Polar amplification in simple models¶

[1]:

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import climlab
from climlab import constants as const

EBM with surface and atm layers¶

[2]:

ebm = climlab.GreyRadiationModel(num_lev=1, num_lat=90)
insolation = climlab.radiation.AnnualMeanInsolation(domains=ebm.Ts.domain)
ebm.add_subprocess('insolation', insolation)
ebm.subprocess.SW.flux_from_space = ebm.subprocess.insolation.insolation
print(ebm)

climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>.
State variables and domain shapes:
  Ts: (90, 1)
  Tatm: (90, 1)
The subprocess tree:
Untitled: <class 'climlab.model.column.GreyRadiationModel'>
   LW: <class 'climlab.radiation.greygas.GreyGas'>
   SW: <class 'climlab.radiation.greygas.GreyGasSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>

[3]:

#  add a fixed relative humidity process
#  (will only affect surface evaporation)
h2o = climlab.radiation.ManabeWaterVapor(state=ebm.state, **ebm.param)
ebm.add_subprocess('H2O', h2o)

[4]:

#  Add surface heat fluxes
shf = climlab.surface.SensibleHeatFlux(state=ebm.state, Cd=3E-4)
lhf = climlab.surface.LatentHeatFlux(state=ebm.state, Cd=3E-4)
# couple water vapor to latent heat flux process
lhf.q = h2o.q
ebm.add_subprocess('SHF', shf)
ebm.add_subprocess('LHF', lhf)

[5]:

ebm.integrate_years(1)

Integrating for 365 steps, 365.2422 days, or 1 years.
Total elapsed time is 0.9993368783782377 years.

[6]:

plt.plot(ebm.lat, ebm.Ts)
plt.plot(ebm.lat, ebm.Tatm)

[6]:

[<matplotlib.lines.Line2D at 0x16b2f2730>]

../_images/courseware_PolarAmplification_7_1.png

[7]:

co2ebm = climlab.process_like(ebm)
co2ebm.subprocess['LW'].absorptivity = ebm.subprocess['LW'].absorptivity*1.1

[8]:

co2ebm.integrate_years(3.)

Integrating for 1095 steps, 1095.7266 days, or 3.0 years.
Total elapsed time is 3.997347513512951 years.

[9]:

#  no heat transport but with evaporation -- no polar amplification
plt.plot(ebm.lat, co2ebm.Ts - ebm.Ts)
plt.plot(ebm.lat, co2ebm.Tatm - ebm.Tatm)

[9]:

[<matplotlib.lines.Line2D at 0x16b42a130>]

../_images/courseware_PolarAmplification_10_1.png

Now with meridional heat transport¶

[10]:

diffebm = climlab.process_like(ebm)
# thermal diffusivity in W/m**2/degC
D = 0.6
# meridional diffusivity in m**2/s
K = D / diffebm.Tatm.domain.heat_capacity * const.a**2
d = climlab.dynamics.MeridionalDiffusion(K=K, state={'Tatm': diffebm.Tatm}, **diffebm.param)
diffebm.add_subprocess('diffusion', d)
print(diffebm)

climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>.
State variables and domain shapes:
  Ts: (90, 1)
  Tatm: (90, 1)
The subprocess tree:
Untitled: <class 'climlab.model.column.GreyRadiationModel'>
   LW: <class 'climlab.radiation.greygas.GreyGas'>
   SW: <class 'climlab.radiation.greygas.GreyGasSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>
   H2O: <class 'climlab.radiation.water_vapor.ManabeWaterVapor'>
   SHF: <class 'climlab.surface.turbulent.SensibleHeatFlux'>
   LHF: <class 'climlab.surface.turbulent.LatentHeatFlux'>
   diffusion: <class 'climlab.dynamics.meridional_advection_diffusion.MeridionalDiffusion'>

[11]:

diffebm.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 3.997347513512951 years.

