Open Journal of Applied Sciences, 2012, 2, 302-318
doi:10.4236/ojapps.2012.24045 Published Online December 2012 (http://www.SciRP.org/journal/ojapps)
The Physical Principles Elucidate Numerous Atmospheric
Behaviors and Human-Induced Climatic Consequences
Ernani Sartori
Universidade Federal da Paraíba, João Pessoa, Brazil
Received September 20, 2012; revised October 22, 2012; accepted November 12, 2012
ABSTRACT
The principles that govern the operation of an open and a closed evaporator are relevant for the understanding of the
open and “closed” Earth’s atmospheric behaviors, and are thus described. In these greenhouses, the water is included,
otherwise the heat and mass balances do not match. It is incorrect to consider the radiation as the only energy transfer
factor for an atmospheric warming. Demonstrations show that when the greenhouse effect and the cloud cover increase,
the evaporation and the wind naturally decrease. Researchers did not understand why reductions in surface solar radia-
tion and pan evaporation have been simultaneous with increased air temperature, cloudiness and precipitation for the
last decades. It is an error to state that the evaporation increases based solely on the water and/or air temperatures in-
crease. Also, researchers did not comprehend why in the last 50 years the clouds and the precipitation increased while
the evaporation decreased and they named such understanding as the “evaporation paradox”, while others “found” “the
cause” violating the laws of thermodyna mics, but more precipitation is naturally con ciliatory with less evaporation. The
same principle that increases the formation of clouds may cause less rainfall. Several measurements confirm the work-
ing principles of greenhouses described in this paper. The hydrological cycle is analyzed and it was also put in form of
equation, which analyses have never been done before. The human influence alters the velocity of the natural cycles as
well as the atmospheric heat and mass balances, and the evaporation has not been th e only source for the clo ud forma-
tion. It is demonstrated that the Earth’s greenhouse effect has increased in some places and this proof is not based only
on temperatures.
Keywords: Evaporation; Clouds; Air Water Temperature; Paradox; Hydrological Cycle; Precipitation; Rain; Drought;
Global Warm ing; Radiation; Con vecti o n; Ae rosols; Greenhouse Effect; Wind; Particulates; Atmosphere;
Climate; Human-Induced
1. Introduction
In general, the attempts to describe climatic changes have
been made solely using extensive experimental data in
order to find empirical connections among phenomena.
However, due to the extremely variable, complex, ran-
dom and vast nature of the atmospheric processes with
their isolate data, almost an infinite time is needed to get
an approximate conclusion on a single phenomenon, and
a definition may not be found or not found with confi-
dence, too.
However, parallel to the experimental data we have the
fundamental laws of physical principles that lead us on a
straight line over these tremendous variability and com-
plexity that do not “speak” clearly. Theoretical principles
and experimental data should be used jointly.
The general literature usually makes representations of
the Earth’s greenhouse effect through the common rural
greenhouse. However, this is an incomplete representa-
tion because it does not include water, which corresponds
to much more than 70% of the planet’s surface because
most part of the remaining 30% is covered by vegetation,
which also contains much water that evaporates and thus
adds heat and mass to the atmosphere. The water makes
all the difference since such a large amount changes all
the heat and mass balances of the atmosphere.
It has been reported that in the last 50 years in some
places of the world (e.g., Russia, India, USA, and Vene-
zuela), the clouds and the rain increased while the pan
evaporation decreased in these same places and periods.
Using the information from the conventional hydrologi-
cal cycle, some researchers asked how less evaporation
could form more precipitation and then named such un-
derstanding as the “evaporation paradox” (e.g., [1]), who
also concluded that more precipitation is not conciliatory
with less evaporation. However, when we pay close at-
tention to the fundamental laws and first principles that
govern the evaporation and the greenhouse effect as well
as knowing that the nature doesn’t work through para-

E. SARTORI 303
doxes, we see that the evaporation decreases in such
conditions and we can explain all these issues naturally
and correctly, and which solution is consistent and has
physical meaning, in contrast to previous solutions based
only on empirical hypotheses. Therefore, more precipita-
tion is perfectly and naturally conciliatory with less
evaporation. The evaporation is in the core of the green-
house effect and accurate understandings and directions
are thus enormously required.
Also, various researchers (e.g., [2,3]) did not under-
stand why reductions in surface solar radiation and pan
evaporation have been simultaneous with observed in-
crease in air temperature, cloudiness and precipitation in
various parts of the world for the last decades. Roderick-
Farquhar [3] draw the corresponding conclusion and
“found” “the cause” through an incorrect understanding
that violates the laws of thermodynamics and thus of the
nature, i.e., creating more energy from less energy. The
main reasons for the increase of the cloudiness, precipi-
tation, humidity and temperatures wh ile the pan evapora-
tion, the surface radiation and the winds have decreased
are given, which explanations correct invalid under-
standings.
It has been a general belief that the evaporation must
increase in an increasing greenhouse effect. Such belief
often comes from considering the water temperature as
having almost the sole and total power for influencing
the evaporation. Although evaporation is a strong func-
tion of the water temperature, this is not the only pa-
rameter that affects the evaporation and it cannot be used
isolately for this purpose. Other parameters such as the
air temperature, relative humidity, wind velocity and
even the atmospheric pressure have relevant influences
as well as some heat transfer factors and the greenhouse
effect have. When a water surface is exposed to the at-
mospheric air, all these variables affect the evaporation
simultaneously, some having more influence, some less,
some increasing and some decreasing the evaporation,
and thus they should be analyzed together and carefully.
Another example is in relation to the air temperature in-
fluence, which increase plays a very important ro le in the
evaporation decrease. In this context, it is also a general
procedure to take into account the radiation as the only
heat transfer factor influencing an atmospheric warming,
but this is incorrect. Besides the fact that the heat and
mass balances do not match if only one factor is consid-
ered, the convection alone represents the change of all
the wind condition inside the greenhouse and this is of
paramount relevance for its warming effects and climatic
changes.
Satellite data [4] showing that the wind speeds are de-
creasing globally associated with the cloud cover and
aerosols increase is a proof and another confirmation,
among the several ones presented, of the physical princi-
ples demonstrated in this paper and also reveal that the
Earth’s greenhouse is changing from an open to a more
“closed” condition, and thus from the forced to the free
convection, i.e., decreasing winds, as previously ex-
pected by this author. These results are also corroborated
by [5] who compiled decades-long database of aerosols
measurements and found that clear sky visibility has
decreased over land globally from 1973 to 2007, in-
dicative of an increase of particulates and darkness in the
air over the world’s continents during that time. Pryor et
al. [6] also did not understand why winds have decreased,
but a study by them based on measurements showing that
the ave rage and p eak winds hav e decre ased 10% or more
per decade from 1973 to 2005, especially in the Midwest
and the East of the USA, is another confirmation of the
demonstrations of this paper on th e correct working prin-
ciples of greenhouses as well as that the Earth’s green-
house effect has increased in some places of the world,
with the consequent reductions in evaporation, surface
radiation and winds, while the clouds, the precipitation,
the humidity and the water and air temperatures have
increased. The work [7] completes and confirms the de-
monstrations of this paper on the correct working prin-
ciples of greenhouses as well as on the real behavior of
the Earth’s greenhouse effect through those authors’ find-
ings which show that more than 170 large lakes water
temperatures worldwide increased since 1985.
All of the issues above and several other relevant ones
are elucidated and solved correctly. The hydrological
cycle is also analyzed physically and mathematically,
which analy s es ha ve never been done before.
2. The Thermal Behaviors of an Open and of
a “Closed” Atmosphere
2.1. The Thermal Behaviors of Equivalent
Systems Built on Earth
To better understand how an open and a “closed” Earth’s
atmosphere behave thermally, it is important and didactic
to make a brief description of the thermal behaviors of
equivalent systems built on Earth, which principles are
valid for both systems. Sartori [8] analyzed this subject
in depth and helps for the present understanding.
The open evaporator suffers direct influence from the
wind flowing over its water surface and then works under
the forced convection, while the closed evaporator (solar
still) has a transparent cover and thus no wind exists in-
side the system. Also, the greenhouse effect and the free
convection take place below the cover. The forced con-
vection over the open evaporator is converted into the
free or natural convection (works according to tempera-
ture and density grad ients) inside the closed syste m. This
makes a big difference in terms of warming and water
balance of both syst ems.

