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Water Vapor Feedback and Global Warming

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Abstract Water vapor is the dominant greenhouse gas, the most important gaseous source of infrared opacity in the atmosphere. As the concentrations of other greenhouse gases, particularly carbon dioxide, increase because of human activity, it is centrally important to predict how the water vapor distribution will be affected. To the extent that water vapor concentrations increase in a warmer world, the climatic effects of the other greenhouse gases will be amplified. Models of the Earth's climate indicate that this is an important positive feedback that increases the sensitivity of surface temperatures to carbon dioxide by nearly a factor of two when considered in isolation from other feedbacks, and possibly by as much as a factor of three or more when interactions with other feedbacks are considered. Critics of this consensus have attempted to provide reasons why modeling results are overestimating the strength of this feedback. Our uncertainty concerning climate sensitivity is disturbing. The range most often quoted for the equilibrium global mean surface temperature response to a doubling of CO2 concentrations in the atmosphere is 1.5oC to 4.5oC. If the Earth lies near the upper bound of this sensitivity range, climate changes in the twenty-first century will be profound. The range in sensitivity is primarily due to differing assumptions about how the Earth's cloud distribution is maintained; all the models on which these estimates are based possess strong water vapor feedback. If this feedback is, in fact, substantially weaker than predicted in current models, sensitivities in the upper half of this range would be much less likely, a conclusion that would clearly have important policy implications. In this review, we describe the background behind the prevailing view on water vapor feedback and some of the arguments raised by its critics, and attempt to explain why these arguments have not modified the consensus within the climate research community.
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Annu. Rev. Energy Environ. 2000. 25:441–75
WATER VAPOR FEEDBACK AND
GLOBAL WARMING1
Isaac M. Held and Brian J. Soden
Geophysical Fluid Dynamics Laboratory/National Oceanic and Atmospheric
Administration, Princeton, New Jersey 08542
Key Words climate change, climate modeling, radiation
Abstract Watervaporisthedominantgreenhousegas,themostimportantgaseous
sourceofinfraredopacity in the atmosphere. As the concentrations ofothergreenhouse
gases, particularly carbon dioxide, increase because of human activity, it is centrally
importantto predict how the water vapordistributionwillbeaffected. Tothe extent that
water vapor concentrations increase in a warmer world, the climatic effects of the other
greenhouse gases will be amplified. Models of the Earth’s climate indicate that this
is an important positive feedback that increases the sensitivity of surface temperatures
to carbon dioxide by nearly a factor of two when considered in isolation from other
feedbacks, and possibly by as much as a factor of three or more when interactions with
other feedbacks are considered. Critics of this consensus have attempted to provide
reasons why modeling results are overestimating the strength of this feedback.
Our uncertainty concerning climate sensitivity is disturbing. The range most often
quoted for the equilibrium global mean surface temperature response to a doubling
of CO2concentrations in the atmosphere is 1.5C to 4.5C. If the Earth lies near
the upper bound of this sensitivity range, climate changes in the twenty-first century
will be profound. The range in sensitivity is primarily due to differing assumptions
about how the Earth’s cloud distribution is maintained; all the models on which these
estimates are based possess strong water vapor feedback. If this feedback is, in fact,
substantially weaker than predicted in current models, sensitivities in the upper half of
this range would be much less likely, a conclusion that would clearly have important
policy implications. In this review, we describe the background behind the prevailing
view on water vapor feedback and some of the arguments raised by its critics, and
attempt to explain why these arguments have not modified the consensus within the
climate research community.
CONTENTS
HISTORICAL INTRODUCTION TO THE BASIC PHYSICS ................ 442
The Greenhouse Effect and the Radiative Properties of Water Vapor........... 442
1The US Government has the right to retain a nonexclusive, royalty-free license in and to
any copyright covering this paper.
441
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Early Studies of Climatic Sensitivity ................................. 443
Radiative-Convective Models ...................................... 445
Energy Balance ................................................ 446
The Satellite Era................................................ 449
Climate Models ................................................ 452
The Simplest Feedback Analysis .................................... 454
THE CLIMATOLOGICAL RELATIVE HUMIDITY DISTRIBUTION .......... 456
The Global Picture .............................................. 456
The Planetary Boundary Layer ..................................... 459
The Free Troposphere ............................................460
RELATIVE IMPORTANCE OF DIFFERENT PARTS OF THE
TROPOSPHERE FOR WATER VAPOR FEEDBACK ..................... 461
THE CONTROVERSY CONCERNING WATER IN THE TROPICAL
FREE TROPOSPHERE ........................................... 465
The Complexity of the Tropics ..................................... 465
Convective Outflow Temperatures ................................... 466
Condensate ................................................... 468
Precipitation Efficiency ........................................... 468
Empirical Studies ............................................... 469
FINAL REMARKS ............................................... 471
HISTORICAL INTRODUCTION TO
THE BASIC PHYSICS
The Greenhouse Effect and the Radiative
Properties of Water Vapor
Joseph Fourier is widely credited as being the first to recognize the importance of
thegreenhouseeffectfortheEarth’sclimate. Inhis1827treatiseonthetemperature
of the globe, Fourier pointed out that the atmosphere is relatively transparent to
solar radiation, but highly absorbent to thermal radiation and that this preferential
trapping is responsible for raising the temperature of the Earth’s surface (1). By
1861, John Tyndal had discovered that the primary contributors to this trapping
are not the dominant constituents of the atmosphere, N2and O2, but trace gases,
particularly water vapor and carbon dioxide, which constitute less than 1% of the
atmospheric mass (2). From a series of detailed laboratory experiments, Tyndal
correctly deduced that water vapor is the dominant gaseous absorber of infrared
radiation, serving as “a blanket, more necessary to the vegetable life of England
than clothing is to man” (3).
Thedevelopmentofquantumtheoryintheearlytwentiethcentury and improved
spectroscopic measurements rapidly produced a more detailed understanding of
the interactions between atmospheric gases and radiation. The qualitative picture
first painted by Fourier and Tyndal has, of course, been confirmed and refined.
The wavelength-dependence of the absorption in the atmosphere is rich in detail,
consisting of thousands of spectral lines for water vapor alone. One might sus-
pect that this complexity of the radiative transfer is itself an important source of
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uncertainty in estimates of climate sensitivity, but this is true only to a very limited
degree.
Themajorsourceofuncertaintyingaseousradiativetransferarisesfromthecon-
tinuum absorption by water vapor (4,5). Far from any line centers, there remains
background absorption due to the far wings of distant spectral lines. Knowledge
of the precise shape of these lines is incomplete. Line shapes in the troposphere
are primarily controlled by pressure broadening, implying that most of the inter-
actions with radiation occur while the radiatively active gas molecule is colliding
with another molecule. The water vapor continuum is distinctive in that it is con-
trolled in large part by collisions of water molecules with other water molecules,
and it therefore plays an especially large role in the tropics, where water vapor
concentrations are highest. Continuum absorption is quantitatively important in
computations of the sensitivity of the infrared flux escaping the atmosphere to
water vapor concentrations within the tropics (6), a centrally important factor in
analyses of water vapor feedback. However, approximations for continuum ab-
sorption are constrained by laboratory and atmospheric measurements and the
remaining uncertainty is unlikely to modify climatic sensitivity significantly.
There is also room for improvement in the construction of broadband radiation
algorithms for use in climate models that mimic line-by-line calculations (7), but
work growing out of the Intercomparison of Radiation Codes for Climate Models
project (8) has helped to reduce the errors in such broadband computations. In
short,we see little evidence to suggest thatourabilitytoestimateclimate sensitivity
is significantly compromised by errors in computing gaseous absorption and emis-
sion, assuming that we have accurate knowledge of the atmospheric composition.
There does remain considerable controversy regarding the radiative treatment
of clouds in climate models, associated with the difficulty in obtaining quantita-
tive agreement between atmospheric measurements and theoretical calculations of
solar absorption in cloudy atmospheres (9). As we shall see below, the treatment
of clouds in climate models presents greater obstacles to quantitative analysis of
climate sensitivity than does the treatment of water vapor.
Early Studies of Climatic Sensitivity
By the turn of the century, the possibility that variations in CO2, could alter the
Earth’s climate was under serious consideration, with both S Arrhenius (10) and
TC Chamberlin (11) clearly recognizing the central importance of water vapor
feedback. In a letter to CG Abbott in 1905, Chamberlin writes,
[W]ater vapor, confessedly the greatest thermal absorbent in the atmosphere,
is dependent on temperature for its amount, and if another agent, as CO2, not
so dependent, raises the temperature of the surface, it calls into function a
certain amount of water vapor which further absorbs heat, raises the
temperature and calls forth more vapor ... (3).
In the following, we will measure the concentration of water vapor either by
its partial pressure eor its mixing ratio r, the latter being the ratio of the mass of
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water vapor in a parcel to the mass of dry air. Since observed mixing ratios are
small, we can assume that re/p, where pis the atmospheric pressure. If there
are no sources or sinks of water, ris conserved as the parcel is transported by the
atmospheric flow.
As understood by Chamberlin, when air containing water vapor is in thermo-
dynamic equilibrium with liquid water, the partial pressure of the vapor, e,is
constrained to equal es(T), the saturation vapor pressure, which is a function of
the temperature Tonly (ignoring impurities in the water and assuming a flat liquid
surface). The ratio He/esis referred to as the relative humidity. Supersatura-
tion of a few percent does occur in the atmosphere, especially when there is a
shortage of condensation nuclei on which drops can form, but for large-scale cli-
mate studies it is an excellent approximation to assume that whenever erises above
esvapor condenses to bring the relative humidity back to unity. In much of the
atmosphere it is the saturation pressure over ice, rather than water, that is relevant,
but we will not refer explicitly to this distinction.
According to the Clausius-Clapeyron relation, es(T) increases rapidly with in-
creasing temperature, albeit a bit slower than exponentially. More precisely, the
fractional change in esresulting from a small change in temperature is propor-
tional to T2. At 200K, a 1K increase results in a 15% increase in the vapor
pressure; at 300K, it causes a 6% increase. In searching for theories for the ice-
ages, Arrhenius and Chamberlin both thought it plausible, if not self-evident, that
warming the atmosphere by increasing CO2would, by elevating es, cause water
vapor concentrations to increase, which would further increase the greenhouse
effect, amplifying the initial warming.
The possibility of CO2increasing because of fossil fuel use helped motivate a
series of studies through the 1930s, 1940s, and 1950s that improved the radiative
computations underlying estimates of climate sensitivity (12–14). Researchers
evidently lost sight of the potential importance of water vapor feedback during
this period. In 1963 F Moller (15) helped correct this situation, from which time
this issue has retained center stage in all quantitative studies of global warming.
At roughly the same time, a runaway greenhouse owing, at least in part, to water
vapor began to be considered as having possibly occurred during the evolution of
the Venusian atmosphere (16).
In his attempt at quantifying the strength of water vapor feedback, Moller
explicitly assumed that the relative humidity of the atmosphere remains fixed as it
iswarmed.Thisassumption of fixed relativehumidity has proven to be a simpleand
useful reference point for discussions of water vapor feedback. The alternative
assumption of fixed vapor pressure requires that relative humidity Hdecrease
rapidly as temperatures increase, the decrease being 6% of Hper C of warming
in the warmest parts of the troposphere, and 15% of Hper C in its coldest parts.
Therelativehumidityis controlled bytheatmosphericcirculation. Motion dries
the atmosphere by creating precipitation. For example, as air moves upwards
it cools due to adiabatic expansion. The vapor pressure edecreases due to this
expansion, but esdecreases much more rapidly, causing the vapor to condense.
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Once sufficient condensate is generated, raindrops form and water falls out of the
parcel. When restored to its original level the air parcel compresses and warms,
and once again the change in esfar outweighs the increase in vapor pressure due
to the compression itself, and the parcel finds itself undersaturated.
To model the relative humidity distribution and its response to global warming
one requires a model of the atmospheric circulation. The complexity of the cir-
culation makes it difficult to provide compelling intuitive arguments for how the
relative humidity will change. As discussed below, computer models that attempt
to capture some of this complexity predict that the relative humidity distribution
is largely insensitive to changes in climate.
Radiative-Convective Models
When Moller assumed fixed relative humidity in a one-dimensional atmospheric
model, he found an implausibly large sensitivity to changes in CO2. His results
were in error owing to a focus on the radiative fluxes at the surface, rather than
at the top of the atmosphere. The atmosphere is not in pure radiative equilibrium;
in fact, the vertical and horizontal temperature structure within the troposphere is
stronglycontrolled by the atmosphericcirculationaswell as by thespatialstructure
of the radiative fluxes. The sensitivity of surface temperature is more closely tied
to changes in the radiative fluxes at the top of the atmosphere or more precisely, at
the tropopause, than at the surface. S Manabe and collaborators (17, 18), working
with simple one-dimensional radiative-convective models in the 1960s, helped
clarify this centrally important point.
On average, temperatures in the troposphere decrease with height at a rate (the
lapse rate) of 6.5 K/km. This vertical temperature structure cannot be understood
from consideration of radiative equilibrium alone, which would produce a much
larger lapse rate. Rather, it is primarily controlled by the atmospheric circulation.
In those areas of the tropics that are convectively active, the lapse rate is close to
that of a moist adiabat, the profile obtained by raising a saturated parcel, which
cools owing to adiabatic expansion, but as a result of this cooling also condenses
water vapor, releasing the latent heat of evaporation that compensates for part of
the cooling. At higher latitudes, the moist adiabat does not provide as useful an
approximation to the lapse rate, as the sensible and latent heat transport by larger
scale circulations, extratropical cyclones, and anticyclones also plays a significant
role. Models for the nonradiative fluxes of energy in the atmosphere are inherently
complex. Different processes are dominant in different regions, and a variety of
scales of motion are involved.
Manabe and collaborators (17, 18) introduced a very simple, approximate way
of circumventing this complexity, by starting with a one-dimensional radiative-
equilibrium model of the horizontally-averaged temperature of the atmosphere but
then adding the constraint that the lapse rate should not be allowed to rise above
some prescribed value. The model then predicts the position of the tropopause,
below which it is forced to maintain the prescribed lapse rate, and above which
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it maintains pure radiative equilibrium. Nonradiative fluxes are implicit in the
upward energy flux required to maintain the tropospheric lapse rate.
In the simplest radiative-convective models, one also sets the temperature of
the surface equal to the temperature of the atmosphere adjacent to the surface. In
pure radiative equilibrium there is a substantial temperature jump at the surface.
Theremovalofthisjumpimpliesthatthereisevaporationorsensibleheatfluxatthe
surface, determined by the radiative flux imbalance. Changes in the net radiation at
the surface are assumed to be perfectly compensated by changes in the evaporation
and the surface sensible heat flux. In contrast, Moller had effectively assumed, as
had others before him, that the surface temperature would adjust to any changes in
radiative fluxes, holding evaporation and sensible heating fixed. Because the latter
are very strongly dependent on the temperature difference between the surface
and the lowest layers of the atmosphere, one is much better off assuming that
the surface fluxes adjust as needed to remove this temperature difference. To the
extent that evaporation dominates over the surface-sensible heat flux, one can, in
fact, argue that changes in the net radiation at the surface control the sensitivity of
the global hydrologic cycle (the mean rate of precipitation or evaporation) rather
than the sensitivity of surface temperatures.
Itis an oversimplificationtoassumethattemperature gradients withinthetropo-
spheredonotchangeastheclimatewarms,butthissimpleassumptionhasprovento
be a very useful point of reference. Using a radiative convective model constrained
in this way, and with the additional assumption that the relative humidity is fixed,
Manabe & Wetherald (18) found that the sensitivity of surface (and tropospheric)
temperatures to CO2is increased by a factor of 1.7 over that obtained with fixed
water vapor. Other radiative-convective models have supported this estimate of
the strength of water vapor feedback, with fixed relative humidity, fixed clouds,
and fixed lapse rate, rarely varying by more than 10% from this value. For further
information on radiative-convective models, see Ramanathan & Coakley (19).
Energy Balance
The simple radiative-convective framework teaches us to think of the energy bal-
ance of the Earth as a whole as the starting point for discussions of climate sensi-
tivity.
Averaged over the surface and over the seasons, the Earth absorbs 70% of the
solar radiation incident at the top of the atmosphere, amounting to 240 W/m2.
To balance this incoming flux, a black body would have to radiate to space at a
temperature of 255 K. We refer to this temperature as the effective temperature of
the infrared emission, Te.WehaveS=σT
4
e, where Sis the absorbed solar flux
and σis the Stefan-Boltzmann constant. The actual mean surface temperature
of the Earth is close to 288 K. The effective temperature of emission occurs in
the mid-troposphere, about 5 km above the surface on average. We refer to this
height as Ze. As pictured in Figure 1, one can think of the average infrared photon
escaping to space as originating near this mid-tropospheric level. Most photons
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Ts
Tropopause
Ts+Ts
Temperature
Altitude
Te
ZeZe + Ze
1xCO2
2xCO2
Figure 1 Schematic illustration of the change in emission level (Ze) associated with an
increase in surface temperature (Ts) due to a doubling of CO2assuming a fixed atmospheric
lapse rate. Note that the effective emission temperature (Te) remains unchanged.
emitted from lower in the atmosphere, including most of those emitted from the
surface, are absorbed by infrared-active gases or clouds and are unable to escape
directly to space. The surface temperature is then simply Ts=Te+0Ze, where
0is the lapse rate. From this simple perspective, it is the changes in Ze, as well
as in the absorbed solar flux and possibly in 0, that we need to predict when we
perturb the climate. As infrared absorbers increase in concentration, Zeincreases,
and Tsincreases proportionally if 0and Sremain unchanged.
The increase in opacity due to a doubling of CO2causes Zeto rise by 150
meters. This results in a reduction in the effective temperature of the emission
across the tropopause by (6.5K/km) (150 m) 1 K, which converts to 4W/m2
using the Stefan-Boltzmann law. This radiative flux perturbation is proportional to
the logarithm of the CO2concentration over the range of CO2levels of relevance
to the global warming problem. Temperatures must increase by 1 K to bring the
systemback to anequilibrium between theabsorbed solar fluxandthe infrared flux
escaping th space (Figure 1). In radiative-convective models with fixed relative
humidity, theincrease in watervapor causesthe effective level of emission to move
upwards by an additional 100 m for a doubling of CO2. Water vapor also absorbs
solar radiation in the near infrared, which feeds back with the same sign as the
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terrestrial radiation component, accounting for 15% of the water vapor feedback
in climate models (20,21).
In equilibrium, there is a balance between the absorbed solar flux Sand the
outgoing terrestrial radiation R. Listing a few of the parameters on which these
fluxes depend, we have, schematically,
S(H2O,I,C)=R(T,H2O,log2CO2,C), 1.
whereCrepresents clouds, Ithe ice and snowcover, log2CO2isthelogarithmof the
CO2concentration (base 2) and Tis either the mean surface temperature or a mean
tropospheric temperature (we are assuming here that these temperatures all change
uniformly). Perturbing CO2and holding H2O, I, and Cfixed, the perturbation in
temperature dT satisfies
0=R
TdT +R
log2CO2dlog2CO22.
Linearizing about the present climate, we can summarize the preceding discussion
by setting
R
T4W/(m2K)3.
and
R
log2CO2≈−4W/m24.
so that
dT
dlog2CO2=− R
log2CO2.R
T101K 5.
for fixed H2O, C, and I.
If we believe that changes in water vapor are constrained by changes in at-
mospheric temperature, we can set H2O=H2O(T). Replacing equation 2, we
have
S
H2OdH2O
dT dT =R
TdT +R
H2OdH2O
dT dT +R
log2CO2dlog2CO2
6.
The temperature response to CO2doubling is now
dT
dlog2CO2=1
0
1βH2O,7.
where
βH2OµR
H2O+S
H2OdH2O
dT .R
T.8.
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The size of nondimensional ratio, βH2O, provides a measure of the strength of
the water vapor feedback. If βH2O0.4, water vapor feedback increases the
sensitivity of temperatures to CO2by a factor of 1.7, assuming that Iand C
are fixed.
If the value of βH2Owere larger than unity, the result would be a runaway
greenhouse. The outgoing infrared flux would decrease with increasing tempera-
tures. It is, of course, self-evident that the Earth is not in a runaway configuration.
