The influence of varying atmospheric CO₂ on global warming potentials and carbon emission impulse response functions

Abstract Impulse response functions (IRF), the response in a climate parameter to an emission pulse of CO 2 , are used to characterize Earth system response timescales and to calculate Global Warming Potentials (GWPs). GWPs are widely used to compare emissions of different greenhouse gases and to compute CO 2 equivalent emissions as reported by governments to the United Nations Framework Convention on Climate Change (UNFCCC). The GWP of any gas x is the absolute GWP of gas x Absolute and relative Global Warming Potential (AGWP x ) divided by AGWP of CO 2 . Ideally, AGWP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and GWP x would be independent of atmospheric CO 2 and climate. However, AGWP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and, in turn, GWP x change under rising atmospheric CO 2 and global warming, affecting the emission reporting under the UNFCCC. Here, we apply perturbed parameter ensemble simulations, constrained in a Bayesian approach by observational data, to investigate how AGWP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and IRF vary under different atmospheric background CO 2 levels (CO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). We provide analytical formulations to compute AGWP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and IRF for CO 2 , ocean and land carbon uptake, global mean surface air temperature, steric sea level, and ocean heat content, and to adjust these metrics to different CO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . AGWP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , given by the time-integrated response in CO 2 at year 100 multiplied by its radiative efficiency, is 101.8(±13.5) 10 −15 yr W m −2 kg-CO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> for CO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> = 425 ppm and decreases by 7% for CO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> = 500 ppm. The decrease is driven by a decrease in the radiative efficiency of CO 2 , partly canceled by a concomitant increase of IRF <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow>