JPRS ID: 10088 USSR REPORT METEORLOGY AND HYDROLOGY NO.5, MAY 1981

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• Document Creation Date: November 1, 2016
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• Content Type: REPORTS

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JPF~S L/10088

, 3 November 1981
U SSR Re ort
p
METEOR~LOGY AND HYDROLOGY
- No. 5, May 1981
,
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JPRS L/10088 ,
3 Novembpr 1981
USSR REPORT
METEOROLOGY AND HYDROLOGY
No. 5, May 1981
Translation of the Russian-language monthly journal METEOROLOGIYA I
GIDROLOGIYA published in Moscow by Gidrometeoizdat.
CONTENTS
Climatic Variability of Total Monthly Precipitation in the Northern
Hemisphere 1
Climatic Characteristics of Vertical Wind Shifts in the Ground Layer of the
; Atmosphere Over the USSR 15
Simulation c~f Thermals 24
' Peculiarities of Variations of the Microstructure of Arid Aerosols 35
~
Effect of Station Network Density on Interpolated Value Variability
! Characteristics 43
~ Relation of Mean Annual Values of the Albedo and Shortwave Radiation
~ Balance to the Same Indices in Early Spring 53
I
! Brightness Variations of Cloud Fields When Observed From Different
j Altitudes 59
Forecasting the Novaya Zemlya Bora by the Method of Canonical
- Correlation 66
Hydrocarbon Distribution in Freshly Fallen Snow and Ice at 'North Pole-22'
~ Station (1977-1978 Observations) 73
Joint De~ermination and Reduction of Statistical Parameters to a
Period of Many Years, Extension and Modeling of Time Series 79
Mechanism of Lifting Solid Particles off the Bottom of a Turbulent
Stream 93
Effect of Temperature on Soil Moisture Potential and Its Availability
to Plants 106
- a- [III - USSR - 33 S&T FOUO]
-
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Analysis of Synoptic Scale Wave nisturbances in TROPEX-72 and GATE......... 114
Informativeness of Meteor Radar Used To Measure the Wind in the
- UPPer Atmosphere 130
Calculating the Humidity of the Air Above the Sea by Air and Water
Temperature 139
- Application of a Computer Graph for Visual Representation of
Hydrometeorological Data Archives 144
Review of Monograph by V. V. Bogorodskiy and V. P. Gavrilo: 'Led.
- Fizicheskiye Svoystva. Sovremennyye Metody Glyatsiologii' [Ice.
Physical Properties. Modern Methods of G'_aciology], Leningrad,
Gidrometeoizdat, 19$0, 384 Pages 149
Seventy-Fifth Birthday of Yevgeniya Semenovna Selezneva 151
High Award :L53
Conferences, Meetings, Seminars 154
Notes From Abroad 162
Obituary of Isay Giigor'yevich Guterman ( 1911-1981) 165
~
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UDC 551�577.21(217.17) ~
CLIMATIC VARIABILITY OF TOTAL MONTHLY PRECIPITATION IN THE.NORTHERN HEMISPHERE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 5, May 81 pp 5-16
[Article by Professor G. V. Gruza,Candidate of Geographic Sci.ences Ye. G. Apascva,
~ Al1-Union Scientific Research Institute of Hydrometeorological Information--World
- Data Center, manuscript received 16 Sep 80]
[Text] Abstract: A study is made of variability characteristics of total
monthly precipitation anomalies with respect to individual regior.s and
latitudinal belts of the northern hemisphere in January and July
1891-197g in the 0-85� north latitude zone.
The quality of the initial data on the precipitation anomalies obtained
by visual interpolation to the nodes of the geographic coordinate
grid with 2.5� grid intervals is estimated.
The statistical parameters of the anomalies were calculated with
respect to several segments of the instrument observation period.
It is demonstrated that depending on the scale of the area
averaging and the time period, the magnitude and sign of the linear
trend vary significantly. On the whole, over an 89-year period
throughout the hemisphere the anomalous nature of the January
precipitation is increasing, and July, decreasing.
By comparison with the temperature, the total monthly precipitation is characterized
by much greater spatial variability. Accordingly, and for other generally known
reasons, climatic conditions have long been studied by station observation data.
However, the necessity for evaluating the precipitation climate for an entire
hemispher~, similarly to how this has been done in a number of global temperature
studies (the last of which [1], also contains recommendations on the forms of
- representation of empirical characteristics), leads to the conclusion of
= expendiency of using a data which are smoother and more regular in space. In
- the present paper, the original maps of [4] ha.ve been selected as the source
of information from which by visual interpo].stion, an archive of precipita~~ion
anomalies has been created for January and July 1891 to 196o in percentages of
the long-term mean (the norm) at the nodes of a coordinate grid of points with
- parallel and meridian intervals of 2.5�. The data for 1961-1975 were prepared
at the GGO [Main Geophysical Observatory] by the procedure of [4], and maps of
the anomalies in percentages of the "Clino" norms (1931-1950) compiled at the
USSR H,ydrometeorological Center were used for 1976-1979�
1
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By comparison with the tetal precipitation fields the anomaly field is more
uniform in space inasmuch aG ti~e division by the "norm" smooths the regional
singularities. Additional smoothing is accomplished by visual interpolation. On
the whole, the quality of the archive data varies as a function of the method of
measuring the precipitation and processing the measurement results, the accuracy
of which is determined by the methods of caiculating tre norms, reproduction of the
uniformity of th~ series, anomaly mapping, and also visual intprpretation from the _
maps, and so on. jdithout discussing the. measurement procedure, which has been
sufficiently discussed in the specialized literature, let us try to evaluate the
quality of the preparation of the archive which will naturally be approximate in-
asmuch as it does not appear possible to d~fine exact quality criteria as yet.
, The precision of th~ interpolated anomaly fields depends primarily on the density
of the network, approximately characteri.zed by the nim~ber of stations used when
preparing the maps (Figure 1).
,V , ~
110a
; OPO
B00 2 . ~
- ~ ~ .
600
' ' :
900 ' ,
_
700e90 ~''19f0 19.f0 1950 1970
Figure 1. Variation of the number of stations in 1891-1979.
1-- northern hemisphere, 2-- foreign territory, 3-- USSR
Until 1910 the network was two or three times smaller than at the present time,
and di~ring the world wars, the number of stations diminished abruptly. Qn the
whole throughout the hemisphere 1400 stations have been recently used. Is this
many or few? Obviously, it is not so simple to answer this question, for calcula-
ti~n of the required nwnber of observations is complicated by the anisotropicity
oC the spatial correlation function which is still unknown to us.
_ _ ~ eu 0 .
0
hg~ DO �o
eo
� � ~ ~ ~
0
~ o ~
~ o
Figure 2. Quantity of data at the nodes of the conrdinate
grid, 1891-1979
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Let us use a map o~ the numher of observations at each node for 89 years to
characterize the ~.ompleteness of th~ data (Figure 2). Its distribution with
_ respect to the hemisphere is far from uniform. The blank spots are tfie central
pa:~~ of the oceans; the series is insufficiently long in the polar and ~~quatorial
regions and in the Tibetian Highlands. The existing gaps, generally speaking, can
be filled in, as has been done, for example, in [10] for precipitation over the
Pacific Ocean. At the present time it is possible to use satellite observations
for this purpose. Establishment of this type af relation is a subject for indepen-
dent research.
As for uniformity of the series, an indirect characteristic of which can be the
value of dR=R-100 characterizing the difference between the ideal anomaly norm
(100%) and the actual long-term mean R for the investigated period, judging
by the maps of dR the uniformity is disturbed in the American sector of the Arctic,
the oceans and at the boundaries of arid zones which have different locations in
January and July, The latter include L~gions where precipitati~n does not fall
annually (Africa, Central Asia). In the temperate latitudes of both continents
8R does not exceed +5%, including the territory of the USSF. where, as is known,
the measurement procedure and norms have changed many times. Thus, it is possible
that the norms calculated over SO or more yeaxs do not depend on the limits of the
period [8]. The procedure for processing the initial data for anomaly maps is
discussed in more detail in [4].
An idea of the accuracy of the interpolation can be obtained when comparing the
spatial correlation of the total monthly precipitation in the central regions of
the European part of the USSR with interrelation between the anomalies in Moscaw
and the grid node closest to it, the distance between which was 174 km (Table 1) .
In the first colurrm of the table the autocorrelation of the station observations
is presented for this distance (according to the data of [6, 7]). In the winter
this autocorrelation turned out to be higher, and in the summer, lawer, then the
precipitation correlation at Moscaa Station and at the nearest node of the grid
included in the investigated archive (the second column). It is possible that
the summer precipitation is smoothed to a higher degrec by visual interpolation
than the winter precipitation.
_ Table 1. Correlation Coefficients of the Total P4onthly Precipitation
Precipitation at the stations Precipitation at the node ~=55�
according to the data of [6, 7] north latitude, a=40� east and
at Moscow Station
January July January July
0.75 O.S4 0.73 ~.62
= In order to check the correspondence of the arr_hive data to the ac'tual fields, a
comparison was also made between the behavior of the deviations from the norm of
the long-term average precipitation for America takenfrom j9] with the curves in
Figure 6, which demonstrates their similarity.
Considering the rounding (10%) used when preparing the archive and the maps of
~SR that we o~tained, the conclusion must be drawn that the errors connected with
nonuniformity of the series and other errors do not go outside this limit in the
temperate zone. Over the American sector of the Arctic and the shipping lanes
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of the oceans the errors increase, and the data become unreliablE. On the whole
it is possible to consider that the archive data_r~flect the basic laws of
precipitation and can be used in the first approximation to estimate the climatic
parameters.
The statistical precipitation characteristics, including smooth~d over large terri-
tories, have been investigated many times, but the global field is the initial
subject only in a small nLUnber of papers [3, 5, 9]. The University of Colorado
is conducting a planned study of the precipitation conditions over the continental
zones American, Eurasia, Africa [9]. Tize precipitation spectra averaged
over 10-degree latitudinal zones in the Noxthern and Southern Hemispheres are pre-
sented in [11;.
Having more complete data over a longer period of time than in [9] and data that
is more reliable than in [11], we are able to obta~,n a number of important varia-
bility parameters, the procedure for the calculation of which was developed in
[2] and used in [3] to process part of the archive. All further conclusions peri
tain to precipitation anomaliPS in January and July characterizing the degree of
disturbance with respect to the long-term mean monthly total precipitation field.
Let us remember that these values, just as the total precipitation, have positive
asymmetry of distrib ution (the mean is greater than the mode), and the ~ower limit
of the anomalies is zero.
The trend of the anomalies over many years can be characteiized approximately by
the linear trend factor S, that is, the tangent of the slope of the approximating
straight line ~alculated by the time series data at each point. of the grid
(Figure 3) . A s~isual estimate of the areas indicates insignificant predominance
of the regions with increased precipitation in January and decreased in July. On
the whole, R does not exceed 1% per year. The R field calculated by the data for
the last 19 years looks different (Figure 4). The order of the values increases
to 4%/yearq and alternation of the regions~,af opposite signs takes place more
. frequently. Let us remember. that in accordance with the value of dR the informa-
tion is reliable everywhere with the exception of the oceans. It is also necess ary
to consider that on the equidistant pro3ection maps in the polar regions, the
scale with respect to the parallels is enlarged, and in the equatorial regions,
reduced by compari~on with the actual scale, which distorts the representation of
the proportion of the corresponding areas on the maps.
In order to ~btain a more definite idea of the secular variability, let us cal-
culate tile mean anomalies over enlaYged regions distinguished'by certain typical
features. The averaging over two continzntal zones of the hemisphere, as was
done in (9], appears to be too generalized, for along ~rith thE continental precip-
itati_on it is useful to have information about precipitation in individual regions
of Asia which have at the present time been distinguished with respect to predom-
inant dir.ect:ion of river runoff and also with respect to the central area where
rhe rivers flaw into inland bodies of water. In Tatile 2 a list of regions is pre-
sented, and the number of nodes,by the data of which the weighted mean (weight
cosl_ne of the latitude) was calculated, is indicated. The information at the
nodes falling in the arid zones (in Asia, America, Africa) where ~R=O is excluded
from the analysis. Analyzing the variability by individual segments of the 89-year
period (the data for 1976-1979 calculated short-series and therefore unrepresenta-
- tive "Clino" norms are excluded from them in the first four intervals) in the
regions with most reliable data (Table 3), it is possible to arrive at the following
conclusions.
4
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8U �D dU~~ 1FU 120 51
- p , ; ~ ' ; ~ ~ p, i
,
. ~i oe ; :
4. '
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i
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1 � ~ ~'o"~ 4
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; Figure 3. Linear trend factor (%/year), 1891-1979.
, a January, b July
- I ~oo 0 0
eo
a~ ~ o
eo 0
% i ~I
G
i 2 � ' '
~ '
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i e
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Figure 4. Linear trend factor (%/year), 1961-1979.
,
a January, b Suly
- 5
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Table 2. Regions o~ the Northern Hemisphere for Calculating
the ?~.ean Precipitation Anoma~~:es
Region No of points
_ Eurasia 1098
Northern Asia 391
Central Asia 180
~ Southern Asia 205
Eastern Asia 1~+5
Europe 235
Af ri ca 285
*lorth America 414
1. The long-t~m average precipitation ~~;ies are, as a rule, t 100%, which
is probably connected witi-~ reducing the local maxima during interpolation
(Southern and Eastern Asia in January, Central Asia in July, Africa). If we
assume that the reduction is systemati~, then the conclusion can be drawn that the
fluctuations of the means reflect the actual variations in the p recipitation con-
ditions.
- 2. The data for 1976-1G79 obtained by the 30-year "Clino" norms are included in
the analysis only in two periods out of c~ine to avoid distortions caused t~y the
- nonuniformity. At the same time it is possible to propose th at the sharp increase
in the precipitation anomalies in the last 16 yea=s ard, especially, the last
10 years, is connected with a decrease in the long-term average participa-
ti:on during the 1931-1960 period by comparison with 1891-1975.
3. On the whole in J anuary data is larger than in July for all periods, including
for the last decade, when a sharp increase in the anomlies took place in both
months.
4. In two periods (1956- 1975 and 1966-1975) a decrease in the J anuary precipita-
tion is noted in the Eastern Hemisphere, and an increase in the Western Hemisphere.
In July, on the other h and, a negative trend is observed for th e greater part of
Asia.
5. The relative dispersion a(the contribution of the linear trend to the total
dispersion) increases with a decrease in length of the series, but it is on the
whole sma11 and obviously reflects the fact that there is no significant, well-
de.fined linear trend in the precipitation over the 85-year period.
Confirmation of some of the indicated singularities can be found on the graphs
of the behavior over many years of the anomalies in a number of regions and for
the 0-85� P1 belt as a whole matched with the third-order trend lines (Figure 5).
It is difficult to distinguish any regularity in the alternation of the maxima
and minima; th erefore the conclusions of [li] of insignificant guarantee of the
_ spectral frequencies of the mean zonal precipitation w~thin the limits of 2 to 6
_ years appears to be convincing. Returning tothe problem of uniformity of the
series, let us note that in the long-term behavior of the January anomlies
in Northern Asia, including the greater part of Che territory of the USSR, there
6
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_ is .3 rositive disruiitinuity in the 1~950's after which the nonn turned uut to he
low. It is possible that this is a consequence of changing instruments, the
effect of which could not be avo~ded, in spite of the carefully devaloped method
of preparing the initial data [4]. Tfie stalile inerease in anomalous nature was
reflected in tt:e largest of all the regions in the 85-year period of positive
- linear trend (s=2.9%/10 years) an~' also in the value of a=16% correaponding to it.
It is obvious that in order to obtain reliable estitnates of the variability, the
uniformity of the time series has primary significance, and from this point of
view retaining the initial method of ineasuring the precipitation, in spite of its
imperfection, would be more useful.
~ 1 ~ GIOC/R/~ AJC~I
~Rr Q; eRx61
- 1?D
f60 y~
BO ~p
6C ~ 2 ~ A~ uKc
f�~
99
sn ~
a
129 ~ 3~ ' ANCAYNQ
0
'00 '
- . 80 70
60 ~4~ Ed a~a~
110
90 9~D
' 100 ( S ~ CtOtpr.
ot ~no,l~r~epae
BO L . 1 ,
1900 1920 19M 196t7 flb0 f900 f910 19f0 1980 19I0
Fi ure S. Lon -term behavior of the third-order trend and anomalies.
g g
' a January, b July.
- , Key:
' 1. Northern Asia � ~
' 2. Africa
3. Ame ri ca
' 4. Eurasia
5. Northern Hemisphere
As has already been pointed out above, in referetice [1] recommendations are pre-
sented with respect to the unif.orm representation of the empirical data on
climate variability. Accordingly, in Tab le 4 eatimates are presented for the
trend in the precipitation anomalies with respect to five latitudinal zones, in-
cluding, in additi.on to the precipitation over the dry land, data on the oeeans
where they exist, that is, in the coastal zone and regions of intense shipping.
It is possible to see that the variation of the sign of S takes place to some
degree comparatively with res~ect to all zones. Thus, in January a$ainst a back-
ground of insignificant positive trends, th~re was an increase in prec pitation
for the entire period in 1940-1964, after which came a decrease in 194~1975 and a
sharp increase at the end of the period. In July the pattern of the sign
'~[(sic) translator's note: probably 1964.]