But it is sobering to realize that it is only after detailed computations with a
realistic model of radiative transfer that we obtain the estimate βH2O0.4 (for
fixed relative humidity). There is no simple physical argument of which we are
aware from which one could have concluded beforehand that βH2Owas less than
unity. The value of βH2Odoes, in fact, increase as the climate warms if the relative
humidity is fixed. On this basis, one might expect runaway conditions to develop
eventually if the climate warms sufficiently. Although it is difficult to be quanti-
tative, primarily because of uncertainties in cloud prediction, it is clear that this
point is only achieved for temperatures that are far warmer than any relevant for
the global warming debate (22).
The Satellite Era
Given that the earth’s climate is strongly constrained by the balance between the
absorption of solar radiation and emission of terrestrial radiation, space-based
observations of this radiation budget play a centrally important role in climate
studies. These observations first became available in the mid-1960s. After two
decades of progress in satellite instrumentation, acoordinated network of satellites
[theEarth Radiation BudgetExperiment (ERBE)] waslaunchedin 1984 toprovide
comprehensive measurements of the flow of radiative energy at the top of the
atmosphere (23). Over a century after John Tyndal first noted its importance, an
observational assessment of our understanding of the radiative trapping by water
vapor became possible.
When analyzing the satellite measurements, it has proven to be particularly
valuable to focus on the outgoing longwave fluxes when skies are free of clouds,
Rclear, to highlight the effectsof water vapor. Following Raval & Ramanathan (24),
in Figure 2a(see color insert) we use ERBE observations to plot the annual mean
clear sky greenhouse effect, Gclear RsRclear, over the oceans, where Rsis the
longwave radiation emitted by the surface. (In the infrared, ocean surfaces emit
very nearly as black bodies, so that Rsis simply σT4
s.) A simple inspection of these
figures reveals several important features regarding the processes that control the
atmospheric greenhouse effect.
The magnitude of greenhouse trapping is largest over the tropics and decreases
steadily as one approaches the poles. Moreover, the distribution of the clear-sky
greenhouse effect closely resembles that of the vertically-integrated atmospheric
water vapor (Figure 2b; see color insert). The thermodynamic regulation of this
column-integrated vapor is evident when comparing this distribution with that of
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surface temperature (Figure 2c; see color insert). Warmer surface temperatures
are associated with higher water vapor concentrations, which in turn, are associ-
ated with a larger greenhouse effect. Regressing Gclear versus Tsover the global
oceans (24,25), one finds a relationship that is strikingly similar to that obtained
from radiative computations assuming clear sky, fixed lapse rate, and fixed relative
humidity.
Such an analysis suggests the tantalizing possibility that the strength of water
vapor feedback might be determined directly from observations rather than re-
lying upon models. Unfortunately, life is not so simple. The vapor distribution
in Figure 2 is not solely a function of surface temperature. Even if the relative
humidity were fixed, variations in atmospheric temperature do not always follow
surface temperature changes in a simple way. For example, the relationship be-
tween Rclear and Tsobtained from geographic variations in mid-latitudes differs
markedly from those obtained from the local seasonal cycle, owing to differences
in the variations in lapse rate; similarly, the relation observed on seasonal time
scales differs markedly from that observed on interannual time scales (26).
More importantly still, the relative humidity distribution is strongly affected by
the atmospheric circulation, with areas of mean ascent moister than areas of mean
subsidence. Over the tropical oceans, in particular, ascent occurs in the regions
of warmest surface temperature, and strong descent occurs in regions where the
surface is only a few degrees cooler. The circulation can be thought of as forced,
in first approximation, by the difference in surface temperature between these two
regions, not by the absolute temperature itself. Let us suppose that the atmosphere
warms uniformly and that the circulation does not change. Schematically, we can
set R=R(T,ω) where ωis the vertical motion. A simple regression of Rwith T
in the tropics that does not take into account that ωis spatially correlated with T
incorrectly suggests the existence of a “super-greenhouse effect” (27).
One attempt to avoid this circulation dependence is exemplified by Soden (28),
who averaged over the ascending and descending regions of the tropics and used
interannual variations produced by El Ni˜no as the source of variability. Figure 3
shows the evolution of Gclear averaged over the tropics for a 4-year period contain-
ing the El Ni˜no event in 1988. An increase in tropical-mean greenhouse trapping
of 2W/m2is observed in conjunction with a 0.4 K increase in tropical-mean
sea surface temperature. These tropical mean results are the small difference be-
tween larger regional changes that are dominated by the dramatic changes in the
pattern of ascent and descent that occur during El Ni˜no. There is no reason to
believe that global warming will be accompanied by similar circulation changes.
One can conceive of a number of ways in which the regional changes might be
nonlinearly rectified to produce a tropical mean infrared trapping that is different
in El Ni˜no warming and CO2-induced warming. Indeed, at face value, the results
in Figure 3 suggest a value of βH2Omuch larger than 0.4.
In recent years, efforts along these lines have been redirected away from at-
tempts at obtaining direct empirical estimates of climate sensitivity, and towards
providing a record of variability against which model predictions may be tested.
As an example, Figure 3 also shows the prediction of a climate model (one
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constructed at National Oceanic and Atmospheric Administration’s Geophysical
Fluid Dynamics Laboratory), when the observed sea surface temperatures are used
as a surface boundary condition. The model simulates the variations in clear-sky
infrared trapping very well, although studies of longer data sets suggest that the
response of the moisture field, and the ability of climate models to reproduce the
observed response, may differ from one El Ni˜no event to the next (29). One also
finds that the model does less well at simulating the observed variations in the net
outgoing radiation (solar plus terrestrial, including cloudy as well as clear skies),
once again strongly suggesting that the prediction of clouds and their radiative
properties are the central difficulty facing the model, not water vapor.
Empirical studies such as that in Figure 3 do not provide a direct proxy for
CO2-included warming. Rather, the degree of similarity between the observed and
modeled response of Gclear to changes in surface temperature provides a measure
ofconfidence in theabilityof the climatemodel to accurately representthe relevant
physicalprocessesinvolvedindeterminingGclear, and therefore tocorrectlypredict
thewatervaporfeedbackthatwouldoccurundervariousglobalwarmingscenarios.
Our dependence on models is unavoidable when analyzing a system as complex
as that maintaining our climate.
Climate Models
The idea of predicting the weather by integrating the equations governing the
atmospheric state forward in time was made explicit by V Bjerknes (30) in 1904.
LF Richardson (31) made the first serious, but famously unsuccessful, attempt at
gathering data to provide an initial condition and actually integrating a version of
these equations. At the dawn of the computer age, J von Neumann, J Charney,
and others realized that the resulting computational power would make numerical
weather prediction feasible. The success of this enterprise has been impressive
(32). Predictions of the atmospheric state for up to 10 days in advance continue
to improve, and the meteorological services of the world continue to be prime
customers of the largest supercomputers in existence, as more computer power
translates into better forecasts.
Building on this effort in weather prediction, through the 1960s and 1970s a
parallel effort began toward the development of numerical models of the Earth’s
climate. In climate modeling, the emphasis shifts to the long-term statistics
of the atmospheric (as well as oceanic and cryospheric) state, and the sensi-
tivity of these statistics to perturbations in external parameters, rather than the
short-term evolution from particular initial conditions. Because they are inte-
grated over longer periods, the spatial resolution of climate models is always
lower than that of state-of-the-art weather prediction models. In the past few
years global warming scenarios have typically been generated using atmospheric
models with effective grid sizes of roughly 200–300 kms, with 10 vertical lev-
els within the troposphere. An order of magnitude increase in computer power
allows roughly a factor of two decrease in the effective grid size. Climate warming
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WATER VAPOR/GLOBAL WARMING 453
scenarios with horizontal atmospheric resolution of 100 km and less will be-
come available in the next few years. Much more ambitious plans are being
laid. For example, the Japanese frontier Research System for Global Change
(http://www.frontier.esto.or.jp) has the goal of constructing a global climate model
with 10 km resolution.
There is a large gap between climate sensitivity experiments with compre-
hensive climate models and computations with simple models like the radiative-
convective model. Because of the turbulent character of atmospheric flows, the
complex manner in which the atmosphere is heated (through latent heat release
and by radiative fluxes modified by intricate cloud distributions) as well as the
rather complex boundary condition that the Earth’s surface provides, it has proven
difficult to develop models of an intermediate complexity to fill this gap, and the
continuing existence of the gap colors the sociology of the science of global warm-
ing. Building and analyzing climate models is an enterprise conducted by a small
number of groups with substantial computational resources.
Many processes occur in the atmosphere and oceans on scales smaller than
those resolved by these models. These scales of motion cannot simply be ignored;
rather, the effects of these small scales on larger scales must be approximated
to generate a meaningful climate. Some aspects of this closure problem have
been reasonably successful, whereas others are ad hoc or are based on empirical
relations that may not be adequate for understanding climate change. Skeptics
focus on these limitations. For a balanced view, it is useful to watch an animation
of the output of such a model, starting from an isothermal state of rest with no
water vapor in the atmosphere and then “turning on the sun,” seeing the jet stream
developandspin off cyclones andanticycloneswith statistics thatclosely resemble
those observed, watching the Southeast Asian monsoon form in the summer, and
in more recent models, seeing El Ni˜no events develop spontaneously in the Pacific
Ocean.
The first results of the sensitivity of such a climate model to an increase in
CO2were presented in 1975 by Manabe & Wetherald (33) with an atmosphere-
only model over an idealized surface with no heat capacity, no seasonal cycle,
and with fixed cloud cover. The equilibrium sensitivity of global mean surface
temperature obtained was 3 K for a doubling of CO2. The model produced
only small changes in relative humidity throughout the troposphere and thereby
provided the first support from such a model for the use of the fixed–relative
humidity assumption in estimates of the strength of water vapor feedback. The
model’s temperature sensitivity was increased over that obtained in the simpler
radiative-convective models primarily because of the positive surface albedo feed-
back, the retreat of highly reflective snow and ice cover near the poles, which
amplifies the warming. (This extra warming is not confined to high latitudes,
as midlatitude cyclones diffuse some of this extra warming to the tropics as
well). The flavor of more recent research on climate sensitivity with global mod-
els can be appreciated by sampling some of the efforts listed in the references
(34–39).
