Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island

Minghao HU; Lingling XIE; Mingming LI; Quanan ZHENG

doi:10.1007/s00343-024-3266-y

Your Location：

Home >

Browse articles >

Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island

Physics | Updated：2025-05-27

- Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island
- Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island
- 海洋湖沼学报(英文) 2025年43卷第3期页码：657-675
- Affiliations：
  
  1.Laboratory of Coastal Ocean Variation and Disaster Prediction, College of Ocean and Meteorology, Guangdong Ocean University, Zhanjiang 524088, China
  2.Key Laboratory of Climate, Resources and Environment in Continental Shelf Sea and Deep Ocean (LCRE), Zhanjiang 524088, China
  3.Key Laboratory of Space Ocean Remote Sensing and Application, Ministry of Natural Resources, Zhanjiang 524088, China
  4.Department of Atmospheric and Oceanic Science, University of Maryland, College Park 20742, USA
- Author bio：
  
  xiell@gdou.edu.cn
- Funds：
  
  the National Natural Science Foundation of China(42276019);the Guangdong Provincial Observation and Research Station for Tropical Ocean Environment in Western Coastal Waters
- DOI：10.1007/s00343-024-3266-y
  中图分类号：
- 收稿：2023-12-08，
  
  录用：2024-03-29，
  
  网络首发：2024-05-21，
  
  纸质出版：2025-05-01
- Accepted：
Scan QR Code
Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island[J]. 海洋湖沼学报(英文), 2025,43(3):657-675.

HU Minghao,XIE Lingling,LI Mingming,et al.Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island[J].Journal of Oceanology and Limnology,2025,43(03):657-675.
Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island[J]. 海洋湖沼学报(英文), 2025,43(3):657-675. DOI： 10.1007/s00343-024-3266-y.

HU Minghao,XIE Lingling,LI Mingming,et al.Parameterization of turbulent mixing by deep learning in the continental shelf sea east of Hainan Island[J].Journal of Oceanology and Limnology,2025,43(03):657-675. DOI： 10.1007/s00343-024-3266-y.

摘要

Abstract

The uncertainty of ocean turbulent mixing parameterization comprises a significant challenge in ocean and climate models. A depth-dependent deep learning ocean turbulent mixing parameterization scheme was proposed with the hydrological and microstructure observations conducted in summer 2012 in the shelf sea east of Hainan Island

in South China Sea (SCS). The deep neural network model is used and incorporates the Richardson number

the normalized depth

the horizontal velocity speed

the shear

the stratification

and the density

as input parameters. Comparing to the scheme without parameter

and region division

the depth-dependent scheme improves the prediction of the turbulent kinetic energy dissipation rate

. The correlation coefficient (

) between predicted and observed lg

increases from 0.49 to 0.62

and the root mean square error decreases from 0.56 to 0.48. Comparing to the traditional physics-driven parameterization schemes

such as the G89 and MG03

the data-driven approach achieves higher accuracy and generalization. The SHapley Additive Explanations (SHAP) framework analysis reveals the importance descending order of the input parameters as:

and

in the whole depth

while

is most important in the upper and bottom boundary laye

rs (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=81358373&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=81358814&type=

1.60866666

0.3

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=81358375&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=81358816&type=

1.60866666

0.65) and least important in middle layer (0.3

0.65). The research shows applicability of constructing deep learning-based ocean turbulent mixing parameterization schemes using limited observational data and well-established physical processes.

关键词

Keywords

references

Alford M H , MacKinnon J A , Nash J D et al . 2011 . Energy flux and dissipation in Luzon Strait: two tales of two ridges . Journal of Physical Oceanography , 41 ( 11 ): 2211 - 2222 , https://doi.org/10.1175/JPO-D-11-073.‍‍1 https://doi.org/10.1175/JPO-D-11-073.‍‍1 .

Beucler T , Pritchard M , Rasp S et al . 2021 . Enforcing analytic constraints in neural networks emulating physical systems . Physical Review Letters , 126 ( 9 ): 098302 , https://doi.org/10.1103/PhysRevLett.126.098302 https://doi.org/10.1103/PhysRevLett.126.098302 .

Bryan K , Lewis L J . 1979 . A water mass model of the World Ocean . Journal of Geophysical Research: Oceans , 84 ( C5 ): 2503 - 2517 , https://doi.org/10.1029/JC084iC05p02503 https://doi.org/10.1029/JC084iC05p02503 .

