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FACTORS INFLUENCING THE MAGNITUDE
OF THE NOCTURNAL INVERSION AND THE MINIMUM TEMPERATURE
By
J. Leith Holloway, Jr.
Submitted in Partial Fulfillment
of the Requirements for the Degree of Master of Science
at the Massachusetts Institute of Technology
May 25, 1953
Table of Contents
Abstract
Two summers of wind, temperature,
and cloudiness data taken at the Brookhaven National Laboratory are analyzed
statistically. Empirical equations are derived for the maximum magnitude of the
of the nocturnal ground inversion between the 410- and 37-foot elevation given the
cloudiness and mean 12-hour 410-foot wind speed during the night. Also, equations
are derived for predicting the fall of temperature from 1830 EST to minimum from
the cloudiness and the 410-foot wind speed. In these equations the magnitude of
the inversion and the fall of temperature to minimum are inversely proportional
to the 410-foot wind speed and the amount of cloudiness. The effect of advection
on the inversion magnitude and temperature fall is determined by examining the
prediction errors of the equations classified according to wind direction. It is
found that the magnitude of the inversion is increased by warm advection and
decreased by cold advection. The fall of temperature to minimum is decreased by
warm advection and increased by cold advection. Finally, the relative effect of
low and high cloudiness upon the net long-wave radiation is estimated from a study
of the equations derived in this thesis.
Thesis Supervisor: James M. Austin
Title: Associate Professor of Meteorology
ACKNOWLEDGMENTS
The author wishes to thank Professor James M. Austin for his assistance as
thesis adviser and Mr. Maynard E. Smith, Mr. Irving A. Singer, and the entire
Meteorology Group at the Brookhaven National Laboratory and Mr. Raymond C.
Wanta of the U.S. Weather Bureau Office at Upton, N.Y. for their guidance while
the author was making his preliminary study at Brookhaven. Also, the author's
appreciation goes to Dr. C. F. Brooks, Director of the Blue Hill Observatory,
Milton, Massachusetts, for his help in locating important references and to
Miss Cynthia Silver for typing the manuscript.
TABLE OF CONTENTS
I. Introduction
II. History of the Subject
III. Instrumentation, Data, and Description of the Site
IV. Nocturnal Inversion
A. Formation and Development of the Inversion
B. Climatology of Inversions at Brookhaven
C. Prediction of the Magnitude of the Inversion
V. Prediction of the Minimum Temperature
VI. Effect of Advection on the Inversion and the Fall of Temperature to Minimum
VII. Conclusions and Recommendations
Figure 1. The 420-foot Tower at the Brookhaven National Laboratory.
Figure 2. A close-up view of the levels of the tower.
Table I. Mean Temperature Differences at Brookhaven during 1951
Table II. Mean Maximum, Minimum, and Daily Range during June 1951
Table III. Mean Deviation of Data from Values
Predicted by the Regression Functions
Bibliography
I. INTRODUCTION
The magnitude of the nocturnal ground inversion and the minimum temperature at
a station are influenced by a great number of factors. Since the strength of the
inversion and the minimum temperature are intimately related, factors influencing
one are also important in controlling the other. The main factors influencing
both are the wind speed, the net nocturnal radiation, and advection. Less important
factors influencing the magnitude of the inversion and the minimum temperature at a
given locality include the release of latent heat of condensation with the formation
of dew and fog, the conductivity and moisture content of the ground, cold air
drainage from a neighboring area, and the length of the night. The effect of all
of the factors mentioned above has long been recognized, and forecasters consider
them qualitatively when preparing minimum temperature predictions.
The purpose of this study is to determine some quantitative relationships between
the strength of the nocturnal inversions and the minimum temperature and the wind
speed and the net nocturnal radiation estimated by cloudiness. These qualitative
relationships are to be modified by a qualitative study of the effect of advection.
The relations will be derived empirically. In the derivations the effects of
factors not considered will either be minimized if the effects are significant or
neglected if not.
