AIDJEX BULLETIN No. 17 Deceber 1972

Second Half, Trudy, "411 Vol 303

TABLE OF CONTEKfS

SEASONAL FEATURES OF THE "POLAR TIDE'' PRESSUdE WAVE OVER THE ARCTIC

--Gudkovich and Santsevich . . . . . . . . . . . . . . . . . . . . 1

THE RELATION OF THE RESULTANT MONTHLY AVERAGE WIND TO THE PRESSURE GRADIENT

--Nikolaeva . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

EXPERIMENTAL DETERMINATION OF THE WIND DRAG ON AN ICE SHEET

-1Karelin and Timokhov . . . . . . . . . . . . . . . . . . . . . . 41

STATISTICAL CHARACTERISTICS OF SOME ICE COVER PARAMETERS I N THE ARCTIC

--Buzuev and Dubovtsev . . . . . . . . . . . . . . . . . . . . . . 55

@ ESTIMATING THE LATERAL MELTING OF DRIFT I C E --Nazintsev . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

SNOW ACCUMULATION ON KARA SEA I C E --Nazintsev . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

SHEAR MEASUREMENTS OF NATURAL I C E WITH OPTICAL THEODOLITES

--Legen'kov, Uglev, and Blinov . . . . . . . . . . . . . . . . . . 85

OBSERVATIONS OF I C E MOTION WITH OPTICAL THEODOLITES

(METHODOLOGY AND ACCURACY) ON THE SEVEWYI POLYUS-I7 DRIFTING STATION

--Legen'kov and Uglev . . . . . . . . . . . . . . . . . . . . . . 89

APPLICATION OF COMPUTERS FOR DETERMINING AGE CHARACTERISTICS OF ARCTIC I C E

--Novikov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 w

Cover; Photogurph of Ccmrp 200, 8Cte o$' the IS72 AIDJEX p i to t study, taken during a rsmofe-ssnshg fl6ght at 3500 ft. bg the NASA 000 researoh &waft Galileo. The used 68 a Wtd- Heerbrugg RC-8 metdo m q g d n g omem CnstaZZed Cn the a%roraft.

December 1972

- SECOND HALF -

TRUDY, AMI, VOL. 303

* * * * $ ?

Fhmc<ai! support f o r A the Nat%onaZ S d e n

Arct ic Ice Dynamics Joint Experiment Di v i s i on o f Mari ne Resources

Universi ty o f Washington Seat t le , Washington 98105

ad-dresaed t o

D%vision o f W n e Resources UNIVERSITY OF WASHINGl'ON

!%e A I D J E X Bulletin aims t o prowide both a f o m for discussing AIDJEX problems and Q source of information pertinent t o a l l AIDJEX partidpants. Issues-numbered, dated, and someCimes subtit led--contain technicaZ nateAa1 closely related t o AIDJEX, informal reports on theoretical and f i e Zd work, trans lation8 of relevant sc ien t i f i c reports, an AIDJEX results.

scu8sidns o f interim

Bulletin 'No. 17 IsraeZ Program the Proceedings (Trudy) of the Arctic and Antarctic Scientific Research Institute. !?he first half ( Bulletin No. 16) dealt With the computation and fomcast f ice-cover . mrLations m d with problems. related t o ice d r i f t . This second half covers (1) the relation of wind and pressure f i e lds t o ice coverage fluctuations, (2) the formation and deterioration o f the ice cover, and (3) methodological topics connected with the s tudy of the p a m t e r s and deformation of +he i ce covep.

Any correspond" concerning the RIDdEX Bulletin should be

Alma Johnson, Editor AIMEX Bu1Zet;n 4050 Roosevelt Wag N.E. Seattle, Washington 98105

Main Administration of the Hydrometeorological Service of the Council of Ministers of the USSR

Lenin-Order Arctic and Antarctic Scientific Research Institute

- SECOND HALF -

T R u D y (PROCEEDINGS)

VOL. 303

INVESTIGATIONS OF THE I C E CONDITIONS I N THE ARCTIC SEAS AND METHODS OF FORECASTING

AND COMPUTATION

Edited by N. A. Volkova

Hydrometeorological Press, Leningrad, 1971

(This docwnent was translated from Russian f o r the National S&ence Foundation b y the IsraeZ Program for S d e n t i fic Trans Zations . 1

TT 72-50022

SEASONAL FEATURES OF THE "POLAR T IDE" PRESSURE VAVE

2. M. Gudkovich mrd T. I, Santsevhh

Successful long-range i c e f o r e c a s t s f o r most a r c t i c seas depend l a r g e l y

on the f o r e c a s t e r ' s a b i l i t y t o foresee the atmospheric processes, e spec ia l ly

a i r motion, occurr ing during the ice melt ing period.

phys ica l and geophysical f a c t o r s , i n p a r t i c u l a r t he e f f e c t of t h e f r e e

nu ta t ion of t he Ear th ' s a x i s , on the atmospheric c i r c u l a t i o n should the r

be s tud ied i n cons iderable d e t a i l .

The e f f e c t of space-

The v a r i a t i o n of t he atmospheric pressure due t o t h e "polar t ide" i n

the atmosphere, which is assoc ia ted with the f r e e nu ta t ion of t h e Ear th ' s

axis, was f i r s t invest l lgate y Meksimov [8,9,10], H e e s t ab l i shed t h a t t he

nu ta t ion " t ide" i n the Northern Hemisphere is a circumpolar pressure wave which r o t a t e s from w e s t t o east i n accordance with the nu ta t ion of t he pole ,

with a per iod of some 1 4 months. The ant inode of t h i s wave i n the Northern

Hemisphere is loca ted a t 65-70°N, i .e., it is s h i f t e d northward relative to

the m a x i m u m deforming f o r c e which is observed a t 45'N.

wave are a t the Equator and the poles .

tude a t these l a t i t u d e s varies from 0.8 t o 1 . 2 mb depending on longitude.

The nodes of the

The mean pressure o s c i l l a t i o n ampli-

A more d e t a i l e d s tudy of t h i s phenomenon i n the Arc t i c [4] confirmed

Maksimov's b a s i c conclusions. Cer ta in a d d i t i o n a l f ea tu re s of t he nu ta t ion

pressure wave were e s t ab l i shed , however:

increase i n c e r t a i n reg ions , and the wave phase was observed t o change

discont inuously between ad jo in ing regions.

t he wave amplitude was found t o

A s p e c i a l hypothesis w a s advanced t o account f o r t h i s phenomenon:

according t o t h i s hypothesis , the r o t a t i n g system of deformation forces

produced by the f r e e nu ta t ion not only generates a "primary" s tanding wave

of atmospheric pressure , bu t a l s o has a considerable inf luence on the

cyclonic a c t i v i t y , mainly i n the cyclogenesis regions i n the northwestern

A t l a n t i c and P a c i f i c [13]. The cyclonic a c t i v i t y i n these regions is

1

enhanced by t h e trough of t h e primary wave, dropping o f f when t h e wave c r e s t

passes.

f r e e nu ta t ion frequency (with a per iod of some 14 months).

t o t h e east and t h e no r theas t from t h e cyclogenesis region thus c o n s t i t u t e

carriers of t h e 14-month components of t h e atmospheric p re s su re anomalies

and c r e a t e a secondary p res su re wave of the same period i n t h e reg ions through

which they pass.

po lar wave and d i s t o r t s its regu la r form.

These changes i n t h e depth and recurrence of t h e cyclones follow t h e

Cyclones moving

The secondary wave is superimposed on t h e primary circum-

Since cyclogenesis and cyclone t r a n s p o r t i n d i f f e r e n t regions are

s e n s i t i v e t o t h e t i m e of year , it seems t h a t t h e e f f e c t of t h e secondary wave

on t h e s e processes should a l s o change from one season t o the next.

however, cannot be i d e n t i f i e d by harmonic a n a l y s i s of t h e success ive series of

monthly-average p res su re corresponding t o the 14-month o s c i l l a t i o n component,

s i n c e t h e period of t h e nu ta t ion wave is c l o s e t o one year.

