from __future__ import division
import numpy as np
from climlab.process.time_dependent_process import TimeDependentProcess
[docs]
class EnergyBudget(TimeDependentProcess):
r"""A parent class for explicit energy budget processes.
This class solves equations that include a heat capacitiy term like
:math:`C \\frac{dT}{dt} = \\textrm{flux convergence}`
In an Energy Balance Model with model state :math:`T` this equation
will look like this:
.. math::
C \\frac{dT}{dt} = R\downarrow - R\uparrow - H \n
\\frac{dT}{dt} = \\frac{R\downarrow}{C} - \\frac{R\uparrow}{C} - \\frac{H}{C}
Every EnergyBudget object has a ``heating_rate`` dictionary with items
corresponding to each state variable. The heating rate accounts the actual
heating of a subprocess, namely the contribution to the energy budget
of :math:`R\\downarrow, R\\uparrow` and :math:`H` in this case.
The temperature tendencies for each subprocess are then calculated
through dividing the heating rate by the heat capacitiy :math:`C`.
**Initialization parameters** \n
An instance of ``EnergyBudget`` is initialized with the forwarded
keyword arguments ``**kwargs`` of the corresponding children classes.
**Object attributes** \n
Additional to the parent class
:class:`~climlab.process.timedependentprocess.TimeDependentProcess`
following object attributes are generated or modified during initialization:
:ivar str time_type: is set to ``'explicit'``
:ivar dict heating_rate: energy share for given subprocess in unit
:math:`\\textrm{W}/ \\textrm{m}^2` stored
in a dictionary sorted by model states
"""
def __init__(self, **kwargs):
super(EnergyBudget, self).__init__(**kwargs)
self.time_type = 'explicit'
self.heating_rate = {}
def _compute_heating_rates(self):
"""Computes energy flux convergences to get heating rates in unit
:math:`\\textrm{W}/ \\textrm{m}^2`.
This method should be over-ridden by daughter classes.
"""
for varname in list(self.state.keys()):
self.heating_rate[varname] = self.state[varname] * 0.
def _temperature_tendencies(self):
self._compute_heating_rates()
tendencies = {}
for varname, value in self.state.items():
#C = self.state_domain[varname].heat_capacity
C = value.domain.heat_capacity
try: # there may be state variables without heating rates
tendencies[varname] = (self.heating_rate[varname] / C)
except:
pass
return tendencies
def _compute(self):
tendencies = self._temperature_tendencies()
return tendencies
[docs]
class ExternalEnergySource(EnergyBudget):
"""A fixed energy source or sink to be specified by the user.
**Object attributes** \n
Additional to the parent class :class:`~climlab.process.energy_budget.EnergyBudget`
the following object attribute is modified during initialization:
:ivar dict heating_rate: energy share dictionary for this subprocess
is set to zero for every model state.
After initialization the user should modify the fields in the
``heating_rate`` dictionary, which contain heating rates in
unit :math:`\\textrm{W}/ \\textrm{m}^2` for all state variables.
:Example:
Creating an Energy Balance Model with a uniform external energy source
of :math:`10 \\ \\textrm{W}/ \\textrm{m}^2` for all latitudes::
>>> import climlab
>>> from climlab.process.energy_budget import ExternalEnergySource
>>> import numpy as np
>>> # create model & external energy subprocess
>>> model = climlab.EBM(num_lat=36)
>>> ext_en = ExternalEnergySource(state= model.state,**model.param)
>>> # modify external energy rate
>>> ext_en.heating_rate.keys()
['Ts']
>>> np.squeeze(ext_en.heating_rate['Ts'])
Field([-0., -0., -0., -0., -0., -0., -0., -0., -0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., -0., -0., -0., -0., -0., -0., -0., -0., -0.])
>>> ext_en.heating_rate['Ts'][:]=10
>>> np.squeeze(ext_en.heating_rate['Ts'])
Field([ 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,
10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,
10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,
10., 10., 10.])
>>> # add subprocess to model
>>> model.add_subprocess('ext_energy',ext_en)
>>> print model
climlab Process of type <class 'climlab.model.ebm.EBM'>.
State variables and domain shapes:
Ts: (36, 1)
The subprocess tree:
top: <class 'climlab.model.ebm.EBM'>
diffusion: <class 'climlab.dynamics.diffusion.MeridionalDiffusion'>
LW: <class 'climlab.radiation.AplusBT.AplusBT'>
ext_energy: <class 'climlab.process.energy_budget.ExternalEnergySource'>
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'>
"""
def __init__(self, **kwargs):
super(ExternalEnergySource, self).__init__(**kwargs)
for varname in list(self.state.keys()):
self.heating_rate[varname] = self.state[varname] * 0.
def _compute_heating_rates(self):
pass