E. SARTORI 304
The thermal operations of the open (free water surface)
and of the closed evaporator (greenhouse effect) are es-
sentially the same. After the water layers of both systems
are heated by the solar radiation, they lose heat by radia-
tion, convection, conduction and heat and mass by
evaporation, and thus heat the corresponding environ-
ments. Thus, there are more forcings for the ambient
warming than only the radiative one. If the heat transfer
processes by evaporation, convection and conduction are
not taken into account, the energy balance does not
match. The heat released per square meter only by
evaporation corresponds to about 60% of the total heat
transfer released, which obviously cannot be neglected,
and is also much greater than the corresponding radiation
transfer from the surface to the cover or to the atmos-
phere [8,9]. Moreover, besides the latent heat addition,
the evaporation adds water mass to the greenhouse and
thus alters the mass balance, which on its turn alters the
heat balance of the system. The water temperature is the
final result of all heat gains and losses of the water layer
and also depends on the physical characteristics of the
system.
The general literature on global warming uses to make
the representation of the Earth’s greenhouse effect through
the common rural greenhouse. However, this is an in-
complete representation because it does not include water,
which corresponds to much more than 70% of this pla-
net’s surface because a great part of the remaining 30%
is covered by vegetation, which also contains much water
that evaporates. The water makes all the difference since
such a large amount changes all the heat and mass bal-
ances of the planet and thus only deserts and construc-
tions could be neglected from this process. We could say
that this is a planet of evaporation.
The evaporated water in the closed evaporator in con-
tact with the glass cover condenses (whenever the inside
air dew point temperature is higher than the cover tem-
perature) and runs down, being the condensate, pure wa-
ter, collected at the cover end. The more the water vapor
within the closed evaporator, the more the condensed
(precipitable) water, but the higher the saturation condi-
tion, the higher the air pressure, and slower becomes the
evaporation.
Figures 3-5 from E. Sartori [8] bring lots of impor-
tant information on the temperatures and evaporation
rates of both systems, which were compared theoretically
and experimentally under the same physical and envi-
ronmental conditions, and in this way close agreement
was obtained. The temperatures of the closed system are
much higher than the ones of the open evaporator, but
despite this the evaporation from the open evaporator is
much higher than that of the closed one. The effect of the
wind over the open evaporator dissipates the heats and
mass much more and more rapidly than this happens in
the closed evaporator, and thus does not allow the corre-
sponding water layer to reach higher temperatures. Over
the open evaporator there is also a much lower humidity
than that within the closed evaporator and this allows a
greater withdrawal of water vapor, thus causing higher
heat and mass transfer by evaporation. The greenhouse
effect of the closed system also plays a very important
role to make its inner temperatures to attain much higher
values. Moreover, inside the closed evaporator, satura-
tion is reached which does not allow faster evaporation.
Within an igloo, the outside temperatures of about –50˚C
are transformed to about +16˚C due to the cover that con-
verts the outdoor forced convection (high heat loss by
bodies) into the free convection inside and also due to the
addition of sensible heat (radiation, convection) and la-
tent heat (evaporation from sweat) to the inner air by
human bodies.
In Figure 5 from E. Sartori [8], w e can also see a time
lag of about 2 h between the evaporation of the open and
closed evaporators. This is due to the higher thermal in-
ertia of the closed system (cover influence) and to its
higher water vapor concentration that delay and reduce
the evaporation. Therefore, we can see that the water
temperature is not the only responsible for a higher and
quicker evaporation and cannot be considered alone for
such evaluation .
It is also very important to note that the water of the
closed evaporator receives less energy than the water of
the open evaporator due to the influence of the glass
cover. For typical values of the glass cover solar reflec-
tance
 = 0.08 and its solar absorptance  = 0.05, the
transmitted solar energy becomes
 = 0.87, and then the
solar radiation that reached the water of the closed sys-
tem was 13% lower, but even so the corresponding tem-
peratures were higher than those of the open evaporator.
This is because the multiple emissions and reflections by
the cover increase the amount of energy trapped inside
the greenhouse as well as the free convection due to the
cover substantially reduces the heat loss from the water.
This is how greenhouses behave and it is another demon-
stration on why any considered amount of solar energy
and water temperatures are not sufficient to guarantee
higher or lower ev aporation and cooling when the green-
house effect is involved .
The air temperature increase also plays a very impor-
tant role in the evaporation decrease. It is well known
that the evaporation is directly proportional to the partial
pressures difference (Pw - Pa) between the water and air.
Since the pressure is function only of temperature, that is,
on tw and ta, respectively, then when ta increases, Pa also
increases and the difference E ~ (Pw - Pa), or the evapora-
tion, decreases. We should also know what this means
physically. A higher ambient temperature means a higher
air pressure that puts a higher resistance or difficulty for

E. SARTORI 305
the air to absorb more water vapor. In the same way as
the voltage difference is the driving force for the electri-
cal current to flow, the temperature difference is the
driving force for the heat to flow and the pressure differ-
ence is the driving force for the mass to flow, and so, the
lower this difference (with higher ta or lower tw), the
lower is the flow of heat by convection and conduction,
and lower is the heat and mass by evaporatio n. Addition-
ally, the specific heat of the air is only 24% of that of the
water and this means that the air temperature fluctuates
more quickly than the water temperatures and also that
the air attains higher temperatures than those of the water
of big reservoirs, thus causing quicker variations in Pa.
Also, the thermal inertia of big water reservoirs is high
and then the corresponding temperatures vary slower and
lower, causing the relative increase of the air temperatur e
to produce lower evaporations.
Additionally, it is very important to mention that the
atmosphere inside the closed evaporator is exactly the
same as the one of the open system, with the same atmos-
pheric constituents, and nothing of the normal Earth’s
atmosphere components has been modified due to the
addition of a cover. Only the water vapor may increase
until the saturation in a closed system. Comparing Fig-
ures 3 and 4 from E. Sartori [8] we can verify that the
closed system (greenhouse effect) has the capacity to
increase its temperatures more than 30˚C - 40˚C above
the ambient one and more than 20˚C - 30˚C above the
open evaporator temperature, and this happens with the
normal atmospheric components without any addition of
CO2. Furthermore, it is generally said that the higher the
ambient temperature, the higher the water vapor the at-
mosphere can hold and thus more water vapor can absorb
more gas, but within any greenhouse more water vapor
can hold only the previous fixed mass amount of gas,
which did not change and even so the temperatures in-
creased substantially.
If in place of a transparent cover we had an opaque
one, the radiant energy would be mostly absorbed by this
cover and then the tran smitted energy would be zero, and
then the energy reaching the greenhouse would be sub-
stantially reduced. The abso rbed energy is converted into
heat and afterwards part of it is emitted back to the out-
side and part to the inside. Since the wind inside does not
exist, the inner ambient continues airless and with high
humidity as well as a warming and the process of evapo-
ration-condensation are kept, although much less than
with a transparent cover. The difference in warming
would be similar to the changing of a glass roof of a
house (without ceiling) by an opaque roof (without ceil-
ing), both under a torrid sun. Although reduced, the am-
bient inside the second condition continues warm.
It is also important to mention other features of open
and closed systems where there is evaporation. When it
is said that the atmosphere has the capacity to absorb
more moisture with higher temperatures, this means that
higher temperatures can hold more moisture only if suf-
ficient mass of water vapor exists or is added to the at-
mosphere (as happens in the closed evaporator), which
does not happen in deserts, that is, the temperature itself
does not create humidity. Such capacity of the air exists,
but it happens only when needed and this must not be
confused with the evaporation capacity.
Any free water surface and its surroundings exposed at
the same time to the atmosphere are both submitted to
the same environmental conditions, that is, the solar ra-
diation, the wind, the relative humidity, the ambient
temperature and even the atmospheric pressure play di-
rect influences on the water layer and on its surroundings
in the same way. Like for the other environmental pa-
rameters, the relative humidity, for example, is the same
for both systems and affects them in the same way. Only
the relative humidity (which is also the final result after
all heat and mass interactions with the atmosphere) that
exists over the water surface affects the corresponding
evaporation, not a distant one, and the evaporation from
the surroundings does not affect directly the evaporation
from a pan and vice-versa. A piece of clothing outdoors
dries according to the environmental conditions, not ac-
cording to the evaporation from distant places.
2.2. The Thermal Behaviors of the Open and
“Closed” Earth’s Atmospheres
2.2.1. The Open (Cloudless) Atmosphere—Forced
Convection
The thermal behavior of the open Earth’s atmosphere is
essentially the same of the open evaporator, since the
Earth’s surface works as an open evaporator and all the
incoming and outgoing heat and mass transfer processes
are the same in both systems. When a free water surface
is exposed to the atmosphere it suffers direct influence
from all of the environmental parameters. The descrip-
tion is given below.
The incoming solar radiation that reaches the Earth’s
surface suffers reflection at the water surface and absorp-
tion in the water layer. Thereafter, the water exchanges
heat with the atmosphere through simultaneous heat
transfer processes by radiation, forced convection (pre-
dominantly) and heat and mass transfer by evaporation.
Heat may also be lost by conduction from the water layer
to the soil through th e water reservoir base and sides. The
solar energy, the wind, the relative hu midity, the ambient
temperature and even the atmospheric pressure play di-
rect influences on the water layer. The convection is
forced due to the presence of wind (Figure 1).

