Geoscience Reference
In-Depth Information
within the boundary layer, adjustments through SH do become important (e.g., Ming et al.
2010
). For simplicity, we here assume that the balance between atmospheric radiative
cooling and latent heating dominates. However, this simple balance between DP and
DQ
atm
ð
DT
Þ
is complicated by a direct influence on atmospheric radiative cooling by the
radiative forcings responsible for determining temperature response in the first place
(Andrews et al.
2010
; O'Gorman et al.
2012
).
Global mean precipitation response, DP, is determined by a ''slow'' component set by
the global mean surface temperature change, DT, (denoted slow since it takes a long time
to heat up the oceans due to their dominating heat capacity) and a ''fast'' component (f DF)
in which the atmosphere (with its small heat capacity relative to the ocean) rapidly adjusts
to changes in top of atmosphere radiative forcing, DF (for simplicity, here defined as the
downward radiative heating into the top of the atmosphere), that is independent of DT
(Allen and Ingram
2002
; Bala et al.
2010
; Andrews et al.
2010
; O'Gorman et al.
2012
):
LDP
kDT
f DF
: ð
2
Þ
In (
2
), L = 2.5 9 10
6
Jkg
-1
is the latent heat of vaporization and k * 2Wm
-2
K
-1
is
the response of atmospheric radiative cooling to surface temperature, qQ
atm
/qT (e.g., Allan
2006
; Lambert and Webb
2008
; Andrews et al.
2010
), set by the atmospheric temperature
and humidity lapse rates (e.g., moist adiabatic lapse rate with near-constant mean relative
humidity is a reasonable approximation).
The fast scaling parameter, f
¼
DF
atm
=
DF, is the instantaneous radiative forcing expe-
rienced by the atmosphere, DF
atm
¼
DQ
atm
ð
DF
Þ
, normalized by the top of atmosphere
radiative forcing (DF) and is specific to the nature of each radiative forcing component
(Andrews et al.
2010
; Ming et al.
2010
). For example, increases in atmospheric CO
2
con-
centrations produce an instantaneous increase in radiative forcing at the top of the atmo-
sphere that is considerably larger than the increase in instantaneous (downward) radiative
forcing at the surface, DF
sfc
(e.g., Ramanathan
1981
; Allan
2006
), where
DF
¼
DF
atm
þ
DF
sfc
. This causes a direct reduction in DP through the last term in (
2
), since
f
CO
2
*0.8 (Andrews et al.
2010
) and a slower increase in DP through the resulting rises in DT
brought about by the positive radiative forcing. The timescale for kDT is increased for smaller
ocean heat uptake and a more positive overall climate feedback (see also McInerney and
Moyer
2012
). The interaction between these two effects is fundamental in determining
the transient response of DP to DF, or hydrological sensitivity (Ming et al.
2010
).
2.1 Simple Model of Global Precipitation
To illustrate the global constraint upon DP, a simple zero-dimensional energy budget
model is employed, based upon the approach of Hansen et al. (
1981
). A mixed-layer ocean
temperature perturbation DT
m
is computed as
dDT
m
dt
¼
1
C
m
ð
DF
YDT
m
D
Þ;
ð
3
Þ
C
m
= 4.218 9 10
8
JK
-1
m
-2
where
is
the
ocean
mixed-layer
heat
capacity,
Y = 1.3 W m
-2
K
-1
is the climate feedback parameter, and
D
¼
c
ð
DT
m
DT
D
Þ=
d
; ð
4
Þ
is the diffusion of energy into the deep ocean (d = 500 m, c = 421.8 W K
-1
m
-1
) where
deep ocean temperature, DT
D
is determined by dDT
D
=
dt
¼
D
=
C
D
, where C
D
= 3.7962 9
