Content uploaded by Ferenc Miskolczi

Author content

All content in this area was uploaded by Ferenc Miskolczi on Nov 27, 2017

Content may be subject to copyright.

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

31

The Greenhouse Effect and the Infrared

Radiative Structure of the Earth's Atmosphere

Ferenc Mark Miskolczi

Geodetic and Geophysical Institute, Hungarian Academy of Sciences, Csatkai Endre u. 6-8, 9400 Sopron, Hungary

fmiskolczi@cox.net

Abstract

This paper presents observed atmospheric thermal and

humidity structures and global scale simulations of the

infrared absorption properties of the Earth's atmosphere.

These data show that the global average clear sky green-

house effect has remained unchanged with time. A theo-

retically predicted infrared optical thickness is fully

consistent with, and supports the observed value. It also

facilitates the theoretical determination of the planetary

radiative equilibrium cloud cover, cloud altitude and Bond

albedo. In steady state, the planetary surface (as seen from

space) shows no greenhouse effect: the all-sky surface up-

ward radiation is equal to the available solar radiation. The

all-sky climatological greenhouse effect (the difference of the

all-sky surface upward flux and absorbed solar flux) at this

surface is equal to the reflected solar radiation. The plane-

tary radiative balance is maintained by the equilibrium

cloud cover which is equal to the theoretical equilibrium

clear sky transfer function. The Wien temperature of the all-

sky emission spectrum is locked closely to the thermo-

dynamic triple point of the water assuring the maximum

radiation entropy. The stability and natural fluctuations of

the global average surface temperature of the heterogeneous

system are ultimately determined by the phase changes of

water. Many authors have proposed a greenhouse effect due

to anthropogenic carbon dioxide emissions. The present

analysis shows that such an effect is impossible.

Keywords

Greenhouse Effect; Radiative Transfer; Global Warming

Introduction

In steady state planetary radiative balance the rela-

tionship that links the short wave (SW) solar radiation

to the long wave (LW) terrestrial or infrared (IR)

radiation may be expressed as :

(1 )

ABE

OLR F

.

Here

A

OLR

is the all-sky outgoing LW radiation,

/

B R E

FF

is the Bond albedo,

R

F

is the all-sky

reflected SW radiation,

0/4

E

FF

is the available SW

radiation over a unit area at the top of the atmosphere

(TOA), and

0

F

is the solar constant at the Earth's orbit.

Isolated planets without any internal heat source must

obey the energy conservation principle, therefore the

E A R

F F F

and

A

A

F OLR

relationships must hold,

where

A

F

is the long term global average absorbed SW

radiation in the system. The balance relationship does

not suggest anything about how, when, and why the

observed thermal energy of the planet is attained

during the evolution of the planet. The only meaning

of the balance equation is the equality between the

thermal energy lost to space and the gained radiative

energy by SW absorption when a steady state has been

reached.

In a planetary atmosphere with condensing green-

house gases (GHGs), the active surface that is relevant

to the radiative balance equation is the combined clear

and cloudy surfaces as seen from space. The ratio of

the overcast areas to the total surface area of the planet

is called geometric cloud fraction,

. Because of the

extreme variability of the planetary cloud cover, the

accurate estimation of

from surface or satellite ob-

servations is one of the most challenging problems of

climate science. The characteristic global average alti-

tude of the cloud top,

C

h

, is also not known with very

high accuracy. Missing from climate science literature

are the quantitative theoretical constraints on the

value of the

and

C

h

parameters. These issues will be

discussed later in detail.

Cloud layers at any altitude present material dis-

continuity in the atmospheric vertical structure which

disrupts the propagation of the LW radiation. In

principle, the global average LW upward radiation

from the ground surface,

U

S

, may be estimated

reasonably well from ground surface temperature

records. Over cloudy areas, however, the upward IR

flux density from the cloud top,

C

U

S

, cannot be easily

measured. The

U

S

from overcast areas does not con-

tribute to the total

A

OLR

:

(1 )

AC

OLR OLR OLR

,

where

OLR

is the clear sky, and

C

OLR

is the cloudy sky

outgoing LW radiation. Estimations of

C

OLR

from a

unit cloudy area must rely on the observed

C

h

,

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

32

therefore they are inherently inaccurate. The radiative

equilibrium constraint for the clear and cloudy areas

are expressed as:

/ (1 ) / 2

U A A

S OLR f OLR T

,

and

/ (1 ) / 2

C C C C C C

U A A

S OLR f OLR T

, where

A

,

A

T

, and

f

are the flux optical thickness, flux

transmittance, and transfer function respectively, and

the superscripts indicate the cloudy condition, see

Miskolczi (2004, 2007, and 2010). Further on we shall

frequently make reference to these publications as

M04, M07, and M10. The breakthrough in the

quantitative greenhouse science happened in 2007,

when the correct mathematical relationship among

U

S

,

OLR

, and

A

for semitransparent atmospheres was

first published in M07. The theoretical derivation of

the

/

U

S OLR f

analytical function was the missing

link which, through the transfer function and flux

optical thickness, connects the surface temperature to

the GHG content of the atmosphere.

Here one has to be careful with the computation of

U

S

from the related ground surface thermodynamic

temperature,

G

t

. For non-black surfaces, the upward

radiation is defined by the skin temperature

S

t

:

44

U S G G G

S t t S

, where

G

is the surface flux

emissivity,

8

5.67 10

Wm-2K-4 is the Stefan-

Boltzmann constant.

()

G G G

S B t B

is the total flux

density radiated into the hemisphere from an ideal

blackbody radiator at

G

t

temperature. In planetary

radiative budget studies

1

G

, and

UG

SS

are usually

assumed. For reference, in Trenberth, Fasullo, and

Kiehl (2009) (TFK09) the broadband emissivity of the

water is

0.9907

G

and the ISCCP-FD

G

t

is

288.70

K.

The clear and cloudy sky LW downward atmospheric

emittance to the ground surface and cloud top are

D

E

and

C

D

E

respectively. The all-sky LW downward flux

to the ground surface is the sum of the clear and

cloudy components:

(1 )

A Cd

DD

E E OLR

, where

Cd

OLR

Cd C d

TD

SE

is the cloudy sky contribution.

Here

Cd

T

S

is the downward transmitted flux from the

cloud bottom, and

Cd

D

E

is the downward atmospheric

emission from below the cloud layer.

C

D

S

is the

downward radiation emitted by the cloud bottom, and

by definition,

Cd C C d

A D T

A S S

is the absorbed part of

C

D

S

. Assuming a thin opaque cloud layer the upward

and downward radiation (emitted by the cloud deck)

are equal,

CC

DU

SS

. The last important flux density

component in the cloudy atmosphere is the total

upward radiation (transmitted from the surface plus

emitted by the atmosphere) at the altitude of the cloud

bottom:

Cu C u C u

TU

OLR S E

. The absorbed surface

upward flux at the cloud bottom is

Cu Cu

A U T

A S S

.

Greenhouse Effect

The planetary greenhouse effect (GE) may be defined

or quantified in different ways. In astrophysics the all-

sky GE is defined via the total available solar radiation

interacting with the system:

AA

UE

G S F

, where

(1 )

AC

U U U

S S S

is the all-sky global average

surface upward flux (from the active surface).

Similarly to

A

U

S

,

A

G

may be obtained from the

weighted sum of the clear sky and cloudy sky

greenhouse effects:

(1 )

AC

G G G

, where

G

U

S OLR

, and

C C C

U

G S OLR

.

In a semi-transparent clear atmosphere,

OLR

is the

sum of the transmitted flux density from the surface,

T

S

and the atmospheric upward emittance,

U

E

:

TU

OLR S E

. In a clear, absorbing GHG atmosphere,

U T A

S S A

and from the definition of

G

, follows the

U A U

S OLR A E

greenhouse identity. Here

A

A

is

the clear sky absorbed

U

S

. Likewise, the greenhouse

identity for the fluxes above the cloud top is

C C C C

U A U

S OLR A E

, where

C

A

A

is the absorbed

C

U

S

above the cloud layer and

C

U

E

is the upward emission

of the air from above the cloud top. For all-sky fluxes,

the

A A A A

U A U

S OLR A E

relationship must be

satisfied as well. By definition, the all-sky,

A

T

S

, and the

cloudy sky,

C

T

S

, transmitted fluxes are:

A A A

T U A

S S A

,

and

C C C

T U A

S S A

, respectively.

(1 )

AC

A A A

A A A

is the all-sky absorbed LW radiation (above the active

surface). In accurate planetary radiative transfer (RT)

computations, the greenhouse identities must be

observed. The normalized all-sky, clear sky and

cloudy sky greenhouse factors (GFs) are the

/

A A A

U

g G S

,

/U

g G S

, and the

/

C C C

U

g G S

ratios

respectively. Here

A

g

is not a simple weighted aver-

age:

/(1 /(1 )/ ) /(1 (1 ) / / )

A C C C

U U U U

g g S S g S S

.

It is anticipated that the thermal structure of the

atmosphere is always affected by both the local, and

the ever-present global average cloud cover. In terms

of the quasi all-sky protocol, clear sky computations of

the flux density components are conducted ignoring

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

33

the possible (random) presence of the cloud cover. The

computed global average fluxes are assumed to

implicitly represent the global average cloud con-

dition. In fact, in climate science the classic definition

of the greenhouse warming (as the difference of the

all-sky global average surface temperature and the

planetary emission temperature) is a version of the

quasi all-sky protocol.