Buckingham C E , Lucas N S , Belcher S E et al . 2019 . The contribution of surface and submesoscale processes to turbulence in the open ocean surface boundary layer . Journal of Advances in Modeling Earth Systems , 11 ( 12 ): 4066 - 4094 , https://doi.org/10.1029/2019MS001801 https://doi.org/10.1029/2019MS001801 .

Chao W T , Young C C , Hsu T W et al . 2020 . Long-lead-time prediction of storm surge using artificial neural networks and effective typhoon parameters: revisit and deeper insight . Water , 12 ( 9 ): 2394 , https://doi.‍org/10.3390/w12092394 https://doi.‍org/10.3390/w12092394 . https://do 10.3390/w12092394 http://dx.doi.org/10.3390/w12092394

Chen D K , Rothstein L M , Busalacchi A J . 1994 . A hybrid vertical mixing scheme and its application to tropical ocean models . Journal of Physical Oceanography , 24 ( 10 ): 2156 - 2179 , https://doi.org/10.1175/1520-0485(1994)024<2156:AHVMSA>2.0.CO;2. https://doi.org/10.1175/1520-0485(1994)024<2156:AHVMSA>2.0.CO;2.

D'Asaro E , Lee C , Rainville L et al . 2011 . Enhanced turbulence and energy dissipation at ocean fronts . Science , 332 ( 6027 ): 318 - 322 , https://doi.‍org/10.1126/science.1201515 https://doi.‍org/10.1126/science.1201515 . https://do 10.1126/science.1201515 http://dx.doi.org/10.1126/science.1201515

Dillon T M . 1982 . Vertical overturns: a comparison of Thorpe and Ozmidov length scales . Journal of Geophysical Research: Oceans , 87 ( C12 ): 9601 - 9613 , https://doi.‍org/10.1029/JC087iC12p09601 https://doi.‍org/10.1029/JC087iC12p09601 . https://do 10.1029/jc087ic12p09601 http://dx.doi.org/10.1029/jc087ic12p09601

Dong C M , Xu G J , Han G Q et al . 2022 . Recent developments in artificial intelligence in oceanography . Ocean-Land-Atmosphere Research , 2022 : 9870950 , https://doi.org/10.34133/2022/9870950 https://doi.org/10.34133/2022/9870950 .

Dong J H , Zhong Y S . 2018 . The spatiotemporal features of submesoscale processes in the northeastern South China Sea . Acta Oceanologica Sinica , 37 ( 11 ): 8 - 18 , https://doi.org/10.1007/s13131-018-1277-2 https://doi.org/10.1007/s13131-018-1277-2 .

Du Y L , Song W , He Q et al . 2019 . Deep learning with multi-scale feature fusion in remote sensing for automatic oceanic eddy detection . Information Fusion , 49 : 89 - 99 , https://doi.org/10.1016/j.inffus.2018.09.006 https://doi.org/10.1016/j.inffus.2018.09.006 .

Duo Z , Wang W K , Wang H Z . 2019 . Oceanic mesoscale eddy detection method based on deep learning . Remote Sensing , 11 ( 16 ): 1921 , https://doi.org/10.3390/rs11161921 https://doi.org/10.3390/rs11161921 .

Gao C , Zhou L , Zhang R H . 2023 . A transformer-based deep learning model for successful predictions of the 2021 second-year La Niña condition . Geophysical Research Letters , 50 ( 12 ): e2023 GL 104034 , https://doi.org/10.1029/2023GL104034 https://doi.org/10.1029/2023GL104034 .

Gaspar P , Grégoris Y , Lefevre J M . 1990 . A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: tests at station Papa and long-term upper ocean study site . Journal of Geophysical Research: Oceans , 95 ( C9 ): 16179 - 16193 , https://doi.org/10.1029/JC095iC09p16179 https://doi.org/10.1029/JC095iC09p16179 .

Gregg M C . 1989 . Scaling turbulent dissipation in the thermocline . Journal of Geophysical Research: Oceans , 94 ( C7 ): 9686 - 9698 , https://doi.‍org/10.1029/JC094iC07p09686 https://doi.‍org/10.1029/JC094iC07p09686 . https://do 10.1029/jc094ic07p09686 http://dx.doi.org/10.1029/jc094ic07p09686

Gutjahr O , Brüggemann N , Haak H et al . 2021 . Comparison of ocean vertical mixing schemes in the Max Planck Institute Earth System Model (MPI-ESM1.2) . Geoscientific Model Development , 14 ( 5 ): 2317 - 2349 , https://doi.‍org/10.5194/gmd-14-2317-2021 https://doi.‍org/10.5194/gmd-14-2317-2021 .

