The variations in snow cover characteristics in the Transbaykal were examined. Results are presented of an experimental verification of the Transbaykal theoretical developments to improve the efficiency of snow measurement photographs

Govsh, R. K.

English

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NATIONAL AERONAUTICS AND SPACE ADMINISTRA
WASHINGTON D.C. 20546	 July
+ NASA TECHNICAL MEMORANDUM
NASA TM- 77917
VARIABILITY OF SNOW COVER CHARACTERISTICS IN THE TRANSBAYKAL
R. K. GovshM^
Translation of "Izmenchivost' kharaketeristik snezhnogo pokrova
,v-mloviyakh zabaykal' ya, " Trudy Glay . Geof. Observ. , No. 130,
196 pp. 78-83
SEP
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(NASA -TM-77917) VARIABILITY OF SNOW COVER
	 N86-11733
CHARACTERISIICS IN THE TRANSEAYKAL (National
Aeronautics and Spice Administration) 12 p
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VARIABILITY FSNOW COVER CE 1RACMUSTI(S IN s. Julrj th5
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ation Of '*Izmenchivost' kharaketeristik snezhnogo pokrova v
 zabaykal'ya," Trudy Glay. Geof. Observ., No. 130, 1962,
pp. 78-83
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Results are presented.of an experimental
verification of the Transbaykal of
theoretical developments by the A.I.
Voyeykov Main Geophysics Observatory to
improve the efficiency of snow measurement
photographs.
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	VARIABILITY OF SNOW COVER CHARACTERISTICS IN THE TRANSBAYKAL
	 /78*
R. K. Govsh
Results are presented of an experimental verification of the
Transbaykal of theoretical developments by the A. I. Voyeykov Main
Geophysics Observatory to improve the efficiency of snow-measurement
photographs.
Snow-measurement observation .
 currently made at stations and
posts ace very cumbersome, especially in the harsh winter of the
Transbaykal, and the extant technique does not ensure a sufficiently
accurate analysis of the characteristic average magnitudes of the
height and density of the snow cover on large areas.
It is common knowledge that selection of the route and number
of measurement points for snow surveys in a certain region is deter-
	
mined by variability in the height and density of the snow cover.
	 It
ismost expedient to use the structural function [1] to characterize
variability in snow cover height and density. By structural function
of a certain magnitude for a specific interval we mean the average
square of the difference in its values at the ends of this interval.
By knowing the magnitude of dispersion of the snow cover height and
the value of the structural function, we can compute the error in
determining the average snow cover height for routes of different
length with varying number of measurement points.
Special snow surveys were	 set up	 in the winter of	 1959
	 -	 1960
at	 individual stations	 in the Transbaykal	 Administration
	 of the Hydro-
meteorological Service to study the horizontal	 variability
	 in	 snow
cover height and density. The	 stations were selected	 so that they -
reflected the main	 landscape
	 zones	 of	 the Transbaykal	 (Table	 1).
The height of the snow cover from the measurement lines indicated
in Figure 1 was measured every 10 m, and density every 200 m.
The materials were processed and dispersion and structural func-
tion were calculated according to the technique developed in the
*N umbers in margin indicate pagination in original foreign text.
1	 t^
f--- X000 w
aS0
Figure 1. Plan of Measurement
Lines for Special Snow
Surveys
A. I. Voyekov Main Geophysics Observatory.
Table 1 presents the dispersion magnitudes for stations where
special snow surveys were made.
TABLE 1. DISPERSION OF SNOW COVER HEIGHT IN THE WINTER OF 1959-60
	
/79
Station	 L Dispersion QZ	 Notes
Baunt	 9.68	 Mountainous taiga
Kalakan	 9.54
Krasnyy chikoy	 4.98
Borzya	 0.81	 Steppe
Chita
	
