Boltzmann

class climlab.radiation.boltzmann.Boltzmann(eps=0.65, tau=0.95, **kwargs)[source]

Bases: EnergyBudget

A class for black body radiation.

Implements a radiation subprocess which computes longwave radiation with the Stefan-Boltzmann law for black/grey body radiation.

According to the Stefan Boltzmann law the total power radiated from an object with surface area \(A\) and temperature \(T\) (in unit Kelvin) can be written as

\[P = A \varepsilon \sigma T^4\]

where \(\varepsilon\) is the emissivity of the body.

As the EnergyBudget of the Energy Balance Model is accounted in unit \(\textrm{energy} / \textrm{area}\) (\(\textrm{W}/ \textrm{m}^2\)) the energy budget equation looks like this:

\[C \frac{dT}{dt} = R\downarrow - R\uparrow - H\]

The Boltzmann radiation subprocess represents the outgoing radiation \(R\uparrow\) which then can be written as

\[R\uparrow = \varepsilon \sigma T^4\]

with state variable \(T\).

Initialization parameters

An instance of Boltzmann is initialized with the following arguments:

Parameters:

eps (float) – emissivity of the planet’s surface which is the effectiveness in emitting energy as thermal radiation [default: 0.65]
tau (float) – transmissivity of the planet’s atmosphere which is the effectiveness in transmitting the longwave radiation emitted from the surface [default: 0.95]

Object attributes

During initialization both arguments described above are created as object attributes which calls their setter function (see below).

Variables:

eps (float) – calls the setter function of eps()
tau (float) – calls the setter function of tau()
diagnostics (dict) – the subprocess’s diagnostic dictionary self.diagnostic is initialized through calling self.add_diagnostic('OLR', 0. * self.Ts)
OLR (Field) – the subprocess attribute self.OLR is created with correct dimensions

Example:

Replacing an the regular AplusBT subprocess in an energy balance model:

>>> import climlab
>>> from climlab.radiation.Boltzmann import Boltzmann

>>> # creating EBM model
>>> model = climlab.EBM()

>>> print model

climlab Process of type <class 'climlab.model.ebm.EBM'>.
State variables and domain shapes:
  Ts: (90, 1)
The subprocess tree:
top: <class 'climlab.model.ebm.EBM'>
   diffusion: <class 'climlab.dynamics.diffusion.MeridionalDiffusion'>
   LW: <class 'climlab.radiation.AplusBT.AplusBT'>
   albedo: <class 'climlab.surface.albedo.StepFunctionAlbedo'>
      iceline: <class 'climlab.surface.albedo.Iceline'>
      cold_albedo: <class 'climlab.surface.albedo.ConstantAlbedo'>
      warm_albedo: <class 'climlab.surface.albedo.P2Albedo'>
   insolation: <class 'climlab.radiation.insolation.P2Insolation'>

>>> #  creating and adding albedo feedback subprocess
>>> LW_boltz = Boltzmann(eps=0.69, tau=0.98, state=model.state, **model.param)

>>> # overwriting old 'LW' subprocess with same name
>>> model.add_subprocess('LW', LW_boltz)

>>> print model

climlab Process of type <class 'climlab.model.ebm.EBM'>.
State variables and domain shapes:
  Ts: (90, 1)
The subprocess tree:
top: <class 'climlab.model.ebm.EBM'>
   diffusion: <class 'climlab.dynamics.diffusion.MeridionalDiffusion'>
   LW: <class 'climlab.radiation.Boltzmann.Boltzmann'>
   albedo: <class 'climlab.surface.albedo.StepFunctionAlbedo'>
      iceline: <class 'climlab.surface.albedo.Iceline'>
      cold_albedo: <class 'climlab.surface.albedo.ConstantAlbedo'>
      warm_albedo: <class 'climlab.surface.albedo.P2Albedo'>
   insolation: <class 'climlab.radiation.insolation.P2Insolation'>

Attributes:

current_time
depth: Depth at grid centers (m)
depth_bounds: Depth at grid interfaces (m)
diagnostics: Dictionary access to all diagnostic variables
elapsed_time
eps: Property of emissivity parameter.
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)
tau: Property of the transmissivity parameter.
timestep: The amount of time over which step_forward() is integrating in unit seconds.
timestep_in_seconds: Return a float value representing the timestep in units of 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[, verbose])	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`.
`step_forward`()	Updates state variables with computed tendencies.
`to_xarray`([diagnostics, timeave])	Convert process variables to `xarray.Dataset` format.

property eps

Property of emissivity parameter.

Getter:

Returns the albedo value which is stored in attribute self._eps

Setter:

sets the emissivity which is addressed as self._eps to the new value
updates the parameter dictionary self.param['eps']

Type:

float

property tau

Property of the transmissivity parameter.

Getter:

Returns the albedo value which is stored in attribute self._tau

Setter:

sets the emissivity which is addressed as self._tau to the new value
updates the parameter dictionary self.param['tau']

Type:

float