Han G Q , Cen H B , Jiang J H et al . 2022 . Applying machine learning in devising a parsimonious ocean mixing parameterization scheme . Deep Sea Research Part II: Topical Studies in Oceanography , 203 : 105163 , https://doi.org/10.1016/j.dsr2.2022.‍105163 https://doi.org/10.1016/j.dsr2.2022.‍105163 .

Jia Y L , Richards K J , Annamalai H . 2021 . The impact of vertical resolution in reducing biases in sea surface temperature in a tropical Pacific Ocean model . Ocean Modelling , 157 : 101722 , https://doi.org/10.1016/j.‍ocemod.2020.101722 https://doi.org/10.1016/j.‍ocemod.2020.101722 .

Kraus E B , Turner J S . 1967 . A one-dimensional model of the seasonal thermocline II. The general theory and its consequences . Tellus , 19 ( 1 ): 98 - 106 , https://doi.org/10.1111/j.2153-3490.1967.tb01462.x https://doi.org/10.1111/j.2153-3490.1967.tb01462.x .

Kunze E , Firing E , Hummon J M et al . 2006 . Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles . Journal of Physical Oceanography , 36 ( 8 ): 1553 - 1576 , https://doi.org/10.1175/JPO2926.1 https://doi.org/10.1175/JPO2926.1 .

Large W G , McWilliams J C , Doney S C . 1994 . Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization . Reviews of Geophysics , 32 ( 4 ): 363 - 403 , https://doi.org/10.1029/94RG01872 https://doi.org/10.1029/94RG01872 .

Li J N , Yang Q X , Sun H et al . 2023 . On the variation of dissipation flux coefficient in the upper South China Sea . Journal of Physical Oceanography , 53 ( 2 ): 551 - 571 , https://doi.org/10.1175/JPO-D-22-0127.1 https://doi.org/10.1175/JPO-D-22-0127.1 .

Li M M , Xie L L , Zong X L et al . 2018 . The cruise observation of turbulent mixing in the upwelling region east of Hainan Island in the summer of 2012 . Acta Oceanologica Sinica , 37 ( 9 ): 1 - 12 , https://doi.org/10.1007/s13131-018-1260-y https://doi.org/10.1007/s13131-018-1260-y .

Liang C R , Chen G Y , Shang X D . 2017 . Observations of the turbulent kinetic energy dissipation rate in the upper central South China Sea . Ocean Dynamics , 67 : 597 - 609 , https://doi.org/10.1007/s10236-017-1051-6 https://doi.org/10.1007/s10236-017-1051-6 .

Liu Y Z , Jing Z , Wu L X . 2017 . The variation of turbulent diapycnal mixing at 18°‍N in the South China Sea stirred by wind stress . Acta Oceanologica Sinica , 36 ( 5 ): 26 - 30 , https://doi.org/10.1007/s13131-017-1067-2 https://doi.org/10.1007/s13131-017-1067-2 .

Liu Z Y , Lozovatsky I . 2012 . Upper pycnocline turbulence in the northern South China Sea . Chinese Science Bulletin , 57 ( 18 ): 2302 - 2306 , https://doi.org/10.1007/s11434-012-5137-8 https://doi.org/10.1007/s11434-012-5137-8 .

Lu Y Z , Cen X R , Guo S X et al . 2021 . Spatial variability of diapycnal mixing in the South China Sea inferred from density overturn analysis . Journal of Physical Oceanography , 51 ( 11 ): 3417 - 3434 , https://doi.org/10.1175/JPO-D-20-0241.1 https://doi.org/10.1175/JPO-D-20-0241.1 .

Lu Z M , Chen G Y , Xie X H et al . 2009 . Study on the microstructure characteristics of summer mixed layer in the northern South China Sea . Progress in Natural Science , 19 ( 6 ): 657 - 663 , https://doi.‍org/10.3321/j.issn:1002-008X.2009.06.011 https://doi.‍org/10.3321/j.issn:1002-008X.2009.06.011 .

Lundberg S M , Erion G G , Chen H et al . 2020 . From local explanations to global understanding with explainable AI for trees . Nature Machine Intelligence , 2 ( 1 ): 56 - 67 , https://doi.org/10.1038/s42256-019-0138-9 https://doi.org/10.1038/s42256-019-0138-9 .

