Brian E. J. Rose, University at Albany
You really should be looking at The Climate Laboratory book by Brian Rose, where all the same content (and more!) is kept up to date.
Here you are likely to find broken links and broken code.
This document uses the interactive Jupyter notebook format. The notes can be accessed in several different ways:
github at https://github.com/brian-rose/ClimateModeling_coursewareAlso here is a legacy version from 2015.
Many of these notes make use of the climlab package, available at https://github.com/brian-rose/climlab
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# Ensure compatibility with Python 2 and 3
from __future__ import print_function, division
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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import climlab
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# for convenience, set up a dictionary with our reference parameters
param = {'A':210, 'B':2, 'a0':0.3, 'a2':0.078, 'ai':0.62, 'Tf':-10.}
model1 = climlab.EBM_annual(name='Annual EBM with ice line',
num_lat=180, D=0.55, **param )
print( model1)
Because we provided a parameter ai for the icy albedo, our model now contains several sub-processes contained within the process called albedo. Together these implement the step-function formula above.
The process called iceline simply looks for grid cells with temperature below $T_f$.
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print( model1.param)
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def ebm_plot( model, figsize=(8,12), show=True ):
'''This function makes a plot of the current state of the model,
including temperature, energy budget, and heat transport.'''
templimits = -30,35
radlimits = -340, 340
htlimits = -7,7
latlimits = -90,90
lat_ticks = np.arange(-90,90,30)
fig = plt.figure(figsize=figsize)
ax1 = fig.add_subplot(3,1,1)
ax1.plot(model.lat, model.Ts)
ax1.set_xlim(latlimits)
ax1.set_ylim(templimits)
ax1.set_ylabel('Temperature (deg C)')
ax1.set_xticks( lat_ticks )
ax1.grid()
ax2 = fig.add_subplot(3,1,2)
ax2.plot(model.lat, model.ASR, 'k--', label='SW' )
ax2.plot(model.lat, -model.OLR, 'r--', label='LW' )
ax2.plot(model.lat, model.net_radiation, 'c-', label='net rad' )
ax2.plot(model.lat, model.heat_transport_convergence, 'g--', label='dyn' )
ax2.plot(model.lat, model.net_radiation.squeeze()
+ model.heat_transport_convergence, 'b-', label='total' )
ax2.set_xlim(latlimits)
ax2.set_ylim(radlimits)
ax2.set_ylabel('Energy budget (W m$^{-2}$)')
ax2.set_xticks( lat_ticks )
ax2.grid()
ax2.legend()
ax3 = fig.add_subplot(3,1,3)
ax3.plot(model.lat_bounds, model.heat_transport)
ax3.set_xlim(latlimits)
ax3.set_ylim(htlimits)
ax3.set_ylabel('Heat transport (PW)')
ax3.set_xlabel('Latitude')
ax3.set_xticks( lat_ticks )
ax3.grid()
return fig
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model1.integrate_years(5)
f = ebm_plot(model1)
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model1.icelat
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deltaA = 4.
model2 = climlab.process_like(model1)
model2.subprocess['LW'].A = param['A'] - deltaA
model2.integrate_years(5, verbose=False)
plt.plot(model1.lat, model1.Ts)
plt.plot(model2.lat, model2.Ts)
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The warming is polar-amplified: more warming at the poles than elsewhere.
Why?
Also, the current ice line is now:
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model2.icelat
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There is no ice left!
Let's do some more greenhouse warming:
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model3 = climlab.process_like(model1)
model3.subprocess['LW'].A = param['A'] - 2*deltaA
model3.integrate_years(5, verbose=False)
plt.plot(model1.lat, model1.Ts)
plt.plot(model2.lat, model2.Ts)
plt.plot(model3.lat, model3.Ts)
plt.xlim(-90, 90)
plt.grid()
In the ice-free regime, there is no polar-amplified warming. A uniform radiative forcing produces a uniform warming.
We will repeat the exercise from Lecture 16, but this time with albedo feedback included in our model.