This f a c t o r ,

The nu ta t ion o s c i l l a t i o n s of atmospheric p re s su re can be analyzed i n

the following way.

produce va r ious f i c t i t i o u s o s c i l l a t i o n s of t h e measured v a r i a b l e which depend

on the r e l a t i o n s h i p between the t i m e i n t e r v a l A t between success ive observa-

Discrete measurements of any pe r iod ic phenomenon i n e v i t a b l y

t i ons and t h e n a t u r a l o s c i l l a t i o n per iod T.

to r (more p rec i se ly , 3 ~ / 4 < At < T o r r < A 5 < 5 r / 4 ) , a f i c t i t i o u s wave is

obtained with a per iod

I n p a r t i c u l a r , i f A$ is c lose

A t T T* = - T c - z q -

I f , on the o t h e r hand, A t i s c l o s e t o ~ / 2 (more p r e c i s e l y , . r /4 < A t

or ~ / 2 < At < 3 ~ / 4 ) , bea t s are observed wi th a period T~ = 2At and a t i m e

i nve rva l between success ive antinodes (o r nodes)

.r/2

A t T I T - 2 A t l T:

It is r e a d i l y seen t h a t t h e t r u e o s c i l l a t i o n s of per iod T and t h e fic-

t i t i o u s wave of period T* have t h e same amplitude, which i n t u r n is equal t o

the maximum "beat" amplitude, Hence, r e l i a b l e information about the t r u e wave

2

C a n obtained from da ta he period, e of the f i c t i t i o q s waves.

sphe r i c pressure values f o r a

below lists t h e per t i o u ted from (1) €or At = 1 year, ~

rs 25.0 13.0

ata i n d i c a t e

the free nu ta t ion per iod appr

f r e e nu ta t ion per iod of t h e Earth

years on the average, f l u c t u a t i n g

r i o d of the atmosp ted with the

"polar t ide" is thus expected t o be 6.7 years on the average.

The nu ta t ion o r i g i n the 7-year f l u e

the hydrometeorological elements is sometimes erroneou

arguing t h a t t h i s is the per iod of the b e a t s obtained when the 14-month

wave assoc ia ted with t h e f r e e n u t a t

one-year c l ima t i c wave. Y e t t he

w i l l not produce year-to-year cha e anomalies even dded t o waves of o the r per iods. This e r r o r presumably stems from the f a c t t h a t

r e l a t i o n (1) is analogous to the s tandard r e l a t i o n f o r the bea t period

produced by superpos i t ion of two waves of c lose per iods.

t he poles is rimposed on the

The o v e r a l l cha rac t e r of the t i d e pressure Wave and i ts monthly

or seasonal f e a t u r e s thus can be i d e n t i f i e d by s tudying t h e 7-year component

of the multiyear v a r i a t i o n of atmospheric pressure, o r , i n o the r words,

the 7-year f i c t i t i o u s wave. Ind iv idua l quasi-periodic components are

genera l ly i s o l a t e d from mult iyear pressure series (or series of o the r

elements) by means of s u i t a b l e f i l t e r s . The simplest f i l t e t i n

involves averaging over n terms followed by subtraction of the averaged series from the original series. The number n and the order of filtration are depen- dent both on the frequency to be filtered out and on the frequency to be

. The characteristic frequency specfrum of the hydrometeorological

elements is naturally of the greatest importance in choosing these parameters.

Cyclic variations of a number of hydrometeorological elements with

cycles of 2-3, 3-4, 5-6, 7-8, 10-11, 19, and 22 years were isolated by various means in [1,2,5,6,12,14,16].

as a rule for 2-3 and 6-7 year cycles. frequency band of the nutation pressure wave was determined by the following

method of processing the seasonal mean values of the atmospheric pressure

anomalies at 42 points in the Arctic over the years 1937-1969* (see Figure la).

The maximum amplitudes were observed

In our etudy, the characteristic

1. Moving averaging of the initial series using the climatic formula,

thus eliminating the high-frequency components (2-3 years).

2. Moving averagiqg of the resultant series (from 1) over 7-year periods \ to eliminate the characteristic frequ

(6-7 years).

3. Subtraction of the second series from the first, to isolate oscilla-

tions of the same frequencies as in 2.

This filtering procedure is naturally far from perfect, and it does not ensure isolation of the nutation pressure wave in a pure form.

clear from the following table which lists the fractional amplitudes (in

fractions of the initial amplitude) of various frequency components which remain after filtering:

This is

T, years 2 3 4 5 6 7 8 9 10 11 15 20

A ' / A 0 0.20 0.57 0.80 0.86. 0.81 0.74 0.64 Oa56 0.50 Oa24 0.15

"Pressure norms

These f i g u r e s were computed from the r e l a t i o n

where A and A ' are the amp

averaging, respectgvely; n used i n moving

before and a f t e r

s of t h e series

It follows tha$ f i l t r a t i o n retains over 80 per cent of t h e o s c i l l a t i o n s

with per iods between 5 7 years , subs ta uppressing the amplitudes

of t h e s h o r t period components and t o a l e

t h e low frequency of t he spectrum. T ed component AP, thus

covers a f a i r l y w i uency band, whic year nu ta t ion

cyc le qay p a r t i a l in o s c i l l a t i o n s of a d i f f e r e ig in , " The main

"impurity" is app year waves associ-

a ted with t h e corresponding s o l a r a c t i v i However, t he

app l i ca t ion of more complep narrow-band t l y con t r ac t s

t he length of t he series and lowers the r e l i a b i l i t y of the r e s u l t s .

n t t h e amplitudes of

due t o t h e 5-6 y

To f ind t h e amplitudes of t he f i l t e r e d " en-year " o s c i l l a t i o n s and

t h e i r f r a c t i o n Tn t he year-to-year v a r i a t i o n s of t he seasonal mean atmo-

sphe r i c pressure , t he AIJ, series f o r each season were p lo t t ed i n graphic

form. Using these graphs, t he mean wave amplitude w a s computed f o r each

f i e l d po in t from the r e l a t i o n

1 - ui3= - 2;\ ( T A P , max - zAP,min) I

where N i s the number of maxim2 (nlinima) i n @, i n each series.

The d i a t r3bu t ion of 2z7, which cha rac t e r i zes the *runpli

"nutation" o s c i l l a t i o n s of atmospheric pressure f o r each season, i

i n Figure 1.. This f i g u r e ind ica t e s t h and F t s space d i s t r i b u t i o n are d i f f e r e n t f o r d i f f e r e n t seasons.

*It is f o r t h i s reason t h a t t he ad jec t ives "seven-gear" are henceforth set off by quotat ion marks.

5

Fig. 1. Distribution of 2;, values in v rious seasom : April-June (a) , July-August (b) , October-December (c) , January-March (d) *

In spring (Fig. la), the largest amplitudes (3-5 mb) are noted in the near-Pacific part of the Arctic basin, in the northern parts of Europe, and

North America ana continental Asia. In er ** (Fig. 1 the region of maximum amplitude and Greenland. are localized in two extensive regions, one stretching from the North Atlantic

. in the Bering Sea, whereas the minimal amplitudes occur over continental

up t o 5 mb and larger) is restricted to the*Arctic basin In autumn and early winter (Fig. IC), the maximum amplitudes

* In Figures 1 through 5, th and minimum (4H) are not translated.

- “The summer season is limited to two months (July-August) due to the

fact that the distribution AP, in September has features which tend to be more characteristic of the following season.

nd West S i b e r udes of up t o 6 mb

other extending from t h e Nort,h P a c i f i c t o Alaska and

North Canada (amplitudes of up t o 6 mb and l a r g e r ) .

regions p e r s i s t i n win ter , but the f i r s t i s s h i f t e d northward, embracing

t h e near-Atlant ic p a r t of the Arc t i c bas in , the Norwegian and Greenland seas,

and the North Atlanti eas the second

t h e Gulf of Alaska.

