THE HEAT BALANCE OF THE EARTH'S SURFACE

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• Release Decision: RIPPUB
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• Document Page Count: 134
• Document Creation Date: January 4, 2017
• Document Release Date: October 28, 2013
• Sequence Number: 3
• Publication Date: January 1, 1958
• Content Type: REPORT

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U. S. DEPARTMENT OF COMMERCE
NO
WEATHER BUREAU
The Heat Balance of the
Earth's Surface
STAT
Translated by Nina A. Stepanova
PB 131692 For sale by Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C. Price $4.00
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10,
U. S. Department of Commerce
Sinclair Weeks, Secretary
Weather Bureau
F. W. Reichelderfer, Chief
THE HEAT BALANCE OF THE EARTH'S SURFACE
by M.I. BUDYKO
from
(Teplovor balans zemnor poverkhnosti.
Gidrometeorologicheskoe izdatel'stvo,
Leningrad, 1956.
255 pages)
Washington, D. C.
1958
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This translation sponsored by:
Department of Commerce
U. S. Weather Bureau
Washington,D. C.
Snow Ice & Permafrost Establishment
Wilmette, Illinois
Headquarters Quartermaster Research & Development Command
Natick, Massachusetts
Translator's Remarks
iii
It was intended to keep this translation as close as possible to the
author's style and avoid rephrasing.
Consecutive numbers were added to the list of references to Russian
literature to facilitate the finding of transliterated Russian names
which are listed according to the Cyrillic alphabet in the original
text.
There are several names mentioned by the author in the text but not
included in the list of references.
a
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iv
p. 42, Table 7, heading
?
eoi
413 Pi r-I
p.
p. 136, Figure 45,
?
Table of Contents
Page
Annotation (author's) 1
Preface (author's) 1
CHAPTER I. Introduction 3
? 1. Heat balance equations 5
2. General review of investigations on heat balance
of the earth's surface 14
CHAera II. Methods for the climatological calculation of the
components of heat balance 27
? 3. Radiation balance 27
4. Turbulent heat exchange between the underlying
surface and the atmosphere 45
5. The loss of heat for evaporation 63
6. The accuracy of determining the components of
heat balance 88
CHAPTER III. Geographical distribution of the components of
heat balance 97
7. Radiation balance 98
? 8. Heat balance 111
? 9. The annual and diurnal variations of heat balance
components 118
CHAPTER IV. Heat balance and the energy factors of the physico-
geographical processes 139
10. The relationship between heat and water balance
on land 140
Heat balance and geographical zonality 152
?12. Heat balance and conditions of plant development 179
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CHAPTER V. Heat balance and meteorological effectiveness
of ameliorative measures
194
?13. Field protective forest growing
194
?14. Irrigation
206
CHAPTER VI. Heat and water balances of the earth
213
?15. The heat balance of the earth
213
?16. The water balance and hydrologic cycle
441
224
Conclusion
231
Literature
233
,
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THE BEAT BALANCE OF THE EARTH'S SURFACE
Annotation
This monograph summarizes the results of investigations in heat balance
climatology of the earth's surface. Various methods for determining the
components of the heat balance are analyzed and systematized. Data on
geographical distribution of all components of the heat balance and of
their annual and diurnal variations are presented. Applications of the
heat balance climatology to various problems of physical geography, agro-
meteorology, and hydrology are interpreted. The utilization of heat balance
data.for the analysis of meteorological effectiveness of ameliorative meas-
ures is investigated.
This monograph can be used by scientists, aspirants and students, who
are working in fields of climatology, meteorology, land geography, and
oceanography, and also, by scientists and practitioners in other profes-
sions who might be interested in problems of the transformation of solar
energy on the earth's surface.
Preface
Investigations of heat balance on the earth's surface are now occupying
an important place in all hydrometeorological disciplines, including mete-
orology, climatology, land hydrologyland oceanography.
The main purpose of these investigations is the study of the causal prin-
ciples which determine the meteorological and hydrological regimes in var-
ious geographical regions and could be used for prognostication and cal-
culation of important hydrometeorological processes and phenomena. In fact,
a whole series of investigations on heat balance has been made in order to:
evaluate the effect of meliorative measures on climatic conditions near the
ground; calculate the evaporation from the reservoirs which have been
planned for construction; develop methods for forecasting the reservoirs'
freezing dates; and solve many other practical problems.
In recent years, due to the initiative of the academician A.A. Grigor'ev,
the data on heat balance have largely been used in studies of the general
V problems in physical geography including the problem of geographical zon-
ality.
The rapid growth in the number of requests for material on heat balance
in various regions has stimulated a considerable progress in climatological
investigations of this subject, especially concerning the geographical dis-
tribution of the heat balance components.
As a result of work along these lines,, that has been accomplished in
the Central Geophysical Observatory (Voeikov's)? and also by some other
groups of scientists, the climatology of heat balance has been established
by now as one of the branches of general climatology.
This monograph is devoted to the interpretation of the problems of
heat balance climatology.
The author expresses his sincere gratitude to all persons who have read
this work in manuscript and offered their comments.
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ChapterI
Introduction
Solar radiation is the main source of heat energy for nlmost all the
natural processes developing in the atmosphere, hydrosphere, and in the
upper layers of the lithosphere.
On the other hand, the utilization of solar energy is of paramount im-
portance in economical activities, and particularly valuable for agri-
cultural production.
Consequently, the problem of the transformation of solar energy in the
atmosphere, in the hydrosphere, and in the upper layers of the lithosphere
e., in the outer geographical medium), is very important for develop-
ment of a large scope of problems in the practical, as well as in the
theoretical field of knowledge.
The general aspect of the basic transformations of solar energy in the
outer geographical medium could be interpreted, according to the most re-
cent conceptions in the following way:
The flux of the solar radiation at the average distance of the earth
from the sun is approximately equal to 1000 kg-cal/cm2 per year. Because
of the spherical shape of the earth, a unit of the surface on the outer
boundary of the atmosphere receives, on the average, 1/4 of the total
flux; i.e., about 250 kg-cal/cm2 per year, and about 150 kg-cal/cm2 per
year is absorbed by the earth as a planet.
It is very significant that the main portion of the absorbed solar
radiation - about 3/4 of the total amount - is absorbed by the earth's
surface, whereas the atmosphere absorbs only 1/4 of it.
The surface of the earth, when heated as a result of solar radiation
absorption, becomes a source of long-wave radiation which, in turn, heats
the atmosphere. The presence of water vapor in the atmosphere, and also of
some gases and dust particles that absorb the long-wave radiation, re-
duces considerably the effective radiation ]) of the surface as compared
with that which would have been observed if the atmosphere would be per-
fectly translucent (the green house effect). As a result of the green
house effect, the radiation balance of the earth's surface (i.e., the
difference between the absorbed radiation and the effective outgoing
radiation) is rendered positive.
Since the radiation balance of the earth as a plLnet is close to zero,
on the average for the year, the radiation balance of the atmosphere,
which is equal to the difference between the radiation balance of the
earth as a whole and the radiation balance of its surface, is rendered
negative.
Besides radiational transformations, a considerable redistribution of
heat in the atmosphere in a vertical direction is accomplished by the
1) The difference between the long-wave radiation from the earth's
surface and the opposite long-wave radiation from the atmosphere.
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processes of moisture exchange which are connected with the expenditure of
heat for evaporation at the level of the underlying surface and the release
of latent heat of condensation in the atmosphere, as well as by processes
of vertical turbulent heat exchange.
Along with the processes of vertical redistribution of solar energy,
vigorous processes of horizontal redistribution of heat are developed in
the outer geographical medium. Among them, of special importance, is the
exchange of heat energy in the atmosphere and hydrosphere which takes place
between the higher and lower latitudes. This exchange is induced by sub-
stantial differences in radiational heating rates over the spherical sur-
face of the earth. It ia accomplished by the macroturbulent heat exchange,
by transfer of heat by sea currents, and also, by the redistribution of
condensation heat in the atmosphere.
All these processes of solar energy transformation are induced by ra-
diational factors and affect?enormoucly, the energy regime in the outer
geographical medium. In particular, they modify considerably the radi-
ation regime on the surface of the earth, which depends a lot on the cir-
culation of the atmosphere and hydrosphere, on condensation and evaporation
processes, etc.
In association with processes of the "first order" transformation of
solar energy, which greatly affect the radiational and thermal regime,
other processes of solar energy transformation are also developed in the
outer geographical medium. These processes involve some comparatively
small quantities of heat, and therefore they do not exert any noticeable
or direct influence on the radiation and heat regime. They are usually
of lesser significance in meteorological investigations, but some of them
are of exceptional interest for some other branches of natural sciences,
as for instance, the process of photosynthesis, which involves the trans-
formation of radiation energy into a relatively stable form of chemical
energy creating organic matter.
The basic data, from which the study of all forms of transformation of
solar energy in the outer geographical medium proceeds now, are the data
on radiation and heat balance. Among them, data on radiation and heat
balance of the earth's surface are especially valuable, since the surface
absorbs 75% of the total amount of solar energy absorbed by the earth, and
consequently, it presents the main source of energy for the outer geo-
graphical medium.
Because of the fact that just at the earth's surface the greatest in-
tensity of the most important natural processes is observed, like the
biological, hydrological, exogenous geomorphological, soil formation proc-
esses, and others, it is obvious that data on the heat balance of the
surface will be of an essential significance for the study of causal re-
lationships of natural processes in the outer geographical medium.
In this monograph, the basic laws governing the radiation and heat bal-
ance of the earth's surface are analyzed in a geographical aspect; i.e.,
the climatology of the heat balance is interpreted.
The climatology of the heat balance includes, first of all, the methods
for processing results of hydrometeorological observations which permit
the calculation of the principal components of the balance.
The method for determining the components (terms) of the heat balance
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by proceeding from data of ordinary hydrometeorological observations is
described in chapter 2.
The application of methods for calculating the balance components per-
mitted us to develop the climatography of heat balance which includes, by
now, the data for almost the whole surface of the terrestrial globe.
The fundamentals of the heat balance clinatography are presented briefly
in chapter 3.
As it turned out/ it was possible to use the data on geographical dis-
tribution of the heat balance in solving various climatological problems,
and also in studying some general problems of physical geography.
Thus, the utilization of heat balance data allows us to derive many
conclusions about the regularities in heat exchange and the turn-over of
moisture in the atmosphere. The results of these investigations are given
in.chapters 3, 4, 50 and 6. They complete the explanation of the causes
of some climatic phenomena and provide for a quantitative interpretation
of those processes which formerly were only qualitatively studied.
Among studies based on application of heat balance data ,a special place
Is occupied by investigations of changes in the climatic regime as effected
by amelioration (Ch. 5). Taking the data on heat balance into account it
WAS possible to make quite a few conclusions of a definite practical im-
portance.
As far as the transformation of solar energy on the earth's surface
exerts a tremendous influence on the dynamics of all exogenous natural
processes, it is obvious that data on heat balance can be successfully
used for studying many geographical regularities. Accordingly/in chapter
4 an analysis is given of those relationships which connect the conditions
of heat energy balance with hydrological processes and with the develop-
ment of natural vegetation. It also turned out that it was possible to
clarify some causal relationships which determine the phenomenon of geo-
graphical zonality that was first discovered by V. V. Dokuchaev.
The data presented in this monograph contributed to an improvement of
existing concepts of the general balance of energy on the earth and of its
water balance, and have also thrown more light on some other questions
connected with the process of heat and moisture exchange.
?1. Heat balance equations
Equations of the heat balance represent some particular cases of the
basic law in physics - the law of energy conservation. These equations
can be derived for various volumes and surfaces in the outer geographical
medium. In recent investigations, equations of the balance for the earth's
surface and the equation of the balance for the system "earth - atmosphere,"
i.e., for the vertical column that extends through the whole geographical
medium, are most frequently used.
To obtain the equation of the heat balance of the earth's surface all
the streams of heat energy flowing between the element of the surface and
the ambient space must be snmarized.
We will designate the value of the radiational flux of heat by R' ;
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the turbulent flux of heat between the underlying surface and the atmosphere
1711; the heat flux between the underlying surface and the lower layers by
Al; and the expenditure of heat for evaporation (or the emission of heat
from condensation) byLE6C-- the latent heat of evaporation,e- the speed
of evaporation or condensation). Since all other components of heat bal-
ance are usually much smaller than the here cited fluxes of heat, we may
write, in the first approximation, the heat balance equation in the fol-
lowing form:
R' =-- LE' 4 P' +A'. (1)
The value of Iris considered to be positive if it designates an inflow of
heat to the underlying surface, anaNall other values are positive if they
designate the expenditure of heat. 41
The scheme of heat streams included in the equation of the heat balance
is shown in fig. 1.