Use these parameter values:
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param = {'A':210, 'B':2, 'a0':0.3, 'a2':0.078, 'ai':0.62, 'Tf':-10.}
print( param)
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Darray = np.arange(0., 2.05, 0.05)
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model_list = []
Tmean_list = []
deltaT_list = []
Hmax_list = []
for D in Darray:
ebm = climlab.EBM_annual(num_lat=360, D=D, **param )
ebm.integrate_years(5., verbose=False)
Tmean = ebm.global_mean_temperature()
deltaT = np.max(ebm.Ts) - np.min(ebm.Ts)
HT = np.squeeze(ebm.heat_transport)
ind = np.where(ebm.lat_bounds==35.5)[0]
Hmax = HT[ind]
model_list.append(ebm)
Tmean_list.append(Tmean)
deltaT_list.append(deltaT)
Hmax_list.append(Hmax)
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color1 = 'b'
color2 = 'r'
fig = plt.figure(figsize=(8,6))
ax1 = fig.add_subplot(111)
ax1.plot(Darray, deltaT_list, color=color1, label='$\Delta T$')
ax1.plot(Darray, Tmean_list, '--', color=color1, label='$\overline{T}$')
ax1.set_xlabel('D (W m$^{-2}$ K$^{-1}$)', fontsize=14)
ax1.set_xticks(np.arange(Darray[0], Darray[-1], 0.2))
ax1.set_ylabel('Temperature ($^\circ$C)', fontsize=14, color=color1)
for tl in ax1.get_yticklabels():
tl.set_color(color1)
ax1.legend(loc='center right')
ax2 = ax1.twinx()
ax2.plot(Darray, Hmax_list, color=color2)
ax2.set_ylabel('Poleward heat transport across 35.5$^\circ$ (PW)', fontsize=14, color=color2)
for tl in ax2.get_yticklabels():
tl.set_color(color2)
ax1.set_title('Effect of diffusivity on EBM with albedo feedback', fontsize=16)
ax1.grid()
Let's add a point heat source to the EBM and see what sets the spatial structure of the response.
We will add a heat source at about 45º latitude.
First, we will calculate the response in a model without albedo feedback.
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param_noalb = {'A': 210, 'B': 2, 'D': 0.55, 'Tf': -10.0, 'a0': 0.3, 'a2': 0.078}
m1 = climlab.EBM_annual(num_lat=180, **param_noalb)
print( m1)
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m1.integrate_years(5.)
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m2 = climlab.process_like(m1)
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point_source = climlab.process.energy_budget.ExternalEnergySource(state=m2.state, timestep=m2.timestep)
ind = np.where(m2.lat == 45.5)
point_source.heating_rate['Ts'][ind] = 100.
m2.add_subprocess('point source', point_source)
print( m2)
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m2.integrate_years(5.)
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plt.plot(m2.lat, m2.Ts - m1.Ts)
plt.xlim(-90,90)
plt.grid()
The warming effects of our point source are felt at all latitudes but the effects decay away from the heat source.
Some analysis will show that the length scale of the warming is proportional to
$$ \sqrt{\frac{D}{B}} $$so increases with the diffusivity.
Now repeat this calculate with ice albedo feedback
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m3 = climlab.EBM_annual(num_lat=180, **param)
m3.integrate_years(5.)
m4 = climlab.process_like(m3)
point_source = climlab.process.energy_budget.ExternalEnergySource(state=m4.state, timestep=m4.timestep)
point_source.heating_rate['Ts'][ind] = 100.
m4.add_subprocess('point source', point_source)
m4.integrate_years(5.)
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plt.plot(m4.lat, m4.Ts - m3.Ts)
plt.xlim(-90,90)
plt.grid()
Now the maximum warming does not coincide with the heat source at 45º!
Our heat source has led to melting of snow and ice, which induces an additional heat source in the high northern latitudes.
Heat transport communicates the external warming to the ice cap, and also commuicates the increased shortwave absorption due to ice melt globally!
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%load_ext version_information
%version_information numpy, matplotlib, climlab
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The author of this notebook is Brian E. J. Rose, University at Albany.
It was developed in support of ATM 623: Climate Modeling, a graduate-level course in the Department of Atmospheric and Envionmental Sciences
Development of these notes and the climlab software is partially supported by the National Science Foundation under award AGS-1455071 to Brian Rose. Any opinions, findings, conclusions or recommendations expressed here are mine and do not necessarily reflect the views of the National Science Foundation.
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