ERF_TwoStreamLW.H File Reference

Longwave (thermal) radiation using gray-gas two-stream model. More...

#include <AMReX_GpuControl.H>
#include <AMReX_Math.H>
#include <AMReX_FArrayBox.H>
#include <AMReX_REAL.H>
#include <cmath>

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Functions
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	compute_thermal_intensity (amrex::Real T, amrex::Real sigma)
	Compute thermal (LW) intensity for a given temperature. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	compute_lw_transmit (amrex::Real tau_lw)
	Compute transmission coefficient through an absorbing layer. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	compute_lw_flux_up (amrex::Real F_up_below, amrex::Real T_layer, amrex::Real sigma, amrex::Real tau_lw)
	Compute upwelling LW flux in one layer of a two-stream sweep. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	compute_lw_flux_down (amrex::Real F_down_above, amrex::Real T_layer, amrex::Real sigma, amrex::Real tau_lw)
	Compute downwelling LW flux in one layer of a two-stream sweep. More...
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	compute_lw_heating_rate (amrex::Real F_net_top, amrex::Real F_net_bot, amrex::Real dz, amrex::Real rho, amrex::Real cp)
	Compute LW heating rate from net flux divergence. More...

Variables
constexpr amrex::Real	stefan_boltzmann = amrex::Real(5.670374419e-8)
	Stefan-Boltzmann constant [W/(m^2 K^4)] used by the two-stream LW model. More...

Detailed Description

Longwave (thermal) radiation using gray-gas two-stream model.

Implements a simplified, clear-sky longwave radiation model using the gray-gas two-stream approximation (Toon et al. 1989):

Vertical orientation follows ERF: the vertical index k increases upward, so layer k = kmin touches the surface and k = kmax the top of the domain. Fluxes live on layer interfaces m = k - kmin (bottom of layer k) and m + 1 (top of layer k); m = 0 is the surface, m = nlev the TOA.

UPWARD SWEEP (from surface to TOA):

F_up(m+1) = F_up(m) * exp(-tau_lw) + sigma * T(k)^4 * (1 - exp(-tau_lw))

Initial condition: F_up(0) = emissivity * sigma * T_surface^4

• (1 - emissivity) * F_down(0) (gray surface: emitted plus reflected downwelling flux, so the downward sweep must be completed before the upward sweep starts)

DOWNWARD SWEEP (from TOA to surface):

F_down(m) = F_down(m+1) * exp(-tau_lw) + sigma * T(k)^4 * (1 - exp(-tau_lw))

Initial condition: F_down(nlev) = 0 (no incoming from space)

NET FLUX AND HEATING:

F_net(m) = F_up(m) - F_down(m) (positive upward) Q_lw(k) = -(1 / (rho * cp)) * [F_net(m+1) - F_net(m)] / dz(k) [K/s]

A layer that emits more than it absorbs has F_net increasing with height, so Q_lw < 0 (radiative cooling).

Layer temperature T(k) is the absolute temperature obtained from rho*theta through the Exner function (see get_temperature_from_rhotheta() in ERF_TwoStreamRadiation.cpp), not the potential temperature.

MODEL SIMPLIFICATIONS:

• Uniform optical depth (tau_lw) per layer
• No scattering
• No clouds

References:

• Toon, O. B., C. P. McKay, T. P. Ackerman, and K. Santhanam, 1989: Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres. J. Geophys. Res., 94, 16387-16405. https://doi.org/10.1029/JD094iD13p16387
• Kirchhoff, G., 1860: Ueber den Zusammenhang zwischen den Emissionsvermögen und den Absorptionsvermögen der Körper für Wärmestrahlung. Monatsberichte der Akademie der Wissenschaften zu Berlin, 783-787.

Function Documentation

compute_lw_flux_down()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real compute_lw_flux_down	(	amrex::Real	F_down_above,
		amrex::Real	T_layer,
		amrex::Real	sigma,
		amrex::Real	tau_lw
	)

Compute downwelling LW flux in one layer of a two-stream sweep.

Implements the downward flux formula in the gray-gas two-stream model:

F_down_current = F_down_above * exp(-tau_lw) + sigma * T^4 * (1 - exp(-tau_lw))

This is called iteratively from the TOA (where F_down_toa = 0) downward to the surface.

Parameters

[in]	F_down_above	Downwelling flux from the layer above [W/m^2].
[in]	T_layer	Temperature of the current layer [K].
[in]	sigma	Stefan-Boltzmann constant [W/(m^2·K^4)].
[in]	tau_lw	Optical depth of the current layer [unitless].

Returns

Downwelling flux at the bottom of the current layer [W/m^2].

Note

This function assumes each layer acts as a semi-infinite slab with uniform temperature and optical depth.

Called within a device-side kernel; must be GPU-safe.

{
  amrex::Real transmit = compute_lw_transmit(tau_lw);
  amrex::Real absorb = 1.0 - transmit;
  amrex::Real I_layer = compute_thermal_intensity(T_layer, sigma);
  return F_down_above * transmit + I_layer * absorb;
}

Referenced by vertical_two_stream_sweep().

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compute_lw_flux_up()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real compute_lw_flux_up	(	amrex::Real	F_up_below,
		amrex::Real	T_layer,
		amrex::Real	sigma,
		amrex::Real	tau_lw
	)

Compute upwelling LW flux in one layer of a two-stream sweep.

Implements the upward flux formula in the gray-gas two-stream model:

F_up_current = F_up_below * exp(-tau_lw) + sigma * T^4 * (1 - exp(-tau_lw))

This is called iteratively from the surface (where F_up_surface = emissivity * sigma * T_surface^4 + (1 - emissivity) * F_down_surface) upward to the TOA.