Lundberg S M , Erion G G , Lee S I . 2018 . Consistent individualized feature attribution for tree ensembles. arXiv preprint arXiv: 1802. 03888 , https://doi.org/10.48550/arXiv.1802.03888 https://doi.org/10.48550/arXiv.1802.03888 .

Lundberg S M , Lee S I . 2017 . A unified approach to interpreting model predictions . In: Proceedings of the 31st International Conference on Neural Information Processing Systems . Curran Associates Inc. , Long Beach, USA . p. 4768 - 4777 , https://doi.org/10.48550/arXiv.‍1705.07874 https://doi.org/10.48550/arXiv.‍1705.07874 .

MacKinnon J A , Gregg M C . 2003 . Mixing on the late-summer New England shelf—solibores, shear, and stratification . Journal of Physical Oceanography , 33 ( 7 ): 1476 - 1492 , https://doi.org/10.1175/1520-0485(2003)033<1476:MOTLNE>2.0.CO;2. https://doi.org/10.1175/1520-0485(2003)033<1476:MOTLNE>2.0.CO;2.

Mashayek A , Reynard N , Zhai F M et al . 2022 . Deep ocean learning of small scale turbulence . Geophysical Research Letters , 49 ( 15 ): e2022 GL 098039 , https://doi.org/10.1029/2022GL098039 https://doi.org/10.1029/2022GL098039 .

Mellor G L , Yamada T . 1982 . Development of a turbulence closure model for geophysical fluid problems . Reviews of Geophysics , 20 ( 4 ): 851 - 875 , https://doi.org/10.1029/RG020i004p00851 https://doi.org/10.1029/RG020i004p00851 .

Osborn T R , 1980 . Estimates of the local rate of vertical diffusion from dissipation measurements . Journal of physical oceanography , 10 ( 1 ): 83 - 89, https://doi.org/10.1175/1520-0485(1980)010 <0083:EOTLRO>2.0.CO;2. <0083:EOTLRO>2.0.CO;2.

Pacanowski R C , Philander S G H . 1981 . Parameterization of vertical mixing in numerical models of tropical oceans . Journal of Physical Oceanography , 11 ( 11 ): 1443 - 1451 , https://doi.org/10.1175/1520-0485(1981)011<1443:POVMIN>2.0.CO;2. https://doi.org/10.1175/1520-0485(1981)011<1443:POVMIN>2.0.CO;2.

Pal A . 2020 . Deep learning emulation of subgrid-scale processes in turbulent shear flows . Geophysical Research Letters , 47 ( 12 ): e2020 GL 087005 , https://doi.org/10.1029/2020GL087005 https://doi.org/10.1029/2020GL087005 .

Polzin K L , Toole J M , Ledwell J R et al . 1997 . Spatial variability of turbulent mixing in the abyssal ocean . Science , 276 ( 5309 ): 93 - 96 , https://doi.org/10.1126/science.276.5309.93 https://doi.org/10.1126/science.276.5309.93 .

Qi Y F , Shang C J , Mao H B et al . 2020 . Spatial structure of turbulent mixing of an anticyclonic mesoscale eddy in the northern South China Sea . Acta Oceanologica Sinica , 39 ( 11 ): 69 - 81 , https://doi.org/10.1007/s13131-020-1676-z https://doi.org/10.1007/s13131-020-1676-z .

Qiao F L , Yuan Y L , Yang Y Z et al . 2004 . Wave-induced mixing in the upper ocean: distribution and application to a global ocean circulation model . Geophysical Research Letters , 31 ( 11 ): L11303 , https://doi.org/10.1029/2004GL019824 https://doi.org/10.1029/2004GL019824 .

Rahmstorf S . 2003 . Thermohaline circulation: the current climate . Nature , 421 ( 6924 ): 699 - 699 , https://doi.org/10.1038/421699a https://doi.org/10.1038/421699a .

Ribeiro M T , Singh S , Guestrin C . 2016 . Model-agnostic interpretability of machine learning. arXiv preprint arXiv : 1606 . 05386 , https://doi.org/10.48550/arXiv.1606.05386 https://doi.org/10.48550/arXiv.1606.05386 .

Schmitt R W , Ledwell J R , Montgomery E T et al . 2005 . Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic . Science , 308 ( 5722 ): 685 - 688 , https://doi.org/10.1126/science.1108678 https://doi.org/10.1126/science.1108678 .