These two high-amplitude

-

The amplitude i n bot

Figure 1 conf ' [ 4 ] of three main regions

i n t h e Arc t i c with -amplitude n u t a t i o very our d a t a

s i g n i f i c a n t l y l a r g e r than w a s previously assumed.

The t a b l e below l ists the averaged "seven-year" amplitudes of atmo-

spher ic pressure 2a, and t h e i r r a t i o

va r i a t ions .

t o t he amplitude of t he many-year *

Jan.-March April-June _. July-August - --I- -_-.--_.- O c t . -Dec . ----

4.5 2 .4 2.8 2a, (mb) 3.4 - ?-I (X) 24 30 26 28

r

The amplitude of t h e "seven-year" o s c i l l a t i o n s is on the average -

24-30 per cent of t he many-year amplitude. I n c e r t a i n regions, reaches

40 per cent . The d i s t r i b u t i o n of t h i s parameter on t h e whole corresponds

t o the d i s t r i b u t i o n of a, f o r each season.

To e s t a b l i s h a r e l a t i o n between the "seven-year" component of atmo-

spher ic pressure and the motion of the Ear th ' s pole , t he A P , series f o r

each season w a s s p l i t i n t o four groups ( types) , each corresponding t o the

p reva i l i ng p af t he radius-vector of po le during th,e p a r t i c u l a r

sAe~ason i n one- of the 90-degree quad 90°W , sec.ond 90°W-180' , t h i r d 18Oo-9O0 r t h 9O'E-O0. The c n of seasons based on

t h i s c r i t e r i o n 1, where p luses ass ign each of t he seasons

i a t i o n s is taken as the d i f f e rence between t h e maximum and the minimum members of t h e series.

7

f o r t h e years 1940-1966 t o one of t h e four group

with Table 1, mean charcs of t h e AF, d i s t r i b u t i o n were constructed f o r each

season.

types) . Zn accordawe

TABLE 1

CLASSIFICATION OF SEASONS ACCORDI~G TO THE POSITXON OF THE RADII -

Year

1957 1958

-VECTOR OF THE EARTH'S POX,E

a oo -90 O w

1,

d a ' E

- I 4

;< -

t +

i- t-

t

+ + 4-

3: and g are the coordinate9

I

* - 1 1 -

1 + / _ j

I i

- 1 . .IT

I -?-

; I L I 2.

i I

I

:he pole.

I - 1

~ ; i i - I - !

tl 7 1 -

.- I

, - 1 - I

-

The c h a r t s shown i n Figures 2-5 may be t r ea t ed a8 representa t ive . The

mean pos i t i on of t he radius-vector of t he pole i s shown on a relative scale,

and the numbers of the s e c t o r s are i d e n t i f i e d by Roman numerals.

Figure 2 shows t h e t y p i c a l c h a r t s f o r spr ing (April-June), which reveal a d i s t i n c t s t r u c t u r e of t h e AP, f i e l d s :

s e c t o r t o which t h e radius-vector of t he pole is d i rec ted) conta ins the

the s e c t o r w J t h the pole ( i .e. , t he

8

Fig. 2. Typical AP, f i e l d s i n April-June with t h e pole loca ted i n d i f f e r e n t s ec to r s .

Arrows i d e n t i f y t h e mean pos i t i on of t h e po la r radius-vector. anomalies i n mb.

The f igu res g ive the pressure

p o s i t i v e pressure anomalies ( t h e crest of the "nutation" wave), whereas the

d iamet r ica l ly opposi te s ec to r contains a region of negat ive anomalies ( t h e

wave trough).

t h e "polar t i de" i n the Northern Hemisphere developed by Maksimov [ lo] and

thus confirms the nu ta t ion o r i g i n of t he wave.

wave i s observed:

and t h e maximum i s s h i f t e d t o higher Lat i tudes than i n the American sec to r .

I n t h e main l i n e s , t h i s corresponds t o the c o t i d a l schemes of

D i s t i n c t asymmetry of the

its amplitude i n the Asian sec to r i s s u b s t a n t i a l l y higher ,

The anomaly d i s t r i b u t i o n s i n Figures 2a and 2c corresponding t o the

pos i t i on of t h e pole i n opposi te ("oceanic") sectors--the f i r s t and the

third--are almost mir ror r e f l e c t i o n s of one another. The c h a r t s i n

9

Figures 2b and 2d correspond t o the pos i t i on of t h e pole i n the second and

the fou r th ("continental") s e c t o r s , and t h i s f e a t u r e is less pronounced.

the l a t t e r case, the l a g ( o r phase s h i f t ) between the p o s i t i o n of t h e wave

c r e s t o r trough and t h e r o t a t i o n of t he pole i s more pronounced.

t o va r i ab le angular ve loc i ty of t he circumpolar pressure wave, as was pre-

viously noted i n [ 4 ] .

I n

This po in t s

The t y p i c a l c h a r t s f o r t he summer (July-August) shown i n Figure 3

r evea l a "polar t i de" pressure wave which, on t h e whole, f i t s our descr ip-

t i o n .

(over several years) and i n space (within + 4 5 O longi tude) , so t h a t t h e

Note t h a t t he AP, values f o r each type were averaged both i n t i m e

c h a r t s present an e s s e n t i a l l y averaged p i c tu re . The amplitude o f t he real

wave should be somewhat l a r g e r and should undergo s i g n i f i c a n t f l u c t u a t i o n s

from year t o year , i n accordance with the changes i n t h e dev ia t ion of t he

pole from i t s mean pos i t i on .

Fig. 3. Typical AP, f i e l d s i n July-August with the pole loca ted i n d i f f e r e n t sectars.

Legend as i n Fig. 2.

10

L e t us now consider t h e t y p i c a l c h a r t s f o r t h e two cold seasons i n Figures 4 and 5. December), t h e nu ta t ion pressure wave s t i l l ret r t a i n f ea tu res which

are c h a r a c t e r i s t i c of t h e w a r m seasons. With i n the second and

fou r th s e c t o r s (Figs. 4b and 4d), extensive re negat ive and p o s i t i v e

anomalies, r e spec t ive ly , are observed over t h e seas from t h e Greenland

Sea t o t h e Laptev Sea. I n the opposi te s ec to r s , no nu ta t ion wave is observed

i n these cases.

They show t h a t i n autumn and e a r l y win ter (October-

A highly c h a r a c t e r i s t i c d i s t r i b u t i o n of hp, i s observed i n t h e e a r l y

win ter months of those years i n which the pole i s i n the f i r s t and t h i r d

s e c t o r s (Figs. 4a and 4c). I n t h e former case, the e n t i r e Arctic bas in ,

Bering Sea, and t h e nor e r n p a r t of t h e North American cont inent are covered

by negat ive pressure anomalies, whereas an ex tens ive p o s i t i v e pressure

anomaly extends east of Baf f in Bay, s t r e t c h i n g across Eurasia . I n t h e

l a t te r case, the d i s t r i b u t i o n of t he anomalies follows a mir ror - re f lec t ion

pa t t e rn . The amplitude of pressure f luc tua t ions reaches 1.5-2 mb i n both

cases.

This s t r u c t u r e of pressure f i e l d s can be in t e rp re t ed using the hypothesis

of [4]. I n autumn-winter, un l ike t h e warm seasons, t h e i n t e n s i t y of t he

zonal a i r streams increases markedly, simultaneously enhancing t h e cyclonic

a c t i v i t y i n t h e Iceland and Aleut ian centers .

f i r s t s e c t o r (Fig. 4a) , t h e crest of t h e "polar t ide" c rosses the Iceland

low, whereas t h e trough l i e s i n the Aleut ian low. As a r e s u l t , t h e cyclo-

genes is i s weakened i n the f i r s t cen ter and enhanced i n t h e second center .

