Introduction
It has long been reported that the sensitivity of near-surface air
temperatures over land is greater than over ocean, with land surfaces warming
about 50 % more strongly than ocean surfaces
. This
phenomenon has also been found in observations, with the ratio remaining
surprisingly constant through time . Several
explanations have been put forth to explain this robust feature, including
the role of heat transport , a balancing effect of oceanic
heat storage , changes in evapotranspiration
and the climatological relative humidity over land as
well as its change . Also,
showed that this effect depends on the nature of the forcing, so that the ratio
of land warming to ocean warming of about 1.5 holds only for changes in the
greenhouse forcing.
Schematic diagram of the surface energy balance of (a) an ocean
surface and (b) the land surface. The main point to explain the different
temperature sensitivity is related here to the different way by which these
surfaces buffer the diurnal variation in solar radiation (Rs). The ocean
surface buffers it by heat storage changes below the surface in the upper
ocean (shown by the red line labeled dUs/dt), while the land surface buffers it primarily in the
lower atmosphere (shown by dUa/dt). This results in stable conditions over
land during nighttime, which prevent turbulent fluxes (J) and which make
surface temperature more sensitive to changes in the greenhouse effect.
Graphics: Annett Boerner.
Here, we explain this phenomenon of a higher climate sensitivity over land by
the different ways of how the strong diurnal variation in solar radiation is
buffered within the system (see Fig. ). This buffering is
accomplished by heat storage changes within the surface–atmosphere system
that are forced by the heating by absorption of solar radiation during the
day. The build-up of heat storage during the day then allows for nighttime
temperatures that are far warmer than those one would expect in the absence
of solar radiative heating at night. For ocean surfaces, these heat storage
changes take place in the surface ocean. Since water is transparent, solar
radiation penetrates the surface ocean to quite some depth before it is
absorbed. Combined with the large heat capacity of water, this results in
diurnal heat storage changes that take place below the ocean surface
(sketched by the red line on the left of Fig. and marked
by dUs/dt). The build-up of heat storage during the day then maintains
radiative cooling and turbulent heat fluxes during the night, resulting in
little diurnal variations in surface temperature and turbulent fluxes. These
characteristics of the ocean surface energy balance are very well observed
and understood (see, e.g., textbooks by , and
, and review paper by ).
Over land this situation is quite different. Solar radiation is absorbed
at the surface (or above in a canopy), but not below the surface.
This is because land surfaces are not transparent as water, and because the
heat conductivity of soils is generally so low that diurnal variations in
surface heating do not penetrate more than 5–10 cm into the ground, resulting
in a ground heat flux that is generally small. Even in desert regions or for
bare ground with strong surface heating and no evaporative cooling, the
ground heat flux does typically not exceed more than 100 Wm-2, which is
small compared to the maximum absorption of 800 Wm-2 or more of
solar radiation during the day (see, e.g., textbooks by , and
, and syntheses by , and
). We argue here that the strong diurnal variation in
solar radiation is thus not buffered below but rather above the surface in
the lower atmosphere. These changes in heat storage manifest themselves in
the diurnal growth of the convective boundary layer. This buffering above the
surface has an important consequence for the fluxes of the surface energy
balance. Turbulent fluxes only take place when the surface is heated by solar
radiation during the day, which causes the near-surface air to become unstable,
while the nighttime is characterised by stable conditions near the surface as
little heat can be drawn from the heat storage below the surface. This
prevents turbulent fluxes from taking place at night. These consequences for
turbulent fluxes over land surfaces are well observed
e.g.. We suggest that because of this
absence of turbulent fluxes at night the cooling at night is thus determined
only by radiative exchange. Turbulent cooling of the surface takes place
during half of the whole day, while during the other half it is cooled by radiative
exchange. This difference in cooling terms should make nighttime temperatures
more sensitive to changes in the greenhouse effect than daytime temperatures,
a well-known phenomenon reported in observations ,
and this should result in a greater climate sensitivity of land surfaces as
well.
We demonstrate this explanation with an extremely simple yet
physically based energy balance model in which we incorporate the effects of
where heat storage changes take place. The model yields analytic expressions
for the different climate sensitivity of land and ocean surfaces as well as
the different sensitivity of nighttime and daytime temperatures. In the
following, we first describe this model in Sect. . We then illustrate the climatological mean state
in Sect. , derive analytic expressions for the ratios of
these sensitivities, and compare these to CMIP5 climate model simulations.
Some of the limitations of the model are then discussed, particularly
regarding the description of terrestrial radiation and effects of the
hydrologic cycle; our explanation is compared to previous interpretations of
the difference in climate sensitivities; and we describe some of the
implications and potentials for future research. We close with a brief
summary and conclusions.
