Tải bản đầy đủ - 0trang
Chapter X. Evaporation from Wet Surfaces
X. E V A P O R A T I O N F R O M W E T S U R F A C E S
To minimize these problems of determination, they can be approached in three ways: as the supply of water to the site where
vaporization takes place, as the removal of vapor from this site, and as
the rate a t which energy is converted at the site into latent heat. Where
does this energy come from?
The Energetics of Evaporation
The simple energy-budget equation is balanced in the form:
radiant energy absorbed by the evaporating surface, including both shortwave and long-wave forms; also called "radiant-energy intake" (see
radiant energy emitted by the evaporating surface in accordance with the
heat exchange with layers below the evaporating surface
exchange of sensible heat with the air
conversion of energy by the vaporization process into latent heat
Here + means energy gained by the evaporating surface and - means
energy lost from it. The fluxes of sensible heat (S and H) might be
directed either toward or away from the evaporating surface under
different conditions of water or air temperature distribution; their
direction is indicated by + or -. We will examine these energy
sources in the order given.
Radiant Enevgy Two forms of radiation impinge on ecosystems and
water bodies at the earth's surface; for convenience they are called
"short wave" and "long wave." Solar radiation falls in the short
wavelengths (shorter than about 4 pm) and radiation emitted by gases
and clouds in the atmosphere is called long wave (wavelengths longer
than about 4 pm). Part of each flux is reflected by the earth's surface,
although in the case of water surfaces the fractions are generally less
than 0.05; the rest penetrates the surface and is progressively absorbed
with distance traveled.
The average rates at which short-wave and long-wave radiation is
absorbed in water bodies are large. For example, during summer in
central North America they are about 200 W m- of short wave and 350
of long wave. These amounts of energy supply correspond to the daily
vaporization of approximately 7 and 1 2 kg of water rnp2 (depths of 7
and 12 rnm day-'). Both forms of radiation vary through the day, the
familiar on-and-off cycling of solar radiation (600 W mP2or more in
the middle of the day, zero during the night) being particularly
D E T E R M I N I N G E V A P O R A T I O N RATES
striking. Long wave is more steady in both the daily and annual
Not all of the energy from absorbed radiation can be converted into
evaporation or other nonradiative energy conversions. The price of
existence as a wet surface is to maintain a surface temperature of at
least O"C, and this implies the emission of long-wave radiation at a
rate of 315 W m-' from the surface.
Summing all the gains by absorption of short-wave and long-wave
radiation and subtracting the 315 W m-' just noted, we have the
accompanying tabulation as typical of day and night in summer and
winter in the interior of North America (in W IT-'),
Midday in summer
Night in summer
Midday in winter
Night in winter
Absorption of radiation from the
the surface temperature as 20°C in summer, 0°C in winte1
Clearly the sum of all the fluxes of radiation is a highly variable
source of energy; it is large in the long summer days, with a net loss
every night. While these variations are more or less predictable, except
for the effect of passing cloud decks, they nevertheless impose a
pattern on the other, or nonradiative fluxes in the energy-budget
expression cited earlier. By definition, the sum of the nonradiative
fluxes, S, H, and E , must be equal and opposite to the sums of the
radiative fluxes given in the accompanying tabulation.
Substrate-Heat Flux One alternative to radiant energy as a source is
the substrate, that is, the layers of soil or water underlying the surface.
The soil-heat flux is directed toward the active surface more than half
the time, i.e., during the hours of later afternoon and darkness. In
some cases it supports a small rate of evaporation from the soil itself.
Heat moves upward from the deeper layers of a water body to its
surface during the months of fall and winter. Low intensity of
radiation in these months has little inhibiting effect on evaporation,
which proceeds vigorously until the time when ice forms on the lake
surface, if it does. The enormous amounts of heat stored in deep water
E V A P O R A T I O N F R O M WET S U R F A C E S
bodies make i t possible for them to evaporate much more water than
do adjacent land surfaces.
Sensible-Heat Flux The second alternative source of energy for
evaporation is the atmosphere itself, which thus is simultaneously
humidified and cooled by turbulent exchange between it and the
underlying wet surface. In this situation the surface must be cooler
than the air and also moister.
