Journal cover Journal topic
Earth System Dynamics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

Journal metrics

  • IF value: 3.866 IF 3.866
  • IF 5-year value: 4.135 IF 5-year
    4.135
  • CiteScore value: 7.0 CiteScore
    7.0
  • SNIP value: 1.182 SNIP 1.182
  • IPP value: 3.86 IPP 3.86
  • SJR value: 1.883 SJR 1.883
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 33 Scimago H
    index 33
  • h5-index value: 30 h5-index 30
Preprints
https://doi.org/10.5194/esd-2020-48
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-2020-48
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  04 Aug 2020

04 Aug 2020

Review status
This preprint is currently under review for the journal ESD.

The Fractional Energy Balance Equation for Climate projections through 2100

Roman Procyk1, Shaun Lovejoy1, and Raphael Hébert2 Roman Procyk et al.
  • 1Physics Dept., McGill University, 3600 rue University, Montreal, Quebec, H3A 2T8, Canada
  • 2Alfred-Wegener Institute Helmholtz Center for Polar and Marine Research, Telegrafenberg A45, 14473 Potsdam, Germany

Abstract. We produce climate projections through the 21st century using the fractional energy balance equation (FEBE) which is a generalization of the standard EBE. The FEBE can be derived either from Budyko–Sellers models or phenomenologically by applying the scaling symmetry to energy storage processes. It is easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value near 1/2.

The FEBE has two shape parameters: a scaling exponent H and relaxation time τ; its amplitude parameter is the equilibrium climate sensitivity (ECS). Two additional parameters were needed for the forcing: an aerosol re-calibration factor α to account for the large aerosol uncertainty, and a volcanic intermittency correction exponent ν. A Bayesian framework based on historical temperatures and natural and anthropogenic forcing series was used for parameter estimation. Significantly, the error model was not ad hoc, but was predicted by the model itself: the internal variability response to white noise internal forcing.

The 90 % Confidence Interval (CI) of the shape parameters were H = [0.33, 0.44] (median = 0.38), τ = [2.4, 7.0] (median = 4.7) years compared to the usual EBE H = 1, and literature values τ typically in the range 2–8 years. We found that aerosols were too strong by an average factor α = [0.2, 1.0] (median = 0.6) and the volcanic intermittency correction exponent was ν = [0.15, 0.41] (median = 0.28) compared to standard values α = ν = 1. The overpowered aerosols support a revision of the global modern (2005) aerosol forcing 90 % CI to a narrower range [−1.0, −0.2] W m−2 compared with the IPCC AR5 range [1.5, 4.5] K (median = 3.2 K). Similarly, we found the transient climate sensitivity (TCR) = [1.2, 1.8] K (median = 1.5 K) compared to the AR5 range TCR = [1.0, 2.5] K (median = 1.8 K). As commonly seen in other observational-based studies, the FEBE values are therefore somewhat lower but still consistent with those in IPCC AR5.

Using these parameters we made projections to 2100 using both the Representative Carbon Pathways (RCP) and Shared Socioeconomic Pathways (SSP) scenarios and shown alongside the CMIP5/6 MME. The FEBE hindprojections (1880–2019) closely follow observations (notably during the hiatus, 1998–2015). Overall the FEBE were 10–15 % lower but due to their smaller uncertainties, their 90 % CIs lie completely within the GCM 90 % CIs. The FEBE thus complements and supports the GCMs.

Roman Procyk et al.

Interactive discussion

Status: open (until 01 Nov 2020)
Status: open (until 01 Nov 2020)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
[Subscribe to comment alert] Printer-friendly Version - Printer-friendly version Supplement - Supplement

Roman Procyk et al.

Roman Procyk et al.

Viewed

Total article views: 403 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
340 59 4 403 1 3
  • HTML: 340
  • PDF: 59
  • XML: 4
  • Total: 403
  • BibTeX: 1
  • EndNote: 3
Views and downloads (calculated since 04 Aug 2020)
Cumulative views and downloads (calculated since 04 Aug 2020)

Viewed (geographical distribution)

Total article views: 320 (including HTML, PDF, and XML) Thereof 318 with geography defined and 2 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 

Cited

Saved

No saved metrics found.

Discussed

No discussed metrics found.
Latest update: 29 Sep 2020
Publications Copernicus
Download
Short summary
This paper presents a new class of energy balance model that accounts for the long memory within the Earth's energy storage. The model is calibrated on instrumental temperature records and the historical energy budget of the Earth using an error model predicted by the model itself. Our equilibrium climate sensitivity and future temperature projection estimates are consistent with those estimated by complex climate models.
This paper presents a new class of energy balance model that accounts for the long memory within...
Citation
Altmetrics