Vol.3, No.12, 971-998 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.312124
Scrutinizing the atmospheric greenhouse effect and its
climatic impact
Gerhard Kramm1*, Ralph Dlugi2
1Geophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska; *Corresponding Author:
2Arbeitsgruppe Atmosphärische Prozesse (AGAP), Munich, Germany.
Received 23 August 2011; revised 30 September 2011; accepted 17 October 2011.
ABSTRACT
In this paper, we scrutinize two completely dif-
ferent explanations of the so-called atmospheric
greenhouse effect: First, the explanation of the
American Meteorological Society (AMS) and the
World Meteorological Organization (W·MO) quan-
tifying this effect by two characteristic tem-
peratures, secondly, the explanation of Rama-
nathan et al. [1] that is mainly based on an en-
ergy-flux budget for the Earth-atmosphere sys-
tem. Both explanations are related to the global
scale. In addition, we debate the meaning of
climate, climate change, climate variability and
climate variation to outline in which way the
atmospheric greenhouse effect might be re-
sponsible for climate change and climate vari-
ability, respectively. In doing so, we distinguish
between two different branches of climatology,
namely 1) physical climatology in which the
boundary conditions of the Earth-atmosphere
system play the dominant role and 2) statistical
climatology that is dealing with the statistical
description of fortuitous weather events which
had been happening in climate periods; each of
them usually comprises 30 years. Based on our
findings, we argue that 1) the so-called atmos-
pheric greenhouse effect cannot be proved by
the statistical description of fortuitous weather
events that took place in a climate period, 2) the
description by AMS and W·MO has to be dis-
carded because of physical reasons, 3) energy-
flux budgets for the Earth-atmosphere system
do not provide tangible evidence that the at-
mospheric greenhouse effect does exist. Be-
cause of this lack of tangible evidence it is time
to acknowledge that the atmospheric green-
house effect and especially its climatic impact
are based on meritless conjectures.
Keywords: Physical Climatology;
Statistical Climatology; Atmospheric Greenhouse
Effect; Earth-Atmosphere System
1. INTRODUCTION
Recently, Gerlich and Tscheuschner [2] listed a wide
variety of attempts to explain the so-called atmospheric
greenhouse effect. They disproved these explanations at
the hand of fundamental physical principles like the
second law of thermodynamics. By showing that 1) there
are no common physical laws between the warming
phenomenon in glass houses and the fictitious atmos-
pheric greenhouse effects, 2) there are no calculations to
determine an average surface temperature of a planet, 3)
the frequently mentioned difference of 33 K is a mean-
ingless number calculated wrongly, 4) the formulas of
cavity radiation are used inappropriately, 5) the assump-
tion of a radiative balance is unphysical, 6) thermal
conductivity and friction must not be set to zero, they
concluded that the atmospheric greenhouse conjecture is
falsified.
Shortly after the paper of Gerlich and Tscheuschner
was published by the International Journal of Modern
Physics B (IJMPB), there was an uproar in the internet
(e.g., http://www.scienceblogs.de/primaklima/2009/03/
chronik-eines-angekundigten-skandals-gerlich-und-tsche
uschner-wurden-peerreview t.php, http://rabett.blogspot.
com/2009/04/die-fachbegutachtung-below-is-elis.html)
resulting in an uncounted attempts to insult Gerlich and
Tscheuschner, even under pseudonyms as done, for in-
stance, by Joshua Halpern (aka Eli Rabett) and Joerg
Zimmermann (aka for4zim) in violating the ethical stan-
dards of scientific debates.
Halpern et al. [3] eventually wrote a comment on the
paper of Gerlich and Tscheuschner [2]. They claimed
that they showed that Gerlich and Tscheuschner’s meth-
ods, logic and conclusions are in error. They pointed out
that Gerlich and Tscheuschner did not come to grips with
how the greenhouse effect emerges at levels of analysis

G. Kramm et al. / Natural Science 3 (2011) 971-998 972
typical of the modern state-of-the-art, such as from line
by line calculations of atmospheric radiative transfer,
global climate models (GCMs) or even on the level of
advanced textbooks, but rather criticize simple, didactic
models for not being complete. Furthermore, Halpern et
al. argued that Gerlich and Tscheuschner made elemen-
tary mistakes. Moreover, Halpern et al. stated that these
authors’ lack quantitative familiarity with the field they
are criticizing, second their claims of complexity or in-
validity, impossibility and occasionally fraud regarding
well-established quantitatively verified analyses of at-
mospheric processes and third their extensive diversions
on topics that do nothing to further their own argument
or a reader’s understanding. In their reply to this com-
ment, Gerlich and Tscheuschner [4] argued that their
falsification paper discusses the violation of fundamental
physical and mathematical principles in 14 examples of
common pseudo-derivations of fictitious greenhouse
effects that are all based on simplistic pictures of radia-
tive transfer and their obscure relation to thermodynam-
ics, including but not limited to those descriptions that 1)
define a perpetualmotion machine of the 2nd kind, 2)
rely on incorrectly calculated averages of global tem-
peratures and 3) refer to incorrectly normalized spectra
of electromagnetic radiation. They continued that Halpern
et al. even did not define the greenhouse effect that they
wish to defend.
It should be noticed that—based on the reviews re-
quested by the IJMPB—the manuscript of Halpern et al.
first submitted in 2009 was rejected. Surprisingly and
unfortunately, it was eventually published by this journal,
but none of the authors’ big physical mistakes criticized
by the reviewers were removed from the manuscript.
The example 2.1 of Halpern et al., for instance, which is
dealing with two heat reservoirs at different temperatures
that exchange energy and entropy by radiation is falsi-
fied because the magnitude of the entropy flux emitted
by a black body is given by 3
43
s
J
T

 [5], where
T is the actual surface temperature and 8
5.67 10 


W·m–2·K–4 is Stefan’s constant. Halpern et al. not only
ignored Planck’s [5] results, but also those of many
peer-reviewed papers published during the past four
decades (e.g., [6-9]). In addition, even the wrong units
for irradiances and entropy fluxes used in their 2009-
version and already criticized by, at least, one of the re-
viewers were not replaced in their printed version by the
correct ones. If it is possible to publish such a physically
inadequate comment, we have to acknowledge that the
discipline of climatology has lost its rational basis.
Is the so-called atmospheric greenhouse conjecture
really falsified as Gerlich and Tscheuschner claimed and/
or is the notion “atmospheric greenhouse effect” only a
misnomer in describing a real effect that may cause a
climatic impact? To answer these questions two com-
pletely different explanations of the atmospheric green-
house effect are to be scrutinized in this paper. First, the
explanation of the American Meteorological Society
(AMS) and the World Meteorological Organization (W·MO)
quantifying the effect by two characteristic temperatures
is assessed in Section 3. Secondly, the explanation of
Ramanathan et al. [1] that is mainly based on an en-
ergy-flux budget is analyzed in Section 4. However, be-
fore we start to scrutinize these two different explana-
tions we debate the meaning of climate, climate variabil-
ity, climate change and climate variation in Section 2.
Such a debate is required to outline in which way the
atmospheric greenhouse effect might be responsible for
climate variability, climate change and climate variation,
respectively. In doing so, it is indispensable to distin-
guish between two different branches of climatology,
namely 1) physical climatology in which the boundary
conditions of the system Earth-Atmosphere play the
most dominant role and 2) statistical climatology that is
dealing with the statistical description of fortuitous
weather events that had been happening in sufficiently
long-term periods of the past.
2. ON THE MEANING OF CLIMATE,
CLIMATE VARIABILITY, CLIMATE
CHANGE and CLIMATE VARIATIONS
Like many other ones disputed by Gerlich and Tsch-
euschner in their paper [2], the explanations of the at-
mospheric greenhouse effect scrutinized in our contribu-
tion are related to the global scale. This relation could be
the reason why often the notion “global climate” is used
and the debate on climate change is mainly focused on
global climate change.
The notion “global climate”, however, is a contradic-
tion in terms. According to Monin and Shishkov [10],
Schönwiese [11] and Gerlich [12], the term “climate” is
based on the Greek word “klima” which means inclina-
tion. It was coined by the Greek astronomer Hipparchus
of Nicaea (190-120 BC) who divided the then known
inhabited world into five latitudinal zones—two polar,
two temperate and one tropical—according to the incli-
nation of the incident sunbeams, in other words, the Sun’s
elevation above the horizon. Alexander von Humboldt in
his five-volume “Kosmos” (1845-1862) added to this
“inclination” the effects of the underlying surface of
ocean and land on the atmosphere [10]. From this point
of view one may define the components of the Earth’s
climate system: Atmosphere, Ocean, Land Surface (in-
cluding its annual/seasonal cover by vegetation), Cryos-
phere and Biosphere. These components play a promi-
nent role in characterizing the energetically relevant
boundary conditions of the Earth’s climate system. Other

G. Kramm et al. / Natural Science 3 (2011) 971-998
973973
definitions are possible. Ocean and cryosphere, for in-
stance, are subcomponents of the Hydrosphere that com-
prises the occurrence of all water phases in the Earth-
atmosphere system [13]. Thus, the interrelation between
the solar energy input and the components of our climate
system coins the climate of locations and regions sub-
sumed in climate zones. An example of a climate classi-
fication is the well-known Köppen-Geiger climate clas-
sification recently updated by Peel et al. [14]. It is illus-
trated in Figure 1.
2.1. The Boundary Conditions and Their
Role in Physical Climatology
First, we have to explain how the inclination of the
incident sunbeams does affect the climate of a location
or region. The solar energy reaching the top of the at-
mosphere (TOA) depends on the Sun’s role as the source
of energy, the characteristics of the Earth’s elliptical or-
bit around the Sun (strictly spoken, the orbit of the
Earth-Moon barycenter) and the orientation of the
Earth’s equator plane. The orbit geometry and the orien-
tation of the equator plane are characterized by 1) the
orbit parameters like the semi-major axis, a, the eccen-
tricity, e, the oblique angle of the Earth’s axis with re-
spect to the normal vector of the ecliptic, ε = 23˚27' and
the longitude of the Perihelion relative to the moving
vernal equinox,

and 2) the revolution velocity and
the rotation velocity of the Earth [15,16]. Note that



, where the annual general precession in lon-
gitude,

, describes the absolute (clockwise) motion of
the vernal equinox along the Earth’s orbit relative to the
fixed stars (see Figure 2) and the longitude of the Peri-
helion,

, measured from the reference vernal equinox
of A.D. 1950.0, describes the absolute motion of the
Perihelion relative to the fixed stars. For any numerical
value of

, 180˚ is subtracted for a practical purpose:
observations are made from the Earth and the Sun is
considered as revolving around the Earth [17,18]. Obvi-
ously, the emitted solar radiation depends on the Sun’s
activity often characterized by the solar cycles that are
related to the number of sunspots observed on the Sun’s
surface (see Figure 3). However, to understand in which
way the solar insolation reaching the TOA is affected by
the Earth’s orbit, a brief excursion through the Sun-Earth
Figure 1. World map of the Köppen-Geiger climate classification (adopted from Peel et al. [14]). The 30 possible climate types in
Table 1 are divided into 3 tropical (Af, Am and Aw), 4 arid (BWh, BWk, BSh and BSk), 8 temperate (Csa, Csb, Cfa, Cfb, Cfc, Cwa,
Cwb and Cwc), 12 cold (Dsa, Dsb, Dsc, Dsd, Dfa, Dfb, Dfc, Dfd, Dwa, Dwb, Dwc and Dwd) and 2 polar (ET and EF).

G. Kramm et al. / Natural Science 3 (2011) 971-998 974
Table 1. Description of Köppen climate symbols and defining
criteria (adopted from Peel et al. [14]).
1st 2nd 3rd Description Criteria*
A Tropical Tcold ≥ 18
f -Rainforest Pdry ≥ 60
m -Monsoon Not (Af) & Pdry ≥ 100 – MAP/25
w -Savannah Not (Af) & Pdry < 100 – MAP/25
B Arid MAP < 10 × Pthreshold
W -Desert MAP < 5 × Pthreshold
S -Steppe MAP ≥ 5 × Pthreshold
h -Hot MAT ≥ 18
k -Cold MAT < 18
C Temperate Thot > 10 & 0 < Tcold <18
s -Dry Summer Psdry < 40 & Psdry < Pwwet/3
w -Dry Winter Pwdry < Pswet/10
f -Without dry season Not (Cs) or (Cw)
a -Hot Summer Thot ≥ 22
b -Warm Summer Not (a) & Tmon10 ≥ 4
c -Cold Summer Not (a or b) & 1 ≤ Tmon10< 4
D Cold Thot > 10 & Tcold ≤ 0
s -Dry Summer Psdry < 40 & Psdry < Pwwet/3
w -Dry Winter Pwdry < Pswet/10
f -Without dry season Not (Ds) or (Dw)
a -Hot Summer Thot ≥ 22
b -Warm Summer Not (a) & Tmon10 ≥ 4
c -Cold Summer Not (a, b or d)
d -Very Cold Winter Not (a or b) &Tcold < –38
E Polar Thot < 10
T -Tundra Thot > 0
F -Frost Thot ≤ 0
*MAP = mean annual precipitation, MAT = mean annual temperature, Thot =
temperature of the hottest month, Tcold = temperature of the coldest month,
Tmon10 = number of months where the temperature is above 10, Pdry = pre-
cipitation of the driest month, Psdry = precipitation of the driest month in
summer, Pwdry = precipitation of the driest month in winter, Pswet = precipi-
tation of the wettest month in summer, Pwwet = precipitation of the wettest
month in winter, Pthreshold = varies according to the following rules (if 70%
of MAP occurs in winter then Pthreshold = 2 × MAT, if 70% of MAP occurs in
summer then Pthreshold = 2 × MAT + 28, otherwise Pthreshold = 2 × MAT + 14).
Summer (winter) is defined as the warmer (cooler) six month period of
ONDJFM and AMJJAS.

Figure 2. Elements of the Earth’s orbit (with reference to Ber-
ger [18]). The orbit of the Earth, E, around the Sun, S, is rep-
resented by the ellipse PAE, P being the Perihelion and A the
Aphelion. Its eccentricity is given by


22
eaba , a being
the semi-major axis and b the semi-minor axis. Furthermore, γ
is the vernal point, WS and SS are the winter and summer sol-
stices, respectively. They mirror their present-day locations.
The vector n is perpendicular to the ecliptic and the obliquity, ε,
is the inclination of the equator upon the ecliptic; i.e., ε is equal
to the angle between the Earth’s axis of rotation and n. The
parameter

is the longitude of the Perihelion relative to the
moving Vernal Equinox (VE) and is equal to ξ + ψ. The annual
general precession in longitude, ψ, describes the absolute mo-
tion of γ along the Earth’s orbit relative to the fixed stars. The
longitude of the perihelion, ξ, is measured from the reference
vernal equinox of A.D. 1950 and describes the absolute motion
of the perihelion relative to the fixed stars. For any numerical
value of

, 180˚ is subtracted for a practical purpose: obser-
vations are made from the Earth and the Sun is considered as
revolving around the Earth.
geometry is indispensable and outlined here.
2.1.1. The Sun-Earth Geometry
The actual distance, r, between the Sun’s center and
the Earth’s elliptic orbit (see Figure 2) can be expressed
by the semi-major axis, a = 149.6 × 106 km, the eccen-
tricity, e = 0.0167 and the true anomaly,

, i.e., the
positional angle of the Earth on its orbit counted coun-
terclockwise from the minimum of r called the Perihe-
lion,

2
1
1cos 1cos
ae
p
ree





(2.1)
Here,


2
pLm

,
 
12
22
12eELm   and
M
m



, where

is the gravitational constant, M is
the mass of the Sun, m is the mass of the Earth and
2.Lmrddtconst
  is the angular momentum con-
sidered as invariant with time, i.e., the angular momen-
tum in a central field like Newton’s gravity field is a con-

G. Kramm et al. / Natural Science 3 (2011) 971-998
975975
Figure 3. Satellite observations of total solar irradiance. It comprises of the observations of seven independ-
ent experiments: (a) Nimbus7/Earth Radiation Budget experiment (1978-1993); (b) Solar Maximum Mis-
sion/Active Cavity Radiometer Irradiance Monitor 1 (1980-1989); (c) Earth Radiation Budget Satellite/Earth
Radiation Budget Experiment (1984-1999); (d) Upper Atmosphere Research Satellite/Active cavity Radi-
ometer Irradiance Monitor 2 (1991-2001); (e) Solar and Heliospheric Observer/Variability of solar Irradiance
and Gravity Oscillations (launched in 1996); (f) ACRIM Satellite/Active cavity Radiometer Irradiance Moni-
tor 3 (launched in 2000) and (g) Solar Radiation and Climate Experiment/Total Irradiance Monitor (launched
in 2003). The figure is based on Dr. Richard C. Willson’s earth_obs_fig1, updated on April 30, 2010 (see
http://www.acrim.com/).
servative quantity. The quantity 2p is called the latus
rectum. The Earth’s elliptic orbit around the Sun, char-
acterized by Johannes Kepler’s first law that the orbit of
each planet is an ellipse and the Sun is at one of the two
foci, is a consequence of the state of energy in this cen-
tral field expressed by [19,20]
12
22
2
2
11 cos
LEL
mr m



 


(2.2)
where

radial eff
ETUr (2.3)
is the total energy,


22
2
eff
UrL mrr

 (2.4)
is the effective potential comprising the centrifugal po-
tential and the gravitational potential [19,20] and

22
radial
Tmdrdt is the radial kinetic energy (equal
to zero in case of a circle). Obviously, Eq.2.2 leads to
formula 2.1 if p and e are inserted. The Perihelion can be
determined by setting

= 0˚ so that rp = a(1 – e) =
147.1 × 106 km, achieved, for instance, on January 3 in
2011. The maximum of r called the Aphelion can be
determined by setting

= 180˚. This leads to ra = a(1 +
e) = 152.1 × 106 km; it will be achieved, for instance, on
July 4 in 2011. Combining these two formulae yields







2
ap apap
err rrrra .
Kepler’s second law reads: The radius vector drawn
from the Sun’s center to the center of the planet sweeps
out equal areas in equal times. The period T of one revo-
lution of a planet around the Sun is given by 2TmAL

,
where

12
22
ππ1Aaba e is the area of the elliptic
orbit and


12
2
1ba e is the semi-minor axis. Thus,
we may write

12
222
d2π1
d
rae
tT

 (2.5)

G. Kramm et al. / Natural Science 3 (2011) 971-998 976
Integrating this equation yields
 
2π12 12
22222
00
2π
d1d2π1
T
raetae
T
  

(2.6)
or [15]

2π12
2222
0
0
1d1
2π
rrae  
 (2.7)
Here,

14
26
01149.6 10ra ea 
km is the aver-
age distance between the Sun’s center and the Earth’s orbit
(1 Astronomic Unit = AU). Since

12
21212
1ba eap ,
we can infer that 23 2
4π.Tam const   Therefore,
we may state that the square of the time of one revolu-
tion in the orbit is proportional to the cube of the semi-
major axis. This is the content of Kepler’s third law.
Even Kepler’s three laws are based on accurate astro-
nomical and planetary observations performed by Tycho
Brahe, these laws only characterize the Earth’s elliptical
orbit around the Sun in an ideal manner.
Quantifying the solar insolation at the TOA as a func-
tion of latitude and time of the year requires two addi-
tional astronomical relationships, namely
2
S
S
r
F
F
r


 (2.8)
and
0
cossinsincoscoscos h

   (2.9)
Here, 5 6.96 10
S
r km is the radius of the Sun, F is
the solar irradiance at the TOA and S
F
denotes the so-
lar emittance [15,21]. Furthermore, 0  is the local
zenith angle of the Sun’s center,

is the latitude,

is the solar declination angle that varies with time of the
year (see also Figure 6) and h is the hour angle from the
local meridian (e.g., [15,21-23]).
Formula 2.8 is based on the fact that the radiant power
(2 4πSS rF) of the Sun is kept constant when the solar
radiation is propagating through the space because of
energy conservation principles in the absence of an in-
tervening medium [15,21,24,25]. If we insert the mean
distance, 0 r, formula 2.8 can be used to define the so-
called solar constant S by (e.g., [23,26]).
2
0
S
S
r
SF
r


 (2.10)
Frequently, a value for the solar constant close to
2
1367 WmS  is recommended (e.g., [15,27,28]),
but the value obtained from recent satellite observations
using TIM (Total Irradiance Monitoring; launched in
2003) is close to 2
1361 WmS  (see Figure 3). The
basis for this modified value is a more reliable, improved
absolute calibration [21]. Combining Formulae 2.8 and
2.10 yields
2
0
r
F
S
r


 (2.11)
Here, the quantity

2
0
rr is called the orbital effect.
It does not vary more than 3.5 percent (see, e.g., [15,21,
22] and Figure 4).
Formula 2.8 may also be written as


22
0
2
0
ππ,d
π,d
SS S
S
S
S
rF r
FBT
rr
rBT
r





 

 

 





(2.12)
where


,S BT 
represents Planck’s blackbody radia-
tion formula [29],

is the frequency and 5771 K
S
T

is the Sun’s surface temperature calculated with
2
1361 WmS

 . Thus, to determine the monochro-
matic intensity of solar radiation with respect to the TOA,
Planck’s radiation formula has to be scaled by

2
S
rr.
Sometimes, also

2
πS rr is considered for the pur-
pose of scaling. Results for the spectral solar irradiance
at the TOA and the spectral terrestrial irradiance for a
temperature of 288 K are illustrated in Figure 5. This
figure also shows the atmospheric absorption spectrum
for a solar beam reaching the ground level (b) and the
same for a beam reaching the temperate tropopause (c)
adopted from Goody and Yung [30]. Part (a) of Figure 5
completely differs from the original twin-peak diagram
of Goody and Yung. We share the argument of Gerlich
and Tscheuschner [2,4] that the original one is physically
misleading. Areasonable version of a twin-peak dia-
gramwas already illustrated in Fortak’s [31] forty years
old textbook on meteorology.
Figure 4. The orbital effect,

2
0
rr , as a function of the
Julian Day.

G. Kramm et al. / Natural Science 3 (2011) 971-998
977977
Figure 5. (a) Spectral solar irradiance the top of the atmosphere (a Sun’s surface
temperature of 5771 K is assumed) and spectral terrestrial irradiance for an
Earth’s surface temperature of 288 K. Also shown: (b) Atmospheric absorption
spectrum for a solar beam reaching the ground level and (c) the same for a beam
reaching the temperate tropopause (adopted from Goody and Yung [30]).
Formula 2.9 is based on the rules of spherical trigo-
nometry. It requires the solar declination angle that is
related to

sinsin sinsin sin

   (2.13)
where

is, again, the oblique angle and

  is
the true longitude of the Earth counted counterclockwise
from the vernal equinox (e.g., [15,17,23]). Since the
latitude is related to the zenith angle by π2

 ,
Formula 2.9 may also be written as
0
coscossinsincoscosh    . Note that θ is
ranging from zero to π,

from 23˚27'S (Tropic of
Capricorn; 3π2

) to 23˚27'N (Tropic of Cancer;
π2

) and h from
H
 to H, where H represents the
half-day, i.e., from sunrise to solar noon or solar noon to
sunset. It can be deduced from Eq.2.9 by setting
0π2 (invalid at the poles) leading to
costan tanH

  (e.g., [15,22,23]).
Based on this information we can calculate the solar
insolation that is defined as the flux of solar radiation per
unit of horizontal area for a given location [15,32]. Thus,
the daily solar insolation at the TOA, Q, is given by (e.g.,
[15,17,22,24,32]).
2
0
00
cos dcos d
ss
rr
tt
tt
r
QF tS t
r




 (2.14)
Here, t is time, where r t and
s
t correspond to sun-
rise and sunset, respectively. If we acknowledge that the
variation of S and r during one day can be neglected, we
will obtain

2
0
0
2
0
cos d
cos sinsincoscosd
s
r
s
r
t
t
t
t
r
QS t
r
rSht
r
 










(2.15)

G. Kramm et al. / Natural Science 3 (2011) 971-998 978
Since the angular velocity of the Earth is given by
dd 2πht radday , Eq.2 .15 may be written as [10,
15,17,21].


2
0
2
0
cos sinsincoscosd
cossinsin cos sin
H
H
rS
Qhh
r
rSHH
r
 
 












(2.16)
According to this formula the daily solar insolation
only depends of two variables, namely the latitude and
time of the year. This dependency is illustrated in Figure
6. In accord with Haltiner and Martin [24] we may de-
duce from this figure for the current values of

2
0
rr
and

that 1) the time-latitude maximum of solar in-
solation occurs at the summer solstice at the pole be-
cause of the long solar day of 24 hours, where a secon-
dary maximum on this date occurs near the latitude of
35˚ in the summer hemisphere and 2) for each latitude,
the southern hemisphere summer (winter) insolation is
greater (less) than that of the corresponding northern
hemisphere latitude in its summer (winter). Its distribu-
tion depends on the latitude, but is independent of lon-
gitude. As illustrated in that figure, there is a slight
asymmetry between the northern and the southern
hemisphere. This is due to the variation in the Sun-Earth
distance when the Earth revolves around the Sun. How-
ever, if Eq.2.14 is integrated over all days of a year, the
annual insolations are equal at corresponding latitudes of
each hemisphere.
As shown before, the orbital effect,

2
0
rr , is af-
fected by the eccentricity, e and the true anomaly,

.
According to Formula 2.13,

dependson

,

and

.
Thus, on long-term scales of many thousands of years
(expressed in kyr) we have to pay attention to Milank-
ovitch’s [33] astronomical theory of climatic variations
that ranks as the most important achievement in the the-
ory of climate in the 20th century [10]. (In accord with
Berger [18], we denote such long-term changes as cli-
mate variations.) Milankovitch’s astronomical theory is
related to the change of the eccentricity and the obliquity
(axial tilting) and to precession and nutation phenomena
owing to the perturbations that Sun, Moon and the prin-
cipal planets of our solar system exert on the Earth’s
orbit (e.g., [10,15,17,18,34,35]) ideally characterized by
Eqs.2.1 to 2.7. It plays a substantial role in time series
analysis of paleoclimate records (see, e.g., [35,36]). Be-
cause of these astronomical phenomena, briefly de-
scribed here, the solar insolation at the TOA will vary
periodically during such long-term periods.
As the Earth is not a sphere, but an oblate spheroid
and because of the obliquity, i.e., the tilt of the Earth’s
rotational axis with respect to the normal vector, n, of
Figure 6. Daily solar insolation (86,400 J·m2) at the top of the
atmosphere as a function of latitude and day of year using a
solar constant of 1366 W·m–2. The shaded areas denote zero
insolation. The positions of vernal equinox (VE), summer sol-
stice (SS), autumnal equinox (AE) and winter solstice (WS)
are indicated with solid vertical lines. Solar declination is
shown with a dashed line (adopted from Liou [15], slightly
modified by Fu [104]).
the plane of the ecliptic pointing to the ecliptic pole (see
Figure 2), mainly the gravitational forces of the Sun and
the Moon cause a torque on it leading to a small tempo-
ral change in the angular momentum, i.e., the assump-
tion that the angular momentum is a conservative quan-
tity used in Subsection 2.1.1 is not exactly fulfilled.This
torque tries to aim the Earth’s rotational axis parallel to n
[20,37]. Like in case of a spinning toy top on which a
torque is acting the Earth’s rotational axis traces out a
cone (see Figure 2) in a cycle of about 25.7 kyr. It is
customarily called lunisolar precession. Since Sun and
Moon change their positions relative to each other their
gravitational forces also cause a nutation of the Earth’s
rotational axis which, however, is much smaller in mag-
nitude than the lunisolar precession (for more details
about precession/nutation variables, see [38-40]). Note
that, according to the recommendation of the Interna-
tional Astronomic Union, Division I Working Group on
Precession and the Ecliptic published by Hilton et al.
[40], lunisolar precession and planetary precession have
to be replaced by precession of the equator and preces-
sion of the ecliptic for general use. Both precession
phenomena are still subsumed under the notion “general

G. Kramm et al. / Natural Science 3 (2011) 971-998
979979
precession”.
A closed elliptic orbit as ideally characterized by Eqs.
2.1 to 2.7 requires that the gravitational potential recip-
rocally depends on r (see the 2nd term on the right-hand
side of Eq.2.4). Deviations from that owing to the per-
turbations of the gravity field by other planets lead to an
open orbit of a rosette-like shape (see Figure 7). It
seems that the Earth’s orbit moves around the Sun re-
sulting in a precession of the Perihelion (see Figure 7).
The combination of the general precession and the pre-
cession of the Perihelion is called the climatic precession
and the related parameter sine

is called the climatic
precession parameter. A combined effect of these preces-
sion phenomena is sketched in Figure 8. Today, the
North Pole tilts away from the Sun at Perihelion (south-
ern summer). On the contrary, the North Pole tilted to-
wards the Sun at Perihelion (northern summer) 11,000
years ago.
Results of computations performed by Berger and
Loutre [41] to reconstruct the astronomical parameters
over the last 5000 kyr (only the last 500 kyr are illus-
trated in Figure 9) suggest that the eccentricity, e, varies
between 0 and 0.057 mainly associated with periods of
about 95 kyr, 124 kyr and 410 kyr (see Figure 10) and
that the obliquity,

, varies between 22˚ and 24˚30'
with a dominant period of about 41 kyr (see Figure 10).
The revolution of the vernal point

relative to the
moving perihelion (which is related to climatic preces-
sion [18]) is mainly associated with periods of about 19
kyr, 22 kyr and 24 kyr (see Figure 10).Whereas relative
to the fixed perihelion of reference, the quasi-period is
25.7 kyr, i.e., the well known astronomical precession of
the equinoxes [18] mentioned before. Figure 9 also
shows the periodically variation of the mid-month inso-
lation for the latitudes 65˚N, July and 65˚S, January,
where the former is ranging between 388 W·m–2 and 502
W·m–2 and the latter is varying between 388 W·m–2 and
498 W·m–2. These insolation variations are associated
with main periods of about 19 kyr, 22 kyr, 24 kyr and 41
kyr (see Figure 10). As reported by Lindzen [35], Mi-
lankovitch stressed the importance of summer insolation
at high latitudes for the melting of winter snow accumu-
lation. Berger et al. [42] and Loutre et al. [16], however,
suggest that insolation at latitudes and/or time of the
year other than the classical “65˚N latitude in summer”
could also be used for comparison with proxy records.
2.1.2. The Energy Conversion in the Atmosphere
A notable portion of the solar radiation penetrating
into the atmosphere (340 W·m–2 on global average) is
absorbed in the ultraviolet and the visible range as well
as in the near infrared range by various gaseous and par-
ticulate constituents of the atmosphere. Especially the
Figure 7. Open orbit of a rosette-like shape and the precession
of the Perihelion. Here, rp is the radius of the circle on which
the Perihelion is advancing by an angle of

 and ra is the
radius on which the Aphelion is moving forward by


(with reference to Mittelstaedt [19]).
Figure 8. Combined effect of the precession phenomena (with
reference to Crowley and North [36]). The symbol P stands for
the Perihelion.
absorption of solar radiation by molecular oxygen (O2)
and ozone (O3), i.e., the O2 Schumann-Runge continuum
(130 - 175 nm; principally located in the thermosphere),
the O2 Schumann-Runge bands (175 - 200 nm; prince-

G. Kramm et al. / Natural Science 3 (2011) 971-998 980
Figure 9. Long-term variations of eccentricity, obliquity, climatic precession (characterized by the climatic
precession parameter, e sin

), the mid-month insolation for the latitudes 65˚N, July and 65˚S, January,
from 500 kyr BP to present (1950.0 A.D.). Note that a solar constant of S = 1360 W·m–2 was considered (all
data are taken from Berger and Loutre [41,105]).
Figure 10. Dominant periods for eccentricity, obliquity, climatic precession and mid-July insolation at a lati-
tude of 65˚N deter-mined by FFT (Welch) on the basis of the orbital data of Berger and Loutre [41,105].

G. Kramm et al. / Natural Science 3 (2011) 971-998
981981
pally located in the mesosphere), the O2 Herzberg con-
tinuum (200 - 242 nm; principally located in the strato-
sphere), the O3 Hartley bands (200 - 310 nm; principally
located in the stratosphere), the O3 Huggins bands (310 -
400 nm; principally located in the stratosphere and tro-
posphere) and the O3 Chappius bands (400 - 850 nm;
principally located in the troposphere) [43], serves to
heat the atmosphere directly. As illustrated in Figure 5,
water vapor (H2O) and O2 are also active in the visible
and near infrared range; nitrogen dioxide (NO2) is active
in the visible range, too. According to Trenberth et al.
[44] the direct heating of the atmosphere owing to the
absorption of solar radiation by atmospheric constituents
consumed 23 percent (or 78 W·m–2), on global average,
of the solar radiation at the TOA (see Table 2 and Fig-
ure 15).
Furthermore, a considerable portion of the solar radia-
tion at the TOA is back-scattered by molecules (Rayleigh
scattering), cloud and aerosol particles (Lorenz-Mie
scattering), where a notable amount of solar radiation
reaching the Earth’s surface is also reflected. These pro-
cesses contribute to a planetary albedo of about 30 per-
cent that results in 102 W·m–2, on global average. Thus,
only the remainder of about 70 percent (or 238 W·m–2)
of solar radiation, on global average, serves to heat the
Earth-atmosphere system (see Table 2).
To investigate the effects of the underlying surface of
ocean and land on the atmosphere to the inclination as
Alexander von Humboldt suggested, we have to consider
the solar insolation at the Earth’s surface. It is absorbed
and reflected, respectively, either by the soil-vegetation
systems and the water systems of landscapes or by the
ocean depending on the location considered (expressed
by longitude and latitude) and time of the year. The ab-
sorbed solar radiation is converted into heat and, hence,
contributes to the warming of the soil and water layers
adjacent to the Earth’s surface, respectively. These re-
spective layers also exchange energy with the atmos-
pheric boundary layer (ABL) characterized by the flux
densities (simply denoted as fluxes hereafter) of sensible
and latent heat. These fluxes serve, on global average, to
heat the atmosphere from below (see Table 2) and cause
convective transports of energy and mass in higher re-
gions of the troposphere. Especially the release of latent
heat in the troposphere while water vapor undergoes
phase changes to form water drops and/or ice particles
Table 2. Summary of the Earth’s energy budget estimates (with respect to Kiehl and Trenberth [95]). The
sources [24,44] and [31] are inserted and source [15] is updated.
Earth’s surface AtmosphereTOA

14
Ea
A
S   (W·m–2)
L
R

(W·m–2)H (W·m–2)E (W·m–2)Aa
E

Source
145 47 20 78 0.22 0.35 [24]
164 70 17 77 0.17 0.36 [31]
174 72 24 79 0.19 0.30 [96]
157 52 17 88 0.24 0.30 [97]
174 68 27 79 0.19 0.30 [98]
171 72 17 82 0.20 0.30 [72]
169 63 16 90 0.20 0.31 [99]
154 55 17 82 0.25 0.30 [100]
161 66 26 69 0.23 0.30 [15]
171 68 21 82 0.20 0.30 [32]
157 51 24 82 0.23 0.31 [101]
171 68 24 79 0.20 0.30 [102]
168 66 24 78 0.20 0.31 [95]
165 46 - - 0.19 0.33 [103]
161 63 17 80 0.23 0.30 [44]

G. Kramm et al. / Natural Science 3 (2011) 971-998 982
by cloud microphysical processes mainly contributes to
establish and perpetuate atmospheric circulation systems
and cycles of different spatial and temporal scales, re-
spectively (see also Figure 11), where also the Earth’s
rotation plays a notable role. The Hadley cells at both
sides of the Intertropical Convergence Zone (ITCZ), for
instance, are essential for maintaining the general circu-
lation in the atmosphere [45]. They are perpetuated by
the release of latent heat in the so-called hot towers em-
bedded in mesoscale convective systems, which are an
order of magnitude greater in area than the hot tower
updraft [46]. These hot towers in which notably diluted
warm moist air of the ABL is transported upward even
penetrates the tropopause and the lower stratosphere [45,
47]. As argued by Lindzen and Pan [35,48], orbital
variations can greatly influence the intensity of the Had-
ley circulation, i.e., orbital variations can also affect the
general circulation in the atmosphere and the related heat
transfer on the planetary scale.
As the absorption of solar radiation by atmospheric
constituents and the exchange of energy between the soil
and/or water layers adjacent to the Earth’s surface and
the atmosphere by the fluxes of sensible and latent heat
already serve to heat the atmosphere (of about 74 per-
cent or 175 W·m–2 of the energetically relevant solar
radiation, on global average, see Table 2), we have to
expect that those atmospheric constituents, which are
able to emit and absorb infrared (IR) radiation (usually
in finite spectral ranges), will emit energy in the IR
range in all directions. The amount of this IR radiation
depends on the temperature of these constituents. From
this point of view it is indispensable to consider the
down-welling IR radiation reaching the Earth’s surface,
where most of it is absorbed.
The soil and/or water layers adjacent to the Earth’s
surface also emit IR radiation depending on the surface
temperature. A notable portion of this IR radiation is
absorbed by atmospheric constituents and emitted in all
directions, too. A smaller one is propagating through the
atmosphere where the extinction by intervening con-
stituents is small. Such a spectral region is the so-called
atmospheric window ranging from 8.3 μm to 12.5 μm
(e.g., [15,25,27,49]) that corresponds to spectroscopic
wave numbers ranging from 1250 cm–1 to 800 cm–1. It
only contains the 9.6 μm-band of ozone. The spectral
region of the atmospheric window ranging from 10 μm
to 12.5 μm is the most common band for meteorological
satellites because it is relatively transparent to radiation
Figure 11. The main energy reservoirs of the system Earth-atmosphere and the energy fluxes (global annual
means) between them which are linked to the existence of circulations and cycles within this system (adopted
from Fortak [31]).

G. Kramm et al. / Natural Science 3 (2011) 971-998
983983
up-welling from the earth’s surface [49].
2.1.3. The Energy Conversion at the Earth’s
Surface
If we consider only bare soil1 for the purpose of sim-
plification (it will play a prominent role in Section 3),
the energy-flux balance at the Earth’s surface for a given
location (characterized, for instance, by the zenith angle,

and the and azimuthal angle,

) reads (only the
components normal to the horizontal surface element
play a role)


 

 
00
4
,, 1,,
,,, ,
,,,,, 0.
S
S
s
L
vs
R
RT
LT QHG
 

 





(2.17)
Here,

0,,
S
R


 is the global (direct plus diffu-
sive solar) radiation,

00
,

  is local zenith
angle of the Sun’s center,


0,, S

  is the albedo in
the short-wave range,

,
L
R


 is the down-welling
long-wave radiation,
 
,1 ,
L

  is the rela-
tive emissivity assumed to be equal to the absorptivity,

,
L

 is the albedo of the long-wave range and

,
s
T

 is the surface temperature. The quantities

,Q

 and

,H

 are the fluxes of water vapor
and sensible heat within the atmosphere caused by
mainly molecular effects in the immediate vicinity of the
Earth’s surface and by turbulent effects in the layers
above. These fluxes are usually not directly measured,
i.e., they have to be computed on the basis of mean
quantities derived from observations. Under horizontally
homogeneous and steady-state conditions these fluxes
can be parameterized by [65].







,
,.
qR s Rs
QCuuqqconst

   (2.18)
and




 

,
,.
ph RsRs
H
cC uuTconst

   (2.19)
Here,

is the mean air density,
p
c is the specific
heat at constant pressure, h C and q
C are the transfer
coefficients for sensible heat and water vapor, respec-
tively. Furthermore,

R
u and

s
u are the mean values
of the wind speed at
R
z, the outer edge of the atmos-
pheric surface layer (subscript R) and at the Earth’s sur-
face (subscript s), where in case of rigid walls the latter
is equal to zero,

R
 is the mean potential temperature
at
R
z,

s
T is the mean absolute temperature at the sur-
face, where usually

s
s
TT is assumed and

r
q and

s
q are the corresponding values of the specific humid-
ity, respectively. As expressed by these equations, these
fluxes at a given location are related to differences of
temperature, humidity and wind speed between a certain
reference height,
R
z and the Earth’s surface.Moreover,


,,
vs
LT

 is the specific heat of phase transition (e.g.,
vaporization, sublimation) and

,G

 is the soil heat
flux. Since reflectivity and relative emissivity depend on
the wavelength, the surface properties


0,, S

 ,


0,, L

  and


,

 represent integral values.
Note that the use of the power law of Stefan [66] and
Boltzmann [67] requires a local formulation because its
derivation is not only based on the integration of
Planck’s [29] blackbody radiation law, for instance, over
all frequencies (from zero to infinity), but also on the
integration of the isotropic emission of radiant energy by
a small spot of the surface (like a hole in the opaque
walls of a cavity) over the adjacent half space (e.g., [15,
68]). The latter corresponds to the integration over a
vector field. We may assume that the condition of the
local thermodynamic equilibrium is fulfilled (usually up
to 60 km or so above the Earth’s surface). Furthermore, a
flux is counted positive when it is directed to the Earth’s
surface.
The water vapor flux,

,Q

 , that occurs in this
energy-flux balance is related to the water-flux balance
given by




,,,,0
O
PR QI 

 (2.20)
Here,


,P

 is the precipitation,

,
O
R

 is the
surface runoff and


,I

 is the infiltration. This cou-
pled set of simple equations already documents the dif-
ficulty and challenge related to the prediction of second
kind. The net radiation,



 


 
00 0
4
,,,,1,,
,,, ,,
NS
S
s
L
RR
RT
 













(2.21)
is not only related to the fluxes of sensible heat and wa-
ter vapor and the soil heat flux, but also on the surface
runoff, infiltration and precipitation caused by cloud
microphysical processes. These cloud microphysical
processes also affect the radiation transfer of both solar
and IR radiation as well as the surface properties like the
integral values of the shortwave albedo and the relative
emissivity. Note that the difference





 


4
,, ,,,
s
LL
RTR

 


(2.22)
is also called the net radiation in the infrared range. This
difference is usually positive (see, e.g., Section 5 of
Kramm and Dlugi [21]).
1The inclusion of a vegetation canopy has been discussed, for instance,
by Deardorff [50], McCumber [51,52], Meyers and Paw U [53,54],
Sellers et al. [55], Braud et al. [56], Kramm et al. [57,58], Ziemann[59]
Su et al. [60], Pyles et al. [61,62] and Mölders et al. [63,64].

G. Kramm et al. / Natural Science 3 (2011) 971-998 984
In comparison with bare soil, the determination of the
temperature at water surfaces is more complex because 1)
a fraction of the incident solar radiation may penetrate
into the water up to a considerable depth without sig-
nificant absorption and 2) at both sides of the atmos-
phere-water interface the transition of a viscous transfer
to a fully turbulent transfer has to be considered (see
Figure 12). Also the exchange of sensible and latent heat
and infrared radiation between the ocean and the atmos-
phere can only be determined for a given location char-
acterized in a similar manner as before, i.e. by

and

. Note that the local flux quantities like

,Q

 ,

,H

 ,

,G

 and

,
L
R



 are required to
calculate global averages of these fluxes, but not global
averages of respective values of temperature and humid-
ity.
2.1.4. The Scope of the Physical Climatology
On the basis of the Subsections 2.1.1 to 2.1.3 we may
state that studying 1) the input of solar energy into the
system Earth-atmosphere, 2) the temporal and spatial
distribution of this energy in the atmosphere and the
oceans by radiative transfer processes, circulation sys-
tems and cycles, governed by fundamentalgeophysical
fluid dynamic processes, 3) the absorption of solar ir-
radiance in the underlying soil, 4) the exchange of en-
ergy between the Earth’s surface and the atmosphere by
the fluxes of sensible and latent heat and the infrared net
radiation and 5) the long-term coinage of the boundary
conditions of the respective climate system under study
is the scope of the physical climatology.
2.2. The Scope of the Statistical Climatology
The scope of the statistical climatology is the statisti-
cal description of weather states over long-term periods
of, at least, thirty years to characterize the climate of
locations, regions or even climate zones by mean values
and higher statistical moments like variance (or its posi-
tive square root, called the standard deviation), skewness
and kurtosis. Since weather states can only be related to
locations and regions at a given time (interval), but not
to a global scale, even from this point of view, we have
to acknowledge that the notion “global climate” is a con-
tradiction in terms.
The difference between weather and climate is illus-
trated in Figure 13. Black curves always characterize the
climate of a location or region for the nth climate period
(usually 30 years) at the hand of a frequency distribution
of an observed quantity of the corresponding weather
events (green dots) assumed, for the purpose of simpli-
fication, to be a normally (Gaussian) distributed random
variable. This probability density function (PDF) of the
nth climate period is characterized by the mean value n

Figure 12. Schematic diagram of the heat flow at the air-sea
interface (adopted from Hasse [106]). Note that Q is the inci-
dent solar radiation an a horizontal surface, A is the fraction of
this radiation penetrating into the water, δ = δ (U) (depending
on the horizontal wind speed U) is the depth of the water layer
mainly governed by molecular effect, T0 is the representative
temperature of the water skin, TW is the water temperature and
HW is the heat flux within the water. Furthermore, Kt is the
eddy diffusivity and ν and λ are the kinematic viscosity and the
molecular diffusivity of water, respectively.
and the standard deviation n

. Red curves characterize
the

th
ni climate period, 1,2,i  , where, again,
a similar shape of the PDF is assumed. In case of a
change from the nth climate period to the

th
ni cli-
mate, the mean values, n

and ni

and/or the stan-
dard deviations, n

and ni

, can differ from each
other indicating, for instance, a change in the occurrence
of extreme weather events. Even the shape of the PDF
may change with time. Harmel et al. [69], for instance,
reported that the results of their analysis indicate that
measured daily maximum and minimum temperature are
not generally normally distributed in each month but are
skewed. They continued that 1) this finding contradicts a
standard assumption in most weather generators that
temperature data are normally distributed and 2) this
violation does not affect reproduction of monthly means
and standard deviations but does result in simulated
monthly temperature populations that do not represent
the distribution of measured data. As any asymmetry in
PDF is already mirrored by the odd central moment of
lowest-order, one may use the third central moment (or
in a further step the skewness) to characterize such an
asymmetry. Thus, long-term periods are indispensable

G. Kramm et al. / Natural Science 3 (2011) 971-998
985985
Figure 13. For distinction between weather and climate (adopted from Meehl et al. [107] and Schönwiese [11]). The black curve
always characterize the climate of a location or region for the nth climate period (usually 30 years) at the hand of a frequency distri-
bution of an observed quantity of the corresponding weather events (simply illustrated some green dots) assumed to be a normally
distributed random variable. This probability density function (PDF) of this climate period is characterized by the mean value, μn and
the standard deviation, σn. The red curves characterize the (n + i)th climate period, i = ±1, ±2, , where for the purpose of simplifi-
cation a similar PDF is assumed. In case of a change from the nth climate period to the (n + i)th climate, the mean values, μn and μni
and/or the standard deviations, σn and σni, can differ from each other indicating, for instance, a change in the occurrence of extreme
weather events.
because describing the weather states in a statistical
manner requires that the weather states of a climate pe-
riod can be characterized by a strong degree of random-
ness. This means that the scope of the statistical clima-
tology clearly differs from that of the physical climatol-
ogy, but the mean values might be related to the bound-
ary conditions of the climate system under study. Such a
distinction between statistical and physical descriptions
of a system is well known in turbulence research.
As pointed out by Monin and Shishkov [10] and
Schönwiese [11], the thirty-year period for defining the
characteristics of the current climate of the atmosphere is
based on the recommendation of the international mete-
orological conferences of 1935 inWarsaw and of 1957 in
Washington. Typical climate periods are 1901-1930,
1931-1960 and 1961-1990. They are called the climate
normals (CLINOs). Currently, the CLINO 1971-2000 is
considered in the United States of America (http://www.
ncdc.noaa.gov/oa/climate/normals/usnormalsprods.html).
Since any change can only be identified with respect to a

G. Kramm et al. / Natural Science 3 (2011) 971-998 986
reference state (e.g., a CLINO), climate change can only
be diagnosed on the basis of two non-overlapping cli-
mate periods for which, at least, 60 year-observation
records are required. Figure 14 shows trends of the an-
nual temperature anomaly for the Northern Hemisphere
and the annual carbon dioxide concentration at Mauna
Loa, Hawaii with respect to the Climate Normal 1961-
1990. Such trends are often considered as an indication
for climate change. From a statistical point of view, such
trends are rather inappropriate for describing climate
change and climate variability, respectively.
The notion “climate change”, in principle, means that
the climate of a location or region has so drastically been
changed that it has switched from one climate zone to
another. This, however, is seldom the case. Instead, the
climate of a location or region varies from one non-
overlapping climate period to another without leaving its
climate zone. It can be described the best by the notion
“climate variability”.
Since it is rather difficult or probably impossible to
identify in which way the atmospheric greenhouse effect
is acting on weather states, we must not expect that the
statistical description of weather states for various cli-
mate periods can provide any reasonable result. Thus,
only the branch of physical climatology, if at all, might
be helpful in this matter.
3. THE EXPLANATION OF THE
GREENHOUSE EFFECT BY THE
AMERICAN METEOROLOGICAL
SOCIETY
In the Glossary of Meteorology of the AMS, the at-
mospheric greenhouse effect is explained by (http://
amsglossary.allenpress.com/glossary/search?id=green-
house-effect1):
“The heating effect exerted by the atmosphere upon the
Earth because certain trace gases in the atmosphere
(water vapor, carbon dioxide, etc.) absorb and reemit
infrared radiation.
Most of the sunlight incident on the Earth is transmit-
ted through the atmosphere and absorbed at the Earth’s
surface. The surface tries to maintain energy balance in
part by emitting its own radiation, which is primarily at
the infrared wavelengths characteristic of the Earth’s
temperature. Most of the heat radiated by the surface is
absorbed by trace gases in the overlying atmosphere and
reemitted in all directions. The component that is radi-
ated downward warms the Earth’s surface more than
would occur if only the direct sunlight were absorbed.
The magnitude of this enhanced warming is the green-
house effect. Earth’s annual mean surface temperature
of 15˚C is 33˚C higher as a result of the greenhouse ef-
fect than the mean temperature resulting from radiative
Figure 14. Trends of the annual temperature anomaly for the
Northern Hemisphere (NH, source: Hadley Centre for Climate
Prediction and Research, MetOffice, UK) and the annual car-
bon dioxide concentration at Mauna Loa, Hawaii (source:
Mauna Loa Observatory, National Oceanic and Atmospheric
Administration, NOAA), with respect to the Climate Normal
1961-1990. The quantity R is the correlation coefficient.
equilibrium of a blackbody at the Earth’s mean distance
from the Sun. The term “greenhouse effect” is something
of a misnomer. It is an analogy to the trapping of heat by
the glass panes of a greenhouse, which let sunlight in. In
the atmosphere, however, heat is trapped radiatively,
while in an actual greenhouse, heat is mechanically
prevented from escaping (via convection) by the glass
enclosure.”
The explanation of the WMO that can be found, for
instance, in its contribution entitled Understanding Cli-
mate (http://www.W·mo.int/pages/themes/climate/un-
derstanding_climate.php) reads:
“In the atmosphere, not all radiation emitted by the
Earth surface reaches the outer space. Part of it is re-
flected back to the Earth surface by the atmosphere
(greenhouse effect) leading to a global average tem-
perature of about 14˚C well above –19˚C which would
have been felt without this effect.”
Even though some numbers slightly differ from each
other (15˚C by AMS; 14˚C by WMO) in both explana-
tions the temperature difference of 33˚C serves to quan-
tify the atmospheric greenhouse effect. Note that the
argument that “part of it is reflected back to the Earth
surface by the atmosphere” is completely irrational from
a physical point of view. Such an argument also indi-
cates that the discipline of climatology has lost its ra-
tional basis. Thus, the explanation of the WMO is re-
jected.
With respect to the explanation of the AMS we may
carry out the following “thought experiment” of a
planetary radiative equilibrium, where we assume the
Earth in the absence ofan atmosphere. A consequence of

G. Kramm et al. / Natural Science 3 (2011) 971-998
987987
this assumption is that atmospheric phenomena like 1)
absorption of solar and terrestrial (infrared) radiation, 2)
scattering of solar radiation by molecules and particulate
matter, 3) emission of energy in the infrared range, 4)
convection and advection of heat and 5) phase transition
processes related to the formation and depletion of
clouds play no role [21]. The incoming flux of solar ra-
diation, S
F
, that is absorbed at the Earth’s surface is,
therefore, given by [70]

2
π1
EE
S
F
rS 
 (3.1)
Here, 6371 km
E
r is the mean radius of the Earth
considered as a sphere,and
E

is the planetary albedo
of the Earth (see also Table 2); the value of 0.30
E


is based on satellite observations of the system Earth-
atmosphere [26] and significantly differs from the mean
albedo of the Earth’s surface.
If we assume that the temperature, e T, of the Earth’s
surface is uniformly distributed, i.e., it is assumed that it
depends neither on the longitude nor on the latitude, the
total flux of infrared radiation emitted by the Earth’s
surface,
I
R
F
, as a function of this temperature and the
planetary emissivity, 1
E

, will be given by [70].
24
4π
E
Ee
IR
F
rT


 (3.2)
This equation is based on the power law of Stefan [66]
and Boltzmann [67]. If we further assume that there is a
so-called planetary radiative equilibrium, i.e., SIR
F
F


,
we will obtain (e.g., [15,26,27,70-72]).

4
14
E
Ee
ST

  (3.3)
This equation characterizes the planetary radiation
balance of this simplified system. Rearranging this equa-
tion yields

1
4
1.
4
E
e
E
S
T





(3.4)
Assuming that the Earth is acting like a black body
(1
E

) and using 2 1367WmS  and 0.30
E

 lead
to 254.9 K
e
T (or 254.6 K
e
T for 2 1361W mS

).
Since in case of the real Earth-atmosphere system the
global average of air temperatures observed in the close
vicinity of the Earth’s surface corresponds to ns T

288 K, the difference between this mean global tem-
perature and the temperature of the planetary radiative
equilibriumgiven by Eq.3.4 amounts to ns e TT T 
33 K. Therefore, as stated in the Glossary Of Meteorol-
ogy of the AMS, the so-called greenhouse effect of the
atmosphere causes a temperature increase of about 33 K,
regardless of the fact that the atmosphere is an thermo-
dynamically open system in which various atmospheric
processes listed before may take place, but not a simple
greenhouse that causes the trapping of solar radiation
[21].
Möller [70]—to our best knowledge—introduced Eqs.
3.1 to 3.4 into the literature without any scientific justi-
fication of the assumptions on which these equations are
based. Thus, it is indispensable to assess these assump-
tions and the result of 254.9K
e
T

which is based on
them:
1) Only a planetary radiation budget of the Earth in
the absence of an atmosphere is considered, i.e., any heat
storage in the oceans (if at all existing in such a case)
and land masses is neglected.
2) The assumption of a uniform surface temperature
for the entire globe is rather inadequate. As shown by
Kramm and Dlugi [21] this assumption is required by
the application of the power law of Stefan [66] and
Boltzmann [67] because, as mentioned before, this
power law is determined a) by integrating Planck’s [29]
blackbody radiation law, for instance, over all wave-
lengths ranging from zero to infinity and b) by integrat-
ing the isotropic emission of radiant energy by a small
spot of the surface into the adjacent half space (e.g.,
[15,68]). Thus, applying the Stefan-Boltzmann power
law to a statistical quantity like ns
T cannot be justi-
fied by physical and mathematical reasons. Even in the
real situation of an Earth enveloped by its atmosphere
there is a notable variation of the Earth’s (near-) surface
temperature from the equator to the poles owing to the
varying solar insolation at the TOA (see Figure 6) and
from daytime to nighttime. Consequently, the assump-
tion of a uniform surface temperature cannot be justified.
Our Moon, for instance, nearly satisfies the requirements
of a planet in the absence of an atmosphere. It is well
known that the Moon has no uniform surface tempera-
ture. There is not only a strong variation of its surface
temperature from the lunar day to the lunar night, but
also from its equator to its poles (e.g., [73-75]). In addi-
tion, ignoring the heat storage would lead to a surface
temperature of the Moon during lunar night of 0 K (or
2.7 K, the temperature of the space, see also Formula
3.11).
3) The choice of the planetary albedo of 0.30
E


is rather inadequate. This value is based on satellite ob-
servations and, hence, contains not only the albedo of
the Earth’s surface, but also the back scattering of solar
radiation by molecules (Rayleigh scattering), cloud and
aerosol particles (Lorenz-Mie scattering). Budyko [76]
already stated that in the absence of an atmosphere the
planetary albedo cannot be equal to the actual value of
0.33
E


(at that time, but today 0.30
E

). He as-
sumed that prior to the origin of the atmosphere, the
Earth’s albedo was lower and probably differed very
little from the Moon’s albedo, which is equal to M



G. Kramm et al. / Natural Science 3 (2011) 971-998 988
0.07 (at that time, but today 0.12
M

). A planetary
surface albedo of the Earth of about 0.07
E

 is also
suggested by the results of Trenberth et al. [44] (see
Figure 15). Thus, if a planetary surface albedo of E


0.07 and a planetary emissivity of 1
M

 (black body)
are considered, Eq.3.4 will provide: 273.6 K
e
T. For
0.12
E

 one obtains: 269.9 K
e
T. Note that Haltiner
and Martin [24] argued that the mean surface tempera-
ture of the Moon must satisfy the condition of radiative
equilibrium so that 266K
e
T (the authors used S

1
1.94 minly, 111 4 8.17 10minKly


 and αM = 0.10,
but this result is slightly too low), as contrasted with the
Earth’s temperature of 288 K
ns
T. Obviously, they
tried to explain the so-called atmospheric greenhouse
effect by the difference between the Moon’s surface
temperature at radiative equilibrium and the globally
averaged near-surface temperature of the Earth.
4) Comparing e
T with ns T is rather inappropriate
because the meaning of these temperatures is quite dif-
ferent. The former is based on an energy-flux budget at
the surface even though it is physically inconsistent be-
cause a uniform temperature for the entire globe does
not exist. Whereas the latter is related to globally aver-
aging of near-surface temperature observations carried
out at the stations of the meteorological network (sup-
ported by satellite observations), where the global aver-
age is defined by [2,21,77]


2
2
,d 1,sindd
4π
d
E
E
r
r


 




 


. (3.5)
Here,


,

  is an arbitrary quantity (e.g., surface
temperature, precipitation), 4π is the solid angle
of a sphere and sind dd



 is the differential
solid angle, where, again,

and

are the zenith and
azimuthal angles, respectively.
5) As illustrated in Figure 16, the Moon’s mean disk
temperature observed at 2.77 cm wavelength by Mon-
stein [78] is much lower than 269.9K
e
T which can
be derived with the Moon’s planetary albedo of M


0.12. Even though the Moon’s mean disk temperature
observed in 1948 by Piddington and Minnett [79] is of
about 26 K higher than that of Monstein [78], it is still
Figure 15. The global annual mean Earth’s energy budget for the Mar 2000 to May 2004 period (W·m–2). The broad arrows indicate
the schematic flow of energy in proportion to their importance (adopted from Trenberth et al. [44]).

G. Kramm et al. / Natural Science 3 (2011) 971-998
989989
Figure 16. Moon’s disk temperature at 2.77 cm wavelength
versus moon phase angle φ during two complete cycles from
twice new moon via full moon to new moon again (adopted from
Monstein [78]).
31 K lower than 269.9 K
e
T. Since the Moon is nearly
a perfect example of a planet in the absence of its at-
mosphere it is often argued that Eqs.3.3 and 3.4 are only
valid for fast-rotating planets so that the Moon must be
excluded. Obviously, this argument plays no role if the
planet Venus is considered that rotates by a factor of four
slower than the Moon. Recently, Pierrehumbert [80]
used Eq.3.4 to calculate the temperature of the planetary
radiative equilibrium. With 0.75
V

 and 1
V


he
obtained 231K
e
T. If we chose 0.12
V

 for the
Venus in the absence of its atmosphere (which is similar
to that of the Moon) we will obtain 317.3 K
e
T and
for 0.90
V

 as listed in NASA’s Venus Fact Sheet
(http://nssdc.gsfc.nasa.gov /planetary/factsheet/ven usfact.
html) 184.2K
e
T.
Because of these facts we may conclude that Eq.3.4 is
based on assumptions that are physically irrelevant and
the results obtained with it considerably disagree with
observations. Consequently, the difference of
33 K
ns e
TT T  cannot be justified by physical
reasons.
Even though Gerlich and Tscheuschner [2] already
criticized it because of its physical irrelevance, Lacis et
al. [81] completely ignore it when they stated recently:
“The difference between the nominal global mean
surface temperature (TS = 288 K) and the global mean
effective temperature (TE = 255 K) is a common measure
of the terrestrial greenhouse effect (GT = TS – TE = 33 K).
Assuming global energy balance, T
E is also the Planck
radiation equivalent of the 240 W/m2 of global mean
solar radiation absorbed by Earth.”
Note that their temperature TS corresponds to our
ns
T and TE to our e T. Calling the globally averaged
irradiance of 240 W·m–2 the “Planck radiation equiva-
lent” shows that the authors are less familiar with basic
physics in this matter. Planck’s [29] blackbody radiation
law describes the monochromatic intensity (also called
the monochromatic radiance), usually expressed by W·m–2
μm–1·sr–1, as a function of temperature [15,68]. As men-
tioned before, the power law of Stefan [66] and Boltz-
mann [67] has to be applied to calculate the irradiance
usually expressed by W·m–2. This power law was already
used by Wien [82] as a constraint in deriving his black-
body radiation law which is an asymptotic solution of
Planck’s radiation law mainly for shorter wavelengths.
This power law is also a constraint for Planck’s radiation
law.
Even in case of this thought experiment we have to
consider that the temperature

,T

 has to be deter-
mined on the basis of an energy-flux budget (instead of a
radiation-flux budget) at a certain location given, at least,
by (the diffuse solar radiation, the down-welling IR ra-
diation and the fluxes of sensible and latent heat that
occurred in Eq.2.17 can be ignored)




 

4
00
1,,cos ,,
,0
Ss
FT
G

 

 
 (3.6)
leading to
 
  

1
4
00
,1,,cos
,,
S
s
GF
T

 


 








(3.7)
Here, F is the solar irradiance reaching a surface element
of the globe. All other symbols have the same meaning
as given before (see Eq.2.17).
Inserting Formula 3.7 into Eq.3.5 yields







2ππ 00
00
1
4
1,,cos
1
4π,
,sind d
,
S
s
F
T
G


 














(3.8)
This integration can only be performed numerically
because 0

depends on time (see Eq.2.9). Using Eq.
3.8 and ignoring


,G

 will lead to
3
2
2144 K
5
se
TT (3.9)
for a non-rotating Earth in the absence of its atmosphere,
if 2 1367 WmS

,


0, ,0.30 SE
  and


,1
E

 

 are assumed [2] (153 K
s
T if E


0.12 and 155 K
s
T if 0.07
E

). It seems, how-
ever, that this globally averaged surface temperature for
the Earth in the absence of its atmosphere is as unrealis-
tic as the temperature of the radiative equilibrium of

G. Kramm et al. / Natural Science 3 (2011) 971-998 990
254.9 K
e
T. Consequently, as already argued by Ger-
lich and Tscheuschner [2] it is indispensable to deter-
mine the true globally averaged surface temperature for
the obliquely rotating Earth by using Eq.3.8. This means
that also the ground heat flux,


,G

 , has to be in-
cluded. The direction of


,G

 is mainly governed
by the difference between the absorbed incoming solar
radiation and the emission of infrared radiation. For the
dark side of a planet having no atmosphere the energy-
flux balance Eq.3.6 reduces to
 
4
,,,
s
TG

   (3.10)
This energy-flux balance provides
 

1
4
,
,,
s
G
T

 





(3.11)
If we assume, for instance, a surface temperature of

,130K
s
T   on the dark side of the Moon and
choose

,1  , the ground heat flux will amount to

2
,16.2 WmG 

. Without the ground heat flux
the predicted surface temperature (see Formula 3.11), for
instance, on the dark side of the Moon would be equal to
zero (or to the temperature of the space of about 2.7 K as
mentioned before). Consequently, the ground heat flux is
not generally negligible.
4. THE EXPLANATION OF THE
GREENHOUSE EFFECT BY
RAMANATHAN ET AL.
In their review paper Ramanathan et al. [1] stated:
“The incoming solar radiation, the reflected solar ra-
diation and the outgoing long-wave radiation at the top
of the atmosphere have been determined by satellite ra-
diation budget measurements and the values inferred
from these measurements are shown in Figure 2 [here
presented as Figure 17]. The surface-atmosphere system
emits to space roughly 236 W·m–2, which balances the
absorbed solar radiation. The emitted radiation is
mostly contained in wavelengths longer than 4 μm and
hence it is referred to as long-wave, infrared (IR), or
terrestrial radiation.
At a surface temperature of 288 K the long-wave
emission by the surface is about 390 W·m–2, whereas the
outgoing long-wave radiation at the top of the atmos-
phere is only 236 W·m–2 (see Figure 2 [here presented as
Figure 17]). Thus the intervening atmosphere causes a
significant reduction in the long-wave emission to space.
This reduction in the long-wave emission to space is
referred to as the greenhouse effect.”
Haltiner and Martin [24] already argued in a similar
manner. As discussed before, applying the power law of
Stefan and Boltzmann to a globally averaged tempera-
ture cannot be justified by physical and mathematical
reasons. Thus, the argument that at a surface tempera-
ture of 288 K the long-wave emission by the surface is
about 390 W·m–2 is meaningless.
Figure 5 illustrates that the wavelength of about 4 μm
mentioned before separates the band comprising most of
the solar radiation (black line) from that comprising
most of the terrestrial (infrared) radiation (red line). This
seems to be awkward because, according to Wien’s [83]
displacement law, the spectral radiation intensities for
Figure 17. Global energy balance and the greenhouse effect (adopted from Ramanathan et al., [1]).

G. Kramm et al. / Natural Science 3 (2011) 971-998
991991
different temperatures must not intersect each other. To
understand the intersection at a wavelength of about 4
μm, we have, therefore, to consider the solar irradiance
reaching the TOA as expressed by Eq.2.12.
Recently, Trenberth et al. [44] published an update of
the Earth’s global energy-flux budget. Their results are
illustrated in Figure 15. These results slightly differ
from those previously published by various authors (see
Table 2), but these slight differences are much larger
than the globally averaged net anthropogenic radiative
forcing that corresponds to

2
1.60.6 to 2.4WmRF


in 2005 relative to pre-industrial conditions defined at
1750 (see Figure 18).
According to Dines [84], Trenberth et al. [44] and
others the global energy budget for the system Earth-
atmosphere may be written as:
Top of the atmosphere:

10
4
EOL
SR


 (4.1)
Earth’s surface:

10
4
Ea L
S
ARHEI 


 (4.2)
Here, 0.23
a
A

is the absorptivity of the atmos-
phere with respect to solar radiation (see Table 2). Fur-
thermore, OL R is the outgoing infrared radiation at the
TOA. According to Trenberth et al. [44] this value is
Figure 18. Global-average radiative forcing (RF) estimates and ranges in 2005 for anthropogenic carbon dioxide (CO2), methane
(CH4), nitrous oxide (N2O) and other important agents and mechanisms, together with the typical geographical extent (spatial scale)
of the forcing and the assessed level of scientific understanding (LOSU). The net anthropogenic radiative forcing and its range are
also shown. These require summing asymmetric uncertainty estimates from the component terms and cannot be obtained by simple
addition. Additional forcing factors not included here are considered to have a very low LOSU. Volcanic aerosols contribute an addi-
tional natural forcing but are not included in this figure due to their episodic nature. Range for linear contrails does not include other
possible effects of aviation on cloudiness (adopted from the Intergovernmental Panel on Climate Change, Climate Change 2007—
Summary for Policymakers, with respect to Forster et al. [108]).

G. Kramm et al. / Natural Science 3 (2011) 971-998 992
balancing the difference between the incoming solar
radiation minus the solar radiation back scattered by the
entire Earth-atmosphere system (see Eq.4.1). Moreover,
H = 17 W·m–2 and E = 80 W·m–2 are the fluxes of sensi-
ble and latent heat, respectively; and 63
L
R  W·m–2 is
the so-called net infrared radiation [32,85] (see also Ta-
ble 2). The term I = 0.9 W·m–2 is a remainder to close
the energy-flux balance. Trenberth et al. [44] interpreted
this term as a net downward radiation. This is clearly a
misinterpretation because it has to be linked to the stor-
age of energy (eventually in form of coal and petroleum
[31]), the heat transfer by precipitation and/or non-sta-
tionary effects. Thus, Eq.4.2 mainly describes the parti-
tioning of the absorbed solar radiation into the flux terms
H, E and
L
R  that serve to heat the atmosphere via
the Earth’s surface. The results of various authors listed
in Table 2 reflect this kind of energy partitioning re-
gardless the wide variety of
L
R

values ranging from
46 W·m–2 to 72 W·m–2.
Combining Eqs.4.1 and 4.2 yields (hereafter the re-
mainder I is omitted)

1.
44
EOLa L
SS
RA RHE 

 (4.3)
This means that the solar irradiance at the TOA reduced
by the amount reflected by the atmosphere (back scat-
tering by molecules, cloud and aerosol particles) and the
Earth’s surface is heating the system Earth-atmosphere,
namely 1) directly by absorption in the atmosphere
(4
a
A
S) and 2) indirectly via the energy conversion at
the Earth’s surface (H and
L
R

), where the flux term E
is linked to the reservoir of latent energy (see Figure 11).
As illustrated in Figure 11, 4
a
A
S, H and
L
R

 con-
tributes to the reservoir of total potential energy (TPE =
internal plus potential energy). The reservoir of latent
energy mainly maintains atmospheric circulations and
cycles, where the accompanied condensation of water
vapor forms clouds and, hence, contributes to the reser-
voir of the TPE that also supports the maintenance of
atmospheric circulations and cycles. Only a very small
amount of the TPE is available for converting into ki-
netic energy [31,86-89]. As expressed by Eq.4.3 and
illustrated by Figure 11, the outgoing infrared radiation
at the TOA, OL R, balances the energy input into the
reservoir of total potential energy. Thus, the “cycle” of
the long-wave radiation between that Earth’s surface and
the atmosphere does not contribute to the heating of the
system as already pointed out by Fortak [31]. We share
Fortak’s [31] argument that the outgoing emission of
infrared radiation only serves to maintain the radiative
equilibrium at the TOA (see Eq.4.1).
Let us further discuss the term
L
R . According to
Haltiner and Martin [24], Möller [85], Ramanathan et al.
[1] and Trenberth et al. [44] and many others this term is
given by

44
EsEE s
LLL
RTRTR  


 (4.4)
where
s
T is the globally averaged Earth’s surface
temperature and
L
R is the down-welling infrared ra-
diation. As discussed in Subsection 2.1.2, the latter is
mainly caused by the temperature distribution in the
troposphere linked to convective heating and the release
of latent heat and the temperature distribution in the
stratosphere related to the absorption of solar radiation
by O2 and O3 molecules, respectively. Despite the fact
that the global emission of infrared radiation by the
Earth’s surface cannot be determined using a globally
averaged (near-)surface temperature, 288K
ns
T
would lead to an emission of 390 W·m–2 if 1
E


is
assumed (e.g., [1]). Using a more realistic value of
0.95
E


, however, would provide 371 W·m–2. These
two results simply document that an attempt to diagnose
a remainder of I = 0.9 W·m–2 so accurately is far beyond
our means with which geophysical processes can be ana-
lyzed. They also document that 4
Ens
L
L
RTR 


would be varying by 19 W·m–2 if
E

is ranging from
0.95
E


to 1
E


.
In two-layer radiative equilibrium models involving
the Earth’s surface and the atmosphere with homogene-
ous temperatures
E
T and a T, respectively, the down-
welling infrared radiation is parameterized by L R