Model description
Our model consists of the energy balances of the surface and the whole
surface–atmosphere system, a parameterisation of terrestrial radiation that
is based on the grey atmosphere approximation, a formulation of turbulent
fluxes derived from the thermodynamic constraint that these yield maximum
power, and expressions for surface temperature that are derived from this
model formulation. A schematic diagram of the model is provided in Fig. . The model formulation largely follows previous studies
.
The main modifications here relate to the representation of heat storage
changes and a formulation of terrestrial radiation based on the grey
atmosphere approximation (as in ). The symbols used in the
following description are summarised in Table .
Variables and parameters used in this study.
Symbol
Variable
Units (or value)
Usage
fland
Fraction of land area
0.29
Eq. ()
G
Convective power
Wm-2
Eq. ()
J
Turbulent fluxes (of sensible and latent heat)
Wm-2
Eq. ()
Jopt
Turbulent fluxes (optimised by max. power)
Wm-2
Eq. ()
kr
Radiative parameterisation constant
Wm-2K-1
Eq. ()
Rs
Surface absorption of solar radiation
Wm-2
Sect.
Rs,toa
Total absorption of solar radiation (surface and atmosphere)
Wm-2
Sect.
Rl,d
Downwelling flux of longwave radiation at the surface
Wm-2
Sect.
Rl,u
Surface emission of longwave radiation
Wm-2
Sect.
Rl,net
Net flux of longwave radiation at the surface
Wm-2
Eq. (), Sect.
Rl,net,opt
Net flux of longwave radiation at the surface (optimised by max. power)
Wm-2
Eq. ()
Rl,0
Radiative parameterisation constant
Wm-2
Eq. ()
Us
Heat storage below the surface
Jm-2
Eq. ()
Ua
Heat storage within the atmosphere
Jm-2
–
Utot
Total heat storage
Jm-2
Eq. ()
Tr
Radiative temperature
K
Eq. ()
Ts
Surface temperature
K
Eq. ()
Tday
Mean daytime temperature on land
K
Eq. ()
Tland
Land surface temperature
K
Eq. ()
Tnight
Mean nighttime temperature on land
K
Eq. ()
Tocean
Ocean surface temperature
K
Eq. ()
Tglobal
Global mean surface temperature
K
Eq. ()
ϕ
Ratio of land to ocean warming
–
Eq. ()
τ
Longwave optical thickness
–
Sect.
σ
Stefan–Boltzmann constant
5.67 × 10-8 Wm-2K-4
Eqs. () and ()
Schematic diagram of the surface energy balance used here in which
turbulent heat fluxes are described as a result of an atmospheric heat engine
operating between the surface and radiative temperatures. The limit to how
much power can maximally be derived from this heat engine provides a means to
parameterise turbulent heat fluxes.
Energy balances
For our description of the surface–atmosphere system, we need two basic
energy balance constraints: the energy balance of the surface and the energy
balance of the whole system.
The surface energy balance is described in terms of heat storage changes that
take place below the surface, dUs/dt; the absorbed solar radiation at the
surface, Rs; the net cooling by longwave radiation, Rl,net; and the
turbulent heat fluxes, J (the sum of the sensible and latent heat flux,
which are combined here for simplicity):
dUsdt=Rs-Rl,net-J.
The energy balance of the whole column is described by
dUtotdt=dUsdt+dUadt=Rs,toa-σTr4,
where dUtot/dt represents the total change of heat storage within the
surface–atmosphere system (consisting of heat storage changes below the
surface, dUs/dt, and within the atmosphere, dUa/dt), Rs,toa is
the total absorption of solar radiation (surface and atmosphere) and Tr is
the radiative temperature by which radiation is emitted to space, and
σ is the Stefan–Boltzmann constant. The radiative temperature is
determined from the mean energy balance taken over a sufficiently long time
so that
Tr=Rs,toa,avgσ1/4,
where Rs,toa,avg is the mean value of Rs,toa. We assume that Tr
does not change at the diurnal scale. This effectively represents our
assumption that the system has sufficient capacity to store heat to balance
out the variations in solar radiation.
The total change in heat storage within the system can be determined from the
approximation that this total heat storage does not change when averaged over
the course of day and night. The total change in heat storage can then be
inferred from the difference between the instantaneous and mean solar
forcing, given by
dUtotdt=Rs,toa-Rs,toa,avg.
In the following, we assume for simplicity that all solar radiation is
absorbed at the surface, so that Rs=Rs,toa. This assumption
simplifies the following considerations, but does not affect the results, as
discussed in Sect. . We then describe the
ocean–atmosphere system as a system in which the heat storage changes take
place below the surface (that is, in the surface ocean), so that dUs/dt=dUtot/dt. For the land–atmosphere system, we neglect the ground heat
flux, which is typically small on a diurnal timescale (as discussed in the
introduction), so that the change in heat storage needs to take place in the
lower atmosphere to meet this diurnal energy balance constraint. As it turns
out, this heat storage change does not enter the formulations explicitly so
that the term dUa/dt does not appear in the equations below.