A
Figure 1
Scheme of the heat balance of the
earth's surface.
Regarding those components of heat balance which have not been included
into equation MI a more considerable value could be attributed to the
expenditure of heat for melting of mow or ice on the earth's surface ( or
to the gain of heat from water freezing processes). However, for longer
It is necessary to mention that in many-papers a different system of
signs (+ and - ) is used for the heat balance, due to which all terms of
heat balance equations have the same sign according to gain or loss of
heat. Such a system of designating, although more logical, canlead, how-
ever, to some inconveniences. According to the system of determining the
signs, the loss of heat by evaporation and turbulence from the earth's
surface to the atmosphere is negative. But this contradicts the usual
practices.
lb
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period averages (for a year or so), the latter value, as a rule, is con-
siderably smaller than the main components of the balance, and only for
some cases (for instance, the periods of snow melt in the middle and upper
latitudes) should this value be included into equation (1) as an additional
term.
The other components of the heat balance - heat streams originated by
dissipation of mechanical energy of wind, of wind waves, tidesland currents,
the heat flux (positive or negative) transferred by fall of precipitation
which has a different temperature than that of the underlying surface, as
well as the expenditure of heat for photosynthesis: and the gain from
oxidation of biological substances are usually considerably smaller than
the main components of the balance, and this is true for averages obtained
for periods of any length.
Exceptions from this rule are possible, (as for instance in case of a
forest fire, when great quantities of heat accumulated formerly by the
process of photosynthesis are rapidly discharged) but are relatively rare.
The problem of accounting for the effect of heat advection must be con-
sidered separately. In some investigations, suggestions have been made to
introduce into equation (1) an additional component representing the ad-
vective inflow of heat to the underlying surface. Therefore, we would like
to give some simple considerations which will illustrate how wrong this
point of view is, and also explain the relation between the horizontal
transfer of heat and the heat balance components (Budyko, 19119b (42 7 )
The equation of heat exchange in the lower layer of the atmosphere, in
the presence of a horizontal transfer of heat, will be:
ad 00 0h dt3
at U &v.= az az )'
(2)
where 0-is air temperature, x - horizontal ordinate, directed according
to wind direction in the lower layer of the atmosphere, z -vertical
ordinate, 11 -wind speed in the lower layer of the atmosphere, k - coeffi-
cient of turbulent exchange, t --time.
Inttvgrating equation (2) by z we obtain the following equation:
(3)
at pop Oz '
P'
where Pcp - is the constant of integration, equal to the heat flux be-
tween the underlying surface and the atmosphere divided by the value of
air density and heat capacity.
The direct effect of horizontal heat transfer on the heat balance of
an air layer is represented by the term f u a the magnitude of
Tidz,
this Member depends, to a considerable deg$ee, on z ; i.e., on the height
of the analyzed layer. Computing the balance for thezearth's surface, z
must be approaching zero, and consequently the (Ierm
z
dz will become
zero (z and -D; are finite values). Since the term TEa-
dz will also be
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equal to zero, the heat exchange between the earth's surface and the at-
mosphere atz 0 will be determined only by term k 4., which shows the
vertical heat flux. Estimating the order of magnitudeof the components
of equation (3)0 it could be established that, even for the lowpr layer
of the atmosphere, 10-100 m thick, the termsdz and ; ? uz
f dO
a
75
dl
dO
are usually so much smaller than the term k 0, that they could be neg-
lected. Thus, the horizontal transfer of heat has no direct effect, either
on the heat balance of the earth's surface, or on the heat balance of the
air layer near the ground.
This statement does not contradict the fact that a considerable effect
is exerted by the horizontal heat transfer on the heat balance of the
earth's surface by changing the values of the components of the balance,
such as: the radiational flux, the turbulent flux of heat, the expenditure
of heat for evaporation, etc.
The effect of horizontal heat transfer in the hydrosphere on the heat
balance could be explained in a similar way. In this case, the effect of
horizontal transfer produces only some changes in the vertical flux of
heat x, and also, in the other components of the balance.
In the equation of heat balance MI the components of the balance re-
presenting the heat streams could be substituted by their suns for the
period of time t. Then, we will obtain an equation which will coincide
with equation (1):
LE+P?A, ep
where the values without primes show the sums of heat for the analyzed
period of time.
The sum of the radiational flux of heat at the level of the earth's
surface (be it positive or negative) is usually called - the radiation
balance.
The radiation balance value is equal to the difference between the
amount of radiation absorbed by the earth's surface and the amount of
effective outgoing radiation,
(5)
where:Q - is the sum of direct radiationlq - the sum of diffused radiation,
a- albedo,/ - the effective outgoing radiation (the difference between
incoming and outgoing heat amounts on the earth's surface, which is de-
termined by radiation from the earth's surface and counter radiation of
the atmosphere).
Many authors have already pointed out, and rightly so, that the term
"radiation balance" is not very good, since the word "balance" in this
case does not have its usual meaning, and accounts for only one category
of energy - the radiation energy. Even so, the application of the expres-
sion "radiation balance" is especially inconvenient to use in the study
of heat balance, since these similar terms have an entirely different
physical meaning (for instance, the radiation balance usually is not equal
Ito zero, whereas the sum of the components of heat balance always equals
'zero, etc.); however, at the present time, it would be very difficult to
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discard this term, since it has been so largely used in all hydrometeorolo-
.
gical studies.
The amount of heat exchange between the active surface and the lower
layers A can be determined by the other heat balance components of the
upper layers of the lithosphere or hydrosphere. The heat balance equation
for a vertical column with the upper limit on the earth's surface, and the
base at a depth where the annual variations of temperature cease, will be:
A./3447, (5)
where A - is the heat exchange between the column and the active surface,
F - the heat exchange between the column and the ambient space of the
litho or hydrosphere in a horizontal direction, B - the change in heat
amount inside the column during the given period of time, (fig. 2).
A
Figure 2
Scheme of the heat balance of the
upper lithosphere or hydrosphere
layer.
Vertical heat exchange through the base of the column could be assumed
to be equal to zero, since the heat flow from the depth of the earth is
usually negligible in comparison with the principal components of the heat
balance.
In the lithosphere, the value f', as a rule, is insignificant, since
the mean horizontal gradients of temperature in soil are very small.
Therefore, for the. land, we have it.B. Due to the fact that, on the aver-
age for the year, the upper layers of soil are neither warmed up nor cooled
off, we must assume that long term annual mean values for the land are
In the heat balance of more or less significant water reservoirs,
analyzed as a whole body, the values of 44 are also very close to B, since
the heat exchange between the reservoir and ground is usually insignificant
in comparison with the principal components of heat balance.
However, for some portions of the oceans (lakes and seas), the values A
and B might be very different, since in this case a redistribution of
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-;.
rather large quantities of heat in a horizontal direction might be affected
by currents and by macroturbulent exchange.
Consequently, under such conditions, the mean annual value of heat ex-
change between the active surface and the lower layers will not equal zero
but will be equal to the sum of heat which is gained or lost through cur-
rents and macroturbulence by the vertical column extending through the
hydrosphere (i.e.p4==f).
Thus, the equation of heat balance for the land, for the mean annual
period, will be: R=LE+P, (7)
and for the ocean:
R=LE+P+F. (8)
In some cases, equations (7) and (8) could be simplified. Thus in
deserts, where the amount of evaporation is close to zero, equation (7)
will simply be:
For the world's ocean as a whole, where the general redistribution of
heat by sea currents, due to recompensation, is zero, equation (8) is
transformed into: R.LE1-1).
Concluding our analysis of the problem of heat balance equations for
the earth's surface it should be noted that when these equations are ap-
plied one must keep in mind that the conception of the "earth's surface"
is somewhat conventional (sometimes it is called the "active surface," or
theunderlying surface"). Actually, the "surface" processes of solar
energy transformation are developed not on a two dimensional surface, but
inside a layer of some thickness, as for example, when the processes of
heat expenditure for evaporation on the mainland take place, or when water
reservoirs are absorbing the solar energy, etc. The "active layer" reaches
a considerable thickness in places with a high vegetation (especially so
in forests).
However, even when dealing with an active layer of considerable thick-
ness we can use the concept of the active surface and it will not lead us
into any noticeable inaccuracies, especially in studies of the components
of balance where longer periods of time are averaged. But in single cases
(studying the rapid changes of the components, etc.) it would be more ex-
pedient to use the concept of an active layer instead of the active sur-
face.
To derive a heat balance equation for the system earth-atmosphere (i.e.,
the balance for the whole outer geographical medium) we must analyze the
gains and losses of heat energy in the vertical column that extends through
the whole atmosphere and upper layers of the hydro and lithosphere down
to those levels where seasonal and diurnal variations in temperature cease.
In our computations we will use the sums of heat streams for a certain
period of time t.
The exchange of heat between the column and the outer space will be
characterized by its radiation balance Rr which actually equals the
difference between solar radiation absorbed by the whole column and the
total long-wave outgoing radiation from this column during the analyzed
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period of time (fig. 3 ). The radiation balance of the system earth- at-
mosphere may have a different sign, and we will consider the value R., as
being positive, when it shows that heat is gained by this system.
atmosphere
? hydrosphere
Figure 3
Scheme of the heat balance of the
earth - atmosphere
system.
Extending this column deeper into the lithosphere or hydrosphere down
to those layers where the thermal regime is no longer .affected by varia-
tions of meteorological factors, we may assume that the inflow of heat
through the base of the column is practically absent, it equals zero.,
The inflow of heat through the lateral surface of the column is deter-
mined by the horizontal transfer of heat in the atmosphere and hydrosphere.
The difference between the gain and loss of heat due to the transfer of
heat in the atmosphere is presented in fig. 3 by the arrow (:, Ind the
similar characteristic for the hydrosphere - by arrow F.
Besides the heat exchange that occurs through the surface or the column,
there are some other factors that also affect the heat exchange, namely
some sources of heat (positive or negative) located inside the column.
Among them, a greater significance is attributed to the surplus or
deficiency of heat, which is associated with the changes of water phases
and especially by the process of evaporation and condensation.
The gain of heat from condensation processes in the atmosphere (the dif-
ference between the gain of heat from condensation of water vapor, and the
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loss of it for evaporation of water droplets in the atmosphere) over a suf-
ficiently homogeneous surface is approximately equal to the poduct of the
latent heat of evaporation Land the sum of precipitation r.-31 The ex-
penditure of heat for evaporation (the difference between the loss of heat
for evaporation from the surface of reservoirs, from vegetation:from soil,
and the gain of heat from condensation on these objects) is equal to LE .
The general influence of condensation and evaporation on the heat balance
of the column could be approximately expressed by the value L(r--E).
Among the other heat balance components of the column, the change in the
heat content inside the column, that occurred during the period for which
the values Bs have been summarized, should be taken into account. The other
components of the balance (the gain of heat from dissipation of mechanical
energy, the difference between the amount spent for ice melting and the
gain from ice formation processes, the difference between the loss of heat
for photosynthesis processes and the gain of it from oxidation of the or-
ganic matters, etc.) are usually insignificant in the heat balance of the
earth-atmosphere system and could be omitted.
The equation of the heat balance of the earth-atmosphere system will be:
R,==(:+17-1-L(E--r)+Bs, (9)
in this instance, we will assume that all the terms on the right side are
positive in case they show the expenditure of heat. For the average annual
period the valuell;will, approximately, be close to zero,and equation (9)
will be transformed into:
Rs--C-FF+L(E?r).
For the mainland this equation will have a simpler form:
Rs= C L (E ? r).
(10)
(H)
Since, for the earth as a whole,E.r, and the horizontal transfer of
heat in the atmosphere and hydrosphere in total is, approximately, equal
to zero, the heat balance equation for the whole outer geographical medium
will assume a simple form of:
(12)
The radiation balance equation of the earth-atmosphere system Rs is
similar to the radiation balance equation for the earth's surface (5):
(13)
where 4113-- is the short-wave solar radiation received on the outer boundary
of the atmosphere, as ?.albedo of the earth-atmosphere system, 4-- total
long-wave outgoing radiation into outer space.