7
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alternation and magnitude o~ R with respect to zones and periods becomes more
spotty. Analyzing the long-term behavior o~ the anomalies by the graphs matched
with the five-year sliding means (Figure 6), it is posstble to distinguish
approximately the same features as in Figure 5.
The basic experi~nental results consist in the follawing.
1. The archive of precipitation anomalies created by visual interpolation hy the
originals maps of [4] has precision sufficient for estimation of the climatic
variability of the precipitation on the continents.
2. The representation of the precipitation data in the form of anomalies in per-
centages of the norm permits us to achieve spatial smoothing and thus convert
from analysis of the point observations to a study of the precipitation fteld in
the hemisphere.
3. The parameters of the field variability vary significantly in space and time;
therefore in order to distinguish the characteristic features it is recommended
that the anomalies be smoothed on the scales of the subcontinents.
- es.a-~z,s
160 ' � 160 b ) ~
_ Q~
170 120
100 F00
eo sQ
60 60 ~
40 71,5� , S
- f10 f20
100 f00
ea Ba
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- BO 40
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110 , -
100
- d0 ~0
50 aso�� �s
100 fOD
DO 00~~~
1900 f9P0 19+0 1960 1l00 1910 1940 1960 f9l0
Figure 6. Long-term behauior of anomalies by latitudinal
zones and 5-year sliding means
a January, b July.
4. The growth of the anomalous nature in JanuaYy and insignificant decrease in
� July are observed on the whole for the hemisphere in 1891-1975.
S. The primary problems of future research mus* be restoration of the uniformity
of the series by converting to a united long-term norm an~ nal.c~~lation of the
climatic characteristics of the total precipitation. It is also possible to note
- the necessity for analyzing the trends af the continuous (in contrast to monthly)
12
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normalized precipitatian series and to calculate the ir_terrelations with the
air pressure and temperature variations.
In conclusion, the authors express their sincere appreciation to G. T. Gnevko for
the organization and performance of the work of creating the archive and
E. Ya. Ran'kova for the library of computer programs put at our disposal for the
calculations.
BIBLIOGRAPHY
1. Vinnikov, K. Ya., et al. "Modern Climate Variations of the Northern
Hemisphere," METEOROLOGIYA I GIDROLOGIYA [Meteorology and Hydrology], No 6,
19 80 .
2. Gruza, G. V.; Ran'kova, E. Ya. "Empirical-Statistical Analysis of the
Structure and Variations of the Observed Climate," TRUDY VNIIGNB-MTSD
[Works of the All-Union Scientific Research Institute of Hydrometeorological
Information World Data Center], No 68, 1980.
3. Gruza, G. V.; Ran'kova, E. Ya.; Apasova, Ye. G. "Statistical Characteristics
- of the Anomaly Field of the January Precipitation in the Northern Hemisphere,"
TRUDY VNIIGMI-tiTSD, No 77, 1980.
4. KARTY MESYACHNYKH I GODOVYKH SUM~ OSADKOV V OTNOSHENII K MNOGOLETNIM
i SREDNIM SEVERNOGO POLUSHARIYA [Maps of the Monthly and Annual Total Precipita-
; tion with Respect to the Long-Term Mean for the Northern Hemisphere], Nos 1-3,
i 1964, Leningrad, Pain Geophysical Observatory.
I 5. Kuz.~etsova, L. P.; Nekhocheninova, V. I. "Time Variations of Temperature
and Precipitation Averaged for the Continents (Europe and North America),"
METEOROLOGIYA I GIDROLOGIYA, No 4, 1977.
I
~ 6. Polish chuk, A.I. "Problem of the Statistical Structure of the Winter Precipi-
I ~ation Field," TRUDY GGO [Works of the Main Geophysical Observatory], No 215,
~ 1968.
I 7. Polish chuk, A.I. "Statistical Structure of Simimer Precipitation," TRUDY GGO,
~ No 268, 1972.
8. SREDNIYE PiI~TTOGOLETNIYE t7ESYACHNYYE I GODOVYYE SLTr4~iY ATMOSFERNYKH OSADKOV PO
ZARUBEZHNOY TFRRITORII SEVERNOGO POLUSHARIYA [Long-Term Mean Monthly ald
Annual Total Atmospheric Precipitation over the Foreign Territory of the
Northern Hemisphere], Leningrad, Gidrometeoizdat, 1972.
q. Corona, T. J. "Further Investigation of the Interannual Variability of
Northern Hemisphere Continental: Precipitation," ENVIRON. RES. PAPER
COLOR STATE UNIV., No 20, 1979.
13 ~
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10. Dorman, C, E.; Bourke, R. H. "Precipitat~on Over the Pacific Ocean,
30�S to 60�N," T~ON. WEATHER REV., Vol 1Q7, No 7, 1979.
~ 11. Xanthakis, Jo; Tritakis, B. "Analytical Expression of the Mean Annual
Variation of tfie Precipitation within Var~ous Latitude Zones of the Earth,"
PRACTICA OF THE ACADE2'!Y OF ATHENS, Vol 51, N~ 47, 1976 (1977).
14
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UDC .551. (510.522:553:554) (47+57)
CLIMATIC CHARACTERISTICS OF VERTICAL WIND SHIFPS IN THE GROUND LAYER OF THE
ATMOSPHERE OVER THE USSR
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 5, Nisy 81 pp 17-23
[Article by F. F. Bryukhan', Professor I. G. Guterman, All-Union Scientific
Research Institute of Hydrometeorological Information World Data Center,
manuscript received 18 Aug 80]
[Text] On the basis of the data from four-time radiosonde observations
in the boundary layer at 146 stations in the USSR for the
period from 1961 to 1970, the climatic characteristics of the
vertical ~oind shifts were calculatesi. The spatial climatic
pattern of the wind shifts was obtained. An analysis is made
' of the shifts on the scale of the USSR in the 0-100 meter layer
a:~d over individual stations vertically. The diurnal behavior
and probability characteristics of the shifts are considered.
I' The consideration of the vertical wind shifts in the ground layer of the atmosphere,
I as emphasized in the resolutions of the Fourth Meeting of the Committee on
, Aviation Meteorology of the World Meteorological Organization (KAM-IV VMO) [16],
' is very important to supporting safe Cakeoff and landing of aircraft. The study
~ of the vertical wind shifts is also important for m~re thorough representation of
' the wind conditions in the ground layer of the atmosphere inasmuch as the magni-
i tude of the wind shifts depends both on the thermal stratification of the
~ atmosphere and the interaction of the air currents with the relief of the under-
lying surface.
The study of wind shifts is the subject of a comparatively small number of papers,
for interest in this problem began to be shown only 10-20 years ago. The study of
- the wind shift in the ground layer has been primarily based on the measurement
data on a meteorological tower at one station (in particular, on the meteorologi-
cal tower in Obninsk) [1-2, 12, 18, and so on]. Balloon data which permit a
der_ailed study of the wind shift conditions in individual regions have been used
more rarely [9]. In references [14, 15], generalized data from temperature-wind
sounding in the boundary layer for one station were used to analyze the wind
pro~iles and shifts. In [8] a detailed analysis is made of the wind shift dis-
trib ution in the fr~e atmosphere by radiosonde data. In reference [10] an
analysis was made of the shifts in the territory of the USSR based on the results
of radiosonde observations in the 1000 to 850 mb layer. However, maps constructed
in [10] for the indicated layer are of no practical significance in. view of the
great thickness of the layer, although they are of interest in climatological
respects.
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In order to study the shift distribution laws and methods of predicting these
shifts to promote flight safety it is first necessary to investigate the basic
climatic features of the wind shift distribution. Snch a study is made in this
paper.
In the paper four-time radiosonde observations over a 10-year period (from 1961
to 1970) at 146 stations distributed uniformly throughout the territory of the
_ USSR, were used. On the average approximately 250 observations were made at each
station at one time of day over the entire 10-year period. Multiplying by zour
we have a total of 1000. The initial wind data were taken on the windvane
level (8-12 meters), at altitud~s of 100, 200, 300, 500, 600 and 900 meters
reckoned from the station level and at altitudes of 200, 500, 1000, 1500, 2000,
and 3000 meters reckoned from sea level.
The described data take up significant space, and for effective use at the
VNIIGMI-P'C~sD, an archive of observations with respect to the boimdary layer was.
created on magnetic tapes on the riinsk-32 computer and the unified system of com-
puters. Information is packed on these tapes with maximum recording dens'ity,
which permits the data from three stations to be recorded on one tape. In the
phase of formation of the archive, a rough check was made of the initial data by
_ the procedure described in [3]. By cooperation between the Arctic and Antarctic
Scientific Research Institute and the N[oscaw Division of the VNIIGMI [All-Union
Scientific Research Institute of Hydrometeorological Information], im der the
direction of K. Ye. Chernin, a set of programs was written for processing the
indicated data, in particular, the programs for calculating the characteristics
of the vertical wind shifts.
As a result of the fast rise of the radiosonde, the accuracy between the wind
- speed and direction is greatly inferior to the accuracy of ineasuring the wind on
meteorological towers and masts. During mast or to~w~er measurements it is possible
to obtain a detailed vertical structure of the wind at several points in the USSR.
Although the radiosonde data are less accurate, they offer the possibilit.y of
obtaining a three-dimensional picture of the wind in the boundary layer of the
atmosphere. A large number of observat3ons and a quite large set of altitudes
obviously permit us to obtain reliable climatic charaeteristics of the wind shifts.
The calculation of the characteristics of the vertical wind shifts based on the
velocity differences of two adjacent levels contains a doub le random error. There-
fore, th~ magnitude of the shift is calculated with less accuracy than the values
of the velocities themselves on the levels. In addition, the accuracy of
determining the wind shift depends on the thickness of the layer for which it is
- determined. Thus, the shifts caleulated for layers of different thickness can not
. he cumpared to each other. Thus, by the results of the calculations presented
below, a maximum shift is easily detected in the 500-600 meter layer comparable
to the values in ~he low~r (3C0-500 meters) and higher (600-900 meters) layers.
The problem of the relation of tfie layer thickness to the wind shift in the
ground layer is investigated in detail in [4], and in the f ree atmosphere, in [8].
The most important of the characteristie shifts used in aviation is Y-- the mean
- value of the modulus of the vector shift. Therefore in the given paper basically
a study is made of the characteristics Y(the monthly mean over many years) and
the recurrence of individual values of the modulus of the vector shifts.
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In Figure 1 the climatic maps of the modulus of the vector shifts in January and
July are presented for the 0-10~ meter layer over the USSR: In ,Ianuary and also
in July the maximum shifts are observed over idorthern Kazakhst3n and Western
Siberia, over the Central part of the European Territory of the USSR, and over the
_ Northe rn part of Kamchatka. The minimum shift regions in January a�re trace4 west
of the Urals, over tfie Eastern Ukraine and Eastern Siberia.
Tn July on the whole throughout the US~SR, the wind shifts are less than in
January. The peaks are located almost in the same regions as in the winter, over
Central Asia and Western Siberia. 0 ver the other regions the wind ahifts are
basically minimal.
A comparison of the maximum and minimum shift zones both in January and in July
indicates that relief has the pre3ominant significance in their formation. In the
anntial behavior the latter acts on the nature of variation of the wind with alti-
tude in practice ~iniformly in contrast to circulation or, in particular, the
horizontal nonuniformity of the temperature field. Both the latter factors, as
is knowns have significant annual variation.
The powerful shift maximum over Nortl~ern Kazakhstan in January is connected with
the influence of the Ura?.P4ountains ~nd the exit of the air currents to the
' Western Siberian Plain. The Southwes*_ern Currents, which prevail over the
European territory of the USS R, flow around the Ural Mountains, change direction
_ to the south and partially cross over the mountain range. Additional turbulence
with unstable stratification or lee waves with lifted inversions can occur depend-
ing on the therma~ stratification of the air after the mount ain obstacles [17].
' In the case of stable thermal stratification the current lines on the l~e side of
the mouatains are clustered toward the ground surface. The indicated factors lead
to large wind shifts.
An analogous phenomenon occurs in July. The difference can sists only in the fact
that the winds blow frum the north and northwest and flaw takes place around the
Urals from north to south. During movement of the air current toward the south
over the Western Siberian Plain and Northern Kazakhstan the wind intensifies, as
a result ot which powerful shifts are observed over this re gion. The powerful
shift maximum in July is also caused by mesoscale circulation.
In the center of the zone of greatest mean monthly shifts over Northern Kazakhstan
~ they reach 7�10'Z sec-1 in January; over the central regions of the European
Territory of the USSR they reach 5�IO-2 sec-1. In the minimum shift zones, for
example, in the foothills of Central Asia, the Baykal region, over the northeastern
part of the USSR in the center of the Siberian winter maximlun (Verkhoyansk,
Yakutskl they amount to only 2.10-2 sec 1.
The Cield of the modulus of the vector wind shifts in .Tuly, as can be determined
by Figure lb is less uniform with respect to territory, and the values of y ti~em-
selves are smaller. In the regi~n of iaximtun shifts over the northern part of
Kazakhstan they reach only S�10 sec . Over the central regions of the
~uropean Territory of the USSR in July their values decrease to 4�10-2 sec`1 in
January. At the same time it is characteristic that in '~ransbaykal, the belt of
increased shifts 5�10'2 sec-1 is retained in both January and July.
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eo ~o ta ~o ~o ea
~ e ji~ 'f
Ql - 3
_ Z~ ~ ~
S ~
D 3 \
~
/ ,r . % ~ \
V ~ i i ) ~ \ ~
~41 ~ , ~ , / ~ ~ ~ ~ 2 .
I ~ 4 3
. ~ ~ ~F
~ ~
p y J 40
~C ~ ~
~ ~2 . .
~ 2~..4 w�
80 AO 100 140
_ ~ g. 2 ?
; . i. ~ , , ~ .r
, ` ~ I b~` ~
.o~ i ~ . ~ �
~ ~ ;
~ ~
~ ~ ~ /
` I
' ,
~ 50
,.,r~ � . ~ \ / / I
~r.. ~ ~ I ~ 4 9
1~ ~ ~
~ . / ~ I
s % J~
_ I / J
~ ~ 1 ~ 4
r ~ / , d 4 J f 4
S .r~
1 ~
/ ~
~ ' �
~�N '
~ ~QO ~ZO - 1
Figure 1. Climatic maps of the modulus of the vector wind
sltifts Y in the 0-100 meter layer (10'2 sec 1).
a-- January, b-- J uly.
In the ground layer, near the underlying surface, the wind and shift characteris-
tics have significant diurnal variation. It is knawn that over the plains the
growtn of the modulus of the wind velocity at the surface of the earth from night
to day and some righthand rotation of the wind vector predominate. At the
100 meter level, that is, on the upper boundary of the layer, inside which a
study is made of the vertical shifts, on the cantrary, there is a decrease in the
velocity modulus in the afternoon hours. Here inversion of the diurnal behavior
is characteristic [10, 12, 15]. The diurnal variation of the wind shifts is
formed accordi~lgly.
18 ~
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- j f0'rC' ` D-f00~ .b ~ . .
6 I o
~
. o
- 4
~~~.p00
- ?00�JPO
~ JCO-S00 ~p0�109
0�J p-S 0
F000�J;;u~~ 7000d000
~
~,3 S ;1 !1 2! 13 S 11 11 13
_ Figure 2. Diurnal variatian of the modulus of the vector shift ~
in various layers in Januaz,y (a) and July (b). Kzyl-Orda.
Figure 2 shows an example of the manifestation of the diurnal behavior of the
wind shiFts. It is clearly expressed in the lawer part of the boundary layer.
The shifts decrease from night to day as a result of a decrease in the wind
velocity at an altitude of 100 meters during the daylight hours. The author of
reference [1.8] arrives at the same conclusion on the basis of using the observa-
j tions at the Obninsk T~wer. With an increase in altitude of the investigated
I layer the diurnal behavior damps, and at altitudes on the order of 500 meters and
~ higher the shifts are insignificant.
;I
In the table the July distribution is presented for the differences of the moduli
; of the wind vector shifts in the 0-100 meter layer between night and day observa-
~ tions. This distribution was obtained by analyzfng the results of th~ observations
~ of all 146 stations. The analysis demonstrated that in the 0-100 meter layer a
decrease in the magnitude of the modulus ot the wind vector shift from night to
day predominates. On the average in July the shift decreases by .(0.8 to 1.0)�10-2
sec-1 The predominant number of cases (34.5%~fall in the gradation (1.1-1.5)�10-2
i sec'l. As was alread}~ noted earlier, this takes place as a result of an increase
, in the wind velocity from night to day a* the surface of the earth with a simul-
! taneous decrease in it at the 100 meter altitude. However, the tab le data indi-
' cate that at some of the stations, a different diurnal behavior of the vector
~ shift modulus is observed. A detailed analysis shows that this diurn al behavior
is characteristic of stations over which local circulations are imposed on the
air currents such as mountain-valley, breeze, foehn, and so on (Nagayev Bay,
Ayan, Chita, Yuzhno-Kuril'sk, Dzhalal-Abad, Ust'-Barguzin).
For estimates of the degree of flight safety in practice frequently the probability
characteristics that the shifts will exceed a given value are used. The authors
constructed maps of the probabilities of the moduli of the vector shifts exceeding
values of 8�10'2 s~c-1 and 12�10-2 sec 1. The shifts of the values of 12�10'2 sec'1
by the KAM-IV VMO scale I16] are considered strong. They can be recognized as
still stronger if we consider that in tfie ground layer the wind gradients decrease
- rapidly with altitude, and for aviation the most sensitive is the shift in the
lower 60-meter layer. The corresnonding maps are not presented in the given paper.
19
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Distribution o~ the Differences of the Wind Vector Shi~t
Moduli Between Night and Day Observations
Gradation, 10- , sec-~
c- 1,1 -1,0 -0,5 0,0 0,6 l,l 1,6 2,1 2,6 3,1
I-O,tiI-U,[ I 0.,5 I 1,0 I 1,5 I 2,0 2,5 . 3,0 I 3,5
_ Recurrence, 1,4 ~ 5,0 8,5 I 17,0 19,5 34,5 9,2 I 3,5 0,7 I 0,?
It must be noted that these maps are to a great extent ana~ogous to the maps pre-
sented in Figure 1. For the majority of stations in the USSR the .recurrence of
the shifts greater than 12�10-2 sec'1 can be estimated in 2-3% of the cases in
January and in 0.5-1% of the cases in July. In the regions of the largest
vertical shifts, shifts larger than 12�10-2 sec 1 can be observed in January over
Kazakhstan with a probability, of 7% and in July over Central Asia with~probability
of 2% and more. The fact of the appearance of strong wind shifts over Central
Asia is conf.irmed in reference [9] on the basis of the analysis of balloon obser-
vations.
In Figure 3 the envelopes of the profiles of the maximwn moduli of the vector
shifts for 10 years are presented for the Kzyl-Orda station. As is obvious in this
figure, shifts:on the order of 20�10-2 sec'1 and more can be observed in the lower
layers. The probabilities of such shifts are small less than 0.5%; hawever,
such shifts present serious danger on takeoff and landing of aircraft and by the
- KAM-IV VMO scale belong to the category of very strong shifts.
Nr+
- 2000
f000
~p ?0 0 10 1~ G'
Figure 3. Envelopes of the profiles of the maximum vector
shift moduli in January (a~ and July (b).
The ca].culation of the probability characteristics of the wind shifts (recurrence,
quanti].es, and so on) directly ~rom the observation series is very labor-consuming;
thereEore indirect calculation of them beginning with the use of hypotheticnl
distribution laws and their parameters is of obvious interest.
Let us assume that the vector of the vertical wind shift is distributed by a
normal law
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f~Ts~ i y~ = 1~.- X
2 n a~ ay j!
X @X - ~ ~1x-Tx)s _ 2 r (7X--~7z.)~7y-7Y~ -I-
p{ 2 I 1- r=) [ Q2 Qx Qy
x
_ , + ~7y r Ty~~ ~1~
z
~
where Yx, Yy are the random shift components in the zonal and meridional direc-
tions;
yX, ~yy are the co~rpon~nts of the mean resultant shift;
6X, c~y are the mean deviations of the component;
r is the correlation coefficient between them.
Let us ~urther assume that aX ~ and r=0. Then the shift vector is scattered by a
circular law. In this case t~ie ~oint density of the modulus Y and the direction
of the random shift R in polar coordinates asstm?es the form
; ~ Y~ - 27r 7 cos - ~r) + 7= ~ � (2~
j f f7~ = eXP ~ '
Ta7
-i
~ where a=~ aX~= ~X lr2 =�y Yl is the vector mean square ~ deviation.
~i By corresponding integration of (2) it is easy to obtain the distribution densi-
~ ties of the direction and modulus of the shifts:
li F e_~R (1 -{-~l~'ze~' (1 ~ (s)~}, ( 3)
= 2n
i G ty, - 2~ PXp l- - ) �le ~ o ~ (4,
' ~x \ ~7
~ ~ Q
- Here ~ = 7,l0~ z = cos -
- ~ ~ _ ~X 7 y, = arctg l'~X~7y)~
yr and ~r are the modulus and direction of the mean resultant shift. The angles
S and Sr are reckoned from the north clockwise.
Distributions of the type of (3) and (4) are known from the literature on the
wind statistics [7, 11]. The distrib ution of (4) is known as the generalized
Rayleigh law.
In order to use the distributions (2)-(4), in addition to the resultant shift
vector it is also necessary to know its dispersion. The mean square deviations
of the shifts usually are not calculated, a1d they are presented extremely rarely
?n the ].iterature. Therefore it is necessary to use another distribution parameter
21
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analogous to the parameter of the climatic wind stability. It is determined by
the ratio of the modulus of the mean resultant shift vector to the mean value
of the vector shift modulus:
_ S - T~ (5)
, This parameter proposed by Ya. Narovlyanskiy, N. V. Kobysheva and
M. Ye. Kaulina [13] characterizes the degree of variability of the wind shifts
with respect to direction. For recalculation of s to ~(this permits deteYmina-
tion of Q), it is possible to use the functions relating the analogous wind
parameters [11). Then it is possible to use relations (2)-(4). Thus, in order
to know the distribution function of the shift vector, parameters Y, Yr, Sr must
be known. For calculations of the probabilities and quantiles of tne vector
sltift moduli, it is sufficient to know two parameters: Y and Yr'
The calc:ulations made by the authors in the example of the stations of the USSR
demonstrated that, as a rule, the hypothesis of Rayleigh distribution of the
vector shif~ modulus does not contradict the observation data for the 5~ level of
_ significance of the Pearson number.
BIBLIOGRAPHY
l. Abramovich, K. G.; Glazunov, 9. G.; Stepina, M. P. "Vertical Wind Shifts
in the Lower I.ayer of the Atmosphere," TRUDY GIDROMETTSENTRA SSSlt
[Works of. the USSR Hydrometerological Center], No 70, 1970.
2. Borisenko, M. M. Peculiarities of the Vertical High Wind Profile According
. to Measurement Data on High Towers," TRUDY GGO [Works of the Main Geophysical
ObservatoryJ, No 241, 1969.
3. Cavri.lova, Z. I.; Guterman, I. G.; Krylova, L. M.; Popkova, L. F.;
Khanevskaya, I. V. "Basic Steps in the Development of Aerological Data Under
the Program for the New Aeroclimatic Reference of L�he USSR," TRUDY VNIIGPTI-
MTsD [Works of the All-Union Scientific Research Institute of Hydrometeorolog-
ical Information World Data Center], No 50, 1978.
4. Glazwnov, V. G. Vertical Wind Shift with Different Layer Thickness in the
Ground Part of the Atmosphere," TRUDY GIDRUMETTSENTRA SSSR, No 70, 1970.
- 5. Glazunov, V. C. "Vertical Wind Shifts for Different Temperature Stratifica-
tion in the Lawer 300-t4eter Layer of the Atmosphere," TRUDY GIDROMETTSENTRA
SSSR, No 60, 1972.
6. Glazunov, V. Conditions of Occurrence of a Strong Vertical Shift in the
Lower Part of the Ground Layer of the Atmosphere," TRiJDY GIDROMETTSENTRA
SSSR, No 62, 1975.
7. ~uterman, I. C;. RASPREDELENIYE VETRA NAD SEVERNYM POLUSH_ARIYEM (Wind
Distribution over the Nortt?ern Hemisphere], Leningrad, Gidromegeoizdat, 1965.
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- 8. Guterman, I. G. "Vertical Wind Shifts," TRUDX NI~AK jWorks of ~the
Scientific Research Institute of Aeroclimatology], No 56, 1969.
9. Isamukhamedova, U. "Powerful Vertical Wind Sh~fts in the Aircraft Takeoff
and Landing Zone at the Airports of Uzhekistan," TRUDY SANIGMI [Works of the
Central Asian Scientific Research Hydrometeorological Institute], No 25(40),
1966.
10. "Climate of the Free Atmosphere and Boundary Layer Over the Territory of the
USSR," edited by I. G. Guterman, TRUDY VNIIGI~-MTsD, No 60, 1979.
` 11. Marchenko, A. S. "Circular and E lliptic Forms of the ~tao-Dimensional Normal
Law in the Aeroclimatology of the Wind," TRUDY NIIAK, No 25, 1964.
_ 12. Mashkova, G. B. "Problem of the Gradient Wind ~Ielocity in the Boundary
Layer," METEOROLOGIYA I GIDROLOGIYA [Meteorology and Hydrology], No 12, 1971.
13. Narovlyan~kiy, G. Ya.; Kobysheva, N. V.; Kaulina, M. Ye. "One of the
Possib le Methods of Calculating the Maximum Vertical Wind Shifts," TRUDY
NIIAK, No 38, 1967.
14. Orlenko, L. R. "Procedure for Processing the Temperature-Wind Sounding Data
~ in the Boundary Layer," TRUDY GGO, No 257, 1970.
_ 15~ Orlenko, L. R.; Shklyarevich, 0. B. "Vertical Wind Shifts in the Boundary
~ Layer of the AtmosPhere (According to the Experimental Data)," METEOROLOGIYA
; I GIDROLOGIYA, No 10, 1974.
~ ~
i 16. Petrenko, N. V. "Resolutions of the Fourth P~xeting of the Commission on
; Aviation Meteorology of the World Meteorological Organization," I~TEOROLOGIYA
I GIDROLOGIYA, No 6, 1968.
I, 17. Smit, K. OSNOVY PRIKLADNOY METEOROLOGII [Fundamentals of Applied Meteorology],
~ Leningrad, Gidrometeoizdat, 1978.
i
j
18. Tsverava, V. G. "Studies of the Vertical Wind Vector Shift by Observations
on a 300-Meter Meteorological Tower,"METEORULOGIYA I GIDROLOGIYA, No 2, 1967.
i
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UDC 551.(558.1+509.6)
SIMULATION OF THERP4ALS
Moscow METEOROLOGIYA I GIDROLO~IYA in Russian No 5, May 81 pp 24-32
[Article by N. K. Didenko, V. N. Ivanov, Candidates of Physical and Mathematical
Sciences V. Y a. Korovin and V. V. Smirnov, Institute of Experimental Meteoro logy,
- manuscript received 26 Aug 80]
[Text] lhe results of studying the evolution of thermals obtained
during volumetric combustion of aerosuspensions in a pure
atmosphere and under conditions of a model cloud environment
are presented. The proposed model of a thermal takes into
account the efficiency of the conversion of the chemical
energy of the suspc~nsion to buoyancy energy and also the
conversion of a spherical thermal to a turbulent vortex ring.
Examples of the practical application of the results are
presented.
Thermals on the order of a meter in size and with a height of rise on the order of .
tens of ineters were simulated by creating local sources of volumetric heat
release in the atmosphere.
The study of the ordered vertical movements of air in the form of thermals and .
plumes is of interest from the point of view of constructing quantitative models
of the development of convection [1], and it has a number of important practical
applications in aviation and atmospheric process modification te~.hnology [13]. ~

~ It is also important for the removal of impurities from atmospheric air [16], and
so on. Some of the laws of the evolution of the structure of thermals with differ-
- ent initial parameters have been investigated theoretically [1-3, 14, 15] and
experimentally (see, for example [1, 12] and the bibliography referenced in them).
Nevertheless, there is no strict quantitative theory of th e evolution of thermals
~aith high initial buoyancy energy. Such thermals (hereafter called intense) are
characterized by conversion to a spherical vortex during movement and then to a
vortex ring [2, 12, 14J. The laws of the temperature distrib ution and variation
of the rate of ascent of intense thermals with altitude under turbulent
atmospheric conditions also requir.e .further study.
The purpoGe of this paper was an experimental study of the dynamics of the
dc~velopment of intense thermals cr~ated both under laboratory conditione and in a
real atmosphere on i~niting an aerosuspension based on a metal aerosol.
24
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Experimental Procedure and Results
Analysis shows:that �or the simulation of artificial thermals with compa~ativelZ~
large initial volumes the use of the reaction of volumetric high-temperature
oxidation of fuel, in particular, based on metals of the aluminum and magnesium
_ type with high heat of combustion and high (by comparison with gas and liquid-
drop fuels) combustion rate of their aerosuspensions turns out to be effective.
An air-atomizing burner Grith an output capacity of about 100 g of powder per
pulse was used to spray the powder. Spark and remote laser techniques were used
to i gnite the aerosuspensions [6]. In order to insure continuous flame propaga-
tion in the aerosuspension, a concentration by mass of the fuel particles ~was
created no less than some limiting value, the so-called lower concentration limit
which for metallic aluminum is 45 g/m3, but no more than a maximum value defined
by the sto~tchiometry of the oxidation reaction (for aluminum, 300-310 g/m3). In
the experiments the concentration by mass of the reagent was 100-200 g/m3, and the
- mean square particle diameter was 10 mi~rons.
~ ~ ~ .
rt x
~ ~
C i X.
f
+ f ~~i.
k ~
~j .t.
7 0,78 0,44 0,20 0.13 U,09 0,07 O,U5
U,31 0,79 U,7~ 0.~0 0,72 0,4ti 0,22 U,18 0,12 0,08 0,05
0,95 0,94 0,92 0,59 0,85 U,55 0,31 0,26 U,21 0,15 O,II
I,00 0,98 0,97 0,60 0,83 0,50 0,25 U,20 0,17 0,13 0,[5
- 1,00 U,99 0,61 0,82 0,45 0,20 0,16 O,14 0,11 O,~J
~,00 U,62 0,84 0,45 0,20 0,15 O,13 O,(U U,09
1.W 0,59 0,35 O,t8 O,15 U,12 0,08 0,08
1~00 U.79' 0,51 0,51 U,43 U,34~ 0,43
I,00 0,77 U,83 0,71 0,55 0,3�~
1,OQ 0,83 0,76 U,til 0,39
. 1~00 0,88 0,65 0,40
~ i,~ 0,77 0,53
1.00 0,59
' 1~00
I'~ Matrix Prirk
I
i
~
=j rx, microns � '
1'6 I ~.9 2~4 I ~.2 I 4,0 5,0 6,0 3.3 It 14 '
~ I I I
~
0,23 0,39 0,47 0,54 -0,2~
I~ 0,13 0,27 0.;;;; -0,15 -0, I8 - 0,47
0,14 U,26 p ~ 0,39 -0, }9 -0,31 -0,2T -0,10 -0,13 -~0,33
0,35 -0,18 --0,30 -0,27 -0,07 -0,12 -0,2fi
0.22 U,34 0.37 p,40 _p,20 _p~~ _p.29 -U,12 -O,14 -0,22
0.44 0,52 0,51 0,51 -0,25 -0,41 - 0,36 -0,16 --0,19 -0,11
0,64 0.75 U,76 0,74 - 0,19 -G,31 -U,27 - 0,13 -O,18 -0,37
0,50 ~,62 O,ti~ 0,6:3 -0,18 ~-U,30 -0,25 -0,13 -U, l9 -0,39
U,G2 O,iO 0,;1 U~bg -p,16 -0,18 -0,12 -0,07 -0,20 -O,~ig
O.i8 ~~31 U,i9 O,i3 - O.lti -0,04 0,04 -O,UI ~-0,19 -U,28
0,91 0,87 0,8U 0,71 -0,~8 -0.(?9 0,01 U,11 --'J,10- -O,ll
0,98 U,93 0,85 p,;2 -0,32 -0,29 -0,21 -0,10 -0,07 0,06
- 1~ W ~~~6 0.88 O~i~ --0,33 -0,40 - 0~33 0,05 =0,07 0,06
~ 0,96 p,$7 -p~3p -p,q4 _p~38 -0,0! -0,13 -0,09
0,95 - 0,25 -0,41 -0,35 --0,07 -0,18 -U,21
I,W -0,22 -0,34 -0,29 -0,07 -0,15 -0,32
1,00 0,23 0,02 0 -0,04 - 0,16
1,Oq 0,96 0,10 -0,06 - 0,25
1,00 0,10 -0,05 -0,23
' 1.,00 0,08 -0,10 '
; ' I,OQ 0,24
� , 1,00
39
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It must be noted tl~at the profile that we obtained for a dust storm is distorted
somewhat in ttie particle size range of r>10 microns, for usually a reduction in
the concentration of particles of the indicated sizes as a result of a decrease
in the aspiration factor with increasing wind velocities is observed in the opto-
electronic spectrometers of the type described in j7] for a number of technical
reasor~s. For the winter season the particle size distribution n(r) (curve 3) is
described by the Junge distrib~ition with index ~=3 which corresponds to the con-
ditions in temperate latitudes [8].
Seasonal differences in the investigated particle size spectra obviously have a
stable nature and must be explained by two basic causes:
1. Karakumy belongs to the subtropical climatic zone: in the fal~l, tropical
air predominates here, but in the winter the air from the temperate latitudes
becomes predominant in the given region.
2. A no less important event for understanding the results is the condition of
the underlying surface. In the fall, as a result of sharp heating of the soil in
the presence of high winds, as a result of gri.nding and fragmentation of the coarse
- grains in the eolian sands characteristic of the regian of investigation, soil
particles are formed with sizes of less than SO microns. In the presence of winds
with velocity of Vg>4 m/sec, the latter are sucked off the earth's surface and
carried by the ascending currents from a state of rest to motion in the suspended
state [5]. In February-March 1979, the sand surface was wet, and above the wet
surface the sand moved near the surface and did not rise into the air [5], that is,
conditions were observed under whict~ the transtormation of the aerosol content of
continental temperate air was not attenuated by the effect of a local particle
source.
The aerosol parti~l.e size distribution spectra obtained during the fall period
were compared wifh the results of ineasurements under the CENEX-70 program [1] and
also wi.th the data of I. Blifford [9]. It is possib le to confirm good cerrespond-
ence of the compared materials, which, first of all, indicates representativeness
of the presented materials and, secondly, indicates the usefulness of the hypothe-
sis of similarity of processes regulating the state of the dispersed material in
the atmosphere within the limits of like geographic regions.
The normalized correlation matrix of prirk defining the spectrum sample {n(r)}
for "normal" conditions in the fall is presented in Table 2, :?nd for the winter,
in Table 3. The corre~.ation matrix prirk characterizing the spectrum sample
{n(r)} .f.or a dust storm was not calculated in view of its statistical uncertain-
ty. During the fall a quite strong correlation (prirk-0.9 to 0.~ was noted
hetween the particle Lractions in the ran~e of 0.23.2 microns the correlation coefficients pri~ pass through zero
and become negative. The correl ation matrix of the winter season is similar with
respect to its structure to the corresponding correlation matrix for haze in the
spring in temperate latitudes (s e e, for example [4]).
Thus, the sessonal variability o f the aerosol size spectra in the arid zone is
determined by the condition of the underlying surface and the circulation condi-
tions in the given geographic re gi.on.
In conclusion the authors expres s their appreciation to G. Maksimov for help in
performing the calculations on a comp uter and also the members of the GAREX-77
- and GAREX-79 expeditions and K. Ya. Kondrat'yev for making it possible to partici-
pate in joint work.
BIRLIOGRAPHY
l. Dmokhovskiy, V. I.; Ivlev, L. S.; Semova, L. Yu. "Aerosol Measurements in the
Layer of the Atmosphere Next to the Earth in Karakumy," TRUDY GGO [Works of
' the Main Geophysics Observatory], No 276, 1972.
' 2. Ivanov, V. P.; Filippov, V. L.; Sidorenko, V. I.; Maslennikov, P. A.
! "Statistical Characteristics of the Aerosol Particle Size Spectrum Variations
in the Arid Zone," IZV. AN S S SR. FIZIKA ~TM~SFERY I OKEANA [News of the
! USSR Academy of Sciences, Phy sics of the Atmosphere and Ocean], 1980, in press.
I 3. Kondrat'yev, K. Ya.; Vasil'y ev, 0. B.; Ivlev, L. S. GLOBAL'NYY AEROZOL'NO-
j RADIATSIONNYY EKSPERIMENT (GA.REKS) [Global Aerosol-Radiation Experiment
(GAREX) Obninsk, VNIIGl~'~i-MTSD, 1976.
I 4. Laktionov, A. G.; Lyubovtseva, Yu. S.; Malkevich, M. S. ':Some Statistical
Characteristics of the Aeros o 1 Microstructure in th~ Layer of the Atmosphere
Next to the Earth," IZV. AN SSSR. FIZIKA ATl~!OSFERY I OKEANS, Vol 9, No 2,
1973.
5. Petrov, P4. P. PUSTYNI ZEMNOGO SHARA [Deserts of the Earth], Leningrad,
Nauka, 19 73.
6. Filippov, V. L. "Atmospheri c Aerosol Formations. Morphology and Seasonal
Gradations," IZVESTIYA VUZOV. FIZIKA [News of the Institutions of H3igher
Learning. Physics], No S, 1 976.
n
- 7. Filippov, V. L.; Kazakov, V. N.; Mirumyants, S. 0. Kvant-902IM Aerosol
- Classifier," I VSESOYUZNOYE S OVESHCHANIYE EO ATMOSFERNOY OPTIKE jAll-Union
Conference on Atmospheric Op tics], Part II, Tomsk, IOA SO AN SSSR, 1976.
41
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8. Junge, H. KHIP4ICHESKIY SOSTAV I RADIOAKTIVNOST`~ATMOSk'ERY jChemical
Composition and Radioactivity of the Atmosphere], r~oscow, Mir, 1965.
9. Blifford, I. H.; Ringer, L. D. "The Size and Number Distribution of Aerosols
in the Continental Troposphere," J. ATT40S. SCI., Vol 26,~No 4, 1969.
10. Patterson, E. M.; Gillete, D. A.; ~rams, G. W. "The Relation Between
Visibility and Size-Number Distribution Soil Particle," J. APPL. ?'~TEOROL.,
Vol 15, No 5, 1976.
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UDC 551.509.314
EFFECT OF STATION NETWORK DENSITY ON INTERPOLATED VALUE VARIABILITY
CHARACTERISTICS
Moscow t'ETEOROLOGIYA I GIDROLOGIYA in Russian No 5, May 81 pp 39-47
[Article by Boctor of Physical and Mathematical Sciences R. L. Kagan and
Candidate of Physical and Mathematical Sciences Ye. I. Khlebnikova, 2~~ain ~-eophysics
Observatory, manuscript received 2 Sep 80]
[Text] Abstract: A study is made of the problem of distorti on
of ineteorological field variability characteristics
during spatial interpolation of them. Evaluations are
made of the underestimation of the dispersion and over-
' estimation of correlation for fields of different
statistical structure. The distortions of nongaussian
li value � distribution are also considered (in the
; example of logarithmtc-normal distributian). It is
' demonstrated that different station network dc:nsity
in different parts of the earth can lead to significant
nonuniformity of the interpo~ated value field even in
cases where the in vestigated field itself is uniform.
li Increasing the station network density during instrument
j observations can lead to a fictitious secular behavior
~ of ~he variability characteristics of ineteorological
fields.
I When investigating climate variations values of the meteorological elements
interpalated to the nodes of a regular (for example, latitudinal-longitudinal)
- grid are often used instead of values actually measured at the stations. Naturally
the variability characteristics of the investigated values must be distorted. The
distortion can be different depending on different factors, including the station
network density. For a comparatively sparse network used when studying climate
variations, underestimat~on of the dispersion and overestimation of the spatial
correlation of the interpolated values by comparison with the corresponding
characteristics of the initial field, underestimation of the gradients and over-
estimation of the precision of the interpolation, and distortion of the non-
gaussian value distribution must occur.
The possibility of such effects has been pointed out many times (see, for
example, [4, 6]), but the ma~ority of specialists use the data at the grid nodes
under the assumption that in quantitative respects the variability distortion is
43
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comparatively Yow. In this art~_cle we shall try to illustrate how significant
this distortion can be and how important it is to consider this distortion when
investigating climate variability.
- Numerical experiments were performed for this purpose in which the following were
given: the statistical structure of the investigated meteorological field,
mutual arrangement of the interpolation nodes and stations at which observation
data are available for the value of f, and also the method of interpolation of
the values iror~i the stations to the grid nodes. Such field characteristics as
the dispersion (a2) and spatial correlation (r) were determined by these data,
evaluation of which with an interpolation of the type of
n
Jl - ~ pRfk' (1>
4=1
where fk are the values at the stations,
f. is the result of the interpolation at the i-th node of the grid,
i
pk is the weight of the interpolation,
can be performed by the following simple formulas:
n n n
r,i= Q~1,~ ~ �P~PiYRr+'~' ~PRP~ ~ (2)
,e_, k_~
~2 n n ~ ~3~
a; _ _ ~ ~p~Pi rkt ~ ~Pk1~�
rr ' R=1 1=1
Here n2 is the measure of the errors in the initial data (see, for example [3]),
rkQ is the correlation coefficient between the actual observation data at stations
k and Q,
r.. is the correlation coefficient between the interpolated values at the nodes
i
i ~nd j,
a2 is the dispersion of the interpolated values.
These Formulds pertain to the case of a unifo~, isotropic field which, generally
speaking, only roughly corresponds to reality, especially for large-scale areas.
However, this is not basic; the indicated estimates can be perform~ed also for a
nonun~form field, but in the given step it is more significant to show that in
the case where the actual initial field is imiform, the field of the interpolated
values turns out to be nonuniform.
- An estimate was also made of the distortion resulting from interpolation of the ,
nature of the distribution of nongaussian meteorological fields. A statistical
Gimulation of the values of the meteorological field at the stations and at the
nodes of the given grid was performed for this purpose with subsequent estimation
of the distribution of the interpolated values and its moments and comparison of
these characteristics with the characteristics of the initial meteorological field.
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In the described experiments, station networks of different density were simu-
lated. Here, alon~ with the reference station network, for which a regular
square network was given with grid spacing H, a study was also made of irregular
networks characterized by the same average statian densi.ty with respect to area
for which the coordinates of the stations were simulated by introducing random
~ shifts in the reference network coordinates. Inasmuch as the characteristics of
the interpolated values depend on how close the interpolation node is to the
reference station, and in this sense, the interpolated value field obviously is -
nonuniform, in order to discover the regular differences of this field from the
, initial field we performed estimates for a group of dense interpalation nodes
with subsequent determination of the average characteristics. The calculations
were performed as applied to correlation functions characterizing the fields of
different meteorological elements. Two procedures were used as the interpolation
algorithms: optimal interpolation, for the application of which data are needed
on the statistical structure of the initial field, and bilinear interpolation
not requiring that information be supplied, f~r which the field is formally
approximated in the vicinity of the node by a first-degree polynomial with respect
to each of the coordinates. Interpolation to the grid nodes was carried out by
the data f"rom four stations, for the selection of which the newest station was
found in each of the quadrants.
Let us present some results obtained for the case of an exponential correlation
function of the type
r (o) = exp p/pal~
(4)
where p is the distance between points,
p~ is the field correlation scale.
The estimates show that the interpolated value field dispersion is significantly
underestimated by comparison with the initial field dispersiran. In the case of
optimal interpolation for distances between statians not exceeding 2p~, this
underestimation i s approximated well by a function of the type
z= c( l- y~~/8)( t- 0,23 t~iPo)� (S)
Thus, for H=2p~ the mean square deviation of the interpolated values ~ turns out
to be hal.f the true values of Q. Comparison of the two interpolation methods
shows that for bilinear interpolation when H;pQ underestimation turns out to be
approximately the same as for optimal interpolation. For a sparser network
(l~>F~p) bilinear interpolation understimates the field dispersion leas than optimal
interpolation, wtiich in some sense compensates for its lawer accuracy.
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Table 1. Correlation r(p) of Interpolated Values for Dif~erent
Methods of Interpolation and Values of the Measure of the
Observation Errors r12
(rlP) = exP PIP~J; H = ?o)
~ p (e Aonax or H) (1) . - _
Cnoco6 Nx-
rep~2~A11NN O,125 0,250I 0,375I 0,,`i0 0.75 1,00 I 1,25 l.~ .
I I
0 OnrHe~am~- 0,99i 0,'J39 O,~J77 I 0,961 I 0,925 I 0.887 I 0,84i I 0,800
Nk,IN I I
EN:INp~~Nd~3 0.997 0.989I 0,976 U,960I 0.923I 0,885I 0,844I 0,793
~ I I
~,OJ O(1TNH3lIV� O,~~J U,~~ ~~~3 0,9.~ 0~~ I 0~~ 0,8~ I ~,g12
H~A 3 I I
6~~n}iHei+nwESI 0,994 I 0,982 I 0~967 0,949 I 0,914 0,383 0,344 0,791'
r~?) U,969 '0.939 I 0,911 I 0.883 0,829 I 0.779 O,Z32 0,687
Key:
1. (in fractions of H)
2. Interpolation method
"i. Optimal
4. Bilinear
Val.~ies of the correlation functions of the variables obtained by optimal and
bilinear interpolation of the initial field are presented in Table 1 for the
given grid size of a regular station network H, for presence and absence of
observation errors. I'rom these data it can easily be seen how much the interpo-
lated value correlation is overestimated by comparison with the initial field
correlation, where the optimal interpolation distorts the correlation function
more than the bilinear interpolation. However, the difference of the correlation
functions of the values obtained by different methods of interpolation, is small
by camparison with the deviation from the true correlation function. The struc-
tural characteristics of the interpolated values also depend comparatively little
on the measure of the initial data errors. Along with overestimation of the
correlation as a result of interpolation, the nature of the correlation function
changes signi.ficantly for small spacings: in contrast to the initial function,
- the correlation Function of the interpolated values is characterized by differ-
entiaU.ility at zero, which can lead to high distortion of the estimates of the
fiel.d ditference characteristics.
As t~as already been noted, the estimates of the distortions of the statistical
structural characteristics of the �ield as a result of interpolation were made
also for nonuniforn~ arrangement of ttie stations. It ~~ias discovered that with
averagin~ over large territories the statistical structural characteristics of
theinterpolated values calculated by the data from nonuniformly arranged stations
turn out to be more distorted than the same characteristics obtain ed by a
- regular station network.
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The calculations performed for the correlation.functions of the type differing
from (4) lead to conclusions analogous to those presented above.
Table 2. Distortion as a Result of Interpolation of the
Distribution of a Logarithmically-Normal Va1ue (mean e~ual to 0;
r~F)=eXP~- F~'ro)~ H~ Po)
Lle~cpepei~uNanb~+aA AN�~cpepeHUxanbMaA
~2~ (pyHhLLNA / ~yHKl1HA
NHTepaan P cnpeaeneH?+A yNrepean _ ~ ~acnpelte~eHNA
~1` HCTHH- IIOCAE NH� NCTHH� IIOCJIC NN-
, ~~CHNA8. iePUNN~4 ~1~ ~ ~ 9EHNR . ~p1lNNA ~~F~
-2,5 -2,0 0,001 0,000 1,5 2,0 0,038 0,025
-2,0 -!,5 0,025 0,003 I 2,0 2,5 0,020 0,0l0
-1,5 -1,0 0, I 14 0,047 2,5 3,0 0,010 0,002
-1,0 -0,5 0,204 0,187 1 3,0 3,5 0,005 U,001
-0,5 0 6.219 0,295 , 3,5 . 4 0 0,003 0,001
0 0,5 0,174 0,235 CT8HA8pT 1,00 0,73
0,5 l,o o,t 16 0,137 Ko~p. acxa~. (6) 1,00 0,77
- 1,0 1,5 0,069 0,057 I KO . 3KCI1. 7 1,83 1,17
Key:
l. Interval 5. Standard
2. Differential distribution function 6. Asymmetry coefficient
3. True values 7. Excess coefficient
4. After interpolation
~ Some estimates of the distribution of the tnterpolated values are presented in
Table 2 for a logarithmically normal value with exponentially decreasing correla-
- tion coefficient (let us note that this model in many cases satisfactorily
~ describes the statistical structure of the precipitation totals). From a compari-
' son of this distribution with the true distribution it is obvious that the
spatial interpolation leads not only to underestimation of the dispersion, but
a].so to sharp distortion of the nature of the investigated value itself, making
i it rapidly approach normal.
The estimates show that the optimal interpolation underestimates the field dis-
persion more than the bilinear interpolation, ~ust as it does with other m~thods
of interpolation. Accordingly, the question arises of to what deg~ee it is
expedient to use it for various purposes. However,. it turns out that it has a
number of advantages by comparison with other methods of interpolation. Let us
- only point out that there is a unique relation between a and the mean square rela-
tive interpolation error e~ described by the simple expression
ac 1-co. (6)
The value of e is calculated automaticall_y during the process of optimal interpola-
tion, and the singularities of its spatial distribution have been studied quite
well for various meteorological fields [1, 3]. This permits estimation of the
= geo~raphic distribution of the meassre of underestimation of the standard in
various parts of the earth for many meteorological elements, using the previously
performed estimates of the accuracy of the optimal interpolation.
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(~uantitar'~~e estimates of. the distortion o~ the variability characteristics for
fields of specific meteorolopical elements depend both on the form of the correl~-
tion function and on the relation between the density of the station network and
the correlation scale. For example, the spatial correlation function of exponen-
tial type (4) is characteristic for a number of ineteorological elements, including
the precipitation totals, radiation, total ozane content, for the monthly values
of which the correlation scale is several hundreds of kilometers, about 1000 km
and 1600 km, respectively. As applied to the precipitation field the estimates
- show that in more populousareas wherethe average distance H between precipitation
- gauging stations is about 50 km, the underestimation is within the limits of 10%.
For sparsely populated areas of the USSR, for which a value of H~150 km is
characteristic, this underestimation is different for different are ~ and in dry
regions, it reaches values of 20-30%. The total radiation has sign ificantly
greater connectedness; inasmuch as, however, the actinometric station network is
much sparser than the precipitation measuring network, even in continental regions
there are broad expanses for which the underestimation of cs exceeds 20%. The
situation is still worse in the oceans in which the actinometric network is in
practice nonexistent. I'or total monttil.y ozone contents in Western Europe where
the distance between stations H is about 400 km, the underestimation of ~ is also
~oithin the limits of 10%. For values of H=800 km, characteristic of the ozono- '
metric network of. the USSR, it is about 20%. For H=2000 km, which approximately
- corresponds to the station density in the North Atlantic, the underestimation of
6 is about 40%. For such regions, of course, the overestimation of the correla-
tion function is very large.
,so
_ ~ .
.
70
. ~ 60 . ~ 1 B~ 0 BO
~ 90 ~
60 o
S 70 .
_ ~Q `
� BO ~ ~ ~
_ ` ~ b ~ j
~gp �
6 ,
,P
6 f
e..
t
6v ' ' ~
r`'~ ~ ~ 90 ~ .v9 ~ ,
` 90
J
~ 60 yG' ~ ~7U
~,9,~ c~ 70
?\108~ ~\`\S1
~ ~
~ 90 \ 90 B~ ~ 1
o i ~2
ao
ri~ure 1.. Measure of the underestimation of the standard (a)
Cor the me~n annu~31 air temperature.
1) ~r.1 ~11)
~ t~t
~I i 3~ _ n1 _ 1 ,
a the asymme try coe f. f icient
n~
c ~x~~ X~~a
Lr
nl 1~ (12)
C~~z CS~ _ ~3 ' (n~- t)ln/-
_
by the Lollowing equalities [5]:
a1-x,-a/l'(1~--~-1, (13)
l ~
~
/ , 1
c~=a~(~11 + ~1)-~'~(1 ' (14,
l \
r~i+ ~r~~+ ~~~r~i+ ~~~~-2r3~~+ ~15~
C.s = ll + ~ r=~~ + ~~3l~ - ~ (~~l�
- Frorn equation (15) the parameter S~ is de�ined as the inverse function of the
asymmetry coefficient .
- fs~ ~ ~r-~ (C,f) ^ ~C.~/), % = 0, 1, . . . , 1. (15' )
Z`wo other parameters a~ and a~ are defined successively from formulas (14) and (13).
The empirical or analytical distribution curves (6) and (9) are used to determine
the curves of the relationship of the values of equal guarantee (xop, x~ ) cf the
investigated hydrologic characteristic x at the reduction point (~=0) an~d at the
point-analo~s (j=1, 2, Q):
xop = Fu ~P ~Xlv?~~ ~ =1~ 2, . . . , l; ~16~
in particular, accordin~ to the Goodrich equation (9)
P~
_ Xu + ao rX1nQ
_ a~l ~0 ~ J = 1 ~ 2, . . . , 1� (17)
v=a~ ~ ~ I
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For identical asy~netry coeff.icients
_ C:~ = C,~o~ _ ~o~ J ~ 1, 2, . . . , l , (18)
the curves for the relationship of the values of equal guarantee (17) are straight
lines
a
X~? = Qo a� (x~p - a~)~ (17' )
~
which, according to equalities (14) and (13), can be represented as follows:
xup = xu (z~a - x~), j = 1, 2, . . . , l. (19 )
/
It must be kept in mind that when approximating the empirical distribution curves
(6) by the Goodrich, type III Pearson and logarithmically normal distribution
equat~ions, the curves of the relationship of values of equal guarantee (16) can be
expressed by the equation
xoP = x a~ ~ ~x~p _ X~), j =1, 2, . . . ,1, (20)
o ~
where ~(p, CS)=(xp x)/Q are values of the normalized quantiles presented in the
form of the tables in references [2, 5, 10].
It is important to note that under condition (la), equation (20) coincides with
linear equation (19).
In reference [7] it was shown that for any given structure of the equation of
the relation of values of equal guarantee (xP, yp)
yp = f ~xp~ Cl, b~ . . . xP ~yp+ a, b~ . . . ~ ~Zl~
the parameters of the equation a, b, can be determined by the method of "least
_ de~~iation rectangles" of the empirical points (xi, yi) from the curve of relation-
ship (21), namely, from the condition of minimum of the function
n
S (a, b, . . . ) R ~ ~Yi - J (x~, a, b. . . . x
-
(22)
X ~f-'~Y~~ a, b, . . . ) - xi~ = min,
where x=f-1 (y, a, is the inverse fimction. The problem reduces to solving
the system of equati~ns
dS (a~ b. . ) _ 0 dS (a, b' � ) _ 0 . . . (23)
da ' b ~
with respect to the parameters a, b,
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Let us note that the "least rectangles" method gives a tmique curve of the rela-
~ionship (21) between the values of equal guarantee (xP, y) at the same time as
Lzao regression curves y with respect to x and x with respe~Ct to y are obtained by
the "least squares" method:
y~=f ~ (X, a, 'b, ~241>
x=~fx ~y, a, b, ~ (242)
which coincide only for a single-valued'functional relation between x and y.
The statistical parameters (mean, C~, CS) are ~ointly reduced to a period of many
years by the following method. Using the curves (or straight lines) of the rela-
tionship of values of equal guarantee t16), (17), (19), (20) with respect to three
reference quantiles at the point-analogs x~p, for example, with guarantee of p=5,
S0, 95%
xfp = X~~ S~ xj, SA~ xJ. 95~ 1~ 2~ ....1~
� (25)
the corresponding 3~ partial reference quantiles x~p~ at the reduction point j=0
reduced to a period of many years are defined
x~P~ = xols? zartsu? x~es~ J= 1, 2, l (26)
anc~ by these auantiles, three calculated weighted mean quantiles x~P at the reduc-
tion point are calculated:
t
xoP x~P>, p= 5, 50, 95�/0� ~2
1=~
The weight coefficients Yl, Y2~ YR, which add up to one, are calculated by the
formula
~(no~ - 1 ~ n~
7~= ~ ~ 1=1,2,. . .,1,
~ ~.o! lnol-~)R/ ~28~
where r~ a~e the pair interseries Correlation coefficients calculated by formula
(3) for ~oint observation peric~ds n~~ at the reduction point (j=0) and th~ point-
analogs (.1=1, 2, k).
Formulas (27) and (2S) are central in the method of joint determination and reduc-
tion of the statistical parameters to a period of many years. The inverse dependence
of the weight coefficients of the point-analog Y. on the mean square errors (4) of
the paired interseries correlation coefficients r~ and on the mean square errors of
the partial reference quantiles (25), which decrea~se inversely proportionally to
the square root of the lengths n1. of the observed time series (1) at the point
analogs j=1, 2, R, is considered in formulas (27) and (28).
83 ~
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The desired statistical parameters reduced to a period of many years are calculated
by three weighted mean quantiles (27) for the reduction point j=0 (see [1, 2, 10]):
the distrib ution bias coefficient
Xp, 5~- Cp: 45 - 2Xp: fi0
Sp = - - -
X0;5-x0;95
(29)
~ M (5'ao ~ Csnl + ~ (9:,%. C,~l - 2~ (~090, Csol ~L ~L'~),
~ C,~) - ~ (95";c, Cs�) '
the distribution asymnetry coefficient
Csu=~V-~ ~So)=f ~So)~ ~30)
mean sq uare deviation
(31)
- xU: 6 - x0; 95
Qu - Q~ (J~~O~ C.tO~ rjn~~0~ Lso) ~
mean value
xo - xo: su - oo ~(50�I o~ Cso) ? ( 32 )
variation coeffici.ent '
- zo~ ~33~
Tlie statistical parameters (mean, C~, CS) are successively reduced to a period of
many years at the points j=1, 2, Q-1 in an analogous manner, taking the
points with longer observation periods as the analogs, that is, successively, with
the numbers
1=~~
j=l, l-1,
j=l, 1-1, 1-2
and so on.
_ By the statistical parameters reduced to a unique period of many years (n~ years)
at Q+1 observation points
X~~ a~~ Cs1, j-0, l, ...,l, (34)
using the Goodrich equati.on (9) or the existing tables of normalized quant:iles
[2, S, 1.0], the analytical cellular probability guarantee curves are constructed
P = P ~X x - F 0, l, . . , ( :35 )
~ ~~P1~ J = � 1,
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and the observed time series (1) are normalized according to these curves by
double functional transformation (see [2, 3]) �
:
uj~=?-'IP(x;~)~=u~x~i1~ c=1~2~. . .,n~; j=0,.1,. . .,1, ~36~
where ~p ~x~~ -un is the inverse function (quantile) of the normalized
normal overestimation probability distribution
� r=
P ( ) - 1 ~ e dt = 4 ~u ~XJ~ (37)
z -
y`2:c u,.r,
(see [2], pp 284 and 287).
' The normalized pair interseries (spatial) correlation coefficients are calculated
by the normalized observed time series (36) for joint observation periods n~k at
the j-th and k-th points
^Jk
~ u~; tlki nJk
u u k#j=~, 1,. . .,1; (38)
- r~R= ~~k Ji k~~
~ t-i
~ ~
i=t
the number of these coefficients
_ t~~Z 1~ ~
- for r~k=rk~ .
The intraseries (time) normalized autocorrelation coefficients for adjacent terms
of each normalized time series are also calculated,
I n~
~ u1~ u~, t-~ n~ ~ 39 )
r~ _ u~i u!, ~-i ~ I= 0, 1, 1.
^ -1 Z t-s
~ u1? ~ L u/!
, ~=1
Zn the case of. significant inequalities of the observation periods (number of
years) at four points 1=0, 1, 2, 3
no I 3 16 15
Ux > I,03 I.19 I.32 Pa ; I 0-19 1 p_s, ~ p_w
' ( 0-~' 10-~z 10-~~
N l64 1S4 120 PS <
Key:
a. Experimental da.ta
b. Experiments
c. Prob ability estimate
Notes. l. All of the dimensionless kinematic parameters of a liquid and particle~
(except acceleration ~ normalized by the amount of gravitational accelera-
tion 9.81 m/sec2) are normalized by the amount of the steady-state free fall speed
of the particles in the liquid W=0.28 m/sec.
2. The provisional notation: VX is the mean longiLUdinal velocity of the
liquid near the bottom; Q[Vx], 6[VZ] are the mean square deviatians of the longi-
tudinal and vertical cor.~onents of the velocity of the liquid near the bottom;
UD is the speed of rolling of the particles along the bottom; UX is the longitudinal
velocity of the particles after lifting off the bottom (in the lay2r z/R=0 to 0.5);
N is the number of particle trajectories processed in the exneriment; the remaining
notation is explained in the text of the article.
Basic Hypotheses and Some Experimental Data on Lifting Particles Off the Bottom
Hypothesis A: A particle lifts,off the bottom as a result of large instantaneous
values of the lift caused b_y asy~??etry of the flow of liquid around the particle
as a result of a significant longitudinal flaw velocity gradient near the b~ttom.
Apparently thishypothesis is most widespread (see, for example, jl, 4, 12, 17, 29,
34]), which raises some doubt inasmuch as the experimental checking of it more than
40 years ago by Goncharov [2] gave negative results.
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- 1~OR nl~Fl('IA1. Iitil? ON1,1'
The experimental data on saltation of bed load varticles moving alang the bottom
known to us contradict hypothesis A, for example, the fact of a decrease in lon~-
itudinal velocity of the particles averaged over a set of trajectories (Fig 1)
~ahen they are lifted off the bottom. It is obvious that the lif ting of the particle
under the effect of gradient lift must in the general case take nlace at instantane-
ous velocities of the liquid si. ~nificantly exceeding the average value and no less
than this amount [16, 17j. Consequently, in accordance with hypothesis A, for the
liquid particles the longitudinal velocity on the average must increase and not
decrease as was observed in the described experiments and also in the experiments
of Franr_is [26]. ~
I /R _ 1. ~ 2
2
9
" 3
,w;
( 0'V ',0 _ `J,/`',, .
, ~ %
Figure 1. Velocities of lifted saltating particles at different
distances from the bottom averaged over a set of trajectories.
1-- vertical, 2-- longitudinal, 3-- speed of rolling along the
bottom.
The vertical velocity ~f the particles averaged over a set of trajectories on
tif:ting them from the bottom decreased monotonically (Figure 1). This result
indicates absence of acceleration of the particles in the vertical direction at
least outside a thin bottom layer (to the first experimenta~. point from the bottom
at the level z=0.5 R) . There is little probability that the gradient li�t, the
average value of which usually is much less than the weight of the particle in
the liquid, could not only lift the narticle off the bottom, but accelerate it so
significantly in the vertical direction in the time it takes to pass through this
thin bottom layer. The numerical estimate of this probability presented below con-
firms the correctness of this argument.
Let us note that in the general case the asymmetry of the flo~a around the particle
causin~ 1if t can arise not only from nonuniformity of the velocity fie_ld of the
liquid, but also the peculiarities of the for.m of the particles (the Joukowsky
- force) ar their rotation (the Magnus f~rce). For snherical particles investigated
- in this paper, their f.orm obviously cannot cause asymfnetry of the streamlining
flow. As for the Magnus �orce, numerical estimates [7, 8] demonstrated that under
the investigated conditions for bed load, this force, althoup,h it promotes
lift, is not its cause.
Hypothesis B: The separation and lift of particles from the bottom are caused by
- the effect of bottom eddies or, in other words, positive pulsations of the vertical
� component of the liquid veloci ty near the bottom.
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~(?P, t)F~'lCIAl. l!5l~: ONLY
According to this also ~tiite widespread [2, 13, 23, 30] point of view, the particles
can be lifte~i'and undergo saltation only in 'turbulent flows. This is contradicted
by the experimental results showing that salta~ion of particles occurred in the
case of almost completely extinguished turbulence j?.5] and even in a laminar flow
L?6]�
In ttie case of developed turbulence, the lifting of the particles off the bottom was
observed both f.or positive and for negative vertical velocities of the liquid wash-
ing over these particles [6]. The results of experiments studying bed load
~ saltatic~n f.c>r different partiele sizes but the same density [6, 17] demon-
strated tiiat under other equal conditions on the average the larger particles rose
higher than the fine particles. These faats are also unexplainable within the
framewor.k of hyPothesis B.
idhen processing one of the exPeriments we tried to cor.sider the movement of parti-
cles with respect to the. liquad surrounding ti~em directly tshen they are lifted.
'Chis is not a simp.l.c Probl.em, for it is necessary that an indicator particle of
neutral density used L-or visual re~resentation of the stream ot liquid be located
near the particle (at a distance not exceeding the diameter) when the particle lifts
off the bottom. In the experiment 170 trajectories of saltating particles were
obtained, ar~d in only 14 cases ~aas an indicator par.ticle near the saltating par~icle
when it lifted off the bottom. Let us note that it is impossible significantly to
increase the concentration of the indicator particles inasmuch as this complicates
their iden tification on adjacent processed frames.
Out of the described 14 cases of lifting, in only two did the vertical velocity of
' the liquid exceed the vertical velocity of the lifting particles, and in the remain-
~ ing cases the particles ros~ more quickly th an the liquid sur.rounding them (see
~ Figure 2). It is obvious that in this situation it is hardly possible to consider
vertical Pulsations of the liquid velocity responsible for lifting the beil
' load. A numerical estimation of the probability of realizing hypothesis B will. be
~ presented below. ~
Z
~ J
I , 1
_ ~
~a '
c
Fi.gure 2. LxamPle of: 1-if.ting o.f. a l~article of.f tl~e bottom for
_ ne~at_ive v~rtical velocities of thE~ liquid.
1. saltati.ng Pzrticle, 2-- indi.cator particle with nei~tral
buoyancy, 3 bottom.
Hyrotl~esis C: Particlcs are l.ifted off the bottom as a result� of collisions with
hoCtum r~~uk;liness ~~l~mcntti ~~r ~c>ll.isiuns wi Ch uLher particles.
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~~tik ~~~'~'t~ ~ t ~~!~t ~
Tlie given hypothesis is not so widespread as the first two, but it also has its
proponents (for e~aarspl~e [7, 14, 26, 33]). All of the above-presented experimental
results fail to contradict hypothesis C, and some confirm it. Thus, the decrease
in longitudinal velocity of particles lifted off the bottom is easily explainable
~aithin the framework of this hypothesrticles alfears as a result of rac~correspond-
vertical velocity component of the pa PP
ing decrease in the horizontal comnonent.
Checking hypothesis C, we tried exnerimental determination of whether the elastic
nroperties of the collisicros of the particles with bottom roughness
elemen~s influence the mechanism of their lifting from the bottom. For this
purpose a study was made of sal.tation of two types of spherical particles in a
turbtilent stream of ~aater. They had the same size R1=R2=(3.50+0.02)�10-3 m and
similar density p1=(1.40+0.01)�103 kg/m3, p2=(1.35+0.01)�103 kg/m3, but they differed
significantly with respect to elastic nroperties ma~nitude o.f the relative
' velocity recovery c~efficient after i.mpact e1=0.65+0.07, e2=0.32�0.06.
= For the experiment 1.00 ~~article~; of each type were selected. They were cbated wittt �
- nitro paint, which insured equalitv of the dynamic friction coefficients. Therefore
the average speed at which the particles rolled along the bottom were similar for
par.ticles of both tyPes (UD~=U.365�0.003 m/sec; UD2=0.370+0.003 m/sec).
robabilit distributions that ~
By talcing movies of the particle trajectories, the p Y i
_ garticles of both types would be at different distances from the bottom of the ;
stream, including the zero distance (the particle on the bottom) were obtained. It
turned out ttlat for the more elastic particles the prob ability of being on the
bottom is lower, and the probability of being at greater Y~eight is higher than for
th e less elastic parti cles (Figure 3).
. i14 ~ w� �
2
'f-' 0 2 0,3 P
~ 0, ;
Fi~ure 3. Protral~ilities that two particles of different elasticity
will be at different distances from the bottom of the stream.
1-- more elastic particles; 2-- less elastic particles
Consequently, in spite of the greater density, the elastic particles lifted off
the bottom more frequently and with greater vertical velocity th an the less
elastic particles, which con�irms hypothesis C regarding the role of collisions
off the bottom. On the othe.r hand,
in the mechanism of liftin~ bed load articles should
within the �rameworic of hypotheses A and B, elasticity of the p
have no defining iniluence on the probability of li~ting.