[12]:

plt.plot(diffebm.lat, diffebm.Ts)
plt.plot(diffebm.lat, diffebm.Tatm)

[12]:

[<matplotlib.lines.Line2D at 0x16b4a7f40>]

../_images/courseware_PolarAmplification_14_1.png

[13]:

def inferred_heat_transport( energy_in, lat_deg ):
    '''Returns the inferred heat transport (in PW) by integrating the net energy imbalance from pole to pole.'''
    from scipy import integrate
    from climlab import constants as const
    lat_rad = np.deg2rad( lat_deg )
    return ( 1E-15 * 2 * np.math.pi * const.a**2 * integrate.cumtrapz( np.cos(lat_rad)*energy_in,
            x=lat_rad, initial=0. ) )

[14]:

#  Plot the northward heat transport in this model
Rtoa = np.squeeze(diffebm.timeave['ASR'] - diffebm.timeave['OLR'])
plt.plot(diffebm.lat, inferred_heat_transport(Rtoa, diffebm.lat))

[14]:

[<matplotlib.lines.Line2D at 0x16b5213d0>]

../_images/courseware_PolarAmplification_16_1.png

[15]:

##  Now warm it up!
co2diffebm = climlab.process_like(diffebm)
co2diffebm.subprocess['LW'].absorptivity = diffebm.subprocess['LW'].absorptivity*1.1

[16]:

co2diffebm.integrate_years(5)

Integrating for 1826 steps, 1826.2110000000002 days, or 5 years.
Total elapsed time is 8.99676981465997 years.

[17]:

#  with heat transport and evaporation
#   Get some modest polar amplifcation of surface warming
#    but larger equatorial amplification of atmospheric warming
#    Increased atmospheric gradient = increased poleward flux.
plt.plot(diffebm.lat, co2diffebm.Ts - diffebm.Ts, label='Ts')
plt.plot(diffebm.lat, co2diffebm.Tatm - diffebm.Tatm, label='Tatm')
plt.legend()

[17]:

<matplotlib.legend.Legend at 0x16b592730>

../_images/courseware_PolarAmplification_19_1.png

[18]:

Rtoa = np.squeeze(diffebm.timeave['ASR'] - diffebm.timeave['OLR'])
Rtoa_co2 = np.squeeze(co2diffebm.timeave['ASR'] - co2diffebm.timeave['OLR'])
plt.plot(diffebm.lat, inferred_heat_transport(Rtoa, diffebm.lat), label='1xCO2')
plt.plot(diffebm.lat, inferred_heat_transport(Rtoa_co2, diffebm.lat), label='2xCO2')
plt.legend()

[18]:

<matplotlib.legend.Legend at 0x16b61b7f0>

../_images/courseware_PolarAmplification_20_1.png

Same thing but with NO EVAPORATION¶

[19]:

diffebm2 = climlab.process_like(diffebm)
diffebm2.remove_subprocess('LHF')
diffebm2.integrate_years(3)
co2diffebm2 = climlab.process_like(co2diffebm)
co2diffebm2.remove_subprocess('LHF')
co2diffebm2.integrate_years(3)
#  With transport and no evaporation...
#  No polar amplification, either of surface or air temperature!
plt.plot(diffebm2.lat, co2diffebm2.Ts - diffebm2.Ts, label='Ts')
plt.plot(diffebm2.lat, co2diffebm2.Tatm[:,0] - diffebm2.Tatm[:,0], label='Tatm')
plt.legend()
plt.figure()
#  And in this case, the lack of polar amplification is DESPITE an increase in the poleward heat transport.
Rtoa = np.squeeze(diffebm2.timeave['ASR'] - diffebm2.timeave['OLR'])
Rtoa_co2 = np.squeeze(co2diffebm2.timeave['ASR'] - co2diffebm2.timeave['OLR'])
plt.plot(diffebm2.lat, inferred_heat_transport(Rtoa, diffebm2.lat), label='1xCO2')
plt.plot(diffebm2.lat, inferred_heat_transport(Rtoa_co2, diffebm2.lat), label='2xCO2')
plt.legend()

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 6.995358148647664 years.
Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 11.994780449794684 years.

[19]:

<matplotlib.legend.Legend at 0x16b6fddf0>

../_images/courseware_PolarAmplification_22_2.png

../_images/courseware_PolarAmplification_22_3.png

A column model approach¶

[20]:

model = climlab.GreyRadiationModel(num_lev=30, num_lat=90, abs_coeff=1.6E-4)
insolation = climlab.radiation.AnnualMeanInsolation(domains=model.Ts.domain)
model.add_subprocess('insolation', insolation)
model.subprocess.SW.flux_from_space = model.subprocess.insolation.insolation
print(model)

climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>.
State variables and domain shapes:
  Ts: (90, 1)
  Tatm: (90, 30)
The subprocess tree:
Untitled: <class 'climlab.model.column.GreyRadiationModel'>
   LW: <class 'climlab.radiation.greygas.GreyGas'>
   SW: <class 'climlab.radiation.greygas.GreyGasSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>