In the case of planetary radiative equilibrium the

global average net energy flux of non-radiative origin

(conduction, convection, advection, turbulent mixing,

etc.) between the solid and liquid surfaces and the

atmosphere must be zero. Of course, the net latent

heat release at the boundary layer must be treated as

of radiative origin. In global radiative equilibrium

A

UE

SF

,

AA

OLR F

,

AR

GF

,

AB

g

,

()

T

A

f

,

/ ( )

T

UA

S OLR f

,

C

A

OLR A

, and

CC

D

OLR E

, where

1.876

T

A

is the planetary equilibrium flux optical

thickness. Note, that the last four relationships are

derived theoretically in M07. It is assumed, that the

equilibrium atmospheric structure is such, that the

cloud cover alone is able to maintain the planetary

radiative balance. At the TOA one may write the

theoretical equilibrium cloud fraction and the Bond

albedo in the simple forms of

( ) / ( )

C

BE

G F G G

,

and

( ( ))/

C

BE

G G G F

.

In climate science, the all-sky and clear sky green-

house parameters are defined through the

OLR

,

A

OLR

, and

G

S

fluxes:

AA

mG

G S OLR

,

mG

G S OLR

,

A

m

g

/

A

mG

GS

, and

/

m m G

g G S

.

m

G

and

m

g

are the

clear sky GE and GF, Ramanathan and Inamdar (2006)

(RI06). Sometimes

m

g

is called as 'normalized trapping'

of

G

S

. We have seen already, that without a realistic

G

the

G

t

temperature alone is not sufficient to convert

G

S

to accurate

U

S

. Further on, one should notice, that

A

m

G

,

m

G

,

A

m

g

, and

m

g

are mixed physical quantities and

they cannot be associated with either clear, or cloud

covered surfaces. To handle the cloud problem, the so-

called LW cloud forcing as the difference of the clear

and all-sky TOA terrestrial radiation is also introduced:

A

L

C OLR OLR

. The frequently used total greenhouse

effect terminology in climate science means that

AA

m m L G

G G C S OLR

. Although both

G

S

and

A

OLR

may easily be observed,

A

m

G

cannot be related

directly to the GHG composition of the atmosphere,

and it has no clear physical meaning. The cloud cover

has nothing to do with the absorption of the GHGs.

Water droplets just like other solid or liquid surfaces

radiate continuous IR spectra. The greenhouse effect

from the GHGs above the cloud layers should also be

taken into account.

The GE based anthropogenic global warming (AGW)

hypothesis rests on the assumption that increasing

atmospheric CO2 concentration of human origin will

result in increasing global average ground surface

temperature. The motivations for writing this paper

are the accumulating evidences that GE in the Earth's

atmosphere is not a free parameter. AGW estimates

based on the classic greenhouse effect explanations of

Fourier, Arrhenius, Tyndall, or the Intergovernmental

Panel on Climate Change (IPCC) are misleading. The

well known, and widely used, semi-infinite opaque

formulas with their predicted surface temperature

discontinuity cannot be used for semi-transparent

atmospheres. AGW predictions, based on modelling

calculations for CO2 doubling, are also not consistent

with the observed global average surface temperature

records of the last decades. Furthermore, observed

local or regional warmings that are usually attributed

to greenhouse warming (like Arctic warming) may be

accounted for by quite natural causes, see Arrak (2010,

2011).

In this paper, the published atmospheric greenhouse

effect and global warming related articles that

appeared in the climate science literature, are not

reviewed. There are excellent articles summarizing the

level of the general understanding (or misunder-

standing) of the phenomenon, see Herzberg (2009),

Kimoto (2009), Gerlich and Tscheuschner (2009), Van

Andel (2010), Hansen et al. (1981), Ramanathan (1981),

Raval and Ramanathan (1989) , Lindzen, (2007), Lacis

et al. (2010), and Pierrehumbert (2011). The usually

quoted quantities are the

44

150

A

m G A

G t t

Wm-2

all-sky GE and the

33

A

m G A

t t t

K greenhouse

warming. Here

288

G

t

K is the all-sky global average

ground surface temperature,

4390

G

t

Wm-2 is the

surface upward radiation,

1/4

( / ) 279

EE

tF

K is the

planetary effective (or equivalent blackbody) tempera-

ture

1/4

( / ) 255

A

A

t OLR

K is the planetary emission

temperature,

342

E

F

Wm-2, and

239

A

OLR

Wm-2.

Note that the astrophysical GE is much smaller than

A

m

G

. Among the authors, there seems to be an

agreement that the absorption and re-emission of the

surface upward infrared radiation by GHGs are the

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

34

principal causes for greenhouse warming. And, due to

well established energy balance principles, increased

atmospheric CO2 concentration will be inevitably

followed by an increased greenhouse effect. However,

the fact is that the greenhouse effect is a differential

quantity, therefore, such statements are not very well

established and demonstrated. We have seen that

m

G

is

a mixed quantity and cannot be associated with the

net absorption of the

U

S

in the system.

The most popular global energy budget schemes were

published by Kiehl and Trenberth (1997) (KT97), and

TFK09. In KT97 and TFK09 the global average

terrestrial radiation field was modeled by using a

version of the US Standard Atmosphere 1976 (USST76)

in which in order to match with Earth Radiation

Budget Experiment, ERBE (2004) observations the H2O

column amount was reduced from 1.42 to 1.26

precipitable cm (prcm). In KT97 and TFK09 the all-sky

A

m

G

and clear sky

m

G

were reported as 155 and 157

Wm-2, subsequently. Newer studies show substan-

tially different greenhouse effects, see Stephens et al.

(2012) (S12), Wild et al. (2013) (W13), and Costa and

Shine (2012) (CS12). In Lacis et al. (2010)

A

m

G

is less by

5 Wm-2 than the one in RI06. The

m

G

in M10 shows

about 10 Wm-2 underestimate, compared to the one in

Lacis et al. (2010). Such differences in the radiative

fluxes may be translated into about 1-2 K uncertainties

in

E

t

and

G

t

temperatures. In Fig. 1, we show how CO2

perturbations affect the

OLR

and how the real world

responds to the changeing atmospheric CO2 amount.

FIG. 1 HARTCODE GHG PERTURBATION STUDY SHOWS THAT

AT THE TOA THE NO-FEEDBACK RESPONSE OF INCREASED

ATMOSPHERIC CO2 IS NEGATIVE. THE OBSERVED 23.6 %

INCREASE IN THE CO2 COLUMN AMOUNT CAUSES -0.75 WM-2

RADIATIVE IMBALANCE (RED DOT). IN THE SAME TIME

PERIOD, BASED ON THE NOAA R1 ARCHIVE THE REAL

CHANGE IS

3.02OLR

WM-2 (BLUE DOT).

Climate modelers are using diverse - and not very

transparent - H2O feedback processes to match their

predicted

OLR

with the reality. Here

OLR

is the

difference between the

OLR

of the unperturbed and

perturbed cases. In this article the High Resolution

Atmospheric Radiative Transfer Code (HARTCODE)

line-by-line (LBL) RT software are used for all flux

computations. Typically, the spectral resolution was

set to 1 cm-1, Miskolczi (1989) .

FIG. 2 SPECTRAL FLUX DENSITY COMPONENTS IN COLD AND

DRY, (LEFT PLOT), AND WARM AND HUMID, (RIGHT PLOT),

SITUATIONS.

D

E

: DOWNWARD ATMOSPHERIC EMITTANCE;

G

: CLEAR SKY GREENHOUSE EFFECT;

E

: RADIATIVE EQUI-

LIBRIUM FLUX OPTICAL THICKNESS. FLUXES ARE IN WM-2.

FIG. 3 SPECTRAL FLUX DENSITY COMPONENTS IN THE

GLOBAL AVERAGE NOAA R1, (LEFT PLOT), AND USST76 ,

(RIGHT PLOT), ATMOSPHERES. FLUXES ARE IN WM-2 .

In Figs. 2 and 3 the theoretical difficulties of the

interpretation of

G

as the measure of the absorption

properties of the atmosphere have been demon-strated.

In Fig. 2 local clear sky greenhouse effects are

computed and compared for cold, and also for warm

real atmospheric structures. The

A

IR flux optical

thicknesses are very similar in the two cases. The H2O

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

35

column amounts and the radiative equilibrium optical

thicknesses,

E

, are largely different and are consistent

with the H2O amounts. Because of the chaotic nature

of the humidity field and cloud cover, one cannot

quantitatively relate the local

G

or

g

to the GHG

content of the atmosphere.

In the second example (see Fig. 3) computations are

performed using the 61 year global average

atmosphere from the NOAA NCEP/NCAR (2008)

reanalysis data time series (NOAA R1), and the

version of USST76, used in KT97 and TFK09. Note that

the H2O column amounts in the two profiles are

dramatically different. In the above example, the

global average

G

and

g

are not sensitive to the roughly

doubled water vapor amount in the atmosphere.

These comparisons clearly show that the greenhouse

effect characterized with

m

G

or

G

is not consistent with

statements that link the increased GHG content of the

atmosphere to increased IR absorption.

Considering the above examples, and the permanent

failure of the most sophisticated general circulation

models (GCMs) in predicting the magnitude of global

warming, one should admit the serious theoretical

deficiencies in using the greenhouse effect as a sole

measure of infrared atmospheric absorption. The

governing mechanisms of the IR absorption prop-

erties of the global average atmosphere are never

studied in sufficient detail and the real nature of the

greenhouse effect is not known. Compared to the

observed ~0.012 K/year positive trend in the surface

temperature over the last 61 years (see M10) and the

recent skills of the GCMs in predicting the changes in

the GE for a hypothetical CO2 doubling, the quan-

titative proof of the CO2 greenhouse effect based AGW

is not imminent.

In any serious greenhouse study, the knowledge of the

functional dependence of the global average IR flux

optical thickness on the GHG concentrations, and the

surface temperature, is absolutely necessary. The flux

optical thickness,

A

, flux absorption,

A

, and flux

transmittance,

A

T

, are defined by the

exp( )

T U A

SS

and

(1 )

T U U A

S S A S T

relationships. For semitrans-

parent atmospheres, except in M04, M07 and M10,

there are no published numerical data available on the

theoretical surface temperature - flux optical thickness

relationship. The obvious reason why the scientific

community does not present such results is twofold.