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_ 'ft~us, thc~ only hypothesis which qualitatively does not contradict the presented
experimental data is hypothesis C. In all fairness, let us note that under other
conditions, for exampte, in the case of bed movement of the sediments, not only
particles moving along the bcttom can saltate, but also particles tliat at first
appear to be stationary. Consequently, hypothesis C does not anpear t.o be abso-
l~itely valid, but only as applied to the conditions of the analyzed experiments.
ror grest~r substantiation of our conclusions regarding the laws of the mechanism
- of the lif.ting of particles off the bottom, let us perform a quantitative es.timate
of the prob ability of realization of the investigated hypotheses under the specific
hydrodynamic con ditions of our experiments.
- Piobability of Diff.erent I,ifting r4echanisms
_ Let us estimate the probability of tlie realization of different lifting mechanisms
as follows. Let us determine what instantaneous values the horizontal (or vertical)
_ component of the liquid velocity mus~ have near the bottom in order that narticles
lifting off the bottom be accelerated in the vertical direction within the frame-
work of hypothesis A(or B), as was observed in the experiments. Then, knowing the
values of the mathematical expectations and mean square deviations of the values
of the components of the bottom velocity of the liq_uid from the experiments, let us
determine the probabilities that the liquid velocity can assume values req~ired by
hypothesis A(or B). These probabilities will also be considered prob abilities of
realization of the indicated hypotheses.
It is possible to write the equation of motion of a single spherical particle in
general form as follows [9, 19, 28]:
~ 7
- r R~[''~ dt + ``p at (U - V) ] _ ~ F,, ~I~
where p is the density of the liquid;
e is the added mass ratio;
U and V are the particle and liquid velocities, respectively;
Fi are the forces: F1 is the hydrodynamic drag; F2 is the gradient lift; F3 are
the effects of interaction of the flaa with the solid boundary (displayed, for
example, with an increase in the values of the dra~ f.actor and added mass ratio
[15, 24]); F4 is the force of the excess pressure gradient for accelerated movement
of the liquid (the acceleration force, according to the terminology of. reference
[9]); P5 is the force caused by rotation of the particle (the Magnus f.orce);
P6 is tize force considering deviation of the stream of liquid from the steady state
(Basset f.orce); r~ i5 the external potential force (in our case the gravitational
force considering the Archimedes force).
- Analysis of equations of the type of (1), which is fruitful to a defined degree for
Stokes particles which, as a rule, in the case of bed load interact nor~
linearly with the liquid (Re=2R~U-VI/v>1), presents sig,nificant, if at the present
time generally surmountable, difficulties [22, 27]. However, we have grounds for
significant simpli~ication of this equation when used �or our purposes.
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'M~e Previous qualitative comparison of hypotheses A and B G~ith the experimental
data indicates low reliability of them. Therefore ~t is sufficien[ for us to
estimate only the upper values of the reliability oi these hynotheses. Here, we
can adopt a number of very significant sin~plifications of equation (1) under the
condition that each of them clearly favors realizations of hypotheses A and B. If
even with such simplificarions the probabilities of the existence of the discussed
lifting mechanisms turn out to be small (and this does occur), they can be taken
as unreliable.
Hypothesis A: The following simplifications are assumed: a) the added mass ratio ~
is eqtial to zero; b) the gradient lift does not decrease with distance of the
particl2 from the bottom; c) the total effect of the forces directed toward the
bottom does not exceed the P4agnus lift. Then the equation of acceleration of the
particle in some layer A by the gradient lift can be written as follows:
3 -R~~, `~tZl = 1 ~'c-'R2P(V.r-Ux)zl . (2)
~ ~
}~ere CL is t}le lift coefficient; the index a denotes averaging with respect to the
ilypothetical acceleration layer
Performing the averaging operation over a set of particles of equation (2)
r
~-R~n~~d~'~ ='1 C~aR=?{~v.r>~~+~=~Vx~1CU,~~~-~'
~
~ Q? ~L~x~ - ? ~ ~ V.r v.r ~ VX ~.1 ~ Ux~~
and neglecting the tertns in the righthand side of the averaged equation, the value
of which is two orders less than the value of the lefthand side of this equation,
after elementary transformations we obtain an estimate of the longitudinal velocity
of the liquid in the vicinity of particles lifting off the bottom:
8R P ~ dU=>~ � (3)
V.t ~ a= C Ur 1 3 C~ dl
~
We took only a positive value of the radical as physically more real~stic. Thus,
if hyPotl~esis A is valid, then when the~articles are lifted the speed of the
liq~iid must differ Lro~ itG mean value VX by , -~.r
VX F~a K,~ = s[ ~Xl
of tlie mean square deviations ajVX].
The probability of this ~vent will be defined using the existing representations
of the bottom velocity of a liquid as a varia~le, the components of which 3re
distributed according to a normal law [1, 17]:
~ - ~ (4)
F=1'(~X-yX>Kn ~ f exp[- 1 t'~dt.
A � ~ ~~.r ~ ) R A 2
1~0
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FpR ~JE~r~r ~ r ~
ic~ n?.~Ly
For numerical estimation ~f the unper bound of the probability PA it is necessarv
to estimate the known acceleration in the acceleration layer entering into the
expression �or the velocity ~ (3). For this purpose let us consider the
motion o.f partic:les in the bottom layer O.SR thick from the time of lifting off
the bottom (level z=0) to reaching a height of z=0.5R..
~ If inside this layer 0.5R, thick there is a layer of acceleration of particles in
- the vertical direction it is obvious that the vertical acceleration of the
_ particles averaged over the acceleration layer cannot be less than their accelera-
tion averaged over the O.SR layer, that is, ~30.5R� In the case of
constant acceleration which is favorable for realization of both hypotheses, its
- value is expressed trivially in terms of the aver age velocity and thickness of the
layer: ~ aU~~ _ 4~ Us~o.s R�
:
d! p6R^ R
As is known [S], the square of the mean value of a random variab le is less than
the mean value ofthe square of this variable; the final estimate of the hypothetical
acceleration ~ has the f.orm
C da!= k< U= >o.s R> R< U: >o,s R� (5)
0
- For determination of the value of ~ (3), in addition to estimation of (5), a
triple value of CL=0.6 favorable for realization of hypothesis A[18, 31] and a
_ value less than - ~ _ ~ Co p dr
that is, it must deviate from its mean value of zero by KB=(Q/6[VZ])=13 to 16
mean square deviations (see the table).
The probability of such events, that is, the probability~of validity of hypothesis g
is still less than the negligibly small probabilitr~ of realization of hypothesis A,
and it is equal to [11]
, M
~r E ~ ~ exp 2 tz dt < 10-=~
P~ P( ~V:~~K ) Y`lr.h [
- G
For numerical estimation of ttie vertical velocity (6).empirical values of
- ~= ,SR ~see the table), th~ acceleration estimate (S) and the high value of
the frontaQ drag CD=3 favorable to hypothesis B were used.
Let us note that if the instantaneous values of the bottom velocity components of
the li.quid are distributed not by a normal law [10, 20], then the validity of our
conclusions is maintained. This is connected with the fact that the values ot K
and Kg are so high (see the table), that we can in ~eneral not make any assumption
about the fornn of the distribution of the liquid velocity components, and for
estimation of the probability of the discussed hypotheses, we can use the
Chebyshev inequality
PI ~"-z h"~ - K-~,
~ ~,C~ - ~
which is valid for any distribution law of thE random variable [5].
Even for such an estimate (using a very weak inequality) hypotheses A and B turn
out in practice to be unrealistic inasmuch as the probability of their realization
is on the order of 10-2, which is an order lower than th at observed experimentally.
A numerical estimate of the probability of reali~ing hypothesis C similar to the
ones performed for hypotheses A and B is procedurally impossible. However, inasmuch
as under tl~e irivestigated condition hypotheses A and B are clearlv unrealistic, we
must ~iJo~~t the third l~ypotliesis that liftin~ of the particles from the bottom
occurred as result of their collisions with bottom roughness ele-
ments. Let us remember that even qualitatively only hypothesis C does not contra-
dict all of the previously investigated experimental results.
Our conclusior~, however, should not be understood as meaning that the factors of
- the dynamic effect of the �low on a particle (~radient lift, Magnus force, effect
of the liquid velocity pulsations, an~ so on), not being the primary cause of lift
uncier the i.nvesti~ated conditions, in general play an insignificant role in
bed load dynamics. Lifting o.f. the particles from the bottom is the
result of t11e interaction oi all of the enumerated factors, and possibly certain
others which have not been sufficiently clearly revealed at the present time.
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The degree of significan.ce of each of these factors in the lifting phenomenon
depends on specific hydrodynamic conditions.
In conclusion, let us note that the lifting mechanism in which the primary role ie
_ played by collisions of the particles with bottom roughness elements
and with each other has as its corollaYy the p~ssibility of greater turbulization
of the flow transporting saltating bed l~ad �particles by comparison with a
pure liquid flow.
BIxLIOGRAPHY
_ 1. Velikanov, M. A. DINAMI:CA RUSLOVYKH POTOKOV [Dynamics of Channel Fl~ws],
- Vol 2, Moscow, GITTL, 1955.
2. Goncharov, V. N. DVIZHENIYE NANOSOV V RAVNOMERNOM POTOKE [~Bed Load
Motion in a Uniform Flow], Leningrad-Moscow, ONTI, 1938.
3. Grishanin, K. V. " Be~ Load Motion as a Renoir Process,"
TRUDY GGI [Works of the State Hydrological Institute], No 190, 1972.
4. Grishanin, K. V. DINAMIKA RUSLOVYKH POTOKOV, Leningrad, Gidrometeoizdat,
- 19 79 .
5. Grishin, V. K. STATISTICHESKIYE METODY ANALIZA REZUL'TATOV IZMERENIY
[Statistical Methods of Analyzing Measurement Results], Moscow, PSGU, 1973.
6. Grishin, N. N. "Kinematics of S~lid Particles in the Bottom Region of a
Turbulent FZow and the Prob ability of Their Collisions," VINITI (IJEP.),
RZH MEKHANIKA [Piechanics Abstract Journal], No 8, 1977.
7. Grishin, N. N. "Some Physical Laws of Moti:dn of Solid Particles in the
Bottom Region of a Turbulent Flow," VINITI (DEP.), RZH MEKHANIKA, No 7, 1~378.
8. Grishin, N. N. "Magnus Effect for a Spherical Particle Lifted Off a Solid
Surface," METEOROLOGIYA I GIDROLOGIYA [Meteorology and Hydrology], No 11, 1979.
9. Kashcheyev, V. M.; Muranov, Yu. V. "Problem of the Effect of Piagnus Pulsation
Forces and Acceleration on the Motion of Particles in a Turbulent Gas Flow,"
- TEPLOFIZIKA VYSOKIKH TEMPERATUR [High Tcmperatur~ Thermal Physics], Vol 13,
No 5 , 19 75 .
- 10. Klein, S.; Reynolds, W. ; Straub, F.; Ranstedler, P. "Structure of Turbulent
Boundary Layers," MEKHANIKA [Mechanics], No 4, 1969.
11. Kramer, G. PiATEMATICHESKIYE N~TODx STATISTIKI [Mathematical Methods of
Statistics], rtoscow, Mir, 1975.
12. Levi, I. I. INZHENERNAYA GIDROLOGIYA [Engineering Hydrology], Moscow,
Vysshaya shkola, 1967.
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13. Mikhaylova, N. A. PERENOS TVERDYKH CHASTITS TURBULENTNYMI POTOKAMI VODX
[Solid Particle Transport by Turbulent Streatns of Water], Leningrad,
Gidrometeoizdat, 1966.
14. Olevinskaya, S. K. "Experimental Study of the Saltation of Gravel in a
Turbulent Stream," author's re view of dissertation for a scientific degree,
rtoscow, MGU, 1976.
15. Riman, I. S.; Kreps, R. L. "Additional Masses of Bodies of Different Shapes,"
TRUDY TSAGI [Works of the Central Institute of Aerohydrodynamics], No 635,
1947.
16. Romanovskiy, V. V. "Study of Bed Load Displacement Velocity,"
TRUDY GGI, No 242, 1977.
17. Rossinskiy, K. I.; Lyubomirova, K. S. "Basic Laws of Motion of River Bed
: Load " VODNYYE RESURSY [Water Resources], No 1, 1972.
- 18. Rossinskiy, K. I.; Arbudiyeva, K. N:. "Flow Around Bodies in a Turbulent
Stream Near a Solid Surface," VODNYYE RESURSY, No 6, 1977.
19. Sou, S. GIDRODINAMIKA MNOGOFAZNYKH SRED. [Hydrodynamics of Multiphase Media], '
Moscaw, ?~Lir, 1971. '
20. Ibragimov, M. Kh.; Subbotin, V. I.; Bobkov, V. P.; Sabeyev, G. I.;
' Taranov, G. S. STRUKTURA TURBULENTNOGO POTOKA I MEKHANIZM TEPLOQBMENA V
KAI~ALA;CH [Structure of a Turbulent Flow and Heat Exchange Mechanism in
Channels], Moscow, Atomizdat, 1978.
21. TABLITSY VEROYATNOSTNYKH FUNKTSIY [Tables of Probability Functions], Moscow,
VTS AN SSSR, Vol 2, 1970.
22. Fidman, B. A. "Theory of the Motion of Suspended Bed Load " DINAMIKA I
TERMIKA RECHNYKH POTOKOV [Dynamics and Thermics of River Flows], Moscow,
_ Naulca, 1972.
23. Fomenko, G. S. "Study of the Kinematic Structure of a Fl.ow and the Motion of
P:~rticles in Its Bottom Zone," author's review of dissertation for scientitic
~ de~ree, I~oscow~ MGU, 1975.
24, tl~irp~l, J.; Brenner, G. GIDRODINAMIICA PRI MALYKH CHISLAKH REYNOL'DSA
[Hydrociynamics in the Presence of Small Reynolds Numbers], Moscaw, Mir,
197G. -
25. Bagnold, R. A. Some Flume Exneriment on Large Grains But Little Denser
Than the Transporting Fluid and Their Application," PROC. INST. CIV. ENG,
London, Vol 4, No 1, 1955.
26. Francis, J. R. D. Experiments on the Motion of Solitary Grains Along the
Bed of. Water Stream," PROC. RO~. SOC., London, A332, No 1591, 1973.
104
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21. ~ierring, R. A. "On the riotion of Small Spheres in Oscillating Liquids,"
CHE.*4. ENG. J. , Lausanne, No Z, 1976.
28. Hii~ze, J. 0. "Some Problem in the Study of Turbulent Transport," PROC. XV
CONG. IAHR, I~tambul, Vol 6, 1973.
29. Jeffreys, H. "On the Transport of Sediment by Streams," PROC. CAMB. PHIL.
SOC., Vol 25, 1929.
30. Mitsuhire, S. Ekhi.me Daygaku Nogak~zby kie," MEM. COLL. AGR. EHIME U1~IIV.,
Vol 22, No 2, 1975 (referenced by RZh MEKHANIKA [Mechanics Abstract Journal],
No 9, abstract B 1095, 1978).
31. Shen, H. W.; Hans, A. "Einstein's Contribution in Sedimentation," JHD ASCE,
No 5, 1975.
32. Todorovic, P.; tdordin, K. Evaluation of Stochastic Models Describing
- ~iovement of Sediment Particles on River Beds," J. RES. US GEOL. SURV., Vol 3,
No 5 , 19 75 .
33. Tsur_hiya, Y. "On the Mechanics of Saltation of Spherical Sand Particle in a
Turbulent Stream," PROC. XIII CONG. IAHR, Kyoto, Vol 2, 1969.
34. Yalin, M. S. "An Expression for Bed Load Transportation," JHD ASCE, 'Vol 89,
No 3, 1963.
,
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UDC 551.579 .
EFFECT OF TEPIPERATURE ON SOIL MOISTURE POTENTIAL AND ITS AVAILABILITY TO PLANTS
Moscow r'IETEOROLOGIYA I GIDROLOGIYA in Russian No 5, May 81 pp 92-98
[Article by Candidate of Biologic3l Sciences N. A. Muromtsev, Soils Institute,
manuscript received 3 Sep 80]
[Text] Abstract: A study is made of setting up experiments to
- study the effect of air temperature and soil on the
capillary potential of soil inoisture under controlled
(laboratory) conditions. .
The s~il temperature distributiar. laws were established
~ as a function of the soil water-physical properties and
air temperature. The relation was established for the
capillary potential of soil moisture as a function of
temnerature in two soils differing with respect to
granulometric composition and water-physical properties.
An interpretation of this function is presented. A
theoretical explanation is affered for the laws of
- temperature impact on moisture potential in different
soils.
The hysteresis phenomena of the soil moisture as a
function of soil temperature consisting in disagreement
of the values of the moisture potential for a decrease
and increase in temperature were established.
The soil moisture potential characterizes the water-retentive forces of the soil and
the availability of moisture to plants. In practical respects the potential is
widely used to diagnose the irrigati.on of farm crops and evaluate their moisture
utilization [1-3], when studying znoisture and salt transport processes [3], when
substantiatin~ ~ optimal drainage parameters, and so on.
