"""Convenience routines for setting up initial conditions."""
from __future__ import division
import numpy as np
from climlab.domain import domain
from climlab.domain.field import Field
from climlab.utils.attrdict import AttrDict
from climlab.utils import legendre
[docs]
def column_state(num_lev=30,
num_lat=1,
lev=None,
lat=None,
water_depth=1.0):
"""Sets up a state variable dictionary consisting of temperatures
for atmospheric column (``Tatm``) and surface mixed layer (``Ts``).
Surface temperature is always 288 K. Atmospheric temperature is initialized
between 278 K at lowest altitude and 200 at top of atmosphere according to
the number of levels given.
**Function-call arguments** \n
:param int num_lev: number of pressure levels
(evenly spaced from surface to top of atmosphere)
[default: 30]
:param int num_lat: number of latitude points on the axis
[default: 1]
:param lev: specification for height axis (optional)
:type lev: :class:`~climlab.domain.axis.Axis`
or pressure array
:param array lat: size of array determines dimension of latitude
(optional)
:param float water_depth: *irrelevant*
:returns: dictionary with two temperature
:class:`~climlab.domain.field.Field`
for atmospheric column ``Tatm`` and
surface mixed layer ``Ts``
:rtype: dict
:Example:
::
>>> from climlab.domain import initial
>>> T_dict = initial.column_state()
>>> print T_dict
{'Tatm': Field([ 200. , 202.68965517, 205.37931034, 208.06896552,
210.75862069, 213.44827586, 216.13793103, 218.82758621,
221.51724138, 224.20689655, 226.89655172, 229.5862069 ,
232.27586207, 234.96551724, 237.65517241, 240.34482759,
243.03448276, 245.72413793, 248.4137931 , 251.10344828,
253.79310345, 256.48275862, 259.17241379, 261.86206897,
264.55172414, 267.24137931, 269.93103448, 272.62068966,
275.31034483, 278. ]), 'Ts': Field([ 288.])}
"""
if lat is not None:
num_lat = np.array(lat).size
if lev is not None:
num_lev = np.array(lev).size
if num_lat == 1:
sfc, atm = domain.single_column(water_depth=water_depth,
num_lev=num_lev,
lev=lev)
else:
sfc, atm = domain.zonal_mean_column(water_depth=water_depth,
num_lev=num_lev,
lev=lev,
num_lat=num_lat,
lat=lat)
num_lev = atm.lev.num_points
Ts = Field(288.*np.ones(sfc.shape), domain=sfc)
Tinitial = np.tile(np.linspace(200., 288.-10., num_lev), sfc.shape)
Tatm = Field(Tinitial, domain=atm)
state = AttrDict()
state['Ts'] = Ts
state['Tatm'] = Tatm
return state
[docs]
def surface_state(num_lat=90,
num_lon=None,
water_depth=10.,
T0=12.,
T2=-40.):
"""Sets up a state variable dictionary for a surface model
(e.g. :class:`~climlab.model.ebm.EBM`) with a uniform slab ocean depth.
The domain is either 1D (latitude) or 2D (latitude, longitude)
depending on whether the input argument num_lon is supplied.
Returns a single state variable `Ts`, the temperature of the surface
mixed layer (slab ocean).
The temperature is initialized to a smooth equator-to-pole shape given by
.. math::
T(\phi) = T_0 + T_2 P_2(\sin\phi)
where :math:`\phi` is latitude, and :math:`P_2` is the second Legendre
polynomial :class:`~climlab.utils.legendre.P2`.
**Function-call arguments** \n
:param int num_lat: number of latitude points [default: 90]
:param int num_lat: (optional) number of longitude points [default: None]
:param float water_depth: depth of the slab ocean in meters [default: 10.]
:param float T0: global-mean initial temperature in :math:`^{\circ} \\textrm{C}` [default: 12.]
:param float T2: 2nd Legendre coefficient for equator-to-pole gradient in
initial temperature, in :math:`^{\circ} \\textrm{C}` [default: -40.]
:returns: dictionary with temperature
:class:`~climlab.domain.field.Field`
for surface mixed layer ``Ts``
:rtype: dict
:Example:
::
>>> from climlab.domain import initial
>>> import numpy as np
>>> T_dict = initial.surface_state(num_lat=36)
>>> print np.squeeze(T_dict['Ts'])
[-27.88584094 -26.97777479 -25.18923361 -22.57456133 -19.21320344
-15.20729309 -10.67854785 -5.76457135 -0.61467228 4.61467228
9.76457135 14.67854785 19.20729309 23.21320344 26.57456133
29.18923361 30.97777479 31.88584094 31.88584094 30.97777479
29.18923361 26.57456133 23.21320344 19.20729309 14.67854785
9.76457135 4.61467228 -0.61467228 -5.76457135 -10.67854785
-15.20729309 -19.21320344 -22.57456133 -25.18923361 -26.97777479
-27.88584094]
"""
if num_lon is None:
sfc = domain.zonal_mean_surface(num_lat=num_lat,
water_depth=water_depth)
else:
sfc = domain.surface_2D(num_lat=num_lat,
num_lon=num_lon,
water_depth=water_depth)
if 'lon' in sfc.axes:
lon, lat = np.meshgrid(sfc.axes['lon'].points, sfc.axes['lat'].points)
else:
lat = sfc.axes['lat'].points
sinphi = np.sin(np.deg2rad(lat))
initial = T0 + T2 * legendre.P2(sinphi)
Ts = Field(initial, domain=sfc)
#if num_lon is None:
# Ts = Field(initial, domain=sfc)
#else:
# Ts = Field([[initial for k in range(num_lon)]], domain=sfc)
state = AttrDict()
state['Ts'] = Ts
return state