The first is the lack of a suitable greenhouse theory

which is based solely on the known fundamental laws

of nature. Apart from the fact, that the use of GCMs

for studying large scale climate change is conceptually

wrong (fundamentally stochastic processes cannot be

diagnosed by a deterministic model), the GCMs with

their numerous tuning parameters are not represent-

ing the principles of physics and the demonstrated

response of the greenhouse effect. Common green-

house effect explanations are not able to account for

the magnitude and the tendency of the phenomenon.

It has been known for a long time that climate change

is controlled by the net radiative fluxes at the TOA and

at the ground surface. The global average state of the

atmosphere (or global average climate) is governed by

the laws that control flows of radiative fluxes at the

boundaries.

The second reason is rather technical, and related to

the accurate computation of the flux optical thickness.

According to RI06 the three dimensional charac-

terization of radiative heating rates from equator to

pole using the LBL approach is impractical. This view

suggests sacrificing accuracy, by using band models in

global scale radiative transfer computations, where it

is most needed. This simplified view is probably the

reason why, in recent textbooks, extensive parts are

devoted to popularizing ancient band model tech-

niques, see for example in Pierrehumbert (2010).

Unfortunately the fact is that there are no publicly

available LBL codes for accurate computations of the

IR flux optical thickness. From a correct LBL spectral

radiance code there is a very long way to a correct

spectral spherical refractive flux density code.

The IR Optical Thickness of the Atmosphere

In astrophysics - for the different kind of radiative

transfer problems - there are different kinds of

definitions for the mean optical thickness (or mean

opacity), see Mihalas and Weibel-Mihalas (1999). They

are the Rosseland, Planck, and Chandrasekhar means,

and they are, in fact, different kinds of weighted

average absorption coefficients. The relevant physical

quantity necessary for the computation of the real

atmospheric IR absorption is the Planck-weighted

greenhouse-gas optical thickness,

A

. The numerical

computation of this quantity for a layered spherical

refractive atmosphere may be found in M10. By

definition,

A

is computed from the spectral hemi-

spheric transmittance and therefore represents the real

spectral feature of the infrared absorption coefficient.

It should be emphasized that

A

is not a weighted

absorption coefficient in the sense of the usual Planck

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

36

mean opacity in Mihalas and Weibel-Mihalas (1999).

A

is a newly defined physical quantity and one

cannot find any reference in the literature to its

computational techniques. The existence of the large

and organized absorption line catalogues and the

development of high speed computers and LBL

computational techniques are the reasons for the

above definition of

A

, see HITRAN2K (2002),

Rodriguez et al. (1999). Only a full blown spherical

refractive LBL radiative transfer code is able to

compute the accurate atmospheric IR flux optical

thickness. In short,

A

may be expressed as:

411

1

ln ( , ) ( , )

MK

kk

A j G A j

jk

G

B t w T

t

, (1)

where

3490M

is the total number of spectral

intervals,

9K

is the total number of streams,

( , )

jG

Bt

is the mean spectral Planck function, and

k

w

is the hemispheric integration weight associated

with the

th

k

direction (stream),

( , )

k

Aj

T

is the direc-

tional mean spectral transmittance over a suitable

short wave number interval:

,

1 , , ,

11

( , ) exp

j

il

LN

k i l i l

A j j lk

li

u

T c k d

, (2)

where

,,

cos( )/

l k l k l

dz

and

,

lk

is the local zenith

angle of a path segment,

,il

c

and

,

il

k

are the contri-

butions to the total monochromatic absorption

coefficient from the continuum type absorptions and

all absorption lines relevant to the

th

i

absorber and

th

l

layer respectively. The vertical geometric layer

thickness is

l

dz

.

11N

is the total number of major

absorbing molecular species and

150L

is the total

number of the homogeneous atmospheric layers

(shells). In Eqn. (2) the wave number integration is

performed numerically by fifth order Gaussian

quadrature over a wave number mesh structure of

variable length. At least

1

j

cm-1 spectral resolution

is required for the accurate Planck weighting. From

Eqn. (1) follows the usual form of the transmitted and

absorbed part of the surface upward radiation. Eqs.

(1,2) with the required spherical refractive ray-tracking

algorithms are implemented into HARTCODE and

facilitate the accurate partition of the

OLR

to its

T

S

and

U

E

components. The oversimplified and, in fact, often

mathematically incorrect computation of

m

G

(for ex-

ample in CS12, RI06, or in the NATURE article of

Raval and Ramanathan (1989)) should be avoided.

FIG. 4 DOWN-LOOKING CASE. HARTCODE SPECTRAL HEMI-

SPHERIC TRANSMITTANCES IN THE 1-3490 CM-1 SPECTRAL

INTERVAL FOR THE 668 CM-1 INTERVAL THE DIRECTIONAL

TRANSMITTANCES ARE ALSO PLOTTED (WITH GREEN LINES).

THE BLACK DOTS REPRESENT THE ISOTROPIC ANGLE AND

INDICATE CONSIDERABLE ERROR IN THE WIDELY USED

ISOTROPIC APPROXIMATION.

FIG. 5 HARTCODE SPECTRAL HEMISPHERIC TRANSMITTAN-

CES IN THE 1-3490 CM-1 SPECTRAL INTERVAL. THESE TRANS-

MITTANCES ARE REQUIRED FOR THE COMPUTATION OF THE

DOWNWARD FLUXES FROM THE TOA OR FROM THE CLOUD

BOTTOM.

Unfortunately, theoretically, no instrument can be de-

vised to measure the monochromatic or spectral

T

S

and

U

E

quantities separately. Since the above radiative

components cannot be measured by any airborne or

satellite spectrometer this is an essential improvement

in the numerical computations of the real IR atmo-

spheric absorption.

In Fig. 4 and Fig. 5 hemispheric transmittances

(obtained from Eq. (2) by integration over the

respective hemispheres) are presented for the global

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

37

average Thermodynamic Initial Guess Retrieval (GAT)

profile and for down-looking and up-looking

geometries. According to the Helmholtz reciprocity

principle the spectral mean downward and upward

hemispheric transmittances must be equal. In M10,

page 234, the atmospheric transfer and greenhouse

functions were introduced by the

( ) 2/ (1 )

A A A

fT

,

and

( ) 1 ( )

AA

gf

definitions. For an atmospheric

air column in radiative equilibrium it was also shown

that

/U

f OLR S

, and

( )/

UU

g S OLR S

. Using the

relationships above, the normalized greenhouse factor

may be expressed with

A

T

,

A

, or

A

. The complex,

nonlinear dependence of

g

on the absorption

properties of the atmosphere and the boundary layer

fluxes is apparent. One must remember that the so

called broadband window radiation is not an adequate

quantity to represent the transmitted surface radiation.

To make use of the satellite measured global average

broadband window radiation in global radiative

budget estimates the data should be corrected (or

calibrated) with global average atmospheric ab-

sorption data of the highest accuracy. Previously, in

Fig. 3 accurate clear sky transmitted flux densities are

presented for the GAT and the USST76 atmospheres.

The 30 Wm-2 difference in

T

S

is large enough to raise

the question of the quality of the KT97 and TFK09

global energy budgets. Although the USST76

atmosphere could be a good representation of an

average mid-latitudinal atmospheric structure, the use

of it in global energy budget assessments is a serious

mistake.

It must be recognized that no consensus in global

warming issues can exist without a declared and

accepted standard global average atmosphere derived

from a well documented global radiosonde archive.

The total IR absorption of such an atmosphere must be

computed for the most realistic chemical and GHG

composition of the atmosphere and with the highest

accuracy. All GHG studies and radiative budget

estimates should be referenced to the absorption and

optical properties of this global average standard

atmosphere. In looking for flux density - optical

thickness relationships, which could be used for

surface skin temperature estimates, or in the quan-

titative computations of the GE sensitivities in GHG

perturbation studies, such an atmosphere would be

extremely beneficial. As an example, it has little merit

to reference to RT computations where the atmo-

spheric thermal and humidity structure (or the related

input data base) are not traceable to the original

sources. In the weakly documented low quality paper

of CS12, no one knows how much water vapor or CO2

is in the air, yet they suggest an accurate global

average

T

S

for other people to use in their energy

budget studies , see S12.

Although, in some cases, empirical estimates of ra-

diative budget components from other authors are

referenced, the critical evaluation of the different

planetary radiative budget schemes is not the purpose

of the present article. In general, in science, a debate

over an issue is initiated when the related subject is

sufficiently well known and both theoretical and

empirical supports are available for the discussion. For

example, no one will seriously comment upon the

fictitious surface energy imbalance of

0.6 17

Wm-2 in

S12, or the

0.6 0.4

Wm-2 in W13.

In the next sections we present numerical results of

observed radiative flux density relationships for the

planet Earth, identify and develop the theoretical

relationships consistent with the observations and give

a new view of the planetary greenhouse effect.

Input Data Sets

Realistic vertical global average thermal and humidity

structures may be obtained from readily available

climatological radiosonde archives, Chedin and Scott

(1983). In this study the GAT global average structure

is constructed from the Thermodynamic Initial Guess

Retrieval (TIGR2) archive containing 1761 weather

balloon observations. An updated version of the

database (known as the TIGR2000 archive) containing

2311 soundings is also available: TIGR Thermo-

dynamic Initial Guess Retrieval (2000). The locations,

meridional, and annual distributions of the two

archives are presented in Fig. 6. Both archives contain

prohibitively large number of soundings for LBL

computations.

One should be aware of some inconsistent and

undocumented modifications of the vertical humidity

structures in the TIGR2000 soundings. In hundreds of

TIGR2000 observations the upper tropospheric hu-

midity is significantly increased which may introduce

biases in the computed global average vertical

radiative structure. After some regional and seasonal

grouping of the TIGR2 soundings a subset of 228

profiles is selected, see Fig. 7. In the subset the

statistical characteristics of the original data set are

preserved. In Fig. 8, two extreme atmospheric struc-

tures from the selected sub-set are presented.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

38

In this article we use the GAT atmosphere as the

representative temperature and humidity structures of

the global average climate. For studying possible long

term changes in the global average optical thickness

(due to changes in GHG content of the atmosphere)

the TIGR2 archive is not suitable. The publicly

available longest time series of annual mean vertical

temperature and humidity structures may be obtained

from the NOAA R1 time series data archive. This

archive, known as the NCEP/NCAR R1 data set,

covers the 1948-2008 time period and is regularly

updated. NOAA R1 has been used by the NCEP

Climate Prediction Center to produce global

atmospheric monitoring and assessment products,

Trenberth (2009). A quick look at the data immediately

shows that the range of variations in the annual mean

over 61 years is very small: 58.87 atm-cmSTP in CO2,

0.0169 prcm in H2O, and 0.687 K in surface tempe-

rature. The related year-to-year relative changes are

also small, 0.35 %/year in CO2, -0.0106 %/year in H2O,

and 0.0039 %/year in surface temperature. In this

study monthly or seasonal variations are ignored.

FIG. 6 THE TIGR CLIMATOLOGICAL DATASETS. DETAILED COMPARISONS SHOW

THAT THE GLOBAL AVERAGE TIGR2 SURFACE AIR TEMPERATURE IS 0.28 K COLDER

AND THE VERTICAL AIR COLUMN CONTAINS 0.1 PRCM (ABOUT 3 %) LESS H2O.

SINCE IN THE TIGR2000 VERSION THE VERTICAL H2O STRUCTURE WAS ARTIFI-

CIALLY MODIFIED (UPPER TROPOSPHERIC HUMIDITY WAS INCREASED) WE

DECIDED TO USE THE ORIGINAL TIGR2 ARCHIVE.

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

39

Obviously, there are very high requirements for the

sensitivity and numerical accuracy of the computed

fluxes and flux optical thicknesses. To quantify the

possible trend in the average absorption properties of

the atmosphere, simulations are performed for six

subsets of different times and time intervals.

Observed Empirical Facts

In 2002, at the National Atmospheric and Space

Administration (NASA) Langley Research Center, the

first set of global scale high accuracy LBL flux optical

thickness and flux density computations for the TIGR2

data set were completed, and the new fundamental

clear sky semi-transparent radiative equilibrium equa-

tion,

( ) ( )/ ( )

U A A A

S OLR f

, was awaiting large scale

empirical verification. A general view of the simulated

flux density components are presented as the function

of the 11 seasonal and geographical classes in Fig. 9. A

quick look at the upper plot immediately confirms the

obviously expected relationships among the fluxes:

T U D A U

S E OLR E A S

. The lower plot sug-

gests a fairly strong linear relationship between the

downward

D

E

and the absorbed

A

A

fluxes. After the

routine plots of

A

,

A

T

,

U

S

,

T

S

,

D

E

,

U

E

, and

OLR

quantities, four rather unusual relationships among

the flux density components and optical thicknesses

emerge. In Figs. 10-13 the TIGR2 simulation results are

plotted for the individual soundings. The tentative

naming of the discovered empirical relationships (they

are called 'rules') reflects the fundamental physical

laws with which they are associated. For complete-

ness, we should also mention the extropy rule, which

is not discussed here, see Miskolczi (2011).

FIG. 7 LATITUDINAL AND SEASONAL GROUPING OF THE

TIGR2 SOUNDINGS. IN THE SELECTED SUBSET 228 SOUNDINGS

WERE DISTRIBUTED AMONG 11 GROUPS HAVING ABOUT 20

SOUNDINGS IN EACH GROUP. LATITUDINAL AND SEASONAL

CLASSES WERE ESTAB- LISHED CONSIDERING THE SOLAR

CLIMATIC ZONES.

FIG. 8 RARE ATMOSPHERIC SITUATIONS. EXTREME DRY AND

COLD AND WARM AND HUMID ATMOSPHERIC STRUCTURES

IN THE TIGR2 DATA .

FIG. 9 SEASONAL-GEOGRAPHICAL DISTRIBUTIONS OF THE

TIGR2 FLUX DENSITIES. CLASSES ARE: 1 - ARCTIC SUMMER, 2 -

ARCTIC WINTER, 3 - NORTH MID-LATITUDE SUMMER, 4 -

NORTH MID-LATITUDE FALL/SPRING, 5 - NORTH MID-

LATITUDE WINTER, 6 - NORTH/SOUTH TROPICAL, 7 - SOUTH

MID-LATITUDE SUMMER, 8 - SOUTH MID-LATITUDE

FALL/SPRING, 9 - SOUTH MID-LATITUDE WINTER, 10 -

ANTARCTIC SUMMER, 11 - ANTARCTIC WINTER. THE LOWER

PLOT SHOWS THAT IN ALL CLASSES THE ATMOSPHERIC

ABSORPTION CAN BE VERY WELL APPROXIMATED BY THE

DOWNWARD ATMOSPHERIC EMISSION.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

40

FIG. 10 THE ATMOSPHERIC KIRCHHOFF RULE SUGGESTS A

VERY STRONG LINEAR RELATIONSHIP BETWEEN THE

EMITTED CLEAR SKY DOWNWARD AND THE ABSORBED

SURFACE UPWARD IR FLUX DENSITIES. COLD AND DRY

POLAR AREAS FIT BETTER TO THE RULE THAN THE WARM

AND HUMID EQUATORIAL AREAS. THE GLOBAL MEAN

CLEAR SKY

1

/

DA

EA

RATIO (WE CALL IT SPHERICAL

EMISSIVITY) IS ABOUT 3 %.

FIG. 11 THE RADIATIVE EQUILIBRIUM RULE IS THE NAME OF

THE THEORETICALLY DERIVED

/U

OLR S f

EQUATION. FOR

THE TIGR2 ARCHIVE THE GLOBAL AVERAGE TRANSFER

FUNCTION IS SLIGHTLY LARGER THAN THE THEORETICALLY

EXPECTED

0.6618f

. THE SCATTER OF THE POINTS SHOWS

THAT THE EXACT LOCAL RADIATIVE EQUILIBRIUM IS A VERY

RARE SITUATION.

At this point we should emphasize that the presented

relationships are not derived from some well known

physical laws of nature, but are obtained from ob-

servations and computations using first principles. It

should also be noted that the newly discovered

empirical relationships are not the results of some

lucky coincidental profile selections from the TIGR2

archive. In the last several years the computations

using the TIGR2000 archive, the updated NOAA R1

archive, some satellite training and calibration data

sets, hundreds of high resolution and high quality

FIG. 12 THE

3 / 2

U

S OLR

RELATIONSHIP SHOWS GOOD AGREE-

MENT BETWEEN THE GLOBAL MEAN (BLACK CIRCLE) AND

THE THEORETICAL EXPECTATION (HORIZONTAL LINE).

SINCE THE POLAR STATIONS OVERESTIMATE, AND THE

EQUATORIAL STATIONS UNDERESTIMATE

U

S

THIS RELATION-

SHIP IS ASSOCIATED WITH THE REDISTRIBUTION OF THE

AVAILABLE THERMAL ENERGY OF THE ATMOSPHERE BY THE

GENERAL CIRCULATION.

FIG. 13 THIS RULE IS THE RELATIONSHIP BETWEEN THE

SURFACE UPWARD FLUX AND THE ATMOSPHERIC UPWARD

IR EMISSION (EMERGENT THERMAL RADIATION FROM THE

ATMOSPHERE ALONE):

2

UU

SE

. AGAIN WE HAVE A GOOD

AGREEMENT BETWEEN THE GLOBAL AVERAGES. THIS

RELATIONSHIP IS A DIRECT CONSEQUENCE OF THE GLOBAL

AVERAGE HYDROSTATIC EQUILIBRIUM STATE .

radiosonde observations from the NOAA Testing and

Evaluation Station are repeated. Many special atmo-

spheric structures from different sources are evaluated

as well.

No atmospheric structures contradicting the above

rules are found. Even artificial profiles (like the

USST76 atmosphere) are consistent with the new flux

relationships. Judging from the correlation coefficients

(Figs. 10-13), none of these rules are perfect. In fact,

tight fits in these types of relationships are not

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

41

expected since the atmosphere is fundamentally a

stochastic medium. We must conclude that the above

rules represent the real radiative transfer properties of

the Earth-atmosphere system, and in order to get

closer to the cause of the greenhouse effect, one should

try to explain and understand all of them.

Although this study focused on IR fluxes at upper and

lower boundaries of the atmosphere, further results

are presented in Fig. 14 for the GAT vertical radiative

structure. Two sets of radiative fluxes (for the upper

and lower portions of the atmosphere) are plotted as a

function of the layer geometric thicknesses:

()zz

top

zz

, and

()z z z

, where

70top

zz

is the 70 km top

altitude of the atmosphere. The lower boundary of the

whole air column is at

00z

km. For some selected

altitudes numerical flux density data are presented in

Table 1.

FIG. 14 GAT UPWARD AND DOWNWARD RADIATIVE FLUXES.

SOLID LINES ARE THE BOUNDARY FLUXES FROM LAYERS

BETWEEN

top

z

AND

z

ALTITUDES. BROKEN LINES ARE THE

BOUNDARY FLUXES FROM LAYERS BETWEEN

0.0

AND

z

ALTITUDES. THE HORIZONTAL BLUE LINES ARE THE

ALTITUDES WHERE

( ) ( )

DU

E z E z

, AND

( ) ( )

U

S z OLR z

. AT THE

ALTITUDE OF THE BLACK CIRCLE

( ) ( )

D

E z OLR z

.

The interesting features here are the approximate flux

equalities at some special altitudes:

22

( ) ( )D

OLR z E z

,

10 10

( ) ( )OLR z B z

, and

10 10

( ) ( )

DU

E z E z

. At the indi-

cated levels the atmosphere has unique equilibrium

states which may largely affect the whole global

energy balance picture. For example, if the Kirchhoff

rule is valid for all altitudes, then the

22

( ) ( )D

OLR z E z

equation means that, at around the 2 km altitude, the

atmosphere above a cloud layer is in radiative

equilibrium. The last two equations imply that slightly

above the 10 km altitude the clear sky atmospheric

greenhouse effect stops,

0

U

G S OLR

.

The detailed analysis of the vertical structure of the IR

radiation field will be the scope of another article.

Note, that the NOAA R1

A

, and

A

T

are practically

the same, but the lower atmospheric thermal structure

of the GAT is considerably colder as there is an

approximate 15 Wm-2 difference in

U

S

at the ground.

This is a clear indication, that

A

depends only upon

the real absorption properties of the atmosphere.

TABLE 1. VERTICAL RADIATIVE STRUCTURE OF THE GAT ATMOSPHERE.

ALTITUDES ARE IN KM, FLUXES ARE IN WM-2 , TRANSMITTANCES AND

OPTICAL THICKNESSES ARE DIMENSIONLESS. THE NOAA R1 61 YEAR

AVERAGE DATA ARE ALSO SHOWN IN RED COLOR.

(z)B

IS THE FLUX

DENSITY PROFILE AND

(z 0)

UG

S B B

.

Altitude

OLR

ED

EU

B(z)

ST

TA

τA

60.0

202.1

0.2008

0.1793

202.1

201.9

.9989

.0011

50.0

253.4

0.7421

0.6553

253.6

252.8

.9969

.0031

30.0

154.9

4.774

5.620

153.5

149.2

.9723

.0281

15.0

115.1

17.52

20.98

111.4

94.11

.8444

.1692

10.0

152.7

52.82

48.73

160.1

103.9

.6490

.4322

5.00

212.3

149.0

108.6

262.4

103.7

.3952

.9284

2.00

239.6

237.6

156.1

331.9

83.42

.2513

1.3810

0.00

251.8

309.9

193.2

379.7

58.6

.1542

1.8691

0.00

256.4

321.5

195.4

395.0

60.95

.1543

1.8688

In the next three figures (Figs. 15-17) the results of the

search for long term optical thickness trends in the 61

year long (1948-2008) NOAA NCEP/NCAR R1 re-

analysis dataset are shown.

Attempts to identify any significant changes in the

absorption characteristics of the atmosphere are

unsuccessful. For the above tasks HARTCODE is

pushed to extreme numerical accuracy, test runs for

small GHG perturbations were presented in M10. In

Fig. 15 the actual and expected atmospheric

absorption trends are compared for the full time

period. No change in the IR absorption is detected. In

Fig. 16 the results of the six sub-sets of the 61 year time

periods are also presented. The theoretical expectation

in each sub-set is met, no changes in the sample mean

optical thicknesses are apparent. However, both the

annual mean optical thickness and H2O column

amount are subject to random fluctuations.

Detailed Fourier analysis of the 61 year long time

series shows that a significant oscillation with a 3.529

year period is present in the data. This 'heartbeat' of

the atmosphere could be related to the ElNino -

LaNina cycles. Fig. 17 displays the observed changes

in

A

t

,

A

t

,

S

t

, H2O, and CO2 . The slight negative trend

in

A

t

and the large increase in CO2 concentrations is

certainly not consistent with the classic GE explana-

tions, found in any textbook on climate change.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

42

FIG. 15 ATMOSPHERIC ABSORPTION TRENDS IN THE LAST 61

YEARS. THE EXPECTED INCREASE IN THE ATMOSPHERIC

FLUX ABSORPTION DUE TO THE ~23 % CO2 INCREASE DURING

THIS TIME PERIOD IS NOT PRESENT.

FIG. 16 OPTICAL THICKNESS COMPUTATIONS FOR DIFFERENT

SUB-SETS OF THE NCEP/NCAR R1 ARCHIVE. SHORT TERM

FLUCTUATIONS ARE NOT RELATED TO CO2 INCREASE. THE

AVERAGE

A

IN ANY TIME SERIES AGREED WITH THE

THEORETICAL EXPECTATION OF 1.87 .

FIG. 17 THE OBSERVED GREENHOUSE TEMPERATURE

CHANGE IS NOT CONSISTENT WITH THE INCREASED CO2

CONCENTRATION. THE SURPRISING STABILITY OF

A

t

CANNOT BE EXPLAINED BY THE CLASSIC VIEW OF GREEN-

HOUSE PHENOMENON, AND DOES NOT SUPPORT THE GE

BASED AGW HYPOTHESIS OF THE IPCC.

Theoretical Interpretations

The analytical equations of the presented rules in Figs.

10-13 are summarized in the next four equations:

(1 )

D A U U A

E A S A S T

, (3)

/

U

OLR S f

, (4)

3 /2

U

S OLR

, (5)

2

UU

SE

. (6)

In the range of the input data sets the atmospheric

Kirchhoff , radiative equilibrium, and virial rules, Eqs.

(3,4) appear to be valid for each individual sounding

and also for the global averages. The energy conserva-

tion rule and virial rule, Eqs. (5,6) are valid for only

the global averages. Although in M07 some successful

modelling and simulation results for the Martian

atmosphere have been published, the validity of Eqs.

(3-6) for other planets are not discussed here. Each

planet or moon in the solar system has its own distinct

physical condition and in each case the radiative

transfer problem must be formulated individually.

Atmospheric Kirchhoff Rule

Recently some researchers have raised the question of

the applicability of the Kirchhoff rule for atmospheric

radiative processes, see for example DeBruin (2010),

Spencer (2011). Since the atmospheric Kirchhoff rule

represents an empirical fact, such critiques do not have

much scientific ground. If a couple of hundred

atmospheric structures show the

DA

EA

approximate

equality, then the only way to refute this relationship

is to show an atmospheric structure which is violating

it. In a planetary radiative equilibrium situation the

strict

DA

EA

relationship at the lower boundary is

established with the material IR emissivity properties

of the ground surface and atmosphere.

The anisotropy in

D

E

and the IR emissivity (or ref-

lectance) of the ground surface cannot be ignored. The

different forms of the monochromatic, flux, directional

etc., Kirchhoff laws are well known in the general

radiative transfer theory. It is also known that the

classic monochromatic Kirchhoff law is not valid in

the close vicinity of strong absorption/emission lines,

see M07. It is also difficult to adopt this law for

atmospheric IR flux densities where the inhomo-

geneous atmosphere is in permanent physical contact

with solid and liquid surfaces. The important finding

here is the ability of any real atmosphere to instantly

adjust its radiative structure to closely satisfy Eq. (3).

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

43

The physical explanation is very simple. The relax-

ation time of the IR radiation field is much smaller

than any macroscopic heat or energy transfer pro-

cesses (related to the motion and thermodynamics) of

the atmosphere. The vibrational-rotational relaxation

time is in the order from 2×10-6 to 2×10-5 sec at 1 atm.

and 200K. The IR radiation field is close to quasi-static

equilibrium with the surrounding environment and it

instantly 'sees' the whole atmosphere, independently

of the dynamics of the system. The strict validity of the

spectral Kirchhoff law for a hypothetical isothermal

atmosphere is obvious. Such computation is presented

in Fig. 18. As can be concluded, the spectral Kirchhoff

law is exact, and perfectly reproduced, (see the red

line). Similar but spectral radiance simulations for

isothermal atmospheres are routinely performed to

test the numerical performance of LBL radiative

transfer codes, see Kratz et al. (2005). The compu-

tational (numerical) accuracy of our LBL code for flux

transmittance is excellent. The relative error in the

DA

EA

equality is

6

100(1 / ) 2.2 10 %

DA

EA

.

The conditions of the stability of the thermal structure

of an air column are also of interest. In Figs. 19 and 20

simulated global average flux transmittance, atmo-

spheric downward emittance, and observed source

function profiles are presented for clear and cloudy

GAT atmospheres. In these simulations the cloud layer

is represented by a perfect black surface at a given

altitude with an infinitesimal vertical extension and in

thermal equilibrium with the surrounding air. The

thermal equilibrium and a perfectly black radiator are

also assumed at the ground surface,

0

()

U

S B z

at zero

altitude. In Fig. 19 the whole atmospheric air column

is in radiative equilibrium with the surface air. This is

the obvious condition for the local thermodynamic

equilibrium (LTE), and the existence of a stable

temperature profile. At higher altitudes this figure

shows that any emitting cloud layer is also in radiative

equilibrium with the atmospheric column above. This

is also the condition of the LTE in the air column

above the cloud layer. We should note that in case the

global average atmosphere represents a long term

average structure which is in overall radiative balance

with the surrounding space, then the ~3 % global

average anisotropy effect in the Kirchhoff rule must be

accounted for by an effective spherical emissivity

factor of

10.9652

. In Fig. 20 the cloud layer is acting

as a cavity and the atmosphere below the cloud layer

is in radiative equilibrium with the emitting surfaces

at the upper and lower boundaries.

FIG. 18 THE SPECTRAL KIRCHHOFF LAW IN ISOTHERMAL

ATMOSPHERE REQUIRES THE FOLLOWING EQUALITIES:

//

U D U

OLR S E A E A

, AND

//

U U D U

E S E S A

. THE

/

U

S OLR f

AND

/

UD

S E A

EQUATIONS CANNOT BE SATISFIED SIMULTA-

NEOUSLY, THEREFORE, SEMI-TRANSPARENT ISOTHERMAL

ATMOSPHERE CANNOT BE IN RADIATIVE EQUILIBRIUM.

FIG. 19 CLEAR SKY KIRCHHOFF LAW. THE ATMOSPHERIC

DOWNWARD EMITTANCE IS EQUAL TO THE ATMOSPHERIC

ABSORPTION OF THE SURFACE UPWARD RADIATION.

FIG. 20 CLOUDY SKY KIRCHHOFF LAW. UP TO ABOUT 3 KM

ALTITUDE THE MEAN ATMOSPHERIC EMITTANCE IS EQUAL

TO THE ABSORBED MEAN SURFACE RADIATION (FROM

GROUND AND CLOUD BOTTOM),

M

T

IS THE WEIGHTED

AVERAGE FLUX TRANSMITTANCE.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

44

FIG. 21 LOW LEVEL TEMPERATURE INVERSION AND

RADIATIVE EXCHANGE EQUILIBRIUM. HARTCODE

DETERMINED THE EQUILIBRIUM ALTITUDE USING THE

YELLOW DOTS FOR INTERPOLATION. THE ACCURACY OF THE

EQUILIBRIUM ALTITUDE IS ~ 4 M.

The question of the radiative exchange equilibrium

(introduced in M10) between the surface and a

particular part of the atmosphere is also studied. In

case thermal inversions are present in the temperature

profile, theoretically the surface must be in perfect

radiative exchange equilibrium with those atmo-

spheric layers having the same temperature. For this

kind of computation 42 inversion cases are selected

from the TIGR2 data and the differences in the

absorbed and emitted radiations in each layer are

computed. Such kind of tests are very useful because

they can point to inconsistencies and programming

bugs in the computational algorithms.

In Fig. 21, results are presented for a cold and dry

arctic atmosphere showing ~5 K close-to-surface

temperature inversion. The return altitude of the

temperature profile (above the inversion layer) is

picked up with quite remarkable accuracy (~ 4 m). To

our satisfaction, HARTCODE computed the layer net

radiation according to our expectations. As we

mentioned already, the IR radiative imbalance at the

ground surface can easily be accounted for by

introducing material IR emission properties of the

atmosphere and the surface. The complete radiative

equilibrium at the surface can be, and must be

established.

Radiative Equilibrium Rule

The naming of “radiative equilibrium rule” is quite

straightforward. The new semi-transparent radiative

equilibrium equations, the derivation Eq. 4 from well

known principles of the general radiative transfer

theory are proved with sufficient mathematical rigor,

(see Appendix B, Eq. B8 in M07 ). However, the use of

radiation equilibrium terminology requires some

clarification. The definition of the piecewise radiative

equilibrium is given by

( ) (3/ 4 )

o

B H B

, where

()

B

is the source function profile,

H

is the Eddington

flux,

0

B

is an integration constant, and

is the average

flux optical depth (measured from the TOA). In our

terminology, once a linear (actual or equivalent)

source function profile is established with the required

slope and

0()

A

B

, then the atmosphere is said to be in

radiative equilibrium. In this case the atmosphere has

the required amount of GHGs (H2O, CO2, O3 etc.) to

support the

/

U

S OLR f

relationship. An equivalent

form of Eq. (4) may be obtained using the

U

E

T

S OLR

defining identity:

/( )

U U A

S E f T

.

It is important to note, that at the theoretical deriva-

tion in M07 the gray approximation is just a simplified

terminology and applied only for the convenience of

dropping the wave number index in the equations. In

case of monochromatic radiative equilibrium, one may

rewrite the solution in the monochromatic form:

U

f S OLR

, where

()

A

ff

and

A

are the mono-

chromatic transfer function, and the monochromatic

flux optical thickness respectively. Integrating both

sides with respect to the wave number and applying

the mean value theorem of the calculus one may easily

arrive at Eq. (4).

In 2002 the only available theoretical relationship

between the IR optical thickness and the source func-

tion profile was the classic semi-infinite Eddington

solution, and its corrected versions (which tried to

resolve the surface temperature discontinuity prob-

lem). However, the related equations for semi-trans-

parent atmospheres turned out to be mathematically

incorrect and should not be used. In a real global

average clear sky atmosphere where the net non-

radiative energy fluxes equal to zero Eq. (4) holds

exactly.

The global average TIGR2 atmosphere used in this

article is quite close to the state of radiative

equilibrium. Test runs in the 0-120 km altitude range

show that

379.688

U

S

Wm-2,

251.004OLR

Wm-2,

0.661144f

, and the error in Eq. (4) is negligible,

/ 0.037

U

S OLR f

Wm-2 . Because of the changes in

OLR

and

f

, reducing the altitude range to 0-70 km, Eq.

(4) will overestimate

U

S

by about ~1 Wm-2, but will

largely reduce the LBL computational burden.

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

45

Energy Conservation Rule

Before going into the details of the physical meanings

of the rules presented in Figs. 12 and 13, we should

spend some more time with the energy conservation

and virial rules. In these two rules the clear sky surface

upward flux is proportional with

OLR

and also, with

U

E

:

3 /2

U

S OLR

and

2

UU

SE

. Unfortunately

these equations do not satisfy an obvious and neces-

sary physical condition which is sometimes called the

transparent limit constraint.

For a transparent atmosphere,

0

A

,

UT

S S OLR

,

and

0

DU

EE

conditions should be satisfied. To

implement the transparent limit constraint the

/2 /10

V T D

S S E

virial term is introduced. Adding

V

S

to the left hand side of Eq. (5), an equation which

obeys the transparent limit, and satisfies both of the

original equations is obtained. It is easy to show that

Eqs. (5) and (6) can be trivially satisfied with

/ 1/6

TU

SS

:

2 2 2 2(2 /3) 2

U U T U T

S E OLR S S S

,

from which follows

6

UT

SS

. The equivalent form of

this equation (using the observed

DA

EA

approx-

imation) is

/5 0

TD

SE

. It is assumed that the general

equation should be in the form of

3 /2

UV

S S OLR

,

where

( 5 )

V T D

S X S E

and

X

is a non-zero multi-

plier. In the transparent atmosphere limit

UU

S X S

3 / 2

U

S

, from which

1/2X

, and

/2 /10

V T D

S S E

.

The final form is

/2 /10 3 /2

U T D

S S E OLR

which can

be reshaped into a much simpler form:

/(3/5 2 /5)

UA

S OLR T

. (7)

From Eq. (7) and the definition of

OLR

the

5/ 3

/

AU

AE

simple relation and the

5/3 /DU

EE

approx-

imation immediately follow. One should not forget,

that Eq. (7) (and its different forms) are applicable only

for global average atmospheres. For example, the

/

AU

AE

ratios for the TIGR2 and USST76 atmospheres

are 1.666, and 1.766 subsequently, (see Fig. 3).

3 /2

U

S OLR

requires the validity of

DA

EA

. This

follows directly from the greenhouse identity, which

expresses the conservation of the radiant energy.

Applying the

DA

EA

approximation one arrives at the

U D U

S OLR E E

equation, from which one may

readily obtain the

3 /2

U

S OLR

relation. In complete

planetary radiative equilibrium

DA

EA

, and

U

S

3 / 2OLR

. The violation of these rules leads to the

violation of the conservation of radiant energy as

explained in M07 Eq. (7) in page 7.

Virial Rule

Climate scientists tend to forget about the virial

theorem and they usually render it unusable for

climate research. The atmospheric virial rule,

2

UU

SE

,

shows a linear dependence between the surface up-

ward flux density and atmospheric upward emittance.

Under hydrostatic balance the virial theorem relates

the potential energy and the internal energy. The virial

theorem may be expressed in different forms :

20 T

, or

3( 1) 0

U

, where

T

is the mean

kinetic energy,

is the gravitational potential energy,

is the specific heat ratio and

U

is the internal energy

of the system, see Chandrasekhar (2010), Cox and

Giuli (1968) and Clausius (1870). In astrophysics the

Vogt-Russel theorem is a relationship between the

mass and luminosity of a star.

The above facts gave enough inspiration to try to

relate

U

E

to the surface pressure or to the mass of the

atmosphere. The computations for the TIGR2 archive

are presented in Fig. 22. It is quite obvious that the

virial theorem is applicable for the Earth's atmosphere

and represents a permanent constraint on the IR radia-

tion field. For the Earth atmosphere the differential

forms of the virial relationship is also confirmed quan-

titatively (not shwn here).

The critiques of the association of Eqs. (6) with the

virial concept in DeBruin (2010), Toth (2010), and in

the comments of other radiative transfer experts (see

E. Rabett, P. DeWitt, G. Schmidt, R. Pierrehumbert,

and B. Levenson in the Real Climate (2008), or Science

of Doom (2014) Blogs) have no theoretical and empir-

ical foundations.

FIG. 22 VIRIAL CONCEPT IN HYDROSTATIC ATMOSPHERE.

INTERNAL ENERGY IS COMPUTED WITH ONE DEGREE OF

FREEDOM. GRAVITATIONAL POTENTIAL ENERGY DENSITY IS

REFERENCED TO THE SURFACE.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

46

Results and Discussion

As soon as sufficient confidence in the validity of the

individual clear sky atmospheric radiative transfer

rules is gained, the author is facing the interesting

problem of the empirically proven constant global

average clear sky flux optical thickness. Obviously the

energy conservation and radiative equilibrium rules

are the relevant equations which may be associated

with the overall planetary radiative balance and give

the needed theoretical support.

