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11 Influence of temperature on the transport of water
Influence de la température sur le transport d'eau
Non-isothermal moisture transfer in unsaturated soils
S . V . Nerpin and A . M . Globus
A B S T R A C T : 1. In moist soils where temperature gradients exist the following mechanisms of thermal moisture transfer can be active: I. Vapour convection; II. Vapour diffusion; III. Vapour thermal slipping; IV. Thermo-capillary flow; V . Thermo-capillary film flow; VI. Liquid transfer induced by changing volume of entrapped gas due to the change of temperature ; VII. Thermo-sel fdiffusion of water; VIII. Thermo-osmosis of liquid; IX. Combined vapour-liquid transfer including the interaction between liquid and vapour within pores of a soil. W h e n the soil freezes another mechanism occurs. It is induced by the liquid to ice phase transition and by the changes in the moisture potential of the system, produced by freezing.
W h e n investigating thermal moisture transfer it is important first of all to estimate the relative importance of vapour and liquid transient transfers because this determines the magnitude of related heat flow, the transfer of dissolved matter and the methods of regulating thermal moisture transfer.
2. W h e n estimating a relative importance of each above-mentioned mechanism of thermal moisture transfer it should be held in mind that during the vegetation season this transfer can be important only in the upper layer of the soil, which has usually a moderate moisture content, a low apparent density and a developed structure. It can be shown that under these conditions the mechanisms I, III, IV and VI cannot contribute significantly to the total thermal moisture movement.
3. In the course of the experimental study w e used radio-active tracers, hydrophobic layers for discriminating between vapour and liquid flow and w e also investigated the relationships between thermal moisture transfer intensity and specific surface, apparent density and structure of soils.
The observations on kinetics of moisture redistribution under non-isothermal conditions m a d e it possible to estimate time rates of thermal moisture transfer and to compare them with time rates of an iso-thermal moisture flow.
4. Within the temperature range of 0-40° the gradient of 1 deg/cm creates a moisture flow time rate of order 10~6 to 10~7 g cm _ 2 sec - 1 .
The extent of moisture transfer depends profoundly upon the permeability of the system for iso-thermal liquid flow and upon its differential moisture capacity; the moisture redistribution is especially large in mellow and structured soils with low values of isothermal moisture diffusivity.
5. Under conditions of moderate-low moisture contents which are met in the uppermost, relatively friable layer of soils, thermo-capillary flows (IV-V) do not contribute significantly to
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S. V. Nerpin and A . M . Globus
the total flux and mechanism IX is the most important one. A m o n g the above listed mechanisms of thermal liquid transfer the thermo-osmosis and thermo-selfdiffusion are probably the most important ones.
6. Moisture flow towards the freezing layer increases with a rise of the system's permeability to liquid.
7. The mutual relation between a temperature profile and a moisture profile can create the conditions of a quasi-closed system in the soil; under these conditions the thermal gradient induces a moisture circulation within the surface layer, which contributes to the accumulation of dissolved matter in this layer.
8. Thermal moisture transfer promotes self-mulching of the soil which reduces non-productive water loss by evaporation.
R É S U M É : 1. Dans les sols humides où se produisent des gradients de température, les mécanismes suivants de transferts d'humidité peuvent exister : I. Convection de vapeur; II. Diffusion de vapeur; III. Déplacement thermal de vapeur; IV. Écoulement thermocapillaire; V . Écoulement thermocapillair par film: VI. Transfert liquide provoqué par le changement de volume de gaz enfermé dû à une modification de tempérautre; VII. Thermodiffusion d'eau; VIII. Osmose thermique de liquide; IX. Transfert combiné de liquide et de vapeur en y comprenant l'interaction du liquide et de la vapeur dans les pores du sol. Quand le sol gèle un autre mécanisme intervient : il est provoqué par la transition de la phase liquide vers la glace et par les changements dans le potentiel d'humidité du système produit par la congélation.
Q u a n d on étudie le transfert thermal d'humidité, il est avant tout important d'estimer l'importance relative des transferts momentanés de liquide et de vapeur, car ceci détermine la grandeur du flux de chaleur mentionné, le transfert de la matière dissoute et les méthodes de régulation du transfert thermal d'humidité.
