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Provides structured guidance covering introduction topics such as licensing, copyrights, trademarks, and acknowledgments, then develops governing equations including propagation and multiple source-term parameterizations for wave physics, wave-ice interactions, and air-sea processes. Extends to numerical approaches (spectral discretization, propagation schemes, grids, partitioning, nesting) and the wave model structure and data flow, including routines and assimilation interfaces.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/wavewatch-iii-user-manual-and-system-documentation-version-516/661963/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/wavewatch-iii-user-manual-and-system-documentation-version-516/661963.png","ImageObject",300,407,{"name":92,"@type":93},"Jacob","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-28",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the document’s purpose?","Question",{"text":112,"@type":113},"It serves as a user manual and system documentation for WAVEWATCH III version 5.16, prepared by the WAVEWATCH III Development Group (WW3DG).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which main technical topics are covered?",{"text":117,"@type":113},"The manual covers governing equations, source terms (including wave-ice and air-sea processes), numerical approaches for wave propagation, and the wave model structure and data flow with relevant interfaces and auxiliary programs.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the manual describe how the model handles spatial propagation and grids?",{"text":121,"@type":113},"Yes. It includes numerical approaches for spatial propagation and discusses multiple grid types and related schemes (e.g., regular grids, curvilinear grids, unstructured grids, and spherical multiple-cell grids).","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},661963,1793191201,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","U. S. Department of Commerce National Oceanic and Atmospheric Administration National Weather Service  \nNational Centers for Environmental Prediction 5830 University Research Court  \nCollege Park, MD 20740  \nTechnical Note  \nUser manual and system documentation of  \nWAVEWATCH III  version 5 .16 †  \nThe WAVEWATCH III  Development Group ‡  \n(WW3DG)  \nEnvironmental Modeling Center Marine Modeling and Analysis Branch  \nOctober 2016  \nTo refer to this manual, please use the following citation:  \nThe WAVEWATCH III Development Group (WW3DG), 2016: User manual and system documentation of WAVEWATCH III version 5 .16. Tech. Note 329, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, 326 pp.+ Appendices.  \n† MMAB Contribution No. 329.  \n‡See Section 1.4 for WW3DG group description.‡Code manager [email: jessica.meixner@noaa.gov](email: jessica.meixner@noaa.gov)  \nThis page is intentionally left blank.  \ni  \nContents  \n1 Introduction 1  \n1.1 About this manual ........................ 1  \n1.2 Licensing terms .......................... 3  \n1.3 Copyrights and trademarks ................... 5  \n1.4 The WAVEWATCH III Development Group (WW3DG) .. 5  \n1.5 Acknowledgments ........................ 9  \n2 Governing equations 11  \n2.1 Introduction ........................... 11  \n2.2 Propagation ........................... 13  \n2.3 Source terms ........................... 14  \n2.3.1 General concepts ..................... 14  \n2.3.2 Snl: Discrete Interaction Approximation (DIA) .... 16  \n2.3.3 Snl: Full Boltzmann Integral (WRT) .......... 18  \n2.3.4 Snl: Generalized Multiple DIA (GMD) ......... 22  \n2.3.5 Snl: Two-Scale Approximation (TSA) ......... 25  \n2.3.6 Snl : Nonlinear Filter ................... 29  \n2.3.7 Sin + Sds: WAM cycle 3 ................. 31  \n2.3.8 Sin + Sds: Tolman and Chalikov 1996 ......... 32  \n2.3.9 Sin + Sds: WAM cycle 4 (ECWAM) .......... 39  \n2.3.10 Sin + Sds: Ardhuin et al. 2010 ............. 42  \n2.3.11 Sin + Sds: Zieger et al. 2015 ............... 48  \n2.3.12 Sln: Cavaleri and Malanotte-Rizzoli 1981 ....... 