Radiative Equilibrium

11. Radiative Equilibrium#

This notebook is part of The Climate Laboratory by Brian E. J. Rose, University at Albany.

1. The observed annual, global mean temperature profile#

Let’s look again the observations of air temperature from the NCEP Reanalysis data we first encountered in the Radiation notes.

In this notebook we’ll define a function to create the Skew-T diagram, because later we are going to reuse it several times.

Click to expand code cells to see Python details

#  This code is used just to create the skew-T plot of global, annual mean air temperature
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import xarray as xr
from metpy.plots import SkewT
ncep_url = "http://www.esrl.noaa.gov/psd/thredds/dodsC/Datasets/ncep.reanalysis.derived/"
ncep_air = xr.open_dataset( ncep_url + "pressure/air.mon.1981-2010.ltm.nc", use_cftime=True)
#  Take global, annual average 
coslat = np.cos(np.deg2rad(ncep_air.lat))
weight = coslat / coslat.mean(dim='lat')
Tglobal = (ncep_air.air * weight).mean(dim=('lat','lon','time'))

def make_skewT():
    fig = plt.figure(figsize=(9, 9))
    skew = SkewT(fig, rotation=30)
    skew.plot(Tglobal.level, Tglobal, color='black', linestyle='-', linewidth=2, label='Observations')
    skew.ax.set_ylim(1050, 10)
    skew.ax.set_xlim(-90, 45)
    # Add the relevant special lines
    skew.plot_dry_adiabats(linewidth=0.5)
    skew.plot_moist_adiabats(linewidth=0.5)
    #skew.plot_mixing_lines()
    skew.ax.legend()
    skew.ax.set_xlabel('Temperature (degC)', fontsize=14)
    skew.ax.set_ylabel('Pressure (hPa)', fontsize=14)
    return skew

skew = make_skewT()

Here we are going to work with some detailed Single-Column Models to understand questions such as

What physical factors actually determine this profile?
Would the profile be different with different gases in the atmosphere?
What are the relative roles of radiation and dynamics (i.e. motion!) in setting this profile?

We will start by ignoring all processes except radiation. We will calculate something called the radiative equilibrium temperature.

2. Radiative equilibrium – the concept#

Models of radiative transfer slice up the atmospheric air column into a series of layer, and calculate the emission and absorption of radiation within each layer.

It’s really just a generalization of the model we already looked at:

Sketch of layer model

The concept of radiative equilibrium means that we ignore all methods of heat exchange except for radiation, and ask what temperature profile would exist under that assumption?

We can answer that question by using a radiative transfer model to explicity compute the shortwave and longwave beams, and the warming/cooling of each layer associated with the radiative sources and sinks of energy.

Basically, we reach radiative equilibrium when energy is received and lost through radiation at the same rate in every layer.

Because of the complicated dependence of emission/absorption features on the wavelength of radiation and the different gases, the beam is divided up into many different pieces representing different parts of the electromagnetic spectrum.

We will not look explicitly at this complexity here, but we will use a model that represents these processes at the same level of detail we would in a GCM.

5. Effects of different gases on the radiative equilibrium profile#

Models are for experimenting and playing with!

We have just built a single-column radiation model with several different absorbing gases. We can learn about their effects by taking them away.

Radiative equilibrium without water vapor#

# Make an exact clone of our existing model
radmodel_noH2O = climlab.process_like(radmodel)
radmodel_noH2O.name = 'Radiation (no H2O)'
radmodel_noH2O

<climlab.radiation.rrtm.rrtmg.RRTMG at 0x163dca8e0>

#  Here is the water vapor profile we started with
radmodel_noH2O.specific_humidity

array([2.16104904e-06, 2.15879387e-06, 2.15121262e-06, 2.13630949e-06,
       2.12163684e-06, 2.11168002e-06, 2.09396914e-06, 2.10589390e-06,
       2.42166155e-06, 3.12595653e-06, 5.01369691e-06, 9.60746488e-06,
       2.08907654e-05, 4.78823747e-05, 1.05492451e-04, 2.11889055e-04,
       3.94176751e-04, 7.10734458e-04, 1.34192099e-03, 2.05153261e-03,
       3.16844784e-03, 4.96883408e-03, 6.62218037e-03, 8.38350326e-03,
       9.38620899e-03, 9.65030544e-03])

Now get rid of the water entirely!

radmodel_noH2O.specific_humidity *= 0.

radmodel_noH2O.specific_humidity

array([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.])

And run this new model forward to equilibrium:

#  it's useful to take a single step first before starting the while loop
#   because the diagnostics won't get updated 
#  (and thus show the effects of removing water vapor)
#  until we take a step forward
radmodel_noH2O.step_forward()
while np.abs(radmodel_noH2O.ASR - radmodel_noH2O.OLR) > 0.01:
    radmodel_noH2O.step_forward()

radmodel_noH2O.ASR - radmodel_noH2O.OLR

Field([-0.00999903])

skew = make_skewT()
for model in [radmodel, radmodel_noH2O]:
    add_profile(skew, model)

What do you think you can learn from this about the radiative role of water vapor?

Exercise: radiative equilibrium without ozone#

Following the steps above, make another model, but this time instead of removing the water vapor, remove the ozone!

Make another skew-T plot comparing all three model results.

If you have time, try a third case in which you remove both the water vapor and the ozone!

6. Summary of radiative equilibrium results#

We used the RRTMG radiation model with prescribed profiles of absorbing gases to calculate pure radiative equilibrium temperature profiles.
Radiative Equilibriu means the temperatures that the surface and air column would have if radiation was the only physical process that could transfer energy between levels.
We computed several different radiative equilibrium profiles, with and without key absorbing gases
- The profile without water vapor is much colder at surface and lower troposphere, but about the same in the stratosphere
- The profile without ozone is much colder in the stratosphere, but about the same near the surface.
- In fact there really isn’t a stratosphere at all without ozone! The temperature is nearly isothermal in the upper atmosphere in that profile.

However the really key takeaway message is that none of these radiative equilibrium profiles look much like the observations in the troposphere.

This strongly suggests that other physical processes (aside from radiation) are important in determining the observed temperature profile.

Plotting on the skew-T diagram makes it clear that all the radiative equilibrium profiles are statically unstable near the surface.

The next step is therefore to look at the effects of convective mixing on the temperatures of the surface and lower troposphere.

Credits#

This notebook is part of The Climate Laboratory, an open-source textbook developed and maintained by Brian E. J. Rose, University at Albany.

It is licensed for free and open consumption under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

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.

Radiative Equilibrium

Contents

11. Radiative Equilibrium#

1. The observed annual, global mean temperature profile#

2. Radiative equilibrium – the concept#

3. Setting up a single-column radiation model in climlab#

Radiation models in climlab#

Water vapor data#

Create a single-column model on the same grid as this water vapor data:#

Explore the single-column model object#

Python exercise: plot the ozone profile#

The RRTMG radiation model has lots of different input parameters#

4. Radiative equilibrium in the single-column model#

Step the model forward in time!#

Diagnostic variables in our single-column model#

Integrate out to equilibrium#

Compare the radiative equilibrium temperature to observations#

5. Effects of different gases on the radiative equilibrium profile#

Radiative equilibrium without water vapor#

Exercise: radiative equilibrium without ozone#

6. Summary of radiative equilibrium results#

Credits#