The practical value of these relationships is apparent. Accurate minimum temperature
forecasts are valuable both in connection with the protection of agriculture from
frost damage and in the prediction of radiation fog. The prediction of the
magnitude of the nocturnal inversion is useful in connection with forecasting
winds near the ground and industrial pollution at night and in the morning.
Back to Table of Contents
II. HISTORY OF THE SUBJECT
The phenomenon of the nocturnal temperature inversion has long been observed
by means of the thermometers either on towers or at various elevations on hill
slopes (see references: 4; 6; 7; 8; 12; 21). However, no one until now to the
knowledge of the author has attempted to derive an empirical equation for
forecasting the magnitude of the inversion. Nevertheless, it will be worthwhile
to review what previous investigators have observed concerning the influence of
wind speed on the magnitude of the inversion. Durst (3) in 1933 suggested that
the breakdown of the ground inversion at night was caused by the development of
excessive wind shear between the top and bottom of the inversion as the magnitude
of the inversion increased. It should be noted in connection with this thesis
that with calm wind at the ground, the wind speed at an elevated level is
equivalent to the wind shear between this level and the ground. Smith (19) has
observed at Brookhaven that a higher wind speed is required to eliminate an
existing inversion than is required to prevent one from forming initially.
In contrast to the lack of empirical formulas for forecasting the inversion
magnitude, the literature contains a multitude of formulas for predicting the
minimum temperature. The reason for this greater emphasis on minimum temperature
formulas is doubtless that a forecast of the minimum temperature is of greater
practical value than a prediction of the magnitude of the inversion. Also, the
minimum temperature is considerably easier to observe than the inversion
magnitude.
Most of the minimum temperature formulas are derived empirically. Generally
they are based on the afternoon surface temperature, dew point and relative
humidity. A number of such formulas are contained in Supplement 16 of the
Monthly Weather Review( 18). Also, Ellison (5), and Sutton (20) discuss
minimum temperature formulas at length. Some of the formulas may be modified for
differences in wind speed and cloudiness but only by qualitative or semi-qualitative
means. That is, cloud amount may be specified as overcast, partly cloudy, or
clear, and wind speed as calm, light, moderate, or strong. In the hands of a
trained forecaster who knows his region the formulas, Ellison claims, should
predict the minimum temperature within 3F on most nights. Brunt (2) gives a
theoretical formula whereby the minimum temperature may be computed from the net
radiation, and the conductivity, specific heat, and density of the ground, and
the length of the night. In the derivation of his formula, Brunt assumes that
all the heat lost by radiation at night comes from the ground. knighting (14),
considering this assumption unrealistic, derives a rather complicated theoretical
formula for predicting the fall of temperature to minimum by considering that the
heat lost by radiation comes from both the ground and the air. However, these
theoretical formulas are of no practical value since the parameters contained
in them, such as soil properties, are variable from night to night and are
never known accurately.
This review of the subject indicates that empirical equations for forecasting
the magnitude of the inversion are needed, and that equations for the minimum
temperature depending directly upon cloudiness and wind speed probably would be
useful. Therefore, this study was undertaken to derive such equations.
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III. INSTRUMENTATION, DATA, AND DESCRIPTION OF THE SITE
This study was made from data taken during the summers of 1950 and 1951 at the
Brookhaven National Laboratory, Upton, Long Island, New York. At Brookhaven there
is a 420-foot micrometeorological tower on which aspirated resistance thermometers
(Thermohms) are mounted on booms at eight levels. See figures 1 and 2.
These levels are 9, 18, 37, 75, 150, 300, 355, and 410 feet.
Figure 1. The 420-foot micrometeorological
tower at the Brookhaven National Laboratory. The plume of smoke comes from a
stack extending to the 355-foot level on the tower. Diffusion of this smoke is
studied at Brookhaven.
Figure 2. A close-up view of the 18- and
37-foot levels of the Brookhaven tower. Note the Aerovanes on the tops of the
booms and the housings for the Thermohms extending downward from the ends of
the booms.
