Climate sensitivity and climate state - Climate Dynamics

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Authors and Affiliations

1. Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, University of Victoria, Canada, PO Box 1700, Victoria, B.C. V8W 2Y2

   G. J. Boer & B. Yu

Corresponding author

Correspondence to G. J. Boer.

Appendix 1

1.1 Sensitivity of feedback calculations to estimates of radiative forcing

We consider the stabilization calculations leading to Fig. 2. From Eq. (4) the global feedback may be expressed as \(\hat \Lambda _\alpha = {{\langle \hbox{d}h^{\prime}_\alpha /\hbox{d}t\rangle - \langle f\rangle} \over {\langle T^{\prime}_\alpha \rangle}} \to {{- \langle f_{g_\alpha} + f_a \rangle} \over {\langle T^{\prime}_\alpha \rangle}}\) at equilibrium where α = 1, 2 identifies the S2050 and S2100 simulations respectively. The stabilized GHG forcing f _g differs considerably between the two cases but the aerosol forcing f _a is essentially the same (the aerosol loading changes very little after 2050). The overall forcing f in each case does not change after stabilization but there may be some error in our estimate of it. We ask to what extent we would have to modify either the GHG or aerosol forcing so that the S2050 and S2100 feedbacks attain the same value (i.e. so that Λ₁ = Λ₂) some 80 decades after stabilization in Fig. 2.

First presume that f _g is correct, and consider the modification to f _a that would be required to make the feedbacks agree. We replace f _a by (1 + ɛ)f _a , set the resulting "corrected" expressions for feedback equal to one another \(\hat \Lambda _1 - \varepsilon \langle f_a \rangle /\langle T^{\prime}_1 \rangle = \hat \Lambda _2 - \varepsilon \langle f_a \rangle /\langle T^{\prime}_2 \rangle \) and solve for ɛ with the appropriate values of the quantities in Figs. 1 and 2. The result gives ɛ ≈ –0.40 so that 〈f _a 〉 would have to be decreased to 60% of its estimated value to cause the feedback values to agree at equilibrium. Similarly, assuming that 〈f _a 〉 is correct and modifying 〈f _g〉 gives ɛ ≈ 0.40 so that the 〈f _g 〉 would have to be increased to 140% of their estimated values to obtain agreement of the Λs. Errors of this magnitude are considered to be unlikely.

Finally, applying the same approach to errors in both forcings and requiring the same (and hence the minimum) magnitude (but not sign) of the fractional error ɛ for both forcings gives |ɛ| ≈ 0.20 requiring a decrease in aerosol forcing to about 80% of its value combined with an increase of GHG forcing to 120% of it value. There is no apparent reason why aerosol forcing should be underestimated while GHG forcing is overestimated by this amount and we conclude that the modest differences between the feedbacks for the S2050 and S2100 cases are likely to be real.

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Boer, G.J., Yu, B. Climate sensitivity and climate state. Climate Dynamics 21, 167–176 (2003). https://doi.org/10.1007/s00382-003-0323-7

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• Received: 29 August 2002

• Accepted: 09 January 2003

• Published: 15 April 2003

• Issue Date: August 2003

• DOI: https://doi.org/10.1007/s00382-003-0323-7

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