A simple example is the wet-bulb thermometer, in which a cotton
wick keeps the bulb wet while i t is strongly ventilated by being
swung. If the air is quite dry, evaporation from the wick removes heat
from the bulb, which has only a small amount of "substrate" heat
storage in its tiny volume and also is shielded from any excess of
radiant energy. The energy budget of the wet bulb thus contains only
two items, the outward flux of latent heat E and the inward flux of
sensible heat H. These offset each other exactly. The drier the air, the
greater are both fluxes since the bulb temperature sinks to a level
much lower than the air temperature.*
In natural situations the other fluxes at the surface of the earth are
usually not zero, so the sensible-heat flux seldom becomes the sole
source of energy for evaporation.
Combined Sources of Energy for Evaporation The energy sources that
support vaporization differ from place to place and time to time. Each
can act singly, but it is more likely that combinations of them provide
the energy that is converted into latent heat.
In a Milwaukee November we see the grass still green, and deduce
that it is continuing its life processes, including transpiration, although at a low rate, powered by the slanting rays of the low sun. It is
not as obvious, perhaps, that at the same time Lake Michigan also is
vaporizing water and at a much higher rate. Its rapid evaporation is
supported less by solar energy than by the heat put into storage in its
deeper layers a few months earlier and now being drawn upon in fall.
Grass evaporation, having little access to stored energy and depending
largely on current radiant energy, which is supplied at a slow rate,
proceeds slowly at this season when lake evaporation is continuing a t
a daily level of 3-4 kg m-' as a result of its good source of heat.
When a surface is energized from large nonatmospheric heat
sources, either by absorbing radiant energy R or receiving a large flow
* This difference is utilized as a means of determining the dryness of the air-the
D E T E R M I N I N G E V A P O R A T I O N RATES
of heat from beneath S, the two heat fluxes from it into the atmsophere
find themselves in competition. Usually the latent-heat flux prevails
over that of sensible heat, if the surface is wet. (If it is dry, there is, of
course, little or no evaporation or latent-heat conversion taking place.)
The ratio between these two competing flows of heat, both transported by turbulent convection in the atmosphere, is called the
”Bowen ratio,”named for the oceanographer I.S. Bowen (1926).Usually
the seflsible-heat flux is much the smaller of the two, and the ratio is
of the order of 0.1-0.3. However, by destabilizing the air this flux
increases its diffusivity for water vapor, and the same vapor flux is
moved at a smaller gradient, which allows a lower temperature at the
evaporating surface. In a study of cooling ponds, those unique
ecosystems built to move heat from thermal power plants into the
environment, Ryan et al. (1974) found that thermal convection made
possible the removal of an added flux of 500 W mp2of dump heat from
a 4-km2 pond, with a rise of surface temperature above the 2-m air
temperature of only 9°C. The rate of evaporation, 14 mm day-’, is one
of the highest from any system at the surface of the earth.
Surface Temperature and Vapor Pressure
Each energy flux, including evaporation, is determined in part by
the temperature of the active surface generating it. Long-wave radiation is emitted in accordance with the fourth power of the absolute
temperature of the surface. The flux of sensible heat moves away from
the surface in proportion to the temperature gradient from the surface
into the adjacent air. The heat exchange between the surface and
substrate depends on the corresponding temperature gradient below
The latent-heat flux associated with evaporation also follows a
gradient, that of specific humidity or vapor pressure. The surface
value determining this gradient is a single-valued function of the
surface temperature, expressed as the Clausius-Clapeyron relation (for
two physicists of the nineteenth century) in the accompanying tabulation from the Smithsonian Institution (1966). The accelerating trend of
specific humdity with increasing temperature (shown in the last
column) means that during a rise in surface temperature the gradient
driving the latent-heat flux usually grows faster than do the gradients
driving the heat fluxes into the atmosphere and soil. Therefore the
conversion of heat in evaporation tends to preempt most of the
E V A P O R A T I O N F R O M WET S U R F A C E S
Specific humidity at
(gm water kg-' air
or parts per 1000)
Rate of change in specific
humidity for a 1" change
in surface temperature
(g kg ' deg-7
Linacre (1964) and Priestley (1966) have shown that over a wet
surface this preeminence of the latent-heat flux becomes virtually
complete at a surface temperature of about 34°C. The water surface,
continuing to humidify the air, has no further power to warm it. Thus
34°C (307K) represents a maximum temperature for any wet surface,
regardless of how i t might be loaded by radiant energy.
