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Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1589 – 1600

www.elsevier.com/locate/jastp

The e ect of the solar eclipse on the air temperature near the ground
Karol Sza lowski1
Faculty of Physics and Chemistry, University of LoÃdzÃ, LoÃdzÃ, Poland Received 1 December 2000; received in revised form 29 January 2002; accepted 25 April 2002

Abstract
This paper describes the e ect of the air temperature decrease in low boundary layer during the solar eclipse with special regard to in uence on convectional events. The phenomenon progress was modelled to predict solar radiation ux changes. Then the basic model of local ground and air temperature changes was constructed. The qualitative features of air temperature– time curve during the eclipse were explained. The e ect was investigated experimentally on the example of the partial eclipse observed from Szczawnica, Poland on 11th August, 1999. The results of the precise air temperature measurements were presented. The general shape of temperature curve was conÿrmed. The problem of convection intensity and temporal scales of convectional events was examined. It was observed that the temperature variance decreased over a factor of 2 in the maximum eclipse- centred, 50 min long time interval which depicts the reduced convection regime. In addition, the temperature spectrum for long periods obtained for this time range seem to di er signiÿcantly from one registered before and after. The convection near the maximum eclipse is characterised by a dominant temporal scale of 22 min, while before and after 11–13 min scale is the most important. c 2002 Published by Elsevier Science Ltd.
Keywords: ; Solar eclipse; Boundary layer; Air temperature; Convection; Temporal scale of convection

1. Introduction
Solar eclipses (especially the total ones) belong to the astronomical phenomena that have been known and observed since the earliest ages. Their terrestrial consequences are noticeable and important. Eclipses are connected with the rapid and short-time, impulse-like decrease of solar energy
ux reaching the area of its visibility, which can be exactly predicted before the occurrence of the phenomenon. Therefore, they cause noticeable changes in the atmosphere, whose main energy source is solar radiation. The strongest e ects concern the layers where solar UV radiation contributes to ionisation process (ionosphere) and the boundary layer which is in direct contact with the ground absorbing shortwave radiation. Eclipses support unique, speciÿc conditions which give the opportunity to numerous varied

meteorological research. Present research works include mainly upper atmosphere studies (in most ionospheric disturbances observations—see for example Bamford, 2001), investigations concerning the in uence on global and mesoscale circulation (acoustic gravity waves creation and propagation, BosÄka and SÄ auli, 2001), observations of chemical processes in the atmosphere (ozone layer changes, see ChudzynÃski et al., 2001). However, the e ects most important for the environment take place in the microscale and involve changes of the boundary layer parameters of physical (thermodynamic processes) and chemical nature (plants response for light level decrease which causes decrease of CO2 ux, etc.) (Fabian et al., 2001). Especially, the impact on air temperature can be important, as the stability and convective processes intensity change.

2. The theoretical model of the solar eclipse phenomenon

1 Private address: 93-414 LoÃdzÃ, Zespolowa 33=7, Poland E-mail address: karol sz@poczta.wp.pl (K. Szalowski).

The site of observation is characterised by its geographic co-ordinates as well as the height above the sea level. In

1364-6826/02/$ - see front matter c 2002 Published by Elsevier Science Ltd. PII: S 1 3 6 4 - 6 8 2 6 ( 0 2 ) 0 0 1 3 4 - 7

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Fig. 1. Geometric model of the solar eclipse.

order to describe the progress of the eclipse phenomenon, the knowledge of functions of time determining the apparent topocentric co-ordinates of the centres of the solar and lunar disc in the equinoctial system (corrected for refraction) and their angular radii is necessary. As the diameters and distances of the celestial bodies involved are relatively small, the spherical co-ordinates system may be replaced by cartesian one to simplify further considerations. To make the description of the eclipse more practical, some useful astrometric indexes visualising the progress of the real phenomenon are usually introduced, like: the magnitude of eclipse f(t), the eclipse obscuration g(t) and the squared length of the chord crossing the common points of the circumferences of the solar and lunar disc c2(t), as well as the moment of the beginning of the eclipse (the ÿrst contact tI), the moment of the maximum tmax and of the end of it (the fourth contact tIV) (in case of a partial eclipse) (Fig. 1).
All quantities are considered further as time dependent, and the values refer to the speciÿed time instant during the eclipse.
The most commonly used phase f is deÿned as a fraction of the solar disc diameter covered by lunar disc

f

=

x 2RS

;

(1)

where x is the angular length of the part of the solar disc diameter covered by the lunar disc, and RS the angular radius of the solar disc.
The x length is

x = RS + RL − d;

(2)

where RL is the angular radius of the lunar disc, and d the angular distance between the centres of solar and lunar disc,

d = ( S − L)2 + ( S − L)2:

(3)

The eclipse obscuration g is determined as a covered-to-total solar disc surface ratio

g = R2S : On the basis of geometric considerations we get

(4) as

= R2S( S − sin S cos S) + R2L( L − sin L cos L);

(5)

where the auxiliary angles are given by

S

=

arc

cos R2S

− R2L + 2dRS

d2

;

(6)

L

=

arc

cos R2L

− R2S + 2dRL

d2

:

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Fig. 2. Astrometric parameters during the 11th August 1999 eclipse in Szczawnica.

The c2 length is very useful, especially when determining the moment of the beginning or the end of the eclipse from observations, as it can be easily measured on the images of solar disc. It is expressed by

c2 = 4R2S sin2 S:

(7)

The tI and tIV moments are determined as the times when f(t) = 0.
The solar eclipse of 11th August 1999 was visible as the total one across Europe, at Middle East and in East Asia. The phenomenon was observable from Poland as a partial eclipse of large magnitude, between 81% in the Pomerania region (near Gdansk) and 93% in some parts of Beskidy Mountains. The most advantageous conditions for observation were in south Poland (Espenak and Anderson, 1997).
Taking into consideration advantageous climatic conditions (large probability of the day without cloud cover in August) and the large magnitude of eclipse, Szczawnica (South Poland) was chosen for the site of observation. The geographic co-ordinates of this site (obtained in WGS 84 system from measurements at the map SpisÄskaà Magura Pieniny. EdÃcia turistickyÃch maÃp 1 : 50 000, 3. Vydanie, Vojenskyà kartograÿckyà uÃstav, sÄ. p., Harmanec, 2000) are presented below:

= 20◦29 1 ± 4 E; ’ = 49◦25 36 ± 3 N;

h = 500 ± 10m:

The theoretical model of the phenomenon for the site speciÿed above was prepared on the basis of the highly accurate ephemerides for Sun and Moon provided via WWW and telnet by JPL Horizons On-Line Ephemeris System. The calculations covered the time range from 9 to

16 h UT with time interval of 1 min. The output variables were: the apparent topocentric co-ordinates in equinoctial system (corrected for refraction) and the observable angular diameter (for details see: Horizons User Manual, http://ssd.jpl.nasa.gov/horizons doc.html). On the basis of the mentioned tables, the values of eclipse parameters, such as f and g were calculated using the presented model of phenomenon. The determined values of f and g are plotted in Fig. 2.
The time moments tI and tIV were obtained from the Win-OCCULT v. 2.0.0 software (International Occultation Timing Organisation, ftp://ftp.lunar-occultations.com/pub/ Windows—Occult 2.0/), as the model presented above is simpliÿed and does not support enough accuracy to determine such moments (while being su cient for estimating g progress for radiation changes model) (Table 1).
The auxiliary observations included the recording of the phenomenon progress in real time using video camcorder with CCD of 1=3 diagonal were lead. The lens of focal length 66:3 mm and diameter 35 mm was protected with welder’s ÿlter of optical density of 12 (additional 6 and 12 ÿlters were used if needed due to changeable cloud cover). The front part of the camera was covered up by re ecting screen to prevent intensive heating. Its aim was to register the moments when the solar disc was covered by clouds.
3. The theoretical model of the near-ground air temperature changes during the solar eclipse
In the area covered by umbra or penumbra the change of the ux of incident solar radiation takes place. It involves decrease of the ux as well as the modiÿcations of the

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Table 1 Characteristic parameters of the eclipse in Szczawnica

First contact tI 9 h 30 min 44 s

Maximum of eclipse tmax 10 h 52 min 38 s

Fourth contact tIV 12 h 13 min 11 s

Maximal magnitude fmax 0.932

Fig. 3. Image of the lunar shadow cone over Europe taken by Meteosat-6 satellite (11th August, 1999, 10:50 UT). ? 2001 EUMETSAT, http://www.eumetsat.de/en/area5/special/eclipse 11081999.html.

spectral distribution of the incident radiation (due to spectral dependence of limb darkening, Koepke et al., 2001). The lunar shadow cone has an usual diameter of the order of magnitude of 103 km (Fig. 3), so it contributes to noticeable changes even in mesoscale in meteorological parameters at that area.
However, the changes most available for observations concern local, micrometeorological parameters. The most important indicator of thermodynamical processes is air temperature in the boundary layer, which can be very easily measured.
It is reasonable to introduce a simple theoretical model of boundary layer thermal response in microscale including air temperature in low boundary layer.
The boundary layer air temperature depends, in general, on the ux of solar radiation and on some features of the ground (albedo, absorptivity, emissivity) and the features of the air (mainly humidity). It can be claimed that these are mainly the conditions of heat transfer between the ground and the near-ground air layers that in uence the air temperature most. The direct absorption of the solar shortwave radiation by air is negligible. The solar radiation is partially re ected by ground (or water) and partially absorbed. The ground irradiates a part of the energy by emitting thermal IR radiation (most intensive at ∼15 m), so in the range of larger wavelengths than the solar radiation (the corresponding value ∼0:5 m). This radiation is much better absorbed

by the air in troposphere as it contains water vapour. The vital role in energy transfer between the ground and the air over its surface has, however, the processes of convection, which intensity depend on the vertical temperature gradient.
In order to model boundary layer air temperature changes, ground temperature variability during the eclipse should be known. The extraterrestrial radiation ux is essential factor shaping the ground parameters and it is necessary to predict its changes before. The model presented does not include any spectral changes.
The incident ux of direct solar radiation I can be expressed by Bouguer law

I = I0pm cos z;

(8)

where I0 means the instantaneous solar constant for the speciÿed site, which decreases during the eclipse:

I0 = S0(1 − g);

(9)

where S0 =1372 W=m2 is the solar constant, and z the zenital angle of the centre of solar disc, whose changes are known from ephemerides. p is transmission coe cient which depends both on the origin of the mass of the air over the considered area at speciÿed time and on the local factors (pollutants emission) and is di cult to be predicted accurately, but its typical values vary from 0.7 to 0.9. Integral air

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mass m may be given by frequently used Kasten and Young formula (Kasten and Young, 1989):

m = [cos z + 0:50572(96:07995 − z)−1:6364]−1:

(10)

Total net radiation can be given by the formula (Blackadar, 1997)

1

I = I0(0:36 + 0:74p cos z ) cos z;

(11)

On the basis of ephemerides calculated in Section 2, a model of direct, scattered and total (net) radiation presented below was made (Fig. 4). It is compared with the values for the same day but with eclipse occurrence omitted.
The further model is based on the assumption that system containing ground and boundary layer consists of homogenous horizontal layers (each layer has the same temperature in the whole volume). What is more, the temperature of the speciÿed layer depends only on the temperature of the underlying layer and does not depend on the temperature of the upper layer (Fig. 5).
Let the ux of radiation I (t) fall on the theoretically separated surface of dry ground S characterised by integral albedo . (All further considerations assume dry air and ground.) As even annular temperature variability in the ground is limited to ¡ 1 m deep layer, we may assume that the changes take place only in the layer with −z0 6 z 6 0 (z0 is the length of temperature variations vanishing), so the ground is separated into two layers—superÿcial with temperature Tg = T (−z0 6 z 6 0) and the underlying layer with constant temperature T0g. In both layers no temperature gradient exists (@Tg=@x = @Tg=@y = 0 and, according to the mentioned simpliÿcation, @Tg=@z ≈ 0). Then, according to the energy conservation law, we can write

(1 − )I (t)S dt

= cm z0S dTg + k1S(Tg − Tg0) dt

+ k2S(Tg − Tp) dt + k3STg3(Tg − Tp) dt;

(12)

where cm is the speciÿc heat of the ground in superÿcial layer, the density, and Tp is the air temperature in the layer closest to the ground. The following terms on the right-hand side describe: the changes of the ground temperature, the heat conduction to the deep layers of the ground, the heat transfer to the air by conduction on the ground surface, the heat transmission caused by the thermal radiation. All considered temperature di erences are small (the di erences do not exceed several per cent in the thermodynamic scale of temperature). We may omit any terms describing energy transfer between ground and air as the main process shaping the ground temperature is conduction to deep layers. This allows us to write

a1I (t) dt = a2Tg dt + a3 dTg:

(13)

This di erential equation can be solved numerically, assuming the radiation ux time-dependent values are known

from earlier considerations (given by function (8)). In such situation Tg depends only on time and its initial value. Then it is easy to notify that

dTg dt

= b1I (t) − b2Tg

(14)

what can be substituted in Euler method by

Tg t

= b1Ii(t) − b2Tgi ;
i

Tgi+1 = Tgi +

Tg ti

t

(15)

in the ith iterative step, where t is the assumed time step.

The method described above allows to obtain the qual-

itative description of the progress of the ground tempera-

ture changes during the eclipse. The simulation starts at the

sunrise and the initial superÿcial ground temperature refers

to this time moment. It does not include many factors like

ground parameters changeability with temperature, height,

humidity and solar radiation spectral distribution, also ne-

glects the temperature dependence of heat exchange factors.

As the di erence in temperatures between air and ground

is small, the term describing radiative energy transfer may have linear form by assuming Tg3 ≈ const. If the power of the
ground–air heat transfer is proportional to the temperature

di erence and the air is submitted to isobaric processes,

then the energy balance of the separated volume of air with

temperature Tp, mass m and molar mass has the form of

K(Tg − Tp) dt = m cp dTp:

(16)

The equation omits the air radiation. It can be solved similar to the previous one

dTp dt

=

c1(Tg

−

Tp):

(17)

In this case the ground temperature values are time-onlydependent variable known from the solution of (13).
In the sample model of air temperature changes in low boundary layer, the following coe cients were assumed:

t = 1; Tg (t = 3:25) = 5; Tp (t = 3:25) = 10;

b1 = 0:0005; b2 = 0:008; d1 = 0:05:

The simulation for the day of eclipse starts at sunrise and ends at sunset. It has only qualitative features.
The chart (Fig. 6) presents the e ect of numeric simulation of Tg(t) and Tp(t) functions for the mentioned model. The beginning, maximum and end of the eclipse were marked with triangles.
The model shows the characteristic time shift (delay) between the maximum obscuration of the eclipse and the moment of extremal value of temperature fall. It also depicts that the air temperature change has lower magnitude than ground temperature decrease. It illustrates the

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Fig. 4. Modelled solar direct, scattered (left) and total (right) radiation ux in Szczawnica at the day of eclipse.

Fig. 5. Ground–air interaction model for predicting temperature changes due to eclipse.

Fig. 6. Qualitative model of air and ground temperature changes during the eclipse in Szczawnica.

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general in uence on the daily temperature, which is signiÿcantly lower that modelled without eclipse. The time range with inversion occurs near the maximum of eclipse.
The model, as simpliÿed one, does not show nocturnal temperature e ects properly, but in this application it is not important.

4. Meteorological observations of the phenomenon

4.1. The method

The phenomenon was observed from the terrace oriented southwards, placed on the last oor of the multistoreyed building.
The observations concerned the near-ground air temperature changes as well as the photometric studies of the brightness of the total sky and of the Sun-centred area. The self-constructed electronic 2-channel thermometer was used. The functioning of it is based on measuring the temperatures of two-temperature sensors having di erent absorptivity, what allows for elimination of the in uence of the solar radiation on the measured value. The thermometer contains two precise monolithic temperature-to-voltage converters LM35Z (TO-92 plastic case) (National Semiconductor), supplied with stabilised voltage. Both elements were placed on the horizontal cardboard stands, about 7:5 cm long, 6 cm wide, ca. 3 cm over the artiÿcial ground (black painted wooden surface) to assure air ow and prevent direct heat transfer from it. The upper surfaces were covered by aluminium foil to reduce intensive heating by the solar IR radiation. One of the sensors was tightly wound with a single piece of thin aluminium foil, the colour of the second one did not need a change as the package was black. The voltage between the output and circuit bulk is proportional to the temperature of the semiconductor junction expressed in degrees Centigrade with the factor of kT = 10:0 mV=◦C. The typical error of non-linearity does not exceed 0:2◦C, the total temperature error is lower than 0:6◦C. The values were not read exactly at the same time, but the time of switching did not exceed 3 s.
The time of reaching 90% of ÿnal voltage value after temperature change is ∼2 min in still air. Taking it into account, the time interval between the measurements during the eclipse was matched to be 2 min (1 min close to the maximum).
Due to this feature of the device, low-pass ÿltering is assured and only long-period (several minutes) temperature
uctuations are remained. For two sensors 1 and 2, characterised by di erent absorptivities, with identical heat capacities and in identical heat exchange conditions, the temperature di erence between sensor and air is proportional to the incident radiation ux I (in terms of instantaneous thermal equilibrium):