The heat balance equation of the atmosphere could be obtained by sum-
The gain of heat from condensation in the atmosphere is equal to the
difference between the gain and loss of heat which is associated with con-
densation and evaporation of water drops in clouds and fogs. Upon a more
or less homogeneous surface the difference between the sums of condensation
and evaporation in the atmoaphere, obtained as the averages from long
periods, is equal to the amount of precipitation. But this might not hold
for regions of a dissected terrain and also for some short time intervals.
?
,
ir Dmrf_ Cnniti7Pd Cony Aooroved for Release
?
13
ming up the relevant heat streams, or simply, by taking the difference be-
tween the heat balance of the earth-atmosphere system and the earth's
surface.
Assuming that the radiation balance of the atmosphere is:
--
RaR3R,
and the change in heat content of the atmosphere is:
Ba==0,--B,
we will find, that
(14)
and for the average annual period
== (3 L r - - . (15)
In many calculations, along with the heat balance equations, we have
to use the equation of water balance also.
The equation of water balance for the land surface is the expression
of the condition when the algebraic sum of all forms of gain and loss of
solid, fluid, and gaseous water received by a horizontal surface from the
ambient space during certain time intervals is equal to zero.
This equation will be:
(16)
where r-- is precipitation, j_ the difference between the evaporation
and condensation on the earth's surface (usually called just evaporation),
J..-- the surface runoffIni?moisture exchange between the earth's surface
and the lower layers. The value m - is the algebraic atm of the gravi-
tational flux of fluid moisture from the soil surface into the deeper
layers, the vertical flux of the film-moiature between soil layers of
various moistening, the vertical flux of water vapor, flux of water which
is raised by the roots of plants, etc., obtained for the analyzed period
of time.
Equation (16) is more often used in some modified form, which could
be derived by considering the fact that the vertical flux of moisture nt
is equal to the sum of the underground runoff Land the change of water
content in the upper layers of the lithosphere b (this equality corre-
sponds to the equation of water balance of the vertical column that ex-
tends through the upper layers of the lithosphere down to depths where
moisture exchange is practically absent).
Keeping in mind the fact that the sum of the surface runoff fwand
underground runoff f is equal to the full runoff .1', we find:
(17)
Equation (17) can also be used for calculating the water balance in water
reservoirs or in some portions of them. In this case, the value f will
characterize the redistribution of water in a horizontal direction for the
analyzed period in the reservoir itself and in the lower layers of the
ground (if there is any noticeable redistribution of moisture). Similarly,
value b 1 if taken for the reservoir, would have to determine the total
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change in water quantity in the reservoir itself, and in the lower layers as
well, if there was a noticeable change in moisture content. Practically, in
many cases value b is determined for the water reservoirs by the change of
water level. For the average annual value b is often very small, and
therefore, the equation of the water balance will be:
(18)
For the whole globe the horizontal redistribution of moisture equals
zero, and therefore the equation of water balance will have the simple
form:
(19)
The equation of water balance has the same form, for the year, in those
portions of land where no runoff is observed, including deserts.
In closing, we will give the equation of water balance in the atmosphere.
By adding up all categories of the gain and loss of moisture in the vertical
column which extends through the atmosphere, we offer the following equation:
E=r+C+ba, (20)
where C-- is the amount of moisture which is gained or lost by the vertical
column as effected by air currents and by the horizontal turbulent exchange;
ba-- is the change in water content of the column during the analyzed
period of time.
Since the atmosphere can contain only relatively small quantities of
water in any of its phases, the value of ba is usually much smaller than
the other components of the balance. The average annual value is close to
zero.
The equations of heat and water balance, which have been given here
actually represent the basis for all constructions and derivations outlined
in this monograph.
?2. General review of investigations on heat balance of the earth's
surface
The formulation of the heat balance investigationsproblem belongs to
the outstanding climatologist and geographer, A.I. Voeikov. In recent
literature we freguently find the citation of this remarkably deep state-
ment by A.I. Voerkov, which concludes the first chapter of his monograph -
The Climates of the Terrestrial Globe, (VoAkov, 1884 /687): "I think
that one of the most important problems of physical sciences at the present
time is - the bookkeeping of solar heat amounts received by the earth with
its gaseous and fluid envelopments.
We have to know: how much of solar heat is received at the upper bound-
aries of the atmosphere, how much is spent, for heating of the atmosphere,
4) Italics by A.I. Voefkov.
15
for the water vapor change of state contained in the atmosphere; and
further on, what is the quantity that reaches the land surface or water
surface, what quantity is spent for heating of various bodies, and what is
spent for the change of their state (from the solid phase into fluid, and
from fluid into gaseous), for the chemical reactions, especially those
connected with organic life; further on, we have to know haw much heat is
spent by the earth through radiation into outer space, and how it happens;
i.e., how much of it occurs on account of a decrease in temperature and
how much on account of changes in the state of bodies, especially of water.
The difficulties in achieving this goal cannot scare the scholars, who
understand the wide problems of science. It cannot be done in one century.
Therefore, I assume it is useful to state this very comprehensive problem
in full size, hiding nothing of the huge difficulties involved in obtaining
not only the complete solution but even in finding some approximate answer."
To estimate the importance of these thoughts of A.I. Voeikov, it must
be remembered, that in those times when The Climates of the Terrestrial
Globe was being prepared, (the eighteen eighties) the problem of the solar
energy transformations occurring in the outer geographical medium was almost
completely untouched. More or less systematic actinometric Observations
were started only at the end of the 19th century, and the earliest attempts
of calculati9g the incoming solar energy to the earth' q surface were not
knmp by Voeikov when he was writing this monograph. 51 Nevertheless,
Voeikov has not only correctly formulated the main problems in the study of
heat balance, but with a scientific optimism, so typical of him, he pre-
dicted with confidence that the huge difficulties in solving these problems
would be successfully overcome.
In many investigations done by A.I. Voeikov, various concrete questions
associated with the study of heat balance have bee9 analyzed. For instance,
in The Climates of the Terrestrial Globe Voeikov has paid much atten-
tion to the calculation of the annual variations in heat content of lakes.
These calculations permitted him to draw some conclusions about the in-
fluence of water reservoirs on climatic conditions in various regions.
In his work The Heat Exchange in the Outer Coating of the Terrestrial
Globe (1904 Lq7) the question about the climate-forming effect of the heat
exchang" in soil and water reservoirs is analyzed in detail. Many ideas
of Voeikov, outlined in this work, have not lost their scientific im-
por.teance, even up to now. It is enough to remember, for one thing,
Voeikov's statement about the exceptionally important conception of the
outer active surface and his deep analysis of the relationship between the
heat-exchange and the annual and diurnal variations in temperature.
However, it is obvious that any, more or less comprehensive, investi-
gations of the heat balance on the earth's surface could be started only
') The work of Angot, 1883, the first investigation of the laws gov-
erning the incoming solar energy to the earth's surface could be utilized
by A.I. Voeikov only when he was preparing the second edition of The
Climates of the Terrestrial Globe published in 1887.
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after an effective method for determining its principal components had been
suggested.
The development of methods for determining the components of the balance
has been started in two principal directions: 1) designing of special in-
struments for measuring the separate components of the balance, and 2)
development of methods for calculating the components proceeding from theo-
retical conceptions and using ample data of regular hydrometeorological
observations.
The first stage in the development of methods for determining the com-
ponents of the balance, based on application of special instruments, was
closely connected with the development of actinometric investigations.
Works of our scientists were of great importance in creating the sci-
entific actinometry. So, in particular, a great advance in development of
actinometric observations was made when 0.D. KHvolson invented his actino-
meter. Systematic observations of direct solar radiation were started
with this instrument at Pavlovsk in 1890. The possibilities for measuring
the solar short-wave radiation were greatly expanded when K.D. Angstrom
invented the pyrheliometer in 1895; V.A. Mikhel'son designed a perfect
actinometer in 1906; in 1910-1911 S.I. Savinov improved' the actinograph
of Crova (Kalitin, 1950 E227) and a series of other actinometric instru-
ments were developed. Much later, at the end of the nineteen thirties,
the more or less accurat9,measuremelits of scattered radiation could be
secured after the IU.D. IAnishevskii pyranometer was introduced in 1934.
(It is described in IAnishevskii's paper 1951 g48J)
The progress achieved in improvements of actinometric instruments con-
tributed to a rather rapid expansion of the actinometric network observing
the flux of short-wave radiation.
Before the Great October Social Revolution in Russia, actinometric Ob-
servations were being taken only at five points, but afterwards, at the
end of the nineteen thirties, these observations were carried on at sev-
eral scores of stations (Kalitin, 1947 L1227). The actinometric network
of the world has grown especially fast during the last decade.
The development of the actinometric network could be characterized by
comparison of the consolidated tables of actinometric observations that
have been published annually. So, for instance, the paper by Kimball that
was published in 1927 and 1930, contains the mean values of total radiation
obtained at only 32 stations, located in various regions of the world. In
Gorczinsky's paper of 1945, observations of 58 stations are' given. In the
first smrprizing Paper by T.G. Berland (1949 /5.67) the mean values of
t9..al radiation are given for 85 stations, and in thesecond paper (Ber-
nand, 1954 g87)- for 139 stations. Even though, the last number is many
times less than the number of meteorological stations taking ordinary ob-
servations, nevertheless, at the present time, a direct generalization of
available data on actinometric observations could be done and could be
utilized for obtaining some climatological conclusions.
However, it must be stated, that up to the present time, actinometric
observations for most of the stations have been limited to measurements
of the flux of short-wave radiation.
The measurements of long-wave radiation, and especially that of the
effective outgoing radiation, were associated with considerable methodical
difficulties and therefore they were started much later than the measure-
4
?
17
ments of short-wave radiation.
The first instrument that was used for more or less systematic measure-
ments of the effective outgoing radiation, was the pyrgeometer of K. Ang-
strom designed in 1905 (Angstrom, 1916). Later on, many investigations
established that the observations made with this instrument ususlly con-
tained fairly large errors. Many authors have tried to improve the con-
struction of instruments measuring the effective outgoing radiation, but
up to recent times, the results have not been quite satisfactory. Only
recently, some instruments have been constructed, although not without
defects, but still permitting measurements of effective outgoing radiations
without any great principal errors, and not only at night but also during
daylight hours. The existing instruments for measuring long-wave radiation
were used for Observations by stations and by expeditions, but results ob-
tained are still too scarce in volume to warrant any climatological general-
izations. Still, these data are valuable in verifying various calculation
metnods for determining the effective outgoing radiation. More details
on this are given on pp. 43-46(pp.40-44 of this translation).
More or less reliable instruments for direct measurements of radiation
balance were constructed not very long ago. The first steps in this di-
rection were made in the nineteen twenties by V.A. Mi4thellson, and later
I.G. Liutershtein and A.A. Skvortsov. Later, IU.D. IAnishevskii and F.
Albrecht devoted much effort for the development of a balance-counter.
As a result of long years of investigations,IU.D. IAnishevskii has designed
a rather simple construction of a balance-meter, which permits the measure-
ment of radiation balance values without any large principal errors
(IAnishevskii, 1949 g477). During recent years, Albrecht suggested sev-
eral improvements of this instrument (Albrecht 1933 and others). Most re-
cently a new construction of a balance-meter has been suggested by D.L.
Lalkhtman and N.B. Kucherov (1952 6:55 & 1517). We will not cite further
the constructions of balance-meters, but will mention the fact that in-
struments for direct measurement of radiation balance are now being ex-
tensively used by expeditions investigating the amelioration of climate
in the lower layers of the atmosphere, and for other problems in physics
of the air layer near the ground. For stationary observations, the ap-
plication of the balance-meters has not been very wide as yet. Conse-
quently, the observational material obtained through balance-meters is,
at the present time, very scarce, and at any rate, it is considerably
smaller than the amount of observations on the effective outgoing radiation.
For this reason, the data of direct radiation balance measurements could
be used mainly for investigation of physicometeorological regularities
and in solving various methodical problems. The application of these data
for comparison of climatic conditions in various regions still involves
considerable difficulties.
Methods for direct measurements of other components of the heat balance
of the earth's surface, and especially of the expenditures of heat for
evaporation and for turbulent heat exchange, are much less developed than
those for measurements of the components of radiation balance.
