ECS-Constraint

Calculation of a posterior ECS probability distribution function weighted by how well models reproduce temporal variability

The code originated from Brient and Schneider (16). A preprocessing averaging (https://github.com/florentbrient/Cloud-variability-time-frequency) is used to identify temporal variability of monthly-mean variations over tropical low-cloud (TLC) regions.

Preprocessing

Input

Frequency	Variable	CMOR labels	Unit	File Format
monthly mean	Relative humidity profile	hur	-	nc
monthly mean	Sea surface temperature	ts	K	nc
	TOA outgoing shortwave flux at the top-of-the-atmosphere	rsut	Wm-2	nc
	Clear-sky outgoing shortwave flux at the top-of-the-atmosphere	rsutcs	Wm-2	nc

We identified TLC regions as the 25% of the tropical ocean area (30°N–30°S) with the lowest midtropospheric (500 hPa) relative humidity. Monthly time series of surface temperature (sst) and cloud albedo (albcld, i.e. the difference between rsutcs-rsut) are created over these TLC regions, for both observations and models.

We averaged over the same equal-area grid with 240x121 cells globally for relevant inter-model and model-to-observations comparisons.

We compute the co-variations between low-cloud albedo and surface temperature for observations, along with uncertainties computed with a bootstrapping framework.

See https://github.com/florentbrient/Cloud-variability-time-frequency for more details about the preprocessing.

Output

Outputs of this preprocessing are listed in "datafile.mat", including co-variations between SST and cloud albedo for the observations and 29 CMIP5 models. Values of Equilibrium climate sensitivity (ECS) for these 29 models are also listed in the file.

Diagnostic calculation

Definition

• The original temporal variability is not needed. We use a statistical significant number of randomly-created samples aiming to reproduce the uncertainty of the original temporal variability (Nb samples). This uncertainty are produced by a bootstrapping procedure.
• The likelihood of a model given the observations and its related weight can be computed by :
  • A Kullback-Leibler measure (use_normal=0, by default). The divergence is the relative entropy between a model's PDF and the observed PDF, which indicate how much information is lost if the model's PDF is used to approximate the observed PDF
  • A log-likelihood function (use_normal=1)
• The routine to call in named "ECS_calcul.mat"

Input

The original code makes use of the output data from the preprocessing analysis. These data are listed in "datafile.mat" for :

• Observations ('slope') : Uncertainty of the original slopes are created through 200 bootstrap samples of the TLC temporal variations (183 months from March 2000 through May 2015).
• CMIP models ('slopeobs') : Unertainties of the model slopes are created through 3*200 bootstrap samples of the TLC temporal variations (based on 3 time periods of 183 months-long from 1959 to 2005).

Inputs listed in "datafile.mat" are those used in Brient and Schneider (16).

Output

• Data

  • The routine diagnoses the prior and posterior ECS modes and 66% and 90% confidence intervals
  • This diagnostics is written in "ECS_prior.txt" and "ECS_posterior.txt", available in https://github.com/florentbrient/ECS-Constraint/tree/master/data/

• Figures

  • The code creates some figures, all of which are available at https://github.com/florentbrient/ECS-Constraint/tree/master/figures:
    • The prior ECS probability density estimate for observations and each model are named "Prior_posterior_PDF_(model).png"
    • The prior and posterior ECS probability density estimate is "Posterior_ECS_29models.png"

One supplementary routine :

• confidence_intervals.mat : Compute 66% and 90% confidence intervals

Remarks

• The code should be rewritten in Python for consistency with the preprocessing.

References

Brient F and Schneider T (2016) Constraints on Climate Sensitivity from Space-Based Measurements of Low-Cloud Reflection. J. Clim., 29:5821–5835, DOI: 10.1175/JCLI-D-15-0897.1