Here is a brief introduction to the climlab.BandRCModel process.
This is a model that divides the spectrum into 7 distinct bands: three shortwave and four longwave.
As we will see, the process works much like the familiar climlab.RadiativeConvectiveModel.
The shortwave is divided into three channels:
The longwave is divided into four bands:
The longwave decomposition is not as easily related to specific wavelengths, as in reality there is a lot of overlap between H$_2$O and CO$_2$ absorption features (as well as absorption by other greenhouse gases such as CH$_4$ and N$_2$O that we are not representing).
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from __future__ import division, print_function
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import climlab
from climlab import constants as const
First try a model with all default parameters. Usage is very similar to the familiar RadiativeConvectiveModel.
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col1 = climlab.BandRCModel()
print(col1)
Check out the list of subprocesses.
We now have a process called H2O, in addition to things we've seen before.
This model keeps track of water vapor. We see the specific humidity in the list of state variables:
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col1.state
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The water vapor field is initialized to zero. The H2O process will set the specific humidity field at every timestep to a specified profile. More on that below. For now, let's compute a radiative equilibrium state.
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col1.integrate_years(2)
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# Check for energy balance
col1.ASR - col1.OLR
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fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot( col1.Tatm, col1.lev, 'c-', label='default' )
ax.plot( col1.Ts, climlab.constants.ps, 'co', markersize=16 )
ax.invert_yaxis()
ax.set_xlabel('Temperature (K)', fontsize=16)
ax.set_ylabel('Pressure (hPa)', fontsize=16 )
ax.set_title('Temperature profiles', fontsize = 18)
ax.grid()
By default this model has convective adjustment. We can set the adjusted lapse rate by passing a parameter when we create the model.
The model currently has no ozone (so there is no stratosphere). Not very realistic!
More reasonable-looking troposphere, but still no stratosphere.
The Band model is aware of three different absorbing gases: O3 (ozone), CO2, and H2O (water vapor). The abundances of these gases are stored in a dictionary of arrays as follows:
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col1.absorber_vmr
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Ozone and CO2 are both specified in the model. The default, as you see above, is zero ozone, and constant (well-mixed) CO2 at a volume mixing ratio of 3.8E-4 or 380 ppm.
Water vapor is handled differently: it is determined by the model at each timestep. We make the following assumptions, following a classic paper on radiative-convective equilibrium by Manabe and Wetherald (J. Atmos. Sci. 1967):
col1.relative_humidityWe need to provide some ozone data to the model in order to simulate a stratosphere. As we did with the original column model, we will use the ozone climatology data provided with the CESM model.
See here for more information, including some plots of the ozone data: http://www.atmos.albany.edu/facstaff/brose/classes/ENV480_Spring2014/styled-5/code-3/index.html
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import netCDF4 as nc
datapath = "http://ramadda.atmos.albany.edu:8080/repository/opendap/latest/Top/Users/BrianRose/CESM_runs/"
endstr = "/entry.das"
ozone = nc.Dataset( datapath + 'som_input/ozone_1.9x2.5_L26_2000clim_c091112.nc' + endstr )
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# Dimensions of the ozone file
lat = ozone.variables['lat'][:]
lon = ozone.variables['lon'][:]
lev = ozone.variables['lev'][:]
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# Taking annual, zonal, and global averages of the ozone data
O3_zon = np.mean( ozone.variables['O3'],axis=(0,3) )
O3_global = np.sum( O3_zon * np.cos(np.deg2rad(lat)), axis=1 ) / sum( np.cos(np.deg2rad(lat) ) )
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fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot( O3_global*1E6, lev)
ax.invert_yaxis()
We are going to create another instance of the model, this time using the same vertical coordinates as the ozone data.
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# Create the column with appropriate vertical coordinate, surface albedo and convective adjustment
col2 = climlab.BandRCModel(lev=lev)
print(col2)
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# Set the ozone mixing ratio
col2.absorber_vmr['O3'] = O3_global
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# Run the model out to equilibrium!
col2.integrate_years(2.)
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fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot( col1.Tatm, np.log(col1.lev/1000), 'c-', label='RCE' )
ax.plot( col1.Ts, 0, 'co', markersize=16 )
ax.plot(col2.Tatm, np.log(col2.lev/1000), 'r-', label='RCE O3' )
ax.plot(col2.Ts, 0, 'ro', markersize=16 )
ax.invert_yaxis()
ax.set_xlabel('Temperature (K)', fontsize=16)
ax.set_ylabel('log(Pressure)', fontsize=16 )
ax.set_title('Temperature profiles', fontsize = 18)
ax.grid()
ax.legend()
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Once we include ozone we get a well-defined stratosphere. We can also a slight cooling effect in the troposphere.
Things to consider / try:
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col3 = climlab.process_like(col2)
print(col3)
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# Let's double CO2.
col3.absorber_vmr['CO2'] *= 2.
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col3.compute_diagnostics()
print('The radiative forcing for doubling CO2 is %f W/m2.' % (col2.OLR - col3.OLR))
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col3.integrate_years(3)
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col3.ASR - col3.OLR
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print('The Equilibrium Climate Sensitivity is %f K.' % (col3.Ts - col2.Ts))
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col4 = climlab.process_like(col1)
print(col4)
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col4.absorber_vmr
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col4.absorber_vmr['CO2'] *= 2.
col4.compute_diagnostics()
print('The radiative forcing for doubling CO2 is %f W/m2.' % (col1.OLR - col4.OLR))
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col4.integrate_years(3.)
col4.ASR - col4.OLR
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print('The Equilibrium Climate Sensitivity is %f K.' % (col4.Ts - col1.Ts))
Interesting that the model is MORE sensitive when ozone is set to zero.
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