58
the efficiency of the transfer of heat from the atmosphere to the ocean. We then use
these two parameters to project global warming.
Here we delve into the mathematics of the EM-GC framework. Those without an
appetite for the equations are encouraged to fast forward to Sect. 2.3. There will not
be a quiz at the end of this chapter.
Our simulation of observed temperature involves finding values of a series of
coefficients such that the model Cost Function:
Cost Function
i
N
i
i
i
MONTHS
=
-
å =
-
1
2
2
1
s
D
D
OBS
OBS
E M GC
T
T
(
)
(2.1)
is minimized. Here, ΔT OBS i and ΔT EM-GC i represent time series of observed and
modeled monthly, global mean surface temperature anomalies, σ OBS i is the 1-sigma
uncertainty associated with each temperature observation, i is an index for month,
and N MONTHS is the total number of months. The use of σ OBS i
2
in the denominator of
Eq. 2.1 forces modeled ΔT EM-GC i to lie closest to data with smaller uncertainty,
which tends to be the latter half of the ΔT OBS i record.
The expression for ΔT EM-GC i is:
D
g
l
D
D
D
T
G HG RF Aerosol RF LUC RF
SOD
EM GC
P
-
-
=
+
+
+
+
+ ´
+
i
i
i
i
i
C
C
1
0
1
6
{(
}
C C
C
C
C
C
Q
i
i
i
i
i
i
2
1
3
3
4
5
6
´
+ ´
+ ´
+ ´
+ ´
-
-
-
TSI
E NSO
AMV
PDO
IOD
OCEAN
P
l
(2.2)
where model input variables (described immediately below) are used to calculate
the model output parameters C i and γ. In Eq. 2.2 GHG ΔRF i , Aerosol ΔRF i , and
LUC ΔRF i represent monthly time series of the ΔRF of climate due to anthropogenic GHGs, tropospheric aerosol, and land use change; λ P = 3.2 W m
−2
°C
−1
is the
response of surface temperature to a RF perturbation in the absence of climate feedback (“P” is used as a subscript because this term is called the Planck response
function by the climate modeling community (Bony et al. 2006)); SOD i−6 , TSI i−1 ,
ENSO i−3 represent indices for stratospheric optical depth, total solar irradiance, and
El Niño Southern Oscillation lagged by 6 months, 1 month, and 3 months, respectively; AMV i , PDO i , and IOD i represent indices for Atlantic Multidecadal Variability
(a proxy for the strength of AMOC), the Pacific Decadal Oscillation, and the Indian
Ocean Dipole; and Q OCEAN i / λ P is the Ocean Heat Export term. The use of temporal
lags for SOD, TSI, and ENSO is common for MLR approaches: Lean and Rind
(2008) use lags of 6 months, 1 month and 4 months, respectively, for these terms.
These lags represent the delay between forcing of the climate system and the
response of RF of climate at the tropopause, after stratospheric adjustment. These
lags are discussed at length in our model description paper (Canty et al. 2013).
Finally, the AMV, PDO, and IOD terms have traditionally not been used in MLR
2 Forecasting Global Warming
the efficiency of the transfer of heat from the atmosphere to the ocean. We then use
these two parameters to project global warming.
Here we delve into the mathematics of the EM-GC framework. Those without an
appetite for the equations are encouraged to fast forward to Sect. 2.3. There will not
be a quiz at the end of this chapter.
Our simulation of observed temperature involves finding values of a series of
coefficients such that the model Cost Function:
Cost Function
i
N
i
i
i
MONTHS
=
-
å =
-
1
2
2
1
s
D
D
OBS
OBS
E M GC
T
T
(
)
(2.1)
is minimized. Here, ΔT OBS i and ΔT EM-GC i represent time series of observed and
modeled monthly, global mean surface temperature anomalies, σ OBS i is the 1-sigma
uncertainty associated with each temperature observation, i is an index for month,
and N MONTHS is the total number of months. The use of σ OBS i
2
in the denominator of
Eq. 2.1 forces modeled ΔT EM-GC i to lie closest to data with smaller uncertainty,
which tends to be the latter half of the ΔT OBS i record.
The expression for ΔT EM-GC i is:
D
g
l
D
D
D
T
G HG RF Aerosol RF LUC RF
SOD
EM GC
P
-
-
=
+
+
+
+
+ ´
+
i
i
i
i
i
C
C
1
0
1
6
{(
}
C C
C
C
C
C
Q
i
i
i
i
i
i
2
1
3
3
4
5
6
´
+ ´
+ ´
+ ´
+ ´
-
-
-
TSI
E NSO
AMV
PDO
IOD
OCEAN
P
l
(2.2)
where model input variables (described immediately below) are used to calculate
the model output parameters C i and γ. In Eq. 2.2 GHG ΔRF i , Aerosol ΔRF i , and
LUC ΔRF i represent monthly time series of the ΔRF of climate due to anthropogenic GHGs, tropospheric aerosol, and land use change; λ P = 3.2 W m
−2
°C
−1
is the
response of surface temperature to a RF perturbation in the absence of climate feedback (“P” is used as a subscript because this term is called the Planck response
function by the climate modeling community (Bony et al. 2006)); SOD i−6 , TSI i−1 ,
ENSO i−3 represent indices for stratospheric optical depth, total solar irradiance, and
El Niño Southern Oscillation lagged by 6 months, 1 month, and 3 months, respectively; AMV i , PDO i , and IOD i represent indices for Atlantic Multidecadal Variability
(a proxy for the strength of AMOC), the Pacific Decadal Oscillation, and the Indian
Ocean Dipole; and Q OCEAN i / λ P is the Ocean Heat Export term. The use of temporal
lags for SOD, TSI, and ENSO is common for MLR approaches: Lean and Rind
(2008) use lags of 6 months, 1 month and 4 months, respectively, for these terms.
These lags represent the delay between forcing of the climate system and the
response of RF of climate at the tropopause, after stratospheric adjustment. These
lags are discussed at length in our model description paper (Canty et al. 2013).
Finally, the AMV, PDO, and IOD terms have traditionally not been used in MLR
2 Forecasting Global Warming