Partial Results - Climate Change: Identification and Projections - page 88

with climatic observations. The subjective impressions in section 7.3 on the
inadequacy of the constrained model were therefore not an illusion.

Confidence regions

Here we consider the joint confidence regions for the pair of parameters
( S clim , S irr ). Regions at 90% are defined by the inequality
1

S = 4.60

ˆ ˆ

, where corresponds to the probability

T V −

( θθ − ) ( θθ − ) < S

θθ

threshold at 90% of a variable of with two degrees of freedom.

Figure 7.11 shows both the confidence region of 90%, from identification
(unbroken line), and the a priori assumed level (grey rectangle). Strictly
speaking, the latter would need to be refined by an ellipsoid taking into
account the interdependence between the two sensitivities S clim and S irr , since
both are connected to the uncertain parameter S . In any case, even taking
into account the ambiguity which characterizes the IPCC's probabilities, the
identified and assumed level are too far from each other for there to be any
possible intersection.

χ

2

40

Assumed domain
identified (90 %)

30

20

10

0

0 2 4 6

Sclim

Figure 7.11. Assumed and identified regions

The couple ( S clim , S irr ) identified under the constraint

W m −

2

S <° 1. 6 2 C /

2

is shown by the mark o. The deviance associated to this model is:

D = 38.3