Low-‐frequency SST and Upper-‐Ocean Heat Content Variability in
the North Atlan?c Martha W. Buckley
George Mason University (GMU/COLA)
Collaborators: Rui M. Ponte
Atmospheric and Environmental Research (AER)
Patrick Heimbach and Gael Forget MassachuseRs Ins?tute of Technology (MIT)
Observed Atlan?c SST anomalies
• Observa(ons indicate Atlan(c SSTs exhibit significant low-‐frequency variability (Bjerknes 1964; Kushnir 1994; Ting et al. 2009).
• The origin of Atlan(c SST anomalies depends on (mescale – Intraannual to interannual: response to local atmospheric forcing (Frankignoul and Hasselmann, 1977), • e.g. the North Atlan?c Oscilla?on (NAO) tripole (Cayan, 1992).
– Longer ?mescales (how long?) ocean circula?on may play a role. • e.g. basin-‐scale SST anomalies in the North Atlan?c, termed Atlan?c Mul?decadal Variability (Kerr, 2000; Knight et al., 2005).
• thought to be related to varia?ons in the Atlan?c Meridional Overturning Circula?on (AMOC; e.g. Kushnir, 1994; Delworth and Mann, 2000) and/or gyre circula?ons (Hakkinen and Rhines, 2004; Hakkinen et al, 2011).
• Rela?ve importance of atmospheric forcing and ocean dynamics in SST variability has implica?ons for predictability. – Dominance of local atmospheric forcing -‐> liRle predictability. – Dominance of slow ocean processes -‐> high poten?al for predictability.
Approach
Method: Es(ma(ng the Circula(on and Climate of the Ocean (ECCO) version 4 state es(mate (1992-‐2010) • MITgcm least squares fit to observa?ons using adjoint (Forget et al., 2015 a,b) • fit achieved by adjus?ng ini?al condi?ons, forcing, and model parameters • sa(sfies equa(ons of mo(on & preserves property budgets (Wunsch & Heimbach,
2013)
• Atmospheric forcing: ERA-‐Interim • Ocean data:
• In-‐situ: Argo, CTDs, XBTs, mooring arrays • AVHRR & AMSR-‐E SST and satellite al?metry
• Model details (Forget et al., 2015b) • New global grid (LLC90), includes Arc?c, 50 ver?cal levels, par?al cells • Nominal 1o resolu?on with telescopic resolu?on to 1/3o near Equator • State of the art dynamic/thermodynamics sea ice model
What are rela?ve roles of local atmospheric forcing and ocean dynamics in upper-‐ocean heat content (UOHC) variability in the North Atlan?c?
Low-‐frequency Atlan?c SST variability Analysis of monthly data, seasonal cycle removed by simply subtrac?ng out the mean monthly climatology.
• Atlan?c SST variability in ECCO similar to Reynolds (2002) gridded SST.
• PaRern resembles classic “NAO tripole”
• Spectra are red at high frequencies: slope=-‐1.6
• Spectra flaRen out at ?mescales of 2—5 years
25% 14%
24% 15%
Slope=-‐1.6
Buckley et al, 2014, J. Climate
Upper ocean heat content variability Heat Content integrated over maximum climatological mixed layer depth, D: • Measure of heat contained in “ac?ve” ocean layers. • Relevant for explaining SST anomalies. • Avoids strong contribu?ons from ver?cal diffusion and eliminates entrainment (Deser et al, 2003; Coetlogon and Frankignoul, 2003).
Brief Article
The Author
June 19, 2013
H = ⇢oCp
Z ⌘
�D
T dz
⇢oCp
Z ⌘
�D
@T
@tdz = �⇢oCp
Z ⌘
�D
r · (uT + u⇤T ) dz
| {z }Cadv
� ⇢oCp
Z ⌘
�D
r ·K dz
| {z }Cdiff
+Qnet
ug =
1
f⇢oz⇥rp,
uek =
⌧ ⇥ z
⇢ofDek
Dek = min(D, 100 m)
w(�D) ⇡Z ⌘
�D
rH · u dz ⇡Z ⌘
�Dek
rH · uek dz
| {z }⌘wek(�D)
+
Z ⌘
�D
rH · ug dz
| {z }⌘wg(�D)
1
Buckley et al., 2014, J. Climate
10 m
100 m
1000 m
10 m
100 m
1000 m
Mixed layer depths in ECCO v4 compare favorable to those in Argo.