iI = a(Ti − T ):

(18)

The absorptivity 1 ≈ 0:1 for the aluminium foil, 2 ≈ 0:9 for the black plastic case of the sensor (especially in IR range).
The real air near-ground temperature can be calculated from

T

=

1 kT

1U2 − 2−

2U1 :
1

(19)

The uncertainty of this value (the possible vertical shift of the curve) practically equals the maximal uncertainty in knowledge of temperature di erence between the sensors, it means about 0:6◦C. However the accuracy referred to the air temperature di erence values is mainly limited by sensor non-linearity and does not exceed 0:2◦C.
The auxiliary role was played by the determinations of the cloud cover taking place at the time of solar eclipse. Two-channel photometer, consisting of two photoresistors of type RPP 131 was employed.
The ÿrst element was placed horizontally on the black, mat carton stand in the site illuminated directly by the Sun, close to the thermometer sensors. The ÿeld of view was only limited by the building’s wall (opposite the position of the Sun) and the ceiling (over the estimated elevation ∼70◦). The second one was inside the mat tube with its ÿeld of view about 56◦ in diameter. The device was installed on the camera’s case, levelled at the position of the solar disc and following the celestial sphere daily rotation with camcorder.
The resistances of both sensors were measured in 2-min intervals. The measurements were based on determining the di erence in resistance between both devices. Due to changes in cloud cover, the angular distribution of sky brightness was varying. In clear-sky conditions most of the radiation comes from the surrounding of the solar disc, so the light uxes registered by both sensors should not di er. Contrary to it, when homogenous cloud cover exists, the sky brightness is almost constant over the whole range of angular distances from solar disc, so the light ux received by the sensor depends on its ÿelds of view and the resistance of the whole-sky sensor is expected to be lower. The sensor’s resistance depends on the illumination E in the range of resistances measured during the eclipse according to

E ∼Rf−(1:10±0:02) :

(20)

The functioning of the device is independent on the total radiation intensity (it is, however, sensitive to sky brightness angular distribution changes). During the solar eclipses the ratio of zenith illuminance to horizontal illuminance does not change towards its normal, clear-sky value, as it was stated by Darula et al. (2001). The measurements let know the time moments when the important cloud cover appeared and the solar disc was covered. They were compared with the visual estimations of the level of solar disc coverage by clouds, as it was registered by camcorder and good correlation between these methods was found.

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Fig. 7. Relative di erence in both sensors’ illumination, being the measure of the cloud cover (compared with its visual estimations).

4.2. The results and discussion
4.2.1. The cloud cover The results of the cloud cover measurements (relative
di erence in illuminances referred to total illuminance) are presented on the chart (Fig. 7).
It must be noticed that the most dense cloud cover corresponds with the maximum eclipse. The zero values do not indicate clear sky. As it was obtained from recorded ÿlm, cloud cover was not present only near the middle of the second part of phenomenon, and the during rest of the time of observation thin clouds were present. The variability of cloud cover is large (observations were made in 2 min intervals). This is not advantageous, but similar conditions in uenced the conditions of observation in the whole Central Europe (Fig. 8).
It is sometimes stated that the mechanism responsible for the cloud cover appearing near the time of the maximal eclipse exists. Their formation is presumed to be caused by water vapour condensation due to temperature decrease. This mechanism requires speciÿc conditions, regarding the fact that the temperature decrease on high altitudes does not have large magnitude. It is not possible to separate this hypothetical e ect from the general cloud cover variability over the speciÿed site of observation.
4.2.2. The air temperature curve general features The registered near-ground air temperature changes curve
is shown on the chart (Fig. 9). If comparison with usual meteorological data is needed,
it is important to note that the temperature was measured