Parameterisation of longwave radiation
To describe the net cooling by terrestrial radiation at the surface,
Rl,net, we use a simple, linearised parameterisation of net longwave radiation of the form
Rl,net=Rl,0+kr(Ts-Tr).
This formulation of net longwave radiation at the surface is similar to
well-established empirical, linearised forms e.g., but
it can also be derived from the grey atmosphere approximation of radiative
transfer in combination with a linearisation of surface emission, as in
. Net longwave radiation, Rl,net, is the difference
between surface emission, Rl,u=σTs4≈Tr+(4σTr3)(Ts-Tr), and the downwelling flux of longwave radiation, Rl,d=(3/4)τ⋅Rs,toa. Here, τ is the longwave optical depth and
Tr is described by Eq. (). This interpretation has the
advantage that the sensitivity of the parameters to a change in greenhouse
forcing can directly be identified. The parameters Rl,0 and kr are
then related to the longwave optical depth, τ; the mean emission of
terrestrial radiation to space, Rs,toa,avg; and the radiative
temperature, Tr, by
Rl,0=1-34τ⋅Rs,toa,avg
and
kr=4σTr3=4⋅Rs,toa,avgTr.
Note that a change in the greenhouse effect is associated with a change
Δτ, which alters the value of Rl,0, but not kr. A change
in absorption of solar radiation, for instance due to enhanced reflectance by
clouds or aerosols, affects both expressions if the total absorption,
Rs,toa, is altered.
Turbulent fluxes determined from maximum power
The turbulent fluxes J in the surface energy balance are derived from the
assumption that these operate at the thermodynamic limit of maximum power
. In this formulation, turbulent fluxes are seen as
the driver of a convective, atmospheric heat engine that generates the power
to sustain motion and the turbulent exchange between the surface and the
atmosphere. This approach uses the common and well-accepted Carnot limit of a
heat engine and combines it with the surface energy balance. The latter
aspect plays a central role, because turbulent fluxes lower surface
temperatures and thus affect the Carnot limit. The approach then assumes that
natural systems evolve to and operate near their thermodynamic limit. This
assumption falls into a broader range of thermodynamic optimality approaches.
In particular, it relates closely to a general hypothesis of maximum entropy
production MEP;
e.g.,
which has been applied rather successfully in the past to describe
atmospheric dynamics
and to
the mean climatological surface energy balance partitioning on land
. As maximising the power of a heat engine results in
maximum frictional dissipation, this is almost the same as maximising the
associated entropy production of this process. The focus on maximising the
power associated with turbulent heat fluxes, however, allows for a more
specific application of thermodynamic optimality to the particular process of
atmospheric turbulent heat transfer in relation to MEP, and it can be more
easily explained using the well-established concept of a heat engine. In the
following, this approach to estimate the magnitude of turbulent heat fluxes
is briefly summarised and extended to include the effects of diurnal heat
storage changes.
The power, G, or work per time, that a heat engine can provide is constrained by the Carnot limit, given by
G=J⋅Ts-TrTs,
where for the application to vertical heat transfer in the atmosphere the
driving temperature difference is set to the difference between the surface
temperature and the radiative temperature. The motivation for using the
radiative temperature as the cold temperature of the heat engine is to not
use the temperature at a specific height of the atmosphere but rather to use the
temperature at which the entropy export by radiative cooling to space is at a
maximum. This temperature is, by definition, the radiative temperature, as it
is the temperature of a blackbody that emits radiation at the rate
Rs,toa,avg.
To derive the maximum power limit from the Carnot limit, we combine this
limit with a fundamental tradeoff by which a greater turbulent heat flux
results in a lower surface temperature, so that the derived power has a
maximum with an associated, optimum value of J and Ts. This tradeoff is
obtained by combining the surface energy balance (Eq. )
and the expression for Rl,net (Eq. ) to express Ts
in terms of the radiative forcing, the heat storage change dUs/dt, and the
turbulent fluxes J,
Ts=Tr+Rs-dUs/dt-Rl,0-Jkr.
When used in the expression for the Carnot limit (Eq. ), we
obtain
G=J⋅Rs-dUs/dt-Rl,0-JkrTs.
This expression has a maximum in power (i.e. maximum generation of turbulent
kinetic energy), which can be derived analytically from dG/dJ=0. When
neglecting the variation in Ts with J in the denominator, the
maximisation yields an optimum heat flux, Jopt, and net longwave flux,
Rl,net,opt, given by
Jopt=Rs-dUs/dt-Rl,02Rl,net,opt=Rs-dUs/dt+Rl,02.