Forget et al., 2015, Ocean Sci. Discuss.
ECCO v4
Argo
Upper ocean heat content variability Heat Content integrated over maximum climatological mixed layer depth, D: • EOFs of H resemble those of SST, but
more variability where deep MLD • PC ?me series
• have more low frequency variability
• Have less high frequency variability
• Spectra of PC ?me series are steeper
• Associated with significant SST variability that resembles first EOFs of SST.
Brief Article
The Author
June 19, 2013
H = ⇢oCp
Z ⌘
�D
T dz
⇢oCp
Z ⌘
�D
@T
@tdz = �⇢oCp
Z ⌘
�D
r · (uT + u⇤T ) dz
| {z }Cadv
� ⇢oCp
Z ⌘
�D
r ·K dz
| {z }Cdiff
+Qnet
ug =
1
f⇢oz⇥rp,
uek =
⌧ ⇥ z
⇢ofDek
Dek = min(D, 100 m)
w(�D) ⇡Z ⌘
�D
rH · u dz ⇡Z ⌘
�Dek
rH · uek dz
| {z }⌘wek(�D)
+
Z ⌘
�D
rH · ug dz
| {z }⌘wg(�D)
1
Slope PC1: -‐2.6 PC2: -‐2.2
Buckley et al., 2014, J. Climate
50% 11%
Upper ocean heat content budget
• Advec?on is important in crea?ng Ht variability along the Gulf Stream Path and in regions in the subpolar gyre
• Diffusive transports only important in boundary regions of subpolar gyre
Brief Article
The Author
April 3, 2013
[H] = ⇢oCp
Z ⌘
�D
T dz
⇢oCp
Z ⌘
�D
@T
@tdz = �⇢oCp
Z ⌘
�D
r · (uT + u⇤T ) dz
| {z }C
adv
� ⇢oCp
Z ⌘
�D
r ·K dz
| {z }C
diff
+Qnet
ug =
1
f⇢oz⇥rp,
uek =
⌧ ⇥ z
⇢ofDek
Dek = min(D, 100 m)
w(�D) =
Z ⌘
�D
rH · u dz ⇡Z ⌘
�Dek
rH · uek dz
| {z }⌘w
ek
(�D)
+
Z ⌘
�D
rH · ug dz
| {z }⌘w
g
(�D)
1
Origin of advec?ve heat transport convergence
Mann Eddy region centered at 45�N, 40�W) and along the boundaries in the subpolar gyre.258
Cadv and Qnet are correlated over broad regions of the subtropical and subpolar gyres and259
anti-correlated over the tropics (see Figure 7a), patterns which likely reflect the role of the260
winds in creating both air-sea heat flux and Ekman transport anomalies. Cadv and Cdiff are261
anti-correlated over the regions where Cdiff plays a sizable role in the H budget (see Figure262
7b).263
b. Separation of advective convergence into Ekman and geostrophic parts264
A primary goal of this study is to determine the dynamical mechanisms that are respon-265
sible for Cadv, specifically whether advective heat transports are due to the local response to266
surface windstress variability (Ekman transports) or ocean dynamics (likely primarily heat267
transport by geostrophic currents). We first note that monthly-averaged Cadv can be written268
as269
Cadv = �⇢oCp
Z ⌘
�D
r·(uT+u⇤T ) dz = �⇢oCp
Z ⌘
�D
r · (uT ) dz| {z }
linear: Clin
�⇢oCp
Z ⌘
�D
r · (u0T 0 + u⇤T ) dz
| {z }bolus: C
bol
,
(2)
where overbars denote monthly mean variables and primes denote deviations from monthly270
means. The variance of Clin and Cbol are plotted in Figure 8a and 8b. The variance of Clin is271
qualitatively quite similar to that of Cadv (see Figure 6b). The correlation coe�cient between272
monthly anomalies of Cadv and Clin (see Figure 9a) is greater than 0.8 almost everywhere.273
Figure 9c shows the fraction of the variance4 of Cadv that is captured by Clin. With the274
exception of shallow regions (particularly in the subpolar gyre) and the region of the Mann275
4The fraction of the variance of a quantity X explained by an estimate Y is given by f = 1� �2(X�Y )
�2X
.
13
Cadv is well reproduced by Clin in many regions
What por?on Cadvis explained by Clin?