Verification of this fact is seen in the absence of ocean areas where
water temperatures exceed 34"C, or where temperatures in oceanic air
exceed 34°C (unless air has moved from hotter surfaces of dry land).
Dry surfaces, on the other hand, are easily heated to high temperatures under strong radiation loading, and in turn heat the overlying
air to temperatures higher than 34°C. The difference between a hot dry
desert surface and the relatively cool foliage of an irrigated field in an
oasis demonstrates that evaporation can remove large amounts of heat.
Surface temperature is a t the same time a cause and a consequence
of energy fluxes. It varies in response to changes in the rate at which
the surface takes in energy and the ease with which i t can get rid of
this energy load. Corresponding variations in the surface vapor
pressure produce changes in the rate of evaporation.
Uncertainties about Evaporation
The central problem in talking about evaporation is the scarcity of
direct measurement. Only one method can be classed as direct
measurement; all others depend (a) on statistical correlations of other
fluxes to the vapor flux, (b) on sets of measurements in the energybudget framework just described, (c) on sets of measurements in the
water-budget framework, or (d) Dalton's evaporation law.
Statistical correlations between the vertical flux of vapor and the
fluxes of momentum, heat, carbon dioxide or other substances are not
E V A P O R A T I O N F R O M DEEP WATER B O D I E S
precise because of our ignorance of the nature of turbulent transport in
the atmosphere. The mechanisms of this transport do not necessarily
work the same for different physical quantities, i.e., for heat as for
In conditions of neutral thermal stability in the lower layers of the
atmosphere 2nd strong air movement, the turbulent transport mechanisms are most alike. In stable conditions marked by inversion, or in
very unstable conditions this similarity cannot be counted on.
Measurements of energy fluxes to the evaporating surface of a lake
are most accurate over long time intervals, for over a short time the
flow of heat out of the lower layers of water is impossible to
determine. The energy-budget method is most often applied to periods of a month or so, over which the cooling of the lower layers can
The water-budget framework also is most useful over long periods
of time, since the movement of water into or out of the lake banks
cannot be evaluated over short times. Over any length of time,
however, the water-budget method is limited by the lack of measurements of precipitation falling into the lake. Because the lake energy
budget often changes atmospheric stability over the lake from the
stability conditions over land and because stability affects precipi tation processes, it is risky to consider that lake rainfall is correctly
represented by rain gages on nearby land sites. (See Chapter V.)
Evaporation from water surfaces is never limited by a shortage of
the evaporating substance, therefore variations are associated with
energy supply or with the vapor gradient from surface to air. Factors
in evaporation can be considered from their connection with either
supplying energy or removing the vapor molecules.
The case of evaporation from snow, which we examined in an
earlier chapter, illustrates this circumstance. In general, evaporation
from snow is limited by a lack of energy supply, as in the Arctic night.
Often, in situations of apparent high energy level, as in advection of
warm marine air over a snow cover, the vapor gradient is toward
rather than away from the snow cover, and no evaporation occurs. Let
us now proceed to examine evaporation from water substance in a
quite different physical state, i.e., bulk water in lake basins and other
EVAPORATION FROM DEEP WATER BODIES
All water bodies except the most shallow are distinguished from
other ecosystems by an extremely large capacity to accept heat into
E V A P O R A T I O N FROM WET SURFACES
storage and subsequently to give it back. The availability of heat at the
water surface to support evaporation depends less on short-time
fluctuations in radiation than on the stirring of the water or the air.
We need to look at this factor of heat storage in the water.
The Role of Heat Storage
Lake Ontario This lake has received considerable study, some of it
connected with the importance of its level to the operation of the St.