[21]:

#  Convective adjustment for atmosphere only
conv = climlab.convection.ConvectiveAdjustment(state={'Tatm':model.Tatm}, adj_lapse_rate=6.5,
                                                       **model.param)
model.add_subprocess('convective adjustment', conv)

[22]:

#  add a fixed relative humidity process
#  (will only affect surface evaporation)
h2o = climlab.radiation.water_vapor.ManabeWaterVapor(state=model.state, **model.param)
model.add_subprocess('H2O', h2o)

[23]:

#  Add surface heat fluxes
shf = climlab.surface.SensibleHeatFlux(state=model.state, Cd=1E-3)
lhf = climlab.surface.LatentHeatFlux(state=model.state, Cd=1E-3)
lhf.q = model.subprocess.H2O.q
model.add_subprocess('SHF', shf)
model.add_subprocess('LHF', lhf)

[24]:

model.integrate_years(3.)

Integrating for 1095 steps, 1095.7266 days, or 3.0 years.
Total elapsed time is 2.998010635134713 years.

[25]:

def plot_temp_section(model, timeave=True):
    fig = plt.figure()
    ax = fig.add_subplot(111)
    if timeave:
        field = model.timeave['Tatm'].transpose()
    else:
        field = model.Tatm.transpose()
    cax = ax.contourf(model.lat, model.lev, field)
    ax.invert_yaxis()
    ax.set_xlim(-90,90)
    ax.set_xticks([-90, -60, -30, 0, 30, 60, 90])
    fig.colorbar(cax)

[26]:

plot_temp_section(model, timeave=False)

../_images/courseware_PolarAmplification_30_0.png

[27]:

co2model = climlab.process_like(model)
co2model.subprocess['LW'].absorptivity = model.subprocess['LW'].absorptivity*1.1

[28]:

co2model.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 5.996021270269426 years.

[29]:

plot_temp_section(co2model, timeave=False)

../_images/courseware_PolarAmplification_33_0.png

[30]:

#  Without transport, get equatorial amplification
plt.plot(model.lat, co2model.Ts - model.Ts, label='Ts')
plt.plot(model.lat, co2model.Tatm[:,0] - model.Tatm[:,0], label='Tatm')
plt.legend()

[30]:

<matplotlib.legend.Legend at 0x16bf71ee0>

../_images/courseware_PolarAmplification_34_1.png

Now with meridional heat tranpsort!¶

[31]:

diffmodel = climlab.process_like(model)

[32]:

# thermal diffusivity in W/m**2/degC
D = 0.05
# meridional diffusivity in m**2/s
K = D / diffmodel.Tatm.domain.heat_capacity[0] * const.a**2
print(K)

5946637.413346613

[33]:

d = climlab.dynamics.MeridionalDiffusion(K=K, state={'Tatm':diffmodel.Tatm}, **diffmodel.param)
diffmodel.add_subprocess('diffusion', d)
print(diffmodel)

climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>.
State variables and domain shapes:
  Ts: (90, 1)
  Tatm: (90, 30)
The subprocess tree:
Untitled: <class 'climlab.model.column.GreyRadiationModel'>
   LW: <class 'climlab.radiation.greygas.GreyGas'>
   SW: <class 'climlab.radiation.greygas.GreyGasSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>
   convective adjustment: <class 'climlab.convection.convadj.ConvectiveAdjustment'>
   H2O: <class 'climlab.radiation.water_vapor.ManabeWaterVapor'>
   SHF: <class 'climlab.surface.turbulent.SensibleHeatFlux'>
   LHF: <class 'climlab.surface.turbulent.LatentHeatFlux'>
   diffusion: <class 'climlab.dynamics.meridional_advection_diffusion.MeridionalDiffusion'>

[34]:

diffmodel.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 5.996021270269426 years.

[35]:

plot_temp_section(diffmodel)

../_images/courseware_PolarAmplification_40_0.png

[36]:

#  Plot the northward heat transport in this model
Rtoa = np.squeeze(diffmodel.timeave['ASR'] - diffmodel.timeave['OLR'])
plt.plot(diffmodel.lat, inferred_heat_transport(Rtoa, diffmodel.lat))

[36]:

[<matplotlib.lines.Line2D at 0x16c19f130>]

../_images/courseware_PolarAmplification_41_1.png

[37]:

##  Now warm it up!
co2diffmodel = climlab.process_like(diffmodel)
co2diffmodel.subprocess['LW'].absorptivity = diffmodel.subprocess['LW'].absorptivity*1.1

[38]:

co2diffmodel.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 8.994031905404139 years.