F = 1� var(Cadv � Clin)
var(Cadv)
Cek = ⇢oCp
Z ⌘
�Dek
r · (uekT ) dz + ⇢oCp wek(�D) T (�D)
Cg = ⇢oCp
Z ⌘
�D
r · (ugT ) dz + ⇢oCp wg(�D) T (�D)
C local = Cadv +Qnet
Hg = ⇢oCp
Z ⌘
�D
r · (ugT ) dz + ⇢oCp wg(�D) T (�D)
H = ⇢oCp
Z xe
xw
Z z
�H
vT dz dx
Hg = ⇢oCp
Z xe
xw
Z z
�H
vgT dz dx
Hek = ⇢oCp
Z xe
xw
Z z
�H
vekT dz dx
corr(T, Tek + Tg + Tair�sea) = 0.98
corr(T, Tair�sea) = 0.90
corr(T, Tek + Tair�sea) = 0.96
2
Overbars denote monthly means, primes are devia?ons from monthly means
Ekman + geostrophic convergences Separate (linear) advec?ve heat transport into Ekman and geostrophic parts. Henceforth drop overbars to indicate monthly means • uek, ug are horizontal Ekman and geostrophic veloci?es • wek, wg calculated from uek, ug using the con?nuity equa?on
b. Separation into Ekman and geostrophic convergences132
BPFH demonstrate that Clin
can be decomposed into Ekman and geostrophic parts, a133
decomposition which is successful away from shallow boundary regions (see Figures 9b and134
9d in BPFH). The Ekman and geostrophic components of Clin
are approximated as:135
Cek
(uek, wek
, T ) = �⇢o
Cp
R⌘
�Dekr · (uekT ) dz + ⇢
o
Cp
wek
(�D) T (�D),
Cg
(ug, wg
, T ) = �⇢o
Cp
R⌘
�D
r · (ugT ) dz + ⇢o
Cp
wg
(�D) T (�D),
(3)
where uek and ug are given by Equations 4 and 5 in BPFH, respectively, and wek
(�D) and136
wg
(�D) are given by Equation 6 in BPFH. Dek
is the depth of the Ekman layer, taken to137
be the shallower of D and a depth of 100 m (a choice motivated by the assumption that138
Dek
= 100 m in the RAPID AMOC estimates at 26�N). Variance maps of Cek
and Cg
(see139
Figures 1e–f) exhibit their largest values in regions of strong currents/fronts. Unlike Cg
, Cek
140
also exhibits significant variability over the interior of the gyres.141
Figure 2b shows the fraction of the variance of Ht
explained by Cek
+ Cg
+ Qnet
. The142
similarity of this quantity to the fraction of the variance of Ht
explained by Clin
(see Fig-143
ure 2a) indicates that approximating the linear convergence as the sum of the Ekman and144
geostrophic parts does not lead to any substantial additional error in the budget for Ht
. The145
areas where the fraction of the variance of Ht
explained by Cek
+ Cg
+ Qnet
is ⇠ 1 are the146
regions where (1) di↵usion and bolus transports and negligible and (2) the decomposition147
of Clin
into Ekman and geostrophic parts is successful. These are the key regions of interest148
for this study.149
We now further decompose Cek
and Cg
into convergences due to variability in the tem-150
7
èCek+Cg≈Clin
ug =
1
f⇢o
z⇥rp,
uek =
⌧⇥z⇢o
fDek
, Dek = min(D, 100 m)
w(�D) ⇡R ⌘
�DrH · u dz
⇡Z ⌘
�Dek
rH · uek dz
| {z }⌘w
ek
(�D)
+
Z ⌘
�D
rH · ug dz
| {z }⌘w
g
(�D)
F = 1� var(Cadv � Clin)
var(Cadv)
F = 1� var(Clin � Cek � Cg)
var(Clin)
F (A,B) = 1� var(A� B)
var(A)
Cek = ⇢oCp
Z ⌘
�Dek
r · (uekT ) dz + ⇢oCp wek(�D) T (�D)
Cg = ⇢oCp
Z ⌘
�D
r · (ugT ) dz + ⇢oCp wg(�D) T (�D)
C local = Cadv +Qnet
Tek ⌘R t
0
Cek
⇢o
Cp
Vdt
Tg ⌘R t
0
Cg
⇢o
Cp
Vdt
Tloc ⌘ Tair�sea + Tek
Tbol ⌘R t
0
Cbol
⇢o
Cp
Vdt
3
Contribu?ons of Ekman and geostrophic parts
• Both Cek and Cg largest in regions of strong currents/fronts In these regions Cg>Cek
• Cek>Cg over por?ons of the ocean’s interior, including the region south of the Gulf Stream and the eastern basin.
