MeridionalHeatDiffusion¶
Solver for the 1D meridional heat diffusion equation on the sphere:
for a temperature state variable \(T(\phi,t)\), a verticallyintegrated heat capacity \(C\), and arbitrary thermal diffusivity \(D(\phi,t)\) in units of W/m2/K.
The diffusivity \(D\) can be a single scalar, or optionally a vector specified at grid cell boundaries (so its length must be exactly 1 greater than the length of \(\phi\)).
\(D\) can be modified by the user at any time (e.g., after each timestep, if it depends on other state variables).
The heat capacity \(C\) is normally handled automatically by CLIMLAB as part of the grid specification.
A fully implicit timestep is used for computational efficiency. Thus the computed tendency \(\frac{\partial T}{\partial t}\) will depend on the timestep.
The diagnostics diffusive_flux
and diffusive_flux_convergence
are computed
as described in the parent class MeridionalDiffusion
.
Two additional diagnostics are computed here,
which are meaningful if \(T\) represents a zonally averaged temperature:
heat_transport
given by \(\mathcal{H}(\phi) = 2 \pi ~ a^2 ~ \cos\phi ~ D ~ \frac{\partial T}{\partial \phi}\) in units of PW (petawatts).heat_transport_convergence
given by \(\frac{1}{2 \pi ~a^2 \cos\phi} \frac{\partial \mathcal{H}}{\partial \phi}\) in units of W/m2
The grid must be evenly spaced in latitude.
The state variable \(T\) may be multidimensional, but the diffusion will operate along the latitude dimension only.

class
climlab.dynamics.meridional_heat_diffusion.
MeridionalHeatDiffusion
(D=0.555, use_banded_solver=True, **kwargs)[source]¶ Bases:
climlab.dynamics.meridional_diffusion.MeridionalDiffusion
A 1D diffusion solver for Energy Balance Models.
Solves the meridional heat diffusion equation
$$ C
rac{partial T}{partial t} =  rac{1}{cosphi} rac{partial}{partial phi} left[ D cosphi rac{partial T}{partial phi} ight]$$
on an evenlyspaced latitude grid, with a state variable $T$, a heat capacity $C$ and diffusivity $D$.
Assuming $T$ is a temperature in $K$ or $^circ$C, then the units are:
$D$ in W m$^{2}$ K$^{1}$
$C$ in J m$^{2}$ K$^{1}$
If the state variable has other units, then $D$ and $C$ should be expressed per state variabe unit.
$D$ is provided as input, and can be either scalar or vector defined at latitude boundaries (length).
$C$ is normally handled automatically for temperature state variables in CLIMLAB.
 Attributes
 D
 K
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 givenvalue
.add_input
(name[, value])Create a new input variable called
name
for this process and initialize it with the givenvalue
.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 statevalue
.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])Convert process variables to
xarray.Dataset
format.
D
¶