E. SARTORI 306
Figure 1. Schematic representation of the open (cloudless)
atmosphere. Observe the high similarity of this behavior
with that of the open evaporator of Figure 2 [8].
2.2.2. The “Cl osed ” (T o tal l y Clou d y) A tmosphere—
No Wind—Free Convection
The greenhouse formed by the cloud cover (Figure 2) is
very similar to a greenhouse where there is evaporation
(Figure 2 from E. Sartori [8]). Thus, the thermal behavior
of the “closed” Earth’s atmosphere is also very similar to
the one of the closed evaporator when the sky is totally
or mostly covered by clouds, because this transparent
cover (sometimes more “solid” and opaque) changes the
conditions of radiation, convection and evaporation, and
works in the same way as the glass cover, where there
are multiple reflections and absorptions within both
transparent media. It is important to no te that for thermal
radiation purposes and thermodynamic analysis it does
not matter how many and what types of effects happen
within the medium (clouds or glass), because what in-
terests is only whether the cover is transparent or opaque,
as well as for convection purposes does not matter
whether the cover is transparent or opaque, because what
interests is whether the atmosphere is “closed” or open.
And in the same manner as the glass, clouds reflect, ab-
sorb and transmit thermal radiation. Also, such as the
glass cover, the cloud cover converts the forced convec-
tion into free convection and causes a possible entire
suppression of the wind. Covers keep heat and humidity
below and human s live under the cloud cover.
The thermal operation of this “closed” system (green-
house) is as follows. After reflection at the cloud upper
surface and multiple reflections and absorptions within
the cloud cover, the solar radiation that is transmitted
through this transparent medium suffers absorption by
the water vapor between the cloud cover and the surface,
reflection at the Earth’s water surface, absorption in the
water layer and may also suffer reflection and absorptio n
at the soil below the water layer when there is a shallow
water layer. When there is a deep water layer, almost all
of the solar radiation is absorb ed in the few meters below
the surface. Not all the reflected energy by the water and
Figure 2. Schematic representation of the “closed” (totally
cloudy) atmosphere.
basin surfaces is lost, because a portion is reflected back
to the water by the cloud cover. A portion of the solar
radiation absorb ed by clou ds is emitted b ack to th e water,
forming together with the reflected energy the green-
house effect. The water exchanges heat with the ambient
air through simultaneous heat transfer processes by ra-
diation, free convection and heat and mass transfer by
evaporation. The consequences of these processes are the
heating of the water and of the ambient air within the
greenhouse. Heat may also be lost by conduction from
the water to the environment through the water layer base
and sides. Heat from the water layer and from the water
vapor inside the system reaching the cover plus a part of
the solar energy absorbed by the cover (and thus con-
verted into heat) are dissipated to the outer atmosphere
by convection and radiation after conduction and con-
vection through th e cloud cover. The ev aporated water in
contact with cooler layers of the atmosphere condenses
(whenever the air dew point temperature is higher than
such layer air temperature) and forms water droplets and
clouds, being this condensate and clouds transformed
into rain. The more the water vapor in the “closed” at-
mosphere, the more the precipitable (condensed) water,
but in the same way as it happens within the closed
evaporator, the higher the saturation conditions, the
higher is the air pressure (Pa) inside the system and
slower becomes the evaporation when saturation condi-
tions approach. The free convection takes place due to
the addition of a cover with the almost entire suppression
of the wind and thus only very small air movements exist.
When the cloud cover is complete or almost complete
and transparent, the ambient below becomes airless and
warm.
Such as other covers, the trend of a full cloud cover is
to homogenize the air temperatures between the surface
and an atmospheric layer inside such greenhouse and
thus reducing the circulation of air currents. Temperature
differences create pressure differences which create wind

E. SARTORI 307
currents. Temperature differences are generated by the
Sun, which heats up different parts of the planet in dif-
ferent ways. For the winds to exist or circulate, openings
are necessary, like in our houses. Openings create pres-
sure differences. A complete or mostly cloudy cover
closes such openings and then converts the wind (forced
convection) into still air or very small air movements
(free convection) caused by density differences (very tiny
temperature and pressure differences). If the sky is
cloudy but there are wind jets, this means that the sky is
not totally covered, because some parts of it are open and
this generates greater temperature differences and thus
greater air movements or winds.
The reflected solar energy by clouds has normally
been considered as the only factor able to change the
warming conditions below the cloud cover. To analyze
the greenhouse effect only in terms of the radiation or of
the reflected radiation is an incomplete analysis. If only
one factor is considered, the energy balance does not
match. Less energy has the potential to reduce the tem-
perature, but as correctly explained in Section 2, there are
many other factors that increase the warming within a
greenhouse rather than where there is not this effect, and
thus even with less energy received a greenhouse is able
to increase the temperatures more than an open system
can. Therefore, small reductions of the incoming solar
energy are not sufficient to determine a supposed high
cooling effect and generate other consequences. Even
with some energy reduction, the greenhouse effect is
built and its temperatures remain relatively high. When
there is no wind for dissipating heats and humidity, all
these heats (by radiation, convection and evaporation)
remain inside this natural greenhouse. It is not only the
reflected radiation by clouds that determine the heating
conditions inside this greenhouse, being the heat added
by evaporation and conv ection into the greenhouse much
greater than that by the outgoing infrared radiation [8].
Therefore, if clouds fully cover the sky but the solar
transmittance is high, then airless and warm conditions
will exist inside the greenhouse independently of rela-
tively small variations of the energy received from the
Sun, because the winds decrease with any cover increase.
This also eliminates those kinds of proposals for
spraying sea water particles into the atmosphere (e.g.,
[10]) aiming at increasing the amount of clouds in order
to increase reflectivity. Because the reflectance is a prop-
erty of surface and not of volume or thickness, and de-
pending on the color, opacity and “solid” conditions of
clouds, as well as knowing that the cloud cover works as
a blanket, the radiation reflectivity may decrease and the
warming increase. Additionally, the absorp tion is a prop-
erty of length of the medium in the radiation direction,
and then the cloud absorption of incoming and outgoing
radiation increases, leading to a further greenhouse effect.
Such proposal also represents another absurd because in
the nature everything that rises must come back, then if
we put more salty water above, more rain will come back,
more intensely, more irregularly and loaded with corro-
sive salt particles. Satellite data [11] showed that clouds
over oceans produce more rain than the previous estima-
tions. This emphasizes that the referred consequences
may happen over land, too. And it is another type of un-
controllable human interference on the climate.
As seen in Section 2, even with less energy received
the inner ambient temperatures of the closed evaporator
increase much more than the open evaporator ones. Al-
though the water temperatures of the experiment [8] are
higher than the normal ambient ones, this serves as an
insight on how greenhouses work and is another demon-
stration on how an increasing greenhouse effect is able to
increase the inner temperatures almost independent of
some variations of the solar energy received. Moreover,
such average water temperature of 47˚C is the same 47˚C
used for measuring the Earth’s infrared radiation at noon
over the Northern Africa [12]. These analyses emphasize
once again the importance of other factors on the build-
ing of the greenhouse effect, and therefore, the radiation
or the reflected radiation cannot be used alone for deter-
mining the warming or cooling effect of the greenhouse.
While clouds continue increasing in amount and thick-
ness but keep transparency, they transmit radiation and
augment the greenhouse effect almost independent of
some variation of the energy reflected by them. In a sec-
ond condition, a very thick, opaque cloud cover (due to
heavy rainy clouds, for example) transmits less solar ra-
diation due to multiple reflections, absorptions and scat-
terings of radiation within the cloud cover, which proc-
esses attenuate the radiation in a great part. Due to its
high thermal inertia, the water vapor works as a buffer: in
the first case, the water vapor absorbs most of the in-
coming and outgoing radiation, and thus increases and
delays the inner warming; in the second case, since there
is almost no direct solar energy entering the greenhouse,
the absorption of such radiation by the water vapor is
almost null, then the absorption is due to the existing
infrared radiation and then the air does not warm too
much and may remain relatively cool.
In all of these issues, what really matters is to be aware
on the principles that govern the greenhouse effect and
how humans can influence such natural system, inde-
pendently of the higher or lower solar energy received
due to seasons or to Sun activities, since these con ditions
represent only natural variations (not controlled by hu-
mans) of an open system, and the human influence on
climate is not and should not be tied to the amount of
solar energy received. It is obvious that higher solar ra-
diation corresponds to a higher atmospheric warming,
but this has nothing to do with human interference. More

E. SARTORI 308
understandings on these subj ects will be given in the fol-
lowing sections.
3. Real Data Confirm the Physical Principles
It has been reported that in the last 50 years in some
places of the world (e.g., USSR, India, USA, and Vene-
zuela), the clouds and the rain increased while the pan
evaporation decreased in these same places and periods.
Using the traditional information which says that the
evaporation should be the only source for the formation
of clouds and rain, some researchers asked how less
evaporation could form more rain and then named such
understanding as the “evaporation paradox” (e.g., [1]),
who also concluded that more precipitation is not con-
ciliatory with less evaporation. It is also a general belief
that the evaporation must increase in times or places of
increased greenhouse effect. However, when we pay
close attention to the fundamental laws and first princi-
ples that govern the evaporation and the greenhouse ef-
fect as well as knowing that the nature doesn’t work
through paradoxes, we can explain all these issues natu-
rally and correctly with solutions that have physical
meanings and are consistent. As demonstrated in this
paper, when the air temperature, the humidity and/or the
greenhouse effect increase, the evaporation decreases.
This author also did a mathematical demonstration based
on first principles which confirms perfectly that when
these factors increase, the evaporation decreases. Due to
space limitations it is not shown in this paper.
If now we consider a scenario where the Earth’s green-
house effect increases (due to a cloud cover and/or water
vapor and other gases increase), we should know that the
inner temperature and the air humidity increase, too.
These are properties of all greenhouses where there is
evaporation (as demonstrated above), as happens with
the Earth’s greenhouse, too. It is also known that most of
the world and the 20th Century became wetter, with in-
creasing precipitation and warming (e.g., [13-15]), espe-
cially in the last decades. According to the IPCC, from
1950 to ~2000 the air temperature increased 0.75˚C
(from 13.75˚C to 14.50˚C). The IPCC also says that in
this same period the sea surface temperature increased
0.5˚C. As also shown in the referred mathematical dem-
onstration, even with this water temperature increase the
evaporation decreases, due to the strong influence of the
air temperature, of the air humidity and of the green-
house effect on evaporation. The main message with-
drawn from these results is that it is a strong error to state
that the evaporation must increase in an increasing
greenhouse effect based solely on the water temperature,
solar radiation or even on the air temperature, and not
taking into account the first principles that govern these
effects as well as other variables that strongly affect the
evaporation in the opposite sense at the same time. Less
evaporation with more rain leads to wetter ambient con-
ditions, being these results also in close agreement with
the observations that “increasingly wet conditions have
been found over the Amazon Basin” [15].
The referred mathematical demonstration also con-
firms that the evaporation decreased in this period in
places where the mentioned conditions applied, as ex-
pected by this author. As known from basic laws, the
evaporation per square meter and unit of time increases
with the wind velocity and water temperature increase,
and decreases with the air temperature, humidity, and
atmospheric pressure increase. Figure 10 from E. Sartori
[8] correlates all these factors and the Sartori equation1
[8,9,16-21] contains all these properties, and any com-
binations among these variables can be obtained correc-
tly with it (very accurate and more accurate than at least
30 others, including those from [22]—see Appendix):

0.8 0.2wa
0.0041P PEVL

  P (1)
where E = evaporation rate (kg/m2s); L = surface length
of water in the wind direction (m), P = atmospheric
pressure (Pascal); Pa, Pw = water vapor partial pressures
at the air and water temperatures (Pascal); V = wind ve-
locity (m/s);
 = relative humidity (fraction).
More humid places show lower evaporation than dry
ones in the same way as clothes dry slower during a wet
day and as demonstrated in Section 2. More humid
places obviously have more precipitation than dry ones.
The higher the precipitation, the higher the humidity and
consequently lower is the evaporation. Also, through [8]
and the present paper we can see that the evaporation
within a greenhouse (free convection) is much less than
that from a free water surface (forced convection) both
under the same physical and meteorological conditions.
This can also be demonstrated mathematically. When we
put a cover over a free water surface we suppress the
wind but not the convection because this only changes
from forced to free convection. As a consequence, we
also make the evaporation to change from the advection
mode to the diffusion mode where the evaporation and
the convection depend only on temperature differences
(slow processes) and not on the bulk or gross and
stronger motion and processes due to the wind flowing
over water surfaces. Hence, more precipitation is per-
fectly and naturally conciliatory with less evaporation. It
is also elemental that in a humid place the evaporation is
lower and slower than in a dry one. Groisman et al. [14]
show clearly that almost the entire world became more
humid in the last 40 years.
1Although not related to evaporation directly, the paper [23] is strongly
recommended because in it the fundamental principles of the boundary
layer theory, which govern the fluid flows over wet and dry flat sur-
faces, are clearly demonstrated.

E. SARTORI 309
The above demonstrations are also in perfect agree-
ment with well-known works which have shown that the
pan evaporation, the surface radiation and the winds de-
creased while the precipitation, humidity and cloudiness
increased in many countries of the world in the last dec-
ades (e.g., [ 2,4, 6 ,13 ,14, 24]) . Since in the last 50 years the
cloudiness, the precipitation, the humidity and the tem-
peratures increased while the pan evaporation, surface
radiation and the wind decreased, this is the perfect proof
that the Earth’s greenhouse effect for the corresponding
regions and periods increased, actually. When the
greenhouse effect increases in an atmosphere where there
is evaporation, the inner temperatures and the humidity
in- crease while the evaporation, the surface radiation
and the wind decrease, automatically. So is the way how
green- houses work and this is also demonstrated [8]. The
increase of the humidity, precipitation and of the water
and air temperatures along with decreasing surface radia-
tion, evaporation and winds is possible only with the
increasing presence of the greenhouse effect.
The “closing” of the Earth’s atmosphere is made either
by increase of the percentage, thickness and darkening of
clouds, which conditions change the convection, evapo-
ration and radiation behaviors. Concentrations of water
vapor and of other greenhouse gases also contribute for
the modification of the normal path and intensity of the
incoming and outgoing radiation. Transparent covers
(glass, clouds, plastic, water vapor, gases, etc.), reflect
and absorb and thus reduce the radiation entering the
system (greenhouse) in comparison to that of a system
that does not own a cover. A thicker and more opaque
cover reduces the transmitted solar radiation because the
absorption of solar radiation by the cover is higher. Fur-
thermore, this cover also changes the wind and the con-
vection condition s within the greenhouse.
The absorbed energy in a common sheet of glass is
much greater than in a thin sheet of plastic, and because
of this the radiation entering the system with glass is
lower than for the greenhouse with plastic, but the green-
house effect with glass cover becomes much stronger
than using this plastic, because of its stronger absorption
of the incoming and outgoing infrared radiation and due
to less heat loss by conduction-convection at the cover,
as may happen with cloud covers. The H2O concentra-
tion in the atmosphere is much higher than the corre-
sponding CO2 concentration and the absorption of infra-
red radiation by the H2O is also much higher than that by
the CO2. Water vapor absorbs strongly in several bands
of the more energetic part of the solar radiation spectrum,
while the CO2 absorbs in a few and small bands of the
less energetic part of the solar spectrum (e.g., [25]).
“When the humidity is high, the water vapor attenuates
the global irradiance from its extraterrestrial value of
53% to about 38% at the Earth’s surface due to absorp-
tion in the infrared portions of the spectrum” [26].
The water vapor combines its greatest amount in the
atmosphere with its physical characteristic of most ab-
sorber to be the main greenhouse gas. A gas must satisfy
these two conditions to be considered a greenhouse gas.
The gases CH4 and N2O do not show absorption bands
for the solar radiation spectrum, which means that they
are not greenhouse gases for these radiation ranges. Mea-
surements of the radiation emitted by the Earth’s surface
at temperatures of about 50˚C at noon over the Northern
Africa [12] show that the CH4 presents an absorption
band at about 7.7 m (7700 nm) and the CO2 at about 15
m, while the water vapor is again the major absorber
over this infrared spectrum. Other online data confirm
that the carbon dioxide is the second greenhouse gas. The
average natural water vapor content (40,000 ppm) in the
atmosphere by volume is about 100 times greater than
the carbon dioxide content (370 ppm) and about 23,000
times greater than the methane content (1.7 ppm) [27].
A simple exercise gives an insight of the relative in-
fluences of each gas on the greenhouse warming. If the
atmosphere was constituted only by water vapor, the
maintenance of its temperature would be 100% due to
this gas, keeping constant all the other conditions. If the
atmosphere was constituted only by water vapor and
carbon dioxide and assuming their influences on the
temperature to be linear, a simple rule of three gives the
influence of each gas on the building of any temperatur e,
taking into account the amounts by volume. For example,
for a total amount of 40,370 ppm and for a 20˚C, the in-
fluence of the water vapor would be 19.82˚C while that
of the carbonic gas would be 0.18˚C. If the carbon diox-
ide was more absorber than the water vapor this result
would be modified, but this is not the case. The relative
influences of the other gases are less than these ones. If
the gases amounts increase, the total amount also must
increase, thus, if the carbon dioxide increased to 500 ppm,
the above relative influences would be respectively equal
to 19.75˚C and to 0.25˚C. And if the water vapor in-
creased to 45,000 ppm and the total atmospheric amount
was 45,500 ppm, the relative influences would be equal
to 19.78˚C and to 0.22˚C, respectively, that is, we cannot
consider an increase of one gas isolately and neglect the
others and the new totals.
The atmosphere of common places (not deserts) does
not reach or remain with zero humidity and the humidity
of the planet has increased in the last decades. The re-
leased heats by evaporation and convection from the
Earth’s surface are also absorbed by the atmosphere and
help to increase the corresponding warming, as it hap-
pens within any greenhouse. Additionally, the CO2 is a
gas that does not condense (such as ozone, nitrous oxide,
methane and chlorofluorocarbons), and it is absorbed by
water or water vapor, and so, with more humidity in the

E. SARTORI 310
air, higher is the precipitation and more gas is withdrawn
from the atmosphere and brought back to the Earth’s
surface.
Measurements confirming the reduction of surface so-
lar radiation in the USA and worldwide in the last dec-
ades showed that this radiation declined 19 W/m2 or 10%
in the United States from the 1960’s to 1980’s and 7
W/m2 or 4% in other regions of the globe in three dec-
ades [2]. Liepert and other researchers (e.g., [3]) did not
understand why reductions in surface solar radiation and
evaporation have been simultaneous with observed in-
crease in air temperature ([28] for the United States),
cloudiness an d precipitation in various parts of the world
for the last decades. This paper (also supported mathe-
matically by the referred demonstration), solves this cor-
rectly. As shown in Section 2, even with less radiation
than for the corresponding open evaporator, the tem-
peratures of greenhouses are much higher and the
evaporation lower. In the case of the increased cloud
cover, the radiation entering this Earth’s greenhouse is
reduced, but even so the inner temperatures increase and
the evaporation decrease (like for other greenhouses).
This greenhouse power for increasing the inner tempera-
tures with comparatively less energy also shows us that
the greenhouse is almost independent of the amount of
solar energy, i.e., it warms with higher or lower solar
energy received. It also shows us that the human influ-
ence on the greenhouse effect should be determined in-
dependently of such variations. Inversely, few clouds
and/or less water vapor and/or other gases indicate that
more direct sunlight reaches the Earth’s surface just in
this case of an open atmosphere, which warming varia-
tion can be due to solar rad iatio n variatio ns, includ ing the
ones caused by the Sun’s cycles. Therefore, it is incorrect
and impossible to attribute such warming to only one
factor (natural or human-induced) without an accurate
scientific analysis, as well as contrarily to the general
belief the air temperature alone is not sufficient and can-
not be used for the determination of a human influence
on an atmospheric warming. The greenhouse effect (due
to clouds and/or more water vapor) is what mainly matters
and it is the concern in relation to the human influence on
an atmospheric warming scenario and climatic chang e s.
Other satellite measurements [29] have also indicated
that cloudy atmospheres absorb 50% more radiation than
predicted, which result harmonizes with the findings
[2,28] and can be a confirmation that the cloud amounts
are increasing and getting thicker. This ARM-ARESE
study also found no evidence for enhanced absorption of
radiation in clear skies, and found strong evidence for
enhanced radiation absorption in cloudy skies.
Satellite data [4] for February and August from 2002
to 2004 over California present a real indication of wind
speed decrease associated with the cloud cover increase,
showing that the average near-surface wind speed over
land in August decreased from 4.2 m/s (when the aerosol
optical depth was low) to 3.5 m/s (when aerosol readings
were high). The trend for February was similar, with a
decrease in wind speed from 7.5 m/s for lower aerosol
counts to 6.5 m/s for higher aerosol counts. According to
the authors, aerosol particles may also explain the re-
duction in the Asian seasonal monsoon and China’s
“disappearing winds”. From 1974 to 1994 the wind speed
in Southeast China dropped by 24% when aerosol optical
depths increased from low to high levels. The authors
also say that observed reduced wind speeds in Europe
may also be due to the increase of cloud cover by aero-
sols. These results are also corroborated by [5] who
compiled decades-long database of aerosols measure-
ments over land and found that clear sky visibility has
decreased over land globally from 1973 to 2007, indi-
cative of an increase of particulates and darkness in the
air over the world’s continents during that time. The
study [6] based on measurements on Earth’s surface
showing that the aver age and peak winds have decreased
10% or more per decade from 1 973 to 2005, especially in
the Midwest and the East of the USA, is another confir-
mation of the demonstrations of the present paper on the
working principles of greenhouses, and also that the
Earth’s greenhouse effect has increased in some places of
the world, with the consequ ent reductions in evaporation,
surface radiation and winds, while the clouds, the pre-
cipitation, the humidity and the water and air tempera-
tures have increased. The cloud cover and greenhouse
gases affect the radiation, but due to its denser and more
solid condition the cloud cover closes the openings and
thus converts the forced convection into the free convec-
tion, i.e., decrease the winds.
The work [7] completes and confirms the demonstra-
tions of this paper on the correct working principles of
greenhouses as well as on the real behavior of the Earth’s
greenhouse effect through their findings that 167 large
lakes water temperatures worldwide increased since 1985.
Using satellite data they found an average warming of
0.45˚C per decade, with some lakes warming as much as
1.0˚C per decade. The warming trends were global and
mainly observed in Europe, North America, Siberia,
Mongolia, China, and in the Southern Hemisphere. The
satellites temperature trends also agreed with trends
measured by nine buoys in the Great Lakes, the Earth’s
largest group of freshwater lakes in terms of total area
and volume. The authors also report that the satellites
measurements were in agreement with independent sur-
face air temperature data from NASA’s Goddard Institute.
The solution [3] believing that the evaporation has de-
creased in the last decades due to the reduction of the
surface solar radiation resulting from energy losses by