Ekman heat transport convergences
perature field and the velocity field:151
Cek
(uek, wek
, T ) = Cek
(uek, wek
, T ) + Cek
(uek0, w0
ek
, T )| {z }C
vek
+Cek
(uek, wek
, T 0)| {z }C
Tek
+Cek
(u0ek, w
0ek
, T 0)| {z }C
vTek
Cg
(ug, wg
, T ) = Cg
(ug, wg
, T ) + v Cg
(u0g, w
0g
, T )| {z }
C
vg
+Cg
(ug, wg
, T 0)| {z }C
Tg
+Cg
(u0g, w
0g
, T 0)| {z }
C
vTg
(4)
Figures 3d–f show variances of monthly anomalies of Cv
ek
, CT
ek
, and CvT
ek
normalized by152
the variance of Cek
. In most regions the variance of Cek
is almost solely due to Cv
ek
, which153
confirms that variability in Cek
is indeed primarily driven by local wind variability rather154
than changes in the temperature field, as hypothesized in BPFH. Exceptions include the155
tropics where CT
ek
plays a significant role and the Eighteen Degree Water formation region,156
the Mann Eddy region, and shallow boundary regions in the subpolar gyre where CvT
ek
plays157
a minor role. Cv
ek
and CT
ek
are essentially uncorrelated except a small region in the tropics158
(see Figure 4d).159
Figures 3g–i show variances of monthly anomalies of Cv
g
, CT
g
, and CvT
g
normalized by160
the variance of Cg
. Both Cv
g
and CT
g
play a dominant role in setting the variance of Cg
161
and are strongly anticorrelated (see Figure 4c). The fact that variability in Cv
g
and CT
g
are162
related is not surprising since geostrophic velocity anomalies are in thermal wind balance163
with temperature anomalies. The anticorrelation between Cv
g
and CT
g
can be explained by164
considering the the propagation of Rossby waves living in the presence of a eastward mean165
zonal flow u (see schematic in Figure 6). A wave ridge is associated with high sea surface166
height, a depressed thermocline, and a warmH anomaly. The anticyclonic circulation around167
the high brings cold water from the north to the east of the ridge (Cv
g
< 0) and warm water168
from the south to the west of the ridge (Cv
g
> 0), leading to the westward propagation of169
8
Separate Ekman heat transport convergences into parts due to variability in the velocity field, temperature field, and their covariability.
• Overbars are averages over ENTIRE 19-‐year ECCO es?mate • Primes are devia?ons from these averages
Changes in Ekman mass transports due to local wind variability—reflects local atmospheric forcing
Changes in temperature field
Co-‐variability of Ekman transports and temperature
Buckley et al, 2015, J. Climate
Variance of Ht explained by various terms
• Over much of the subtropical and subpolar gyres, Qnet+Cek+ Cg explains most of the variance of Ht.
• Cekv+Qnet explains more of the variance than Qnet alone, par?cularly in gyre interiors. • Cg plays a role along the Gulf Stream path.
0.8 0.8
0.5 0.7
Role of local atmospheric forcing
Cloc* explains >70% of the variance of Ht in the interior of the subtropical and subpolar gyres.
• Response of the atmosphere to mid-‐la?tude SST anomalies is modest compared to internal atmospheric variability (Kushnir et al., 2002; Schneider and Fan, 2012)
• Hypothesis: Cekv+Qnet= Cloc* is a measure of impact of local atmospheric forcing on H
Analysis of budgets in various regions and ?mescales will aid in confirming/rejec?ng this hypothesis (see Buckley et a., 2014, 2015).
0.7
Conclusions • We u?lize a dynamically consistent ocean state es?mate (ECCO) to
quan?fy the upper-‐ocean heat budget in the North Atlan?c on monthly to interannual ?mescales.
• We introduce 3 novel techniques:
• Heat content is integrated over the maximum climatological mixed layer depth (integral denoted as H).
