A THEORY OF ANNUAL TEMPERATURE VARIATION

94 Pages·03.006 MB·English

by  GLEESON, THOMAS ALEXANDER

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•®Z Gleeson, Thomas Alexander, 1920-
1950 a theory of annual temperature
variations. New York, 19^0*
xiii,77 typewritten leaves, diagr
29cm.
Thesis (Ph.D.) - New York Univer­
sity, Graduate School, 1950*
Bibliography: p.76-77•
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THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
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SEW 1081 0NIV5R6ITY
milVlRSITI HEIGHTS
A THEORY OF ANNUAL TEMPERATURE VARIATIONS
By
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THOMAS A. GLEESON
April 1, 1950
A dissertation in the department of
meteorology submitted in partial ful­
fillment of the requirements for the
degree of Doctor of Philosophy at New
York University.
ACKNOWLEDGMENTS
Professors B. Baurwitz, J. E. Miller and Dr. E. W.
Hewson have offered useful comments on this work, which are
appreciated. The author is particularly grateful to Pro­
fessor H. A. Panofsky for very many valuable suggestions and
criticisms, and to Dr. W. A. Baum for providing facilities
and suggestions that were exceedingly helpful. Mrs, J.
Massey very kindly typed the manuscript.
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PHELIMIHART STATEMENT OP OBJECTIVES
The primary purpose of this thesis is to obtain a theoretical
representation of the annual variation of temperature at a geographic
location in terms of important components of the vertical energy bal­
ance for the atmosphere and earth. To this end, the procedure outlined
below is followed.
Three models are studied consecutively:
Model 1. The troposphere is considered to be composed of two lay­
ers, (l) a surface layer of constant mean density wherein a vertical
heat exchange coefficient is assumed to increase linearly with eleva­
tion, and (2) an upper layer wherein the exchange coefficient is assumed
to be constant but the decrease of density with elevation is recognized.
The surface layer of the earth is a third layer within which the soil
density and coefficient of heat conduction are assumed to be constant.
Differential equations of vertical heat transport are chosen to
represent each of these three layers. Solutions to these equations are
obtained and inter-related by suitable conditions at intervening bound­
aries. In particular, one of the two boundary conditions at the earth's
surface consists of a theoretical energy balance composed of factors that
influence the temperature. When the boundary conditions are satisfied,
the annual temperature variation may be computed by means of values for
these factors.
Data exist for all factors but the exchange coefficient in air.
Evaluation of this coefficient is then necessary. By trial and error the
annual temperature variation at a chosen station is found to be determined
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accurately when this coefficient is assigned a particular value which
is approximately the same at all elevations.
Model 2. The above result then suggests that a surface layer of
the troposphere wherein the exchange coefficient varies linearly with
elevation is not necessary. This surface layer is no longer postulated;
the solution for the upper layer is extended to include the total depth
of the troposphere. The surface boundary conditions and the solution to
the differential equation for the surface layer of the earth are retained
from the first model.
Unsatisfactory theoretical descriptions of the annual temperature
variation at the same station are obtained by means of this second model.
Inherent in this model is an unreal!stically large decrease of vertical
heat transport upward from the surface.
Model *3. The troposphere is then considered to be one layer charac­
terized by a constant mean density for which there exists a constant mean
exchange coefficient. A differential equation of heat transport is chosen
to represent this layer. The solution to this equation is related to the
previous solution of the differential equation for the surfacel ayer of the
earth by means of previous boundary conditions at the surface.
This third model is simpler to use than the first model and yields
better results than the second model when applied to annual temperature
variations at the same station. Therefore the first two models are neg­
lected entirely, while the third model is applied to temperature varia­
tions at variousl evels at three additional stations, and is used to com­
pute the vertical heat exchange coefficient in the ocean.
Neglect of certain physical processes, particularly advection,
limits the regions wherein the theoretical representation of annual
temperature variations can he successful.
CONTENTS
ACKNOWLEDGMENTS........................................ ii
PRELIMINARY STATEMENT OP OBJECTIVES..................... iii
TABLE OP SYMBOLS....................................... ix
INTRODUCTI ON............................................1
PAST I. THEORETICAL CONSIDERATIONS OP HEAT VARIATIONS
IN THE LOWER TROPOSPHERE.........................A
PART II. THEORETICAL CONSIDERATIONS OF THE HEAT
VARIATIONS IN THE GROUND.......................11
PART III. BOUNDARY CONDITIONS AT THE EARTH*S
SURFACE..................................... 13
PART IV. THEORETICAL CONSIDERATIONS OF HEAT VARIATIONS
IN THE UPPER TROPOSPHERE....................... 25
PART V. CONSIDERATIONS OP CERTAIN QUANTITIES.............30
PART VI. AN ALTERNATIVE SOLUTION FOR THET ROPOSPHERE.......Al
PART VII. APPLICATIONS OP MODEL THREE................... A7
PART VIII. SECONDARY RESULTS OBTAINED BY MEANS OP
MODEL THREE.................................66
PART IX. CONCLUSIONS...................................73
BIBLIOGRAPHY...........................................7 6
TABLES
TABLE 1, Amplitudes of the annual temperature
variations for one year and computed
values of Kc at Seahrook Farms, New
Jersey.................................. .8
TABLE 2. Ratios of average evaporation to average
precipitation for various types of "bare
soil. ........................... 18
TABLE 3. Mean monthly temperatures (°C) for 7 A.M.
and 2 P.M., local time, at 8 mm and 2.2 m,
Potsdam, Germany..........................33
TABLE A. Data for Ely, Nevada......................35
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TABLE 5. Data for Hebron, Labrador................. 48
TABLE 6. Data for Ciudad Lerdo, Mexico..............51
TABLE 7» Data for Chicago, Illinois........... 53
TABLE 8. Data for the North PacificO cean.............67
TABLE 9. Eddy conductivities at various depths
in the Bay of Biscay and the Kuroshio
Area......... 70
FIGURES
FIGURE 1, Computed and observed annual variations of
temperature at 2 m above the surface,
Ely, Nevada..............................,36
FIGURE 2. Computed and observed annual variations
of temperature at 2 m above the surface,
Hebron, Labrador ..................... 50
FIGTJFE 3. Computed and observed annual variations
of temperature at 2 m above the surface,
Ciudad Lerdo, Mexico...............’......52
FIGURE 4, Computed and observed annual variations
of temperature at 2 m above the surface,
Chicago, Illinois........................5^
FIGURE 5. Maximum amplitudes and phase retardations
of the annual variations of temperature
in the ground, computed from Hebron data
and observed at Konigsberg................55
FIGURE 6. Computed and observed maximum amplitudes
and phase retardations of annual varia­
tions of potential temperature at the sur­
face, and at 3» 6, and 10 Ion above mean
sea level, Ely, Nevada................... 58
FIGURE 7. Computed and observed maximum amplitudes
and phase retardations of annual varia­
tions of potential temperature at the
surface, and at 3 and 6 km above mean sea
level, Hebron, Labrador...................59
FIGURE 8. Computed and observed maximum amplitudes
and phase retardations of annual varia­
tions of potential temperature at the
surface, and 3» 6* and 10 km above mean
sea level, Ciudad Lerdo, Mexico........... 60
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FIGURE 9. Computed and observed maximum amplitudes
and phase retardations of annual varia­
tions of potential temperature at the
surface, and 3» 6« and 10 km above mean
sea level, Chicago, Illinois..............6l
FIGURE 10. Computed and observed annual variations
of temperature at the surface, North
Pacific Ocean........................... 68
FIGURE 11. Theoretical energy balance in the ver­
tical direction at Ely, Nevada............ 71
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