Note how this formulation of surface energy balance partitioning depends on
heat storage changes below the surface, dUs/dt, but not on heat storage
changes that take place in the lower atmosphere, dUa/dt. We use these
two contrasting cases of heat storage change to describe how this
partitioning looks for ocean (day and night) and land surfaces (daytime
only).
For the ocean surface, the dominant heat storage changes take place below the
surface, so that dUs/dt≈dUtot/dt=Rs,toa-Rs,toa,avg
(see Eq. ). With this expression for dUs/dt, the
optimum surface energy partitioning is then given by
Jopt,ocean=Rs,avg-Rl,02Rl,net,opt,ocean=Rs,avg+Rl,02.
This partitioning describes no temporal changes during the course of the day,
as the turbulent fluxes as well as net longwave radiation are described by
the mean solar radiation at the surface, Rs,avg, rather than the
instantaneous forcing, Rs.
For the land surface, we assume that the heat storage changes take place in
the lower atmosphere and dUs/dt≈0. Then, the energy balance
partitioning during the day is given by
Jopt,land=Rs-Rl,02Rl,net,opt,land=Rs+Rl,02.
Note how this partitioning includes the instantaneous rate of absorption of
solar radiation, Rs, thus resulting in a pronounced diurnal variation in
surface energy balance partitioning as it is commonly observed on land.
During night where Rs=0 and J=0 due to the prevalent stable
conditions, we assume Rl,net≈0. This simplification is
reasonable as observations typically show that the cooling of the surface by
net longwave radiation at night is less than 100 Wm-2
e.g. and thus much smaller than the peak
heating rate by solar radiation during the day.
Surface temperatures
For the two contrasting cases of land and ocean surfaces, we can derive
expressions for surface temperature by equating the optimum expressions for
the net longwave radiative flux with Eq. ().
For the ocean surface, surface energy balance partitioning does not change
over the course of day and night. Hence, surface temperature is constant and
depends only on the mean absorption of solar radiation:
Tocean=Tr+Rs,avg-Rl,02kr.
For land, we split the surface energy balance partitioning into two parts of
night and day. The nighttime temperature is derived directly from Rl,net≈0. This yields an equation for the nighttime temperature of
Tnight=Tr-Rl,0kr.
During the day, the mean absorption of solar radiation is about Rs,day=2⋅Rs,avg, which we use for Rs in Eq. ().
The mean daytime surface temperature is then given by
Tday=Tr+Rs,day-Rl,02kr.
This yields a mean surface temperature over land, Tland=1/2⋅(Tnight+Tday), of
Tland=Tr+Rs,avg-3/2⋅Rl,02kr.
When both temperatures are combined, the global mean surface temperature, Tglobal, is described by
Tglobal=(1-fland)⋅Tocean+fland⋅Tland,
where fland=0.29 is the fraction of land area of the total surface
area of the Earth.
Global mean surface energy balance partitioning predicted from the
approach used in this study in comparison to observations of
. The respective values are provided in Table .
Equations ()–() represent the key equations
used in the following to evaluate the sensitivity of surface temperature to a
change in radiative forcing. These estimates are then compared to the
respective sensitivities derived from the CMIP5 climate model simulations
, using the 4×CO2 and preindustrial control
simulations (a list of models used is provided in Table ).
Results and discussion
Global energy balance
We first evaluate the energy balance partitioning and expressions for
temperatures using global means. The forcing is described by observations of
the total mean absorption of solar radiation of the surface–atmosphere system
of about Rs,toa,avg=240 Wm-2 and the mean absorption at the
surface of Rs,avg=165 Wm-2 . To obtain a
global mean surface temperature of about 288 K, we choose a value of τ=1.74 for the longwave optical depth. This is the only parameter in the
formulations that we adjusted to match observations. From this radiative
forcing, the parameters Rl,0 and kr are derived for the surface
energy balance partitioning. The resulting surface energy balance
partitioning is illustrated in Fig. and the respective
values are provided in Table . The turbulent
fluxes of 119 Wm-2 and net longwave radiation of 46 Wm-2 derived
from the maximum power limit compare reasonably well to the estimates from
observations of 112 and 53 Wm-2 .
Note that the radiative properties as well as continental area show strong
geographic variations that are not accounted for here, so that this
evaluation merely shows the plausibility of the formulations.
Estimates for the global mean forcing, a global warming for a 4×CO2 scenario, and a scenario of solar brightening.