The assoc ia ted p o s i t i v e and negat ive pressure anomalies propagate f a r t o the

east from the source, toge ther with the leading zonal stream, forming exten-

s i v e b e l t s of high and low pressure s t r e t c h i n g i n t h e longi tudina l d i r e c t i o n

(Fig. 4a) . i s observed (Fig. 4c). I n e i t h e r case, t h e spreading of the Aleut ian low

When the po le s h i f t s i n t o the

When the pole is s h i f t e d i n t o the t h i r d s e c t o r , a reverse p a t t e r n

anomalies t o t h e Arctic bas in a l s o corresponds t o t h e d i r e c t i o n of t he lead ing

streams, which are meridional i n these regions i n winter [13].

Note t h a t some pressure anomalies may form due t o f a c t o r s o the r than

t h e depth and frequency of the passing cyclones. They apparent ly have an

11

Fig. 4 . Typical AP, f i e l d s i n October-December with t h e pole loca ted i n d i f f e r e n t s e c t o r s ,

Legend as i n Figure 2 ,

i n d i r e c t in f luence , s i n c e they determine the cloudiness and hence t h e condi-

t i o n s of r a d i a t i v e cooling of t h e su r face , which l a r g e l y determine t h e

formation of seasonal an t icyc lones , e.g., t h e S iber ian , t h e Canadian, and

the Arctic.

When the pole s h i f t s t o the second and fou r th s e c t o r s (Figs. 4b and

4d), t he nodal l i n e s of t h e circumpolar pressure wave pass over t h e main

cyclogenesis regions, and the e f f e c t of t h e "polar t ide" wave on the pressure

f i e l d i s therefore weak and r e s t r i c t e d i n space.

is most pronounced a t t h e trough of t h e I ce l and ic low.

deeper i n Figure 4b and p a r t l y f i l l e d i n Figure 4d.

are s i g n i f i c a n t meridional components of a i r motion over t he Greenland and

Norwegian seas, un l ike the zonal components c h a r a c t e r i s t i c of types a and c.

I n e i t h e r case t h i s wave

The trough i s thus

I n these cases t h e r e

12

The typical AP, fields for January-March (Fig. 5) show that with the pole located in the first and third sectors (Figs, 5a and 5c) the tion of pressure anomalies is markedly different from that for the corresponding field types of the earlier season. anomalies, which in October-December were restricted to the Arctic basin,

spread over the entire Arctic in January - March, of 3-3.5 mb in the p anomalies of the opposite sign is displaced to more s

northern boundary is hardly visible on our charts. T retains its mirror-ref lection pattern in pole motion. There is a characteristic crest in AP, in the direction of the radius-vector of the pole and a trough in the opposite direction, i,e.,

negative and pos i t ive

reaching amp1 Legion and over the Greenland Sea. The belt of

herly latitudes ; it;s @ 7 distribution

wit

over Baffin Bay and the northeastern part of Asia.

Fig. 5 . Typical @, fields in January-March with the pole located in different sectors. Legend as in Figure 2.

13

I

When t h e pole s h i f t s i n t o t h e second and fou r th s e c t o r s (Figs. 5b and

5d), t he amplitude of t h e anomalies is r e l a t i v e l y small everywhere, and the

d i s t r i b u t i o n shows no obvious c o r r e l a t i o n with the p o s i t i o n of t h e pole.

One of t h e poss ib l e reasons for t h e s e changes i n t h e AP, d i s t r i b u t i o n

between autumn and win te r i s t h e southward s h i f t i n win ter of t h e leadfng

zonal streams as a r e s u l t of t h e deepening and broadening of t h e circumpolar

cyclonic vor tex i n t h e troposphere. This i s a l s o evident from t h e increased

frequency Of t h e win ter cyclones c ross ing the North A t l a n t i c along southern

t r a j e c t o r i e s and continuing f a r t h e r east across the Mediterranean [7,13].

Another reason f o r t hese changes may be t h e state of t h e su r face ,

which changes i n the seas and oceans due t o air cu r ren t s i n autumn and has

a r ec ip roca l e f f e c t on atmospheric c i r c u l a t i o n i n winter. Let us consider

from t h i s po in t of view t h e poss ib l e changes i n t h e s ta te of t h e su r face due

to t h e "nuta t ion anomalies" i n a i r c u r r e n t s over t he Norwegian and Greenland

seas, where these anomalies are p a r t i c u l a r l y l a r g e (Figs. Sa and 5c). Given

t h e d i r e c t i o n and angular v e l o c i t y of r o t a t i o n of the polar radius-vector,

we should expect a d e f i n i t e sequence of bp, f i e l d types from autumn t o winter.

Thus, using Table 1, we can r e a d i l y f ind t h a t i n some 80 per cent of t he

cases t h e f i e l d types of Figures Sa and 5c i n January-March are preceded,

r e spec t ive ly , by t h e f i e l d types of Figures 4b and 4d i n October-December.

The f i e l d s of Figure 4b are cha rac t e r i zed by ehhanced nor thern a i r c u r r e n t s

over Fram S t r a i t and the East Greenland Current and a l s o southwestern cu r ren t s

over t he Faeroe-Shetland S t ra i t . A l l t h i s should enhance t h e d r i f t of ice from t h e Arc t i c bas in i n t o t h e Greenland Sea, while a t t h e same t i m e increas-

i n g t h e inf low of w a n n A t l a n t i c water from t h e south t o t h e Norwegian Sea

and consequently sharpening t h e ho r i zon ta l water and a i r temperature gradi-

e n t s i n t h i s region. This, i n t u r n , w i l l s t e p up t h e cyclogenesis and lead

t o a drop i n atmospheric pressure .

Conversely, with f i e l d t y p e s of Figure 4d i n autumn, t h e d r i f t of i c e

from the A r c t i c bas in i n t o t h e Greenland Sea and the flow of warm A t l a n t i c

rater i n t o t h e Norwegian Sea both dec l ine , t h e ho r i zon ta l water and a i r

Qemperature grad ien ts become smaller, the cyclogenesis is weakened , and t h e

pressure correspondingly inc reases over t h e s e regions i n the subsequent

14

period.

Figures 5a and 5c.

produced by these proces s, as w e see from re 5, act t o s u s t a i n t h e

corresponding processes: t h e type a anomaly i o n enhances the

temperature c o n t r a s t s and cyclonic a c t i v i t y , wherea

he lps t o reduce the temperature con t r a s t s and cyclo

These t rends are c l e a r l y r e f l e c t e d i n t h e win ter c h a r t s of

It is s i g n i f i c a n t t h a t t pressure anomalies

t h e type b d i s t r i b u t i o n

As a r e s u l t , t h e corresponding t y p i c a l f i e l d s p e r s i s t during the e n t i r e

win ter and a f f e c t the following s (April-June). This t rend is f u r t h e r

re inforced by t h e conservat ive thermal anomalies i n the ocean. The regular

ro t a t ion of t h e po la r radius-vector i nd ica t e s t h a t t h e win ter

Figure 5a g ive way t o sp r ing f i e l d s of Figure 2d.

t he p o s i t i v e pressure anomaly i n the four th sec to r is f a i r l y i n d i s t i n c t i n

t h i s case; t h i s i s probably due t o t h e increased cyclonic a c t i v i t y of t he

preceding win ter processes i n t h e area (Fig. 5a) . Conversely, t h e win ter

type of AP, i n Figure 5c general ly evolves i n t o the sp r ing type of Figure 2b:

t h e nega t ive AP, anomalies i n the four th s e c t o r are replaced by p o s i t i v e

anomalies. This a l s o may be a t t r i b u t e d t o the e f f e c t of l i k e anomalies from

t h e earlier season, s p e c i f i c a l l y t o the development of processes which

a t t enua te the cyclonic a c t i v i t y i n t h i s area.