[39]:

#  With transport, get polar amplification...
#   of surface temperature, but not of air temperature!
plt.plot(diffmodel.lat, co2diffmodel.Ts - diffmodel.Ts, label='Ts')
plt.plot(diffmodel.lat, co2diffmodel.Tatm[:,0] - diffmodel.Tatm[:,0], label='Tatm')
plt.legend()

[39]:

<matplotlib.legend.Legend at 0x16c212220>

../_images/courseware_PolarAmplification_44_1.png

[40]:

Rtoa = np.squeeze(diffmodel.timeave['ASR'] - diffmodel.timeave['OLR'])
Rtoa_co2 = np.squeeze(co2diffmodel.timeave['ASR'] - co2diffmodel.timeave['OLR'])
plt.plot(diffmodel.lat, inferred_heat_transport(Rtoa, diffmodel.lat), label='1xCO2')
plt.plot(diffmodel.lat, inferred_heat_transport(Rtoa_co2, diffmodel.lat), label='2xCO2')

[40]:

[<matplotlib.lines.Line2D at 0x16c10c760>]

../_images/courseware_PolarAmplification_45_1.png

Same thing but with NO EVAPORATION¶

[41]:

diffmodel2 = climlab.process_like(diffmodel)
diffmodel2.remove_subprocess('LHF')
print(diffmodel2)

climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>.
State variables and domain shapes:
  Ts: (90, 1)
  Tatm: (90, 30)
The subprocess tree:
Untitled: <class 'climlab.model.column.GreyRadiationModel'>
   LW: <class 'climlab.radiation.greygas.GreyGas'>
   SW: <class 'climlab.radiation.greygas.GreyGasSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>
   convective adjustment: <class 'climlab.convection.convadj.ConvectiveAdjustment'>
   H2O: <class 'climlab.radiation.water_vapor.ManabeWaterVapor'>
   SHF: <class 'climlab.surface.turbulent.SensibleHeatFlux'>
   diffusion: <class 'climlab.dynamics.meridional_advection_diffusion.MeridionalDiffusion'>

[42]:

diffmodel2.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 8.994031905404139 years.

[43]:

co2diffmodel2 = climlab.process_like(co2diffmodel)
co2diffmodel2.remove_subprocess('LHF')
co2diffmodel2.integrate_years(3)

Integrating for 1095 steps, 1095.7266 days, or 3 years.
Total elapsed time is 11.992042540538852 years.

[44]:

#  With transport and no evaporation...
#  No polar amplification, either of surface or air temperature!
plt.plot(diffmodel2.lat, co2diffmodel2.Ts - diffmodel2.Ts, label='Ts')
plt.plot(diffmodel2.lat, co2diffmodel2.Tatm[:,0] - diffmodel2.Tatm[:,0], label='Tatm')
plt.legend()

[44]:

<matplotlib.legend.Legend at 0x16bf71850>

../_images/courseware_PolarAmplification_50_1.png

[45]:

Rtoa = np.squeeze(diffmodel2.timeave['ASR'] - diffmodel2.timeave['OLR'])
Rtoa_co2 = np.squeeze(co2diffmodel2.timeave['ASR'] - co2diffmodel2.timeave['OLR'])
plt.plot(diffmodel2.lat, inferred_heat_transport(Rtoa, diffmodel2.lat), label='1xCO2')
plt.plot(diffmodel2.lat, inferred_heat_transport(Rtoa_co2, diffmodel2.lat), label='2xCO2')

[45]:

[<matplotlib.lines.Line2D at 0x16bf236a0>]

../_images/courseware_PolarAmplification_51_1.png

Warming effect of a DECREASE IN EVAPORATION EFFICIENCY¶

Take a column model that includes evaporation and heat transport, and reduce the drag coefficient by a factor of 2.

How does the surface temperature change?

[46]:

diffmodel3 = climlab.process_like(diffmodel)
diffmodel3.subprocess['LHF'].Cd *= 0.5
diffmodel3.integrate_years(5.)

Integrating for 1826 steps, 1826.2110000000002 days, or 5.0 years.
Total elapsed time is 10.995443571416446 years.