Temperature as an environmental factor is the most important thermodynamic parame-
ter fiinctionally related to moisture potential. Hence, it is necessary to perform
a caref ul study of the influence of temperature on the moisture potential and
consider ttiis influence when developing reco~mnendations for hydrotechnical
amelioration measures. However, the effect of temperature on soil moisture,
especially in the optimal soil moisture range, has been studied very little. The
scientific literature availabl_e on the given sub~ect [2] is meager, and the
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information contained in it is highly contradictory. Thus, Richter j6] per�ormed
- studies on four soils differin~ wi_th respect to clayey frwction (from 9.4 to 48.6%),
and he es tablished that the air temperature has the s trongest inf luence on the
capillary moisture potential (Pk) in argillaceous and sandy soils: with a rise in
temperature from 15 to 45�C, Pk increased by 50 to 10 kPa in both soils. According
to Gardner's data [4), an increase in temperature in the range fram 0 to 50�C leads
to an increase in Pk by 0.9 kPa for each degree in coarse-grained sand, fat sandy
- clay~ and mountain-meadow humus soil. In Taylor's opinion j7], the temperature
effect in the high soil moisture range is low, and it increases as the moisture
cont:ent decreases, reaching a maxi.mum for moisture corresponding to the lower .limit
, of moisture availab le to plants, that is, for maximum hy groscopicity. Kedziora [5]
- adheres to an analogous opinion, but he points out that the effect of temperature
- on Pk is felt more sharply in sandy soils than in argi~laceous soils.
The primary deficiency of some of. the referenced papers is tre use of air tempera-
ture, but not the soil temperature, inasmuch as the dynamics of the air temperature
- cannot coincide in time with the dynamics of the soil temperature. On the other
hand, a number of experiments have been performed under uncontrolled conditions,
which complicates discovery of the effect of the temperature on Pk in pure form.
In this paper a study is made of the effect of the air and soil temperatures on the
capillary moisture potential using information obtained under laboratory (controlled)
conditions. The procedure followed in the studies is as follows. Soi1 weighing
10 kg was nlaced in metal pots, in the centers of which a tensiometer and thermometer
were located. After establishment of the required moisture in the soil, its surfar.e
was mulcheci with a 2-centimeter layer of coarse-grained sand, and the entire pot was
sealed with three layers of polyethylene film. An upper (0-25 cm) layer of alluvial
loamy and dern-podsolic sandy-loam soils widespread in the floodplain of the Moscow
River (the Odintsovskiy Rayon of Moscow Oblast) was used in the experiments.
The upper layer of alluvial loamy soil is light loam with respect tu granulometric
composition and is characterized by the following properties: density 1.3 g/cm3,
porosity 45%, specific weight 2.70 g/cm3, least water capacity 22%, humus content
2.8%, granulometric composition sandy loam. 'I~ao moisture level were created for each
soil: moisture on the HB level (2.~.0% for alluvial loamv soil and 22% for dern-
podsolic sandy loam) and 0.7 HB. The studies were performed in the fall-winter
period of 1978/79; the air and soil temperature variations were created by alter-
= nately placing the pots in heated and unheated rooms.
The nature of variation of. the soil and air temperature, the temperature gradient
(between the air ai~d soil) and Pk can be determined by the data in Figure 1
(alluvial meadow soil, 0.7 HB). On the whole, during the study period, the air
_ temperature varied from 31 to 0�C; the soil temperature also varied within the
same limits. The maximum temPeratiire gradient is observed in alluvial loatny soil
up to HB moist~~re; for both soils with 0.7 HB moisture the temperature gradients are
_ approximately the same. Analysis of the temperature dynamics indicates that all
the soil temperature variations are synchronous with the air tsmperature variations.
Here, some delay in the soil temperature variations with respect to aix temperature
variations is observed for entirely understandable reasons in all versions. In
accordance with the temperature dynamics, the moisture potential gradient d~namics
were found which, however, correlate mare with the temperature gradients than w3:th
the temperatures themselves. This is explained by some "inertia" of Pk bv
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r,
.r~ ~ ~h
~ ~ ~ , n
~ ~
~ ~ r ~ ~t~ }
~ r`2 ~'j t ~ ( ' ' i ~ ~ i A i
~ ~ ~ II ~ ~ Z~1
Z01 ~Y ~ ~ ' + ~I ~ ~
~ i ~i~ j ~ ~ H
~ ~ ~ i ~ if
i~ I '
~I ~
' i ~ ; P �~a (a)
� ' l BO
i
: J ~."~r~
ra 4`~ ~ `ti
r''' ti'~ `
~ . ~ ~a
_ iu~y 1 ~ ~ !
K
ZD
Q
~
1 '
Z ;S d1d >S JOlI 15 JOlll 1S1
Figure 1. Behavior of the air temperature (1) an:l soil temperature
(21, the temperature ~radient between the air and soil (4) and the
soil moisture potential gradient (3) in alluvial meadow loamy soil.
1978/79.
Key ~
a. P, kPa
comparison with the soil temperature (the more so by comparison wit.h the air
temperature). Table 1 gives a visual representa~ion of the nature of the soil
_ temperature variation and Pk as a function of the air temperature variations.
Three cases of soil temperature distribution with time presented in Table 1 as a
function of the air temperature variation were selected fxom a large data file,
because the most f.requent temnerature determinations during the course of the
experiment were made on these days, and they can be cansidered random rather th an
especially selected. Analysis of the data indicates that in each case on redu~-
tion o.f. the air temperature from maximum values to minimum (4 Qctober 1978 and
~ February 1979) and with a rise in air temperature from minimum to maximum
(6 October 1978), the variation rate of the soil temperature is different and denends
on the type of soil and its moisture. The temperature drops and rises most rapidly
in version 4(sandy loam, 0.7 HB) and most slowly, in version 3(sandy loam, HB).
T~':ith higher moisture (versions 1 and 3), although tk~e rate at which the soil temp-
erature drops is insignificant, it is still lower than for low moisture. This is
explained by the hi.fih heat capacity of water by comparison�with the heat cagacity
of the mineral skeleton of the soil.
With an increase in the soil temperature (and the air temperature) the moisture
- potential decreases, and with a decrease in temperatur~, i.t increases. This takes
- place because the surface tension (Q) of the water decreasesy a rise in temperature
from 0 to 5U�C causes a decrease in surface tension by 7.73 dynes/cm [2]. Inasmuch
as an increase in temperature causes a decrease in Q, the energy expenditures on
extraction of a unit mass (volume) of water from the soil consequently decrease,
- that is, the water becomes more active. However, the degree of variation of the
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_ Table 1. Soil temperature (T �C) and capillary notential of the soil
moisture (Pk, kPa) as functions of the air temperature (TB�C) in
alluvial meadow loamy soil (for HB 1; for 0.7 HB 2) and in
dern-podsolic sandy-loam (for HB 3; for 0.7 HB 4)
Version -
T ~ 2 3 I 4
Time � I
' T I PK 7'n I PK T
n ~ PK Tn ~ pr
n
4 October 1978
19,6 22 3,32 31,8 46,82 21,4 4.26 21,4 42,i,6
2i,0 22 3,32 23,0 44,02 22,4 4,52 22,0 38,30
10,0 21,2 3,32 21.0 46.02 21,0 3.72 20,2 43.89 .
b,2 14,0 3,3? 20,0 47.88 21,0 3,72 18,0 45,88
i,0 16,5 3.32 16,3 ~0,27 1(i.9 3,59 15,6 47,48
6.S 14,8 3,32 14,5 52,00 14,8. 3,46 1E,4 48,13
6,fi 10,4 3,32 10,6 5~3,86 12,4 3.46 11,2 48,41 �
6,4 10,4 3,32 10,3 53,60 ]0,8 3,46 10,4 48,41
- ;,H 9,4 3,32 9,2 5:,,06 9,2 3,46 9,6 47,8g
6 OctoheY 1978 -
g~ h,6 9,1 3,32 ~I,l 46,15 8.6 4,26 8,4 44,82
4a:k~ 20,5 10,0 3,72 10,4 46.95 9,6 5,72 10,0 41,10
- ~pu~ 24,6 11.0 3,46 ll,i 4~F,67 II,U 6,fi5 12,9 37,90
11:;" 1;,4 3.4G 1;,,2 42,43 14,5 6,92 15,6 36,31
12:~" 2.i,:f 16,9 3.4!i 1i,5 42,~~i IG,i 7,0:~ 18,0 35,51
13'u~ 2~,3 15,7 3,46 1'1, ~ 38.70 15,4 7,05 19,fi 35,24
14�~~~ 24,~ 20.Q 3,41~ 20.7 3i,37 19.G 7,0~ 20,7 35.24
~b:k~ 45,8 20,8 3,32 21,6 3G,31 20,6 1.U5 21,6 33,24
lt;'s" 2;.U 21,G 3.32 22.2 ~;3:i.73 21.4 7,05 22,2 35,24
21y~ ~~.2 24,0 ~,3`1 2~1,8 ~35.24 23,4 7,4:~ 24,0 35,51
23,~~ 26,2 24,3 3,32 2~,2 3~.24 2~,0_ i,8~ 24,2 35,51
~19 l~ebruary~ 1979 .
' y~! IS.1 t7,4 3.99 17,5 4t,89 17,4 5.4~ 17,4 53,20
, 1i?~,~ p.? 1g.i d,1;5 17.2 46,15 16,6 5,32 16,1 51,74
1 lo~ _ I,`' t'3.9 4.6i 1~.0 S~~,OI 14,U ~.0~ 12,9 54,53
~ 12~�~ -l.6 It.l' 4,6~ 19.8 53,73 11,3 5,19 9,9 55,46
, 13~}~ -I.0 a.8 4.65 9,8 55,39 9,2 5,3? 7,6 55,73
' Iti~� -'J.3 4.6 ~,6~ 5,8 57,99 4,9 5,45 3,6 55,86
I capillarv potential of the moisture with variation of the temperature differs and
depends strongly both on the moisture content and on the type of soil and its
water-physical pro~erties. The data in Table 1 indicate the magnitudes of the
moisture potential variations with variation of the soil temperature. It is
obvious that the maximum influence of the soil temperature on the potential is
observed in version 2(alluvial loamy soil for 0.7 HB), and the minimum, in
version 1(the same soil, but for HB). In the first case the maximum decrease in
Pk occurred on 19 October 1978 and amo w-~ted to 13.3 kPa (100 mm Hg) for 18�C;
in the second case the temperature variation of the alluvial loamy soil (version 1,
for HB) by 13�C (4 October 1978) did not cause potential variations (3.32 kPa).
Ttie data characterizing the variation of Pk per �C are presented in Table 2.
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'C;il~lt� li~~~r~~~i;cc~ in t'k E~ar ~~n varlat:ion of the temperatur~ in
a1.1 uvi 11 me:idow loamy soi 1(}[B 1, 0.1 HB 2) and dern-podsolic
sandy loam (HB 3 and 0.7 FiB 4)
I _ Versitm " ~
Date i ~ 2 3 _ 4
i
I , T I ("K I ,
;K ~ , T I ~ /'K ( ,~K .I T I , I ~T" ' ~ T I , P~ .I TN
' i I
~3 X 1978 I 13 0 0 13 3.2:i 0,64 13 O,gO O,Q6 12 :i,5~ 0.~9
6 X 16 0,27 ~,Ol t-1 10,91 It,7i 14 3,46 0,24 l6 9,31 O,~S
19 X 13 0,~0 , 0,0:3 I~i I;i,30 0,73 12 2.13 0,17 12 3,25 0,6$
I X[ 1~1 0,93 O,Oi }3 9,#4 U,72 12 2,39 0,20 l2 6,92 0,:~7
1~ !C[ I~ 11.13 U.~)1 13 IO,QI O,S4 13 2,26 0,17 t3 11,44 0,38
- 2o X[I ~ U,2i O,U3 3 10,91 U.M1 8 1,33 0,16 8 7,45 O,~J:3
19 I[ 1979 1'? U,66 O,U~~ t3 1~),84 0,60 12 0,13 U l4 2,66 0, l9
- Note. ~T is the soil temperature gradient, �C; OPk is the moisture potential
gradient , kPa; ~Pk/~T is the increase in moisture potential per �C, kPa/�C.
The data contained in Table 2 were calculated by twice-daily ' observations. They
indicate that the temperature gradients in all versions are close to each other,
- but ttie potential gradients differ. In versions 1, ~Pk are insi~nificant, and
they are frequently in the meas~rement accuracy limits. The maximum value is
0.065 kPa, and the minimum is close to zero. In version 2, which is an analog
with respect to moisture content (HB) of version 1, OP /~T are also insignificant, ~
but nevertheless, noticeably higher than in version 1~fram 0.01 to 0.24 kPa). ;
The values of 4Pk in versidns 2 and 4(0.7 HB) are appreciaUly higher than in the
investigated cases. In alluvial loamy soil (version 2), ~Pk/~T are in a narrower
range of potential values by comparison with version 4(0.60-Q.84 kPa and 0.19-0.88
kPa per �C, respectively), and the absolute values of Pk for in practice identical
temperature gradients are appreciably higher for alluvial loamy soil. Thus, for
example, for T=18�C, Pk was 13.3 kPa and 8.25 kPa, respectively, in versions 2 and 4.
Consequently, the data in Table 2 indicate that the nature of the effect of the
temperature on Pk is identical in soils that differ with respect to granulometric
composition and with different moisture. However, the degree of the temperature
effect differs and depends both on the granulometric composition of the soil and
the moisture content in it. The strongest temperature effect with high moisture
(HB) is observed in sandy loam dern-podsolic soil; in loamy alluvial soil this
effect is very low, and it can be neglecte~d for practical purposes. With a decrease
in the moisture content to 0.7 HB the greatest reduction in Pk with an increase in
- temperature takes place in alluvial l~aury soil.
The relations for the capillary moisture potential as a function of temperature are
presented in ~'ip,ure 2(alluvial loamy soil, 0.7 HB) and Figure 3(dern-podsolic
sandy loam, 0.7 HB) . It is obvious that in the first case (Fipure 2) the relation
constructed by observations on different days is expressed by a straight line and
can be approximated by the empirical equation y=-Axf-B. In the second case
(Figure 3) the function is expressed by a parabola type curve, and it is approximated
by an empirical equation of the type y=-Ax+Bx+C. Here the experimental points
corresponding to observations of T and Pk on different days, for alluvial meadow
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6~~ne (a) . ,
~ .
' - ~a~ . .
0
PxAa ""'-`~r ~
1 ss � SS - ~ .
" � s
e
� ~
� s
x
~ k
30 ~ ~c SD x
~ 2
� ~
2 �
~ , - -
�
- y5 � i e 45 ~ ' .
. 1 ~ "
~ o ~
i
44 yQ ~y 1 ~
ss "s
,,F x �6
�J
ug o .0
~9
- ~S ~f 20 T'~ JSO JO . ZO T'C
Figure 2. Soil moisture potential as a Figure 3. Soil moisture potential as a
function of temperature in alluvial function of temperature in dern-
meadow loamy soil. podsolic sandy loam.
1-- with an increase in soil ~emnerature 1-- with an increase in soil tempera-
from 9.6 to 25�C; 2-- with a decrease in ture from 8 to 20�C; 2-- with a
soil temperature from 30 to 4�C accord- decrease in soil temperature from 20
ing to observation dates: 3-- 4 Oct 78, to 9�C; 3-- with a decrease in soil
4-- 19 October, 5-- 1 November, 6-- temperature from 30 to 4�C by observa-
~ 14 November, 7-- 25 December,~ 8-- tion dates: 3' 4 October 1978,
19 Feb ruary 1979 and 9-- 6 October 1979. 4-- G October, 5-- 19 October, 6--
Key� 14 November, 7-- 25 December, 8--
.a. P, kPa 19 February 1979.
Key:
a. P, kPa
loamy soil are characterized by less dispersion than for sandy loam dern-podsolic
soil.
The relations reflecting the effect of temoerature on Pk with an increase in temper-
ature (from minimum values to maximum occurrin~ in the experiments) do not coincide
with the relations (Figures 2 and 3, lines 1, 2) Pkf(T) with a decrease in tempera-
ture, forming the "plane" Pk hereafter called hysteresis. The function Pkf(T) for
I both soils with higller moisture content (moisture for HB) is characterized by
very low closeness of the relation (a correlation coefficient of about 0.1).
Thus, the studies reveal the followin~; interesting characteristic features. For
the same range of temperature variations (increase or decrease) the variation of Pk
is different and depends both on th.e moisture content in the soil and on the prop-
i erties of its solid phase, nrimarily the granulometric composition. With a high
' moisture content the effect of the temperature on Pk in loamy meadow alluvial soil
~ is in practice absent, and in sandy loam it is insignificant.
i 111
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For moisture correspanding to 0.7 HB, the effect of temperature on Pk is signifi-
cunt; The function Pkf(T) for loamy alluvial soil is expressed by a straight line,
and for san~iy loam, by a parabola type curve.
The function Pkf(T) is ch.aracterized by hysteresis, that is, the dependence of the
potential on temperature during a reduction of it from the provisional maximum to
the provisional minimum does not coincide with the dependence of the potential on
temperature when it increases.
The discovered laws of the effect of temperature on the capillary notential of soil
moisture arise from the peculiarities of the water-retentive forces of the soil
determined by the properties of its solid phzse and the water content in it. For
high moisture content in the soil (HB and higher) a significant part of the moisture
is held by the soil as a result of canillaYy forces and it is characterized by
comparatively high activity (the free energy of the soil moisture is relatively
high). In this case the temperature effect le ads to an insignificant in crease in
its activity; here the absolute magnitude of the increased activity depends on the
temperature variation rate, as a result of which the potential variation per �C is
different in time. In this soil moisture range the properties of the so].id phase
ot the soil are poorly manifested.
