A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

Abstract

In several recent large-eddy simulation studies, the lowest grid level was located well within the roughness sublayer. Monin-Obukhov similarity-based boundary conditions cannot be used under this scenario, and in this note we elaborate on this fundamental problem and suggest potential solutions.Keywords Inertial sublayer · Large-eddy simulation · Monin-Obukhov similarity theory · Roughness sublayer · Surface layerIn the era of petascale computing, very high-resolution (the grid size, Δ = O(1) m or finer) large-eddy simulation (LES) of atmospheric boundary-layer (ABL) flows is gradually becoming a norm. For example, in a recent study (Sullivan et al. 2016), Δ = 0.39m was utilized in the idealized simulation of the stable boundary layer. It is a well-known fact that all the contemporary LES codes utilize the conventional Monin-Obukhov similarity theory (MOST) as lower boundary conditions (e.g., Heus et al. 2010;Maronga et al. 2015). It is also common knowledge (e.g., Lumley and Panofsky 1964;Monin and Yaglom 1971;Wyngaard 2010) that MOST is only valid for heights z z • , where z • is the aerodynamic roughness length. MOST is not applicable for z < αh, where h denotes the height of the roughness elements. Typically, α is assumed to be between 2 and 5 based on laboratory studies (see Raupach et al. 1991, and references therein). Unfortunately, a number of recent LES studies (e.g., Beare et al. 2006;Basu et al. 2011; Maronga 2014;Sullivan et al. 2016;Udina et al.

Coupling a three-dimensional subsurface flow and transport model with a land surface model to simulate stream–aquifer–land interactions (CP v1.0)

“…2.1), which is only valid when the surface layer depth z z 0 , where z 0 is the aerodynamic roughness length. As reviewed by Basu and Lacser (2017), it is highly recommended that z > 50 z 0 , which should be proportional to the horizontal grid spacing to guaran-tee the validity of the Monin-Obukhov similarity theory (Arnqvist and Bergström, 2015). In our simulations, the majority of the Hanford 300 Area domain is covered by bare soil (z 0 = 0.01 m), grass (z 0 = 0.013 m), shrubs (z 0 = 0.026-0.043 m), and riparian trees (varies across the seasons, z 0 = 0.008 m when LAI = 2 in the summer and z 0 = 1.4 when LAI = 0 in the winter).…”

An Improved Surface Boundary Condition for Large-Eddy Simulations Based on Monin–Obukhov Similarity Theory: Evaluation and Consequences for Grid Convergence in Neutral and Stable Conditions

“…As an example, following this suggestion and for typical roughness lengths for surfaces covered with low vegetation (heights in the order of 0.1 m), this imposes a minimum vertical grid spacing of 5 m for LES models with a common MOST boundary condition. Basu and Lacser (2017) reported correctly that, in practice, MOST also is applied for much smaller grid spacings, despite this violation of MOST assumptions and in the lack of an alternative (e.g., Beare et al 2006;Basu et al 2011;Maronga 2014;Sullivan et al 2016;Udina et al 2016). This is particularly true for LES of the stable boundary layer, where grid spacings < 5 m are required to resolve the small-scale turbulence (Beare and MacVean 2004).…”

“…This correction, however, was derived for a specific forest canopy and for neutral atmospheric stratification only. Referring to this previous work, Basu and Lacser (2017) suggested considering z * = 50z 0 as a general rule for LES models. As an example, following this suggestion and for typical roughness lengths for surfaces covered with low vegetation (heights in the order of 0.1 m), this imposes a minimum vertical grid spacing of 5 m for LES models with a common MOST boundary condition.…”

“…First, when using grid spacings in the order of a few metres, the application of MOST can become problematic. Several researchers pointed out that MOST can only be considered valid within the inertial sublayer, the upper part of the surface layer, but fails in the roughness sublayer below, in which direct effects of single surface roughness elements are present (Garratt 1980;Raupach 1992;Physick and Garratt 1995;Harman and Finnigan 2007;Basu and Lacser 2017). Garratt (1980) found, for high vegetation and neutral and unstable conditions, that the lower boundary of the inertial sublayer (z * ), i.e., the top of the roughness sublayer, depends on the average horizontal distance between trees (δ), and estimated z * ≈ 3δ, which corresponded to z * = 35z 0 , where z 0 is the roughness length.…”

Implementation of a roughness sublayer parameterization in the Weather Research and Forecasting model (WRF version 3.7.1) and its evaluation for regional climate simulations

“…The turbulent transport in the RSL has a mixing layer analogy, and the atmospheric flow depends on the roughness element properties (Raupach et al, 1996). Accordingly, the flux-gradient relationships in the RSL deviate from the MOST predictions, and the eddy diffusion coefficients are larger than the values in the ISL (e.g., Shaw et al, 1988;Kaimal and Finnigan, 1994;Brunet and Irvine, 2000;Finnigan, 2000;Hong et al, 2002;Dupont and Patton, 2012;Shapkalijevski et al, 2016;Zhan et al, 2016;Basu and Lacser, 2017).…”