[47]:

#  Reduced evaporation gives equatorially enhanced warming of surface
#  and cooling of near-surface air temperature
plt.plot(diffmodel.lat, diffmodel3.Ts - diffmodel.Ts, label='Ts')
plt.plot(diffmodel.lat, diffmodel3.Tatm[:,0] - diffmodel.Tatm[:,0], label='Tatm')
plt.legend()

[47]:

<matplotlib.legend.Legend at 0x16bf1e610>

../_images/courseware_PolarAmplification_54_1.png

Same calculation in a two-layer EBM¶

[48]:

diffebm3 = climlab.process_like(diffebm)
diffebm3.subprocess['LHF'].Cd *= 0.5
diffebm3.integrate_years(5.)

Integrating for 1826 steps, 1826.2110000000002 days, or 5.0 years.
Total elapsed time is 8.99676981465997 years.

[49]:

#  Reduced evaporation gives equatorially enhanced warming of surface
#  and cooling of near-surface air temperature
plt.plot(diffebm.lat, diffebm3.Ts - diffebm.Ts, label='Ts')
plt.plot(diffebm.lat, diffebm3.Tatm[:,0] - diffebm.Tatm[:,0], label='Tatm')

[49]:

[<matplotlib.lines.Line2D at 0x16bdab4f0>]

../_images/courseware_PolarAmplification_57_1.png

Pretty much the same result.

Some stuff with Band models¶

[50]:

#  Put in some ozone
import xarray as xr

ozonepath = "http://thredds.atmos.albany.edu:8080/thredds/dodsC/CLIMLAB/ozone/apeozone_cam3_5_54.nc"
ozone = xr.open_dataset(ozonepath)

#  Dimensions of the ozone file
lat = ozone.lat
lon = ozone.lon
lev = ozone.lev

# Taking annual, zonal average of the ozone data
O3_zon = ozone.OZONE.mean(dim=("time","lon"))

[51]:

#  make a model on the same grid as the ozone
model1 = climlab.BandRCModel(lev=lev, lat=lat)
insolation = climlab.radiation.AnnualMeanInsolation(domains=model1.Ts.domain)
model1.add_subprocess('insolation', insolation)
model1.subprocess.SW.flux_from_space = model1.subprocess.insolation.insolation
print(model1)

climlab Process of type <class 'climlab.model.column.BandRCModel'>.
State variables and domain shapes:
  Ts: (64, 1)
  Tatm: (64, 59)
The subprocess tree:
Untitled: <class 'climlab.model.column.BandRCModel'>
   LW: <class 'climlab.radiation.nband.FourBandLW'>
   SW: <class 'climlab.radiation.nband.ThreeBandSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>
   convective adjustment: <class 'climlab.convection.convadj.ConvectiveAdjustment'>
   H2O: <class 'climlab.radiation.water_vapor.ManabeWaterVapor'>

[52]:

#  Set the ozone mixing ratio
O3_trans = O3_zon.transpose()
# Put in the ozone
model1.absorber_vmr['O3'] = O3_trans

[53]:

model1.param

[53]:

{'timestep': 86400.0,
 'water_depth': 1.0,
 'albedo_sfc': 0.299,
 'Q': 341.3,
 'abs_coeff': 0.0001229,
 'adj_lapse_rate': 6.5}

[54]:

#  Convective adjustment for atmosphere only
model1.remove_subprocess('convective adjustment')
conv = climlab.convection.ConvectiveAdjustment(state={'Tatm':model1.Tatm}, **model1.param)
model1.add_subprocess('convective adjustment', conv)

[55]:

#  Add surface heat fluxes
shf = climlab.surface.SensibleHeatFlux(state=model1.state, Cd=0.5E-3)
lhf = climlab.surface.LatentHeatFlux(state=model1.state, Cd=0.5E-3)
#  set the water vapor input field for LHF process
lhf.q = model1.q
model1.add_subprocess('SHF', shf)
model1.add_subprocess('LHF', lhf)

[56]:

model1.step_forward()

[57]:

model1.integrate_years(1.)

Integrating for 365 steps, 365.2422 days, or 1.0 years.
Total elapsed time is 1.0020747876340685 years.

[58]:

model1.integrate_years(1.)

Integrating for 365 steps, 365.2422 days, or 1.0 years.
Total elapsed time is 2.0014116660123062 years.