Fig. 8. Overview of general meteorological situation over Central Europe after the maximum of the eclipse (the images near to the maximum are almost dark). Thanks to the courtesy of the University of Nottingham, http://www.nottingham.ac.uk/meteosat/ eclps99/.
3 cm over the artiÿcial ground, while typical meteorological measurements are taken on the height of 2 m.
It is interesting to notify that the temperature decrease began in fact at the moment of the ÿrst contact. Due to ground-air system properties, the presence of a delay is expected. The air temperature minimum, however, showed the characteristic delay towards the moment of maximal obscu-

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Fig. 9. Near-ground temperature changes during the eclipse.

ration g. The maximal temperature decrease value was ca. 11◦C, about 11:18—25 min after the maximum (its value for air temperature it depends on the type of climate and increases with height over the ground). It can be compared with the value of 20 min registered by Foken et al. (2001) for total eclipse and temperature measured 6 m above the ground). The decrease value was considerably great, but it has to be emphasised that the temperature was measured very close to the ground having high absorptivity.
4.2.3. The in uence on convectional events It is clearly noticeable from the visual inspection of Fig. 9
that two time ranges with di erent magnitude of temperature uctuations exist on the graph, what is depicted by measure
points spread. This spread corresponds to long-period uctuational component T of the temperature T (t)=T (t)+T (t). The time range between 10:30 and 11:18 is characterised by considerable decrease of uctuations intensity. It is commonly assumed that a temperature variance T is a good measure of convectional turbulent uctuations intensity. The analysis of the variance is direct when the mean temperature T (t) varies negligibly (as it happens especially for short measurement series for investigating high frequency temperature
uctuations in stable weather conditions). On the opposite, such measurements of long-period uctuations are more difÿcult, because even relatively slow-acting non-convectional factors may overlap the temperature changeability over a period of a few hours which is necessary. The special di culty is caused by eclipse-connected rapid change of mean temperature. So when calculating the variance T , the shape of T (t) function must be known. The uctuation process is random what implicates T = 0 and allows for T (t) estimation by least-squares ÿt. Then T (ti) = Tpred and the residuals

Table 2 Time ranges for temperature analysis

A

B

C

9:30 –10:34 10:34–11:22 11:22–11:36

D 11:36 –12:20

Tobs(ti) − Tpred(ti) = T (ti) for each realisation of temperature measurement in time instant ti. The usage of running mean was also taken into consideration, but obtained result was not smooth enough and indicated some oscillations (which could be removed only by averaging wider range of measurements). The mentioned oscillations could produce misleading results of spectrum analysis in the range of long periods. In our opinion, it is very advantageous to employ smooth function (polynomial of the low degree). Moreover, it is not necessary to ÿnd one function for total time range, but di erent function for each range can be applied. This is possible as the total range will be divided into separate subranges with visually di erent temperature variance. The ranges (assumed arbitrary) are in Table 2.
For this reason the function can be non-smooth in the points limiting the ranges. In ÿnal data handling, linear functions were used for ranges B, C and D and parabolic function was ÿtted to A range points. The e ects of such ÿtting and the residuals are plotted in Figs. 10a and b, Fig. 11 The eclipse beginning, maximum and end was marked with triangles.
The measure of quality of smoothing is that the regression line ÿtted to residuals (showed on the plot) which is almost exactly equal to zero.
The temperature variance for each range is presented in Table 3.

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Fig. 10. (a) The measured temperature towards the ÿtted model of mean temperature. (b) Residual values for air temperature.

Table 3 Variance and its uncertainty (normal distribution assumed) for temperature analysis ranges

Time range A

B

C

D

T ± T (◦C) 0:98±0:13 0:38±0:05 1:15±0:29 1:17±0:18

As the variance value depicts convection intensity, it is obvious that B range is characterised by its noticeable decrease. The range of much reduced convection covers

approximately 25 min before and after maximum. It is in excellent consistence with data obtained by Foken et al. (2001), showing 1 h long, totality-centred time range with low uctuations magnitude. On the basis of the theoretical model, we should observe that before maximum eclipse thermal inversion takes place what produces stable stratiÿcation, which is expected to vanish with restoration of normal stratiÿcation, after the maximum.
The FFT was applied to such prepared residuals. However, this method has disadvantage, namely it may indicate poor resolution for short time intervals and the results may

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Fig. 11. The histogram of the residuals over the whole series of measurements. Normal distribution curve ÿtted.