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As climate models have evolved to include realistic geography, predicted cloud
cover, and interactions with sea ice and ocean circulation, certain robust conclu-
sions have emerged. In particular, all comprehensive climate models of which we
are aware produce increases in water vapor concentrations that are comparable to
those predicted by fixing the relative humidity. Differences in equilibrium sensi-
tivity among different models appear to be due primarily to differences in cloud
prediction schemes and, to some extent, the treatment of sea ice, and only in a mi-
nor way to differing predictions of water vapor distribution. This point was made
very clearly by the intercomparison study of Cess et al (40), in which a variety of
atmospheric models in an idealized setting were subjected to a uniform increase
in surface temperature. The changes in net radiation at the top of the atmosphere
in the clear sky were generally consistent across the different models, and consis-
tent with fixed relative humidity radiative computations. The total-sky (clear plus
cloudy) fluxes were much less consistent across models.
Recently, Hall & Manabe (41) have artificially removed the radiative conse-
quences of increasing water vapor from a full coupled atmosphere-ocean climate
model. The sensitivity of their model is reduced by more than a factor of 3.5. As
described in the following section, this large response can be understood, to a
rough first approximation, by taking into account how water vapor feedback can
interact with other feedbacks.
The Simplest Feedback Analysis
We can take ice/snow albedo feedback into account schematically by assuming
that Iin equation 1 is a function of T. We then have instead of equation 7,
dT
dlog2CO2=10
1βH2OβI,9.
where
βIS
I
I
T.R
T.10.
Suppose that the strength of the ice/snow albedo feedback has the value of βI=
0.2. In the absence of water vapor feedback, albedo feedback of this strength
increases the temperature response to CO2doubling from1Kto1.25 K. How-
ever, in the presence of water vapor feedback of strength βH2O=0.4, albedo feed-
back increases sensitivity from 1.67 K to 2.5 K. The key here is that the water
vapor and ice/snow albedo perturbations feed on each other, with less ice imply-
ing warmer temperatures, implying more water vapor, and so on. The existence
of strong water vapor feedback increases the importance of other temperature-
dependent feedbacks in the system.
Suppose now that we have a variety of models, all with βH2O0.4, but
that produce sensitivities from 1.5–4.5 K for doubling of CO2, owing to dif-
fering treatments of other temperature-dependent feedbacks (cloud cover as well
as ice and snow). Figure 4 shows the range of sensitivities that would result if βH2O
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Figure 4 The change in surface temperature 1Tsfor doubled CO2as a function of the water
vaporfeedbackparameterβH2O.Resultsareshown for twodifferentscenariosofothertemperature-
dependent feedbacks βother that encompass the current range of predictions in 1Ts=1.5–4.5K
when βH2O=0.4.
had a smaller value in these models. If there were no water vapor feedback, the
maximum sensitivity would be close to 1.5 K, which is the minimum sensitivity
for βH2O=0.4. The figure also predicts a result roughly consistent with the Hall
and Manabe coupled model in which water vapor feedback alone is suppressed,
given that that model’s sensitivity is greater than 3.5 K for CO2doubling.
Because cloud and water vapor feedbacks are obviously related at some level,
they are often confused in popular discussions of global warming. In the current
generation of climate models, water vapor feedback is robust and cloud feedback is
not. A robust water vapor feedback sensitizes the system, making the implications
of the uncertainty in cloud feedbacks of greater consequence.
The total radiative effect of increases in water vapor can be quite dramatic,
depending on the strengths of the other feedbacks in the system. For the remainder
of this review we return our focus to water vapor feedback in isolation, represented
by βH2Oin the preceding discussion.
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THE CLIMATOLOGICAL RELATIVE HUMIDITY
DISTRIBUTION
The Global Picture
In Arrhenius’ and Chamberlin’s time, discussions of water vapor feedback neces-
sarily took place without knowledge of the climatological distribution of humidity
except near the Earth’s surface. With the advent and continued maintenance of the
remarkable network of twice-daily balloon ascents, designed for weather forecast-
ing after World War II, the climatological water vapor distribution throughout the
troposphere began to be defined with greater clarity. However, the routine mea-
surement of water vapor, especially in the upper troposphere, is inherently more
difficult than that of temperature and winds, owing in part to problems of contam-
ination as instruments pass through the far wetter lower troposphere. [See Elliott
& Gaffen (42) on the difficulties in using the water vapor fields from the weather
balloon, or radiosonde, network for climate studies.] Additionally, there are rela-
tively few radiosonde ascents in the dry subtropical regions of special interest to
the water vapor feedback debate.
Satellites fill this gap nicely, however. By measuring the upwelling radiance in
different spectral bands that are sensitive to absorption by water vapor, one can ob-
tainmeasurementsof water vapor concentrations in variouspartsoftheatmosphere
(43). An example of our current remote sensing capabilities is shown in Figure
5 (see color insert), which depicts the distribution of relative humidity averaged
over the upper troposphere. Note the presence of deep convective clouds (white),
detraining cirrus anvils (gray), the convective moistening of adjacent regions of
high relative humidity (red ), and the gradual reduction in relative humidity as air
is expelled from convective towers and is carried towards the subtropics, subsiding
and warming owingto adiabatic compressionalong theway, ultimately resulting in
relative humidities <10%. An international network of satellites provides global
observations of water vapor several times a day and has greatly enhanced our
understanding of its distribution and its radiative effects. Although the measure-
ments shown in Figure 5 are limited to cloud-free regions, satellite sensors capable
of penetrating cloud cover also exist, thus enabling observations of water vapor
under nearly all weather conditions. Whereas better observations would allow us
to test models more definitively, the existing radiosonde/satellite database leaves
little room for major surprises concerning the climatological distribution of water
vapor in the troposphere.
Operational weather prediction centers gather water vapor, temperature, and
wind data from all available sensors, including satellites and radiosondes, and
combine these with predictions from previous forecasts to generate their best es-
timate of the current atmospheric state for use as the initial condition for the
next forecast. Figures 6 and 7 show the relative humidity fields generated by
the European Centre for Medium-Range Weather Forecasting, averaged in time
over the month of July 1987. Figure 6 is an average over longitude. Figure 7 is a
horizontal map of the vertical average over the free troposphere, excluding the
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Figure 6 Height-latitude cross sections of the zonal-mean relative humidity for July 1987 as produced by the European Centre
for Medium-Range Weather Forecasts (ECMWF) analysis system (left) and predicted by the GFDL (Geophysical Fluid Dynamics
Laboratory) General Circulation Model (GCM) (right).
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Figure 7 The geographic distribution of relative humidity, vertically averaged over the free troposphere for July 1987 from
the ECMWF (European Centre for Medium-Range Weather Forecasts) analyses (left) and the GFDL GCM (Geophysical Fluid
Dynamics Laboratory General Circulation Model) (right).
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lowest 2 km. Also shown are the comparable relative humidities from a climate
model in use for global warming and atmospheric dynamics studies in our labora-
tory (34,44), assuming as a surface boundary condition the observed sea surface
temperatures from the same time period.
The general features of the humidity distribution are similar in both the opera-
tional analyses and the General Circulation Model (GCM). Note the high values of
relative humiditywithin theplanetaryboundary layernear thesurface; theinterme-
diate values in the free troposphere in midlatitudes, the dryness of the subtropics,
and the high values near the equatorial tropopause. Detailed evaluations of the
GCM climatologies indicate that most models compare favorably with satellite
observations of the vertically-integrated water vapor mass, although there is a ten-
dency in many GCMs to underestimate the water vapor concentrations by about
5% (45,46).
The Planetary Boundary Layer
Intheplanetaryboundary layer,the lowest1–2 km, strongverticalturbulentmixing
strives to create a layer of uniform mixing ratio, which given the decrease in
temperature with height forces the relative humidity to increase with height. This
mixing results in a layer of maximum cloudiness near the top of this layer, and
dries the air in the immediate vicinity of the surface, reducing the relative humidity
in the lower parts of the boundary layer to 80%, on average.
Most of the Earth’s surface is ocean, and evaporation Efrom the ocean can be
modeled as proportional to the difference between the saturation vapor pressure at
the surface temperature T*and the vapor pressure in the atmosphere at some small
convenient reference height (typically taken to be 10 m), where the temperature is
Taand the relative humidity is Ha:
EC[es(T)Haes(Ta)].11.
The constant of proportionality Cis itself roughly proportional to the wind speeds
at this reference height. We can rewrite this expression as
EC[es(T)(1Ha)+Ha(es(T)es(Ta))].12.
The temperature difference T*Tais small enough (especially in the tropics,
where Eis the largest) that the term proportional to 1 Hais the larger of the two
terms in Equation 12. Suppose the surface and atmosphere both warm by2Kand
the vapor pressure in the atmosphere does not increase. Hawould decrease from
0.8 to 0.7, and 1 Hawould increase by 50%. The surface winds are highly
unlikely to change dramatically enough to compensate for this large effect. The
energy for this increased evaporation would have to come from the net downward
radiation at the surface, which cannot plausibly change by this amount for such a
small temperature change. On this aspect of the problem there is little controversy:
Water vapor in the boundary layer will increase as climate warms to prevent the
near-surface relative humidity from decreasing appreciably.
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The Free Troposphere
It is useful to have in mind an explicit, even if oversimplified, picture of the main-
tenance of subsaturation in the free troposphere in order to appreciate the pat-
terns in Figures 6 and 7 and discuss their sensitivity. Recall first that the water
vapor mixing ratio ris conserved as air parcels are carried by the winds, except
for the sources and sinks of vapor. Assume that an air parcel is brought to satu-
ration whenever it comes within the planetary boundary layer, and that this is the
only source of vapor. Assume also that whenever erises above es, condensation
immediately reduces eto esand that rain removes all condensate instantaneously
without moistening the underlying atmosphere.
Nowpickalocationwithintheatmosphere,x,withtemperatureTandpressurep.