Since the latent heat of evaporation represents a well known physical
value, there is always a possibility to find the amount of heat lost on
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18
evaporation by measuring the evaporation from the earth's surface. The
instruments for determining evaporation from land surfaces (evaporimeters
of various makes) were being developed by numerous authors during a. long
period of time. Some of the soil evaporimeters have been applied for ob-
servation by some hydrometeorological stations. 6)
Data on evaporation obtained by evaporimeters are relatively scarce and,
as it has been pointed out by many authors, they are not free from con-
siderable systematic errors. Therefore, the soil evaporimeters could not
be accepted as a universal method for determining the evaporation from the
soil surface. Various kinds of evaporimeters have been used to determine
the evaporation from water surfaces. However, these observations also con-
tain some errors, and are insufficient to warrant any larger climatological
generalizations. 7)
In recent years, many authors have used gradient methods for determining
evaporation and the loss of heat associated with it.
These methods involve the calculating of evaporation proceeding from
measurements of vertical moisture gradients, and simultaneously taking
into account the values of the coefficient of turbulent exchange. Another
variation of the gradient method for determining evaporation is the so
called balance-method; this determines the evaporation or loss of heat for
evaporation by measuring the vertical gradients of temperature and humidity
In the air layer near the ground, and by measuring the radiation balance
and heat exchange in soil.
The gradient method also permits us to determine the magnitude of the
turbulent heat flux - one of the most difficult components of the heat
balance for direct measurement.
Numerous works with gradient methods made in the USSR (Budyko, 1946a
57,1948a 2397; Timofeev? 1951 gig; Budyko and Timofeev, 1952 597;
Methodical Instructions, edited by Rusin, 1954 5717, and many others) and
also abroad (Thornthwaite and Holzman, 1942; Holzman, 19432 and many otheri
have corroborated the great importance of these methods. However, the
observations needed for determining the components of heat balance by
gradient methods are still very scarce; since the network of hydromete-
orological stations has not been taking them as yet.
Among other methods for direct determination of heat balance com-
ponents, the idea of B.A. Aizenshtat (19480 1951 & 37 and others) should
be pointed out. This author suggested designs of several instruments which
measure the components of the heat balance (including heat exchange between
the eptive surface and atmosphere) by the method of compensation.
Aizenshtat's instruments have been used by several expeditions, and in-
) So in some periods, the evaporimeter designed by M.A. Rykachev (1898
5997 was used by several stations. Data of observations obtained by these
instruments and also by some other evaporimeters have been subsequently
published, (Data of observation on evaporation ... 1939 and others).
0 Summaries of observations with water evaporimeters and evaporation re-
servoirs are available in papers published by B.D. Zaikov (1949 5027),
Follansby (1933) and others.
19
teresting results were obtained. But regrettably, the Aizenshtat method
is best fitted for determining the components of the balance of the active
surface without vegetation. Quite recently, a new instrument for measuring
turbulent heat flow has been suggested by N.V. Kucherov (1952 2T517). In
many respects it is similar to those suggested by B.A. AlZenshtat.
The great progress in experimental meteorology has made it possible, at
the present time, to measure all the principal components of heat balance
in various physiographical regions. However, these observations are usu-
ally insufficient for making any larger climatological generalizations,
since these special observations were taken mainly during the course of
some special investigations and are not included in the program of ob-
servations taken by the hydrometeorological network except for short-wave
radiation measurements.
Therefore, at the present time, methods for determining the components
of heat balance from data in standard meteorological observations are of a
great importance.
The first calculations of the components of heat balance determined the
changes of heat content in limited water reservoirs and in the upper layers
of soil. Similar calculationslishich are relatively simple, have been made
in the last century by A.I. Voeikov, Ferrel and others. Among the works
in this direction, the investigations by Homen (1897) must be pointed out.
He was the first to compare the diurnal heat exchange of a granite rock
with those of a peat meadow and of a sandy soil.The results obtained by
Homen have been cited many times in various meteorological textbooks.
The first fundamental investigations concerning the calculations of the
transformation of solar energy in the atmosphere were published at the end
of the 19th century. They include the above mentioned investigation by
Angot on determining the amount of short-wave radiation which reaches the
earth's surface in various latitudinal zones of the globe.
However, the first calculations of the components of heat balance on the
earth's surface have only been accomplished in the first few years of the
20th century. Of great importance, for the investigation of heat balance,
was the work of W. Schmidt (1915). Using the calculation methods, he de-
termined the mean annual values of heat balance components for the latitu-
dinal zones of the ocean in the Northern and Eastern hemispheres, including
calculation of the mean quantities of heat, for each latitude, which are
transferred inside the ocean in a horizontal direction as a result of sea
currents and macroturbulence. Though the calculation methods used by
Schmidt were rather rough, (especially that for determining the loss of
heat for evaporation and turbulent exchange) nevertheless he managed to
obtain a proper order of magnitude for the principal components of heat
balance.
It must be mentioned here that, Schmidt was the first who tied up the
calculations of the components of heat balance with determination of water
balance in the world oceans.
Among all subsequent investigations of heat balance it is proper to
mention the works of A. Angstrom. In a paper published in 1920, Angstrom
determined all the components of heat balance for a limited reservoir -
the Lake Vassi Jaure in Sweden. Simultaneously, he essentially improved
1
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20.
the methods for calculating the components of radiation and heat balances,
though the problem of calculating the amounts of heat lost for evaporation
and turbulent exchange has not been successfully solved by Angstrom without
using a rather conventional hypothesis.
In 1925, Angstram published a paper (1925b) containing the results of
calculations of all components of heat balance in the Stockholm region for
ail months of the year. The principal defect of this, in many respects a
very valuable work, was the neglect of the use of reflected radiation in
determining the radiation balance for the warm season. Annual and monthly
values of radiation balance without this brincipal error have been cal-
culated for the first time by Savinov for Pavlovsk. These calculations
are published in the Course of Geophysics by P.N. Tverskoi (1934 gig).
For development of investigatlons on heat balance of the seas, the
paper contributed by V.V. SHuleikin (1935fo}(27) was of great importance.
In this work, for the first time, the components of radiation balance of a
single sea (the Kara Sea) were calculated by using the results of special
observations and of some calculations. V
Having determined the components of the heat balance, 011eikin also
demonstrated the great importance of the warm current affecting the thermal
regime of the Kars Sea. This conclusion was confirmed later by direct ob-
servations (SHuleikin, 1941 L541.7).
When these works were pliblished? many authors started investigations of
heat balance, and the amount of calculations of the radiation and heat
balance at various points on land and for water reservoirs grew rapidly.
In the work: by F. Albrecht (1940) the values of the components of radi-
ation and heat balance were determined for 12 points, 6 of these were lo-
cated in various regions on land, 5 in various regions of the ocean and 1
on a small lake. Using largely the calculation methods for determining
the components of the balances, Albrecht also worked up some data from
special observations. Along with the values of the components of balances
for a month and for an annual period, Albrecht has obtained some data
(though very limited) on diurnal variations of the components of radiation
and heat balance.
Attention must be paid especially to some conclusions in this paper con-
cerning the interrelations between the climatic conditions and the regime
of heat balance components.
Among the works done for determining the components of heat balance for
single points on land, the investigation by S.A. Sapozhnikova (1948b 5017)
should be considered.
S. A. Sapozhnikova accomplished the calculations of the annual and sea-
sonal values of heat balance components for 8 points, in various geograph-
ical zones of the USSR. The analysis of these materials on heat balance
has enabled Sapozhnikova to explain some physicQgeographical regularities
(for instance, the factors determining, the northern boundary of the forest
zone).
Calculations of monthly values of radiation balance at some points in
the Lower Volga region have been carried out by B.M. Galtperin (1949b fig).
It must be also mentioned that the calculations of radiation balance for
some regions in the Arctis,have been accomplished by A.S. Kaledkina (1939
(u7)and R.N. SHpakovskaia (1940 g3,27). A detailed investigation of the
we.
21
radiation regime and radiation balance in the Moscow region has been pub-
lished by M.S. Averkiev (1947 L.1.7). There are also some works containing
the results of calculations of the components of radiation and heat bal-
ance for a series of points in Western Siberia, (Orlova, 1954 5.82.7) for
the Yakutsk region (Gavrilova, 1954 /727)and some other points in the USSR.
The calculations of radiation and heat balances of various water bodies
are methodically much simpler than the computations of heat balance for
the land, and they have been very much in use for the last 20-30 years.
In developing these investigations it was important that, in the cal-
culations of the relationship between the loss of heat for evaporation
and turbulent heat exchange, the so called "Bowen relationship" could be
used. This relationship ties up the evaporation and turbulent heat ex-
change on one side with the difference between the temperature of the water
surface and air, and the corresponding difference in specific humidity, on
the other. The application of this formula 6.3y Cunnings and Richardson,
(1927), and others7 has greatly facilitated the determination of heat bal-
ance components fiom data of ordinary meteorological observations.
Among the works on radiation balance and on the components of heat bal-
ance for water reservoirs, the investigations of the following authors,
on the heat balance of various seas, must be mentioned: KH.K. Ulanov -
for the Black Sea (1938 5227);0. Mertsalova - for the Barents Sea (1938
5707);V.V.T;monov and P.P.-kuz,min - for the White Sea (1932 P1(7); N.T.
CHtFnigovskii - for the Arctic Seas (19408, 1940b30 & 237)iL.F.
Rudovits (1927 /1977); and I.A. Benashvili i1941 2g) - for the Caspian
Sea; B.D. Za5.k67 --for the Aral Sea (1946 LlOg"); B.A. SH1finin - for the
Azov Sea (1947 ff3?7); A.F. SHishko - for the White Sea (1948 5317); N.I.
Egorov - for th-e Red Sea (1950 587) and others.
In modern literature on the heat balance there are also some investi-
gations concerning the heat balance of the ocean's surface. Mosby (1936)
has compiled the radiation balance for the latitudinal zones of the world
oceans, and determined the amount of evaporation from the oceans. At the
beginning of the nineteen forties the first attempt was made to construct
maps for the components of heat balance in some regions of the world
oceans. Jacobs (1943) and Sverdrup (1945) designed schematic maps of the
components of heat balance faethe northern portions of the Atlantic and
Pacific Oceans. Albrecht (1949, 1951) computed the components of heat bal-
ance for the Pacific and Indian Oceans and constructed a series of maps
showing the distribution of the balance components for single months and
for the year.
The computations of the components of water balance for the region of
the Gulf Stream were published by Konoplev (1953 LI37). Sauberer and
Dirmhirn (1954) made computations and constructed maps of radiation bal-
ance for the oceans of the N.orthern Hemisphere for four single months -
March, June, September, and December.
The heat balance of lakes and evaporation basins has been studied by
Cunndngs and Richardson (1927), Richardson (1931), Cummings (1936), L.N.
Demchenko (1952 /?.07),Sauberer (1953) and others. Investigations of the
heat balanse in artificial reservoirs have been carried out by A.P.
Braslavskii and Z.A. Vikulina (1954 /337).
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Some works, which have contributed some improvements to the calculation
methods for determining the components oZ heat balance, must be mentioned
here too. Among those works are the investigations by A. Angstrom (1922)
and S.I. Savinov (1933 if02 &2037) dealing with methods for calculating
the total short-wave radiation.? Methods for calculating the long-wave
radiation that first were suggested by Angstrom (1916) and Brunt, (1934)
were developed later in the theoretical investigations by K. IA. Kondrat'ev
(19490, 1949b /133 & 1347 etc.), by M.E. Berland and T.G. Berland (1952
547)0 by T.V.?KirillovET (1951 /1267), in an experimental work by Bolz and
Falkenberg (1949) and in a series of other investigations.
During the last 10-15 years the calculations and experimental investigations
of heat balance on the earth's surface have been widely extended, stimulated
by rapidly growing demands and requests for this type of data to meet the
needs of all hydrometeorological sciences.
In meteorological researches the data on heat balance are now used in
calculating the transformation of air masses. Works along these lines
include the investigation of V.G. Kastrov (1933 L124/) dealing with the
physical mechanism of drought development, and also some works by M.E.
Berland (1952, 1953 etc. /22 & 237) and M.V. Zavarina (1953 /1007) in
which the calculations of the transformation processes are associated with
development of methods for the forecasting of thermal regimes.
Among the agrometeorological investigations in which data on heat bal-
ance have been utilized are the works by Sapozhnikova. In one of her re-
searches (19488 if067) the calculations of heat balance for a cultivated
field made it possible to obtain valuable practical conclusions about the
reasons that prevent the extension of grain crops in a northerly direction.
