Zilitinkevich

Zilitinkevich#

class abcmodel.atmos.stable_layer.zilitinkevich.ZilitinkevichState(h_sbl, theta, q, co2, u, v, surf_pressure, thetav=<factory>, ustar=<factory>, obukhov=<factory>, wtheta=<factory>, wq=<factory>, wCO2=<factory>, thetatend=<factory>, qtend=<factory>, co2tend=<factory>, utend=<factory>, vtend=<factory>)[source]#

Bases: AbstractState

Stable boundary layer (SBL) state.

Fields with default_factory are diagnostic and are populated during run(); user-provided fields are set at initialization.

h_sbl: Array#
theta: Array#
q: Array#
co2: Array#
u: Array#
v: Array#
surf_pressure: Array#
thetav: Array#
ustar: Array#
obukhov: Array#
wtheta: Array#
wq: Array#
wCO2: Array#
thetatend: Array#
qtend: Array#
co2tend: Array#
utend: Array#
vtend: Array#
class abcmodel.atmos.stable_layer.zilitinkevich.ZilitinkevichModel(coriolis_param=0.0001, zilitinkevich_const=0.4, is_wind_prog=True, gamma_theta=0.006, gamma_q=0.0, gamma_co2=0.0, gammau=0.0, gammav=0.0)[source]#

Bases: object

Stable boundary layer model.

Computes the SBL height using the Zilitinkevich (1972) formula and provides tendencies for thermodynamic variables.

Parameters:

  • coriolis_param (float) – Coriolis parameter [s-1]. Default is 1e-4.

  • zilitinkevich_const (float) – Zilitinkevich constant [-]. Default is 0.4.

  • is_wind_prog (bool) – Prognostic wind switch. Default is True.

  • gamma_theta (float) – Free-atmosphere theta lapse rate [K/m]. Default is 0.006.

  • gamma_q (float) – Free-atmosphere q lapse rate [kg/kg/m]. Default is 0.0.

  • gamma_co2 (float) – Free-atmosphere CO2 lapse rate [ppm/m]. Default is 0.0.

  • gammau (float) – Free-atmosphere u lapse rate [s-1]. Default is 0.0.

  • gammav (float) – Free-atmosphere v lapse rate [s-1]. Default is 0.0.

init_state(h_sbl=100.0, theta=288.0, q=0.008, co2=422.0, u=6.0, v=-4.0, surf_pressure=101300.0)[source]#

Initialize the SBL state.

Parameters:

  • h_sbl (float) – SBL height [m]. Default 100.0.

  • theta (float) – SBL potential temperature [K]. Default 288.0.

  • q (float) – SBL specific humidity [kg/kg]. Default 0.008.

  • co2 (float) – SBL CO2 [ppm]. Default 422.0.

  • u (float) – SBL zonal wind [m/s]. Default 6.0.

  • v (float) – SBL meridional wind [m/s]. Default -4.0.

  • surf_pressure (float) – Surface pressure [Pa]. Default 101300.0.

run(state, h_residual)[source]#

Run the SBL model.

Computes SBL height via Zilitinkevich and tendencies.

Parameters:

  • state (AbstractCoupledState) – The coupled state.

  • h_residual (Array) – Residual layer height [m] (upper bound for SBL).

Returns:

Updated SBL state.

statistics(state)[source]#

Compute SBL diagnostic statistics.

Parameters:

state (AbstractCoupledState) – Coupled state with SBL.

Returns:

Updated SBL state with diagnostic fields.

integrate(state, dt)[source]#

Integrate SBL state forward in time.

Parameters:
Returns:

Updated SBL state.

compute_sbl_height(ustar, obukhov, h_residual)[source]#

Compute SBL height using the Zilitinkevich (1972) formula.

\[h_{sbl} = C_z \, \sqrt{\frac{u_* \, L}{f}}\]

where \(C_z\) is the Zilitinkevich constant, \(u_*\) is the friction velocity, \(L\) is the Obukhov length (positive in stable conditions), and \(f\) is the Coriolis parameter.

The result is clamped between 10 m and h_residual.

Parameters:

  • ustar (Array) – Friction velocity [m/s].

  • obukhov (Array) – Obukhov length [m] (positive in stable conditions).

  • h_residual (Array) – Residual layer height [m] (upper bound).

Returns:

SBL height [m].

compute_thetatend(h_sbl, wtheta)[source]#

Compute potential temperature tendency for SBL.

\[\frac{d\theta}{dt} = \frac{w'\theta'}{h_{sbl}}\]

where \(w'\theta'\) is the surface kinematic heat flux (negative at night, cooling the SBL).

Parameters:

  • h_sbl (Array) – SBL height [m].

  • wtheta (Array) – Surface kinematic heat flux [K m/s].

Returns:

Potential temperature tendency [K/s].

compute_qtend(h_sbl, wq)[source]#

Compute specific humidity tendency for SBL.

\[\frac{dq}{dt} = \frac{w'q'}{h_{sbl}}\]
Parameters:

  • h_sbl (Array) – SBL height [m].

  • wq (Array) – Surface kinematic moisture flux [kg/kg m/s].

Returns:

Specific humidity tendency [kg/kg/s].

compute_co2tend(h_sbl, wCO2)[source]#

Compute CO2 tendency for SBL.

\[\frac{dCO_2}{dt} = \frac{w'CO_2'}{h_{sbl}}\]
Parameters:

  • h_sbl (Array) – SBL height [m].

  • wCO2 (Array) – Surface kinematic CO2 flux [mgC/m²/s].

Returns:

CO2 tendency [ppm/s].

compute_utend(h_sbl, uw, du, dv)[source]#

Compute zonal wind tendency for the SBL.

\[\frac{du}{dt} = -f \, dv - \frac{\overline{u'w'}}{h_{sbl}}\]

where \(\overline{u'w'}\) is the surface momentum flux and \(f\) is the Coriolis parameter.

Parameters:

  • h_sbl (Array) – SBL height [m].

  • uw (Array) – Surface zonal momentum flux [m²/s²].

  • du (Array) – Zonal wind jump at SBL top [m/s].

  • dv (Array) – Meridional wind jump at SBL top [m/s].

Returns:

Zonal wind tendency [m/s²].

compute_vtend(h_sbl, vw, du, dv)[source]#

Compute meridional wind tendency for the SBL.

\[\frac{dv}{dt} = f \, du - \frac{\overline{v'w'}}{h_{sbl}}\]
Parameters:

  • h_sbl (Array) – SBL height [m].

  • vw (Array) – Surface meridional momentum flux [m²/s²].

  • du (Array) – Zonal wind jump at SBL top [m/s].

  • dv (Array) – Meridional wind jump at SBL top [m/s].

Returns:

Meridional wind tendency [m/s²].

compute_thetav(theta, q)[source]#

Compute virtual potential temperature.

\[\theta_v = \theta (1 + 0.61 q)\]
Parameters:

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

  • q (Array) – Specific humidity [kg/kg].

Returns:

Virtual potential temperature [K].