The mixing ratio at this point, at a particular time, can be computed by examining
the trajectory of the air parcel at this location. Assuming that the parcel is not
saturated, follow this trajectory backwards in time until one encounters the point
at which saturation last occurred. Label the temperature and pressure at this
point Tcand pc. (If the parcel is already saturated, set Tc=Tand pc=p.) In
general, this condensation point will occur at lower pressure pc<p, where Tcis
sufficiently cold; an unsaturated parcel has most likely subsided since it was last
saturated. The vapor pressure at this point is es(Tc). Conserving mixing ratio
along the trajectory, one finds that vapor pressure at the original point xis given by
(p/pc)es(Tc). To compute the time-averaged vapor pressure, one needs to think of
Tcand pcas suitably averaged using the ensemble of trajectories that pass through
xat different times. As climate changes, the degree of subsaturation at xwill be
affected by changes in T(x) and in Tcand pc. In practice the changes in pcare
not very important, and we can think of ees(Tc). It is not difficult to show
that fixing TTcis now practically equivalent to fixingH. Therefore, within this
simple model, the assumption of fixed relative humidity is in practice equivalent to
the assumption that the change in the temperature of last saturation is on average
similar to the temperature change itself.
The most important effects ignored in this picture are those due to transport and
subsequent re-evaporation of the condensed phase. We return to this complication
below.
One can imagine the change in Tcdiffering from the change in Tfor a variety of
reasons. For example, one can imagine that the warming is spatially uniform but
thattheverticalexcursionsofair parcels increase in extent,sothatthetypical parcel
reaching point x last experienced saturation at a higher altitude where the temper-
ature is colder, thereby causing Tcto increase less than it otherwise would. The
result would be an increase in TTcand a reduction in H. The assumption of fixed
TTcor Hcan be thought of as a conservative stance in the absence of convincing
demonstrations to the contrary from models of the atmospheric circulation.
Outside of the tropics, poleward of 30, the cyclones and anticyclones exert
primary control on the relative humidity above the boundary layer (47). In these
extratropical circulations, typical trajectories projected onto the latitude-vertical
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Figure 8 A height-latitude schematic of the large-scale atmospheric trajectories involved
in the transport and mixing of moisture within the troposphere.
plane are as shown schematically in Figure 8, with poleward moving air rising and
equatorward moving air descending. The slopes of these trajectories typically take
airfromthe boundary layer in thesubtropicstothetropopause in subpolar latitudes.
Relatively dry air is produced by lifting moist subtropical boundary layer air along
these slantwise paths in the warm sectors of extratropical waves, precipitating out
much of this water, and then descending while returning equatorward.
With this picture in mind, there is no reason to expect that relative humidity will
be exactly maintained in this region as the climate warms. Changes in the strength
or paths of the mid-latitude storms, and the associated trajectories of air parcels,
could alter the relation between the local temperature change and the average tem-
perature change at the point of last saturation. However, the scale of these storms
isrelativelylarge and reasonablywell simulated inclimate models. Changes inthe
extratropical circulation predicted by these models, although potentially of conse-
quence for regional weather patterns, are not large enough to substantially modify
the relative humidity of the extratropical atmosphere as a whole. Distortions due
to subgrid scale processes are less worrisome in extratropical latitudes than in the
tropics, and there is less reason to question the generic model prediction of small
changes in relative humidity.
Before turning to the tropics, we pause to explain why the free troposphere in
the tropics is of primary concern in any analysis of water vapor feedback.
RELATIVE IMPORTANCE OF DIFFERENT PARTS OF THE
TROPOSPHERE FOR WATER VAPOR FEEDBACK
Fixattention ona horizontal locationat a particulartime of year. Giventhe vertical
profile of temperature, water vapor, and cloud aerosols, andthe CO2concentration,
wecancompute the outgoing infraredfluxRusinga radiativemodel. Fixingclouds
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and CO2, and dividing up the atmosphere in the vertical into a number of layers N,
we can think of Ras a function of the surface temperature and of the temperature
and the water vapor pressure in each of these layers. We can then linearize around
the values of these temperatures and water vapor pressures in the current climate
to compute the sensitivity of Rto each of these values
δR=
N
X
k=1·R
TkδTk+R
ekδek¸.13.
Rather than treat the dependence on surface temperature separately, we assume
thatthe change in temperatureatthe surface is equaltothechange in temperaturein
the lowest atmospheric layer, and include the response to the surface temperature
change in R/∂Tkwithin the lowest layer.
The vapor pressure change required to maintain fixed relative humidity, H,in
the face of a small temperature change δTis H(des/dT)δT.If(a)His assumed to
be unchanged and if (b) the temperature change is spatially uniform, then
δR=
N
X
k=1£Qk
T+Qk
e¤δT,14.
where
Qk
TR
Tk;Qk
eR
ekHdes
dT .15.
The temperature change that produces a given global and annual mean change
in outgoing infrared radiation δRis
δT=δR
MT+Me=δR/MT
1βH2O,16.
where
MT
N
X
k=1
Qk
T;Me
N
X
k=1
Qk
e17.
and
βH2O=−M
e
M
T.18.
The overbar refers to an average over latitude, longitude, and season.
Figure 9 (see color insert) shows a particular estimate of the functions Qeand
QTobtained by the authors. We divide the atmosphere into 10 layers of equal mass
in the vertical, use temperature and humidity data from the European Centre for
Medium-Range Weather Forcasting, and cloud data from the International Satel-
lite Cloud Climatology Project (48). We also average over longitude for display
purposes, and show the result for July only. We obtain from these results that
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βH2O0.33 owing to infrared effects alone. Solar absorption, not discussed in
detail here, increases this to 0.38
ThefunctionQTisstronglyaffectedbytheclouddistribution. Whereupperlevel
clouds are prevalent, the outgoing infrared radiation is most sensitive to tempe-
ratures at the level of these emitting surfaces, and is relatively insensitive to tem-
peratures deeper in the atmosphere. Where skies are clearer, lower tropospheric
temperatures control the outgoing flux.
The function Qeprovides one view of the relative importance of different levels
and latitude zones for the strength of the infrared water vapor feedback. If temper-
atures change uniformly and if relative humidities remain unchanged, this figure
tells us how much of the reduction in outgoing radiation is due to the water vapor
in different regions. One sees that the middle and upper troposphere dominates
the feedback under these conditions. This is a critical and at first glance, perhaps,
a surprising result, given the distribution of vapor, which thins very rapidly as one
moves upwards. The centers of water vapor spectral lines are fully saturated under
atmospheric conditions, and the photons emitted from the lower troposphere can
only escape to space if they are emitted from the wings of spectral lines, where
the upper tropospheric absorption is sufficiently weak but where the emission is
correspondingly inefficient. Emission from the upper troposphere occurs closer
to the centers of these lines, where the emission is stronger.
Figure9showsthat the subtropical dryzonesaresomewhatmoreimportant than
the moister zone in the deep tropics for the strength of the fixed relative humidity
water vapor feedback. This feature is a consequence of the presence of clouds. If
clear skies are assumed to exist everywhere, the maximum in this figure shifts to
the moister regions in the tropics.
The question of the relative importance of different regions for water vapor
feedback is a source of some confusion in the literature. In assessing this relative
importance, one approach has been to assume equal fractional perturbations in
mixing ratio (or, equivalently, vapor pressure), as in Shine & Sinha (6):
δee.19.
Alternatively, Spencer & Braswell (49) perturb the relative humidities in different
regions by equal amounts, so that
δees,20.
which weights dry regions more strongly, thereby emphasizing the free tropo-
sphere at the expense of the boundary layer and the subtropics over the tropics,
as compared with Shine & Sinha. With the normalization we have chosen, the
uppertroposphere is alsoweighted more heavilythanin Shine & Sinhabecause the
assumption of fixed relative humidity for a uniform temperature change requires
δee
es
des
dT e
T2.21.
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However, the weight of the subtropics versus the tropics, which have similar
temperatures, is similar to that obtained with Equation 19; the dry subtropics
are weighted much less heavily than in Spencer & Braswell (49).
There is no ambiguity as to how to compute the relative importance of different
regions for water vapor feedback in a model that predicts changes in water vapor
concentrations; the confusion only arises from differing presumptions as to a
plausible model-independent starting point. Our justification for Equation 21 is
only that it better resembles GCM predictions.
Low resolution can make a climate model too diffusive and can result in the dry
regions of the troposphere being too moist. Yet the radiative transfer is such that,
foragiventemperatureprofile, changes in the absorptivityareroughlyproportional
to changes in the logarithm of the water vapor concentration (24). If the changes
in vapor pressure are proportional to the vapor pressure itself (as in Equations 19
or 21) the impact on sensitivity of such errors in mean humidity is small. Only if
one assumes that the fractional changes in vapor pressure are much larger in dry
than in moist regions, as implied by Equation 20, can one argue that the absence
of very dry regions in a climate model seriously distorts the sensitivity.
An additional source of confusion is that some studies assume clear skies in
the radiative computation. This has the consequence of inappropriately weighting
the lower troposphere, since clouds interfere with the outgoing infrared radiation
emitted by the lower troposphere more frequently than that from the upper tropo-
sphere. If we regenerate Figure 9 (top) assuming clear skies, the maximum values
occur much lower in the troposphere, in the 500–600 millibar (mb) layer.
If temperature changes are uniform and relative humidities remain unchanged
as the climate warms, these results show that the humidity response in the free
troposphere above 800 mb is responsible for almost all of the infrared water vapor
feedback, leaving only 10% to be contributed by the boundary layer. Roughly
55% of the total is due to the tropical free troposphere (30N–30S)(N=North;
S=South), and 35% to the extratropics. Of this tropical contribution, about
two-thirds, 35% of the total, is due to the upper half of the troposphere, from
100–500 mb.
Ifrelativehumidity does changeand if thetemperature changes arenot spatially
uniform, one can generalize Equation 16 to read
δT=δR
MT+Me=δR/MT
1βH2O,22.
where now
MT
N
X
k=1
Qk
Tδ˜
Tk;Me
N
X
k=1
Qk
eδ˜
ekδ˜
Tk.23.
δT*is the change in mean surface temperature, δ˜
Tis the temperature change
normalized by δT*, and δ˜
eis the vapor pressure change normalized by the vapor
pressure change required to maintain fixed H. The kernels Qk
Tand Qk
ein Figure 9
are unchanged.
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Thetemperature changes predictedby climate models arenot spatially uniform.