Symbol
Present day
Global warming
Difference
Solar brightening
Difference
Forcing
Rs,toa,avg (Wm-2)
240
240
0
240
0
Rs,avg (Wm-2)
165
165
0
175
10
τ (–)
1.74
1.924
0.18
1.74
0
Derived radiation properties
Tr (K)
255
255
0
255
0
Rl,0 (Wm-2)
-73.2
-106.3
-33.1
-73.2
0
kr (Wm-2K-1)
3.76
3.76
0
3.76
0
Predicted surface energy balance
Jopt (Wm-2)
119
136
16.6
124
5.0
Rl,net,opt (Wm-2)
46
29
-16.6
51
5.0
Predicted temperatures
Tocean (K)
286.7
291.1
4.4
288.0
1.3
Tland (K)
291.6
298.2
6.6
292.9
1.3
Tglobal (K)
288.1
293.2
5.0
289.5
1.3
The difference in diurnal energy balance partitioning between the ocean and
land surface is illustrated for global mean conditions in Fig. . Note that these global mean conditions are
hypothetical and used here to illustrate the difference in energy balance
partitioning using the formulations described in the methods section. At the
top of Fig. , the diurnal variation in the total
heat storage within the surface–atmosphere system is shown (compare with Eq. ) for a mean absorption of solar radiation at the
surface of 165 Wm-2 and the respective diurnal variation in Rs. The
differences in energy balance partitioning for ocean and land surfaces, using
Eqs. () and (), are then illustrated
in Fig. b and c. This figure clearly illustrates
that by buffering the diurnal variations in solar radiation below the
surface, the ocean surface energy balance has no diurnal variation in
turbulent fluxes. If the buffering takes place above the surface, as is
mostly the case for land surfaces, this results in a pronounced diurnal
variation in turbulent fluxes.
Mean diurnal heat storage variations inferred from the solar forcing
(a) and the associated diurnal variations in surface energy balance
partitioning of (b) an ocean surface and (c) a land surface as predicted by
the approach described here. The pale red line in panels (b) and (c) refers to
the average of absorbed solar radiation at the surface of Rs,avg=165 Wm-2.
The dotted lines in panels (b) and (c) refer to the respective values
for a global mean warming of ΔTs=5 K due to changes in greenhouse
forcing.
Temperature sensitivity to greenhouse forcing
We next evaluate the case of global warming. An increase in the greenhouse
effect is represented in our formulation by an increase in the longwave
optical depth, Δτ>0. We used a value of Δτ=0.18 to
obtain a global temperature increase of ΔTglobal=5.0 K. The
increase in optical thickness then changes Rl,0 by ΔRl,0=-3/4⋅Rs,toa⋅Δτ<0. Using the grey atmosphere approximation,
this change in τ implies an increase in the downwelling longwave
radiation of about ΔRl,d=33 Wm-2. This increase compares
fairly well to the range found in CMIP5 simulations used here, which range
from 20 to 42 Wm-2 (global mean) and are associated with a warming of
2.9 to 6.0 K in surface temperatures (4×CO2 scenario – PI control; see
Fig. ). The effect of this change in optical thickness on
the diurnal course of surface energy balance partitioning is shown in Fig. b and c by the dotted lines. The consequences for
mean ocean and land temperatures as well as for daytime and nighttime
temperatures on land is illustrated in Fig. , with
values given in Table . These sensitivities can be
derived analytically, using the expressions derived in Sect. .
Difference in ocean and land temperatures as well as daytime and
nighttime temperatures resulting from an enhanced greenhouse effect (ΔRl,d=+33 Wm-2) and from enhanced absorption of solar radiation at
the surface (ΔRs=+10 Wm-2), using the values from Table .
The warming of the ocean surface, ΔTocean, is then given by
ΔTocean=-ΔRl,02kr.
When the same change of optical thickness is applied to land, it results in a
warming of the land surface, ΔTland, of
ΔTland=-32ΔRl,02kr.
When taking the ratio, ϕ, of these two changes, we obtain
ϕ=ΔTlandΔTocean=32.
Hence, the land surface is 50 % more sensitive to a change in longwave
optical depth than the ocean surface. We can also translate this fixed ratio
between land and ocean warming into respective expressions that relate land
and ocean warming to the global temperature change:
ΔTocean=11+0.5⋅fland⋅ΔTglobal≈0.87⋅ΔTglobalΔTland=32-fland⋅ΔTglobal≈1.31⋅ΔTglobal.
When using the global mean values as shown in Table ,
a global mean temperature increase of 5 K due to
an increased greenhouse effect translates into an increase by 6.6 K over land
(or 31 % more than the global mean increase), while oceans only increase by
4.4 K (or 13 % less than the global mean increase). In Fig.
we compare the predicted ratio ϕ as well as
the temperature differences ΔTland and ΔTocean to
ΔTglobal to the respective simulated values of CMIP5 climate
model simulations. Although some deviations can be seen, our estimates
overall compare very well to the global mean changes found in the CMIP5
simulations.
Global mean response of 25 CMIP5 climate model simulations. Shown
is the mean warming of the ocean surface (ΔTocean,gcm, blue solid
squares), the land surface (ΔTland,gcm, red solid circles), and
the global mean (ΔTglobal, black dots) between the 4×CO2 and
preindustrial control simulations. Also shown are the equivalent changes
(ΔTocean,simple, blue open squares, and ΔTland,simple,
red open circles) predicted from the energy balance considerations made here.
