LargeScaleCondensation

climlab process for large-scale condensation

The process object climlab.dynamics.LargeScaleCondensation does the following at each timestep:

Calculate saturation specific humidity given air temperatures at every grid point
Calculate supersaturation by comparing actual specific humidity to saturation specific humidity
Compute a specific humidity tendency based on a relaxation toward saturation (if supersaturated)
Compute a heating rate and temperature tendency due to the latent heating of condensation
Compute precipitation rate at the surface, assuming all condensate in each column is instantly precipitated

State variables:

Tatm: air temperature in K
q: specific humidity in kg kg^-1

Input parameters and default values:

condensation_time: condensation time constant in units of seconds (default: 4 hours)
RH_ref: reference relative humidity value, dimensionless (default value 0.9)

Diagnostics:

latent_heating: latent heating rate (every grid cell) in units of W m^-2
precipitation: precipitation rate (column total) in units of kg m^-2 s^-1 or mm s^-1

The condensation rule follows the SPEEDY model (Molteni 2003 doi:10.1007/s00382-002-0268-2). Condensation is modeled as a relaxation of relative humidity toward a specified profile wherever the tropospheric relative humidity exceeds the target.

Given specific humidity \(q\) and saturation specific humidity \(q_{sat}(T,p)\), relative humidity is calculated from

\[r = \frac{q}{q_{sat}}\]

which is compared against a specified reference profile \(r_{lsc}\) which may vary spatially.

At grid cells where \(r > r_{lsc}\), the specific humidity tendency is calculated from

\[\left(\frac{\partial q}{\partial t}\right)_{lsc} = -\frac{(q - r_{lsc} q_{sat})}{\tau_{lsc}}\]

and is zero otherwise.

The two parameters of the scheme are the relaxation time constant \(\tau_{lsc}\) and the reference RH profile \(r_{lsc}\).

We follow SPEEDY and set an “aggressive” default time constant \(\tau_{lsc} = 4\) hours.

For the reference profile, SPEEDY sets a smoothly decreasing vertical profile with \(r_{lsc} = 0.9\) at the surface and \(r_{lsc} \approx 0.8\) at the tropopause. For simplicity, we will default to a uniform default value of \(r_{lsc} = 0.9\).

The temperature tendency due to latent heating (in units of K s^-1) is calculated from

\[\left(\frac{\partial T}{\partial t}\right)_{lsc} = -\frac{L}{c_p} \left(\frac{\partial q}{\partial t}\right)_{lsc}\]

with the associated heating rate diagnostic (in units of W m^-2) computed from

\[h_{lsc} = C \left(\frac{\partial T}{\partial t}\right)_{lsc}\]

where \(C = \frac{c_p dp}{g}\) is the heat capacity per unit area in J K^-1 m^-2, and the precipitation rate is calculated from the vertical integral:

\[P = -\frac{1}{g} \int_0^{p_0} \left(\frac{\partial q}{\partial t}\right)_{lsc} dp\]

or equivalently

\[P = + \int_0^{p_0} \frac{h_{lsc}}{L}\]

where the integral implies a sum over all grid cells in each atmospheric column.

class climlab.dynamics.large_scale_condensation.LargeScaleCondensation(condensation_time=14400.0, RH_ref=0.9, **kwargs)[source]

Bases: TimeDependentProcess

Climlab process class for LargeScaleCondensation. Condensation is modeled as a relaxation of relative humidity toward a specified reference value wherever the tropospheric relative humidity exceeds the target.

State variables:

Tatm: air temperature in K
q: specific humidity in kg kg^-1

Input parameters and default values:

condensation_time: condensation time constant in units of seconds (default: 4 hours)
RH_ref: reference relative humidity value, dimensionless (default value 0.9)

Diagnostics:

latent_heating: latent heating rate (every grid cell) in units of W m^-2
precipitation: precipitation rate (column total) in units of kg m^-2 s^-1 or mm s^-1

Attributes:

depth: Depth at grid centers (m)
depth_bounds: Depth at grid interfaces (m)
diagnostics: Dictionary access to all diagnostic variables
input: Dictionary access to all input variables
lat: Latitude of grid centers (degrees North)
lat_bounds: Latitude of grid interfaces (degrees North)
lev: Pressure levels at grid centers (hPa or mb)
lev_bounds: Pressure levels at grid interfaces (hPa or mb)
lon: Longitude of grid centers (degrees)
lon_bounds: Longitude of grid interfaces (degrees)
timestep: The amount of time over which step_forward() is integrating in unit seconds.

Methods

`add_diagnostic`(name[, value])	Create a new diagnostic variable called `name` for this process and initialize it with the given `value`.
`add_input`(name[, value])	Create a new input variable called `name` for this process and initialize it with the given `value`.
`add_subprocess`(name, proc)	Adds a single subprocess to this process.
`add_subprocesses`(procdict)	Adds a dictionary of subproceses to this process.
`compute`()	Computes the tendencies for all state variables given current state and specified input.
`compute_diagnostics`([num_iter])	Compute all tendencies and diagnostics, but don't update model state.
`declare_diagnostics`(diaglist)	Add the variable names in `inputlist` to the list of diagnostics.
`declare_input`(inputlist)	Add the variable names in `inputlist` to the list of necessary inputs.
`integrate_converge`([crit, verbose])	Integrates the model until model states are converging.
`integrate_days`([days, verbose])	Integrates the model forward for a specified number of days.
`integrate_years`([years, verbose])	Integrates the model by a given number of years.
`remove_diagnostic`(name)	Removes a diagnostic from the `process.diagnostic` dictionary and also delete the associated process attribute.
`remove_subprocess`(name[, verbose])	Removes a single subprocess from this process.
`set_state`(name, value)	Sets the variable `name` to a new state `value`.
`set_timestep`([timestep, num_steps_per_year])	Calculates the timestep in unit seconds and calls the setter function of `timestep()`
`step_forward`()	Updates state variables with computed tendencies.
`to_xarray`([diagnostics, timeave])	Convert process variables to `xarray.Dataset` format.

_compute()[source]

Where the tendencies are actually computed…

Needs to be implemented for each daughter class

Returns a dictionary with same keys as self.state