A very robust feature across models is the polar amplification of the temperature
signal, which implies that δ˜
Tis larger than unity in high latitudes, thereby en-
hancing the extratropical as opposed to the tropical contribution to water vapor
feedback. Of potentially greater importance, many climate models predict that
warming in the tropics will be larger in the upper troposphere than in the lower
troposphere (50), ultimately because the moist adiabatic lapse rate decreases with
increasing temperature. If this is the case, and if His fixed, the tropical upper
troposphere becomes even more dominant in its contribution to Me. But MTalso
increases in value, because the outgoing infrared radiation is sensitive to the tem-
perature of the cloud tops [as in Figure 9 (bottom)]. As a result, the value of βH2O
does not increase significantly. In fact, we have found it difficult to raise βH2O
much above 0.4 for any plausible temperature change profiles, with fixed relative
humidity. [We caution the reader that water vapor feedback is often defined with
δ˜
T1inM
T(21, 51)]. Similarly, estimates of βH2Oare also insensitive to modest
biases in the water vapor climatology that may be present in a climate model. For
example, introducing a dry bias of 5%, which is typical of that found in many
GCMs (45, 46), into the humidity climatology used in Figure 9 results in less than
a 3% bias in the corresponding estimate of βH2O.
Extending the approach of Hall & Manabe (41), one can artificially remove the
effect of the water vapor perturbations on radiative fluxes in a climate model, but
onlyinoneregionat a time. Schneider et al (52)haverecentlypresentedananalysis
of this kind, which suggests that extratropical moisture is of greater importance for
climatic sensitivity than is implied by the purely radiative computations leading
to Figure 7. The reasons for this difference are unclear at present.
THE CONTROVERSY CONCERNING WATER
IN THE TROPICAL FREE TROPOSPHERE
The Complexity of the Tropics
When different groups attempt to construct numerical simulations of an incom-
pletely understood complex system, one might hope that intercomparisons of the
sort described by Cess et al (40) would indicate where the major uncertainties lie.
But it is also possible that all models are making similar mistakes. Indeed, it has
been argued that global climate models all err in their treatment of water vapor
in similar ways, particularly in the tropics (53–57). The source of this concern is
the fact that much of the vertical transport of heat, momentum, and moisture in
the tropics occurs on scales of a few kilometers or less, in turbulent eddies gener-
ated by moist convection, scales that are not explicitly resolved in global climate
models.
Figure 10 (see color insert) is a scene from a numerical simulation (58) of a
small part of the tropical atmosphere, with horizontal extent 130 km ×130 km,
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which is about the the size of a single grid cell in a global climate model. This
simulation has a horizontal resolution of 2 km, which is barely sufficient to resolve
theenergy-containing eddies ofthe moist convectiveturbulence that dominatesthe
convectively active parts of the tropics. Such models have been under develop-
ment for several decades, but it is only recently that computer power has become
sufficient that they can be integrated over the time required for the atmosphere
to equilibrate, through radiative and convective fluxes, with the underlying sur-
face, even over such small domains (59–62). We estimate that a research group
would require at least a petaflop (1015 floating point operations per second) of
computer power to perform useful climate sensitivity experiments with a global
model at this resolution. Unfortunately, we already know that models of this class
are themselves dependent in important ways on assumptions concerning cloud
microphysics, the micron-scale physics of individual water drops that controls the
cloud droplet (and ice particle) size distributions to which the radiative transfer,
among other things, is sensitive.
It is the existence of these layers of complexity on ever smaller scales, which
potentially play a particularly important role in the tropics, that fuels the debate
on the reliability of GCM climate predictions and the robustness of water vapor
feedback in particular.
One can sense an increasing uneasiness, and an increasing focus on the tropical
upper troposphere, in this series of excerpts from the reports of the Intergovern-
mental Panel on Climate Change from 1990, 1992, and 1995.
1990: “The best understood feedback mechanism is water vapor feedback,
and this is intuitively easy to understand” (63).
1992: “There is no compelling evidence that water vapor feedback is
anything other than positive—although there may be difficulties with upper
tropospheric water vapor” (64).
1995: “Feedback from the redistribution of water vapor remains a substantial
source of uncertainty in climate models—Much of the current debate has
been addressing feedback from the tropical upper troposphere” (65).
At least three distinct mechanisms have been suggested by which changes in moist
convection in the tropics could reduce the strength of water vapor feedback. As
the climate warms, the temperature of the upper tropospheric outflow from the
convective cores could increase less than the temperature itself; the condensate
amounts in this upper tropospheric outflow could decrease; and the precipitation
efficiency of the convection could increase.
Convective Outflow Temperatures
A simple picture that serves as a starting point for thinking about the tropical
circulation is one in which air is subsiding everywhere except in convectively
active areas in which there is concentrated upward motion. The subsidence is
weak, requiring a few weeksto take airfrom the uppertroposphere to the boundary
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WATER VAPOR/GLOBAL WARMING 467
layer; its strength is determined by the rate at which the air cools radiatively. The
upwardmotionismuch stronger, and is confinedtoasmallfraction of the totalarea.
The outflow from theseconvective areas isat its largest near 200 mb, just below the
tropopause. When air emerges in thisoutflowit is at ornear saturation, as inFigure
5. As the air subsides, the adiabatic warming due to compression accompanying
thedescent will producerelativehumiditiesas low as afewpercentbefore reaching
the boundary layer, assuming that no moisture is added to the parcel.
In this simple picture of the tropics, the relative humidity is tightly coupled to
thecharacteristic temperature ofthese convectiveoutflowsbeneaththe tropopause,
as this will be the temperature of last saturation, Tc, for much of the tropical
troposphere. R Lindzen’s initial critique of water vapor feedback (53) argued that
this outflow temperature should, in fact, warm less than the temperature at a fixed
location in the troposphere; it might possibly even cool as the troposphere warms.
One expects deeper convection in a warmer atmosphere, in which the boundary
layer air contains more moisture. If the height of the convection increases enough
that the extra cooling obtained by following a moist adiabatic profile to higher
levels over-compensates the warming at a given level, Tcwould decrease and
water vapor feedback from the bulk of the tropical troposphere would be negative.
Even if Tcincreases, but not as much as Titself, the positive water vapor feedback
would still be weakened.
Thedepth of moistconvectiondoes increase inall climate modelsasthe climate
warms. The characteristic temperature of the outflow from the deepest convective
cells must therefore increase less than does the temperature at fixed height. One
might expect these models to show large reductions in tropical relative humidity
on this basis, but this does not occur. It has sometimes been argued that numer-
ical deficiencies prevent the memory of the water vapor mixing ratio from being
retained during the slow descent through the model’s troposphere. However, in
a recent study it has been shown that air parcel trajectories accurately computed
from the wind fields generated by a global model predict humidity distributions
that differ only slightly from the distribution in the model (66). A far more plausi-
ble explanation is that air parcel trajectories in the tropics are more complex than
envisioned in this simple picture.
The tropical atmosphere is far moister than it would be if most of the air in the
tropics last experienced saturation just below the tropopause. Yet detailed stud-
ies of observed air parcel trajectories (67–69) confirm that the tropical humidity
distribution in the free troposphere can indeed be understood by following tra-
jectories backwards in time to obtain the temperature of last saturation. Several
elements must be added to our idealized picture of the tropics to make it more re-
alistic. When moist convection occurs, a spectrum of convective cores of different
vertical extents expel saturated parcels at different levels, and horizontal motions
carry air into and away from convective centers throughout the troposphere, mix-
ing moisture into drier regions. Finally, whereas some of air in the very driest
parts of the tropics can be traced back directly to the cold trap at the top of the
deepest convective cores, some of this air is also mixed in from mid-latitudes (70).
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468 HELD ¥SODEN
More research is required to understand how the statistics of this complex set of
trajectories changes as climate warms, so as to better understand why the relative
humidities in models do not decrease as much as one might suspect based on the
change in temperature of the deepest convective outflows.
Condensate
Cloud anvils form near the tops of convective regions, and the more condensate
(primarily ice) that is held in these regions without precipitating, the moister the
atmosphere will be. As an air parcel is expelled from a convective region and
begins to subside and warm, this ice must first sublimate or fall and evaporate into
unsaturated layers before the relative humidity can begin to fall. One can argue
that the relative humidity of the tropics will decrease if the amount of condensate
produced in the convective outflows decreases (56).
A prerequisite for the plausibility of this argument is robust evidence for an
effect of condensate on the present-day humidity distribution, since we require
this effect to weaken as the climate warms in order to weaken the water vapor
feedback. This case has not been made convincingly. Indirect evidence to the
contrary is provided by the tropical trajectory studies referenced earlier, in which
models with no condensate are able to reproduce much of the observed humidity
distribution. Additionally, many climate models attempt to incorporate prediction
equationsforthe condensed phases ofwater. Whilemodificationstotheseschemes
certainly have a dramatic influence on cloud feedback (71), there are no reports
that the prediction of condensate reduces water vapor feedback.
The intuition on which this argument is based is that the convection in a warmer
climate will be more intense, but occupy a smaller fraction of the horizontal area
of the tropics at any one time. There is no direct evidence for this claim at present.
Convection-resolving models of the sort pictured in Figure 10 (see color insert),
when integrated to a radiative-convective equilibrium, albeit in idealized geome-
tries of small spatial extent, generally do not predict a reduction in upper tropo-
spheric ice cloud concentrations as the temperature is increased; to first order they
typically predict that the distribution is simply shifted upwards consistent with the
deeper troposphere (59,62).
If there are reductions in upper level cloud coverage in the tropics as climate
warms, these will directly reduce climate sensitivity by removing the infrared trap-
ping due to the clouds themselves. The climate modeling community has admitted
and been frustrated for years by its inability to converge on robust estimates of
such cloud feedbacks. But this uncertainty should not obscure the fact that cli-
mate models do all possess a strong water vapor feedback which, as we have seen,
sensitizes the system to possible cloud feedbacks, whether positive or negative.
Precipitation Efficiency
Closureschemesformoist convectioninclimatemodels differin their precipitation
efficiency—the ratio of the water rained out to that condensed, the remainder
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WATER VAPOR/GLOBAL WARMING 469
re-evaporating as it falls and moistening the air. As a result, closure schemes differ
in the relative humidity of the mid-troposphere in convecting regions. (Higher in
the troposphere, all schemes agree that the atmosphere is quickly driven close to
saturationby the convection). It has been argued(55–57)thattropical precipitation
efficiency could increase in a warmer world, for microphysical reasons related to
an increase in the rate of coalescence of small into large drops, causing the mid-
troposphere to dry. The quantitative relevance of this argument is difficult to
evaluate in the context of global climate models in which the convective motions
are not explicitly resolved.