In works accomplished under the supervision of S.A. Sapozhnikova (as,
for instance - Climatological data for the region between the Volga and
Ural rivers, 1951), and also in investigations of V.V. Orlova (1954 L1827)
the data on heat balance are used in explaining the laws governing the
agrometeorological regime in various regions of the USSR.
The most recent investigations of amelioration of climate have also been
based mainly on heat balance data. For instance, in works by M.I. IUdin
(Budyko, Drozdov, L'vovich, Pogosian, Sapozhnikova and lUdin, 1952 567),
D.L. Lafkhtman (1953 /1567) and other authors the data on heat balance
are used for calculating changes produced by irrigation in the hydro-
meteorological regime.
The calculations of heat balance components have also been used by M.I.
IUdin and by the author in works dealing with methods for evaluating the
hydrometeorological effect of the forest shelter belts (Budyko and Udin,
1951, 1952 /62 & 637) and in other works by the author which will be
mentioned in chapter V.
It must be rioted, that considerable progress in the study of hydromete-
orological effectiveness of ameliorative measures, made on the basis of
heat balance investigations, has been achieved by the complex expeditions
sponsored by the Central Geophysical Observatory and, particularly, by
the expedition to Kamennaa Step' in 1951 (headed by Prof. Drozdov) and
by the expedition to the irrigated oasis of Pakhta-Aral in 1952 (headed
by Prof. D.L. Laikhtman). Results of observations gathered by these ex-
23
peditions (Trudy GGO, no. 39, 1953 and no. 4o, 1953) and stationary obser-
vations organized and carried out by special agrometeorological stations
have shown that the accounting of the heat balance regime is of paramount
importance for estimating the effectiveness of the ameliorative measures.
Accordingly, in numerous modern investigations, the data on heat bal-
ance have been used in selecting the most effective construction of field
protective shelter belts; in estimating the effect of irrigation on the
climate of the layer near the ground; in studying the dependence of water
amounts, needed for irrigation, upon weather factors; etc.
Among the theoretical problems in modern meteorology that could be
solved by using data on beat balance of the earth's surface, we will point
out the works on the theory of climate (L.R. Rakipova, 19520 1953, J.94 &
1927 etc.).
The utilization of data on beat balance permitted us to verify the
initial hypotheses and improve some of the principal statements in the
theory of climate origin.
Also, heat balance data are used in solving many questions of dynamic
meteorology, where the equation of heat balance is applied as shoving the
boundary conditions. Among these investigations are works on the theory
of diurnal variations of meteorological elements, on the theory of local
circulations, etc. Also, data on heat balance are now used extensively
in investigations of land and sea hydrology as well. In particular, the
computations of heat balance are now one of the principal methods for
forecasting the snow melt regime. A series of important investiNions
of this problem has been made by P.P. KUzImin (1947, 1950, 1951 1 7, 149
& 159.7 etc.). Among other methods of hydrological forecasting that are
based mainly on data of heat balance of water reservoirs, the forecasting
of the thermal regime in reservoirs including the forecast of freezing and
melting of water surfaces and the process of ice melting should be men-
tioned.
Data on heat balance are also used in investigations of the hydrological
regime of swamps, including computations of the amounts of evaporation from
swamps; in calculations of the amounts of evaporation and runoff for var-
ious regions; and in studies of climatic conditions of moistening. Works
along this latter line will be treated in more detail in chapter IV.
Calculations of heat balance are also of great importance in determin-
ing the amounts of evaporation from the existing and from planned reser-
voirs. This problem, elaborated in a particular case by A.P. Braslavskii
and Z.A. Vikulina (1954 637), is of a great practical importance.
The heat balance calculations of the existing reservoirs that have been
made in order to allow an evaluation of changes in the hydrometeorological
regime, when accomplishing larger ameliorative measures, must also be men-
tioned here. These works are directly associated with investigations of
the heat balance of the seas and oceans which)primarily have been made for
clarifying the regularities in the hydrometeorological regime of the
analyzed reservoirs. In developing these investigations the works of
V.V. SBUlelkin were of great importance.
Data on heat balance have been used not only in hydrometeorological
studies but also in investigations of general problems in physical geo-
graphy. It is obvious, that in an investigation of the mechanism of
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natural processes and their interaction, it would be very important to
have certain concepts about the geographical regularities in transformation
of solar radiation on the earth's surface, which actually is the main basis
and source of energy for all natural exogenous processes. Accordingly,
A.A. Grigor'ev has established many relationships connecting the character-
istics of radiation and heat balance of the earth's surface and atmosphere
with the intensity of major physicogeographical processes (his papers of
1937, 1946, 1948, 1951, 1954 /Bo, 81, 82, 83 & 847 etc.). Among the stud-
ies in this direction we will also note the investigations done by D.L.
Armand (1949, 1950 /1:3 & 147) and by author (these will be reviewed later).
A rapid growth of requests for data on heat balance stimulated a con-
siderable expansion of climatological investigations concerning the dis-
tribution of the components of radiation and heat balance.
Up to the middle forties, the climatological regularities of the com-
ponents of heat balance had not been sufficiently studied. Data on the
mean values of the components of heat balance on land were available in
literature for only a few points, and the accuracy of their calculation
was completely unknown. For water reservoirs, there was more data avail-
able (calculations for some seas and lakes and schematic maps for some
portions of the ocean surface); however, for the oceans, there were no
world maps of the distribution of balance components, and the degree of
accuracy of accomplished calculations was oftentimes debatable.
Taking all this into account, a group of scientists in the Central Geo-
physical Observatory has undertaken detailed studies of the climatological
regularities of radiation and heat balance. In these studies, attention
has been paid to development of methods for an independent determination
of all components of heat balance, which would permit an objective veri-
fication of the degree of accuracy of the accomplished computations of
the balance equation. This question was first solved for single point
conditions (Budyko, 1946c /377), and later for a large land region--the
southern areas of the European USSR (Budyko 1947 /387). Having confirmed,
in this way, a sufficient reliability of developed methods for determining
the components of the balance, the authors was able, for the first time,
to construct maps of the distribution of heat balance components for the
mainland's surface.
In ensuing works of the Central Observatory many other naps have been
designed: seasonal and annual maps of the components of heat balance for
the European part of the USSR (T.G. BerlAnd, 1948 /257); annual maps of
the balance components for the extratropical portion of the northern
hemisphere (T.G. Berliand, 1949 /267); annual maps of radiation balance
for West Europe and for the eastern part of North America (Zubenok, 1949a
/1027); and some calculations of the latitudinal values of the components
in the Northern Hemisphere have been accomplished (Budyko, 1949b F27).
Having made all these investigations, which were to a certain?eitent
of a preparatory nature, the authorsIT.G. Berliand, and L.I. Zubenok have
carried out a work on designing the world maps of the balance components
for single months and for the year. This series of maps contains indices
of the total short-wave radiation, of radiation balance on the earth's
?
25
surface, on evaporation and heat losses for evaporation, on turbulent heat
exchange between the underlying surface and the atmosphere, and also, a
map (for the year) of the heat amounts gained or lost by the ocean surface
as affected by the sea currents. In total, this series contains 66 maps
which show the general geographical regularities in the transformation of
solar energy on the earth's surface.
Annual maps of this series have been published in the Marine Atlas,
Vol. 2 (Budyko, Berliind, Zubenok, 1953 /507) together with the explanatory
text in an article (Budyko, BerlAnd, ZuTierlok, 1954a r5717). The whole
series of maps has been published in 1955 in The Atlas of Heat Balance 527.
Since the world maps of heat balance are necessarily of a schematic
nature, more detailed maps have been designed by T.G. BerlAnd and M.A.
Efimova (1955 /297) for the USSR. They show the total radiation and radi-
ation balance (-monthly and annual). The latter series contains a total of
26 maps.
In addition, detailed maps of evaporation and amount of heat spent for
evaporation have been constructed in the Central Observatory for a portion
of the USSR for single months.
Along with this work, the calculations of diurnal variations of the
radiation balance components in various climatic zones (Biriukova, 1955
/317) have been made, and some features in the variations of the components
have been studied.
Evaluating the whole scope of data on the climatography of heat balance
that have been obtained during the recent years, we can say that, at the
present time, the knowledge of the distribution of some balance components
in time and space is not less than that about the basic meteorological
elements (for instance, we now have world maps of total radiation and radi-
ation balance for all months of the year, whereas no similar maps exist
for such important meteorological elements as precipitation). However, it
must be noted that the majority of heat balance maps are of a schematic
nature, and their reliability is not always adequate, especially for
regions with scarce data on the hydrometeorological regime - in higher
latitudes, in the oceans of the southern hemisphere, etc.
When these new data on the climatography of heat balance were obtained
they permitted a considerable expansion for the study of climatological
regularities in heat balance and provided new conclusions of a general
nature. Thus, these data, in conjunction with some special studies of
heat exchange in the atmosphere, provided a basis to refute the earlier
ideas that the atmosphere, by and large)transfers the heat to the earth's
surface through a trubulent heat exchange (Budyko and IUdin, 1946, 1948
/615 &617). The accomplished calculations of heat balance have promoted,
For the firsttime, a comparison of quantities of heat carried from the
lower to the upper latitudes in the atmosphere and hydrosphere (Budyko,
1949b 527).
Without the mention of other climatological regularities, which have
been found by analyzing maps of heat balance components, we will note only
that, these data have been used in works on the theory of climate mentioned
above; in investigations of the general circulation of the atmosphere
(Usmanov, 1953 A-247 etc.); in works on description of climates in various
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I
26
regions (as, for instance, in works of Fedorov and Baranov, 1949; 5257
Orlova, 1954 5827, and others); in synoptic climatology; and also in many
Investigations of thehydrometeorological effects of ameliorative measures,
which have already been mentioned above.
The new data on the climatograpy of heat balance have been used exten-
sively in various physicogeographical investigations. Among these are
recent works by A.A. Grigortev (1951, 1954 /U3 & 847) on the theory of geo-
graphical zonality, and also some works by the author (1948b, 1949a, 1950a,
1951b So, 41, 43, & 467 and others).
In these works the authorhas tried to apply the data of the energy bal-
ance to the study of physicogeographical regularities by a deductive method,
on the basis of general physical laws. This method combined with utiliza-
tion of empirical data and generalizations, greatly expands the possibilities
of geographical investigations.
The utilization of data on heat balance has made it possible to estab-
lish certain regularities and relationships that exist between the climatic
factors on one side, and the hydrometeorological regime, the geobotanical
zonality, soil zones, and some indices of the productiveness of natural
vegetation on the other.
The development of investigations in this direction reflects the recent
tendency to tie up more closely the sphere of physical geography with geo-
physics, on the basis of more extensive use of the quantitative methods and
physical methods of analysis in tackling the .problems of physical geography.
It is conceivable that, a combined use of the physicogeographical and geo-
physical method of investigation will expand the possibilities of solving
many practical and theoretical problems, related to physical geography as
well as to geophysics.
27
Chapter II
Methods for the Climatological Calculation of the Components of
Heat Balance
In the preceding chapter it is stated that the existing data of direct
observations of the components of heat balance are very scarce and, as a
rule, are not sufficient to warrant more extensive climatological general-
izations. Therefore, the studies of spatial distribution of the balance
components are based, at the present time, principally on indirect cal-
culation methods, making use of ordinary meteorological observations of
temperature, humidity, cloud amounts, precipitation, wind, soil and water
temperatures, etc.
The methods of climatological calculations of the heat balance compo-
nents may be more or less complicated, depending on what kind of mete-
orological data could be used in these calculations (wheLher, for instance,
there are available data on clouds for various heights or only on total
amounts, etc.). On the other hand, the degree of details in the method
used must also depend on the nature of the problem to be tackled - so, a
calculation of schematic maps of some mean values of the heat balance com-
ponents for the land and oceans could be accomplished by using a less
differentiated method, as compared with that used in calculating these
data for small regions in microclimatic investigations, or for separate
short periods of time.
The methods for climatological calculations of the balance components
for the long period averages (long-period mean values, monthly and annual)
have already been developed to a more or less higher degree by now. The
problem of developing methods for calculating the components of heat bal-
ance for shorter periods, by using the basic meteorological observations,
has not been solved in its entire scope as yet.
3. Radiation Balance
In climatological calculations of radiation balance, its value is
usually determined by formula (5) as the difference between the absorbed
radiation ((?-11-q) (1--m) (where (2-- is the direct radiation, q--the
scattered radiation, a-- the albedo) and the effective outgoing radiation
1. When using this method for calculating the radiation balance, the
amount of the total radiation ((2-17q) must be determined first.