The simultaneous validity of Eqs. (4,7) requires the

solution of the

/(3/5 2 / 5) /

A

OLR T OLR f

transcen-

dental equation which can be simplified into the

2 /5gA

form. The only unknown in these equations

is the equilibrium flux optical thickness which is the

sole function of the thermal and humidity structure of

the global average atmosphere.

The numerical solution of the equation resulted in a

unique theoretical equilibrium flux optical thickness of

1.867561

T

A

. The other theoretical quantities are

derived from

T

A

:

0.1545

T

A

T

,

0.8455

T

A

,

0.6618

T

f

,

0.3382

T

g

.

10.9572

T

. Apparently this

T

A

does not

depend on any particular GHG concentration and it

might better be regarded as an invariant climate

parameter of the Earth-atmosphere system.

The first verification of the

T

AA

equality is based

upon the TIGR2 and NOAA R1 radiosonde archives

(

A

is the observed global average). The combined

results are summarized in Fig. 23. All annual global

mean optical thicknesses are practically equal to

T

A

and supporting the

T

AA

theoretical expectation. Fig.

23 shows also the TIGR2

/

UU

ES

ratios (gray dots) and

the associated theoretical

A

fT

function (magenta

curve).

One should note that despite the relatively large

spread of the

/

UU

ES

dots, the global average

/ 0.5089

UU

ES

ratio is consistent with the

2

UU

SE

virial rule. In our atmosphere the individual

/

UU

ES

ratios are also constrained by the

A

T

,

A

,

f

, and

g

radiative transfer functions (see the yellow shaded

area). The theoretical upper limit of

A

is set by the

1/2fg

constraint:

ma x 2.9475

A

. The

1 2 /5A

(broken red curve) is a version of the energy conser-

vation rule, and the green dot in the intercept of the

f

and

1 2 /5A

curves marks the position of

T

A

.

FIG. 23 COMBINED TIGR 2 AND NOAA SIMULATIONS. THE AN-

NUAL MEAN NOAA R1 DATA NOT RESOLVED SUFFICIENTLY

TO SEE THE INDIVIDUAL SOUNDINGS. THE EMPIRICAL

1.87

T

AA

RELATION SHIP IS FULLY SUPPORTED.

FIG. 24 STEADY-STATE CLEAR SKY CLIMATE MODEL WITH

CONSTANT IR OPTICAL THICKNESS. RED NUMBERS:

1OLR

;

BLUE NUMBERS:

1

U

S

. IN RADIATIVE EQUILIBRIUM

/

UA

S F f

,

AND

(1 ) /

U E B

S F f

, THEREFORE,

U

S

MAY CHANGE ONLY

THROUGH

E

F

OR

B

.

The observed stability of the clear sky absorption

properties of the global average atmosphere may be

demonstrated with a heuristic clear sky RT model

presented in Fig. 24 (here

F

is the absorbed part of

A

F

within the atmosphere). This model is simplified in a

sense that the effects of the LW emissivity, re-

flectance,and anisotropy are ignored on the basis the

sustained radiative equilibrium requirement will

compensate all related imbalances. The net non-

radiative processes

KK

are zeroed out on the basis,

that the planet is in radiative equilibrium and the

hydrological sub-system (or water cycle) is a closed

equilibrium process. The only requirement from the

model is the constant average IR optical thickness

which can be maintained around the

T

A

theoretical

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

47

value by the stochastic fluctuations of all flux density

ratios (around their respective planetary averages).

Compared to the real world relationships among the

boundary fluxes in Table 1, this model gives quite a

reasonable estimate of the normalized flux densities.

The constant long term global average clear sky flux

optical thickness does not leave much room for the

system to obey the energy conservation principle. It is

quite plausible to assume that the cloud cover is

responsible for simultaneously maintaining the radi-

ative equilibrium and energy conservation require-

ments. Some aspects of the global average cloud cover

will be discussed in the next section, but the full

account of the detailed role of the hydrological cycle

and its quantitative effect on the flux density

components will be discussed elsewhere.

Radiative Equilibrium Cloud Cover

One of the most elusive problems of climate science is

the correct handling of the radiative effects of the

global average cloud cover. After decades of struggle

with the cloud forcing parameter and other mixed

physical quantities, the role of clouds in the climate

system remains hidden. It has been known for a long

time that the cloud cover follows the annual solar

cycle which is present in the SW energy input

(

330.25 353.00

E

F

Wm-2), but a solid theoretical

foundation for the mechanism and the quantitative

methods for the practical evaluation of the

and

C

h

parameters are not present in climate literature.

Accurate RT computations using HARTCODE lead to

the discovery of four fundamental atmospheric

radiative transfer rules. As an application, in this

section the radiative equilibrium

, and

C

h

which are

consistent with the above rules and the related

constraints are determined. In view of the

T

AA

and

()

T

UA

OLR S f

clear sky LW radiative equilibrium

requirements it is obvious, that the task of assuring the

all-sky radiative balance and the

AER

OLR F F

top

level energy conservation constraint, is left entirely to

the

, and

C

h

parameters.

We should mention, that in M07 an attempt is already

made to compute

, and

C

h

from the atmospheric

Kirchhoff, and the energy conservation rules:

( 3 / 2) / ( )

AC

U U U

S OLR S S

, where

382

U

S

Wm-2,

235

A

OLR

Wm-2, and

333

C

U

S

Wm-2. The resulted

0.6

and the related

2.05

C

h

km cloud top alti-

tude fit well into the wide range of published cloud

cover data, but unfortunately, large uncertainties in

the satellite

A

OLR

may result in any

within the

0.45 0.75

range. Because of the

AC

OLR OLR

assumption and the limited capability of the

HARTCODE vertical layering routines (at that time),

the accuracy of our

and

C

h

was unknown. It was

impossible to prove the consequential

()

CC

A

A h OLR

,

()

T

A

f

, and

()

CC

D

E h OLR

relationships from the

Kirchhoff rule (see page 19 in M07).

In the recent approach it is assumed that the GAT

atmosphere represents the global average structure

reasonably well, and the

0

F

, (and consequently

E

F

),

are also known with sufficient accuracy. One may

construct two discrete sets of data (

( , )

AC

Bh

, and

( , )

EC

Bh

) from LBL simulations of the

A

OLR

,

OLR

,

and

C

OLR

flux densities:

((1 ) )/( ( ) )

A C C

BE

S OLR OLR h OLR

, (8)

( /(1 ) )/( ( ) )

E A C C

B U U U

OLR S S h S

. (9)

( , )

AC

Bh

and

( , )

EC

Bh

are the cloud fractions

from the

(1 )

A C A A

OLR OLR F

and

EC

U

S

(1 )

EUE

SF

equations, respectively. Note that in

spherical geometry the cloud fraction does not depend

on the altitude. In the two-dimensional optimization

problem, only one global average cloud layer is

assumed and the

2

|| ||

AE

norm is minimized. For

obtaining accurate

, and

B

, the vertical resolution of

the HARTCODE altitude vector is set to 40 cm.

FIG. 25 RESULTS OF THE MULTIVARIABLE NONLINEAR

OPTIMIZATION. THE EQUILIBRIUM CLOUD COVER, BOND

ALBEDO, AND CLOUD TOP ALTITUDE ARE

( ) 0.6618

TT

A

f

,

0.3013

BE

G

, AND

1.9160

C

h

KM.

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

48

The range of

B

is not that critical, here the solution

somewhere between

0.294 0.306

B

is expected. In

Fig. 25 the three-dimensional view of the opti-

mization results are shown. In the close vicinity of the

minimum, the norm changes 2-3 orders of magnitude,

indicating a very sharp extremum. The results show

extremely good numerical agreement between

T

and

T

f

:

7

( ) 0.6618 10

TT

A

f

.

The equilibrium albedo and cloud top altitude are:

0.301290611

B

, and

1.9160

C

h

km, respectively.

Some other ways of finding the accurate

, and

C

h

have been presented in Miskolczi (2014).

The independent empirical global average cloud cover

estimates from the ISCCP are consistent with our

results. From a 20 year long time series (ISCCP−D2

198307−200806 in Van Andel (2010)) a global mean

of 66.38 +/− 1.48 % was reported. The 10 year average

ISCCP data show similar global cloud cover,

66

%,

Ollila (2013).

According to the

A C d

DD

E g E f OLR

relationship the

LW back radiation (through the

Cd

OLR

term) depends

on the cloud altitude. Using our equilibrium transfer

function

T

f

and

C

h

the back radiation is

345.98

A

D

E

Wm-2. This value is quite consistent with the observed

345.4

A

D

E

Wm-2 (ISCCP-FD value for the CERES

period from March 2000 to May 2004 ), see Table 2 in

TFK09, and the

345.6 9

A

D

E

Wm-2 quoted by S12 in

their NATURE article. W13 gives the best estimate of

the back radiation as

342 5

A

D

E

Wm-2.

The spectral distributions of the all-sky fluxes of the

GAT atmosphere are presented in Fig. 26. The all-sky

spectral GE shown in Fig. 27. The numerical values of

the integrated fluxes show that the GAT atmosphere is

practically a radiative equilibrium structure.

Evidently, the all-sky greenhouse effect locked to the

reflected solar radiation:

103.0418

A

G

Wm-2, and

103.032

R

F

Wm-2. The clear sky

g

locked tightly to

T

A

:

( )/

UU

S OLR S

0.33684

,

( ) 0.3382

T

A

g

. In Fig. 26

superscripts are references to the NASA planetary fact

sheets, NASA GSFC NSSDC (2012). For reference, in

Table 2 the detailed numerical results of the

equilibrium flux density components are shown. The

Kirchhoff rule seems to be perfectly satisfied. The

C

A

A OLR

and

CC

D

E OLR

equalities put the full con-

trol of the planetary radiative equilibrium into the

hand of the global average cloud cover.