• Advec?ve heat transports are separated into Ekman and geostrophic parts, a technique which is successful away from boundary regions
• Air-‐sea heat fluxes and Ekman heat transport convergences due to velocity variability are combined into one “local forcing” term.
• We find:
• Over broad swaths of the North Atlan?c, including the interiors of the subtropical and subpolar gyres, >70% of the variance of Ht can be explained by local air-‐sea heat flux + Ekman transport variability.
• Geostrophic convergences play a role along Gulf Stream Path.
Conclusions (cont.) North Atlan?c separated into regions based on underlying dynamics and budgets of H analyzed in detail (see Buckley et al., 2014, 2015) • Subtropical gyre
• local forcing dominates on all ?mescales resolved by the 19-‐year ECCO state es?mate.
• Gulf Stream • local forcing dominates for periods less than 6 months; geostrophic convergences increasingly important on longer ?mescales. • Geostrophic transports are an?correlated with air-‐sea heat fluxes, sugges?ng H variability is forced by geostrophic convergences and damped by air-‐sea fluxes.
• Subpolar gyre: • local forcing dominates for periods less than 1 year • geostrophic transports, bolus transports, and diffusion play a role on longer ?mescales.
The (mescale at which ocean dynamics becomes important in seLng H depends strongly on region.
Future work • Can origin of upper-‐ocean heat content (UOHC) anomalies aid in understanding regional varia?ons (and model spread) in predictability of UOHC? • Dominance of atmospheric forcing -‐> low predictability? • Role of geostrophic ocean dynamics -‐> high predictability? • Applying these ideas to understand predictability in CMIP5 models.
• Determine origin of geostrophic convergence anomalies over the Gulf Stream path • Shiv of Gulf Stream path due to remote wind forcing? • Change in strength of deep western boundary current?
• H variability is associated with AMOC variability. Is AMOC variability passive thermal wind response to H variability or does AMOC play role in H budget in some regions (e.g. Gulf Stream)?
• Analysis has determined regions where more complex dynamics are important in H budget. • e.g. diffusion and bolus transports are important in Mann Eddy region. • Region may be important in decadal AMOC variability (Buckley and Marshall, subm.)
Acknowledgements Thanks to the CVP program for organizing this webinar series. Funding for this work was provided by the NOAA Climate Variability and Predictability Program (CPV) Grants: • NA100AR4310199 (AER, PI R. M. Ponte) • NA130AR4310134 (AER, PI M. W. Buckley) • NA10OAR4310135 (MIT, PI P. Heimbach)
References related to this work 1. Buckley, M. W., R. M. Ponte, G. Forget, and P. Heimbach (2014). Low-‐frequency SST and upper-‐ocean heat content variability in the North Atlan?c. J. Climate, 27, 4996—5018.
2. Buckley, M. W., R. M. Ponte, G. Forget, and P. Heimbach (2015). Determining the origins of advec?ve heat transport variability in the North Atlan?c, J. Climate, 28, 3943—3956.
3. Buckley, M. W. and J. Marshall, Observa?ons, Inferences, and Mechanisms of Atlan?c MOC Variability: a Review. SubmiRed to Reviews of Geophysics.
4. Forget, G. and R. M. Ponte (2015). The par??on of regional sea level variability, Progress in Oceanography, 137, 173—195.
5. Forget, G., J.-‐M. Campin, P. Heimbach, C. N. Hill R. M. Ponte and C. Wunsch (2015). ECCO version 4: an integrated framework for non-‐linear inverse modeling and global ocean state es?ma?on. Geosci. Model Dev. Discuss., 8, 3653—3743.
6. Forget, G., D. Ferreira and X. Liang (2015). On the observability of turbulent transport rates by Argo: suppor?ng evidence from an inversion experiment. Ocean Sci. Discuss., 12, 1107—1143.
7. Heimbach, P. and C. Wunsch (2013). Dynamically and kinema?cally consistent global ocean circula?on and ice state es?mates. Ocean circula=on and climate: observing and modelling the global ocean.
Extra slides
Mean temperature: comparison to in-‐situ data
Non-‐op?mized simula?on Op?mized solu?on: ECCO v4 (r3/iter3)
Misfits to in-‐situ observa(ons: Te-‐To
Forget et al., 2015b GMD
Regional Analysis Divide into regions based on dynamics: • Gyre interiors: frac?on of variance of Ht
explained by Cloc*>0.7 • Subtropical and subpolar gyres divided
by zero in mean barotropic streamfunc?on.
