Standard

Standard#

class abcmodel.rad.standard.StandardRadiationState(net_rad, in_srad=<factory>, out_srad=<factory>, in_lrad=<factory>, out_lrad=<factory>)[source]#

Bases: AbstractRadiationState

Standard radiation model state.

net_rad: Array#

Net surface rad [W m-2].

in_srad: Array#

Incoming solar rad [W m-2].

out_srad: Array#

Outgoing solar rad [W m-2].

in_lrad: Array#

Incoming longwave rad [W m-2].

out_lrad: Array#

Outgoing longwave rad [W m-2].

class abcmodel.rad.standard.StandardRadiationModel(lat=51.97, lon=-4.93, doy=268.0, cc=0.0)[source]#

Bases: AbstractRadiationModel[StandardRadiationState]

Standard radiation model with solar position and atmospheric effects.

Calculates time-varying solar rad based on geographic location and atmospheric conditions. Includes both shortwave (solar) and longwave (thermal) rad components.

Parameters:

  • lat (float) – latitude [degrees], range -90 to +90. Default is 51.97 (Cabauw, NL).

  • lon (float) – longitude [degrees], range -180 to +180. Default is -4.93 (Cabauw, NL).

  • doy (float) – day of year [-], range 1 to 365. Default is 268.0.

  • cc (float) – cloud cover fraction [-], range 0 to 1. Default is 0.0.

init_state(net_rad=400.0)[source]#

Initialize the model state.

Parameters:

net_rad (float) – Net surface radiation [W m-2]. Default is 400.0.

Returns:

The initial radiation state.

run(state, t, dt, tstart)[source]#

Calculate rad components and net surface rad.

Parameters:
Returns:

The updated rad state object.

compute_solar_declination(doy)[source]#

Compute solar declination angle based on day of year.

Parameters:

doy (float) – Day of year [-], range 1 to 365.

Returns:

Solar declination angle [radians].

Notes

Calculates the solar declination angle \(\delta\) using

\[\delta = 0.409 \cdot \cos\left( \frac{2\pi \cdot (\text{D} - 173)}{365} \right)\]

where \(\text{D}\) is the day of the year, \(0.409\) is the approximate Earth’s axial tilt in radians (23.45°), and \(173\) is the approximate day of the summer solstice, which acts as the phase shift for the cosine wave.

compute_solar_elevation(t, dt, tstart, solar_declination)[source]#

Compute solar elevation angle (sine of elevation).

Parameters:

  • t (Array) – current time step index [-].

  • dt (float) – time step duration [s].

  • solar_declination (Array) – solar declination angle [radians] from compute_solar_declination().

Returns:

Sine of the solar elevation angle [-].

Notes

First, the latitude \(\phi\), longitude \(\lambda\), and time of day \(t\) are converted to radians with

\[\phi_{\text{rad}} = \frac{2\pi \cdot \text{lat}}{360},\]
\[\lambda_{\text{rad}} = \frac{2\pi \cdot \text{lon}}{360},\]
\[t_{\text{rad}} = \frac{2\pi \cdot (t \cdot dt + t_{\text{start}} \cdot 3600)}{86400}.\]

The sine of the solar elevation is then calculated as

\[\sin(\alpha) = \sin(\phi_{\text{rad}})\sin(\delta) - \cos(\phi_{\text{rad}})\cos(\delta) \cos(t_{\text{rad}} + \lambda_{\text{rad}}),\]

where \(\delta\) is the solar declination. The result is clipped at a minimum value of 0.0001 to represent night-time and avoid mathematical instability in subsequent calculations.

compute_air_temperature(surf_pressure, h_abl, theta)[source]#

Compute air temperature at reference level using potential temperature.

Parameters:

  • surf_pressure (Array) – surface pressure [Pa].

  • h_abl (Array) – atmospheric boundary layer height [m].

  • theta (Array) – potential temperature [K].

Returns:

Air temperature at the reference level [K].