2. Quand on estime l'importance relative de chacun des mécanismes mentionnés ci-dessus, il ne faut pas perdre de vue qu'au cours de la période de végétation, le transfert peut n'être important que dans la couche supérieure du sol qui a d'habitude une teneur modérée en humidité, une faible densité apparente et une structure développée. O n peut montrer que dans ces conditions, les mécanismes I, III, IV et VI ne peuvent guère contribuer au mouvement thermal total de l'humidité.
3. A u cours de l'étude expérimentale, nous avons utilisé des traceurs radio-actifs, des couches hydrophobes pour faire la discrimination entre les écoulements de vapeur et de liquide et nous avons aussi recherché les relations entre l'intensité des transferts thermiques et la surface spécifique, la densité apparente et la structure des sols. Les observations sur la cinétique de la redistribution de l'humidité sous conditions non isothermalles permettent d'estimer les taux des temps de transfert thermique de l'humidité et de les comparer avec les taux de temps d'écoulement isothermique d'humidité.
4. Dans l'intervalle de température de 0 à 40°, le gradient de 1 degré/cm crée un taux d'écoulement d'humidité de l'ordre de 10~6 à 10~7 g cirr2sec-1. La grandeur du transfert d'humidité dépend profondément de la perméabilité du système pour un écoulement liquide isothermal et aussi de sa capacité différentielle d'humidité; la redistribution d'humidité est spécialement importante dans des sols structurés et friables ayant de faibles valeurs de diffusivité isothermale d'humidité.
5. Sous condition d'une teneur modérément basse en humidité du sol qui se rencontre dans la couche supérieure relativement friable, les écoulements thermocapillaires (IV et V ) ne contribuent pas pour une part importante au flux total et le mécanisme IX est le plus important. Parmi les mécanismes de transfert thermal liquide mentionnés ci-dessus, la thermo-osmose et la thermo-diffusion sont probablement les plus importantes.
6. L'écoulement d'humidité vers la couche qui se congèle augmente avec l'accroissement de la perméabilité du système aux liquides.
7. L a relation mutuelle entre un profil de température et un profil d'humidité peut créer les conditions pour un système quasi fermé; dans ces conditions, le transfert thermal d'humidité provoque l'ameublissement automatique du sol qui réduit les pertes non productives d'eau par evaporation.
762
Non-isothermal moisture transfer in unsaturated soils
1. INTRODUCTION
The temperature variations at the soil surface induce gradients of temperature in the upper layer of the soils. Several mechanisms can operate by means of which soil moisture can m o v e due to a temperature gradient.
A . W h e n the moisture content exceeds that of the permanent wilting point the relative humidity of the soil air is equal approximately to one, and partial pressure of water vapour is determined mostly by the temperature. The temperature field induces vapour diffusion in a direction of lower temperature. This process ceases only when a decrease in the moisture content within the evaporation zone brings about a lowering in the relative humidity which equalizes vapour concentration throughout the soil layers having different temperatures.
B . The difference in densities of cold and w a r m air induces a convective flow of water vapour. However, theoretical calculations (Luikov, 1954) show that in bodies with pore diameters smaller than 5 m m , the part played by transient convective vapour flow in thermal moisture transfer ( T M T ) is negligibly small if the temperature gradients are not rather large. Nevertheless micro-convection can contribute to the moisture transfer within individual water-free pores. Experiments carried out by Taylor and Cavazza (1954) and by us have shown that in the moisture content range in which it is reasonable to expect a considerable vapour movement the magnitudes of T M T in horizontal and vertical columns differed no more than to 10-15%.
C . In air-filled pores with radii nearly equal to a free path length of water vapour molecules (~ 1 0 ~ 5 c m ) thermal slipping of vapour can take place resulting in moisture transfer in the direction of a higher temperature (Luikov, 1954). However this process cannot play a significant part in transient T M T because of the absence of sufficiently long micro-capillaries and because the finest pores are the last to loose water.
D . The temperature gradient is accompanied by the gradient of surface tension at the air-soil water interface. Existence of the latter gradient can produce two types of thermo-capillary movement of a liquid phase.
1. In those capillaries where menisci of liquid exist, the temperature variation induces the variation of capillary pressure and the corresponding shifting of a liquid column. However, elementary calculations show (Globus, 19626) that in order to compensate for a capillary pressure difference induced by a temperature change of 1 °C it will be sufficient that the meniscus moves into the region of a pore with a radius which differs from the initial pore-radius as little as 0 .2%. Therefore, a thermo-capillary mechanism involving menisci is capable of producing only little if any moisture content change and such a change must be of short duration.
2. The gradient of surface tension at the water film surface can produce thermo-capillary film flow (Derjaguin and Melnikova, 1958). The velocity profile in the film during such a flow is different from that of the Poiseuille flow. Hence, the permeability of a med ium for thermo-capillary flow must differ slightly from its permeability for the flow induced by the pressure difference.
E . The temperature variation causes a change in the volume of entrapped air. This has two effects: (a) the air bubbles change their volume and m a y cause liquid transfer (Pokrovski, 1940); and (b) an apparent increase m a y take place in the temperature coefficient of the capillary potential (Peck, 1960; Shagal, 1965). The first effect can produce transient T M T in very moist soils. However, in such soils large temperature gradients seldom exist. The second effect as the experiments show (Shagal, 1965) is of importance at the soil moisture content range in the vicinity of field capacity. In drier soils this effect is insignificant.
763
S. V. Nerpin and A. M . Globus
F . The molecules of a liquid or the molecules associated with them are in constant thermal motion accompanied by jump-like transitions from one temporary equilibrium state to another. The frequency of the transitions depends upon the temperature, and it probably is somewhat modified also by the influence of the solid surface. Consequently, the number of molecules transversing a certain section of the liquid layer in the direction of a temperature gradient is statistically less than the number of molecules moving in the opposite direction. This produces a net liquid transfer in direction of the lower temperature. Such a mechanism of T M T can be named as self-thermo-diffusion of a liquid. Its significance was stressed in works of Ananian (1960) and Cary and Taylor (19626).
G . The enthalpy of a liquid layer next to the solid surface differs from the heat content of bulk liquid. Hence, heat must be liberated at the entrance of the porous body and be absorbed at the outlet when, due to a pressure difference, a liquid passes through sufficiently fine pores. According to irreversible thermo-dynamics an appearance of the temperature gradient must, in its turn, induce a pressure difference and as a consequence thermal transfer of a liquid, i.e. thermo-osmosis (Derjaguin and Sidorenkov, 1941).
The two last mentioned types of T M T can occur in partially as well as fully saturated media. This has been confirmed by the experiments of Habib and Soreiro (1957) and Cary and Taylor (1962a). However, it was not as yet estimated what is the relative contribution of each one of these two mechanisms.
H . In partially saturated soils, thermally transferred moisture passes through the zones occupied by a liquid as well as by air. During the process of transfer, multiple evaporation-condensation cycles can take place and they m a y be accompanied by capillary movement in films and wedges. The role of these processes has been stressed for the first time by Morosov (1938) w h o pointed out that an interaction of vapour and liquid (in a certain range of soil moisture content) can compensate for the decrease in a cross-section available for vapour diffusion (a decrease which is due to the presence of a liquid). In greater detail this mechanism has been analysed by Philip and de Vries (1957) w h o were the first to note that the temperature gradient in water-free pores must be greater than a mean temperature gradient in the medium. Combination of both factors can increase considerably the velocity of this series-parallel vapour-liquid flow, so that it m a y be 7-8 times as large as the rate of simple vapour diffusion.
In agricultural practice, the temperature gradients have a significant magnitude only in the upper (0-20 c m ) layer of a soil, a layer which has as a rule a moderate to low moisture content, relatively friable constitution and a more or less well-defined structure. Under such conditions, thermal moisture transfer can involve primarily only mechanisms A . , D . 2 , and F . - H .
Both from the scientific and practical points of view, it is important to elucidate the relative role played by each of these mechanisms in total thermal moisture transfer under various conditions.
O f the greatest importance is the estimation of the proportion of vapour to liquid transfer because the first can contribute essentially to effective heat conductivity of soil and the second influences the distribution of soluble matter in the soil. In addition, the methods of regulating each of these flows are principally different.
II. E X P E R I M E N T A L
W e have investigated thermal moisture transfer in closed horizontal columns of quartz sand, several soils and granulated porous ceramics. The latter media were used as models of structured porous materials. S o m e characteristics of the used media are listed in table 1.
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Non-isothermal moisture transfer in unsaturated soils
T A B L E 1. Characteristics of investigated media
Material and texture
Quartz sand
Podsol. soil, clay loam
Chernozem, clay loam
Crushed ceramsite
Dimensions of particles
(mm)
0.25-0.50
1
1
1
Granular porous ceramics 1
Moisture content (% on dry weight basis)
at relative humidity 0.98
0.1
4.8
9.8
0.3
0.2
at potential -33kj /kg
2.0
33.0
37.0
9.2
4.6
at potential -1 .5kj /kg
1.5
8.1
17.9
— —
Specific surface area
m 2 g - »
1.5
49.9
97.5
2.1
2.0
Cation exchange capacity
mg.-eq/100 gr
0.1
16.2
37.5
0.7
0.5
In addition to the materials mentioned in the table, sandy loam and silt loam podzolic
soils were used.
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• quartz sand — o chernozem, clay loam
F I G U R E 1. Net thermal moisture transfer in the investigated media
765
S. V. Nerpin and A. M. Globus
The method used has secured the establishment of a linear temperature distribution along several columns simultaneously (Globus, 19626). This distribution become stable 1-2 hours after the start of an experiment. At the end of a test the columns were dismantled and the resulting moisture distribution was determined by means of drying at 105 ° C . W e studied the influence of initial moisture content w , , of temperature gradient dT/dx and of the mean temperature Tm on the moisture redistribution in tests of various duration. The following characteristics of T M T were measured: a quantity of moisture transferred through the middle section of a column, q(gfcm~ 2 ) (the moisture content in the mentioned section having been nearly constant during a test): a difference of moisture content beween the 'cold' and 'hot' ends of a column, \uch(%); ratio of moisture quantity transferred to all the moisture in the system, />(%); the extent of the initial moisture content range AÍ/ ¡ (%) where the influence of the temperature results in a net moisture redistribution (fig. 1).
U °/o
20
18
16
14
12
10
8
i . i , I i I i I i I
0 2 4 6 8 10 Distance from cold end ,cm
• • 24 hours of thermal influence
(dT/dx = 1°C/cm, T m =27°C )
o o the same thermal influence plus 240 hours
of isothermal regime
— ' initial moisture content
F I G U R E 2. Thermal moisture transfer as compared with isothermal back-flow in Ceramsite
The investigation of T M T kinetics revealed that, in the range of u¡ between maximal hygroscopy (corresponding to relative humidity 0.98) and a certain moisture content uic
specified for each med ium (under conditions of experiments), the net mass transfer is almost a linear function of time during the first 10 to 20 hours of a test. During this time, the moisture gradient in the middle section is very small. A s a consequence, the mean
A
X
766
Non-isothermal moisture transfer in unsaturated soils
time rate of T M T during this period is approximately equal to the true time rate of the process and can be used for comparative estimations.
A s a check the following experiment was conducted: 6 columns of loam soil (//, = 9.8 % ) were subjected to the influence of the temperature gradient 1 7 c m at Tm = 22 ' C during 48 hours; thereafter columns 1 and 2 were dismantled; columns 5 and 6 were kept under isothermal conditions for the same time period and dismantled simultaneously with the former pair. Calculation of the transfer mean time rate for each pair resulted in a mean time rate of T M T equal to 5.6 x 10~ 7 g c m _ 2 s e c ~ ' and a mean time rate of moisture transfer due to moisture gradient equal to 0.70 x 10~ 7 g c m - 2 s e c " '.
In another experiment a pair of columns of Ceramsite (w¡ = 15.9 %) was subjected to a temperature gradient of 1 °/cm for 24 hours. Thereafter the first column was dismantled and the second was kept under isothermal conditions for 240 hours before dismantling. Fig. 2 shows the time rate of moisture transfer due to the gradient of the chemical potential in such a granular medium is significantly less than the time rate of T M T .