The right diagram directly compares the ratio ϕ=ΔTland/ΔTocean from the GCM simulations (diamonds) to the prediction made here
(dashed line).
As argued in the introduction, the difference in the climate sensitivity of
land and ocean surfaces should be attributable to the different behaviour of
the land surface at night than during the day. To evaluate this in our
formulations, we also looked at the sensitivities of nighttime and daytime
temperatures as proxies for minimum and maximum temperatures. The minimum
temperature typically occurs at the end of the night, and we approximate it
by the use of Tnight. The maximum temperature occurs at the end of the
day, and for this temperature we use Tday. Using the above expressions
for these temperatures, we obtain
ΔTnight=-ΔRl,0krΔTday=-ΔRl,02kr=12ΔTnight.
Hence, minimum temperatures increase at twice the rate of maximum
temperatures in our formulation, thus reducing the diurnal temperature range.
This is broadly consistent with observations, for which a range of about 1.6–2.4
is reported for most seasons ,
although in observations the ratio varies between hemispheres and seasons.
We did not perform an evaluation of the diurnal temperature range for the
CMIP5 simulations for a few reasons. There are other effects, e.g. due to
changes in the hydrologic cycle, as well as model biases that quite
substantially affect the trend in the diurnal temperature range in the CMIP5
simulations so that this direct effect of an
enhanced greenhouse forcing is not the dominant factor in the 4×CO2
simulations. These effects would need to be accounted for in our expressions
before a more detailed comparison could be made. Yet, the well-established
observation that the diurnal temperature range decreases with global warming
is consistent with our interpretation why the climate sensitivity of land is
higher than for ocean surfaces.
Temperature sensitivity to solar forcing
To illustrate that changes in solar radiation affect the temperature
sensitivity quite differently, as described in , we
consider a case in which the total absorption of solar radiation is
unchanged, but more solar radiation is absorbed at the surface (i.e. ΔRs,avg=+10 Wm-2). This magnitude of change in solar absorption is
comparable to observed changes associated with solar dimming and brightening
over the last decades e.g., which in turn relates mostly
to changes in aerosol concentrations in the atmosphere. For comparability, we
use the same value for the longwave optical depth and considered the case of
solar brightening to better compare the effects of solar changes to changes
in greenhouse forcing. The sensitivity to absorbed solar radiation at the
surface is shown in Fig. by the red bars, with the
values given in Table in the column labelled
“Solar Brightening”.
Our simple estimates partition the increase in surface solar absorption
equally into increases in ΔJ and ΔRl,net (see
Eqs. and ). The change in ocean and
land temperatures is given by (see Eqs. and )
ΔTocean=ΔRs,avg2kr=ΔTland,
and the land surface warms on average by the same amount as the ocean surface.
This is quite different than the result from the change
in the greenhouse effect, where the sensitivities were different. The effect
on the diurnal temperature range on land is also markedly different. While
the nighttime temperatures remain unchanged as they do not depend on Rs,
the daytime temperatures are increased by twice the mean warming, with
ΔTday=ΔRs/kr=2ΔTland. This effect of solar
radiation on maximum temperatures is well known e.g. and
has been used to infer solar radiation from the diurnal temperature range
e.g..
Our formulations thus show that the temperature sensitivities of ocean and
land surfaces, as well as sensitivities of minimum and maximum temperatures on land,
and thus of the diurnal temperature range, are closely connected and react
differently depending on the type of radiative change at the surface.
Discussion
Limitations
Despite its physical basis, our model has, obviously, several potential
limitations due to its extremely simple nature. These potential limitations
relate to the parameterisation of radiation and turbulent fluxes, as well as to how
evaporation is treated in our formulations.
To start, the use of the grey atmosphere approximation for the downwelling
flux of longwave radiation is an approximation. It represents a more
mechanistic approach of parameterising longwave radiative transfer, with the
main difference to earlier work
being the additive constant Rl,0 in Eq. () that played
here an important role. The use of the grey atmosphere approximation,
however, is likely to overestimate the downward longwave flux for a given
optical depth. Turbulent fluxes cause a lower surface temperature than in
radiative equilibrium, which results in a colder lower atmosphere that is in
radiative–convective equilibrium. This, in turn, should be associated with a
lower downwelling flux of longwave radiation. By using the grey atmosphere
approximation, we do not account for this effect, which is likely to result
in some biases in our formulation. This is likely to result in an
overestimation of the sensitivity of surface temperature to changes in the
optical depth. However, as we do not calculate optical depths or use
observations but rather adjust it to represent the global mean temperature
or a given temperature change, the effect of this bias in the radiation
parameterisation is likely to be small for our results.