E. SARTORI 311
more clouds is erroneous at least by two reasons. First:
the increase of the air and water temperatures in an open
atmosphere is impossible with less energy and their
statement violates the first law of thermodynamic, i.e.,
creates more energy from less energy. Second: if the Sun
froze, all temperatures on Earth would go below zero,
and thus would not rise, in contrast to how was simply
supposed by the authors. The increase of the humidity,
precipitation, water and air temperatures along with de-
creasing surface radiation, evaporation and winds is pos-
sible only with the increasing presence of the greenhouse
effect! The greenhouse works like a second energy
source storing energy and mass, and losing less heat and
mass than a free water surface of an open atmosphere,
while the free convection and the higher air temperature
and humidity inside the greenhouse (caused by the addi-
tion of a cover) cause the evaporation and the wind to
decrease, as well demonstrated in this paper.
However, since we have learned in basic studies that
in the natural hydrological cycle the amount of precipita-
tion is equal to the amount of evaporation a question
arises: how is it possible that clouds and rain have in-
creased with less evaporation? Let’s analyze the hydro-
logical cycle and put it in form of equation (this has
never been done before). Hence, making the water mass
balance for a selected system (control volume) at the
Earth’s surface we get:
Rate of water mass accumulation (at water, soil and
vegetation bodies) = Rate of water mass in (precipitation) –
rate of water mass out (evaporation),
or
dMas ddMpddMevd

   (2)
where Mas = accumulated water mass at a selected sys-
tem of the Earth’s surface (kg), Mev = mass of water by
evaporation (kg), Mp = mass of water by precipitation
(kg), and  = time (h).
Therefore, in places where there was high precipitation,
high humidity and low evaporation, there was an accu-
mulation on the Earth’s surface, or, the variation of water
mass accumulation dMas was positive and the places
became more humid; in places where there was higher
evaporation than precipitation, such variation was nega-
tive and the places became drier. We can have different
precipitation and evaporation rates in a same place in
different periods and conditions, and different precipita-
tion and evaporation rates in different places. It is normal
and natural to have variations in the rate of accumulation,
due to variations in rates of precipitation and evaporation,
which rates depend on several facto rs and conditions.
The equation of the natural hydrological cycle is com-
pleted when we make the water mass balance for a sys-
tem (control volume) of the atmosphere:
Rate of water mass accumulation (clouds + water va-
por) = Rate of water mass in (evaporation) – rate of water
mass out (precipitation),
or
dMaa ddMevddMpd



 (3)
where Maa = accumulated water mass in a selected layer
of the atmosphere (kg).
Equation (3) also tells us that what matters is the
amount of water vapor in the atmosphere, or, in other
words, the variation of the accumulated amount is inde-
pendent whether the molecules are new or old, because
their influences in producing the green house effect is the
same, as also verified in the experimental tests of the
closed evaporator, where new water molecules constantly
rise, absorb thermal radiation, transfer heat by convection
and heat and mass by evaporation, and help the warming
in the same way as old molecules do. When there is a
rainfall this does not mean that the air remains with zero
water vapor, on the contrary, the air humidity (mass)
increases. The water vapor and its influence do not exist
only in clouds. When eventually the amount of precipita-
tion, say new (or old) molecules, equals the amount of
evaporation, say old (or new) molecules, this does not
mean that there is zero water vapor in the atmosphere,
this only means that the variation of such mass is zero in
that moment and place. In humid climates, at any time,
there is always a certain amount of water vapor in the air,
composed by new and old molecules, and both are sub-
mitted to the same processes of absorption, reflection,
transmission and emission of radiation, as well as both
exchange heat by convection and heat and mass by
evaporation with different layers of the atmosphere and
help to change the greenhouse effect. A humid atmos-
phere does not reach zero water vapor, likewise the
evaporation is never zero (unless the extreme case of
saturation with equal temperatures is reached, as shown
[9]). Thus, with higher or lower cyclic velocities of water
in the air, the humid air will always contain significant
amounts of water mass that continuously suffer the re-
ferred influences. And since the planet’s humidity has
increased this means that the Earth’s greenhouse effect
has increased due to the addition of more cover that traps
the heat and humidity below. When you wish to cook
more rapidly and save energy you must put the cover
onto the pot, because this attitude increases the cooking
temperatures. A food inside a closed pot with water is
cooked, not grilled, because the humidity remains and
gives the characteristic food flavor and texture. When a
meat or other food is grilled (i.e., at an open system),
there is not additional water as well as the food water
evaporates and the food becomes dried and gives the
characteristic flavor and texture. The conventional hy-
drological cycle can be seen schematically in Figure 3.

E. SARTORI 312
The human influence alters the velocity of the natural
cycles and the atmospheric heat and mass balances, being
the solution to the question raised before given by the
explanation that the evaporation has not been the only
source for the cloud formation and the main reasons are:
a) because droplets of condensed water vapor aggregate
on microscopic dust particles (the cloud droplet nuclei or
cloud condensation nuclei) the emissions of lots of tons
of solid particles every second all over the world inten-
sify the cloud formation and precipitation. Hence, we can
say that there is also the “dust or aerosols cycle”; b) tons
of superheated gases (including water vapor) emitted by
fossil fuel power plants, nuclear plants, industries, and
other sources are released with extremely high tempera-
tures and then the air dew point temperature is reached
more often and more water vapor is condensed in less
time and form more clouds and rain; c) the emissions
from nuclear plants, industries, fossil fuel power plants,
etc, contain tons of superheated water vapor and when
they make contact with cooler layers of the atmosphere
more condensed water and clouds are formed; this also
corresponds to mass and latent heat addition, which also
increases the humidity of the air, which is an additional
cause for the evaporation decrease. These causes explain
why the cloudiness, the precipitation and the humidity
have increased in almost the entire world.
Some places eventually less humid may present higher
precipitation than more humid ones if their atmospheres
contain more solid particles and heat and mass emissions,
because these factors increase the formation of clouds
and rain faster than the natural cycle does. Measurements
[30] confirm that “the more the aerosol present, the more
the cloud droplets”. Such higher precipitation may be
also due to wind currents that transport humidity, heat
and pollutants. We could say that vertical currents feed,
while horizontal currents transport.
Therefore, the behavior, the amount of water, the regu-
larity of waters, the distribution of rain and the velocity
of the hydrological cycle no longer depend solely on the
natural processes of evaporation and precipitation as they
were conceived and taught, and thus there is a new hy-
Figure 3. A simple representation of the conventional hy-
drological cycle.
drological cycle and climatic changes which are con-
sequences of certain human activities.
Thus, the new hydrological cycle has been discovered
and registered by this author, which water mass balance
for a system (control volume) at the Earth’s surface in-
cludes the withdrawal of water from the surface and/or
subterranean waters and released to the atmosphere by
certain human activities:
Rate of water mass accumulation (at water, soil and
vegetation bodies) = Rate of water mass in (precipitation) –
rate of water mass out (evaporation) – rate of water mass
out (human activities),
or
dMasddMpddMevd dMhd



 (4)
where Mh = mass of water released to the atmosphere by
human activities (kg).
The equation of the new hydrological cycle is com-
pleted when we make the mass balance for a system
(control volume) of the atmosphere:
Rate of water mass accumulation (clouds + water va-
por) = Rate of water mass in (evaporation) + Rate of wa-
ter mass in (total clouds and water vapor caused by hu-
man activities) – rate of water mass out (precipitation),
or
dMaaddMev ddMh ddMpd