The comparison between the time rate of T M T in the range of ui < uic and the time rate of vapour diffusion was accomplished by means of untroducing a layer of a hydrophobic medium in the middle section of columns (Globus, 1960). Time rate of vapour diffusion was equal to 0.9-1.4 g c m ~ l sec" ' degree C ~ ' , being 1.1-1.4 times the calculated rates (de Vries, 1950) and 10-15% of the m a x i m u m time rate of T M T studied.
Starting with u¡ greater than the maximal hygroscopy, moving moisture is accumulated against the 'hot' side of the hydrophobic layer thus indicating the participation of the liquid phase in a mechanism of T M T . At the same time the experiments with a radio-active tracer of liquid phase (Co 6 0 — E D T A ) show that in all the media studied net tracer transfer was opposite in direction to net moisture transfer for all but shortest periods of a test (fig. 3).
The investigation of the relationship between T M T - t i m e rate and mean temperature (at the same temperature gradient) revealed that T M T - t i m e rates, though exceeding the time rate of vapour diffusion, increase linearly with the existing vapour pressure gradients.
The study of T M T in aggregated soils and porous ceramics has shown that magnitudes of q, AttcA and A « ; for these media were greater than in nonaggregated materials even when the former had smaller specific surface areas.
The investigation of the dependence of T M T intensity on the free porosity a and the apparent density y of clay loam at the same u¡ (dry weight basis) has shown that the m e a n time rate ot T M T rise is described by the expression: VT = 1.57 x 10" 5 «4 (g c m " 1
sec"1 degree"1), (0.28 < a< 0.50). The vapour diffusion time rate must increase approximately linearly with a. This was
confirmed by the authors' re-calculation of the data of Rollins, Spangler, and Kirkham (1954) which was obtained for a system without reverse moisture flow. This resulted in the expression VT — (0.76 + 5.9a) 10" 5 ( g c m " ' sec"1 degree).
The decrease in apparent density influences most profoundly the net T M T in the range u¡ > uic and results in an appearance of the net transfer in a wider range of u¡ (curves 1 and 2, fig. 1).
The study of moisture movement in porous media under freezing conditions has shown that in the range of u¡ < uu. the time rate of mass transfer and its main relationships are the same as if the temperatures were positive. In the soil of greater u¡ the typical peak of the moisture profile arises at the freezing front and the corresponding depression in the adjacent layer of the thawed soil (fig. 4).
Examination of the moisture content profile in the soil under freezing conditions revealed that in spite of the constancy of the temperature gradient throughout the column the velocity of moisture movement in the zone adjacent to the freezing front exceeds that of other zones. The experiments with labelled water have confirmed the wellknown fact of water migration to the freezing front (fig. 5). The flux of moisture increases with initial moisture content.
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Non-isothermal moisture transfer in unsaturated soils
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0 2 4 6 8 10 Distance from "cold" end (cm)
o o final moisture content *— » temperature arrows indicate position of O-isotherm
F I G U R E 4. Moisture transfer in freezing clay loam as influenced by initial moisture content
769
S. V. Nerpinand A. M. Globus
III. D I S C U S S I O N
Study of the reported data obtained under various conditions and their comparison with the results of measuring heat effect of T M T (Cary, Taylor, 1962 a) shows that increased time rate of T M T (as compared with the vapour diffusion time rate) cannot be explained by thermal liquid transfer in the range of u¡<uíc. This does not mean that the latter does not exist at all.
18
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T°C
3 _
4 6 8 10 Distance from "cold" en (cm)
- - initial moisture content and radioactivity -o final moisture content - • final radioactivity -» temperature
F I G U R E 5. Transfer of moisture and radio-active tracer in freezing loam
The time rate of T M T depends rather weakly upon such medium characteristics as cation exchange capacity, specific surface area and texture. Though the specific surface area increases 10-100 times, the corresponding increase of T M T time rate is only 2-3 times. Nevertheless the magnitude of the specific surface area influences profoundly the values of uic and the range A « ; when the net thermal moisture transfer occurs. Both characteristics increase significantly with specific surface area. This can be explained as follows. With an increase of the specific surface area there must take place an increase in the amount of moisture which is necessary for creation of the film thickness (or capillary filling) sufficient for T M T compensating the reserve liquid flow.