Notes

The calculation is a two-step process:

  1. First, the pressure at a reference level \(P_{\text{ref}}\) is estimated from the surface pressure \(P_{\text{surf}}\) using the simplified hydrostatic approximation

    \[P_{\text{ref}} = P_{\text{surf}} - 0.1 \cdot h_{\text{ABL}} \cdot \rho \cdot g,\]

    where \(h_{\text{ABL}}\) is the atmospheric boundary layer (ABL) height, \(\rho\) is air density, and \(g\) is gravity.

  2. Second, the potential temperature \(\theta\) is converted to the actual air temperature \(T_{\text{air}}\) at the reference level using Poisson’s equation (for an adiabatic process)

    \[T_{\text{air}} = \theta\left( \frac{P_{\text{ref}}}{P_{\text{surf}}} \right) ^{\kappa},\]

    where the exponent \(\kappa = R_d / c_p\) is the ratio of the gas constant for dry air \(R_d\) to the specific heat capacity of air \(c_p\).

compute_atmospheric_transmission(solar_elevation)[source]#

Compute atmospheric transmission coefficient for solar rad.

Parameters:

solar_elevation (Array) – sine of the solar elevation angle [-].

Returns:

Atmospheric transmission coefficient [-].

Notes

This is a simplified empirical parameterization (linear model) for atmospheric transmission (\(\tau\)).

  1. A clear-sky transmission \(\tau_{\text{clear}}\) is calculated based on the solar elevation \(\sin(\alpha)\) as

    \[\tau_{\text{clear}} = 0.6 + 0.2 \cdot \sin(\alpha).\]

  2. A cloud reduction factor \(f_{\text{cloud}}\) is calculated based on the cloud cover \(\text{cc}\) as

    \[f_{\text{cloud}} = 1.0 - 0.4 \cdot \text{cc}.\]

  3. The final transmission is then the product of these two factors, giving

    \[\tau = \tau_{\text{clear}} \cdot f_{\text{cloud}}.\]
compute_rad_components(solar_elevation, atmospheric_transmission, air_temp, alpha, surf_temp)[source]#

Compute all rad components and update attributes.

Parameters:

  • solar_elevation (Array) – sine of the solar elevation angle [-].

  • atmospheric_transmission (Array) – atmospheric transmission coefficient [-].

  • air_temp (Array) – air temperature [K].

  • alpha (Array) – surface albedo [-].

  • surf_temp (Array) – surface temperature [K].

Returns:

A tuple containing net rad, incoming shortwave rad, outgoing shortwave rad, incoming longwave rad and outgoing longwave rad [W/m^2].

Notes

This function calculates the four components of the surface rad budget and the resulting net rad.

Shortwave rad:

  1. Incoming shortwave \(SW_{\text{in}}\) is the solar constant \(S\) attenuated by the atmos and projected onto the surface, given by

    \[SW_{\text{in}} = S \cdot \tau \cdot \sin(\alpha),\]

    where \(\tau\) is the atmospheric transmission and \(\sin(\alpha)\) is the sine of the solar elevation.

  2. Outgoing shortwave \(SW_{\text{out}}\) is the fraction of incoming rad reflected by the surface (albedo, \(\alpha\)), given by

    \[SW_{\text{out}} = \alpha \cdot SW_{\text{in}}.\]

Longwave rad:

Both longwave components are calculated using the Stefan-Boltzmann law \(E = \epsilon \sigma T^4\).

  1. Incoming longwave \(LW_{\text{in}}\) is the rad from the atmos, which is treated as a grey body with an emissivity \(\epsilon_{\text{atm}} = 0.8\), given by

    \[LW_{\text{in}} = 0.8 \cdot \sigma \cdot T_{\text{air}}^4,\]

    where \(\sigma\) is the Stefan-Boltzmann constant const.bolz.

  2. Outgoing longwave \(LW_{\text{out}}\) is the rad from the surface, assuming an emissivity of 1.0, given by

    \[LW_{\text{out}} = \sigma \cdot T_{\text{surf}}^4.\]

Net rad:

Finally, the net rad \(R_{\text{net}}\) is given by the balance

\[R_{\text{net}} = (SW_{\text{in}} - SW_{\text{out}}) + (LW_{\text{in}} - LW_{\text{out}}).\]
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