32.39	 Forest-steppe
The calculated structural function values are presented in Table
2.
It is evident from Table 2 that when the interval between the
measurements increases, the structural function values rise. This
rise, however, cannot continue unlimitedly, since any of the studied
magnitudes always has certain change limits.
2
ORIGINAL PAGE 13
OF POOR QUALITY
TABLE 2. VALUES OF STRUCTURAL FUNCTION IN THE WINTER
OF 1959-60
Distance between points (m)
Station
1i) 1 20 1 50 1 60 1 70 1 100 1 200 1 300 1 400 1 500
Ka^aKan '	 2 11,6 17,8 19 , 8 19 , 5 19,6 18 8 19,1 23 , 6 25 8
Krasnyy Chi koy,1;6
!i2 17,5
9,7
18,9
9,8
19,0
10,0
19,3
9,9
19, 1
10,4
19,3
10,6
18,0
10,8
20,1
11,0
21,0
10,7
60 rtya
	
. . . 0,97 1,09 1,23 1,27 1,28 1,30 1,33 1,30 1,38 1,34
Chita 42,0 51,0 63,0 65,0 64.8 Q. 4 63,6 61,8 70,8 62,4
The saturating value of structural function (when it remains
almost unchanged) is equal to the double value of dispersion [1].
Before using the structural function to determine Errors, it is
expedient to smooth it. Smoothing is done graphically [2]. The
values of the structural function corresponding to different values
of the interval are taken from the curve obtained as a result of
smoothing. Table 3 has the smoothed values of the structural function
for the Transbaykal stations.
The errors in determining the average snow cover height for dif-
ferent lengths of the route and number of measurement points were com-
puted for the formula
a-1bs (l, n) 2  - n X(n -o b (a4' ( 1 )
where d2 (1, n)--total error depending on the length of the route 1
and the number of measurement points on it n, b.--value of the struc-
tural function on infinity, i--ordinal number of point measurement on
3
the route,o 1--distance between the measurement points, b(iol)--
	 /80
value of the structural function for the io1 interval.
TABLE 3. SMOOTHED VALUES OF STRUCTURAL FUNCTION
Distance between points (m)
Station
10 20 50	 I 60	
1
f
70	 I 100 200 300 400 500
Gaunt 7 2 11 6 17,8 19,0 19,4 19,4 19,4 19,4 19,4 19,4
Kal a k n,	 .
^hl 16,5 17,2 18,8 19,0 19,1 19,1 19,1 19,1 19,1 19,1Krasnyy	 koy 8,6 9,7 10.0 10,0 10,0 10,0 10,0 10,0 10,0 1010
Bo rzya	 . . 0,97 1.09 1,25 1,27 1,28 1,30 1,33 1,35 1.38 1,41
Chita	 •	 •	 • 42,0 48,5 64,0 64,8 643 64,8 64,8 64,8 64,8 64,8
TABLE 4. NUMBER OF MEASUREMENTS OF SNOW COVER HEIGHT ON ROUTE 1000
m LONG Ph <1.0 cm
tation
	
Number of Heiaht	 Measurements
Baunt
	
10
Kalakan
	
10
Krasnyy chikoy
	
5
Chita
	
50
Borzya
	
2
Table 4 shows how many snow cover altitude measurements must be
made on a route 1000 m long for the root-mean-square error of height
analysis not to exceed 1.0 cm.
It is convenient to use graphs for practical utilization of the
results of computing analysis Prrors in the average snow cover height.
In order to construct a graph, the length of the route 1 is
plotted on thF x- axis, and the number of measurements n on the y-axis.
4
A point on the graph at which the computed error P h is indicated cor-
responds to each pair of values 1 And n. Then isolines are made
through the points corresponding to equal values of error. Figure 2
presents this graph for the Baunt station.
By using the graph, we can find the error in determining the
snow cover height for any values 1 and n through interpolation. One
can judge from the graph how the route will be selected so that the
average error of snow cover height does not exceed a certain prespeci-
fied magnitude. Assume that in our example it is necessary for prac-
tical purposes for His error not to exceed 1.0 cm. In this case, 1
and n are needed for the selected route so that the point corresponding
to them on the graph lies above the isoline P h = 1.0 cm. The required
accuracy will be attained with 1 = 500 m, n = 15 or 1 = 1000 m, n = 11
are selected.
The snow cover density was measured during special snow surveys
as indicated above every 200 m. The relationship between individual
measurements at these distances was insignificant, it can be ignored /81
in this case. Therefore in order to compute the snow cover density
error, the known formula was used
T2 	 02099d	 in
where 61 d (m)--densityerror, Qz m --density dispersion, m--number of
density measurements.
Table 5 presents the magnitudes of root-mean-square error of den-
sity for Transbaykal stations.
It follows from these data that with an increase in the number
of density samples, the error noticeably diminishes.
Until now we have been concerned with questions of variability
	 /82
in height and density of the snow cover and correspondingly their
5
ORIGINAL PAGE IS
OF POOR QUALITY
a \	 ^,o
	
