guess pattern p 0 is given by Σ’1 p . near-surface temperature observed at time t in

the (i, j)th 5—¦ — 5—¦ box, and let …k (i, j), for

Furthermore, if Tt represents the detection

k = 1, . . . , 10 represent the 10 EOFs. Also,

variable at time t (i.e., observed near-

let A(i, j) be the area of the (i, j)th box. Then

surface temperature projected onto the four-

tt is found by minimizing

dimensional subspace), then the optimized

detection variable is given by 2

ˆ

to (i, j, t) ’ to (i, j, t) A(i, j),

±0 (Tt ) = p 0 , Tt . (7.1)

where

Hegerl et al. [172] performed the analysis 10

ˆ

to (i, j, t) = t(k, t)…k (i, j),

with both the raw guess pattern and the

optimized guess pattern.20 We limit our k=1

18 The ¬rst 10 EOFs of the transient simulation were used and where the double sum is taken over those

grid boxes that contain data.21 Simulation

because they capture the guess pattern much more effectively

than the EOFs of the control simulation.

19 We treat Σ as known since it was estimated from a very 21 For a more detailed representation of the problem of

long simulation. determining EOF coef¬cients in case of gappy data, refer to

20 Also sometimes called a ˜¬ngerprint.™ [13.2.8].

7.4: Detecting the ˜CO2 Signal™ 139

experiments have shown that changes in data 1.6

Detection Variable

density may cause inhomogeneities in ±0 (t). 1.4

20 YEAR TRENDS

1.2

1.0

To limit this effect, Hegerl et al. used only 0.8

those grid boxes for which the record from 0.6

obs

0.4

GFDL

1949 onwards was complete. Therefore the 0.2

0

entire southern and northern polar regions and -0.2

-0.4

the Southern Ocean are disregarded. -0.6

-0.8

-1.0

Figure 7.8 shows the optimized guess pattern 1900 1940 1980 2020 2060 2100

1860

Time [year]

truncated to the area that has complete data

observed EIN simulation

coverage for 1949 onwards.

3 The natural variability of the optimized Figure 7.9: Time evolution of 20-year trends of the

optimized detection variable ±o (t) = p o , t for

detection variable cannot be estimated from

the observations. The observed record is near-surface temperature. Labels on the abscissa

contaminated by the presumed signal and the identify the last year (1879 until 1994) of each

data are correlated in time so that only a 20-year period.

few independent realizations of the ˜naturally The solid line is derived from observed data

varying™ state variable are available. since 1860. The dotted line, labelled ˜EIN™, is

derived from 150 years of climate model output.

There are, in principle, two ways to deal with

The climate model was forced with anomalous

this problem. The ¬rst approach is to remove

radiative forcing corresponding to the observed

the expected climate signal from the observed

1935“85 greenhouse gas concentrations during

record by constructing a linear model of the

the ¬rst 50 years of the simulation. A scenario

form

(IPCC scenario A) was to prescribe greenhouse

T— = Tt ’ TCO2 gas concentrations from ˜1985™ onwards. Twenty-

(7.2)

t

t

year trends from the simulation (dashed curve) are

∞ C(t ’ )

TCO2 = S( ) ln d. shown to compare the observed evolution with that

t

C(0)

0 anticipated by a climate model.

The narrow shaded band, labelled ˜GFDL™, is an

Here Tt is the observed temperature record,

estimate of the natural variability of the 20-year

TCO2 is an estimate of the CO2 induced trend derived from a 1000-year control simulation

t

temperature signal, and T— is the residual. (Manabe and Stouffer [266]). It should contain

t

The variability of T— is assumed to be the the trend coef¬cient 95% of the time if there

t

same as that of the undisturbed climate is no trend. The wider band, labelled ˜obs™, is

system. The function C(t) is the atmospheric derived from observations after an estimate of the

CO2 -concentration at time t, and S(·) is greenhouse gas (GHG) is removed. From Hegerl et

a transfer function. The variability of the al. [172].

detection variable is then derived from T—

instead of T.22

is not stationary since the concentration of

One problem with this approach is that it does airborne pollutants increases substantially in

not eliminate the effects of serial correlation; the latter part of the observed record.

even without the signal it is dif¬cult to

To cope with this problem, the null hypothesis

estimate the natural variability of the climate

should be reformulated to state that observed

on decadal and longer time scales from the

variations are consistent with natural variabil-

observed record.

ity originating from natural external proces-

Another problem with this approach, apart ses as well as internal dynamical processes.

from adopting the model (7.2), is that the The anthropogenic aerosol effect probably

remaining variability also includes contri- causes a cooling that counteracts the expected

butions from other external factors such as greenhouse warming; the presence of this ef-

aerosol forcing caused by human pollution fect in the observed data in¬‚ates the estimate

and volcanos. While volcanos may be consid- of the variability and dampens the signal,

ered stationary in time, the effect of pollution diminishing the overall power of the test.

The second approach is to consider the

22 Subsection 17.5.7 also deals with the problem of removing

output of ˜control™ climate model runs

a suspected signal from a time series.

7: Analysis of Atmospheric Circulation Problems

140

without any external forcing so that all then performed with the ¬tted auto-regressive

variability originates from internal dynamical models to estimate the natural variability of

processes. This approach has the advantage 20-year trends in the optimized detection

variable.24 The test is eventually performed

that, at least in principle, very long samples

can be created without inhomogeneities in by comparing recent 20-year trends with the

accuracy or varying spatial coverage. A major estimated 95% con¬dence intervals.

disadvantage, though, is that the models

The result of the exercise is summarized in

may not simulate the natural low-frequency

Figure 7.9, which shows the time evolution of

variability correctly.

20-year trends of the optimal detection variable

Hegerl et al. used both approaches. In together with the 95% con¬dence intervals derived

two steps, 95% con¬dence intervals for from several sources. The latest trends do indeed

the natural variability of 20-year trends exceed the upper con¬dence limit, so we may

in the optimized detection variable were conclude that the prevailing trend is not likely to

constructed from both observed anomalies be due to internal processes. This conclusion, of

(7.2) and climate model output. In both course, depends crucially on the validity of the

cases an auto-regressive process of order natural variability estimates. For further reading on

1 was ¬tted to the optimal detection climate change detection and attribution see Santer

variable.23 Monte Carlo simulations were et al. [340] and Zwiers [445].