Paris Climate Agreement Beacon of Hope

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:

CostFunction i

N

i

ii

=-MONTHS

å= 1 2 -

(^12)
s

DD

OBS

()TTOBSEMGC

(2.1)

is minimized. Here, ΔTOBS i and ΔTEM-GC i represent time series of observed and
modeled monthly, global mean surface temperature anomalies, σOBS i is the 1-sigma
uncertainty associated with each temperature observation, i is an index for month,
and NMONTHS is the total number of months. The use of σOBS i^2 in the denominator of
Eq. 2.1 forces modeled ΔTEM-GC i to lie closest to data with smaller uncertainty,
which tends to be the latter half of the ΔTOBS i record.
The expression for ΔTEM-GC i is:

D

g

l

TGHGDDRF AerosolRFLUCDRF

SOD

EMGC

P

• 
  
  
  
  • 
    
  
  
  
  

=

+

+++

+ ́ +

iiii

i

C

C

1

0

16

{( }

CCC

CCC

Q

ii

iii

i

2133

456

́+ ́

+ ́ + ́ + ́

-

TSIE--NSO

AMVPDO IOD

OCEAN

lP

(2.2)

where model input variables (described immediately below) are used to calculate
the model output parameters Ci and γ. In Eq. 2.2 GHG ΔRFi, Aerosol ΔRFi, and
LUC ΔRFi represent monthly time series of the ΔRF of climate due to anthropo-
genic GHGs, tropospheric aerosol, and land use change; λP = 3.2 W m−^2 °C−^1 is the
response of surface temperature to a RF perturbation in the absence of climate feed-
back (“P” is used as a subscript because this term is called the Planck response
function by the climate modeling community (Bony et al. 2006 )); SODi− 6 , TSIi− 1 ,
ENSOi− 3 represent indices for stratospheric optical depth, total solar irradiance, and
El Niño Southern Oscillation lagged by 6 months, 1 month, and 3 months, respec-
tively; AMVi, PDOi, and IODi represent indices for Atlantic Multidecadal Variability
(a proxy for the strength of AMOC), the Pacific Decadal Oscillation, and the Indian
Ocean Dipole; and QOCEAN i / λP 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