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);

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 = 1 / (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).

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 1.0 / (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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