300	 boo	 INN
	 WWI
Figure 2, Dependence of Error in Determining
Snow Cover Height on Length of Rout
and Number of Measurement Points
TABLE 5. DEPENDENCE OF ERROR IN DETERMINING DENSIT
ON NUMBER OF MEASUREMENT POINTS
Number of measurements
Station
_	 1	 2-	 3	 4	 S
Caunt 	 ; •	 0,0620 0,0374 0,0306 0,0265 	 P,D:Kalakan^	 .........
	
. .^ t 0,0283	 0,0200	 0,0161	 0,0141	 0,0126
Kra^ny -y Chi kov ;	 0 .0141 0 ,0i00 0 ,0061 0 ,0071	 0,0063
Chita .
	
.... ,	 o.OW O,M 0,0200 0,0173 0,0156
Number of neasureinents;
's sStation	 *: ,
Raunt 
Kalakanz
Krasnoy Chi koy
'	 0110'
I; .Ch	 -	 s?yJ.	 R	
`a:u	
_	
s	 r T „-.f xs'r w	 3 .r	"'-j
6
ORIGINAL PAGE IS
OF POOR QUALITY
average error over the territory. It is also very interesting to
select the most expedient time intervals between the snow measurement
observations. It is common knowledge that this selection is deter-
mined by errors in interpolating the snow cover characteristics in
the time between the observations C1, 33.
We used observation materials from the permanent measuring rods
o f
 six Transbaykal stations (Table 6) to study temporal variability
and snow cover height.
TABLE 6. BRIEF
Station
Kalakan
Chasovaya
Petrovskiy zavo
Chita
Yamkun
Khorinsk
Landscape Zone	 Section
Mountainous taiga
	 Protected
Open
Forest-steppe	 Protected
Open
Steppe	 "
Period
1955-1959
1952-1958
1950-1959
1947-1956
1952-1956
1950-1955
TABLE 7. MAGNITUDES OF TEMPORAL STRUCTURAL FUNCTION
Station Period
uengT,o of interval
	 (days)
1	 I	 2	 3	 4	 5	 10	 I	 15	 20
Kal akan Increase	 2,0 3,1 4,0 4,8 5.4 9,4 11,3 14,6
Decrease	 2,5 7,6 14,0 21,2 29,3 89.5 163,5 262,0
Petrovskiv Zavod Increase	 06 1,5 2,2 2,8 3,4 6,4 9,4 12,0
• Decrease	 3,4 7,7 12,6 16,7 22,4 51,8 81.7 114,2
`:.:.Chasovava • Increase	 0,9 2,0 3,0 3,7 4.5 6.1 11.2 .-15.5
Decrease	 3,0 6,6 11,8 16,2 21.5 50.6 83,2 115,0
Chita Increase	 0,7 1,2 1,6 1,9 2.1 3,3 4,2 5.4
Decrease	 1,8 3,0 4,1 4,9 5,8 9,8 12,9 16,0
Khorinsk Increase	 0;5 0,6 0,8 1.0 1.1 2,0 2,6 3.1
Decrease	 0,4 0.9 1.7 2,4 2.8..;5,9 8.9 12.7
Yamkun Increase 0.6 1.2 1,9 2,5 3.2 7,0 11.0 14,pg
: Decrease f 2.2 5,0 8,0 11,2 14,1 . 4,2 61,3 72.b
7
s,
The calculated values of the temporal structural function for
the periods of increment and decline of snow cover [3] are presented
in Table 7.
In order to use the structural function in further computations,
it is necessary to establish the nature of the relationship between
the function values corresponding to different time intervals. The
temporal structural function over the snow cover height generally is
an exponential relationship
(3)
If the graph of structural function of type (3) is constructed 	 /83
in logarithmic coordinates, then it will look like a straight line,
since
,gb jt) lq c + k lg %.
(4)
The exponent k is computed from the formula
k . L19 )
aigt	 1	 (5)
where o1gT--difference in logarithms between the two selected points
on the graph,olgb(T)°•-difference in logarithms of the structural func-
tion at these same points. By knowing the exponent k and the values
of the structural function, we can compute the average magnitude of
error for interpolating snow cover height in time [3].
Table 8 presents values of the root-mean-square error in inter-
polating height.
Using the graphs for the dependence of interpolation error on
the magnitude of the selected time interval, we can define the fre-
quency measurements needed to obtain intermediate values of the snow
cover characteristics with preselected accuracy.
8
ORCG ryAL F' lvm is
OF POOR QUALITY
TABLE 8. ERRORS IN INTERPOLATING SNOW COVER
HEIGHT
` Time intervrl(days)
c
c
station ----- n
1 . I 2( 3( 4	 1 5	 I l0 15
	 I 20
Period of increase
Kalakan 0,72 0,89 1.02 1,12 1,18 1,53 1.72 1.94 0,65Petrovskiv Zavod : ; 032 0,50 00 0,68 0,75 1,03 1,25 1,41 1,00
rhacnvaya 0:43 0,64 0.78 0,87 0.96 1,26 1,51 1.77 0.88
Chita 0,46 0,60 0,70 0,76 0,80 1,00 1.13 1.28 0,62
Khorins k	: : 0,36 0,37 0.46 0,51 0,54 0,72 0,82 0,90 0,72
Y am k u n
	