We also did not specifically consider absorption of solar radiation within
the atmosphere (which can be seen by comparing Rs,toa,avg to Rs,avg
in Table ). This atmospheric absorption would
result in some diurnal variation in heat storage within the atmosphere over
oceans. However, since our expressions do not explicitly depend on changes in
atmospheric heat storage, the effect of this should not change our results.
Another limitation relates to our representation of turbulent fluxes. We used
the Carnot limit and the assumption that turbulent fluxes operate near the
limit of maximised power. Yet, the diurnal variation in heat storage in the
lower atmosphere over land may need to be accounted for in the derivation of
thermodynamic limits, which may then result in a different partitioning of
energy fluxes at the surface. However, as long as the turbulent fluxes on
land are proportional to the instantaneous value of absorbed solar radiation
at the surface (which is a good assumption as turbulent fluxes on land show a
strong diurnal variation), turbulent fluxes must then be small at night. The
basic reasoning would then still apply that nighttime temperatures are more
sensitive to a change in greenhouse forcing, thus resulting in an altered
climate sensitivity of land surfaces compared to ocean surfaces, although the
specific ratio ϕ may differ from our value of 3/2.
Furthermore, we do not explicitly consider evaporation in our formulation,
but include it in the turbulent fluxes J. Evaporation and the associated
latent heat flux cools the surface, yet it only heats the atmosphere (and the
surface) when it condenses. At the global scale in steady state, evaporation
needs to balance precipitation, so that evaporation does not necessarily need
to be represented as a separate term in the surface energy balance. Yet,
spatiotemporal imbalances between evaporation and precipitation due to
storage changes of water vapour and moisture transport can result in regional
temperature variations due to evaporation .
Furthermore, differences in radiative parameters during dry and wet periods
may result in further modulations of surface temperatures that we did not
account for and that could have an effect . Those
effects would clearly need to be addressed when our formulations are applied
to the regional scale, which could form a topic of future research.
Yet, overall, it would seem that despite these deficiencies, our simple
representation is able to adequately illustrate our explanation from the
introduction in a parsimonious way as it captures the difference in climate
sensitivity of ocean and land surfaces, and connects this difference to the
difference in sensitivity between minimum and maximum temperatures.
Interpretation
Our explanation for the difference in temperature sensitivity between oceans
and land is quite different, yet not in contradiction to previous approaches,
which we explain in the following. Previous attempts to explain the
difference in temperature sensitivity typically start with the reduced water
availability on land. In arid regions, water limits evaporation, so that the
radiative heating results in an enhanced sensible heat flux and thermal
emission, which is accomplished by a warmer surface temperature. When ocean
and land are exposed to an equal increase in the downwelling flux of longwave
radiation by an enhanced greenhouse effect, the land surface in arid regions
should respond by a stronger warming than the ocean surface (which to some
extent is found in climate model simulations). These effects then result in
different levels of humidity and affect lapse rates in the lower atmosphere.
This line of explanation was developed and extended by
, and .
Our approach uses a systems approach to the surface–atmosphere system, so it
neither focuses entirely on the surface energy balance nor on the atmosphere,
but rather on the coupled system. This system is subjected to the energy
balance constraint during the diurnal cycle, which we use to infer the
buffering needed to level out the strong variation in solar radiation. While
the buffering below the ocean surface is relatively straightforward and
established for the ocean–atmosphere system, the buffering in the lower
atmosphere for the land–atmosphere system is less established but central to
the explanation presented here. This buffering implies the formation of a
convective boundary layer on land during the day to heat the lower atmosphere
and to accomplish the diurnal heat storage change. It also implies unstable
conditions during the day that drives the sensible heat flux, dry convection,
and boundary layer development. This likely results in a greater lapse rate
that is closer to the dry adiabatic lapse rate as the heating of the lower
atmosphere is primarily driven by the sensible heat flux and dry convection.
These consequences link to the properties that were used before to explain
the difference in temperature sensitivity, so our explanation is consistent
with previous interpretations in this respect. Yet, what our approach shows
is that these dynamics do not need to be resolved in detail to derive the
difference in climate sensitivity, as these essentially follow from the
energy balance closure assumption applied to the surface–atmosphere system
over the whole day. It would thus seem that this energy balance closure and
the way by which the land surface–atmosphere system accomplishes it are the
primary cause for the difference in temperature sensitivity.
Our explanation can not only explain the difference in temperature
sensitivity over land and ocean but also connects to the well-established
difference in sensitivity of minimum and maximum temperatures as well as the
distinctively different diurnal course of turbulent fluxes between land and
ocean. In this sense, our explanation appears to be more general, as it is
able to explain more phenomena by a less complex approach.
Further implications and potential for future research
We can draw a few broader implications from these insights that open up
possibilities for a range of further research.