With a decrease in moisture content to 0.7 HB the forces of its retention by the
- soil increase, the moisture becomes m~re bound (the thermodynamic notential of the
moisture increases), its activity decreases, and viscosity increases. In this
case a rise in temperature leads to a significantly higher degree of increase in
activity of the soil moisture and its free znergy.
With a decrease in temperature from 30 to 10�C in sandy loam dern-podsolic soil
the potential increases progressively to 55.9 kPa; with a further decrease in temp-
- erature to 7�C, the rate of increase in the potential drops noticeably, and in the
7-4�C range the rise in Pk in practice stops. Here the rate of increase in the
potential depends on from what maximum level the temperature begins to decrease,
which causes significant fluctuatian of ~Pk /~T. In loamy alluvial soil the moisture
(with the same moisture content) is bound by high matrix forces; its a~tivity is
lower than in sandy loam. The different rate of decrease in temperature has a
lesser de~ree of effect on the potential variation, as a result of which the values
- of ~Pk/r1T are in a narrower interval (Table 2). With a decrease in temperature
from 30 to 4�C, the moisture potential increases progressively in the entire temp-
erature range. As for the hysteresis phenomenon of the function Pkf(T), its nature
and mechanism are still not entirely clear. It is possible that this is connected
with different variation of the surface tension and viscosity of the water with a
� rise and fall in temperature.
Th us, the data obtained indicate that the variation of the capillary notential of
soil moisture in the temperature range from 0 to 30�C is hip,hly signi�icant. The
decrease in potential connected with an inc~ease in temperature in this range is
different and depends on the soil nroperties and the water content in the soil.
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Up to now all scientific research, design and groduction work (the latter includes
the diagnosis of farm crop irrigation, estimation of availability of soil
molsture to plants and predictian of their moisture utilization) has been done in
= practice without considering the potential variations. Ignoring this phenomenon
leads to serious errors in all hydrophysical, hydrolo gic and land improvement
calculations and in the plans and designs. Accordingly, it becomes obvious that it
is necessary to introduce the corresponding corrections to the potential in all
' cases whPre a noticeable decrease or increase in the air and soil temperature
occur.
BIBLIOGRAPHY
1. Muromtsev, N. A. "Diagnosing the Irrigation of Plants by Tensiometers,"
POCHVOVEDENIYE [Soil Science], No 1, 1974.
2. Muromtsev, N. A. ISPOL'ZOVANIYE TENZIOMETROV GIDROFIZIKE POCHV. [Use of
Tensiometers in Soil Hydrophysics], Leningrad, Gidrometeoizdat, 1979.
3. Sudnitsyn, I. I. DVIZHENIYE POCHVENI`IOY VLAGI I VLAGOPOTREBLENIYE RASTENIY
[Movement of Soil Moisture and Moisture Consumption of Plants], Mos cow,
Izd-vo MGU, 1979.
4. Gardner, R. "Relation of Temperatu~re to Moisture Tension of Soil," SOIL SCI.,
Vol 79, No 4, 1955.
5. Kedziora, A. "Wplyw Zmizn temperatury i wilgatnosci gleby na wartose
- pot~nejalu kapilarnego wody glebowei," PRZ. (1LOXIZ, Vol 18, No 1-2, 1973.
6. Richter, J. "Zur Abhandingkei~ des Bodenwassertessides von der Temperatur,"
Z. PFLANZENERNI~HR UND BODONK, Vol 131, No 3, 1972.
7. Taylor, S. A. "Measurements Soil Water Potential," ARID ZONE RES., No 26,
1965.
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~ UDC 551.509.313(-062.5)
- ANALYSIS OF SYNOPTIC SCALE WAVE DISTURBANCES IN TROPEX-72 AND GATE
_ Moscow M~TEOROLOGIYA I GIDROLOGIYA i:~ Russian No 5, May 81 pp 99-108
[Article by Professor Xe. M, nobryshman, Candidate of Physical-Mathematical
Sciences I. G. Sitnikov, Atmospheric Physics Institute, USSR Hydrometeorological
Scientific Research Center, manuscript received 11 Nov 80]
[Text] Abstract: An analysis is made of the characteristic
features of the wave nrocesses in the tr~pics by Soviet
research data gathered on the TROPEX-72 and GATE
expeditions. The methods of determining the wave dis-
turbances are discusse~d, and a brief description of the
results of their application is presented. jJaves with
� previously known period (a day, half-day) are determined
directly. OtheYtaise the periods are determined by thz
spectral density. Examples of long-period oscillations
detected in GATE are indicated. An analysis of the
quasibiannual zonal wind cycle is presented. Some
characteristics of the tz'adewinds circ~~lation are dis-
cussed.
One of the knotty problems of GATE was the problem of establishing the interrelation
of processes at low latitudes with processes in the rest of the atmosphere. There-
- f.ore f:rom the very beginning of the preparations for GATE in a number of the
national programs, in particular, in the national program of the USSR, the problems
of studying the large-scale Processes in the tropics were considered as separate
items. In addition to the general problematics, individual aspects of st~sdying
various circulation mechanisms were specified. Thus, one of the goals of the
TROPEX-72 expedition was determination of the phase of the quasibiannual
cyclicity of zo~ial flows in the equatorial atmosphere" [7, p 12], on the TROPEX-74
expedition one of the ~oals caas estimation of the wave disturb ance parameters
in the GATE region and, in particular, in the intratropical convergence zone"
[8, Vol 1, p 8], and so on.
The primary concern durin~ the TROPEX e~editions and all of GATE was compilation
of synoptic and aerological maps with maximum detail, the analysis of which was
not only to confirm the results o~ the observation data processing at various points,
but also to give impetus to subsequent analysis of the characteristic features of
the processes in low latitudes. For these purposes the basic data are the atlases
of synoptic and aerolo gical maps [2] and the cloud photograph atlas [10].
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Before proceeding with a descrintion of the characteristic features of wave pro-
cesses in the tropics, it is necessary to determine what is to be understood by
disturbances (often identified with waves) in low latitudes and what the character-
istics of these disturbances are. Usually, by a disturbance we mean an object of
synoptic scale, that is, a scale of 1000 km detected against a background of a
zonal pattern, in other words, disturbance of the zonal distribution of the
- corresponding r~teorological element or parameter. Here the dimensions of the dis-
turbance from west to east and from north to south appro~dmately coincide. This
imderstanding is unacceptable for the lowest latitudes: large-scale disturb~ances
are anisotropic here, and they are sharply elongated in the zonal direction. The
clearest example is the intratropical convergence zone (ICZ): its length is several
thcusands of kilometers with a width of a few hundred kilometerc. (The structure
of the ICZ is highly varied and closely related to the nati~re of the processes in
the converging flows [9], that is, the processes occurring on different sides of the
ICZ). The anisotropy of disturbances at low latitudes should not be forgotten,
especially in cases where the characteristics of disturbances of light nature are
compared with those for temperate latitudes.
A.s is known, CATE lasted 100 days; on 58 days of these 100 days (three phases) more
frequent observations were made by special programs. The disturbances having more
- or less periodic nature, a period of T days, were manifested approximately
n="100/T times. If T is several days, then n will be sufficient to talk confidently
about the correspondin g disturbance and its characteristics. For T~10 to 30 days
the confidence in the results will be low. Analogous arguments are properly
applicable also to space data: the GATE region is elongated longitudinally, approx-
imately 4000 km long; latitudinally it is 2500 km 1ong. Disturbances more than
2000 km in size must be interpreted quite cautiously. This is especially true in
that the African continent has a strong influence on the processes in the GATE
region; the conditians in the Indian and Pacific Oceans are different. Therefore
one of the next goals of studying the characteristic features of atmospheric move-
ments in th e tropics is a careful comparison of the results of GATE and the Monsoon
experiments in order to dis cover common features and, primarily, differences of the
processes in t~ese regions.
l. Methods of Detecting Wave Distur.bances
Characteristically, disturbances having a neriodic nature can be divided into two
groups. The fir~~ groixp includes those, the period of which is equal to the natural
period determir~ed Uy external factors: the diurnal and annual rotation of the
earth. On the basis of. the neculiarities of the equations of atmospheric dynamics,
in a number of cases a semidiurnaJ. neriod appears as the natural period. The
second group includes waves propagated with defined phase velocities not connected
with the mentioned natural periods. 'fhese phase velocities, that is to say, the
periods are defined as eigenvalues of some operator describing the dynamics of the
corresponding atmospheric processes. In the general case the operator is complex,
and to facilitate analysis of the broad spectrum of wave movements in the atmosphere
simplifications are introduced permitting isolation of waves generated by a defined
mechanism: Rossby waves (the gyroscopic effect), gravitational waves (gravita-
tional force), mixed Rossby-gravitational waves (the name itself defines their
genesis), and so on.
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V,irl~~u:; ~~rln~�[~~1~~~; ;~r~~ ~c.~~~l [I~~~ b~i5[5 fur wave clar~sification. `Phe mentioned
types c~f w~3ves ~re detined by ~lefined physical factors rotation of the earth,
gravity, and so on. For analysis of the mecha.zism of atmospheric processes, the
cause of the occurrence of certain types of waves plays a no less important role.
The occurrence o~ waves frequet~tly is connected with disturbance of the stability
of some process. Three basic mechanisms of loss of stability of the zonal flow in
the tropics are disringuished: a) barotropic and baroclinic instability, b) in-
stability caused by the release of heat during cloud formation (for axamnle, CISK),
c) instability caused by the presence of heat sources in a flow that is nonuniform
with respec_t to coordinates, especially with respect to z.
~
.;,0 6 a~ ~ I~s ~j p"
o,s i ~ ~96e
' ~ (7) 10n
~ -D~ ?~1 35,J0
~ ~
1Z0 ~
~ ~
-1,0 i ~ . ~ JS,10
(2) k/c 1~a~a (~3) ~ ~
~
G, s b~ ~ ; JJ,fo
~ , ~
~ ~ ~ ,
~r i
Q . .
~ JS,00
-O,S Y~7,5 I 16,4 8) 30M
26,1 ~ 35,70
D~a,o (4) 7S,e', r'' ~ ,
0,5 ~ ~
if ~ , J~60
'
v
~ 23~
SO N
Y� 8,75
-0,3 199 i 35,Bk ,
~l ~aia 19,6 . - 35,80 ~
~(5? ' i
- 19,3 35,76,
~ 1ODM
~t;.~ .
_ 14,D
- J00 ro
11,2._ - J5,44
- ~s~ 500 ,~.~40
B,2
QO - : ~ J4,B2
~~0 6 11 1b ?4'~4,7d
Figure 1. Diurnal behavior of ineteoralogical elements.
a) pressure at sea level; b) modulus of the horizontal wind
velocity in the tradewinds zone (the dotted line represents two
harro~nics of thc~ Fourier series); c) temPerature (solid curve)
and salinity (dotted curve) on various levels accordinR to the
TROPEX-72 and TROPi.X-74 data.
Ke.y:
1. millibars 6. 0 meters
2. m/sec 7. 20 ~ters
3. phase I 8. 30 meters
4, phase II
5. phase III
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This division is conditional for two reasons. First, it is not always possible
clearly to isolate only one factor causing the generation of a wave, let us say,
naroclinic instahility (the velocity profile with respect to z or the horizontal
temperature gradient). Secondly, other principles can be used as the basis for
the classification, �or example, the occurrence of disturbances as a restilt of
orography~ as a result of a sharp temperature gradient along the flow (land-sea),
and so on.
Here, if the appearance of an almost periodic disturbance of the wave type is
interpreted as a result of loss of stab ility of some (or seveual) mechanism, then
the systematic appearance of disturbances must be interpreted as a stabl.e process.
For detection of periodic processcs basically two methods are used: 1) direct
determination of the amplitude (and sometimes the phase) of the fluctuation of an
- entirely clear a priori known period (diurnal, annual, semidiurnal). 2) Obscure
_ periods are defined by the application of the appropriate procedure based on using
statistical characteristics of a sufficiently long series of observations. These
- methods are often combined the period (quasibiannual zonal wind cycle in the
upper troposphere and lower stratosphere) is established approx~mately by empirical
data, then the fluctuation parameters are determined on the basis of statistics.
The most widespread method of discovering periodicities is the construction of a
spectra~,density graph (directly or as the Fourier transformation of the correlation
function); the peaks are interpreted as the presence of oscillation,with the
corresponding frequency.
Oscillation with given frequency in the spectral functian theoretically corresnonds
to a"spike" of the Dirac d-functian type. On the spectral density graph this is
never obtained either on the basis of the limited volume of the initial data or
because there is no "pure" oscillation F~ith an exact period in nature. An auto-
oscillatory mode with variable narameters can exist; the parameter variation alters
the oscillation period. tObviously, this is the situation with the quasibiannual
cyclicity of the zonal wind and its three-five-day wave. The nature of these
oscillations is still to a great extent unclear.) These facts limite d natu~e of
the sample ~d absence of a clear physical period lead to "blur.ring" o� the peak
on the spectral density graph. F'requently it is very difficul:t to estimate the
effect of each of the factors separately; therefore conclusions about the presence
of one clear period or another must be taken with a known degree of precaution.
[~Then processing the data from the TROPEX-72 and TROPEX-74 expeditions and all of
GATE, both methods of determining the characteristics of "purely" periodic and
quasiperiodic fluctuations of the meteorological element fields were used.
2. Brief Description of the Results of Studying ~dave Disturbances
a) Direct Determination of Characteristics (Diurnal and Semidiurnal Periods).
According to the data from the stepped-up observations during the expeditions
graphs were constructed of the diurnal behavior of in practice all the meteorologi-
cal parameters. These parameters can be divided into three groups. The first.group
(Figure 1) includes those which are measured directly pressure, temnerature,
modulus of the horizontal wind velocity, and so on. The second group includes
tllose which are obtained from observation data as a result of processing these data
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1~(1R > ~17~
nR - q~~
Perf.orming analogous c~~lculations for other methods of determining the dopnler
freq~lency shif.t, wc obtain the expression �or the dispersion ~DR~i
~ (18)
lUR 1~ _ .9ii
134
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Here the coe�ficients Bi characterize the accuracy of each of the methods. For
- a s~nple size Ni for each of the methods used to determine the doppler frequency
shift considering (13), (14), (16), we obtain the following expression:
~ /V;= ` f P(T)P(9)F(T1 dTclq= Qoq~) (19)
~Q
Key: 1. noise
where the coefficient ~ reflects the variation of the " noticeability" of the radio
echo responsible for the drift.
Nnaise is the number of cases of radio echo on the noise level q~=1.
Substituting values of Dr, DR. N from (18), (19) and (7) in (6), for the informative-
ness I- we obtain the following expression:
v
' N~, A~ D' 20
~v-~O~' ~ l,3B; -2 ^ , ~ )
Q + 40 ( Dl + Dtl V y+ ~u- Dh l
0
_ 1? <
, ~,p R- ~X
x
j QB ~ ~ . 4
~x~
i v
I 0,6
0,4
I~ .
0,1 ,
i ~n=
S , 2 f G B qo
% Informativeness L as a functi.on of. the threshold amplitude qp for
th~ time-Ph1sn_ meYhod (1), the time-Phase method with fourfold
frequency multiplication (2), the "Stan�ord" me thod (3) and the d~/dt
measurement method (4)
i
In the figure the relation calculated by (20) f.or the informativeness I~ in rela-
tive units is presented as a function of the threshold value of q~ for
V=5 m/sec, D1=400 m2/sec2, L1u=0, T=0.25 sec for four radiometeor data processing
algorithms for the drift rates.
As follows frc~m the figure, for all the processing algorithms the curve for the
informativeness L as a function of q~ is characterized by the presence of one
v
peak for Gmall vaZues of q0 and quite slow decrease in I~ with an increase in q~.
135
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Ft)R nNHI('IAl. tl~i~: nN1,Y
'Cli~~ ui.t\llllllltl v:~lii~' ,~t l-- l:: r~~:t~�tt~il ~~h~n tlic~ dertondnator ln ~ipE`rua~ht�~ tttt:
minimum. From the con~ition of the minimum of the denominator it is possible to
find the ontimal value of the relative threshold q~. The values of q~ thut~.are
optimal for several values of the wind velocity distributlitudesaareeTresented~in
values of the decay constant of the meteor radio echo amp P
Table 1. For example, for the method of ineasuring d~/dt, the value of q0 of the
optimal relative threshold varies within the limits of 1.23 to 2.4, whicfi differs
significantly from the value of q~=5.9 presented in [6, 7)�
- F~r tY~e same parameters for a val.ue of q~=2 according to (20), the informativeness
L was calculated. The values of L in relative units are presented in Tab le 2.
A~S' is obvious from this table, the ~iost informative are the "Stanford" method
and the method of ineasuring d~/dt. The informativeness of the time-phase method
and the methods of frequency multiplication depends on the meas ured mean values
of the wind velocity and decreases with a decrease in them.
Table 1
Dl, m /sec
Processing algorithm 400 1600 400 1600
Radio echo with Radio echo with
T=0.25 sec T=0.125 sec
1.94 1.23 2.4 1.49
1~leasurement of d~/dt (LAA) ~1 1.5 ~1
"Stanford" f~=40 hertz 1.49 ~1