Bonus Tutorial 5: Vertical Structure of the Atmosphere

Bonus Tutorial 5: Vertical Structure of the Atmosphere#

Week 1, Day 5, Introduction to Climate Modeling

Content creators: Jenna Pearson and Brian E. J. Rose

Content reviewers: Mujeeb Abdulfatai, Nkongho Ayuketang Arreyndip, Jeffrey N. A. Aryee, Younkap Nina Duplex, Will Gregory, Paul Heubel, Zahra Khodakaramimaghsoud, Peter Ohue, Abel Shibu, Derick Temfack, Yunlong Xu, Peizhen Yang, Ohad Zivan, Chi Zhang

Content editors: Abigail Bodner, Paul Heubel, Brodie Pearson, Ohad Zivan, Chi Zhang

Production editors: Wesley Banfield, Paul Heubel, Jenna Pearson, Konstantine Tsafatinos, Chi Zhang, Ohad Zivan

Our 2024 Sponsors: CMIP, NFDI4Earth

Tutorial Objectives#

Estimated timing of tutorial: 30 minutes

Note that the previous, the present, and the subsequent tutorials contain solely Bonus content, that serves experienced participants and for later investigation of 0- and 1-dimensional models after the course. Please check out these tutorials after finishing Tutorial 7-8 successfully.

In this tutorial, you will run a one-dimensional radiative equilibrium model that predicts the global mean atmospheric temperature as a function of height. Much of the code shown here was taken from The Climate Laboratory by Brian E. J. Rose. You are encouraged to visit this website for more tutorials and background on these models.

By the end of this tutorial you will be able to:

Implement a 1-D model that predicts atmospheric temperature as a function of height using the python package climlab.
Understand how this model builds off of the energy balance models developed in the previous tutorials.

Setup#

# installations ( uncomment and run this cell ONLY when using google colab or kaggle )

# note the conda install takes quite a while, but conda is REQUIRED to properly download the
# dependencies (that are not just python packages)

# !pip install condacolab &> /dev/null
# import condacolab
# condacolab.install()

# !mamba install -c anaconda cftime xarray numpy &> /dev/null    # for decoding time variables when opening datasets
# !mamba install -c conda-forge metpy climlab &> /dev/null

# imports

# google colab users, if you get an xarray error, please run this cell again

import xarray as xr              # used to manipulate data and open datasets
import numpy as np               # used for algebra/arrays
import climlab                   # one of the models we are using
import matplotlib.pyplot as plt  # used for plotting
import metpy                     # used to make Skew T Plots of temperature and pressure
from metpy.plots import SkewT    # plotting function used widely in climate science
import pooch
import os
import tempfile

/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/climlab/radiation/cam3.py:46: UserWarning: Cannot import and initialize compiled Fortran extension, CAM3 module will not be functional.
  warnings.warn('Cannot import and initialize compiled Fortran extension, CAM3 module will not be functional.')

/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/climlab/convection/emanuel_convection.py:14: UserWarning: Cannot import EmanuelConvection fortran extension, this module will not be functional.
  warnings.warn('Cannot import EmanuelConvection fortran extension, this module will not be functional.')

Figure settings#

Helper functions#

Video 1: Vertical Structure of the Atmosphere#

Section 3: Running the Radiative Equilibrium Model Forward in Time#

We can run this model over many time steps, just like the simple greenhouse model, but now we can examine the behavior of the temperature profile rather than just the surface temperature.

There is no need to write out a function to step our model forward - climlab already has this feature. We will use this function to run our model to equilibrium (i.e. until \(OLR\) is balanced by \(ASR\)).

# take a single step forward to the diagnostics are updated and there is some energy imbalance
radmodel.step_forward()

# run the model to equilibrium (the difference between ASR and OLR is a very small number)
while np.abs(radmodel.ASR - radmodel.OLR) > 0.001:
    radmodel.step_forward()

#  check the energy budget to make sure we are really at equilibrium
radmodel.ASR - radmodel.OLR

Field([0.0009879])

Now let’s can compare this to observations.

skew = make_skewT()
add_profile(skew, radmodel)
skew.ax.set_title("Pure Radiative Equilibrium")

Text(0.5, 1.0, 'Pure Radiative Equilibrium')

../../../_images/7a50f394a52ebbe754a7ebcbdeb9119401f7810c4111715ef1e32ed71450d0bf.png

Questions 3: Climate Connection#

The profile from our model does not match observations well. Can you think of one component we might be missing?
What effect do you think the individual gases play in determining this profile and why?

Click for solution

Coding Exercises 3#

Create a second model called ‘Radiation (no H20)’ that lacks water vapor. Then re-create the plot above, but add on this extra profile without water vapor.

# make an exact clone of our existing model
radmodel_noH2O = climlab.process_like(radmodel)
# change the name of our new model
radmodel_noH2O.name = ...

# set the water vapor profile to all zeros
radmodel_noH2O.specific_humidity *= 0.0

# run the model to equilibrium
radmodel_noH2O.step_forward()
while np.abs(radmodel_noH2O.ASR - radmodel_noH2O.OLR) > 0.01:
    radmodel_noH2O.step_forward()

# create skewT plot
skew = make_skewT()

# add profiles for both models to plot
for model in [...]:
    ...

../../../_images/fe1d2c65ec4bb6fd28dca658e0e0534624b05757411146a9153a87d2c971942b.png

Click for solution

Example output:

Summary#

In this tutorial, you’ve learned how to use the python package climlab to construct a one-dimensional radiative equilibrium model, and run it forward in time to predict the global mean atmospheric temperature profile. You’ve also visualized these results through SkewT plots.

Resources#

Data from this tutorial can be accessed for specific humidity here and reanalysis temperature here.

Useful links:

The Climate Laboratory by Brian E. J. Rose
Specific Humidity
Rapid Radiative Transfer Model
SkewT plots - Advanced Tutorials