As has been said in chapter I, only total radiation is the one single
component of the radiation and heat balance which is measured by compara-
tively numerous actinometric stations (at present, totaling about 200
stations on all continents).
However, it must be indicated, that the network measuring the total
radiation is of a very irregular density. Most of the stations are located
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in the European part4of the USSR and in North America. Due to this fact,
N.N. Kalitin was able to construct a map of annual amounts of total radi-
ation for the European USSR as early as 1945, Kalitin (1945 L1207). A
little later, Hand constructed a similar map for the United States, Hand
(1953).
In other regions the net of actinometric stations is very sparse and
does not permit any climatological generalization or any, more or less,
detailed construction of maps for total radiation. On the oceans there
are practically no observations of this type of any, more or less, system-
atic nature.
Therefore, it is impossible to make a comprehensive investigation of the
distribution of total radiation over the world without using the methods
of climatological calculations.
The first investigations in calculating the amounts of short-wave radi-
ation received by the earth's surface were confined to the determination of
the direct radiation only. In the work by Angot, cited above,. and also in
ensuing investigations by S.I. Savinov (19251_1928 /200 & 201/), M. Milan-
kovich (1939 /1737), V.G. Kastrov (1928 L1217), B.M. Gallperin (19498 0-57)
and other authors, certain methods have been developed for calculating the
amounts of direct radiation received by the earth's surface as dependent
on the degree of transparency of the atmosphere.
Later some attempts were made to also determine the amount of diffused
radiation by the theoretical or empirical methods, and to evaluate the
effect of cloudiness on the total radiation.
The results of most of these investigations have not been used very
much for calculating total radiation because of the cumbersome formulas,
their insufficient accuracy, and the necessity to take into account many
parameters that are quite variable and have not been studied sufficiently.
A simple and sufficient method for determining the total radiation has
been suagested by A. AngstrOm (1922), Kimball (1928) and Savinov (1933a,
1933b L202 & 2037).
In an investigation published in 1922 Angstrom suggested the following
formula for determining the total radiation:
(Q- - (Q+ q) [k + (1 ?
(21)
where ((2-11-q) and (Q+q),,?. the total radiation with natural conditions
and a clear sky (no clouds), S-- the ratio of observed sunshine hours to
the possible amount for the given period, k ? a coefficient, determining
what portion of the possible radiation consists of actual radiation with
overcast sky conditions. Using the observational data from Stockholm,
Angstrom found that coefficient k was equal to 0.235.
Kimball (1928) found a similar relationship using the data of several
American stations:
(C2 q) =(Q ? q)0 [0,29+0,71(1 ? n)],
where is the mean cloud amount in tenths.
S.I. Savinov (1933a, 1933b ?202 2037) investigated in detail the
Interrelations between the Values S and (1--n), using observations taken
(22)
29
In Pavlovsk, and he found that these values usually differed considerably
from each other. Savinov came to the conclusion that the best agreement
with the true value of the ratio of the actual amount of solar radiation
to the possible radiation could be obtained by using the mean arithmetic
value of S and (1?n).
For calculations of the direct and total radiation Savinov suggested
the following formulas:
and
where
Q Qo (1 ?70 (23)
(Q+ 11) = (Q+ 9) 0(1 ? c-n)
n
1?n-i-S
2
(24)
c--coefficient showing the effect of clouds on radiation.
According to the conclusions reached by Savinov, and also by B.M.
Gal'perin (1949a LW) and other authors, in the calculations of total
radiation the utilization of factor-i gives better results in comparison
with those obtained by using the characteristics of the general cloudiness
or sunshine hours. However, for many regions there are no reliable data
on sunshine hours and therefore this compels us to use the data on clouds
when determining the amount of total radiation.
The works of S.I. Savinov have contributed to the popularity of the
formulas given above and they have been largely used in climatological
calculations of the amounts of short-wave radiation. Of great importance
is the fact that the amount of possible radiation 02-1-00, that is included
in formulas (21), (22), & (24) appears to be a rather stable factor, which
depends mostly on the latitude and season. This facilitated the use of
these formulas for calculating the total radiation.
Among other empirical methods for determining total radiation, the
formulas suggested by V.N. Ukraintsev, (1939 L2217) and Albrecht (1940)
must also be mentioned.
Using observations of stations located inside the zone between 35? and
70?N, Ukraintsev has set up the following formula:
(Q-1-q)=m1S-I-n, (n)
where ES?is the total amount of sunshine hours, in and n-- are the co-
efficients, which depend on the season and latitude.
Having computed these coefficients, Ukraintsev presented them in tables
for each month and for various latitudes.
The testing of Ukraintsev's method on results of recent observations
has shown that oftentimes it gives extenuated values of total radiation.
It is possible, that this is the result of using the observations on
scattered radiation which have been taken by obsolete instruments that
give extenuated values.
The formula; suggested by Albrecht is:
1
(Q + (7) = a sin he b ?ho (1 ? 71) cal/cm2/min. 1 (26)
1/ sin
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where ?is the altitude of the sun, a, b andm?are numerical coefficients.
When calculating the amount of total radiation for more or less longer
periods of time, the data obtained by this formula must be summed up accord-
ing to diurnal variations of the sun's altitude.
Having determined the values of coefficients a and b by using the scarce
observational data, Albrecht found a.. 0.31-0.34 cal/cm2/min, b--=
Comparing the results obtained by Albrecht's formula with observational
data it could be found that the formula usually shows rather large syscem-
atic errors, mainly extenuating the values of total radiation.
This is apparently connected with the fact that Albrecht started with
very insufficient observational data when deriving formula (26) and deter-
mining its coefficients. Some better results, as it seems, could be ob-
tained by using the other Albrecht formula which has, with some simpli-
fications, the following form:
(Q+ (ao sin ho ? ha/sin ho ) [1 ?(1 ? 11) al cal/cm2/min (26a)
The coefficient al, according to observational data, varies in limits
1.7-2.4; the coefficient 60 approximately equals 0.32.
The physical meaning of this relationship was explained by K. IA.
Kondrat'ev (1954 /1377).
In investigations on the climatology of heat balance, made by the
Central Geophysical Observatory, the following equation has been used for
calculating total radiation:
(Q.+ --= (Q+ 00 [1 ?(1 ?k)ai
(27)
In modern literature this formula is usually called the Savino-.Angstrom
formula.
The parameters, included in ths formula, have been determined by T.G.
BerlAnd from data of actinometric observations (Budyko, Berliiknd, Zubenok,
1954a, 1954b & 527).
The mean monthly values of possible radiation .(C2-1-00 have been found
for various latitudes and for all months of the year by the suggested
method of V.N. Ulraintsev (1939 (f21.7). Using this method, graphs have
been constructed for stations located in various latitudes, showing, by
the abscissa, the day of the year, and by the ordinate, the corresponding
daily amounts of total radiation derived from several years of observations.
The pointson the graphs were located inside certain regions with a very
definite upper boundary. Since the upper points on these graphs apparently
shay the clear days conditions, we can draw a curve through these points
and obtain the annual march of the daily values of total radiation under
cloudless sky conditions. The data which have been determined from this
graph are presented in table 1.
It must be said here that the values of poanible radiation, shown by
_
31
this table, are a little larger than those found in most of the preceding
investigations. This difference is apparently connected, to a certain
degree, with the utilization of the values of possible radiation from
comparatively limited observational data, oftentimes obtained by obsolete
instruments, which extenuated the values of the diffused radiation. On
the other hand, some features of Ukraintsev's method (whlch gives the
possible radiation of a highly transparent atmosphere, 1) rather than
conditions of average transparency) could contribute to the fact that the
values of possible radiation given in table I could be a little bit exag-
gerated. However, as will be explained later, this fact should not lead
to any noticeable systematic errors in calculations of total radiation by
formula (27).
For determining the coefficient k, which accounts for the effect of
cloudiness on the total radiation, data of observations from various '
latitudinal zones have also been used. The coefficient k presents the
ratio between the actual radiation under overcast sky conditions and the
possible radiation. It must depend on the mean altitude of the sun, on
the properties of clouds and on the conditions of reflection of short-wave
radiation (the value of the albedo).
Consequently, the mean values of the coefficient k, will be different
for different regions, and also, this coefficient will change according
to diurnal and annual variations.
The mean annual values of coefficient k, averaged for various latitudes
are presented in table 2.
The values of coefficient k given in table 2 have been computed from
data of actinometric observations at 62 locations. Since this coefficient
was computed by formula (27) with the actually observed mean values (Q-1-11)
and calculated the values (2-I-a)0, by the above cited method, it is quite
clear, that a small systematic error in values kQ-1-q)0 will accordingly
change the values of the coefficient k. This provides for some compen-
sation of the effect of errors which arose by determining the parameters
in formula (27) for the evaluation of total radiation.
In determining the total radiation by formula (27) and from tables 1
and 2, the effect of changes in the transparency of the atmosphere and
the effect of changes in the mean heights and forms of clouds are counted
only as the mean factors of the latitude hrough the latitudinal changes
of values (Q-11-q)0 and k7. Besides, these calculations do not account for
the annual variations of coefficient k, which,according to many authors,
could be quite significant.
Consequently, the analyzed method for calculating total radiation must
be regarded as a rather schematic one and mainly for use in calculating
the distribution of radiation over vast areas of a continent and over the
whole globe. An important advantage of this method is seen in the pos-
1) Besides, in determining the possible radiation by Ukraintsev's method,
in some cases, its values could be exaggerated because of the insignificant
cloudiness (less than 2-3 tenths), which sometimes does not reduce but
increases the total radiation in comparison with a cloudless sky.
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? 1. ?-n!".."7..7am
sibility of using only the most readily available data on general cloudi-
ness (since climatological data on frequency of various forms of clouds
are missing or are not sufficiently reliable for many foreign countries
and many portions of oceans). The question of the accuracy of total radi-
ation amounts calculated by using formula (27) and tables 1 and 2 will be
analyzed in ? 6.
Table 1.
LatitudeJFMAMJJAS
0 N D
ar N
0,0
0,0
2,5
9,6
17,9
20,3
18,9
10,8
3,6
0,4
0,0
0
75
0,1
0,6
4,0
11,2
18,7
20,9
19,7
12,3
5,3
1,7
0,2
0
70
0,2
1,4
5,8
12,7
19,4
21,4
20,3
13,7
7,0
3,0
0,7
0
65
0,8
2,5
7,6
14,1
20,1
21,9
21,0
15,1
8,8
4,5
1,5
0
60
1,7
3,9
9,6
15,4
20,8
22,3
21,6
16,4
10,5
6,1
2,6
1
55
3,0
5,6
11,5
16,6
21,5
22,7
22,1
17,7
12,3
7,7
4,1
2
50
4,7
7,5
13,5
17,8
22,1
23,0
22,5
18,8
14,2
9,6
5,8
3
45
6,6
9,4
15,4
19,0
22,6
23,3
22,9
20,1
16,0
11,6
7,7
5
40
8,7
11,5
17,0
20,0
22,9-
23,5
23,2
21,1
17,6
13,4
9,7
7
35
10,8
13,6
18,5
21,0
23,0
23,5
23,3
21,8
18,8
15,1
11,8
9
30
12,7
15,2
19,5
21,6
23,0
23,5
23,3
22,2
19,8
16,5
13,6
11
25
14,3
16,5
20,3
21,8
22,9
23,4
23,1
22,3
20,5
17,6
15,0
13
20
13,5
17,5
20,8
21,8
22,6
22,9
22,7
22,2
21,0
18,5
16,3
14
15
16,6
18,3
21,0
21,6
22,0
22,2
22,1
21,8
21,1
19,2
17,3
15
10
17,4
19,0
21,0
21,3
21,2
21,2
21,2
21,2
21,1
19,6
18,0
16
5
18,0
19,5
20,8
20,8
20,4
19,8
20,1
20,5
20,8
19,9
18,6
17
0
18,5
19,8
20,4
20,2
19,2
18,0
18,7
19,6
20,4
20,0
19,0
18
.1)
0
A
a
,a
,7
7
4
1
7
6
3
0
Total radiation with a cloudless sky (Q+9)o kg-cal/cm2/month.
Table 2.
75 70 65 60 55 50 45 40
0,55 0,50 0,45 0,40 0,38 0,36 0,34 0,33
pO 35 30 25 20 15 10 5 0
0,32 0,3; 0,32 0,33 0,33 0,34 0,34 0,35
Mean latitudinal values of the coefficient k.
A more differentiated method of calculating total radiation should take
into account the effect of forms and heights of clouds on total radiation
in each location, and should also account for the effect of changes in the
transparency of the atmosphere.
?
33
The effect of changes in properties of clouds on the annual march of
radiation could be approximately accounted for by changes of the values
of coefficient k..
The annual variations of the correponding coefficients in the formulas
of Savinov and Angstrom are analyzed in the paper by B.M. Gallperin (1949a
557). In this investigation it is pointed out that coefficient c of
Savinov's formula (24)0 in some regions, changes considerably during the
year.
Our calculations have proven that, by utilization of formula (27) the
changes of coefficient k during the annual period are also perceivable,
but usually the neglect of these changes will not produce any considerable
errors in the calculations of total radiation amounts.
Another way of estimating the effect of cloud properties on the total
radiation is the inclusion of indices in the calculation formulas, showing
cloud quantities at various cloud heights. So, for instance, P.P. Kuzimin
(1950 J.497) assumed that the ratio of the actual amount of total radi-
ation to the possible is:
1 --- (nD - nm) ---ctita,
where no- is the total amount of clouds; n? the amount of lower clouds;
CI and C2- are the coefficients; the first is equal to 0.14, the second
to 0.67. This method of calculation could be applied to those cases when
data on lower clouds are available.
In the investigation by A.P. Braslavskii (Braslavskif and Vikulina,
1954 /37), the problem of estimating the effect of some additional factors
in determining the amount of total radiation has been studied. Braslavskif
indicated, and rightly so, that in calculations of the possible radiation
by theoretical methods, the effect of the albedo of the surface on the dif-
fused radiation (this means, on the total radiation as well) must be
directly estimated. The effect of the albedo on the total radiation is,
to a certain degree, taken automatically into account when used in cal-
culating the amounts of possible radiation, that have been found by ob-
servations, for the actual state of the surface.
The calculations made by Braslavskii showed that changes in the at-
mospheric transparency which are associated with changes in humidity of
the air, and also changes in heights of places up to a level of several
kilometers, exert only an inconsiderable influence on the amount of total
radiation.
The problem of methods for climatological calculations of diurnal var-
iations in the total radiation has been elaborated by L.A. Birilkova (1955
/317). For this purpose she has used formula (27) and has determined the
parameters of this formula from observational data.
Diurnal variations of the amounts of Possible radiation have been com-
puted by Birnkova,using the idea of Ukraintsev's method. The graphs of
diurnal variations have been constructed for all months of the year for
7 locations in the USSR: Pavlovsk, Riga, Sverdlovsk, Irkutsk, Odessa,
Vladivostok, Tbilisi. The calculations showed that, the values of the
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/28: CIA-RDP81-01043R002500010003-6
r
possible radiation depend basically on the latitude, season and hour of
the day. The computed values of the possible radiation (i.e., the total
radiation of a cloudless sky) at various latitudes are given in table 3.
Table 3
Total radiation with a cloudless sky ?2-1-0p kg-cal/cm2/hour
(according to observations made in the U.S.S.R.).
Hours
?
21
20
19
18
17
16
15
14
13
12
at.
)4o.
3
4
5
6
7
819

10
11
60?N
I
II
III
2
1
6
5
15
2
13
25
6
19
31
10
24
49
12
29
37
IV
V
1
4
3
10
10
19
21
29
31
39
40
47
49
55
53
58
56
60
VI
2
5
13
22
31
40
48
55
60
62
VII
1
5
12
19
29
40
47
55
59
61
VIII
2
7
14
24
34
40
47
51
53
IX
1
4
12
21
30
39
43
'.
44
X
3
11
19
27
31
34
X1
2
5
10
15
18
XII
2
3
6
8
55
I
II
2
2
8
7
18
13
38
18
33
20
36
III
3
13
21
33
42
46
49
IV
3
10
20
31
42
50
56
58
V
2
6
17
28
39
50
57
60
62
VI
1
4
11
20
30
41
50
58
62
66
VII
3
8
15
27
37
47
56
62
63
VIII
2
5
13
24
34
42
50
55
58
'IX
1
6
14
24
36
45
50
53
X
1
5
13
23
32
39
40
XI
3
10
18
24
27
XII
2
6
11
13
50
I
3
11
19
25
27
11
1
4
11
21
34
42
45
III
1
4
12
24
38
48
52
54
IV
3
10
21
33
44
54
61
63
V
5
15
28
41
53
60
65
68
VI
2
9
19
30
44
54 '
62
68
70
VII
2
6
14
27
40
52
61
66
68
VIII
1
4
12
25
36
46
54
61
63
IX
6
15
27
40
51
57
69
X
2
7
16
26
36
43
46
XI
1
5
13
23
29
31
XII
1
6
12
18
20
45
I
1
5
15
24
32
35
II
1
4
14
25
39
46
50
III
4
13
25
42
53
59
61
IV
2
9
21
35
48
59
66
68
V
4
14
30
45
58
66
70
73
VI
2
7
19
31
46
58
69
75
77
VII
1
5
15
30
45
58
66
71
74
VIII
3
11
26
39
50
61
67
70
IX
5
16
30
45
57
64
66
X
2
9
19
30
43
49
51
XI
2
5
17
28
34
37
XII3
?
10
20
26
29
Icifi1a - Sanitized Coov AoIDrov
35
Having at hand the data on diurnal variations of the possible radiation
and comparing them, according to formula (27), with data of observations
on total radiation, it is easy to compute the diurnal variations of co-
efficient k and to determine its average relationship to the altitude of
the sun.
This relationship, determined from calculation data for several points
in the USSR, is presented in fig. 4.
he
-
50
40
30
.20
10
0 A
0 .5 10 15 20 25 30 35 40 45 .50 55 N ;02
Figure 4
Relationship of coefficient k
with the sun's altitude.
As can be seen from this graph, the magnitude of coefficient k decreases
with the diminishing height of the sun. The reason for such changes is
apparently found in the fact that, in the presence of clouds the increasing
length of the sunbeam path in the atmosphere diminishes considerably the
amount of radiation that reaches the earth's surface, as compared with the
amount during cloudless conditions.
Using formula (27), table 3 and fig. 4, the diurnal variations of total
radiation for average conditions could be computed. The question of the
possibility of using this method for calculating the total radiation for
short periods of time is still not clear.
Having at hand the data of total radiation, the value of the albedo of
the underlying surface for short-wave radiation must be computed to enable
us to determine the amount of absorbed radiation.
At present, ample data from observations on the mean values of the al-
bedo for various underlying surfaces are available. Among the numerous
works of determining the albedo we will mention the papers by A. Angstrom
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/28: CIA-RDP81-01043R002500010003-6
36
_
(1925a), A.A. Skvortsov (1928 gig), N.N. Kalitin (19* glg7), B.M.
Gal'perin (1938 547), P.P. KuzImin (1939 J467),I.N. IAroslavtsev (1952
g42/),T.V. Kirillova (1952 5217), which inauded surface observations
of the albedo; and works by L.I. Zubenok (1949b 50g), Fritz (1949), and
V.L. Gaevskif (1953 537) where the albedo of the underlying surface was
determined from an airplane.
The consolidated results of albedo measurements for various types of
surfaces have been given in works by Budyko (1948:#97), Berlfend (1948
017), Gaevskif (1953 537), Kondratiev (1954 537 and others. The mean
values Of the albedo', obtained by the most reliable measurements in vari-
ous physical geographical conditions, are presented in table 4.
Albedo of the natural
Table 4
surfaces.
Types of surface
Albedo
Types of surface
Albedo
Snow and ice
Fields, meadows, tundra
Fresh, dry snow
0.80-0.95
Rye and wheat fields
0.10-0.25
Pure, white snow
0.60-0.70
Potato plantations
0.15-0.25
Polluted snow
0.40-0.50
Cotton plantations
0.20-0.25
Sea ice
0.30-0.40
Meadows
0.15-0.25
c
Dry steppe
0.20-0.30
I 'k
Tundra
0.15-0.20
Bare soil
Forests
Dark soils
0.05-0.15
Moist grey soils
0.10-0.20
Coniferous forestb
0.10-0.15
Dry, clay or grey soils'
0.20-0.35
Deciduous forests
0.15-0.20
Dry, light, sandy soils
0.25-0.45
37
For better schematic climatological computations of the absorbed radia-
tion, it is more convenient to use the more generalized average values of
the albedo, which are shown in table 5 (Budyko, BerlAnd, Zubenok(1954b
L527).
From data in tables 4 and 5 we can see that) in moderate altitudes the
values of the albedo from the land surface will change considerably in the
annual course, reaching the maximum in winter months when a stable snow
cover is observed.
Table 5
Mean values of the albedo for the in types of natural land surfaces.
Stable snow cover of higher latitudes
(60? and higher)
0.80
Stable snow cover of the middle latitudes
(below 60?)
0.70
Unstable snow cover
0.45
Coniferous forest
0.14
Tundra, steppe, deciduous forest, savanna in the moist season
0.18
Savanna in the dry season and semideserts
0.25
Deserts
0.30
The highest values of the albedo are observed in winter in the high
latitudes, where the surface of snow is preserved pure and is not polluted,
since the air contains only insignificant amounts of dust. Very large
values of the albedo for fresh snow are also noticed in moderate latitudes.
Compared with that in moist areas, a higher albedo has been observed, in
dry regions and especially deserts. Even km, the albedoes measured in
deserts are subject to wide fluctuations 2), however, as a rule, they are
still larger than that of the vegetation covered surface.
The modern investigatigps by LA. fkroslavtsev (1952 5497), V.L.
Gaevski/ (1953 /737), K. IA. Kondrateev and N.E. Ter-Markariants (Kondratt-
ev, 1954 /1.317),'Wnd other authors, have shown that the values of the land
surface albedo often change considerably during the day. With the lower
altitudes of the sun (in the morning and evening hours), the albedo is
2T The color of soil surfaces in deserts is very variable, which provides
for a corresponding variability of albedoes and this fact is oftentime en-
countered even within a limited geographical, region.
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38
usually considerably larger. The reason for this is seen in the different
reflective capacity of the rough underlying surfaces, for sun rays falling
at different angles (at high sun, its rays penetrate deep into the vegeta-
tion layer and are absorbed there, whereas at low sun the rays do not pene-
trate as much into the vegetation layer and a larger portion is reflected
by the surface.).
Besides, the diurnal variations of the albedo are sometimes also affected
by the spectral composition of short-wave radiation at different heights of
the sun.
In climatological calculations of diurnal variations of the amount of
absorbed radiation, the relationship between the value of the albedo and
height of the sun, as found by L.A. Biriukova (1955 Z.32.7), from observa-
tional data, could be applied. Birrikova has noticed that, for the snow-
less period the albedo in its diurnal variations changes diurnally, de-
pending on the height of the sun and cloud amounts. It has also been found
that an increase in cloudiness diminished the degree of dependence of the
albedo on the height of the sun, because the increase in cloud amounts re-
duced the direct sun radiation and augmented the diffused one, the absorp-
tion of which does not depend directly on the height of the sun.
The relationship between Aa (difference between the value of the albedo
at a given hour and at noon) and the height of the sun under average con-
ditions of cloudiness is presented in fig. 5.
ho
50
4.5
40
35
30
25
20
1
5
10 12 14 16 18 20 od -102
Figure 5
Dependence of the albedo on the sun's altitude.
39
This graph can be used for an approximate estimation of the diurnal
variations of absorbed radiation during the snowless periods. When there
is a snow cover, according to Biriakova, there is no need of estimating
the albedo variations in determining the amount of absorbed radiation.
The albedo of water surfaces is, on the average, less than that of most
of the natural land surfaces. A relatively great absorption of short-wave
radiation in water reservoirs is explained by the fact that the sun rays
penetrate the upper translucent water layers, where they are scattered and
almost completely absorbed. This is why the albedo of muddy water reser-
voirs is considerably higher.
For direct radiation the albedo of a water surface depends greatly on
the altitude of the sun, and varies from a few per cent at high sun to
almost 100% for the sun near the horizon.
The dependence of the albedo on the angle of the sun rays could be
calculated theoretically by Fresnel's formula. Many authors have shown
that theoretical calculations of the albedo for direct radiation comply
fairly well with observational data (Kondrat'ev, 1954 L1377)?