55  \n2.3.13 Sbot: JONSWAP bottom friction ............ 56  \n2.3.14 Sbot: SHOWEX bottom friction ............. 57  \n2.3.15 Smud: Dissipation by viscous mud (D&L) ....... 59  \n2.3.16 Smud: Dissipation by viscous mud (Ng) ........ 60  \n2.3.17 Sdb: Battjes and Janssen 1978 .............. 61  \n2.3.18 Str: Triad nonlinear interactions (LTA) ........ 63  \n2.3.19 Sbs: Bottom scattering .................. 64  \n2.4 Source terms for wave-ice interactions ............. 66  \n2.4.1 Sice: Damping by sea ice (simple) ............ 67  \n2.4.2 Sice: Damping by sea ice (generalization of Liu et al.) 69  \n2.4.3 Sice: Damping by sea ice (Shen et al.) ......... 70  \n2.4.4 Sice: Frequency-dependent damping by sea ice ..... 73  \n2.4.5 Sis: Di􀀋usive scattering by sea ice (simple) ...... 75  \nii  \n2.4.6 Sis: Floe-size dependent scattering and dissipation .. 76  \n2.4.7 Sref: Energy re􀀍ection at shorelines and icebergs ... 80  \n2.4.8 Second-order spectrum and free infragravity waves .. 83  \n2.4.9 Sxx: User de􀀌ned ..................... 85  \n2.5 Air-sea processes ......................... 86  \n2.5.1 General concepts ..................... 86  \n2.5.2 Sea-state dependent τ : Reichl et al. 2014 ....... 88  \n2.5.3 Sea-state dependent τ : Donelan et al. 2012 ...... 90  \n2.6 Output parameters ........................ 91  \n3 Numerical approaches 100  \n3.1 Spectral discretization ...................... 100  \n3.2 Splitting of the wave action equation .............. 101  \n3.3 Depth variations in time ..................... 103  \n3.4 Spatial propagation ....................... 104  \n3.4.1 General concepts ..................... 104  \n3.4.2 Traditional regular grids ................. 106  \nFirst-order scheme ................. 107  \nSecond-order scheme (UNO) ........... 108  \nThird-order scheme (UQ) ............. 108  \n3.4.3 Curvilinear grids ..................... 111  \n3.4.4 Triangular unstructured grids .............. 112  \n3.4.5 Spherical Multiple-Cell (SMC) grid .........","cbCaii4YAGeZSSVh","https://ap.wps.com/l/cbCaii4YAGeZSSVh","pdf",3798754,361,"English","# 1 Introduction\n## 1.1 About this manual\n## 1.2 Licensing terms\n## 1.3 Copyrights and trademarks\n## 1.4 The WAVEWATCH III Development Group (WW3DG)\n## 1.5 Acknowledgments\n# 2 Governing equations\n## 2.1 Introduction\n## 2.2 Propagation\n## 2.3 Source terms\n## 2.4 Source terms for wave-ice interactions\n## 2.5 Air-sea processes\n## 2.6 Output parameters\n# 3 Numerical approaches\n## 3.1 Spectral discretization\n## 3.2 Splitting of the wave action equation\n## 3.3 Depth variations in time\n## 3.4 Spatial propagation\n## 3.5 Intra-spectral propagation\n## 3.6 Non-ice source term integration\n## 3.7 Ice source terms integration\n## 3.8 Simple ice blocking (IC0)\n## 3.9 Winds and currents\n## 3.10 Use of tidal analysis\n## 3.11 Wave crest and height space-time extremes\n## 3.12 Spectral partitioning\n## 3.13 Spatial and temporal tracking of wave systems\n## 3.14 Nesting\n# 4 Wave Model Structure and Data Flow\n## 4.1 Program design\n## 4.2 The wave model routines\n## 4.3 The data assimilation interface\n## 4.4 Auxiliary programs","[{\"question\":\"What is the document’s purpose?\",\"answer\":\"It serves as a user manual and system documentation for WAVEWATCH III version 5.16, prepared by the WAVEWATCH III Development Group (WW3DG).\"},{\"question\":\"Which main technical topics are covered?\",\"answer\":\"The manual covers governing equations, source terms (including wave-ice and air-sea processes), numerical approaches for wave propagation, and the wave model structure and data flow with relevant interfaces and auxiliary programs.\"},{\"question\":\"Does the manual describe how the model handles spatial propagation and grids?\",\"answer\":\"Yes. It includes numerical approaches for spatial propagation and discusses multiple grid types and related schemes (e.g., regular grids, curvilinear grids, unstructured grids, and spherical multiple-cell grids).\"}]","WAVEWATCH III - User manual and system documentation - version 5.16 | PDF",910]