The type of structure and the apparent density of a soil also influence strongly the net thermal moisture transfer. It was shown that the decrease in the apparent density reduces the permeability of a media for unsaturated flow (Staple and Lehane, 1954). This is relevant to thermal as well as to isothermal liquid transfer. Therefore, the increase of net T M T fer a given ui (on the dry weight basis) with a decrease in the apparent density can be
770
Non-isothermal moisture transfer in unsaturated soils
taken as a proof of small participation of the transient thermal liquid transfer in the process in this range of u¡. Liquid flow operates under the influence of a moisture content gradient and results in decreasing the net thermal moisture transfer with the rise of the initial moisture content.
At the same time the absence of a significant increase in time rate of T M T through a hydrophobic porous layer proves the interaction between vapour and liquid phases to be an essential element of a mechanism which causes an increased time rate of thermal moisture transfer. According to the authors' opinion the totality of data reported here and the data of Cary and Taylor (1962a) suggest that the mechanism 8 proposed by Philip and de Vries (1957) plays a dominant role.
The results of a comparative study on the thermal transfer of H 2 0 , C 2 H 5 O H , C 6 H 6
C C I 4 and dibutylphtalate obtained by the authors recently suggest that the thermal liquid transfer in wetter media (Cary, Taylor, 19626) is mainly a non-thermo-capillary one. Experiments by Hallaire (Hallaire and Baldy, 1963) showed that 1.5-2.0 fold decrease of surface tension results in a rather weak depletion of the moisture content appropriated to a given p F (in the range of moderate to high suctions). Hence these experiments also support such a deduction. Consequently the attention is to be paid to thermo-osmosis and thermo-selfdiffusion when investigating liquid thermal transfer.
Experimental data show that under the conditions corresponding to that of the upper soil layer in the summer (presence of structure, moderate to low moisture content and relatively low apparent density) thermal moisture transfer can influence significantly the moisture regime of soils. This would be difficult to expect in case of significant participation of thermal liquid flow in the process in question.
The maximal temperature gradients in soil occur during day time and are directed upward. Because of this the thermal moisture transfer produces a downward movement of moisture from the upper soil layer. This promotes a quicker drying of the latter, thus reducing a non-productive loss of moisture by means of facilitating the formation of a mulch.
For the same reason thermal moisture transfer can promote the formation of a surface crust in non-structured heavy soils during day time.
It follows from experimental data that management of the apparent density and structure of the soil provides an effective method of regulation of net thermal moisture transfer. Interrelation between moisture and temperature profiles corresponding to the upper soil layer during day time creates conditions of a 'quasi-closed' system in the soil. Because of this the thermal moisture transfer can produce a circulation of moisture within this layer. As a result the uppermost soil layer can enrich itself with soluble matter like the 'hot' zone of our columns (fig. 3). Such a process can influence the plant nutrition regime and salinisation of the soil.
W h e n the soil freezes under the conditions of a sufficient moisture content u¡ > uic the essential influence upon the moisture migration is exerted by ice formation. Examination of the moisture content profile in partially frozen soil reveals that forces caused by ice formation create gradients of a moisture transfer potential greater than those induced by the temperature gradient itself (Globus and Nerpin, 1960).
The freezing process does not only fix the moisture moved to the frozen zone but also creates a depression in the moisture content profile in the thawed soil next to the freezing front. This reduces the velocity of moisture movement to frozen soil but at the same time it favours moisture migration from the more distant layers towards the sone adjacent to the freezing front.
REFERENCES
A N A N I A N , A . A . 1960. Study of moisture transfer and formation of segregation ice in freezing and permafrost soils. Tr. Gidroproekta, Sb. 3 (in Russian).
771
L.A. Razoumova
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Influence of freezing and thawing out processes on migration and soil moisture content in the upper layers of the unsaturated zone
L . A . Razoumova U S S R Hydrometeorological Research Center, Moscow
A B S T R A C T : The results of laboratory and field investigations of freezing and thawing out of soil and of their role in formation and migration of soil moisture are shown in the paper. Some characteristics of soil moisture content fluctuations in the European part of the U S S R during the cold period of the year are shown as well.
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