FIG. 26 FLUX DENSITY SPECTRA OF THE ALL-SKY GAT ATMO-

SPHERE. THE EQUIVALENT BLACKBODY SPECTRA

()

A

Bt

, AND

()

S

Bt

ARE EQUAL TO THE EQUIVALENT BLACKBODY SPECTRA

OF

NASA

()

A

Bt

, AND

NASA

()

S

Bt

.

FIG. 27 SPECTRAL ALL-SKY GREENHOUSE EFFECT

A

G

.

R

F

AND

THE EFFECTIVE

e

A

G

AGREE REASONABLY WELL.

FIG. 28 SOLAR AND TERRESTRIAL EQUILIBRIUM BLACKBODY

SPECTRA. THE LIGHT BLUE CURVE IS THE SOLAR SPECTRUM,

THE DARK BLUE IS THE OBSERVED LW SPECTRAL

A

OLR

FROM

THE GAT ATMOSPHERE. THE CYAN DOT MARKS THE MAXI-

MUM OF THE 273.15 K BLACKBODY SPECTRUM.

Development in Earth Science Volume 2, 2014 http://www.seipub.org/des

49

TABLE 2. GAT HIGH ACCURACY BOUNDARY FLUXES IN WM-2 . REGION

BOUNDARIES ARE IN KM. IN CLOUDY ATMOSPHERE THE

C

A

A OLR

(RED)

AND

CC

D

E OLR

(GREEN) EQUALITIES ARE ONLY SATISFIED AT A SINGLE

1.916

C

h

KM ALTITUDE.

REGION

UPWARD

DOWNWARD

U

S

A

A

OLR

D

E

0-70

379.69

321.12

251.79

309.93

1.92-70

333.82

251.12

240.14

240.15

Considering the temporal and areal variability in the

local water vapor content of an air column, one has to

admit that the Earth's atmosphere possesses enor-

mous stability against fluctuations in its global aver-

age flux optical thickness. In our understanding, the

source of this stability is related to two natural causes.

One is the favourable orbital parameters of the Earth,

and the other is the permanent presence of the three

phases of the H2O in the boundary layer. According to

the Maxwell rule, the system as a whole has zero

thermodynamic degree of freedom, the phase temper-

ature of the system must be the triple point of the H2O

(273.16 K). In Fig. 28 we demonstrate, that the

maximum of the all-sky thermal emission spectrum of

the planet is, in fact, a spectral distribution of max-

imum radiation entropy.

Conclusions

In this research the IR radiative processes in the

climate system are studied quantitatively. Observed

empirical facts point to the existence of a climate

invariant constant global average clear sky flux optical

thickness of

1.87

A

. Theoretical support has also

been established with four fundamental radiative

transfer relationships and a theoretical

1.8676

T

A

flux

optical thickness. The clear sky

251.79OLR

Wm-2

and

379.69

U

S

Wm-2 fluxes are fully consistent with

the

()

T

UA

OLR S f

, and the

(0.6 0.4 )

T

UA

OLR S T

theoretical requirements. It is also shown that the

global average atmosphere with its effective cloud

layer at

1.9160

C

h

km and a geometric cloud fraction

of

( ) 0.6618

T

A

f

is in radiative balance with the

341.97

E

F

Wm-2 TOA available solar radiation. It has

been proven quantitatively that the conservation of

radiant energy is established by the

A

Bg

0.3013

and

( ) 0.6618

T

A

f

equalities. In this respect the

two equations linking the Bond albedo to the cloud

cover and the all-sky normalized greenhouse factor

have fundamental importance. As long as the Earth

has unlimited water supply (in the oceans) with its

three phases permanently present in the atmosphere

and two phases on the ground surface, the stability of

the planetary climate will be controlled by the

( ) / ( )

C

BE

G F G G

and

( ( ))/

C

BE

G G G F

equations. These two equations, together with the

Clausius-Clapeyron equation, will regulate the

transfer of the latent heat through the boundary layer

in such a way that the net amount maintains the

planetary radiative balance. In this regard the thermo-

dynamic boundary layer may be defined as the

combined surfaces where the different phases of the

water are in direct physical contact with each other

and with the surrounding material.

The apparent role of the Clausius-Clapeyron equation

is to convert temperature differences to radiative

fluxes (to and back), and by doing so to assure that no

temperature-radiation feedback exists in the system.

The only solution to the Earth's ground surface

temperature is

1/4

1

( / / ) 288.6 0.1

GU

tS

K. The

1/4

1

( ) / 2

P M G

t t t

phase temperature is

273.17 0.1

K,

where

4 1/3 260.29

MM

tt

K is a unique universal

temperature. The empirically established climato-

logical normalized GF of

0.4

A

m

g

is also reproduced

well and proved by the

4

1 / 0.3992

AA

mG

g OLR t

equation.

Of course the whole dynamically controlled system

has no real instantaneous equilibrium state. However,

the radial (or mass) oscillation of the system will be

able to handle the energy conservation and energy

minimum principles as required by the time constants

of the different latent heat reservoirs. In summary, the

complex task of the relatively fast responding global

mean cloud cover is to assure the conservation of

radiant energy and momentum on a global scale,

maximize the LW cooling to space (radiative

equilibrium), while observing the thermodynamic

constraints applicable to large heterogeneous systems

(Maxwell rule).

The quantitative proof of the radiative equilibrium

state of the Earth-atmosphere system is alone a

remarkable achievement of planetary science. The

proposition here is to consider the global average

cloud cover as the only component of the climate

system, which is able to respond to and regulate the

planetary radiation budget in a relatively short time.

The greenhouse effect of the Earth's atmosphere is a

global scale equilibrium process which rests on the

chaotic nature of the humidity field and the stability of

http://www.seipub.org/des Development in Earth Science Volume 2, 2014

50

the total atmospheric mass. Consequently, none of any

local or regional weather phenomenon is related

directly to its magnitude and tendency.

Unfortunately the Nobel Laureate IPCC is not a scien-

tific authority, and their claim of the consensus and

the settled greenhouse science is meaningless. The

quantitative results of this paper massively contradict

the CO2 greenhouse effect based AGW hypothesis of

IPCC.

In our view the greenhouse phenomenon, as it was

postulated by J. Fourier (1824), estimated by S.

Arrhenius (1906), first quantified by S. Manabe and R.

Wetherald (1967), explained by R. Lindzen (2007), and

endorsed by the National Academy of Science and the

Royal Society (2014), simply does not exist.

However, research must continue to find and establish

the real causes and the true trends in global temper-

ature change that may be present behind the natural

fluctuations. The greenhouse science is not settled, the

presented results warrant further efforts to investigate

many detailes of the surface radiative equilibrium

processes.

ACKNOWLEDGEMENTS

I am very grateful for the help and support obtained

from K. Gregory, and C. Game. Without their comput-

ational assistance, this research project could not exist.

I also wish to thank K. Vinnikov, A. Rörsch, D. Hagen,

S. Welcenbach, C. Wiese, G. Fulks, D. Brooks, W.

Guang, Y. Shaomin, L. Szarka, V. Wesztergom, Sz.

Barcza, Z. Kollath, Z. Toth, S. Kenyeres and P. Nemeth,

for their continuous attention and valuable advice. The

help and scientific contributions from my two friends,

N. VanAndel and J. Pompe, who both died while in

the midst of this work should also be remembered.

Credit also go to C. Dubay, E. Carbone and J. Ginsberg

for their help with the technical editing of the

manuscript. The work of the reviewers and the editors

of the journal is highly appreciated.

REFERENCES

Arrak, Arno. "Arctic warming is not greenhouse warming"

Energy and Environment 22, 8 (2011) 1069-1083

Arrak, Arno. " What Warming? Satellite view of global tem-

perature change" Second edition, CreateSpace, 2010

Arrhenius, S. "On the Influence of Carbonic Acid in the Air

upon the Temperature of the Ground. " Philosophical

Magazine and Journal of Science 5,41 (1896) 237-276.

Chandrasekhar, S. " An Introduction to the Study of Stellar

Structure " 51-53, Dover Publications, 2010

Chedin, A., and Scott, N., A. " The Improved Initialization

Inversion Procedure (3I)" Laboratoire de meteorologie

dynamique, CNRS, Note Interne No. 117, LMD, 1983

Clausius, R., J., E., 1870: On a mechanical theorem applicable

to heat ; Philosophical Magazine, 4,40 (1870) 127

Costa, S., M., S., and Shine, K., P. "Outgoing Longwave

Radiation due to Directly Transmitted Surface Emission"

Journal of the Atmospheric Sciences 69 (2012) 1865-1870

Cox, J., P., and Giuli, R., T."Principles of Stellar Structures"

408, Gordon and Breach Science Publishers, 1968

De Bruin, H., A., R." Comments on 'Greenhouse effect in

semi-transparent planetary atmospheres' by Ferenc M.

Miskolczi." Időj{r{s 114, 4 ( 2010) 319-324

ERBE Monthly Scanner Data Product. NASA Langley

Research Center, Langley DAAC User and Data Services

2004, userserv@eosdis.larc.nasa.gov

Gerlich, G., and Tscheuschner, R., D."Falsification Of The

Atmospheric CO2 Greenhouse Effects Within The Frame

Of Physics." International Journal of Modern Physics, B,

23, 3 (2009) 275-364 , doi:10.1142/S021797920904984X

Fourier, J. "Remarques générales sur les températures du

globe terrestre et des espaces planétaires." Annales de

Chimie et de Physique 27 (1824) 136-167

Hansen, J., et al. "Climate impact of increasing atmospheric

carbon dioxide." Science 213 (1981) 957–966.

Hertzberg, M. "Earth's radiative equilibrium in the solar

irradiance." Energy and Environment 20,1 (2009) 83-93

HITRAN2K, (2002) . http://cfa-www.Harvard.edu/HITRAN

/hitrandata

Kiehl, J., T., and