 (5)
Since everything that rises must come back, the more
intense and irregular the water mass and aerosols re-
leased to the atmosphere by human activities (Mh), the
more intense and irregular will be such return to the
Earth’s surface after physical and chemical interactions
in the atmosphere. The new hydrological cycle can be
visualized schematically in Figure 4.
However, there should be a saturation limit for water
vapor and particulates to generate more clouds and rain,
since in a certain time in big and industrialized cities,
over large agricultural dry field s, with intense burning of
crops and forests, or at deforested areas, for example, the
solid air particles in excess may not find sufficient water
vapor to form more clouds and rain and thus accumulate
in the atmosphere for a certain time creating a “solid”
barrier or cover (Figure 5). This is apparently confirmed
by Wang J. et al. [31] who found that shallow clouds tend to
form over deforested areas of the Amazon while deep
clouds are more prevalent above the dense and humid
intact forest as well as the shallow clouds that developed
over the forested areas normally became deep clouds.
Rosenfeld et al. [32] also corroborate with this analysis
through their findings that increasing aerosol concentra-
tions below the optimum will boost rainfall, whereas
increasing levels above the optimum will decrease rain-
fall. With intense burnings, the heat from smokes to-
gether with the air humidity may increase the formation

E. SARTORI 313
Figure 4. The new hydrological cycle reveals that certain
human activities increase the formation of clouds and gen-
erate excess and irregular amounts and distributions of
precipitation with consequent decreased evaporation.
Figure 5. The new hydrological cycle also reveals that par-
ticles in excess in the air beyond the limit of water vapor
due to certain human activities can generate the formation
of solid barriers in skies and/or more “solid” cloud cover
with consequent less precipitation and more droughts in
uncertain periods and places.
of clouds and rain in a first moment, because the dew
point temperature is reached more rapidly, however,
when the limit of saturation approaches, more solid par-
ticles tend to remain in th e atmosphere for a certain time.
In the case of polluted cities, such “solid” and con-
taminated barrier can cause the population to face respi-
ratory and other health problems. It is interesting to note
that the same principle (cloud condensation nuclei) that
increases the formation of clouds when there is sufficient
water content in the air may cause a “solid” barrier in the
sky, with a consequent more opaque cover for the trans-
mittance of light and radiation as well as for the outgoing
infrared radiation. Such “solid” barrier also causes the
cover to become more “closed” for the convection effects
independently of the corresponding particles color. With
such a “solid” and more “closed” atmosphere in these
conditions, the rate of formation of clouds an d rain is less
(as also happens in the closed evaporator where the con-
densation of water vapor is less with an opaque cover),
leading to an airless ambient and some drought condi-
tions in uncertain periods and places.
In short, the new water cycle reveals and explains that
certain human activities are more and more rapidly
throwing water, heat and particulates in the air than the
natural processes can do and which factors until certain
limits of saturation in crease the formation of clouds, pre-
cipitation and the greenhouse effect, with the consequent
reduction of surface solar radiation, evaporation and
winds. There is an increase of irregular amounts and ir-
regular geographical and temporal distributions of pre-
cipitation and above the limits of saturation may cause
droughts and other climatic changes due to several fac-
tors. However, many of the human-induced climatic
causes and effects have technological and collaborative
solutions just on Earth’s surface.
4. Conclusions
The first principles that govern the operation of an open
evaporator (free water surface) and of a closed evapora-
tor (greenhouse effect) have been described in depth.
Such physical principles are relevant for the better un-
derstanding of the very similar behaviors of the open
(cloudless) and of the “closed” (totally cloudy) Earth’s
atmospheres. In these greenhouses, the water has been
included, otherwise the corresponding heat and mass
balances do not match. Thus, it is also incorrect to con-
sider the radiation as the only energy transfer factor or
forcing for an atmospheric warming. Most of the heat
transfer from the Earth’s surface to the atmosphere per
square meter, per temperature difference and per total
area is by evaporation, which increases substantially the
greenhouse warming.
It is incorrect to state that the evaporatio n of open and
closed evaporating systems increase based solely on the
water or air temperatures, because there are many other
factors that affect the evaporation at the same time in the
opposite sense. For example, the ambient temperature
increase plays a strong role in the evaporation decrease.
It is also a strong error to state that the evaporation
must increase with the greenhouse effect increasing in
comparison to an open evaporating system. Demonstra-
tions (supported by mathematical calculations) based on
fundamental laws that govern the evaporation have been
performed and confirm these findings. It has been shown,
among several other things, that when the cloud cover
increases, the evaporation decreases. The evaporation is
in the core of the greenhouse effect and of an atmos-
pheric warming scenario, and accurate understandings
and directions are thus enormously required.
Among several other things, it is very important to
note that the interior of a greenhouse receives less energy
than an open system and even so the temperatures of the
closed one reach much higher values. This is how
greenhouses behave and is another demonstration on why

E. SARTORI 314
any considered amount of solar energy and water and air
temperatures are not sufficient to guarantee higher or
lower warming and evaporation when the greenhouse
effect is involved.
Various researchers did not understand why reductions
in surface solar radiation and pan evaporation have been
happening simultaneously with observed increase in air
temperature, cloudiness and precipitation in various parts
of the world for the last decades. Some of them stated
that more precipitation is not conciliatory with less
evaporation and named their understandings as the
“evaporation paradox”, while others “found” “the cause”
violating the laws of thermodynamics. However, more
precipitation is perfectly and naturally conciliatory with
less evaporation. Since in the last decades the cloudiness,
the precipitation, the humidity and the water and air
temperatures increased while the pan evaporation, the
surface radiation and the winds decreased in some places
of the world, this is the perfect proof that the Earth’s
greenhouse effect increased in such places and periods.
The increase of the humidity, precipitation an d water and
air temperatures along with decreased surface radiation,
evaporation and winds are possible only with the in-
creasing presence of the greenhouse effect and of the
cloud cover, as described in this paper. In the literature,
temperatures increase have been related to only one fac-
tor (radiation), but there are many other parameters and
causes that increase or decrease the temperatures.
It has also been generally said that in a greenhouse the
convection is suppressed , but on ly the w ind is su ppressed ,
because when there are temperature differences the con-
vection is not suppressed. Even tiny temperature differ-
ences keep small air movements, which keep the convec-
tion. That is, when an open system is covered, the con-
vection is converted from forced to free convection, and
this means that in an increasing Earth’s greenhouse effect
due to cloud cover increase the wind decreases, too.
Various studies with measurements by satellites and on
Earth present a real indication of a global wind speed
decrease associated with the cloud cover increase, as
expected and demonstrated by this author. Satellite data
showing that more than 170 large lakes water tempera-
tures worldwide increased since 1985 complete and con-
firm this paper description of the working principles of
greenhouses as well as of the real and altered behavior of
the Earth’s greenhouse effect in some places and periods
of the world.
Since the winds tend to disappear in a full greenhouse
effect, how then tornadoes and hurricanes are explained?
These are not linked to the greenhouse effect, but to
strong pressure differences (where humans can also act),
which can also be demonstrated physically and mathe-
matically.
The hydrological cycle has been analyzed and put in
form of equation (which analyses have never been done
before) and the new hydrological cycle which is conse-
quence of certain human activities (e.g., fossil fuel power
plants, nuclear plants, industries, etc.) was discovered.
The human influence alters the velocity and the behavior
of the natural cycles as well as the atmospheric heat and
mass balances, and th e evaporation has not been th e only
source for the cloud and rain formation. Interesting to
note that the same principle (cloud condensation nuclei),
that increases the formation of clouds and rain may cause
less precipitation and droughts. Several other relevant
issues have been elucidated and correctly solved in the
paper.
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E. SARTORI 316
Appendix
There are lots of equations for calculating the evapora-
tion rate from free water surfaces and it is impossible to re-
view all of them in a single paper or in an ap pendix. Sar-
tori [9] reviewed 21 of them while [22] evaluated 13 of
them. Singh-Xu made such evaluation based on generic
data and using statistical analysis that focused almost only
on errors and t hat produced ge neric resul ts for uncertain water
surfaces and uncertain periods and places of the planet.
Thus, in this appendix the 13 equations from [22] plus
the Sartori equation are reviewed through direct compa-
risons with real experi mental data, which comp arisons pro-
duce objective results on the accuracy of each equation.
The paper [33] probably is the only one or the very
rare one that presents almost all of the real data needed
for the proper application of equations, such as the water
temperature, the air temperature, the wind velocity, the
relative humidity, periods of tests, pan sizes, pan colors,
etc., and is thus very appropriate for direct comparisons of
real data from pans working under different conditions.
The evaporation does not have different names, because
the only corresponding real physical phenomenon that hap-
pens from any wet surface, independently of water body
sizes, for example, is only and simply the evaporation.
When a free water surface is exposed to the atmos-
phere it suffers influence from the wind velocity, the air
temperature, the relative humidity, the solar radiation,
and also from the atmospheric pressure and the physical
structure. The water temperature is the final result of all
interactions of the water layer with the env ironment after
all heat and mass gains and losses.
The 14 equations are:
Dalton:



15in mo
sa
Eee (A1)
Fitzgerald:
  

0.40.199uin mo
sa
Eee  (A2)
Meyer:
  

11 10.1uinmo
sa
Eee  (A3)
Horton:
   

0.42exp2uin mo
sa
Eee  (A4)

  
Rowher :0.771.4650.0186Pb
0.440.118uin day
sa
E
ee

  (A5)
Penman:
  

2
0.35 10.24uinday
sa
Eee  (A6)
Harbeck1:
 

8
0.0578uin day
sa
Eee (A7)
Kuzmin:
 

8
6.0 10.21uin mo
sa
Eee  (A8)




Harbeck2: 0.001813u
10.03 inday
sa
aw
Ee
Tt

 
e
(A9)




 
1
1
Konstantinov :0.024u
0.166u
Wa
sa
Ett
ee





2
a
Romanenko:0.0018 T25
100rhcm mo
E
 (A11)


 




2
28
Sverdrup:
0.623K uPbln800 200
cm s
sa
Eee   (A12)





282
2
Thornthwaite-Holzman :
0.623 KuuPb
ln800200cm s
sa
Ee
 

 e (A13)

0.8 0.22
wa
Sartori:
0.0041PPkgm sEVLP





(A14)
Since [33] did not measure the wind velocity u8, then
it has been estimated from the data [33] through the for-
mula

0.15
8383
uuhh
In these equation s, E = evaporation rate; ea, es = water
vapor partial pressures at the air (ta) and water (tw) tem-
peratures, respectively (inHg); h3, h8 = heights at 3 m and
8 m (m); K = von Kármán constant = 0.41; L = surface
length of water in the wind direction (m); P = atmos-
pheric pressure (Pascal); Pb = atmospheric pressure (in
Hg); Pa, Pw = water vapor partial pressures at the air and
water temperatures (Pascal); rh = relative humidity (per-
cent); tw = water temperature (˚C); Ta = ˚C + 1.9 ˚C (for
eq. A9 only); u, u1, u2, u3, u8 = wind velocity at surface
level and at heights 1 m, 2 m, 3 m and 8 m above surface
(miles/h); V = wind velocity (m/s);
 = density of air (l
b/ft3);
 = relative humidity (fraction).
Yu and Brutsaert tested 3 pan sizes painted black,
white, gray and green. The sizes 4 ft (1.2 m) and 8 ft (2.4
m) and the colors black and white are sufficient for the
present comparisons and validation. Figures A1-A4
show the results of these comparisons. All equations
were calculated as they are with their own units, being
the final results converted to mm/h and then included in
the graphs.

(A10)
The results from the Romanenko and Sverdrup equa-
tions could not be included in the graphs because their
values fall off the scales. For each one of the four pans
(4B, 4W, 8B, 8W) the minimum and maximum values
from the Romanenko equation are always 6.98 and 78.77
mm/h, while from the Sv erdrup equation these values are:
4B = –6.28 and 17.16 mm/h; 4W = –11.41 and 3.26
mm/h; 8B = –5.33 and 21.27 mm/h; 8W = –11.52 and
3.6 mm/h, respectively.
It is not the scope of this appendix to make a full
analysis of the equations, but the equations that use the

E. SARTORI 317
(es - ea) difference consider that tw is always higher than
ta (because es and ea depend directly on tw and ta, re-
spectively), which is not always true, and then such dif-
ference often gives negative values that generate an inva-
lid condition for the evaporation. These negative values
do not correspond to the condensation of the water vapor
on the water surface (“negative evaporation”), as calcu-
lated correctly and experimentally verified [16].
The Romanenko equation owns parameters only for
the air and not for the water, therefore, it has nothing to
do with water and evaporation and for it doesn’t matter
whether there is an ocean or a desert, because it does not de-
pend on the water conditions and does not produce results
for water surfaces. This is also verified in present calcu-
lations. Only an analysis not based on real and objective
data could rank such equation as one of the most important.
As can be seen in the graphs, only one equation pro-
duced the correct and close agreement with experimental
tests and best reproduces with high accuracy the behavior of
the nature, independently of sizes, colors, differen t ambi-
ent conditions and amounts of water. It is also interesting
to note in Figures A1-A4 that the Sartori equation
-2 .5
-1 .5
-0 .5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
1 2 34 5 6 78 910111213141516171819202122232425
Run
Evaporation, mm/h
YB
Dalton
Fitz
Meyer
Horton
Rowher
Penman
Harb1
Kuzmin
Harb2
Thorn
Konst
Sartori
4B
19.1
YB
Sart
Figure A1. Comparison of equations results with the experimental data [33] for a 1.2 m square pan painted black (4B).
-5
-4
-3
-2
-1
0
1
2
3
1 2 3 4 5 6 7 8 910111213141516171819202122232425
Run
Evaporation, mm/h
YB
Dalton
Fit z
Meyer
Horton
Rowher
Penman
Harb1
Kuzmi n
Harb2
Thorn
Konst
Sart ori
4W
Sart
Figure A2. Comparison of equations results with the experimental data [33] for a 1.2 m square pan painted white (4W).

E. SARTORI 318
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8910111213141516171819202122232425
Run
Evaporation, mm/h
YB
Dalton
Fitz
Meyer
Hor to n
Rowher
Penman
Har b1
Ku z min
Har b2
Thorn
Kons t
Sartori
8B
YB
Sart
24.7
Figure A3. Comparison of equations results with the experimental data [33] for a 2.4 m square pan painted black (8B).
-4
-3
-2
-1
0
1
2
3
12345678910 11 12 131415 1617 18 19 20 21 22 23 24 25
Run
Evaporation, mm/h
YB
Dalton
Fitz
Meyer
Horton
Rowher
Penman
Harb1
Kuzmin
Harb2
Konst
Thorn
Sartori
8W
YB
Sart
Figure A4. Comparison of equations results with the experimental data [33] for a 2.4 m square pan painted white (8W).
produced almost the same excellent accuracy for all of
the situations, independently of sizes and of several other
conditions. For example, the difference between L =
(1.2)–0.2 and L = (2.4)–0.2 is 13% and if the L was not
taken into account such error would be introduced in the
results.
Furthermore, through the Sartori equation the evapo-
ration can be calculated ev en for the condition when t a >
tw, as well as the inedited condensation (dew) of the wa-
ter vapor of the air onto the water surface can be ob-
tained when td > tw. In this equ ation the laws that govern
the evaporation are taken into account and no other
equation owns all these correct requirements and funda-
ental features. m
The Sartori equation is the result of the combination
among the Bowen equation [34], the Bowen-Sartori
equation and the boundary layer theory [8,9,16,17]. Bo-
wen’s equation was derived theoretically through an
analysis on a differential control volume of a fluid ele-
ment flowing over a water surface. The boundary layer
theory is the basis of the science on convection heat and
mass transfer, is based on first principles verified ex-
perimentally and is mandatory for any fluid flow over
wet and dry surfaces. Also, as demonstrated [9,23], the
evaporation and the convection coefficient depend on
V0.8 and L–0.2 (for turbulent flow) and not linearly on V
and L, as used in the 13 and in the lots of other equiva-
lent equations obtained empirically.