Shang X D , Liang C R , Chen G Y . 2017 . Spatial distribution of turbulent mixing in the upper ocean of the South China Sea . Ocean Science , 13 ( 3 ): 503 - 519 , https://doi.org/10.5194/os-13-503-2017 https://doi.org/10.5194/os-13-503-2017 .

Shapley L S . 1953 . A value for n-person games . In: Kuhn H W, Tucker A W eds. Contributions to the Theory of Games (AM-28), Volume II . Princeton University Press, Princeton. p. 307 - 318 , https://doi.org/10.1515/9781400881970-018 https://doi.org/10.1515/9781400881970-018 .

Simmons H , Chang M H , Chang Y T et al . 2011 . Modeling and prediction of internal waves in the South China Sea . Oceanography , 24 ( 4 ): 88 - 99 , https://doi.org/10.5670/oceanog.2011.97 https://doi.org/10.5670/oceanog.2011.97 .

St . Laurent L . 2008 . Turbulent dissipation on the margins of the South China Sea. Geophysical Research Letters , 35 ( 23 ): L23615 , https://doi.org/10.1029/2008GL035520 https://doi.org/10.1029/2008GL035520 .

Sun H , Yang Q X , Tian J W . 2018 . Microstructure measurements and finescale parameterization assessment of turbulent mixing in the northern South China Sea . Journal of Oceanography , 74 ( 5 ): 485 - 498 , https://doi.org/10.1007/s10872-018-0474-0 https://doi.org/10.1007/s10872-018-0474-0 .

Sun H , Yang Q X , Zhao W et al . 2016 . Temporal variability of diapycnal mixing in the northern South China Sea . Journal of Geophysical Research: Oceans , 121 ( 12 ): 8840 - 8848 , https://doi.org/10.1002/2016JC012044 https://doi.org/10.1002/2016JC012044 .

Sun M , Chen L , Li T et al . 2023 . CNN-based ENSO forecasts with a focus on SSTA zonal pattern and physical interpretation . Geophysical Research Letters , 50 ( 20 ): e2023 GL 105175 , https://doi.org/10.1029/2023GL105175 https://doi.org/10.1029/2023GL105175 .

Thorpe S A . 1977 . Turbulence and mixing in a Scottish loch . Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences , 286 ( 1334 ): 125 - 181 , https://doi.org/10.1098/rsta.1977.0112 https://doi.org/10.1098/rsta.1977.0112 .

Tian J W , Yang Q X , Zhao W . 2009 . Enhanced diapycnal mixing in the South China Sea . Journal of Physical Oceanography , 39 ( 12 ): 3191 - 3203 , https://doi.org/10.1175/2009JPO3899.1 https://doi.org/10.1175/2009JPO3899.1 .

Wang H Y , Hu S N , Li X F . 2023 . An interpretable deep learning ENSO forecasting model . Ocean-Land-Atmosphere Research , 2 : 0012 , https://doi.org/10.34133/olar.0012 https://doi.org/10.34133/olar.0012 .

Wang X W , Peng S Q , Liu Z Y et al . 2016 . Tidal mixing in the South China Sea: an estimate based on the internal tide energetics . Journal of Physical Oceanography , 46 ( 1 ): 107 - 124 , https://doi.org/10.1175/JPO-D-15-0082.1 https://doi.org/10.1175/JPO-D-15-0082.1 .

Wunsch C , Ferrari R . 2004 . Vertical mixing, energy, and the general circulation of the oceans . Annual Review of Fluid Mechanics , 36 : 281 - 314 , https://doi.‍org/10.1146/annurev.fluid.36.050802.122121 https://doi.‍org/10.1146/annurev.fluid.36.050802.122121 .

Xie L L , Pallàs-Sanz E , Zheng Q A et al . 2017 . Diagnosis of 3D vertical circulation in the upwelling and frontal zones east of Hainan Island, China . Journal of Physical Oceanography , 47 ( 4 ): 755 - 774 , https://doi.org/10.1175/JPO-D-16-0192.1 https://doi.org/10.1175/JPO-D-16-0192.1 .

Xu Z H , Yin B S , Hou Y J et al . 2013 . Variability of internal tides and near-inertial waves on the continental slope of the northwestern South China Sea . Journal of Geophysical Research: Oceans , 118 ( 1 ): 197 - 211 , https://doi.org/10.1029/2012JC008212 https://doi.org/10.1029/2012JC008212 .