The temperatures measured are recorded every 5.8 minutes on a Leeds and
Northrup, triple range, twelve point, Micromax indicating recorder.
The temperature difference between 410 and 37 feet is recorded on a Leeds
and Northrup single point, Model R recorder. Standard Bendix-Friez Aerovanes
are installed on all levels of the tower except at the 9-foot level.
Wind speeds and directions indicated by these Aerovanes are recorded on
Esterline-Angus recorders. The temperatures indicated on the
Micromax recorder are accurate to within 0.10. However, the values of the
hourly average temperature differences determined graphically from the Model R
traces may be in error as much as 0.30 due to accumulated instrument and human
errors. The wind speeds indicated by the Aerovanes are accurate to within
two or three-tenths of a meter per second except at speeds less than five
meters per second where they are somewhat less accurate. For further information
on the instrumentation at Brookhaven see reference (15).
Data from the tower instruments along with regular surface observations have
been compiled by the Meteorology Group at the Brookhaven Laboratory since 1948.
However, mainly only 1950 and 1951 data are used in this study because of their
accuracy, completeness, and convenient tabulation.
The ground in the vicinity of the tower and the Meteorology Group's
building is essentially level. To the south of the tower lies a flat field
covered with tall grass and weeds and to the north, a pine forest about
twenty-five feet high. The standard U.S. Weather Bureau thermometer shelter
where the minimum temperatures are observed is located on the ground near the
Meteorology Group's building about 700 feet to the southwest of the tower.
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IV. NOCTURNAL INVERSION
A. Formation and Development of the Inversion
A brief discussion on the mechanisms producing and maintaining the ground
inversion should aid the reader in interpreting the results presented in this
thesis. The ground, being for all practical purposes a black body, is a better
long-wave radiator than the air. Therefore, at night the ground cools much
more rapidly by radiation than the air. Thus, the air in contact with the
ground cools faster at night than the free air. The free air will be defined
here as the air several hundred feet above the ground. As long as there is
a temperature decrease with height in the lower atmosphere during the evening,
the cooling at the surface will be distributed upward readily by turbulent
mixing, and the free-air temperature will fall almost as rapidly as the surface
temperature. However, when inversion is formed, the stratification in the
lower atmosphere becomes stable, and convective heat exchange is damped out.
Therefore, the free air is virtually isolated from any further surface cooling.
One might say that the free air is then insulated against the coldness below at
the surface by the greatly reduced eddy conductivity of the inverted lower
atmosphere. It has been found in this study that almost simultaneously with the
formation of the inversion, the free-air temperature as a rule decreases its
rate of fall noticeably and remains nearly constant throughout the rest of the
night whereas the surface temperature generally continues to fall steadily until
morning. However, if there is cold advection, the free-air temperature will
continue to fall even after the inversion has formed. This decrease in
temperature results mainly from the horizontal influx of cool air from a colder
region, not from vertical transport of cool air from the surface. On the other
hand, with warm advection the free-air temperature may rise during the inversion
while at the same time the surface temperature is continuing to fall due to
radiation.
After the inversion is formed, its development during the night is controlled
principally by the interaction of two opposing forces, namely, radiation and wind.
Radiation tends to increase the strength of the inversion by indirectly cooling
the surface air, whereas the wind tends to decrease the inversion by causing
vertical mixing of the air near the ground. In addition to radiation and wind
speed, a third variable which affects the magnitude of the inversion is the
sign of the advection. Cold advection decreases the strength of the inversion
by transporting colder air to higher levels faster than to the surface. On the
other hand, warm advection increases the inversion.
