# Climate sensitivity

The climate sensitivity is defined as the amount of equilibrium warming caused by a doubling of CO_{2 }(or equivalent change in radiative forcing). Over the concentration range of most interest, this relation can be approximated as a logarithmic function (as Plimer acknowledges on page 338). Thus about the same warming is expected for doubling from 200 ppm to 400 ppm as from 300 ppm to 600 ppm. Denoting the climate sensitivity as X, means that the temperature change a s a f u n c t i o n o f c o n c e n t r a t i o n c h a n g e f r o m C 1 t o C 2 c a n b e w r i t t e n a s :

T_{1 2 }

= T ( C 2 )

T ( C 1 ) = X [ l o g 2 ( C 2 )

l o g 2 ( C 1 ) ] = X × l o g 2 ( C 2 / C 1 )

# This logarithmic relation has been known since the time of

rrhenius (1896) (who estimated

# X= 5^{◦}C). It can be written in terms of natural logarithms (logarithms to base e) as

T_{1 2 }

= X [ l o g e ( C 2 )

l o g e ( C 1 ) ] × l o g 2 e ≈ 1 4 4 X × l o g e ( C 2 / C 1 ) = 1 4 4 X × l n ( C 2 / C 1 )

T h e I P C C h a s g i v e n a r a n g e o f 1 . 5 ◦ C t o 4 . 5 ◦ C . J a m e s H a n s e n ( e . g . B j e r k n e s l e c t u r e a t 2 0 0 8 G U F a l l M e e t i n g ) e s t i m a t e s X = 3 0 ± 0 5 ◦ C . T h e l o g a r i t h m i c r e l a t i o n w o n ’ t a p p l y a t l concentrations — a linear dependence is expected. The logarithmic dependence will also break down at sufficiently high concentrations. o w

Plimer’s treatment of this lacks consistency. On a number of occasions he claims X = 0.5^{◦}C (e.g. page 488), while on page 426 (see item 104) he claims 1.5^{◦}C, and his example above (see item 124) of 7^{◦}C for 20 times CO_{2 }implies 1.61^{◦}C. (Note that since a division of logarithms is involved, the result of the calculation 7 × log(2 0)/ log(20 0) does not depend on what base is used for the logarithms, as long as the same base is used in both cases).

F o r a fi x e d i n i t i a l c o n c e n t r a t i o n C 1 , o n e c a n l o o k a t h o w m u c h t h e t e m p e r a t u r e i n c r e a s e s f o r e a c h u n i t i n c r e a s e i n t h e c o n c e n t r a t i o n , C 2 :

∂

∂ C 2

T 2 =

# 1 44X

C 2

This will have units of degrees C per unit of CO_{2}. Plimer’s plot in figure 50 (page 375) which

lacks any supporting citation, seems to reflect this (remembering that the won’t apply at low concentrations) with:

∂T ∂C

∝ 1/C relation

•

taking the CO

_{2 }unit as 20 ppm jumps as implied by the bars (i.e. the plot is of temperature

increase for each extra 20 ppm CO_{2});

•

assuming that X = 0 5

^{◦}C;

•

incorrectly omitting the factor of 1.44 (i.e. log

_{2 }e) that comes from going from base-2 to

base-e logarithms.

ccuracy Precision and Standards

ll scientific measurements are subject to error. Even when an instrument repeatedly measures the same object or sample, the results will not all be the same. For example Bischof [reference

42