，12 h模型的RMSE为0.448 m、0.834 s、94.630°。“轩岚诺”期间4种不同预报时长模型的预测基本合理，但在“梅花”期间12 h模型表现不佳。
5 结论
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本文基于LSTM神经网络结构，利用舟山南部外海单观测站点的多要素实测气象与水文数据搭建并训练了深度学习海浪预报模型，探讨了输入序列与输出序列的比例、输入要素的数量对模型性能的影响，实现了对该站点未来有效波高、有效波周期及波向的多要素海浪预报，并评估了多要素海浪预报模型在非极端海况和极端海况下的预报能力，具体结论如下：
（1）短时预报（12 h及以下）模型能准确预报观测站附近海域的海浪状况，预测误差随着预报时长的增加而增加。输入输出序列比为1∶1时，预报时长为1 h、3 h、6 h、12 h三要素模型的有效波高RMSE为0.116 m、0.149 m、0.181 m、0.232 m，有效波周期RMSE为0.569 s、0.704 s、0.850 s、0.954 s，波向RMSE为24.583°、31.565°、45.581°、48.260°。
（2）不同设定下的模型训练耗时在10 min至320 min不等，总体趋势为输入输出序列比越大、预报时长越长，模型训练耗时越长。
（3）增大输入输出序列比对模型预报准确度影响不大，相同预报时长、不同序列比例设定下的RMSE差异在0.006 m、0.016 s、1.148°左右浮动。
（4）输入要素数量的增加对模型准确度的提升并不显著，且在进行长时预报时（12 h以上）训练时间会大幅提高。输入输出序列比为1∶1、预报时长48 h时，三要素模型的有效波高RMSE和训练耗时分别为0.372 m、32 min，七要素模型则为0.367 m、52 min。
（5）尽管训练集中台风数量不多，但短时预报模型仍能较好地预测台风期间的有效波高和波周期，输入输出序列比为1∶1时1 h三要素模型在有效波高和波周期的 RMSE值为0.191 m、0.636 s。
综合考虑时间成本及数据可获得性，本研究推荐使用输入输出序列比为1∶1的短时预报三要素模型作为最终的海浪预报模型。
基金
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  • 国家自然科学基金项目(42376212)
  • 浙江大学科研项目资助(XY2023018)
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2024年第46卷第6期
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文章信息
doi: 10.12284/hyxb2024049
  • 接收时间：2024-02-22
  • 首发时间：2025-11-26
  • 出版时间：2024-06-30
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  • 收稿日期：2024-02-22
  • 修回日期：2024-05-10
基金
国家自然科学基金项目(42376212)
浙江大学科研项目资助(XY2023018)
作者信息
    1.浙江大学 海洋学院，浙江 舟山 316021
    2.浙江大学 海南研究院，海南 三亚 572025
    3.中国空气动力研究与发展中心 空天技术研究所，四川 绵阳 621000

通讯作者:

*白晔斐（1980—），男，内蒙古自治区呼和浩特市人，研究员，博士，主要从事海洋环境与海洋灾害领域的研究。E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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