B. Climatology of Inversions at Brookhaven
Large inversions and low minimum temperatures are favored at Brookhaven by the
surface of sandy soil prevalent here. Sandy soil cools rapidly by radiation
because of its low conductivity. Therefore, 100 inversions and summer minimum
temperatures below 45F are common here. The maximum inversion recorded was
17.8C between the 9- and 355-foot levels in the early morning of 28 December
1950. The temperature at the 9-foot level was -25.6C while the 355-foot
temperature was -7.8C. An almost equally strong inversion of 17.7C occurred on
the morning of 17 December 1948. At this time the surface temperature was
-13.4C. A minimum temperature of 33F wass reported on the morning of 9 September
1952. However, inversions at Brookhaven probably appear large only because
detailed observations in the lowest several hundred feet of the atmosphere are
still relatively rare especially in rural areas where the nocturnal inversions
are most pronounced and the minimum temperatures lowest. Data from other
meteorological towers and soundings show that large inversions are also common
in a number of other areas (7; 9; 16; 21).
The nocturnal ground inversion is generally rather shallow. On most nights
the 420-foot Brookhaven tower extends above the top of the inversion. On many
nights eighty per cent of the temperature difference in the inversion occurs
below the 150-foot level.
Of twenty-three large inversions (410- to 37-foot temperature difference
greater than 11C) reported from January 1950 to September 1952, nearly half
occurred in September and October. It has been discovered elsewhere (8) that
both the most stable and unstable atmospheric conditions occur in the summer.
Probably warm advection off the Atlantic Ocean in autumn is instrumental in
shifting the period of maximum stability at Brookhaven from summer to fall.
The mean diurnal variations of surface and free-air temperatures are
illustrated in tables I and II. Nine- and 355-foot temperatures at 0300, 0700,
1100, 1500, 1900, and 2300 EST are averaged for the entire month of June 1951.
These data are presented in Table I.
This table shows that in the mean the 355-foot temperature tends to become
steady at night whereas the 9-foot temperature continues to fall throughout the
night. Also included in this table are the mean temperature differences between
these two levels at these six times and the mean temperature for the month at
each level. The mean maximum and minimum temperatures and the mean daily
temperature ranges at the two levels for June 1951 are tabulated in
Table II. Notice that the mean
daily temperature range at 355 feet during June 1951 was only 54 per cent of the
mean range at 9 feet. This decrease in the amplitude of the temperature wave
with height has been observed at a number of other stations (1; 4). For
comparison, the average daily range of temperature at the base of the Eiffel
Tower in July is 9.20 whereas at the top of this 990-foot tower the diurnal
range of temperature is only 6.90 (4). Since the data in tables I and II are a
mean picture of the month, the effects of advection and differences in radiation
are approximately averaged out. For further information on climatology at
Brookhaven see references (17) and (19).
C. Prediction of the Magnitude of the Inversion
One of the purposes of this study is to determine a quantitative relationship
between the wind speed and the magnitude of the nighttime ground inversion.
The question arises as to what would be good criteria for the strength of the
inversion and the wind speed. The criterion chosen for the strength of the
inversion is the maximum hourly average temperature difference between 410 and
37 feet. An hourly average temperature difference is chosen in order to eliminate
the effect of sporadic fluctuations. In regard to a suitable wind criterion,
obviously a wind speed near the the surface would not be a good parameter, for
the surface wind almost invariably becomes calm during inversions. From a
forecast standpoint, the mean geostrophic wind speed for the night would be
the best parameter since this could be estimated from a prognostic pressure
chart. In a study of old data such as this, the geostrophic wind speed could
be computed from actual surface pressure maps. However, geostrophic wind is
difficult to estimate accurately from synoptic charts especially in a region
such as Brookhaven where the pressure patterns are complicated by land-sea
effects. Therefore, the mean wind speed from 1800 to 0600 EST at the 410-foot
level is used in this study as an estimate of the average geostrophic wind
speed during a given night. At Brookhaven the 410-foot wind very seldom
becomes calm at night. In fact, the wind speed at this level generally
increases and more nearly approaches the geostrophic speed during the night.
This phenomenon of the reversal of the diurnal variation of the wind speed at
levels above about 200 feet elevation has also been observed at other places
(10; 11). On the nights studied the mean 410-foot wind speed ranged from 2.1
to 11.4 meters per second.