Parameters

[in]	F_up_below	Upwelling flux from the layer below [W/m^2].
[in]	T_layer	Temperature of the current layer [K].
[in]	sigma	Stefan-Boltzmann constant [W/(m^2·K^4)].
[in]	tau_lw	Optical depth of the current layer [unitless].

Returns

Upwelling flux at the top of the current layer [W/m^2].

Note

This function assumes each layer acts as a semi-infinite slab with uniform temperature and optical depth.

Called within a device-side kernel; must be GPU-safe.

{
  amrex::Real transmit = compute_lw_transmit(tau_lw);
  amrex::Real absorb = 1.0 - transmit;
  amrex::Real I_layer = compute_thermal_intensity(T_layer, sigma);
  return F_up_below * transmit + I_layer * absorb;
}

Referenced by vertical_two_stream_sweep().

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compute_lw_heating_rate()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real compute_lw_heating_rate	(	amrex::Real	F_net_top,
		amrex::Real	F_net_bot,
		amrex::Real	dz,
		amrex::Real	rho,
		amrex::Real	cp
	)

Compute LW heating rate from net flux divergence.

Given the net LW flux (F_up - F_down, positive upward) at the top and bottom interfaces of a layer, compute the radiative heating rate:

dF_net/dz = [F_net_top - F_net_bot] / dz Q_lw = -dF_net/dz / (rho * cp) [K/s]

Net upward flux increasing with height means the layer loses more energy through its top than it gains through its bottom, i.e. the layer cools (Q_lw < 0). This is the same sign convention as the SW heating rate: energy converging into the layer warms it.

Nonuniform dz Support & Sanity Checks

This function accepts per-level dz values to support terrain-aware or nonuniform vertical grids. When dz <= 0, or rho <= 0, or cp <= 0, returns 0 (heating rate is undefined or unphysical).

The computed heating rate is guarded against NaN/Inf via the same parameter validation.

Parameters

[in]	F_net_top	Net flux at the top of the layer [W/m^2].
[in]	F_net_bot	Net flux at the bottom of the layer [W/m^2].
[in]	dz	Vertical thickness of the layer [m]. Must be positive. For nonuniform grids, use per-level spacing.
[in]	rho	Density [kg/m^3]. Must be positive.
[in]	cp	Specific heat at constant pressure [J/(kg·K)]. Must be positive.

Returns

Heating rate [K/s]. Positive values indicate warming. Returns 0 if inputs are unphysical (dz, rho, cp <= 0).

Note

The sign convention is: positive dF_net/dz (net upward flux increasing with height) corresponds to cooling (dT/dt < 0).

For terrain-aware grids, pass dz = z_cc(k+1) - z_cc(k) for each level.

{
  if (dz <= 0.0 || rho <= 0.0 || cp <= 0.0) {
    return 0.0;
  }
  // Net flux divergence: (W/m^2) / (m) = W/m^3
  amrex::Real flux_divergence = (F_net_top - F_net_bot) / dz;
  // Heating rate: -(W/m^3) / (kg/m^3 * J/(kg*K)) = K/s
  // Check for NaN/Inf as defensive sanity check
  amrex::Real heating = -flux_divergence / (rho * cp);
  if (!amrex::Math::isfinite(heating)) {
    return 0.0;
  }
  return heating;
}

Referenced by vertical_two_stream_sweep().

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compute_lw_transmit()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real compute_lw_transmit

(

amrex::Real

tau_lw

)

Compute transmission coefficient through an absorbing layer.

For a layer with optical depth tau_lw, the fraction of incident radiation that is transmitted (not absorbed or scattered) is:

transmit = exp(-tau_lw)

The fraction absorbed/scattered is:

absorb = 1 - exp(-tau_lw)

This is used in the two-stream upward/downward sweep formulas.

Parameters

[in]

tau_lw

Optical depth of the layer [unitless]. Must be ≥ 0.

Returns

Transmission fraction [0, 1]. Satisfies transmit + absorb = 1.

Note

If tau_lw = 0, returns 1 (fully transparent).

If tau_lw >> 1, returns ≈ 0 (fully opaque).

{
  if (tau_lw < 0.0) {
    return 1.0;  // Unphysical, but defensive
  }
  return std::exp(-tau_lw);
}

Referenced by compute_lw_flux_down(), and compute_lw_flux_up().

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compute_thermal_intensity()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real compute_thermal_intensity	(	amrex::Real	T,
		amrex::Real	sigma
	)

Compute thermal (LW) intensity for a given temperature.

Using the Stefan-Boltzmann law, compute the upwelling or downwelling thermal radiation intensity:

I_rad = sigma * T^4

where sigma is the Stefan-Boltzmann constant and T is absolute temperature.

This is a GPU-safe inline function.

Parameters

[in]	T	Absolute temperature [K]. Must be positive.
[in]	sigma	Stefan-Boltzmann constant [W/(m^2·K^4)].

Returns

Radiative intensity [W/m^2]. Always non-negative.

Note

If T ≤ 0, returns 0 (unphysical, but defensive).

For typical terrestrial temperatures (200-400 K), this ranges from ~1 W/m^2 to ~1500 W/m^2.

{
  if (T <= 0.0) {
    return 0.0;
  }
  return sigma * T * T * T * T;
}

Referenced by compute_lw_flux_down(), compute_lw_flux_up(), and vertical_two_stream_sweep().

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Variable Documentation

stefan_boltzmann

constexpr amrex::Real stefan_boltzmann = amrex::Real(5.670374419e-8)

constexpr

Stefan-Boltzmann constant [W/(m^2 K^4)] used by the two-stream LW model.

Referenced by vertical_two_stream_sweep().