Chapter 10 Higher-Order Equations Closed by the Assumed PDF Method: Suitability for Parameterizing Cumulus Convection Vincent E. Larson, Vincent E. Larson Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA Pacific Northwest National Laboratory, Richland, WA, USASearch for more papers by this author Vincent E. Larson, Vincent E. Larson Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA Pacific Northwest National Laboratory, Richland, WA, USASearch for more papers by this author Book Editor(s):Yangang Liu, Yangang LiuSearch for more papers by this authorPavlos Kollias, Pavlos KolliasSearch for more papers by this author First published: 30 November 2023 https://doi.org/10.1002/9781119529019.ch10Book Series:Geophysical Monograph Series AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat Summary One method for parameterizing turbulence and clouds in the Earth's atmosphere is higher-order closure. In this method, equations are formed for relevant subgrid-scale moments, such as vertical turbulent fluxes and vertical velocity variance. These equations contain unclosed terms. Some of these terms may be closed via an assumption about the shape of the probability density function (PDF) of fields on the subgrid scale. This chapter briefly summarizes the method of higher-order PDF closure. This method is compared to two other methods: the mass-flux method and low-order closure. It is argued that higher-order closure contains sufficient physics to parameterize cumulus convection. References Abdella , K. , & McFarlane , N. ( 1997 ). A new second-order turbulence closure scheme for the planetary boundary layer. Journal of the Atmospheric Sciences , 54 , 1850 – 1867 . 10.1175/1520-0469(1997)054<1850:ANSOTC>2.0.CO;2 Web of Science®Google Scholar Abdella , K. , & McFarlane , N. ( 1999 ). Journal of the Atmospheric Sciences , 56 , 3482 – 3483 . 10.1175/1520-0469(1999)056<3482:R>2.0.CO;2 Web of Science®Google Scholar Abdella , K. , & Petersen , A. C. ( 2000 ). Third-order moment closure through a mass-flux approach . 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Higher‐Order Equations Closed by the Assumed PDF Method: Suitability for Parameterizing Cumulus Convection