As w e see from Figure 2d,

L e t us t r y t o e s t a b l i s h t o what extent t h e actual seasonal average

f i e l d s 0f pressure anomalies correspond t o the average t y p i c a l AP, f i e l d s

o r , i n o the r words, what t h e r e l i a b i l i t y of t h e fo recas t s based on these

f i e l d s is.*

regions i n the Arctic (charac te r ized by maximum 0, amplitudes) over a per iod

of years (1940-1966).

seasons t h e r e l i a b i l i t y is 64% f o r t h e s ign of t h e anomaly and 66% f o r the

magnitude, assuming an accuracy test of +20% A. Since the r e l i a b i l i t y of

t he pressure norm f o r t h e same accuracy test is 57%, t he method i s 9%

These ca l cu la t ions were first ca r r i ed out f o r a number of

The r e s u l t s show t h a t on the average f o r t he four

e f f ec t ive .

* Since the nu ta t ion is f a i r l y regular , t h e pos i t i on of t he pole can be fo recas t without d i f f i c u l t y several months i n advance. t he fo recas t s of the t y p i c a l f i e l d s may be taken c lose t o 100%.

The r e l i a b i l i t y of

15

I n view of t he g rea t importance of t h e spring-summer pressure f i e l d fore-

casts f o r ice s i t u a t i o n fo recas t ing ( these fo recas t s are mainly concerned with

the pressure grad ien ts and not t he absolu te pressure, ' as t h e grad ien ts deter-

mine the a i r movement i n t e n s i t y ) , similar r e l i a b i l i t y estimates were prepared

f o r fo recas t s of another p re s su re f i e l d index, namely, t h e d i f f e rence i n

pressure anomalies between two poin ts :

(where t h e "seven-year'' component is s u b s t a n t i a l ) , and i n t h e middle of t h e

Laptev Sea.

c h a r t s was 78% f o r t h e sign and 67% f o r t he magnitude (+20% A) i n April-June;

i n July-August, t h e r e l i a b i l i t y was 60% f o r s i g n and 74% f o r magnitude.

t he pressure norm is r e l i a b l e t o 56% i n both cases, t h e method i s 11% and 18%

e f f e c t i v e , respec t ive ly ( i . e . y b e t t e r than f o r t h e pressure anomalies themselves).

nor th of t he Novosibirsk Archipelago

The r e l i a b i l i t y of t h e fo recas t of t h i s index using t h e t y p i c a l

Since

Unfortunately, no cons i s t en t procedure has been devised f o r es t imat ing

The p test commonly used i n the r e l i a b i l i t y of pressure grad ien t fo recas t s .

synopt ic meteorology f o r assess ing t h e r e l i a b i l i t y of fo recas t ing t h e s i g n

of pressure anomaly f i e l d s was computed using 42 po in t s f o r the spring-summer

per iod (Table 2) of 1940-1966."

p o s i t i v e i n 67% of t h e cases f o r April-June (during the e n t i r e observat ion

period) and i n 87% of t h e cases i n Ju ly and August. The many-year average

of p f o r summer i s a l s o s i g n i f i c a n t l y higher than the sp r ing va lue (0.26 and

0.17, respec t ive ly) .

We see from Table 2 t h a t t h e p test i s

The p test is f a r from being pe r fec t : i t responds t o even the smallest

devia t ions from zero (e.g., an erroneous fo recas t is indica ted when the fore-

cast and the a c t u a l anomalies are +0,1 and -0.1 mb, respec t ive ly) . I f i n a l l

cases of un l ike s igns , an e r r o r of up t o 20% is allowed i n t h e magnitude of

t he many-year pressure amplitude, t he p values w i l l be s i g n i f i c a n t l y higher

(Table 3).

This zearked inc rease i n p (compared with the f i g u r e s of Table 2) ind i -

cates t h a t errors i n t h e s ign of t he f o r e c a s t mostly correspond t o cases of

low anomalies.

(p > 0.6).

The average r e l i a b i l i t y of t hese f o r e c a s t s is over 80%

*The last th ree years of t h e series (1967 1968, 1969) were omitted from the construct ion of t h e t y p i c a l 0, f i e l d s .

w

16

TABLE 2

S FOR s s m

Year

1940 1941 1942 1943 1'344 1945 1946 1947 1948 1949 1950 1951 1 952 1953 1954

April- July- June August

0.22 0.33

-0.03 0,M 0,54 0.21

-0.17 0.22

-0.12 0.45 0.47

-0.13 0,31 0.42 0. $2

-0.05 0,53 0.50 0.56 0.32 0,16

-0.05 0.41 0,17 0,oo 0.14 0.05 0.37 0.30

-0.03

Apri 1- July- June IAug

0.O.i I 0.37

Average for 1940-1969. . . . . . . . . 0.17 0.26

TABLE

RELIABILITY OF FORECASTS FOR THE SIGN OF THE SEASONAL-

ALLOWANCE FOR MAGNITUDE) AVERAGE ATMOSPHERIC PRESSURE ANOMALIES (THE p TEST WITH

Year I April- I June

19-10 I 19z1 191.2 194.3 1944 1945 1946 1947 1948

1 95% 1 953 1954

0.67 0.81 0.43 0,!10 1 ,00 0 , 3 3 0.33 0.33 0.3s 0.86 0.71 0.48 0.67 0.86 0.71

Average for 15

July August

0.52 0. S6 0.76 0.90 0.52 0.67 0.48 0.62 0.90 0. iG I). '15 0.71 0.76 0.95 0.33

April- I July- June (August

0.29 0.67

0.76 O,-N 0.67

0-1969 . . . . . . 0.62

O: 67 0,76 0.62 0, '76 0 , i f i 0.76 0.57 0.76 0.67 0.86 0, :n 0.11

0.64

17

The r e l i a b i l i t y of a fo recas t of seasonal-average pressure f i e l d s should

increase i f w e take i n t o account both t h e pos i t i on of t h e po le and t h e magni-

tude of i ts displacement, which is known t o f l u c t u a t e between wide limits.

Moreover, a certain improvement is poss ib l e by using typical AP, c h a r t s

constructed f o r in te rmedia te pos i t i on o f t he pole i n s e c t o r s o t h e r than those

used i n the present study.

Other components of t he c y c l i c v a r i a t i o n of atmospheric pressure should

This app l i e s pr imar i ly t o t h e cyc les of two-three years and a l s o be s tudied .

longer which are assoc ia ted with s o l a r a c t i v i t y .

The f a c t s discussed i n t h i s paper i n d i c a t e t h a t c e r t a i n fo rces e x t e r n a l

t o the atmosphere, such as t h e deformation fo rces assoc ia ted with nuta t ion ,

probably provide a mechanism which r egu la t e s t he release of t h e i n s t a b i l i t y

energy of the atmosphere. The e f f e c t of t hese forces on atmospheric c i rcu-

l a t i o n the re fo re depends on the s ta te o f t he atmosphere, t he state of the

su r face , and t h e i r i n t e r a c t i o n s . Of dec i s ive importance is the i n t e r a c t i o n

of t h e atmosphere and the ocean i n zones of maximum ho r i zon ta l temperature

grad ien ts , where cyclogenesis is observed.

BIBLIOGRAPHY

1. Volkov, N . A. and B. A. Sleptsov-Shevlevich. S tudies of the two-year cyc le of f l u c t u a t i o n s i n the i c e coverage of arctic seas. A r k t i k i i A n t a r k t i k i , No. 3 4 . Leningrad: Gidrometeoizdat, 1970.

I n ProbZemy

2. Volkov, N. A. and B. A. Sleptsov-Shevlevich. Cyclic v a r i a t i o n of t he ice-cover c o e f f i c i e n t of t h e arctic seas ( t h i s c o t t e c t i o n ) . [See AILVEX BuZZetin No. 16, p. 1 .1

3. Gneyvshev, M. N. and B. I . Sazonov. The e f f e c t of s o l a r a c t i v i t y on the processes i n the lower atmosphere. Astronomioheskii ZhwvlaZ, Vol. 41, No. 5, 1964.

4. Gudkovich, Z. M., E. I. Sarukhanyan, and N. P. Smirnov. "Polar t i de" i n t h e atmosphere a t high l a t i t u d e s and f l u c t u a t i o n s i n t h e ice coyerage of t he a r c t i c seas. Doklady -AN SSSR, Vol. 190, No. 4, 1970.

18

5 . Zakharov, V. F. Changes i n t h e ice coverage of t h e Laptev Sea assoc ia ted wi th p re s su re f i e l d changes i n t h e Arc t ic . arkt.icheskogo Ins t i tu ta , Vol. 257, 1967.

T m d y Arkticheskogo i Ant-

6. Kovalev, E. G. Cyclic f e a t u r e s i n the f l u c t u a t i o n s of t he ice coverage of t h e Novosibirsk Archipelago and its app l i ca t ion t o fo recas t ing . DokZpdy AN SSSR, Vol. 135, No. 2, 1960.

7. Kryzhanovskaya, A, P. T r a j e c t o r i e s of cyclones and an t icyc lones et sea l e v e l i n the Northern Hemisphere. Tsentra SSSR, Leningrad, No, 26, 1968,

T d y GidronreteoroZo~cheskugo

8. Maksimov, I. V. The "polar t i de" i n t h e sea and i n t h e Ea r th ' s atmo- sphere. DokZady AN SSSR, Vol. 86, No. 4, 1952.

9. Maksimov, I. V. Nutation circumpolar wave i n the Ea r th ' s atmosphere. DokZady AN SSSR, Vol. 100, No. 1, 1955.

10. Maksimov, I. V. Nutation e f f e c t s i n the Ear th ' s atmosphere a t high l a t i t u d e s . ProbZemy Sevara, No. 1, 1958.

11. Maksimov, I. V. Some aspec ts of studying the many-year f l u c t u a t i o n s of t h e genera l ice coverage of a r c t i c seas. A n t a r k t i k i , No. 2.

I n ProbZemy A r k t i k i Leningrad : Morskoi Transport , 1960.

12. Maksimov, I. V. and N. P, Smirnov. A long-range fo recas t of t h e main forms of atmospheric c i r c u l a t i o n i n t h e Northern Hemisphere cons t ruc ted by t h e component-harmonic method. kogo Ins t i tu ta , Val. 262, Leningrad, 1965.

!7!~udy Arkticheskogo i Antarktiches-

13. Pogosyan, Kh. I?. GeneraZ Chculation of the Atmosphere. Leningrad: Gidrometeoizdat, 1959.

14. Santsevich, T . I. Methodology of long-range hydrometeorological fore- c a s t i n g f o r t h e Arctic. Ins t i tu ta , Vol. 292, Leningrad, 1970.

Trudu Arkticheskogo i Antarkticheskogo

15. Sarukhanyan, E. I. ''Polar t i d e " i n t h e World Ocean, DokZady AN SSSR, Vol. 188, No. 3, 1969.

16. Chaplygin, E. I. and A. V. Yanes. ground oceanographic f o r e c a s t s . Znstituta, Vol. 285, Leningrad, 1968.

Space and g loba l f a c t o r s f o r back- T d y Arkticheskogo < Antarkticheskogo

,

19

THE RELATION OF THE RESULTANT MONTHLY AVERAGE WIND TO THE PRESSURE GRA

A . Ya. NikoZaeva

The r e l a t i o n of t h e su r face wind t o the pressure g rad ien t is of

cons iderable i n t e r e s t .

4,6] who der ived , f o r var ious regions and t i m e per iods , empir ica l equations

This t op ic w a s t r ea t ed by a number of au thors [1,2,.

of t h e form

v = a r + b

and a and b are empirical c o e f f i c i e n t s .

t h i s equation obtained by var ious authors.

Table 1 lists t he c o e f f i c i e n t s of

The r e l a t i o n s h

used i n computing w i f o r checking t h e winds and t h e pressure g rad ien t s on

cha r t s . Successful development af t h e theory of i c e

bas in a l s o l a r g e l y depends on t h i s question.

of t he dependence of t he speed and t h e d i r e c t i w of su r face wind on meteoro-

l o g i c a l elements make but r e s t r i c t e d use of experimental d a t a f o r cor robora t ion

of t h e t h e o r e t i c a l conclusigns,while i n experimental s t u d i e s the conclusions

are seldom compared with t h e o r e t i c a l r e s u l t s .

t h e experimental and t h e o r e t i c a l data. o f t e n d i f f e r widely even f o r oqe area.

It is t h e r e f o r e e s s e n t i a l t o check t h e r e a u l t s of earlier s t u d i e s f o r d i f f e r e n t

p a r t s of the Arctic and compare them with t h e o r e t i c a l data.

en wind speed q d pressure grad ien t i s o f t e n

h and l o w . f i e l d s , and and wind

However, t h e o r e t i c a l analyses

I n t h i s paradoxical s i t u a t i o n ,

For rectilinear s t a t i o n a r y motion of a i r i n the f r i c t i o n k e s s case, t h e

os t rophic wind i s given by the r e l a t i o n [3]

1 2 1 ”

g p 2w s i n 9

1.

where v

v e l o c i t y of t he Ear th ' s r o t a t i o n , and r$ is the l a t i t u d e .

is the geostrophic wind speed, p i s t h e a i r dens i ty , w i s t h e angular 9

Since , p = - P

RT

where P is atmospheric pressure , R is t h e s p e c i f i c gas cons tan t , and T is

the abso lu te a i r temperature, equation (1) may be write- in t h e a l t e r n a t i v e

form

We see t h a t t he geostrophic wind i s a func t ion of a i r tempe

pressure , p re s su re g rad ien t , and t h e l a t i t u d e .

wind is always along the i soba r s , so t h a t the low pressure region i s t o t h e

l e f t ( i n the Northern Hemisphere) and the high pressure region is t o t h e r i g h t .

The d i r e c t i o n of t h e geostrophic

The viscous fo rces assoc ia ted mainly with the atmospheric turbulence '

play an iinportant r o l e i n the a i r l a y e r near t h e sur face . Because of these

fo rces , both the speed and t h e d i r e c t i o n of t h e wind are s i g n i f i c a n t l y d i f f e r e n t

from the geostrophic wind and are seen t o vary wi th a l t i t u d e .

n the d i r e c t i o n of t h e wind and t h e i soba r s ( i .e.%

the geostrophic wind) is given by the t h e o r e t i c a l r e l a t i o n [3]

(2) tg a =

where

Here z is the v e r t i c a l coordinate , wz = w s i n $, and k i s t h e c o e f f i c i e n t of v e r t i c a l tu rbulen t exchange.

Near the su r face , f o r z = 0, w e have 6 = 0, so t h a t t g a = l.* Hence

the wind makes an angle of 45" with the i soba r s ( o r with t h e g

As t h e a l t i t u d e is increased, the angle a d i m h i s h e s t o Oo f o r 5 = nn. Observations show t h a t i n f a c t t h i s angle i n the su r face l a y e r is about

trophic wind).

*Resolving t h e indeterminacy i n (2) f o r 5 = 0 , w e g e t t g a = 1.

22

0

H 3 3

mu)

1?

*)

\o

0

I-.- cv

m

W

00

0

9'9 3

I1

I

I I

II

00

CO

U

s: m

00 m

0

rl

ma

h

VI Q

) m

ha U

u)

\o

hlc

v 0

U

U

8 rl d Fc

8 2

d

I.

a a

1

1

7

a

a

a

E2

0

0

4

cn a p9

a aJ V

m

d

U

a

u I, a

2

M

a

a P) m q

)V

J

p4

u

(I) W

a a

Lt &

' cd M

a a

20-30' (Table 2 ) , i .e . , about two-thirds t o one-half of t he t h e o r e t i c a l f i g u r e .