The issue is more readily addressed in integrations of convection-resolving
models in idealized geometries (59,62). We are unaware of simulations of this
type that demonstrate a significant effect of this kind.
This argument is complementary to the previous two, in that it requires that the
mid-tropospheric humidity in the convective regions be mixed horizontally into
the rest of the tropics. If the bulk of the trajectories pass through the cold trap in
the upper troposphere before descending, any information about mid-tropospheric
humidities in the convecting regions will be lost. The single-column models of the
tropics on which these arguments are typically based provide an extreme limiting
case in which the horizontal mixing can be thought of as perfectly efficient, and
so overestimate the impact this effect can have on the rest of the tropics, even if
one accepts the microphysical arguments.
Empirical Studies
In order to help evaluate these critiques of the treatment of convection in cli-
mate models, a variety of studies have been undertaken using satellite data, the
radiosonde network, and analyses of the atmospheric state generated through nu-
mericalweatherprediction. In addition to thetrajectoryanalysesmentioned above,
numerous investigators have focused on local relationships between convection
and upper tropospheric water vapor (72–76). These studies demonstrate that deep
convection serves to moisten the upper troposphere locally and that global climate
models are reasonably successful in reproducing the observed relationships be-
tweenconvectionanduppertropospheric water vapor on regionalscales. Giventhe
need to analyze water spatially integrated over entire circulation systems (77,78),
investigations of such large-scale behavior (27, 28,79) have also been undertaken,
focusing primarily on clear-sky greenhouse trapping rather than humidity itself.
The agreement with climate models is often quite impressive, as in Figure 3 and in
Inamdar& Ramanathan’s study (80)of the sensitivityofthe global-mean clear-sky
greenhouse trapping to surface temperature.
An exception is the study of Sun & Held (81), in which an attempt is made to
use the radiosonde database to relate tropical mean humidity at different levels in
the troposphere to the mean surface temperature on El Ni˜no time scales. At face
value, the results imply that the humidity increases less rapidly with increasing
temperature than in the models examined, and that the observed free tropospheric
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470 HELD ¥SODEN
humidity and surface temperatures are less strongly coupled than in the model.
Sun & Held state that their observed regressions, if applied uncritically to the
global warming problem, imply that the model is overestimating the global mean
water vapor feedback by 15%. In light of the estimates presented above, we
now believe that the stakes are somewhat higher—closer to 25%. However, the
adequacy of the radiosonde data for drawing this conclusion is suspect due to
the lack of observations over vast regions of the tropical oceans, as Sun & Held
themselves observed. Indeed, comparison with satellite observations have clearly
highlightedtheinability of the radiosondenetworktoaccuratelymonitor variations
in tropical water vapor (82). It is also difficult to reconcile the Sun & Held result
with analysis of the tropical mean clear-sky greenhouse trapping (28).
Other pieces of information exist that, taken together, increase our confidence
in the existence of strong water vapor feedback. As one example, models with
strong water vapor feedback, when forced with ice-age boundary conditions and
CO2concentrations, produce sea surface temperature changes that are consistent
with paleo-data in the tropics (83), although the error bars on ice-age tropical
ocean temperatures remain disturbingly large due to the difficulty of reconciling
different paleo-temperature indicators.
In addition, the observed twentieth century warming is itself difficult to recon-
cile with a greatly reduced climate sensitivity. An alternative to the theory that
greenhouse gases have been responsible for the bulk of the observed warming
is that it is simply due to natural climatic variability. But the natural variability
on long time scales is sharply reduced when water vapor feedback is artificially
removed from a climate model (41). One can think of stronger “spring constants”
as reducing the response to internally generated noise as well as the response to an
external force. It is thus doubly difficult to explain the observed twentieth century
record with such a stiff model.
Finally, empirical confirmation or refutation of the models will surely emerge
eventually from the analysis of trends in water vapor. Some careful regional
studies have documented increasing amounts of tropospheric water vapor over
North America (84), China (85), and the tropical western Pacific (86). One study
of trends over the tropics as a whole (87) claims a downward trend, but the data
quality has been questioned (88), and discrepancies are found when compared to
other data sets (89). None of these studies focus specifically on upper tropospheric
water vapor, for which the radiosonde data are more problematic.
We have examined the tropical water vapor trends simulated in global warming
scenarios generated with a model developed in our laboratory. Five realizations
have been generated (34) so that one can compare the externally forced signal
with the model’s natural variability. The linear trend in the tropical mean water
vapor mixing ratio at 200 mb, computed from the years 1965–2000, ranges among
the different realizations from a low of 1.5%/decade to a high of 3.7%/decade.
The trends near the surface are closer to 1%/decade. This large upper tropospheric
moistening is dependent on the fact that the warming in the model tropics is
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WATER VAPOR/GLOBAL WARMING 471
top-heavy—more so than in the observed warming of the past few decades (50).
Therefore, this is an upper bound on the moistening that we expect to be occurring.
Even so, the model’s natural variability suggests that the current 20-year satellite
record is not long enough for unambiguous detection of trends in humidity, even
if there were no issues with regard to changing instrumentation.
FINAL REMARKS
No empirical or model/data comparisons suggest that water vapor feedback is
negative, even in the tropical upper troposphere. Indeed, models with strong water
vapor feedback, comparable to that obtained in simple models with fixed relative
humidity,areabletosimulatemanyaspectsoftheobservedstructureandvariability
of the humidity field.
Our tests of models are limited to observations of natural climate variability
and thus provide information on the validity of the mechanisms that maintain and
modify the distribution of water vapor within the models, rather than direct con-
firmation of the predictions of increasing vapor accompanying global warming.
This difficulty will persist until observed time series are compiled with sufficient
accuracy and length to detect trends in water vapor on a global scale. Given the
acceleration of the trends predicted by many models, we believe that an additional
10 years may be adequate, and 20 years will very likely be sufficient, for the com-
binedsatelliteandradiosondenetworkto convincinglyconfirmorrefute the predic-
tions of increasing vapor in the free troposphere and its effects on global warming.
Current climate models invariably support the estimates of the strength of wa-
ter vapor feedback obtained from the simplest assumption that relative humidity
remains unchanged as climate warms. These numerical models are simply tools
we use to generate the climates consistent with our hypotheses regarding the rel-
evant physics, including our hypotheses as to how best to treat unresolved scales
of motion. If one has a coherent idea for a mechanism that might reduce climate
sensitivity, one should be able to incorporate the idea in an idealized and tentative
way into a comprehensive climate model. This would enable the community to
quantitatively evaluate competing theories about the strength of water vapor feed-
back, rather than relying on qualitative arguments. If a weak water vapor feedback
climate model could be constructed, climate modelers could then analyze it sys-
tematically to see if its fit to data is comparable to or better than other models. No
such model currently exists.
ACKNOWLEDGMENTS
We wish to express our thanks to James Fleming for information on the history
of climate research, to Jerry Mahlman, Ron Stouffer, V Ramaswamy, and Tony
Broccoli for careful readings of an earlier draft, and to Kerry Emanuel and Ray
Pierrehumbert for helpful discussions.
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472 HELD ¥SODEN
Visit the Annual Reviews home page at www.AnnualReviews.org
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P1: FQP
November 2, 2000 18:32 Annual Reviews AR118-COLOR
Figure 2 The annual-mean observed distribution of the clear-sky greenhouse effect Gclear
(top), vertically-integrated water vapor concentration (middle), and sea surface temperature
(bottom). Data are missing over land and ice-covered oceans due to uncertainties in their
surface emission.
P1: FQP
November 2, 2000 18:32 Annual Reviews AR118-COLOR
Figure 5 The upper tropospheric relative humidity (color) and cloud cover (grey) as
observed from the Geostationary Operational Environmental Satellite (GOES-8) on April
27, 1999.
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November 2, 2000 18:32 Annual Reviews AR118-COLOR
Figure 9 Height-latitude cross-sections of the sensitivity of the outgoing longwave radia-
tion to perturbations in water vapor Qe(top) and temperature QT(bottom) in 100 hPa thick
layers. The results are expressed in units of Wm2K1.
P1: FQP
November 2, 2000 18:32 Annual Reviews AR118-COLOR
Figure 10 Distribution of cloud water (light blue) and precipitation (dark blue) simulated
by the Geophysical Fluid Dynamics Laboratory resolved cloud model. Note the difference
inscale between the regions of active convectionwith respect to a typicalgeneralcirculation
model grid box (yellow box).
... ater vapor is the most important and the most abundant natural greenhouse gas in the atmosphere [1], [2], which is considered an essential variable in association with the hydrological cycle [3], [4], energy transportation [5], and climate change [6], [7]. The distribution of water vapor in the Earth's atmosphere usually presents a high variability in both temporal and spatial domains [8], [9]. ...
... (1) ( , ) = 1 − 0.00266 cos 2 − 0.00028 (2) where Ps is the pressure (hPa) at the height of the ground-based GPS station, θ and H are the latitude and height (km) of the in-situ GPS site. Then, ZWD can be estimated by subtracting ZHD from ZTD. ...
Article
Full-text available
We performed a thorough validation of the precipitable water vapor (PWV) products from near-infrared (NIR) bands of very similar instruments, i.e. Moderate Resolution Imaging Spectroradiometer (MODIS) and advanced Medium Resolution Spectral Imager (MERSI-II). The PWV products validated are those derived from MODIS/Aqua, MODIS/Terra, and MERSI-II/FY-3D sensors. The PWV data from Global Positioning System (GPS) in 453 in-situ sites situated in the interior and coastal areas of Australia from June 1, 2019 to May 31, 2020 were utilized as reference values. The accuracy of the satellite PWV products was studied under different weather conditions. The evaluation results show that all the three PWV products did not provide good quality water vapor observations in the presence of clouds, with a correlation below 0.2 and a root-mean-square error (RMSE) above 10 mm. Under confident clear sky conditions, MERSI-II/FY-3D instrument had the highest retrieval accuracy with an RMSE of 2.801 mm, but had the worst correlation with reference GPS PWV (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.841). By contrary, MODIS/Terra instrument had the lowest retrieval accuracy (RMSE = 4.903 mm), but had the best correlation with a correlation of 0.903. Both MODIS/Aqua and MODIS/Terra instruments tended to overestimate PWV value, while the MERSI-II/FY-3D instrument tended to underestimate PWV value. All PWV data records showed better retrieval accuracy with higher correlation and lower RMSE under the dry condition than under the wet condition. The performance analysis of all the three satellite PWV products was also studied per day, per station, per season, and per land-surface-type in this study.