Sixty-eight fogless, rain-free nights in the summer months (June through
September) of 1950 and 1951 are studied. These nights include those not having
inversions as well as those that do. The data are analyzed statistically by
the method of least squares. The regression function for the magnitude of the
inversion with respect to the one variable, wind speed is
I = 8.6 - 0.7 W, (1)
where
I is the maximum hourly average temperature difference between 410 and 37 feet
in centigrade degrees between 1800 and 0600 EST (positive during inversions),
and
W is the mean 410-feet wind speed in meters per second from 1800 to 0600 EST.
Note: Values of this hourly average 410- minus 37-foot temperature differences
are tabulated for each hour by the Meteorology Group. The maximum value for
each night is taken as I. Perhaps slightly higher values of I could have been
obtained on many nights by taking means over hour periods not beginning on the
hour.
The correlation coefficient for this regression function is -0.52. The correlation
is high enough to indicate that a good inverse relationship exists between the
wind speed at 410 feet and the magnitude of the inversion between 410 and 37
feet. Nevertheless, the relation is not good enough to be useful for predicting
the maximum strength of the inversion from a forecast of the 410-feet wind.
It is noteworthy, however, that equation (1) states that a ground inversion can
develop at Brookhaven even when the mean twelve-hour wind speed at 410 feet is
greater than ten meters per second.
In addition to wind speed, a second major factor influencing the magnitude of
the nighttime ground inversion is the amount of net long-wave radiation.
Therefore, in order to obtain a better equation for the magnitude of the
inversion, the effect of differences in radiation is added to the statistical
analysis. Since nocturnal radiation is not measured at Brookhaven, its
intensity has to be estimated by means of a meteorological variable which is
observed. Wet nocturnal radiation is controlled mainly by cloudiness, and
surface temperature and humidity. In this study the intensity of the net
radiation is estimated by the amount of cloudiness. The sixty-eight nights
chosen for this study are selected only from summer months so that surface
temperatures and humidities would be approximately the same for all nights.
A tendency toward reduced radiation at the end of the summer due to lower
surface temperature is probably approximately compensated by longer nights and
lower humidities occurring then. Also, nights with fog reported at any time
are excluded from this study since fog complicates the development of the
inversion in two ways. First, the formation of fog releases latent heat of
condensation which slows the fall of temperature at the surface. Secondly, the
presence of fog reduces the net nocturnal radiation. It is hoped that by
eliminating nights having fog, those with heavy dew fall would also be excluded
from this study. The presence of haze during some of the nights studied is
disregarded since measurements of nocturnal radiation by other investigators (13)
has shown that haze has no appreciable effect upon net radiation.
For convenience in the statistical analysis clouds are divided into only two
groups, low and high clouds, instead of the three groups common in synoptic
meteorology. Low clouds in this study are clouds classed as low or middle clouds
in present synoptic codes, and high clouds are the same as in synoptic
meteorology. This seems to be a logical division especially since the cloud
observations used were taken at night when low and middle clouds cannot be
easily distinguished. The number of tenths of low and middle cloudiness reported
at each of the twelve hourly observations from 1830 to 0530 EST are totaled to
obtain for a given night a number representative of the total amount of low
cloudiness as defined here. Thus, the maximum number obtained (for ten-tenths
low cloudiness all night) would be 120. The number representing the amount of
high cloudiness is obtained in the same manner. In the application of this
scheme, no hour is allowed to have a total of low, middle, and high clouds
greater than ten-tenths. The tenths of lower clouds always takes precedence over
the tenths of higher clouds. For instance, if six-tenths low clouds and
nine-tenths high clouds were reported one hour, hour-tenths of low and high
clouds would be computed on the basis of six-tenths low clouds and only
three-tenths high clouds.
When cloudiness variables are used in addition to the 410-feet wind speed, the
resulting regression function for the magnitude of the inversion is
I = 12.7 - 0.06 L - 0.01 H - 1.02 W, (2)
where
L is the number of hour-tenths of low cloud from 1830 through 0530 EST,
H is the number of hour-tenths of high cloud during the same period, and
I and W are the same as in (1).