Equation (2) i n d i c a t e s i n d i r e c t l y t h e dependence of t h e angle a on the su r face

wind speed. It is known [3,11] t h a t as t h e wind speed inc reases the c o e f f i c i -

e n t of v e r t i c a l t u rbu len t exchange k grows, and the angle a computed from (2)

f o r a f ixed a l t i t u d e z w i l l correspondingly a l s o inc rease .

The dependence of a on k f o r z s 10 m, t$ = 85' . w z = 7 l / s e c is

given below.

k (m2/sec) . . . . 0.006 0,012 0.060 0.100 0.200

. . . . . . . 40 43 c1 (deg). 2 1 26 31 37

The growth of a with increas ing a n d speed (and hence increas ing exchange

c o e f f i c i e n t ) , which is i n d i r e c t l y obtained from equation (23, is i

t ive agreement with the experimental d a t a of d r i f t g s t a t i o n s ( s e

b (m/sec) . . . . . 1 2 3 4 a (deg) . . . . . . 18 22 24 27

Number of cases . . 115 109 92 11

a here was determined from monthly average d a t a f o r t h e

and t h e corresponding monthly average p res su re c h a r t s construc-

ted a t the I c e Forecast ing Divis ion of t he Arc t i c ' and Antarctic Research

I n s t i t u t e . The inc rease of a from summer t o win ter i n the Kara Sea and i n

the Arc t i c bas in ( s e e Table 2 ) provides a certain confirmation of t h i s conclu-

s i o n , s i n c e t h e w i n t e r wind speed i n these regions i s s i g n i f i c a n t l y higher

than t h e wind speed i n sgmer.

Romanov [7] analyzed a l a r g e v o l of processed observa t ion d a t a from

a l l the polar s t a t i o n s and confirmed t h a t t he angle a increases wi th the

inc rease of t he geostrophic wind from 0 t o 22-23 m/sec.

Equation (2) i s v a l i d i f the'exchange c o e f f i c i e n t remains cons tan t with

a l t i t u d e . The d e l of t h e v e r t i c a l wind p r o f i l e [ l O , l l ] is based

on the assumpt

su r face l a y e r t o some a l t i t u d e h, above which k remains cons tan t . This model

xchange coef i c i e n t k i nc reases l i n e a r l y i n the

:2A

TABLE 2

ANNUAL VARIATION OF a ACCORDING TO VARIOUS AUmOW

-27 lo' -28 -27.5' 1 2 3 c 26 137

- 7-

Month

-27 -26.9' -32.0' 37 -27 -25

Jan. Feb . March Apr i l

133 -22 - 2 1 . 5 - 20 - 19 126 -21

-26 104 -23 -20 -24.0 138 -24 -23 - 2 4 . 0 -26

May June J u l y Aug

- 2 2 . 0 27

-30.0 31 Sep t Oct. NOV. Dec .

Labzovskii I N Kare l in 1, , ,

I ten-day aver- ages ,Kara Sea I i nd iv idua l , Kara Sea

-28' 103 I -26' I

-20 1 4 1 I -23 I

ogaeva

monthly averages, Arctic Basin

-23' 24 24 -24.0' 22 - 24

-24 -26 14

-16 22 25 -13.0 25 -14

- 7 - 14 24

-24 24 22 -24 -25.0 24 -24

-29 22 ---

Minus s i g n s i g n i f i e s devia t ion t o the f t of tbe i sobar ,

y i e l d s the following equation between a and I C :

1/"""; 11 ctg 2 = 1 -;- 2 - I n - kl ZIJ (3)

where h is t h e height o f the upper boundary of the su r face h y e r , k, is t h e

exchange coe f f i c i en t a t 1 m a l t i t u d e , and

sur f ace.

is the roughness of t h e

As t he wind ve loc i ty increases , both k, and h grow. Therefore, i n

order t o determine the dependence of a on wind speed from ( 3 ) , w e computed

the value of a f o r a number of c h a r a c t e r i s t i c values of k, f o r h = cons t ,

h = ak,, and h = ak:, where a is a c m s t a n t coe f f i c i en t (Table 3).

* I

TABLE 3

42'(h = 0.018) 40 ( h = 0.072)

The wind speeds corresponding t o these values qf k, (see Table 3) were 1 .

derived f o r z = 10 m from the equation i n [ll].

Qua l i t a t ive comparison of t he r e s u l t s of cdmputations obtained using

equations (2) and (3) and t h e experimental 'data of d r i f t i n g s t a t i o n s (see

above) ind ica t e s t h a t the r e s u l t s obtained from'(2) show a b e t t e r f i t wi th

observation da ta . . Thus, f o r wind. speeds of 0-5-4.6 m/secr (which corresponds

t o k = 0.006-0.060 m2/sec), t h e angle of wind devia t ion from the i sobar

v a r i e s approximately from 21' t o 31'. The observat ion d a t a of d r i f t i n g

s t a t i o n s give a range of v a r i a t i o n of from 1 an average. Calcula-

t i ons based on (3) show q u a l i t a t i v e f i t only f o r constant h ( see Table 3).

However, s ince both k and h inc rease with increas ing wind speeds, t he r e s u l t s

obtained from (3) with l i n e a r l y growing h (h = ak, ) and with h propor t iona l

t o the square of k, (h = ak,) do not f

8

2 e

According t o Radikeviah's latest t h e o r e t i c a l

increases a t higher wind speeds.

equations f o r t he nd speed and t h e

the r a t i o u / v on au thors , does not agr

The author derived a closed system of

9 observations.

We did not imtes t fga t e t h e dependence.of a on atmospheric s t a b i l i t y .

We did compare the values of a f o r the Kara Sea and the Arc t i c bas in both i n

winter and i n summer; the angle w a s observed t o be s u b s t a n t i a l l y higher i n

% -

t he Kara Sea than i n the Arctic bas in (see Table

is more s t a b l e above t h e Arctic bas in than over t dependence of a on atmospheric s t a b i l i t y possibly

There is a p o s s i b i l i t y , wever, t h a t the h ig ues of a f o r t h e Kara

Since t h e atmosphere

ra Sea, t h e observed

due t o s u b s t a n t i a l l y higher r e s u l t a n t wind speeds.

The wind speed i n the su r face l aye r is s u b s t a n t i a l l y less than

geostrophic wind (1) due t o viscous f r i c t i o n . For t h e c e n t r a l p a r t

Arct ic bas in (80-90°N), with the a i r dens i ty varying from p = 1 .276010-~ g/cm3

( i n summer f o r P = 1000 mb and t = 0 " ) t o p = 1.56*10-3 g/cm3 (

P = 1040 mb and t = -4 , the geostrophic win 1) changes from v = 540.r

t o v = 440*r , r e spec t ive ly , where r is the pressure g rad ien t i n mb/km. 9

g The c o e f f i c i e n t on the r i g h t i n equat ion (1) thus varies on an average

from 440 (winter) t o 540 (summer). The empir ical equat ions obtained from

the d a t a of d r i f t i n g s t a t i o n s f o r t h e su r face wind ve loc i ty are the following:*

Summer (May-October)

( 4 ) I v = 280-I' (Gudkovich and Nikolaeva) v = 250.I' (Nikolaeva)

Winter (November-April)

v = 240.I' v = 230-r (Nikolaeva)

(Gudkovich and Nikolaeva)

Comparison of these equations shows t h a t t h e r a t i o of t h e su r face wind

phic wind i n winter i s somewhat higher (0.52-0.55) than i n smmer

(0.46-0.52).**

meteorological condi t ions are more va r i ab le than i n the c e n t r a l region, t h e

change i n v / v from summer t o winter is apparent ly mo nounced. Because of t he v a r i a t i o n of U / U

empir ical equat ions f o r wfnd versus pressure grad ien t are v a r i a b l e (Table 1).