4
aa
T

 [15]. If we assume, for instance, 1
E


and an
integral emissivity of the atmosphere of 0.75
a


, a
homogeneous Earth’s surface temperature of TE = 288 K
and a homogeneous radiative temperature of the atmos-
phere of 296.1 K
a
T

, we will also obtain: 63
L
R


W·m–2. The same is true for the following pairs of tem-
peratures TE = 273 K and Ta = 277.4 K as well as TE =
255 K and Ta = 253.9 K. Since
L
R  is only one of the
flux terms related the partitioning of absorbed solar ra-
diation the temperature ns T = 288 K cannot be intro-
duced into Eq.4.2 (as done by Haltiner and Martin [24]
and Ramanathan et al. [1]) because the globally aver-
aged Earth’s surface temperature is statistically deter-
mined on the basis of (near-)surface observations. It has
no physical link to the global energy-flux budget scheme
in which representative temperatures for the Earth’s skin
and the entire atmosphere occur. This fact can be ex-
plained at the hand of a Dines-type scheme for the global
energy balance of the Earth-atmosphere system [84]
expressed by the following pair of equations [21,77]:
Top of the atmosphere:
 
44
110
4
EaaaEE
STT
 

  (4.5)
Earth’s surface:

G. Kramm et al. / Natural Science 3 (2011) 971-998
993993

44
10
4
Ea EaaEE
S
ATTHE
  , (4.6)
where
E
T and a T are, again, considered as homoge-
neous temperature (even though these temperatures are
volume-averaged temperatures for the upper layer of an
aqua-planet and the whole atmosphere, respectively [21]).
Here,

4
1aEE T

  is the infrared radiation that is
propagating through the atmosphere (it also includes the
terrestrial radiation that is passing through the atmos-
pheric window). Furthermore, the reflection of infrared
radiation at the Earth’s surface is included here, but
scattering of infrared radiation in the cloudless atmos-
phere is ignored, in accord with Möller [90] and Kramm
and Dlugi [21]. The latter substantially agrees with the
fact that in the radiative transfer equation the Planck
function is considered as the only source function when
a non-scattering medium is in local thermodynamic
equilibrium so that a beam of monochromatic intensity
passing through the medium will undergo absorption and
emission simultaneously, as described by Schwarzschild’s
equation [15,91,92]. Note that Arrhenius [93] considered
a similar scheme for a column of the atmosphere, i.e., he
already included the absorption of solar radiation by
atmospheric constituents and the exchange of heat be-
tween the Earth’s surface and the atmosphere. Further-
more, Miskolczi [94] also used such a Dines-type
scheme.
The solution of the non-linear pair of equations is
given by [21,77]




 


1
4
11
4
11 11
aaE aa
a
aEa aEa
S
AA HE
T
 
 




 



 



(4.7)
and




1
4
11 4
11
EEa
E
EEa
S
A
HE
T

 












(4.8)
It is obvious that
E
T and a T are dependent on the
emissivity values of the Earth and the atmosphere, re-
spectively, the atmospheric absorptivity in the solar
range and the planetary albedo. Results provided by Eqs.
4.7 and 4.8 using 0.30
E


and some combinations of
E

and a

, where a
A
is ranging from zero to 0.3, are
illustrated in Figure 19. Assuming, for instance, that the
atmosphere acts as blackbody emitter leads to an at-
mospheric temperature of Ta = 254.9 K which is inde-
pendent of a
A
. This temperature completely agrees with
e
T predicted on the basis of Eq.3.4. This is not surpris-
ing because for 1
a


the Eqs.3.4 and 4.7 would be
equivalent. Considering, in addition, the Earth as a black-
body emitter provides a surface temperature of about TE
= 286.4 K if a
A
is assumed to be zero.
This temperature hardly differs from 288 K
ns
T.
However, in such a case the infrared net radiation would
Figure 19. Uniform temperatures for the Earth’s surface and the atmosphere provided by the two-layer model
of a global energy-flux budget versus absorptivity Aa (adopted from [21,77]).

G. Kramm et al. / Natural Science 3 (2011) 971-998 994
amount to

44
142
Ea
L
RTT 

  W·m–2. This value
is much larger than all
L
R  values listed in Table 2.
Note that in case of 0.95
E

 and 0.6
a

 the Earth’s
surface temperature would be lower than the temperature
of the radiative equilibrium of Te = 254.9 K for 0.17
a
A,
i.e., the Earth’s surface temperature would be lower than
the temperature of the atmosphere. In such a case it has
to be expected that, at least, the sensible heat flux should
change its direction. For εE = 1.0, εa = 0.8 and Aa = 0.23
the Earth’s surface temperature would only be slightly
higher than Te. In this case the temperature of the at-
mosphere would be Ta = 254.9 K, i.e., it would corre-
spond to the vertically averaged temperature of the tro-
posphere. Consequently, it is forbidden to insert the glob-
ally averaged near-surface temperature, ns T = 288 K,
into such a global energy-flux scheme.
5. SUMMARY AND CONCLUSIONS
In this paper, we scrutinized the atmospheric green-
house effect, where we debated the meaning of climate,
climate change, climate variability and climate variation
to outline in which way this effect might be responsible
for climate change and climate variability, respectively.
In doing so, we distinguished between two different
branches of climatology, namely 1) physical climatology
and 2) statistical climatology. We argued that studying 1)
the input of solar energy into the system Earth-atmos-
phere, 2) the temporal and spatial distribution of this
energy in the atmosphere and the oceans by radiative
transfer processes, circulation systems and cycles, gov-
erned by fundamental geophysical fluid dynamic proc-
esses, 3) the absorption of solar irradiance in the under-
lying soil, 4) the exchange of energy between the Earth’s
surface and the atmosphere by the fluxes of sensible and
latent heat and the infrared net radiation and 5) the
long-term coinage of the boundary conditions of the
respective climate system under study is the scope of the
physical climatology. We described, for instance, how
the daily solar insolation at the TOA is varying with
latitude and time of the year, not only for present day
orbital parameters, but also for long-term scales of many
thousands of years, where we paid attention to Milank-
ovitch’s [33] astronomical theory of climatic variations.
On the contrary, the scope of the statistical climatol-
ogy is the statistical description of weather states over
long-term periods of, at least, thirty years to characterize
the climate of locations, regions or even climate zones
by mean values and higher statistical moments like
variance (or its positive square root, called the standard
deviation), skewness and kurtosis. We argued that cli-
mate change or climate variability can only be identified
on the basis of two non-overlapping climate periods for
which, at least, 60 year-observation records are required.
From the perspective of the statistical description of
weather states as described before, we have to acknowl-
edge that trends often considered as an indication for
climate change are rather inappropriate in describing
climate change and climate variability, respectively.
In fathoming whether the atmospheric greenhouse
conjecture is really falsified as Gerlich and Tscheuschner
[2] claimed or the notion “atmospheric greenhouse ef-
fect” is only a misnomer that describes a real effect, we
scrutinized two completely different explanations of the
atmospheric greenhouse effect: First, the explanation of
the AMS and the WMO, secondly, the explanation of
Ramanathan et al. [1]. Both explanations are related to
the global scale. This relation could be the reason why
often the notion ‘global climate’ is used and the debate
on climate change is mainly focused on global climate
change. However, as outlined in our paper, the notion
“global climate” is a contradiction in terms.
We showed that the explanation by AMS and W·MO
related to the temperature difference ns e TT T 
33 K, where ns T = 288 K is the globally averaged
near-surface temperature and 255 K
e
T is the tem-
perature of the planetary radiative equilibrium, has to be
discarded because of physical reasons. As argued in Sec-
tion 3, various assumptions on which e T is based are,
by far, not fulfilled. Furthermore, the temperature of the
planetary radiative equilibrium estimated for the Moon,
269.9 K
e
T

, is much higher than the Moon’s averaged
disk temperature of about 213 K obtained by Monstein
[78] at 2.77 cm wavelength. Moreover, comparing e T
with ns T is rather inappropriate because the meaning
of these two temperatures is quite different. The former
is based on an energy-flux budget at the surface even
though it is physically inconsistent because a uniform
temperature for the entire globe does not exist; whereas
the latter is related to the global average of observed
near-surface temperatures. We argued that only the av-
erage temperature inferred from Eq.3.8 is comparable
with ns
T = 288 K. Consequently, the argument of
Gerlich and Tscheuschner [2] that this 33 K is a mean-
ingless number is quite justified.
We showed on the basis of a Dines-type energy-flux
budget for the Earth-atmosphere system that Fortak’s [31]
forty years old statement that the “cycle” of the long-
wave radiation between that Earth’s surface and the
atmosphere does not contribute to the heating of the
system must not be rejected. Even though there is a large
scatter (see Table 2), the results of various researchers
confirm Fortak’s [31] statement, too. Thus, we ac-
knowledged Fortak’s [31] argument that the outgoing
emission of infrared radiation only serves to maintain the
radiative equilibrium at the TOA.
We also showed that the globally averaged near-sur-

G. Kramm et al. / Natural Science 3 (2011) 971-998
995995
face temperature of ns T = 288 K cannot be thermo-
dynamically related to the Dines-type energy-flux budget
for the Earth-atmosphere system because the tempera-
tures
E
T and a T are volume-averaged quantities [21].
Thus, the related long-wave emission by the Earth’s sur-
face of about 390 W·m–2 is meaningless in such an en-
ergy-flux budget. Consequently, the explanation of the
atmospheric greenhouse effect by Ramanathan et al. [1]
is physically inappropriate.
Based on our findings, we conclude that 1) the so-
called atmospheric greenhouse effect cannot be proved
by the statistical description of fortuitous weather events
that took place in past climate periods, 2) the description
by AMS and WMO has to be discarded because of
physical reasons, 3) energy-flux budgets for the Earth-
atmosphere system do not provide tangible evidence that
the atmospheric greenhouse effect does exist. Because of
this lack of tangible evidence it is time to acknowledge
that the atmospheric greenhouse effect and especially its
climatic impact are based on meritless conjectures.
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