TY - JOUR

T1 - On the Formulation and Universality of Monin–Obukhov Similarity Functions for Mean Gradients and Standard Deviations in the Unstable Surface Layer

T2 - Results from Surface-Layer-Resolving Large-Eddy Simulations

AU - Maronga, Björn

AU - Reuder, Joachim

N1 - Funding information: First of all, we would like to emphasize the quality of the very helpful comments of the anonymous reviewers that identified deficiencies in our initial manuscript and who provided excellent ideas for further analysis of our data that entered the revised version. Moreover, we thank Siegfried Raasch, Dieter Etling, and Christoph Knigge (all at Leibniz Universität Hannover, Germany) for reading a draft of the manuscript and/or for various discussions on the topic. Most part of the analyses in this paper were done during a research visit of the first author at the Geophysical Institute at theUniversity of Bergen inMay 2016, for which financial support was provided by Leibniz Universität Hannover and the University of Bergen, which is gratefully acknowledged. The simulations conducted for this study were supported by the German Research Foundation (DFG) under Grants RA 617/20-1 and RA 617/20-3. All simulations were performed on the former SGI Altix ICE at The North-German Supercomputing Alliance (HLRN),Hannover/Berlin.NCL (NCAR2013) has been used for data analysis and visualization.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - Surface-layer-resolving large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to study Monin-Obukhov similarity theory (MOST) functions. The LES dataset, previously used for the analysis of MOST relationships for structure parameters, is extended for the mean vertical gradients and standard deviations of potential temperature, specific humidity, and wind. Also, local-free-convection (LFC) similarity is studied. The LES data suggest that the MOST functions for mean gradients are universal and unique. The data for the mean gradient of the horizontal wind display significant scatter, while the gradients of temperature and humidity vary considerably less. The LES results suggest that this scatter is mostly related to a transition from MOST to LFC scaling when approaching free-convective conditions and that it is associated with a change of the slope of the similarity functions toward the expected value from LFC scaling. Overall, the data show slightly, but consistent, steeper slopes of the similarity functions than suggested in literature. The MOST functions for standard deviations appear to be unique and universal when the entrainment from the free atmosphere into the boundary layer is sufficiently small. If entrainment becomes significant, however, we find that the standard deviation of humidity no longer follows MOST. Under free-convective conditions, the similarity functions should reduce to universal constants (LFC scaling). This is supported by the LES data, showing only little scatter, but displaying a systematic height dependence of these constants. Like for MOST, the LFC similarity constant for the standard deviation of specific humidity becomes nonuniversal when the entrainment of dry air reaches significant levels.

AB - Surface-layer-resolving large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to study Monin-Obukhov similarity theory (MOST) functions. The LES dataset, previously used for the analysis of MOST relationships for structure parameters, is extended for the mean vertical gradients and standard deviations of potential temperature, specific humidity, and wind. Also, local-free-convection (LFC) similarity is studied. The LES data suggest that the MOST functions for mean gradients are universal and unique. The data for the mean gradient of the horizontal wind display significant scatter, while the gradients of temperature and humidity vary considerably less. The LES results suggest that this scatter is mostly related to a transition from MOST to LFC scaling when approaching free-convective conditions and that it is associated with a change of the slope of the similarity functions toward the expected value from LFC scaling. Overall, the data show slightly, but consistent, steeper slopes of the similarity functions than suggested in literature. The MOST functions for standard deviations appear to be unique and universal when the entrainment from the free atmosphere into the boundary layer is sufficiently small. If entrainment becomes significant, however, we find that the standard deviation of humidity no longer follows MOST. Under free-convective conditions, the similarity functions should reduce to universal constants (LFC scaling). This is supported by the LES data, showing only little scatter, but displaying a systematic height dependence of these constants. Like for MOST, the LFC similarity constant for the standard deviation of specific humidity becomes nonuniversal when the entrainment of dry air reaches significant levels.

KW - Boundary layer

KW - Large eddy simulations

KW - Microscale processes/variability

KW - Numerical analysis/modeling

KW - Parameterization

KW - Surface fluxes

UR - http://www.scopus.com/inward/record.url?scp=85016759530&partnerID=8YFLogxK

U2 - 10.1175/JAS-D-16-0186.1

DO - 10.1175/JAS-D-16-0186.1

M3 - Article

AN - SCOPUS:85016759530

VL - 74

SP - 989

EP - 1010

JO - Journal of the Atmospheric Sciences

JF - Journal of the Atmospheric Sciences

SN - 0022-4928

IS - 4

ER -