• Gulf Stream path: mean speed > 7 cm s-‐1 and frac?on variance of Ht explained by Cloc*<0.7
SST and upper-‐ocean temperature T=H/(ρoCpV)
SST T
Regional budgets
Present budgets in two ways: • Fluxes contribu?ng to Ht • Temporally integrated budgets (contribu?ng to T), V=volume of region
•
• Similarly dividing Clin, Cbol, Cek, Cg, Cloc by ρoCpV and integra?ng in ?me yields Tlin, Tbol,Tek, Tg, and Tloc.
Brief Article
The Author
January 26, 2014
Z t
0
Ht
⇢oCpVdt
| {z }⌘(T�T
o
)
=
Z t
0
Cadv
⇢oCpVdt
| {z }⌘T
adv
+
Z t
0
Cdiff
⇢oCpVdt
| {z }⌘T
diff
+
Z t
0
Qnet
⇢oCpVdt
| {z }⌘T
Q
. (1)
[H] = ⇢oCp
Z ⌘
�D
T dz
⇢oCp
Z ⌘
�D
@T
@tdz = �⇢oCp
Z ⌘
�D
r · (uT ) dz| {z }
Cadv
� ⇢oCp
Z ⌘
�D
r ·K dz
| {z }C
diff
+Qnet
ug =
1
f⇢oz⇥rp,
uek =
⌧ ⇥ z
⇢ofDek
Dek = min(D, 100 m)
1
Subtropical gyre interior FLUXES • Dominant terms: Qnet, Cekv, • Cloc* dominates on intrannual ?mescales
• CekT+CekvT role for τ>2 yrs. • Cg, Cdiff, Cbol negligible => Cloc=Cek+Qnet
• Cloc dominates on all ?mescales
TIME INTEGRATED • Tloc explains 92% of the
variance of T • T anomalies are locally
forced on all ?mescales resolved by ECCO
10 5 2 1
0.1 1 1010−2
100
102
(W m
−2)2 c
py−1
cpy
yrs
Ht
Qnet
Cekv C
ekT +C
ekvT C
gC
diff+C
bol
10 5 2 1
0.1 1 100.4
0.6
0.8
1
cpy
yrs
Qnet
Cloc* C
locC
loc+C
g
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010−0.5
0
0.5
Time
° C
T−To
TQ
Tekv T
ekT +T
ekvT T
gT
diff+T
bolT
loc
Power spectra Coherence
Gulf Stream Region
FLUXES • Cloc dominates for τ< 6 mo. • Cg plays an increasing role on longer ?mescales
• CekT+CekvT negligible • Cloc* and Cloc are indis?nguishable
TIME INTEGRATED • Tg important in T-‐To budget • Tg and TQ highly
an?correlated (-‐0.90) • TQ likely reflects damping
of T anomalies created by ocean dynamics
Power spectra Coherence 10 5 2 1
0.1 1 10100
102
(W m
−2)2 c
py−1
cpy
yrs
Ht
Qnet
Cekv C
ekT +C
ekvT C
gC
diff+C
bol
10 5 2 1
0.1 1 100.4
0.6
0.8
1
cpy
yrs
Qnet
Cloc* C
locC
loc+C
g
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010−2
−1
0
1
2
Time
° C
T−To
TQ
Tekv T
ekT +T
ekvT T
gT
diff+T
bolT
loc
Subpolar gyre interior
FLUXES • Cloc dominates for τ< 1 yr. • Cg , Cdiff, Cbol play a role for τ> 1 year
TIME INTEGRATED • Tdiff +Tbol has significant low frequency variability
• Tdiff +Tbol and TQ are an?correlated (-‐0.77)
• TQ likely reflects damping of T anomalies created by ocean dynamics
Power spectra Coherence
10 5 2 1
0.1 1 10
100
102
(W m
−2)2 c
py−1cpy
yrs
Ht
Qnet
Cekv C
ekT +C
ekvT C
gC
diff+C
bol
10 5 2 1
0.1 1 100.4
0.6
0.8
1
cpy
yrs
Qnet
Cloc* C
locC
loc+C
g
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010
−1
−0.5
0
0.5
1
Time
° C
T−To
TQ
Tekv T
ekT +T
ekvT T
gT
diff+T
bolT
loc