On a Solution of the Closure Problem for Dry Convective Boundary Layer Turbulence and Beyond

We consider the closure problem of representing the higher-order moments (HOMs) in terms of lower- order moments, a central feature in turbulence modeling based on the Reynolds-averaged Navier–Stokes (RANS) approach. Our focus is on models suited for the description of asymmetric, nonlocal, and semiorganized turbulence in the dry atmospheric convective boundary layer (CBL). We establish a multivariate probability density function (PDF) describ- ing populations of plumes that are embedded in a sea of weaker randomly spaced eddies, and apply an assumed delta-PDF approximation. The main content of this approach consists of capturing the bulk properties of the PDF. We solve the clo- sure problem analytically for all relevant HOMs involving velocity components and temperature and establish a hierarchy of new non-Gaussian turbulence closure models of different content and complexity ranging from analytical to semianalyti- cal. All HOMs in the hierarchy have a universal and simple functional form. They refine the widely used Millionshchikov closure hypothesis and generalize the famous quadratic skewness–kurtosis relationship to higher order. We examine the performance of the new closures by comparison with measurement, LES, and DNS data and derive empirical constants for semianalytical models, which are best for practical applications. We show that the new models have a good skill in predict- ing the HOMs for atmospheric CBL. Our closures can be implemented in second-, third-, and fourth-order RANS turbu- lence closure models of bi-, tri-, and four-variate levels of complexity. Finally, several possible generalizations of our approach are discussed

A Package of Momentum and Heat Transfer Coefficients for the Stable Surface Layer Extended by New Coefficients over Sea Ice

ingredients of numerical weather prediction and climatemodels. They are needed for the calculation of turbulent fluxes in the surface layer and often rely on the Monin–Obukhov similarity theory requiring universal stability functions. The problem of a derivation of transfer coefficients based on different stability functions has been considered by many researchers over the years but it remains to this day. In this work, dedicated to the memory of S.S. Zilitinkevich, we also address this task, and obtain transfer coefficients from three pairs of theoretically derived stability functions suggested by Zilitinkevich and co-authors for stable conditios. Additionally, we construct non-iterative parametrizations of these transfer coefficients based on earlier work. Results are compared with state-of-the-art coefficients for land, ocean, and sea ice. The combined parametrizations form a package in a universal framework relying on a semi-analytical solution of the Monin-Obukhov similarity theory equations. A comparison with data of the Surface Heat Budget of the Arctic Ocean campaign (SHEBA) over sea ice reveals large differences between the coefficients for land conditions and the measurements over sea ice. However, two schemes of Zilitinkevich and co-authors show, after slight modification, good agreement with SHEBA although they had not been especially developed for sea ice. One pair of the modified transfer coefficients is superior and is compatible to earlier SHEBA-based parametrizations. Finally, an algorithm for practical use of all transfer coefficients in climate models is given

A package of momentum and heat transfer coefficientsfor the stable atmospheric surface layer

The polar atmospheric surface layer is often stably stratified, which strongly influences turbulent transport processes between the atmosphere and sea ice/ocean. Transport is usually parametrized applying Monin Obukhov Similarity Theory (MOST) which delivers transfer coefficients as a function of stability parameters (see below). In a series of papers (Gryanik and Lüpkes, 2018; Gryanik et al., 2020,2021; Gryanik and Lüpkes, 2022) it has been shown that differences between existing parametrizations are large, especially for strong stability. One reason is that they are based on different data sets, for which the origin of differences is still unclear. In this situation Gryanik et al. (2021) as well as Gryanik and Lüpkes (2022) proposed a numerically efficient method, which can be used for most of the existing data sets and their specific stability dependences. A package of parametrization resulted that is suitable for its application in weather prediction and climate models. Especially, calculation of fluxes over sea ice were improved. Combined with latest parametrizations of surface roughness it has a large impact on large scale fields as shown recently by Schneider et al. (2021) who applied some members of the package

Parametrization of Turbulent Fluxes over Leads in Sea Ice in a Non-Eddy-Resolving Small-Scale Atmosphere Model

Leads (open-water channels in sea ice) play an important role for surface-atmosphere interactions in the polar regions. Due to large temperature differences between the surface of leads and the near-surface atmosphere, strong turbulent convective plumes are generated with a large impact on the atmospheric boundary layer (ABL). Here, we focus on the effect of lead width on those processes, by means of numerical modeling and turbulence parametrization. We use a microscale atmosphere model in a 2D version resolving the entire convective plume with grid sizes in the range of L/5 where L is the lead width. For the sub-grid scale turbulence, we developed a modified version of an already existing nonlocal parametrization of the lead-generated sensible heat flux including L as parameter. All our simulations represent measured springtime conditions with a neutrally stratified ABL capped by a strong temperature inversion at 300 m height, where the initial temperature difference between the lead surface and the near-surface atmosphere amounts to 20 K. We found that our simulation results obtained with the new approach agree very well with time-averaged results of a large eddy simulation (LES) model for variable lead widths with L ≥ 1 km and different upstream wind speeds. This is a considerable improvement since results obtained with the previous nonlocal approach clearly disagree with the LES results for leads wider than 2 km. In conclusion, considering L as parameter in a nonlocal turbulence parametrization seems to be necessary to study the effect of leads on the polar ABL in non-eddy-resolving small-scale atmosphere models