First, our results explain why the diurnal dynamics of the surface energy
balance of ocean and land surfaces are so distinctively different. While
these differences are well established in observations and are described in
textbooks e.g., we can explain these by the
different means by which the diurnal variation in solar radiation is being
buffered, with critical implications for the temperature sensitivity. For the
ocean, variations in solar radiation are buffered by heat storage changes
below the surface, so that turbulent fluxes do not show much of a diurnal
variation. On land, however, it is well known that turbulent fluxes show a
pronounced diurnal variation during the day and are practically absent
during the night. We interpreted this different behaviour of land surfaces
here as a result of the buffering taking place in the lower atmosphere above
the surface, rather than below as in the case for the ocean, which results in
stable conditions during nighttime that are more sensitive to changes in the
greenhouse effect. As variations in solar radiation are buffered in the lower
atmosphere over land, this symbolises the strong coupling between the land
surface and the lower atmosphere, with this coupling nevertheless being
constrained by the energy balance over day and night over the whole
surface–atmosphere system. Our approach could thus serve as the basis for a
parsimonious approach to better understand land surface–atmosphere
interactions.
Our interpretation that diurnal heat storage variations explain the
difference in climate sensitivity can, clearly, be analysed in much greater
detail in observations, reanalyses, and climate models. The variations in
heat content in the lower atmosphere should be relatively straightforward to
analyse in observations and model output, and one would expect a noticeable
difference in variations over oceans and land. However, such an analysis
requires the ability to diagnose diurnal heat storage variations in the
atmosphere at sufficient temporal resolution. Measurements by radiosoundings,
for instance, are available only twice a day, which is insufficient to
diagnose the magnitude of diurnal heat storage variations. For climate
models, this would require a substantial amount of model output at the
diurnal scale, which is typically not available. It would thus require
measurements and output at higher temporal resolution to evaluate these heat
storage variations in greater detail.
One can also evaluate and extend this approach with respect to some of the
simplifying assumptions, for instance regarding evaporation (as already
discussed above), the ground heat flux, and different land cover types as
well as inland water bodies such as lakes and rivers. While the role of the
ground heat flux has been neglected here for the land surface, observations
show a noticeable magnitude of this flux, especially for non-forested
surfaces. Our interpretation would suggest that regions with a greater ground
heat flux would show diurnal temperature variations that are reduced for the
given radiative forcing and somewhat more similar to ocean surfaces
(resulting in a lower ratio ϕ). To evaluate this further and go into
more regional variations in the diurnal temperature range would, however,
require a more specific treatment of the different factors that vary
geographically. For instance, the ground heat flux is typically larger in
desert regions, which are dry, lack evaporative cooling, and typically have
comparatively low optical thicknesses. To expand this approach to regional
variations and different processes would thus require more spatial details in
the forcing and may need to consider other relevant effects (such as
evaporation and lateral heat transport), but would form interesting
extensions for further research.
The ability of our rather simple formulation of the surface–atmosphere system
to explain the difference in climate sensitivity suggests that diurnal
variations in temperature contain a lot of information to learn from. When
our approach is extended to derive analytical solutions of the whole diurnal
cycle, with possible extensions regarding the role of the ground heat flux
and evaporation, one may use observed temperature variations and invert these
to infer the magnitude of turbulent fluxes at the land surface, evaporation,
and other aspects of the land surface energy balance. This could provide an
additional means to better understand the functioning of the highly coupled
and interactive yet constrained land–atmosphere system that complements
data-driven approaches and land surface modelling.
Last, but not least, our explanation should also be applicable to the
different climate sensitivity of the seasonal cycle. It is well known that
winter temperatures increase more strongly than summer temperatures with
global warming, particularly at high latitudes. Our interpretation here would
suggest that this can be explained by winter conditions being shaped by short
hours of daylight. As turbulent fluxes would only play a role during daylight
in winter, this should result in a longer period of the whole day which are
shaped by stable conditions and which are more sensitive to changes in
longwave radiation. This longer period of stable conditions, in turn, could
result in values of ϕ that exceed ϕ=1.5. (Note that here we assumed
an equal length of daytime and nighttime, which resulted in the amplification
of 50 %.) In the extreme case of the polar night, one would actually expect a
ratio of ϕ=2 in the absence of any absorption of solar radiation, so
stable conditions prevail over the whole day. During the polar day, one would
still expect a ratio of ϕ=1.5 because the variations in solar radiation
are still buffered by the lower atmosphere, resulting in a heat gain over
half of the day, while losing heat over the other half of the day. This, in
turn, can explain why our value of ϕ=1.5 appears to set a lower bound in
the comparison to climate models (as shown in Fig. ), and this can explain the greater sensitivity of
high latitudes to global warming. However, a detailed analysis would be
necessary in future research to substantiate this reasoning.