The albedo of a water surface for diffused radiation varies in much
closer limits, and on the average it is on the order of 8-10%. The esti-
mate of albedo variations for diffused radiation, as dependent on cloudi-
ness and on other factors, might be of some importance in calculating
amounts of radiation reflected by the water surface. However, for those
climatological calculations of amounts of absorbed radiation that are of
interest to us (the absorbed portion is usually larger than the reflected
one), the possible variations of the albedo for diffused radiation are
insignificant and do not affect the results of the computations very much.
Because of a very close dependence of the albedo of water reservoirs
on the sun's altitude, the albedo of the total radiation shows a definite
annual and diurnal course.
To determine the average values of the albedo of water reservoirs.z. in
the investigations made by Budyko, Berland, Zubenok (1954a, 1954b /518g
527), the data of S.I. Sivkov (1952 ?2107) have been utilized. On the basis
of experimental data, and also using some results obtained by theoretical
calculations, Sivkov found a relationship between the albedo of the water
surface for direct radiation and the altitudes of the sun. Assuming the
albedo for diffused radiation as being, on the average, 0.10 and estimating
the mean relationship between direct and diffused radiation at various lati-
tudes, we found the values of the albedo of water surfaces for the total
radiation and they are given in table 6.
These data can be also used in calculations for the Southern Hemisphere,
taking into account the proper changes of seasons.
In climatological calculations of solar radiation absorbed by water
reservoirs, it must be kept in mind that, the change in the state of water
surfaces produced by the rise of waves, exerts a definite effect on the
albedo value. However, it must be pointed out that, these changes cannot
affect, to any substantial degree, the values of absorbed radiation. Since
the mean values of the albedo of, water surfaces usually do not exceed 0.10,
it must be clear that, the comparatively large changes in this value will
affect the values of absorbed radiation only to a relatively insignificant
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/28 CIA-RDP81-01043R002500010003-6
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degree. This permits a neglect of the effect of waves on the albedo when
calculating the sums of absorbed radiation for periods on the order of a
month, of ten days, etc.
Table 6
Water surface albedo for total radiation.
41
Angstram or with some instruments that were previously calibrated with it.
This pyrgeometer, as was discovered later, gave substantially exaggerated
readings (M.E. Berland and T.G. Berland, 1952 Logy.
The most satisfactory, of all modern instruments for measuring outgoing
radiation, is the effective pyranometer by Anishevskirand the vibrational
pyranometer by Falkenberg, though these instruments are not without fault
either. Observational data, obtained by various instruments measuring the
effective outgoing radiation, have often been used for determining the rate
of dependence of the effective outgoing radiation on meteorological factors.
Most of the formulas connecting the value of the effective outgoing
radiation under a cloudless sky with the temperature and humidity of the
air, have the following form:
Lat. J F PI A Mj J A S 0 ND
4==ce4(aid-bi?10-cl, (28)
700 N
60
50
40
30
20
10
0
-
0,20
0,16
0,11
0,09
0,07
0,06
0,06
0,23
0,16
0,12
0,09
0,08
0,07
0,06
0,06
0,16
0,11
0,09
0,08
0,07
0,06
0,06
0,06
0,11
0,08
0,07
0,07
0,06
0,06
0,06
0,06
0,09
0,08
0,07
0,06
0,06
0,06
0,06
0,06
0,09
0.07
0,06
0,06
0,06
0,06
0,06
0,06
0,09
0,08
0,07
0,06
0,06
0,06
0,06
0,06
0,10
0,09
0,07
0,06
0,06
0,06
0,06
0,06
0,13
0,10
0,08
0,07
0,06
0,06
0,06
0,06
0,15
..0,14
0,11
0,08
0,07
0,06
0,06
0,06
0,19
0,14
0,11
0,08
0,07
0,06
0,06
or
0,21 10.0? (a24-b2-pfe), (29)
0,16
0,12 where 4-- is the effective outgoing radiation, 0-- air temperature,
0,0g
0,07 e--vapor pressure, al, b c? a2 and b2--coefficients.
0,07 The first of these equations was suggested by Angstrdm, the second by
0,06 Brunt.
The coefficients in formula (28) and (29) were determined, in some in-
vestigations, from observational data.
In climatological calculations of effective outgoing radiation, the
Angstrom formula had earlier been used with the coefficients given in
In the calculations of radiation balance it is necessary to take into
account not only the amounts of short-wave radiation lost by reflection
but also the loss of radiation heat through the effective outgoing radia-
tion.
The radiation of the underlying surface follows the Stefan law and is
equal to sat cal/cm2/min., where0.--is the temperature of the surface,G--
-the Stefan-Boltzmann's constant, which according to recently obtained
data is equal to 8.14 ? 10-11- s-- is the coefficient which characterizes
the deviation of radiation of the given surface from that of a black body.
According to measurements made by Aleksandrov and Kurtener (1941 /17),
Falkenberg (1928) and other authors, the values of coefficient s for the
most natural surfaces are equal to 0.85-1.00.
A considerable portion of the flux of long-wave radiation that is radi-
ated by the underlying surface is compensated by counter radiation from
the atmosphere, which depends mainly on the content of water vapor, air
temperature, and cloud conditions.
The methods for measuring counter radiation from the atmosphere and
alSo for the effective outgoing radiation have been under development for
a long time, but only recently the instruments for measuring outgoing radi-
ation at various hours without sizeable errors have been contructed. The
instruments that were employed earlier had some constructive defects and
oftentimes had a faulty calibration, which was the reason for the exag-
gerated values of the effective outgoing radiation /this is explained by
the fact that the calibration was usually done with the pyrgeometer of
Linke's meteorological textbook (Linke, 1934), a1=0.194, 1;1.0.236, cl..
0.069, for determining the effective outgoing radiation in cal/cm2/min.
and air humidity In mm.
In researches of recent years the theoretical methods for determining
values of effective outgoing radiation have been developed. In this field
the papers by K. A. Kondrat'ev (1949a, 19491) 0:33 & 134J; etc.) were of
great significance. He established and put in use the scheme of a dif-
ferentiated accounting of the spectrum of absorption coefficients of long-
wave radiation in the atmosphere.
Utilizing the results obtained by R. fA. Kondrat'ev, M.E. Berland has
established a theoretical relation of the effective outgoing radiation in
a cloudless sky to air temperature and humidity (M.E. Berland and T.G.
Berlfand, 1952 A-47).
This relation an be approximately expressed in the following analytical
form:
/0=S004(0,39--0,0581re), (30)
where e--is in mm., cal/cm2/min.
For practical computations it is convenient to use table 7, which has
been computed according to Berliand's calculations.
It should be noted that the relation that has been established by M.E.
Berland, theoretically, turned out to be very close to the empirical re-
lationship which was found by Bolz and Falkenberg (1949) from 1320 obser-
vations taken with a vibrational pyranometer under a cloudless sky.
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50-Yr
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"orr,,et..,r7r5?-"I^
Besides the air temperature and humiditylsome other factors exert a
substantial influence on the effective outgoing radiation. These are:
amount of clouds and the difference in temperatures between the soil sur-
face and the air.
Table 7
Effective outgoing radiation with a cloudless sky
in kg-cal/cm2/min.
Humidity of the air mm
rempeL--
ature
-
1
-
2
3
_
4
1 5 .
6
7
8
10
12
15
-2V
0,11
-15
0,12
-10
0,13
0,12
_
-5
0,14
0,13
0,12
0
0,15
0,14
0,13
0,12
5
0,16
0,15
0,14
0,13
0,13
0,12
10
0,17
0,16
0,15
0,14
0,14
0,13
0,12
0,11
15
0,17
0,16
0,15
0,15
0,14
0,13
0,12
0,11
0,10
20
0,17
0,16
0,16
0,15
0,14
0,13
0,12
0,11
* 25
0,17
0,17
0,16
0,15
0,14
0,13
0,12
0,10
30
0,18
0,17
0,16
0,15
0,14
0,13
0,11
The estimate of the effect of clouds on effective outgoing radiation was
done earlier by formula:
1..4(1 --cn), (31)
where /-- effective outgoing radiation at the existent cloud amount, It -
- cloud amount in tenths, c-coefficient.
Angstrom found the average value of c to be 0.75, Askl6f, Dorno and
other authors found the average value of c varied for clouds of dif-
ferent heights - for high clouds the magnitude of this coefficient turned
out to be much smaller than that of lower ones. Considering this fact,
N.G. Efimov (1939 L977) suggested the following formula for calculating
the effective outgoing radiation dependent on clouds
1.4 [1 - (can, d- cHn?)] , (32)
where /ix, nc and. nB -are amounts of clouds for the higher, middle, and lower
layers, es, cc and c.-- the corresponding coefficients. Efimov estimated
0.1
43
these coefficients as being: 4=0.15.0.20; cc == 0.5-0.6; cit == 0.7-0.8.
In the work by I.G. latershtein and A.F. CHudnovskir (1946 ffogr) some
larger values of these coefficients are given:
c? =0,20, cc =0.6- 0.7, CH = - 0,9.
Recent investigations show that according to observational data the
effective outgoing radiation decreases with increasing cloudiness not
linearly but noticeably faster. Therefore, the following formula has been
developed for determining the effective outgoing radiation:
1=4,(1 - cni (33)
where n: 1.5-2.0
Obviously, when determining the value of c under overcast sky conditions,
this value will be the same whether derived by formula (31) or (33).
The theoretical cVculations of the mean values of coefficient c for
various latitudes has been done by M.E. Berland. In these calculations
he has taken into account the mean frequency of clouds at various heights
in various latitudes. The obtained values of coefficient c are presented
in table 8.
Table 8
The mean values of coefficient c .
,0 75
70
65
60
55
50
45
40
c 0.82
0.80
0.78
0.76
0.74
0.72
0.70
0.68
?. 35
30
25
20
15
10
5
c 0.65
0.63
0.61
0.59
0.57
0.55
0.52
0.50
Smaller values of this coefficient in lower latitudes are explained
mainly by greater heights of middle layer clouds in these regions.
In some works (Kuzsmin, 1948 D-.47; Bolz, 1949) the effect of clouds on
outgoing radiation is taken into account by introducima corrections but
this correction does not refer to the effective outgoing radiation, but to
the value of the counter radiation from the atmosphere. As has been shown
by K. tA. Kondrat'ev (1951 D-30, such a method for calculating the effect
of clouds on outgoing radiation has no substantial advantages in comparison
with the use of formulas (31) and (33).
In the latest works of the Central Geophysical Observatory on construc-
tion of radiation balance maps, the effective outgoing radiation bas been
calculated by the following formula:
t= - cn2) 4sob8(8-8). (34)
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The second term of this formula permits an estimate of the effect of
temperature differences between the underlying surface and the air on the
effective outgoing radiation.
When there is a difference in temperatures, the effective outgoing radi-
ation changes, and this change is represented by -sat ?s364, which is
approximately equal to:
4sa03(0?,
The theoretical explanation of this correction can be found in several
works (Kondrattev, 1951 5357; M.E. Berland and T.G. Berland, 1952 g47;
and others).
When using formula (34) coefficient s was on the average taken as 0.9,
values c and 4 were computed from tables 7 and 8. The temperature of
the active surface for water reservoirslcan be determined from observe
tional data. Since there are usually no reliable data on temperatures of
the underlying surface on the mainland it is feasible to use an indirect
method.
In the author's works (Budyko 1949a 527, 1950b gy and others), the
turbulent stream of heat has been determined by formula: /)==b&--69,
where b__ is the coefficient of proportionality (more details about this
relationship can be found in ?4). Taking into account this relationship
and also formulas (4), (5) and (34) the following equation may be set up:
. 4s003 (0 e) (Q+) (1 -- a) -40(i -- al2) -- LE -- A
b 0315)
?1-4s.70
The term TiRiE is variable and, in particular, it depends substantially
on the intensity of the turbulent exchange in the air layer near the ground.
However, considering the fact that the term 4s093(6,.--0) usually presents
a comparatively small correction to the radiation balance value (except
-wisame-
for the cold season in temperate and higher latitudes), we can use, for
art approximate calculation of radiation balance, just the mean value of
the mentioned term.
The results of the computations permitted the following conclusions
about the average climatic values of the term ,.?_.
4 scre3 ?
1) For conditions when
the value of the ratio b is, on the average, 3;
4 so03
2) For conditions when
(Q-1- q) (1 ?a) ?4C1 ?a2) ? LE ? A> ,
(Q4-4) (1 a) ? 4(1 ? at') ? LE ? A