The multiple correlation coefficient for this regression function is 0.78.
Note: The multiple correlation coefficient is always taken positive in
sign regardless of the signs of the regression coefficients.
Furthermore, the mean prediction error of (2) is only 1.5C. In this thesis the
prediction error of a regression function will be defined as the absolute value
of the difference between the observed and predicted values. Therefore, (2) is
a useful equation for predicting the maximum development of the nocturnal
inversion at Brookhaven in the summer.
The introduction of cloudiness into the analysis increased the absolute value
correlation coefficient by 0.26. However, this increase in correlation due to
the addition of cloudiness is only half the degree of correlation obtained
between wind speed and inversion magnitude in (1). This fact should indicate
that cloudiness is less important in controlling the magnitude of the 410- to
37-foot inversion than is the 410-foot wind speed provided cloudiness
and wind speed are independent of each other. This supposition was checked by
computing the regression function for the magnitude of the inversion with
respect to only the two variables, low and high cloudiness. This regression
function is
I = 4.2 - 0.03 L - 0.007 H . (3)
The multiple correlation coefficient for (3) is 0.31 which is significantly
smaller than the absolute value of the correlation coefficient of (1).
Therefore, the preceding supposition is correct. It also follows that for all
practical purposes wind speed and cloudiness are, indeed, independent of each
other at Brookhaven in the summer.
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V. PREDICTION OF THE MINIMUM TEMPERATURE
Since the minimum temperature is very closely associated with the strength of
the ground inversion, and high correlation between the magnitude of the inversion
and the wind speed and cloudiness indicates that an equally high correlation can
be expected to exist between the minimum temperature and wind speed and
cloudiness. Furthermore, a good empirical equation for predicting the minimum
temperature would be of definite practical value. However, the value of the
minimum temperature itself would not be a good variable to use in this study
since it is so much a function of the minimum temperature of the preceding day
that day to day variations in the temperature maxima would obscure the influence
of wind speed and cloudiness on the minima. Therefore, in order to avoid the
influence of day to day temperature changes on the minima, the fall of temperature
from near the time of sunset to minimum is used in this study as a measure of the
lowness of the minimum.
The temperature fall to minimum is analyzed statistically using data from the
same 68 nights used in the inversion study. The regression function for the
fall of temperature in respect to the mean 410-foot wind speed is
F = 21 - 0.9 W, (4)
where
F is the fall of temperature in Fahrenheit degrees from 1830 EST to minimum
observed at the instrument shelter.
The correlation coefficient of (4) is -0.30.
This is significantly smaller in absolute magnitude than the correlation
coefficient of (1). Thus, it appears that the wind speed at 410 feet is not as
good a predictor of the temperature fall to minimum as it is a predictor of
the magnitude of the inversion between 410 and 37 feet. The explanation for
this paradox probably lies in what occurs below the 37-foot level during an
inversion night. On some nights, the temperature stratification below the
37-foot level is nearly isothermal whereas on other nights the shelter
temperature may be as much as 10F colder than the 37-foot temperature.
During most inversions the 37-foot wind becomes nearly calm no matter what the
wind speed at 410 feet may be. Therefore, the 410-foot wind speed has little
effect on the temperature stratification below 37 feet. The thermal
structure below 37 feet is probably mainly influenced by the net radiation and
surface dew point. Thus, the wind speed at 410 feet plays a larger part in
determining the strength of the inversion between 410 and 37 feet than it does
in controlling the fall of surface temperature to minimum because the
temperature to minimum because the temperature fall at the ground is to a
large extent influenced by what occurs in the layer of air below the 37-foot
level whereas the inversion magnitude by definition here is independent of
this layer. Undoubtedly, if the criterion for the strength of the inversion
had been chosen as the temperature difference between 410 feet and a level
nearer the ground than 37 feet, the correlation between the 410-foot wind
speed and the magnitude of the inversion defined in this manner would have been
less than is obtained in (1). It should be remarked that the 410- to 37-foot
temperature difference is recorded at Brookhaven rather than the temperature
difference in a layer extending closer to the ground because it is considered
that the 410- to 37-foot temperature difference is more representative of the
stratification in the lowest 400 feet of the atmosphere than a temperature
difference affected by the thermal structure in the surface layer below 37 feet.