Lawrence Seaway, in hydroelectric production, and as a hazard to
riparian property. In one study of its water budget, a heat budget was
developed (Table I) that illustrates the annual cycle. Like the mountain
snow covers described earlier, evaporation is absent in spring. Even a
contribution of sensible heat from air warmed over surrounding lands
in April and May does little to speed evaporation. Most of the heat
from the warm air, like that from absorbed solar radiation at this
season, simply goes to warm the deep water of the lake. The surface
warms up slowly, and generates little outward movement of water
During the cooling phase of the annual cycle, which lasts from
August until February or March, the situation is reversed as heat
stored in the depths of the lake in earlier months now comes to the
surface. Here it makes a large addition to the waning surplus in the
radiation account. The total heat available to go into the atmosphere is
now very great, and supports rapid evaporation during the dark
winter. In fact, evaporation continues through nine months of the
year, and is large in six months (September-February). Its energy
support in September and early October comes chiefly from radiation,
the rest of the time it comes from subsurface heat, which also buffers
the thermal environment of the fish species in this aquatic ecosystem.
The Influence of Lake Depth The depth of a water body affects heat
storage in the water because with sufficient stirring by wind-up to a
depth of 50 m or more-a large mass of water is brought into thermal
communication with the evaporating surface. The great heat-storage
capacity keeps the surface cool and evaporation slow in the spring and
summer and maintains a warm surface and rapid evaporation in the
fall and winter. In May, for example, the latent-heat flux (dashed
curve, in Fig. X-la) from a 5-m deep lake or reservoir is 120 W m?, or
about 4 mrn day-', whereas from a 20-m lake it is only 30 W m-', a
quarter as much. The deep lake is still taking more heat into storage in
May than the shallow, and allowing much less to escape upward into
the air. The converse occurs in fall.
Water a n d Energy Budget of Lake Ontaiio"
Net income of energyfrom
Bxchmge of hcat betwecn lake t250
surface and d e e p water*
Nei transport of hoat in inflow
and outflow rivers and snow
Energy available at lake
Surface vapor pressure'
Atmospheric vapor pressure"
Sensible-heat flux as residual'-155
~ 8 3 -140
Units: energy fluxes i n W m .',water Fluxes in m m d ~ y - l ,vapor pressure i n nib, tempcraturcs in "C. Note: 'I'hc olcIer data, c!spc~ially,
are subject to change ds findings of the International .Fie!.d Year on the C~-eatLakes are publishecl. Figul-es dre roundcd. Evaporation E is
calculated by t h e Llalton q u a t i o n E = KVic, .- P A , in wiiich V is wind speed over the Iakc, c,, is vapor pressure over the lakc: c , is vapor
pressure at lak+surfacc ternpcrabi:e. and K is a coefficient (Rich;irds and Irbe, ICjbS).
Bruce and Iiodgers (1962).
Richards and Fortin (1962).
Richards and Irbe (1969).
E V A P O R A T I O N F R O M WET SURFACES
' E 100
DEPTH OF RESERVOIR ( m \
Fig. X-1. Energy fluxes in (a) May and (b) October in lakes and reservoirs of different
mean depth (m). The net surplus of radiation of all wavelengths (solid line) is large in
May at the surfaces of all the lakes. The change in heat content of the water ( - X - X ) is
greatest in the deep lakes. In May, the larger lakes extract sensible heat (--.--.) from the
air, while in October they give it up. Evaporation (- - -) decreases in deep lakes in May,
increases in October (Nesina, 1967). From the standpoint of the water surface rather
than the water body itself, the sign for change in heat content would be reversed, as it
represents a removal of energy from the surface in May. The sign for latent heat flux
would also be reversed.
The depth of the lake basin itself is, of course, not a s critical as the
depth of the layer in thermal communication with the lake surface. In
a stratified water body under winter or summer conditions, the depth
of the mixed layer above the thermocline is important. This is related
to the fetch of wind on the lake. Arai (1966) shows that lake
evaporation in spring and summer decreases with greater fetches F,
which mix more cold water to the surface, the coefficient of diffusivity
in the water being proportional to F"' (Arai, 1972). He finds winter
evaporation from deep mid-latitude lakes to increase proportionally to
Reservoirs If water from a deep storage reservoir in summer is
taken from its middle or lower layers, which are usually colder than its
E V A P O R A T I O N FROM DEEP WATER B O D I E S
surface layer,* the result is that less energy is removed in the discharge
water than is brought into the reservoir by inflowing streams. Energy
accumulates in the reservoir, its surface temperature rises, and evaporation increases. In Roosevelt Lake in Arizona this fashion of withdrawal probably increases annual evaporation 150 mm (Koberg, 1960).