Yang Q X , Zhao W , Liang X F et al . 2016 . Three-dimensional distribution of turbulent mixing in the South China Sea . Journal of Physical Oceanography , 46 ( 3 ): 769 - 788 , https://doi.org/10.1175/JPO-D-14-0220.1 https://doi.org/10.1175/JPO-D-14-0220.1 .

Yang Q X , Zhao W , Liang X F et al . 2017 . Elevated mixing in the periphery of mesoscale eddies in the South China Sea . Journal of Physical Oceanography , 47 ( 4 ): 895 - 907 , https://doi.org/10.1175/JPO-D-16-0256.1 https://doi.org/10.1175/JPO-D-16-0256.1 .

Yosinski J , Clune J , Bengio Y et al . 2014 . How transferable are features in deep neural networks? In: Proceedings of the 27th International Conference on Neural Information Processing Systems . MIT Press , Montreal, Canada . p. 3320 - 3328 , https://doi.org/10.48550/arXiv.1411.1792 https://doi.org/10.48550/arXiv.1411.1792 .

Yu Z J , Schopf P S . 1997 . Vertical eddy mixing in the tropical upper ocean: its influence on zonal currents . Journal of Physical Oceanography , 27 ( 7 ): 1447 - 1458 , https://doi.org/10.1175/1520-0485(1997)027<1447:VEMITT>2.0.CO;2. https://doi.org/10.1175/1520-0485(1997)027<1447:VEMITT>2.0.CO;2.

Zanna L , Bolton T . 2020 . Data-driven equation discovery of ocean mesoscale closures . Geophysical Research Letters , 47 ( 17 ): e2020 GL 088376 , https://doi.org/10.1029/2020GL088376 https://doi.org/10.1029/2020GL088376 .

Zaron E D , Moum J N . 2009 . A new look at Richardson number mixing schemes for equatorial ocean modeling . Journal of Physical Oceanography , 39 ( 10 ): 2652 - 2664 , https://doi.org/10.1175/2009JPO4133.1 https://doi.org/10.1175/2009JPO4133.1 .

Zhang R H , Zebiak S E . 2002 . Effect of penetrating momentum flux over the surface boundary/mixed layer in a z -coordinate OGCM of the Tropical Pacific . Journal of Physical Oceanography , 32 ( 12 ): 3616 - 3637 , https://doi.org/10.1175/1520-0485(2002)032<3616:EOPMFO>2.0.CO;2. https://doi.org/10.1175/1520-0485(2002)032<3616:EOPMFO>2.0.CO;2.

Zhang S W , Xie L L , Cao R X et al . 2012 . Observation of upper-ocean mixing in the region west of the Luzon Strait in spring . Journal of Coastal Research , 28 ( 5 ): 1208 - 1213 , https://doi.org/10.2112/JCOASTRES-D-11-00145.1 https://doi.org/10.2112/JCOASTRES-D-11-00145.1 .

Zhang X D , Li X F , Zheng Q A . 2021 . A machine-learning model for forecasting internal wave propagation in the Andaman Sea . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 14 : 3095 - 3106 , https://doi.org/10.1109/JSTARS.2021.3063529 https://doi.org/10.1109/JSTARS.2021.3063529 .

Zhu Y C , Zhang R H . 2019 . A modified vertical mixing parameterization for its improved ocean and coupled simulations in the Tropical Pacific . Journal of Physical Oceanography , 49 ( 1 ): 21 - 37 , https://doi‍.‍org/10.1175/JPO-D-18-0100.1 https://doi‍.‍org/10.1175/JPO-D-18-0100.1 . https://do 10.1175/jpo-d-18-0100.1 http://dx.doi.org/10.1175/jpo-d-18-0100.1

Zhu Y C , Zhang R H , Moum J N et al . 2022 . Physics-informed deep-learning parameterization of ocean vertical mixing improves climate simulations . National Science Review , 9 ( 8 ): nwac 044 , https://doi.‍org/10.1093/nsr/nwac044 https://doi.‍org/10.1093/nsr/nwac044 . https://do 10.1093/nsr/nwac092 http://dx.doi.org/10.1093/nsr/nwac092

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

A physics-enhanced deep-learning model for estimating turbid shallow water depth from SAR images

Prediction of sea surface pCO₂ in the South China Sea using Spatiotemporal Convolutional LSTM model

Deep neural network based on adversarial training for short-term high-resolution precipitation nowcasting from radar echo images

A deep learning-based hybrid model for improved SST prediction in the tropical Pacific Ocean

基于模态频率的V型缺口梁裂纹扩展速率模型