Cloudiness is next added to the analysis of the temperature fall to minimum.
The regression function for the temperature fall with respect to the three
variables, 410-foot wind speed, and the low and high cloudiness is
F = 32 - 0.014 L - 0.08 H - 1.6 W. (5)
The multiple correlation coefficient for (5) is 0.62 which is nearly as high as
that of (2). Also, the mean prediction error of equation (5) is only 4F. Thus,
(5) is good enough to be useful in forecasting the fall of temperature to
minimum at Brookhaven on summer nights without fog. If in actual practice (5)
predicts a minimum temperature far below the dew point at sunset, this indicates
that fog will probably form. Therefore, in such situations (5) should not be
expected to be accurate.
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VI. EFFECT OF ADVECTION ON THE INVERSION AND THE FALL OF TEMPERATURE TO MINIMUM
The sign and magnitude of deviations of data from the values predicted by the
regression functions (2) and (5) are definitely a function of wind direction.
This fact indicates that advection caused a large part of these deviations.
Since the multiple correlation coefficient of the temperature-fall regression
function (2), it appears that the sign of the advection has greater influence on
the temperature fall than on the magnitude of the inversion. This seems paradoxical
since one would think advection would have little effect on the surface temperature
during inversions due to accompanying light surface winds. However, advection is
quite instrumental in controlling the surface temperature before the inversion
is formed in the evening. At this time substantial wind exists at the surface.
Furthermore, the effect of advection upon the magnitude of the inversion is
relatively small because the inversion is not modified directly by advection but
by a differential of advection between the top and bottom of the inversion.
Table III gives the mean deviation of the
data from the values predicted by the regression functions classified according
to wind direction. The wind direction chosen for this analysis is the geostrophic
wind direction determined from the 0130 EST surface pressure map for the night in
question. It is thought that the direction obtained in this way would be more
representative of the type of advection present than a wind direction obtained
from the tower observations. On thirteen of the nights studied the pressure
gradient was so weak that the geostrophic wind direction could not be determined
with certainty. This table show that larger than normal inversions occur at
Brookhaven with west and northwest winds, and that inversions smaller than
expected develop on nights with north and northeast winds. The effect of
southwest winds on the strength of the inversion appears to be neutral. On the
other hand, temperature falls were less than the regression function predicted
with west and southwest winds and greater than predicted when the wind was from
the northwest, north, and northeast. Not enough data are available for winds
from the south, southeast, and east for conclusions to be made on the effect of
wind from these directions upon the inversion or the temperature fall. Therefore,
minimum temperature and inversion magnitude forecasts made using (5) and (2) should
be modified qualitatively by means of an estimate of the effect of advection based
on the forecast wind direction and the results shown in Table III.
The result that in the mean northwest winds are accompanied by larger inversions
than (2) predicts, probably does not indicate that northwest winds give warm
advection at Brookhaven, but that northwest winds bring drier air over the area
and increase the net outgoing radiation for a given amount of cloudiness. This
influence of the drier air probably affects the tendency for cold advection with
northwest winds to decrease the strength of the inversion. The sign of the
advection for different wind directions is better determined from the deviations
of data from values predicted by (5) than by (2), for advection produced deviations
are larger in the case of the equation for temperature fall. Therefore, it is
concluded that at Brookhaven in the summer warm advection generally occurs with
west and southwest winds, and cold advection with northwest, north, and northeast
winds. The sign of the advection with south, southeast, and east winds is
undetermined for lack of data.