In contrast, smaller reservoirs downstream on the same river, which
are fed by cold water from Roosevelt Lake, experience less evaporation. For the system of reservoirs on the Salt River the total change
10" m '
more evaporation from Roosevelt Lake
less evaporation from the lower reservoirs
added loss of water by evaporation
If all reservoirs in the system are not under the same administration, a
transfer of income equal to the value of the changed evaporation also
takes place to the benefit of the downstream managers.
In warm dry regions where reservoirs must hold water over periods
of drought, the radiation surplus is usually large, and adjacent lands
generate streams of hot, dry air moving over the reservoirs. The result
is that reservoir regulation of stream flow for irrigation or other
purposes incurs excessive costs of water storage in the form of high
This fact sets limits in physical terms, quite in addition to the
economic costs of construction labor and materials, to the degree of
regulation that is logical on any stream, regardless of the availability of
subsidized low-interest funds. On the Colorado River, reservoir storage of 36 x 10' m3 in 1959 provided an annual regulation of 7.8 X 10'
m3 at a cost of 1.0 x 10' m3 lost by evaporation (Langbein, 1959). Net
gain is 6.8 x lo9 m3 (7.8 less cost of 1.0).
Proposals to build more reservoirs to store a total of 97 x 10' m" of
water would provide 9.8 x 10' m3 of annual regulation, less 2.6 x lo9
m3 lost by evaporation. This is nearly three times the present amount
of evaporation. A large expenditure on dam construction results in a
net annual regulation of 7.2 X 10' m3, not much more than the earlier
6.8 gain. Hydrologically, this gain over the present situation is
insignificant. The toll of evaporation is a major obstacle in the way of
reaching an artificially controlled water supply, in which the yearly
* In some cases, cold water is drawn to preserve downstream habitat for cold-water
species of fish. In others, it is withdrawn for operating convenience and might cause
damage to downstream water users, e.g., rice irrigators.
E V A P O R A T I O N F R O M WET S U R F A C E S
regime of natural input would be completely transformed into a yearly
regime fitted to man's requirements.
The Role of Surface and Atmospheric Conditions
In Lake Ontario in fall, heat storage provides a large flow of heat to
the surface, keeping it warm and its vapor pressure high. A large
amount of heat is available for transfer from surface to atmosphere.
The rate of transfer and the partition of the total between sensible heat
and latent heat (as vapor) depends on two gradients from the surface
into the air. These are the gradient of temperature, depending on the
water-to-air temperature difference (3" in fall over Lake Ontario), and
the gradient of vapor pressure, depending on the difference between
surface vapor pressure (a function of surface temperature, as noted
earlier) and atmospheric vapor pressure. The water-to-air difference in
vapor pressure above Lake Ontario runs about 2 mb (Table I).
Estimates of the evaporation from a deep water body can be made
from data on its surface temperature (and hence surface humidity q s ) ,
atmospheric vapor pressure q , and wind speed u . Based on Dalton's
law, a later form of the relation is the Shuleikin-Sverdrup equation
in which x is a coefficient and p is air density, the product xp
approximately equal to 2.5 x
g cmP3(or 2.5 g m-") (Budyko, 1971,
Eq. 2.88, p. 108).
Wind speed is important for two reasons: high winds accelerate the
upward turbulent movement of vapor (and sensible heat) from the
surface; and heat stored in deep water is brought to the surface by
vertical mixing within the water body, brought about by wind stress
on its surface.
If the second effect did not exist, the removal of sensible and latent
heat from the surface would chill it, reducing both flows. As the Lake
Ontario data show, however, the removal of as much as 200 W m-'
from the surface in fall reduces its temperature only slowly because the
reservoir of subsurface heat prevents such chilling. Otherwise, cooling
of the surface would result in a lowering of vapor pressure to a point
a t which evaporation would cease.
Wind-generated turbulence brings dry, often warmer air down to
the water surface and carries vapor up from it. Because the vapor
pressure of the surface is maintained reasonably constant, these
variations in atmospheric turbulence produce large short-term variations in evaporation.