Fig. 12. FFT spectra of thermal uctuations for ranges A, B and D.

show the leaking e ect. The suitability of such methods to convection investigations is discussed by Petenko and Bezverkhnii (1999). The discrete wavelet transform (DWT) is advised, but this algorithm has even worse resolution. DWT is advantageous when longer data series are considered. The undoubted positive feature of wavelet transform is the ability of presenting the changes of power distribution vs time. In our opinion FFT is better method for this data handling, as time dependence of spectra is obtained by analysing separate data ranges and better resolution is required. In order to increase the resolution, the common method of padding the time series with zeroes was used (50 zeroes were concatenated to each range residuals sample). This leads to more smooth spectral density function. Windowing was used additionally with Hamming weighs and averaging of 5 periodogram points. The e ects are depicted on the two plots in linear and logarithmic scale (Fig. 12). The range C was not analysed as too short.
The graphs show that the spectra for the ranges A and D are very similar and both indicate strong, two-peak maxima at 11–13 and 22–24 min. This is generally consistent

with the temporal convective scales obtained by Petenko and Bezverkhnii (1999). They conclude the presence of signiÿcant temporal scales of 7–9 and 18–22 min, but, under the conditions of less-developed convection, the 11–16 min scale replaces the longer one. According to their data, the temporal scale increases with convection development. The behaviour of smaller scales is explained by the structure of large convectional plumes that consist of smaller ones. The spectrum for B series (covering the time near of maximal obscuration) is signiÿcantly di erent. The lower peak of the two-peak maximum (22 min) increases while the second one (11–13 min) is more reduced. What is more, an additional maximum with shorter period of 5:5 min occurs. The most noticeable e ect is the decrease of the uctuations intensity by a factor of 10. The temporal scales during 1999 eclipse were investigated by Foken et al. (2001). As it was mentioned, their results indicate convection intensity reduction around totality, and the total absence of uctuations with period shorter than 3 min. They also conclude that shorter time scales occur in coincidence with cloud cover appearance (see especially their Fig. 3b, p. 177).

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Our conclusion concerning temporal scale is that the development of longer timescale (22 min) is due to eclipse and the shorter one (5:5 min) might be caused by cloud cover. It also might be stated that the smaller convectional plumes become more “sharp” as the convection intensity decreases. It should be connected with the character of the structure of large plumes that consist of smaller ones. We must emphasise that cloud cover intensity increased more during the maximum and before and it overlapped the eclipse e ect. However, it is not possible to separate both factors. For more accurate conclusions, further investigations using continuous wavelet transform are desired (they show temporal changes of uctuations intensity in di erent time scales in continuous manner).
5. Conclusions
The observations conÿrmed that the occurrence of the stable stratiÿcation in the low boundary layer can be expected due to solar eclipse phenomenon occurrence. The general fall of convection intensity is visible in temperature uctuation component variance decrease at least by a factor of 2. The temporal scales of convection analysed on the basis of temperature uctuating component variance FFT obtained inside 1 hour maximum eclipse-centred time range seem to be di erent from ones observed under the typical conditions. It was not possible to separate e ects of eclipse and of changeable cloud cover, but the increase of the temporal scale seem to take place. The most important temporal scale changes from 11–13 min to 22 min. The behaviour of such parameters can only be explained by analysis of the convectional plums structure and interactions between larger plumes that consist of smaller ones.
Only if microscale processes are known in details, it is possible to simulate the mesoscale e ects of eclipses.
Acknowledgements
I am very grateful to express my acknowledgements to Dr. Wojciech KolasinÃski from 13th High School in LoÃdzà for his very valuable and useful advice and encouragement while I was preparing this article. I also wish to thank Zbigniew

WisÃniakowski, Ma.E. from the 1st Laboratory of Physics, Institute of Physics, Technical University of LoÃdzà for making possible the experimental testing and determining the parameters of my own-constructed equipment and his essential help in it. I would like to thank Ewa BrodzinÃska-Karolewska, M.A. from 13th High School in LoÃdzà for her help in preparing the ÿnal language version of the paper.
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