Since advection caused a great deal of the deviation of data in (5), a better
equation for the temperature fall can be obtained by minimizing the effect of
advection. The strength of the advection is proportional to the wind speed and
the strength of the temperature gradient. Thus, the influence of advection can
be reduced by restricting the study to nights with light wind. Therefore, from
the original 68 nights studied, 32 are chosen during which the mean 12-hour
410-foot wind speed did not exceed 7.5 meters per second. Since the range of
wind speeds is restricted, the effect of differences in wind speed on the
temperature fall is thereby minimized. Thus, wind speed can be regarded as
constant in the study of these 32 nights especially since wind speed is not a
very good predictor of temperature fall in (4). The resulting regression
function for the temperature fall to minimum with respect to low and high
cloudiness is
F = 22 - 0.12 L - 0.05 H. (6)
The multiple correlation coefficient for (6) is 0.80, and the mean prediction
error is only 3F. Therefore, (6) should be very useful for forecasting minimum
temperatures at Brookhaven in the summer. The advantage of this equation is that
as long as it can be predicted that the mean 12-hour 410-foot wind speed will not
exceed 7.5 meters per second on a given night, the minimum temperature can be
predicted from from (6) without need of a more detailed 410-foot wind speed
forecast. Only a cloud forecast is needed. As with (5), equation (6) should
not be expected to be accurate when the minimum it forecasts is far below the
evening dew point, for then fog would probably form.
The deviation of data from the values predicted by (6) may come from the effect
of differences in wind speed or advection not completely filtered out of the data
by restricting the study to nights having only light wind. However, more
probably the deviations come mainly from errors introduced into this work by
assuming that the same net radiation always occurs with a given amount of
cloudiness. Also, the deviation may be caused by the multitude of minor factors
which had to be neglected from this study. For instance, the moisture content
of the soil influences the fall of temperature at night by affecting the
conductivity of the soil. The presence or absence of cold air drainage from
higher areas on the northern shore of Long Island during a particular night
could also affect the temperature fall at Brookhaven. However, a thorough
analysis of any of these minor factors is beyond the scope of this thesis.
The reader may have noted that the ratio of the regression coefficients for
low cloudiness to that for high cloudiness is different in each of the
regression functions containing cloudiness. This ratio varies from six in (2)
to one and three-quarters in (5). Therefore, it is difficult to derive from
these regression functions any conclusions concerning the relative effects of
low and high cloudiness upon the strength of the inversion, the fall of
temperature to minimum, or the net nocturnal radiation. However, since (6) has
the highest correlation coefficient and contains only cloudiness variables, it
probably most accurately indicates the relative effect of low and high cloudiness
upon the net radiation. Thus, low cloudiness, as defined in this thesis, is
probably about two and one-half times as effective in reducing net radiation as
high cloudiness.
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VII. CONCLUSIONS AND RECOMMENDATIONS
A useful empirical equation can be derived for the magnitude of the nocturnal
ground inversion or the fall of temperature from sunset to minimum based on the
amount of cloudiness and the wind speed several hundred feet above the ground.
Deviations of the inversion magnitude and the temperature fall from the values
predicted by the equations are to a large extent a function of the sign of the
advection. Therefore, minimum temperature and inversion forecasts made from
equations presented in this thesis should be modified qualitatively according
to the sign of the advection. The empirical equations derived for Brookhaven
in this study do not necessarily apply to other localities. Studies similar to
this should be made in other areas to see how much modification the equations
in this thesis must undergo for them to be useful elsewhere. In fact, a more
thorough study at Brookhaven, with emphasis upon other seasons beside summer,
would be worthwhile.
Bibliography
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BIBLIOGRAPHY
1. Ballard, J. C., 1933: The diurnal variation of free-air
temperature and the temperature lapse rate.
Monthly Weather Review, Vol. 61, No. 3, pp 61-80.
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London, Cambridge University Press, 124-46.
3. Durst, C. S., 1933: The breakdown of steep wind gradients
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Quarterly Journal of the Royal Meteorological Society, 59: 131-36.
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Monthly Weather Review, 56, 485-95.
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Vol. 10, part I, Appendix C, 131-7. (Blue Hill data)
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Cambridge, Mass., Harvard University Press, 49, 80-5.
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New York, McGraw-Hill Co., 213-5.
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