[59]:

plot_temp_section(model1, timeave=False)

../_images/courseware_PolarAmplification_69_0.png

[60]:

co2model1 = climlab.process_like(model1)
co2model1.absorber_vmr['CO2'] *= 2

[61]:

co2model1.integrate_years(3.)

Integrating for 1095 steps, 1095.7266 days, or 3.0 years.
Total elapsed time is 4.999422301147019 years.

[62]:

plot_temp_section(co2model1, timeave=False)

../_images/courseware_PolarAmplification_72_0.png

Model gets very very hot near equator. Very large equator-to-pole gradient.

Band model with heat transport and evaporation¶

[63]:

diffmodel1 = climlab.process_like(model1)
# thermal diffusivity in W/m**2/degC
D = 0.01
# meridional diffusivity in m**2/s
K = D / diffmodel1.Tatm.domain.heat_capacity[0] * const.a**2
d = climlab.dynamics.MeridionalDiffusion(K=K, state={'Tatm': diffmodel1.Tatm}, **diffmodel1.param)
diffmodel1.add_subprocess('diffusion', d)
diffmodel1.absorber_vmr['CO2'] *= 4.
print(diffmodel1)

climlab Process of type <class 'climlab.model.column.BandRCModel'>.
State variables and domain shapes:
  Ts: (64, 1)
  Tatm: (64, 59)
The subprocess tree:
Untitled: <class 'climlab.model.column.BandRCModel'>
   LW: <class 'climlab.radiation.nband.FourBandLW'>
   SW: <class 'climlab.radiation.nband.ThreeBandSW'>
   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>
   H2O: <class 'climlab.radiation.water_vapor.ManabeWaterVapor'>
   convective adjustment: <class 'climlab.convection.convadj.ConvectiveAdjustment'>
   SHF: <class 'climlab.surface.turbulent.SensibleHeatFlux'>
   LHF: <class 'climlab.surface.turbulent.LatentHeatFlux'>
   diffusion: <class 'climlab.dynamics.meridional_advection_diffusion.MeridionalDiffusion'>

[64]:

diffmodel1.integrate_years(3.)
plot_temp_section(diffmodel1, timeave=False)

Integrating for 1095 steps, 1095.7266 days, or 3.0 years.
Total elapsed time is 4.999422301147019 years.

../_images/courseware_PolarAmplification_76_1.png

[65]:

Rtoa = np.squeeze(diffmodel1.timeave['ASR'] - diffmodel1.timeave['OLR'])
plt.plot(diffmodel1.lat, inferred_heat_transport(Rtoa, diffmodel1.lat))

[65]:

[<matplotlib.lines.Line2D at 0x16c3c2af0>]

../_images/courseware_PolarAmplification_77_1.png

[66]:

plt.plot(diffmodel1.lat, diffmodel1.Ts-273.15)

[66]:

[<matplotlib.lines.Line2D at 0x16c421ee0>]

../_images/courseware_PolarAmplification_78_1.png

[67]:

#  Now double CO2
co2diffmodel1 = climlab.process_like(diffmodel1)
co2diffmodel1.absorber_vmr['CO2'] *= 2.
co2diffmodel1.integrate_years(5)

Integrating for 1826 steps, 1826.2110000000002 days, or 5 years.
Total elapsed time is 9.998844602294039 years.

[68]:

#  No polar amplification in this model!
plt.plot(diffmodel1.lat, co2diffmodel1.Ts - diffmodel1.Ts, label='Ts')
plt.plot(diffmodel1.lat, co2diffmodel1.Tatm[:,0] - diffmodel1.Tatm[:,0], label='Tatm')
plt.legend()
plt.figure()
Rtoa = np.squeeze(diffmodel1.timeave['ASR'] - diffmodel1.timeave['OLR'])
Rtoa_co2 = np.squeeze(co2diffmodel1.timeave['ASR'] - co2diffmodel1.timeave['OLR'])
plt.plot(diffmodel1.lat, inferred_heat_transport(Rtoa, diffmodel1.lat), label='1xCO2')
plt.plot(diffmodel1.lat, inferred_heat_transport(Rtoa_co2, diffmodel1.lat), label='2xCO2')
plt.legend()

[68]:

<matplotlib.legend.Legend at 0x16c4de8e0>

../_images/courseware_PolarAmplification_80_1.png

../_images/courseware_PolarAmplification_80_2.png

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