... ater vapor is one of the most important atmospheric components in the climate system [1]- [3]. It plays a prominent role in atmospheric circulation [4], [5], energy transportation [6], and meteorological and hydrological processes [7], [8], which in return exerts a fundamental effect on both regional and global climate change [9]. It also indirectly contributes to the formation of clouds when the evaporation from ocean and inland waters is increased due to the rise of the Earth's temperature [10], [11]. ...
... The results displayed in Figs. 9 15.539 to 2.371 for cloudy group, and from 11.502 to 1.505 for all MODIS/Aqua NIR PWV pixels. Similarly, the slopes and offsets of the linear regression lines for Terra satellite were much closer to 1 and 0. The monthly comparison between the MODIS NIR PWV data and the reference ERA5 PWV data was performed, with results displayed in Table III. ...
Article
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Precipitable water vapor (PWV) products derived from the near-infrared (NIR) channels of the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments, onboard Aqua and Terra satellites, were calibrated using a linear differential PWV (LinearDP) calibration model based on GPS-retrieved PWV observations. All MODIS NIR PWV pixels were classified into two groups according to the cloud mask of each pixel. For each group, MODIS NIR PWV products and ground-based PWV data from 453 GPS sites in Australia from January 2017 to December 2018 were utilized to determine the differential PWV by subtracting GPS PWV from MODIS PWV. Then empirical regression relationship between the differential PWV data and the MODIS PWV products was developed using a linear regression approach. The LinearDP model coefficients were independently obtained from each month for each group. The period for model validation spans from January to December in 2019. Comparison of calibrated MODIS NIR PWV versus GPS-derived PWV over Australia showed that the root-mean-square error (RMSE) of Aqua has reduced 42.61% for clear group, 41.43% for cloudy group, and 41.45% for both clear and cloudy groups; and has respectively reduced 53.76%, 37.03%, and 39.33% for Terra. By comparing against ERA5 PWV data, the RMSE reduced 37.21%∼43.14% for Aqua and 38.73%∼53.87% for Terra. The improvement of MODIS NIR PWV products is further validated in China, with an RMSE reduction of 24.53%∼31.78% for Aqua and 28.26%∼38.69% for Terra against reference PWV from 214 GPS stations. The mean bias was reduced to -0.415∼0.752 mm in Australia and to -0.382∼2.013 mm in China.
... File generated with AMS Word template 1.0 Global warming leads to the concentration of moisture in warmer atmosphere that in turn increases the intensity of extreme precipitation events (Zhou et al., 2017). Water vapor has strong feedbacks on global warming as the most abundant greenhouse gas in the air, whose variation strongly correlates with that of precipitation (Held et al., 2000). Given the great harm and possible growing trend of extreme hourly precipitation in cities, exploring the relationship between PWV and precipitation developing trends can help provide a reference for long-term precipitation forecasting. ...
Article
Correlation analysis between precipitable water vapor (PWV) and precipitation over China was conducted combining high-quality PWV data based on 1999-2015 Ground-Based Global Positioning System (GPS) observations with the measurements at matched meteorological stations in the same period. The mean correlation coefficient (R) at all the stations is approximately 0.73, indicating that there is a significant positive correlation between PWV content and precipitation measurements, and the comparison of correlation among different climate types suggests that the distribution characteristics of the correlation coefficients are distinctively related to different climate types. There is also some positive correlation between PWV and precipitation long-term trends with the correlation coefficients of monthly anomalies ranging generally from 0.2 to 0.6. Furthermore, the intensity of both PWV and precipitation extremes shows a long-term upward trend overall, with the most intense events showing more significant increases. The extreme precipitation-temperature scaling rate of changes can reach above Clausius-Clapeyron (CC) scaling, while that of the extreme PWV-temperature is sub-CC overall, with regional differences in the specific scaling values. The correlation analysis in this work is of great significance for long-term climate analysis and extreme weather understanding, which provides a valuable reference for better utilizing the advantages of PWV data to carry out the studies above.
... The water vapor feedback is the process whereby an initial warming of the planet, caused, for example, by an increase in atmospheric carbon dioxide, leads to an increase in the humidity of the atmosphere. Because water vapor is itself a greenhouse gas, this increase in humidity causes enhanced warming by a factor of 2 to 3 of the initial warming (Held & Soden [2000]). The rate at which water vapour increases per 1 K of temperature increase is controlled by the Clausius-Clapeyron (CC) relation (see e.g. ...
Thesis
L'homogénéisation est une étape importante et cruciale pour améliorer l'utilisation des données d'observation pour l'analyse du climat. Ce travail est motivé par l'analyse de les données journalières de Contenu Intégré en Vapeur d’Eau (CIVE) mesurées par GNSS (Global Navigation Satellite Systems), appelées GNSS CIVE (IWV Integrated Water Vapor en anglais) qui n'ont pas encore été utilisées dans ce contexte. Ces séries sont affectées par des inhomogénéités liées à des changements dans l'instrumentation, dans l'environnement et dans la procédure de traitement des données. En raison de la variabilité naturelle de la série, nous travaillons en fait sur la série chronologique des différences, en utilisant la réanalyse ERA-Interim comme référence pour le signal climatique. Une hypothèse de base est que les différences contiennent seulement la signature des changements brusques de la série GNSS qui peuvent être détectés au moyen d'un algorithme de segmentation. Une analyse minutieuse des résultats de la segmentation permet de trier les cas où cette hypothèse n'est en fait pas vraie. La principale contribution de cette thèse a été le développement d'une nouvelle méthode de segmentation dédiée à la détection des changements dans la moyenne de la série de différences GNSS-ERA-Interim CIVE. Ce modèle de segmentation intègre un biais périodique et une variance hétérogène, variable mensuellement, pour s'adapter correctement aux caractéristiques de la série. La méthode consiste à estimer d'abord la variance à l'aide d'un estimateur robuste puis à estimer les paramètres de segmentation (les positions des points de changement, les moyennes des segments) et le modèle de biais périodique de manière séquentielle. Les paramètres de segmentation et le modèle de biais périodique sont estimés de manière itérative pour un nombre fixe de points de changement. L'inférence est obtenue par la procédure classique du maximum de vraisemblance en utilisant l'algorithme de programmation dynamique pour l'estimation des paramètres de segmentation qui fournit la solution exacte dans un laps de temps raisonnable. La procédure est répétée pour tous les nombres de points de changement testés entre 0 et un maximum (environ 30). Enfin, le nombre optimal de points de changement est choisi en utilisant une stratégie de sélection de modèle pénalisée. Plusieurs critères sont testés. La méthode est implémentée dans le package R GNSSseg disponible sur CRAN. Les performances de la méthode proposée ont été évaluées par des simulations numériques. Une application pour un ensemble de données réel de 120 stations GNSS mondiales dans le réseau mondial IGS est présentée pour la période de janvier 1995 à décembre 2010. L'inspection des résultats révèle que les points de changement détectés contiennent une fraction (~20%) de valeurs aberrantes qui se caractérisent par des détections doubles avec deux grands décalages, généralement de signes opposés, rapprochés, p.ex. à quelques dizaines de jours d'intervalle. Afin de détecter et d'éliminer les valeurs aberrantes, une méthode de dépistage a été développée. L'ensemble final de points de changement est validé par rapport aux métadonnées GNSS qui contiennent des informations sur les changements d'équipement survenus dans les stations. Le pourcentage de validation reste modéré au niveau de 20% malgré tous les changements sont statistiquement significatifs. Certains des points de changement peuvent en fait être dus à la série de référence (ERA-Interim). Enfin, les informations de segmentation (dates des points de changement) sont incluses dans un algorithme de régression linéaire qui est utilisé pour estimer les tendances GNSS CIVE. Les tendances estimées sont testées pour leur signification et comparées aux tendances ERA-Interim. Une plus grande cohérence spatiale dans les tendances GNSS et une meilleure cohérence sont trouvées après l'homogénéisation avec ERA-Interim dans les régions où la réanalyse est connue pour ses performances...
... Under the background of climate change, the near-surface air humidity content has been increasing since the last 1970s, but the precipitation and atmospheric water vapor content corresponding to the climate change in different regions are significantly different ). In the Northern Hemisphere, both atmospheric water content and precipitation may increase significantly (Held and Soden 2000;Sherwood and Meyer 2006). ...
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As the climate continues to change, suicide is becoming more frequent. In this study, absolute humidity (AH) was included for the first time and Wuhu, a typical subtropical city along the Yangtze River, was taken as the research object to explore the impact of suicide death risk on meteorological factors. The daily meteorological factors and suicide mortality data of Wuhu city from 2014 to 2020 were collected. Guided by structural equation model (SEM), a time series analysis method combining distributed lag nonlinear model (DLNM) and generalized additive model (GAM) was adopted. To investigate the correlation among different populations, we stratified age and gender at different meteorological levels. A total of 1259 suicide deaths were collected in Wuhu. The results indicated that exceedingly low and low levels of AH short-term exposure increased suicide mortality, with the maximum effect occurring at lag 14 for both levels of exposure, when the relative risk (RR) was 1.131 (95% CI: 1.030, 1.242) and 1.065 (95% CI: 1.006, 1.127), respectively. Exposure to exceedingly high and exceedingly low levels of temperature mean (T mean) also increased suicide mortality, with maximum RR values of 1.132 (lag 14, 95% CI: 1.015, 1.263) and 1.203 (lag 0, 95% CI: 1.079, 1.340), sequentially. As for diurnal temperature range (DTR), low-level exposure decreased the risk of suicide, while high-level exposure increased this risk, with RR values of 0.955 (lag 0, 95% CI: 0.920, 0.991, minimum) and 1.060 (lag 0, 95% CI: 1.018, 1.104, maximum), sequentially. Stratified analysis showed that AH and DTR increased the suicide death risk in male and elderly people, while the risk effect of T mean have no effect on young people only. In summary, male and elderly people appear to be more vulnerable to adverse weather effects.
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