•	 •	 •	 •	 •	 •	 .
0.30 0,42 0,53 0.61 0,69 i.o2 1,28 1,44 1.07
Period of decrease
Kalakan 0,28 0,62 0.84 1,03 1,21 2,12 2.86 3,55 1.55
Petrovskiy Zavod: 0,64 0,97 1.24 1,43 1.65 2,51 3,15 3,73 1,18
Chasovaya
	
. 0.58 0,86 .1,15 1.35 1.55 2.38 3,06 3,59 1,22
l:hita	 .	 .	 .
Khori nsk	 . .... .
0,660,26 0.880.39
1,040,53 1,090,63
1,230,68
1,580,99
1.84
1,22
2.04
1.46
0.72
1.00
Yamkun• ..	 .	 .	 .	 .. 0,39 0,48 0,94 1,12 1.25 1,96 2.39 2,84 1,23
The experimental verification on materials of individual stations
that we made thus allows us to conclude that the scientific-method
developments of the A. 1. Voyekov Main Geophysics Observatory to
improve the efficiency of snow measurement surveys are quite applic-
able for the Transbaykal Administration of Hydrometeorological Service
Station Network. The results of calculating the average error that
we obtained for several stations apparently cannot be extended to the
entire territory of the administration of the hydrometeorological ser-
vice. In order to improve the snow measurement surveys on the Trans-
baykal Administration of the Hydrometeorological Service Network using
the technique of the A. I. Voyekov Main Geophysics Observatory, calcu-
lations need to be made for a large number of stations.
BIBLIOGRAPHY
1.	 Laykhtman, D. L.; Kagan, R. L. "Some Questions of Improving the
Efficiency of Snow Surveys." Trudy GGO, No 108, 1960.
9
10
2. Dunayeva, A. V.; Zanina, M. S.; Tsyganova, A. M. "Studying the
Spmtial Variability of Snow Cover Characteristics," Tr_ udy-GGOj
Nrr .08, 1960.
3. Gushchina, M. V.; Trifonova, T. S. "Variability and Snow Cover
Characteristics in Time and Selection of Intervals Between Snow
Surveys," Trudy GGO, No 108, 1960.
1
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Variability of snow cover characteristics in the Transbaykal

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