Estimating Equilibrium Climate Sensitivity

Overview¶

Equilibrium Climate Sensitivity (ECS) is defined as change in global-mean near-surface air temperature (GMST) change due to an instantaneous doubling of CO$_2$ concentrations and once the coupled ocean-atmosphere-sea ice system has acheived a statistical equilibrium (i.e. at the top-of-atmosphere, incoming solar shortwave radiation is balanced by reflected solar shortwave and outgoing thermal longwave radiation).

This notebook uses the “Gregory method” to approximate the ECS of CMIP6 models based on the first 150 years after an abrupt doubling of CO$_2$ concentrations. The Gregory method extrapolates the quasi-linear relationship between GMST and radiative imbalance at the top-of-atmosphere to estimate how much warming would occur if the system were in radiative balance at the top-of-atmosphere, which is by definition the equilibrium response. In particular, we extrapolate the linear relationship that occurs between 100 and 150 years after the abrupt quadrupling.

Since the radiative forcing due to CO$_2$ is a logarithmic function of the CO$_2$ concentration, the GMST change from a first doubling is roughly the same as for a second doubling (to first order, we can assume feedbacks as constant), which means that the GMST change due to a quadrupling of CO$_2$ is roughly $\Delta T_{4\times\mathrm{CO}_2}=2\times\mathrm{ECS}$. See also Mauritsen et al. 2019 for a detailed application of the Gregory method (with modifications) for the case of one specific CMIP6 model, the MPI-M Earth System Model.

For another take on applying the Gregory method to estimate ECS, see Angeline Pendergrass’ code.

Prerequisites¶

• Time to learn: 30 minutes

Imports¶

Compute Cluster¶

Here we use a dask cluster to parallelize our analysis.

Initiate the Dask client:

Data catalogs¶

This notebook uses intake-esm to ingest and organize climate model output from the fresh-off-the-supercomputers Phase 6 of the Coupled Model Intercomparison Project (CMIP6).

The file https://storage.googleapis.com/cmip6/cmip6-zarr-consolidated-stores.csv in Google Cloud Storage contains thousands of lines of metadata, each describing an individual climate model experiment’s simulated data.

For example, the first line in the .csv file contains the precipitation rate (variable_id = 'pr'), as a function of latitude, longitude, and time, in an individual climate model experiment with the BCC-ESM1 model (source_id = 'BCC-ESM1') developed by the Beijing Climate Center (institution_id = 'BCC'). The model is forced by the forcing experiment SSP370 (experiment_id = 'ssp370'), which stands for the Shared Socio-Economic Pathway 3 that results in a change in radiative forcing of $\Delta F=7.0$ W m$^{-2}$ from pre-industrial to 2100. This simulation was run as part of the AerChemMIP activity, which is a spin-off of the CMIP activity that focuses specifically on how aerosol chemistry affects climate.

The file pangeo-cmip6.json describes the structure of the CMIP6 metadata and is formatted so as to be read in by the intake.open_esm_datastore method, which categorizes all of the data pointers into a tiered collection. For example, this collection contains the simulated data from 28691 individual experiments, representing 48 different models from 23 different scientific institutions. There are 190 different climate variables (e.g. sea surface temperature, sea ice concentration, atmospheric winds, dissolved organic carbon in the ocean, etc.) available for 29 different forcing experiments.

Use Intake-ESM¶

Intake-ESM is a new package designed to make working with these data archives a bit simpler.

Here, we show the various forcing experiments that climate modellers ran in these simulations.

Loading Data¶

Intake-ESM enables loading data directly into an xarray.DataArray, a metadata-aware extension of numpy arrays. Xarray objects leverage Dask to only read data into memory as needed for any specific operation (i.e. lazy evaluation). Think of Xarray Datasets as ways of conveniently organizing large arrays of floating point numbers (e.g. climate model data) on an n-dimensional discrete grid, with important metadata such as units, variable, names, etc.

Note that data on the cloud are in Zarr format, an extension of the metadata-aware format NetCDF commonly used in the geosciences.

Intake-ESM has rules for aggegating datasets; these rules are defined in the collection-specification file.

Here, we choose the piControl experiment (in which CO$_2$ concentrations are held fixed at a pre-industrial level of ~300 ppm) and abrupt-2xCO2 experiment (in which CO$_2$ concentrations are instantaneously doubled from a pre-industrial control state). Since the radiative forcing of CO$_2$ is roughly a logarithmic function of CO$_2$ concentrations, the ECS is roughly independent of the initial CO$_2$ concentration.

Prepare Data¶

The following functions help us load and homogenize the data. We use some dask.delayed programming to open the datasets in parallel.

Create a nested dictionary of models and experiments. It will be structured like this:

{'CESM2':
  {
    'piControl': <xarray.Dataset>,
    'abrupt-2xCO2': <xarray.Dataset>
  },
  ...
}

Open one of the datasets directly, just to show what it looks like:

Now use dask to do this in parallel on all of the datasets:

Reduce Data via Global Mean¶

We don’t want to load all of the raw model data into memory right away. Instead, we want to reduce the data by taking the global mean. We need to remember to weight this global mean by a factor proportional to cos(lat).

We now apply this function, plus resampling to annual mean data, to all of the datasets. We also concatenate the experiments together into a single Dataset for each model. This is the most complex cell in the notebook. A lot is happening here.

Do the Computation¶

Up to this point, no computations have actually happened. Everything has been “lazy”. Now we trigger the computation to actual occur and load the global/annual mean data into memory.

Now we concatenate across models to produce one big dataset with all the required variables.

Calculated Derived Variables¶

We need to calculate the net radiative imbalance, plus the anomaly of the abrupt 2xCO2 run compared to the piControl run.

Plot Timeseries¶

Here we plot the global mean surface temperature for each model:

We can see that the models cover different time intervals. Let’s limit the rest of our analysis to the first 150 years.

Same thing for radiative imbalance:

Calculate ECS¶

Also, make sure that we set a couple of the variables to be coordinates.

We’re at the end of the notebook, so let’s shutdown our Dask cluster.

Summary¶

In this notebook, we estimated ECS for a subset of CMIP6 models using the Gregory method.

What’s next?¶

We will plot global average surface air temperature for a historical run and two branching emissions scenarios.

Additional resources¶

• Original notebook in the Pangeo Gallery by Henri Drake and Ryan Abernathey