Section 4.4: The Greenhouse Detection Problem
69
Results are taken from experiments with two different types of forcing:
step-function and time-dependent. In the former (OSU, GFDL, UKMO and
LLNL), the steady-state response to a step function doubling of CO2 is considered. In the latter (the GISS Transient A experiment; see Hansen et al.,
1988), greenhouse forcing commences in 1958 and increases with time in a
manner similar to the IPCC "Business as Usual" scenario (Houghton et al.,
1990). Control run data and information from years 81-90 of the GISS perturbed run are used.
4.4.2 Spatial Correlation Methods
Let us consider two observed data sets D1 and D2 (D = Data) , and two model
data sets Mi and M2 (M = Model). Each are two-dimensional (x, t) arrays
where x and t are independent discrete variables running over space (gridpoints) and time (years), with x = 1 ... m and t = 1 ... n respectively. Here,
Dl and D2 represent near-surface temperatures averaged over two different
periods of time. Mi and M2 are corresponding temperatures simulated in a
control run and a greenhouse-gas experiment, respectively. If Mi and M2 are
derived from equilibrium experiments, we are concerned with a signal pattern which has no time dependence viz. the equilibrium surface temperature
change between a 2 x C02 experiment and a 1 x C02 control run
(4.1)
Our detection strategy, which follows that used by Barnett (1986) and Barnett and Schlesinger (1987), is to compare the signal pattern, M(x), with a
series of time-evolving observed patterns of change
(4.2)
where the index t runs over the total number of observed mean change fields.
Here, D1(x) is the time-average over some fixed reference period, defined as
1 to+p-l
D1(x) = - L: D(x, u)
P u=to
(4.3)
where p < n and to is the initial year of the reference period. Similarly,
D2(x, t) is defined by
1 to+p-l
D2(X, t) = - L D(x, u)
p u::t
(4.4)
where t > to + p. Here we take p = 10 (years). The use of decadal averages
and overlapping observed decades yields a smoother estimate of the observed
changes. In later examples we assume that to = 0, corresponding to the year
1900, and therefore compare a single model-derived signal pattern with 71
69
Results are taken from experiments with two different types of forcing:
step-function and time-dependent. In the former (OSU, GFDL, UKMO and
LLNL), the steady-state response to a step function doubling of CO2 is considered. In the latter (the GISS Transient A experiment; see Hansen et al.,
1988), greenhouse forcing commences in 1958 and increases with time in a
manner similar to the IPCC "Business as Usual" scenario (Houghton et al.,
1990). Control run data and information from years 81-90 of the GISS perturbed run are used.
4.4.2 Spatial Correlation Methods
Let us consider two observed data sets D1 and D2 (D = Data) , and two model
data sets Mi and M2 (M = Model). Each are two-dimensional (x, t) arrays
where x and t are independent discrete variables running over space (gridpoints) and time (years), with x = 1 ... m and t = 1 ... n respectively. Here,
Dl and D2 represent near-surface temperatures averaged over two different
periods of time. Mi and M2 are corresponding temperatures simulated in a
control run and a greenhouse-gas experiment, respectively. If Mi and M2 are
derived from equilibrium experiments, we are concerned with a signal pattern which has no time dependence viz. the equilibrium surface temperature
change between a 2 x C02 experiment and a 1 x C02 control run
(4.1)
Our detection strategy, which follows that used by Barnett (1986) and Barnett and Schlesinger (1987), is to compare the signal pattern, M(x), with a
series of time-evolving observed patterns of change
(4.2)
where the index t runs over the total number of observed mean change fields.
Here, D1(x) is the time-average over some fixed reference period, defined as
1 to+p-l
D1(x) = - L: D(x, u)
P u=to
(4.3)
where p < n and to is the initial year of the reference period. Similarly,
D2(x, t) is defined by
1 to+p-l
D2(X, t) = - L D(x, u)
p u::t
(4.4)
where t > to + p. Here we take p = 10 (years). The use of decadal averages
and overlapping observed decades yields a smoother estimate of the observed
changes. In later examples we assume that to = 0, corresponding to the year
1900, and therefore compare a single model-derived signal pattern with 71