ERF_PBLScaleAwareBlending.H File Reference

GPU-inline blending functions for PBL diffusivity at grey-zone resolution. More...

#include <AMReX_REAL.H>
#include <AMReX_GpuQualifiers.H>
#include <cmath>

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Functions
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	pbl_blend_factor (amrex::Real dx, amrex::Real L_blend) noexcept
	Boutle et al. (2014) blending factor. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	pbl_kh_ceiling_smag (amrex::Real dx, amrex::Real SmnSmn, amrex::Real C_s) noexcept
	Smagorinsky-Lilly K_h ceiling. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	pbl_kh_ceiling_powerlaw (amrex::Real dx, amrex::Real c_max) noexcept
	Power-law K_h ceiling (fallback when SmnSmn not available). More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	pbl_kh_blend_and_cap (amrex::Real K_h, amrex::Real dx, amrex::Real L_blend, amrex::Real C_s, amrex::Real c_max, amrex::Real SmnSmn, bool use_smag) noexcept
	Apply scale-aware blending and ceiling to a single K_h value. More...

Detailed Description

GPU-inline blending functions for PBL diffusivity at grey-zone resolution.

Provides scale-aware reduction of PBL vertical diffusivity (K_h) when the horizontal grid spacing falls between mesoscale and LES resolution.

Designed as a standalone header callable from any PBL scheme (MRF, YSU, MYNN) without code duplication. All functions are AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE free functions with no state.

Usage in an MFIter loop after K_h is computed: K_h_eff = pbl_kh_blend_and_cap(K_h, dx, L_blend, C_s, c_max, SmnSmn, use_smag);

K_h is a kinematic diffusivity [m^2/s], because that is the unit of the ceilings applied here. Schemes that carry rho*K in K_turb (all of the ERF PBL models do) must divide by rho on the way in and multiply by rho on the way out, or the cap ends up scaling like 1/rho instead of being a constant diffusivity.

Gating: pbl_kh_blend_and_cap returns K_h unchanged when L_blend <= 0. Setting L_blend = 0 recovers original PBL behaviour exactly.

References: Boutle, I.A. et al. (2014). Mon. Wea. Rev., 142, 1655. https://doi.org/10.1175/MWR-D-13-00229.1 Smagorinsky, J. (1963). Mon. Wea. Rev., 91, 99. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 Honnert, R. et al. (2011). J. Atmos. Sci., 68, 2742. https://doi.org/10.1175/JAS-D-11-025.1 Beare, R.J. (2014). Bound.-Layer Meteor., 153, 345. https://doi.org/10.1007/s10546-013-9881-3 Hong, S.-Y., & Pan, H.-L. (1996). Mon. Wea. Rev., 124, 2322. https://doi.org/10.1175/1520-0493(1996)124<2322:NBLVDI>2.0.CO;2

Function Documentation

pbl_blend_factor()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real pbl_blend_factor ( amrex::Real  dx, amrex::Real  L_blend  )

noexcept

Boutle et al. (2014) blending factor.

f = (dx/L_blend)^2 / (1 + (dx/L_blend)^2)

Returns 1 when L_blend <= 0 (gate: no blending). Asymptotes to 1 as dx >> L_blend (mesoscale grid, full PBL K_h). Asymptotes to 0 as dx << L_blend (LES grid, no PBL K_h contribution).

This is the weight on the parameterized (subgrid) part of the turbulence, so it must grow with dx: the coarser the grid, the less of the boundary layer overturning is resolved and the more the PBL scheme has to supply. It was previously written as 1/(1+(dx/L_blend)^2), which has both limits backwards – it switched the PBL scheme off at mesoscale resolution and left it at full strength at LES resolution, on top of whatever the resolved motions were already doing (issue #3619).

Parameters

dx	Horizontal grid spacing [m].
L_blend	Blending length scale [m]. Typical: 750 m. 0 = disabled.

{
    if (L_blend <= 0.0) return 1.0;
    const amrex::Real r = dx / L_blend;
    return (r * r) / (1.0 + r * r);
}

Referenced by pbl_kh_blend_and_cap().

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pbl_kh_blend_and_cap()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real pbl_kh_blend_and_cap ( amrex::Real  K_h, amrex::Real  dx, amrex::Real  L_blend, amrex::Real  C_s, amrex::Real  c_max, amrex::Real  SmnSmn, bool  use_smag  )

noexcept

Apply scale-aware blending and ceiling to a single K_h value.

K_h_eff = min(K_h * f_blend(dx, L_blend), K_h_max)

Gate: returns K_h unchanged when L_blend <= 0.

Ceiling selection: use_smag = true and SmnSmn >= 0: Smagorinsky ceiling. otherwise: power-law ceiling.

Callable from any PBL scheme (MRF, YSU, MYNN) without modification.

Parameters

K_h	PBL vertical diffusivity [m^2/s] before blending.
dx	Horizontal grid spacing [m].
L_blend	Boutle blending length [m]. 0 = no blending (returns K_h).
C_s	Smagorinsky coefficient (used when use_smag=true).
c_max	Power-law coefficient [m^(2/3)/s] (used when use_smag=false).
SmnSmn	Strain rate squared [s^-2]. Use -1 when not available.
use_smag	Use Smagorinsky ceiling when SmnSmn >= 0.

Returns

Blended and capped K_h [m^2/s].

{
    if (L_blend <= 0.0) return K_h;
 
    const amrex::Real f       = pbl_blend_factor(dx, L_blend);
    const amrex::Real K_blend = K_h * f;
 
    amrex::Real K_max;
    if (use_smag && SmnSmn >= 0.0) {
        K_max = pbl_kh_ceiling_smag(dx, SmnSmn, C_s);
    } else {
        K_max = pbl_kh_ceiling_powerlaw(dx, c_max);
    }
    return amrex::min(K_blend, K_max);
}

Referenced by ComputeDiffusivityMRF().

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pbl_kh_ceiling_powerlaw()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real pbl_kh_ceiling_powerlaw ( amrex::Real  dx, amrex::Real  c_max  )

noexcept

Power-law K_h ceiling (fallback when SmnSmn not available).

K_h_max = c_max * dx^(4/3)

Derived from dimensional analysis of the inertial subrange. Reference: Honnert et al. (2011). https://doi.org/10.1175/JAS-D-11-025.1

Parameters

dx	Horizontal grid spacing [m].
c_max	Coefficient [m^(2/3) s^-1]. Typical: 0.1.

{
    return c_max * std::pow(dx, amrex::Real(4.0) / amrex::Real(3.0));
}

Referenced by pbl_kh_blend_and_cap().

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pbl_kh_ceiling_smag()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real pbl_kh_ceiling_smag ( amrex::Real  dx, amrex::Real  SmnSmn, amrex::Real  C_s  )

noexcept

Smagorinsky-Lilly K_h ceiling.

K_h_max = (C_s * dx)^2 * sqrt(2 * SmnSmn)

Used when strain rate SmnSmn is available (e.g. from SmnSmn_lev in ERF).

Parameters

dx	Horizontal grid spacing [m].
SmnSmn	S_ij*S_ij strain rate squared [s^-2]. Must be >= 0.
C_s	Smagorinsky coefficient. Typical: 0.17.

{
    const amrex::Real Lmix = C_s * dx;
    return Lmix * Lmix * std::sqrt(2.0 * amrex::max(SmnSmn, amrex::Real(0.0)));
}

Referenced by pbl_kh_blend_and_cap().

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