I n the coas t a l regions of the Arctic bas in , where the

9 both i n t i m e and i n space, t h e c o e f f i c i e n t s i n the 9

*A'constant term equal t o 0.5 m/sec has been omitted from t h e equations.

**Note t h a t i n der iv ing t h e equation f o r ice d r i f t i n t h e Arctic bas in ,

The equations have been der ived fo r t h e case v = f ( r ) .

Zubov took VIv = 0.5. 9

27

These equations sometimes d i f f e r s i g n i f i c a n t l y even f o r t he same region

and the same season. One of t he reasons f o r t he d i f f e rences i s t o be sought

i n t he nonuniform observat ion da ta and nonstandard processing methods; some

authors used ind iv idua l wind speed and pressure gradient observat ions, while others employed monthly averages o r ten-day averages f o r t he resultant wind and monthly o r ten-day average pressure cha r t s .

t he equation 2, = f(r) holds t r u e f o r t he instantaneous s teady wind speeds

and the corresponding gradien t , i t should a l s o be v a l i d f o r t h e monthly o r

ten-day average r e s u l t a n t wind speed and t h e corresponding average pressure

gqadient. This conclusion emerges from the comparison of t h e two equations

derived by Kare l in and Nikolaeva ( see Table 1 ) f o r the Kara Sea.

However, i f i t i s assumed t h a t

Note t h a t t hese equations are somewhat inaccurate . The same d a t a f o r

t he Kara Sea polar s t a t i o n s give the following more exact equations:

For t h e instantaneous wind speed (Kare1in)--

(5) v = 364r - 1.02

For the ten-day r e s u l t a n t wind speed--

v = 37or - 0.34 (6)

The las t equat ion corresponds t o . t h e average of two regress ion l i n e s .

The r e s u l t s of t hese authors are thus very c lose t o one another , although

Karel in used the r e s u l t s of ind iv idua l observat ions and Nikolaeva used ten-

day averages.

the same region may be due only t o inaccura te pressure c h a r t s used by the

authors and inaccura te wind speed observat ions.

t o a reas with sketchy coverage.

Differences i n the r e s u l t s obtained f o r the same period and

This app l i e s p a r t i c u l a r l y

Because of t he inaccuracies i n pressure c h a r t s and wind speed observat ion

e r r o r s , t he c o r r e l a t i o n between the wind and the pressure gradient-diminishes .

I n processing the da t a of d r i f t i n g s t a t i o n s f o r t he period between 1937 and

1966, w e f ind t h a t the c o r r e l a t i o n c o e f f i c i e n t between v and I' f o r t he indi-

vidual months ranges from 0.60 (k0.07) t o 0.70 (k0.05) (Table 4). With

TABLE 4

DEPENDENCE OF v ON r ACCORDING TO DATA OF DRIFTING STATIONS FOR DIFFERENT PERIODS

- - u / r from Corre-

l a t i o n Coef f i-

Period cien_t_ , 1 2 3 4 5 6 7 -

Feb .-March 0.62 March-April 0.66 Ap r il-Ma y 0.61 May- June 0.60

July-Aug . 0.70 Sept.-Oct. 0.66 Oct.-NoV. 0.65 Dec. -Jan. 0.64

v=210r 47

v=270I'-O. 13 38 V=igor+o. 06 38

~=275r-0.12 45

~=300r-o. 37 46

~=250r-o. 04 46 ~=250r-o.17 48

~ = 2 3 8 r 45

210 1.80 198 1.53 250 1.60 255 1.60

247 1.77 238 1.63 245 1.75 233 1.83

- - v and T are, respec t ive ly , t h e monthly average r e s u l t a n t wind speed ( i n m / s e c ) and pressure grad ien t ( i n mb/km) .

these c o r r e l a t i o n c o e f f i c i e n t s , t h e form of t h e equat ion depends on the

p a r t i c u l a r assignment of t h e dependent and t h e independent. va r i ab le .

I f w e take v = f ( r ) , the c o r r e l a t i o n equat ions take the form shown

i n column 4 of Table 4. I f , however, w e assume t h a t t he monthly average

r e s u l t a n t wind is determined more accura te ly than t h e grad ien ts read of f

t h e monthly average pressure cha r t s , so t h a t t h e grad ien t should be

regarded as a func t ion of t h e r e s u l t a n t wind, t h e equat ions have a

d i f f e r e n t form (see column 3 , Table 4) .

I n equat ions der ived f o r t h e Kara Sea 141 and t h e Laptev Sea, as w e l l as f o r t h e East S iber ian and Chukchi seas [2] , t h e pressure grad ien t

w a s t r e a t e d as a func t ion of t he wind speed. I n o the r equat ions i n Table 1,

the wind speed w a s s e l ec t ed as the dependent va r i ab le .

The equat ions obtained f o r t he average of two regress ion l i n e s are

apparent ly more accurate .

is o f t e n used.

pressure grad ien ts over t he wind gradien ts , e s p e c i a l l y i n the case of

To save t i m e , however, one regress ion l i n e only

With one regress ion l i n e , i t is p re fe rab le t o average the

29

po-orly covered regions, where t h e pressure g rad ien t s read o f f t h e pressure

c h a r t s contain l a r g e e r r o r s .

The presence of a f r e e term (mostly negat ive) i n almost a l l t h e equations

ind ica t e s t h a t t he wind i s a nonl inear func t ion of t h e p re s su re grad ien t and

t h a t the r a t i o u/I' Tncreases with t h e inc rease i n the pressure grad ien t (or

t he wind speed).

Figure 1 is a p l o t of t h e empir ical dependence of u/I' on I'. The curves

of u/I' vs. I' were constructed as follows: f i r s t u/I' w a s obtained as a func t ion

of I' wi th t h e r a t i o u/I' averaged over t h e pressure grad ien t grada t ions and then

with t h i s r a t i o averaged over the wind gradat ions; a f t e r t h a t , average curves

f o r the two sets were drawn.

llA ---

100

1. u/I' vs. I' from the d a t a of ifting stations If1 i s

the summer curve obtained by grouping u / r according t o wind gradat ions. grouped according t o pressure grad ien t gradat ions. The a rab ic numerals i n d i c a t e the number of observa- t i o n s f o r averaging.

1937-1966) f o r summer (I) and winter (11).

I V is t h e same as 111, with u/I'

We see from e 1 t h a t t he r a t i o u / r increases with t h e inc rease i n

pressure grad ien t . This conc lmion agrees wi th t h e observat ion r e s u l t s f o r

t he Kara Sea, which is much b e t t e r covered than the Arctic bas in (Fig. 2 ) .

Since t h e geostrophic wind u is a func t ion of t h e pressure grad ien t , the $7

30

r 10 (km2 /mb* sec)

. - K n

4001 . . 0

F" A 0

100 4 3 2mp!- . 4

01 0 2

I

Fig. 2. Generalized curve of V i r vs. r. I--from i nd iv

ra ing

da ta Q€ d r i f t i n g stBtion8, winter.

i nc rease of v / v with t h e inc rease i n v which emerges Om observations does no t agree wi th t h e r e s u l t s of some t h e o r e t i c a l a tudies .

9 g According t o

t h e t h e o r e t i c a l r e s u l t s of [5,10,11] and the work of Radikevich (1968) , t he

r a t i o v / v d i r e c t l y from t he b a s i c t h e o r e t i c a l equat ion ( 7 ) , which has t h e form

diminishes with t h e increase i n v 9' The same conclusion follows 9

-- (7)

-?E L!L:.-. 1 1 --2e't'cosE+t? T'K

Here t h e no ta t ion is t h e same as i n equation (2). Calcula t ions based on

show t h a t as h (which depends on wind speed) inc reases , 6 and

9 t h e r a t i o vh/v decrease.

Using t h e following equation f r a n 1111 ( i t allws for t h e growth of k with a l t i t u d e ) , w e somewhat improve t h e results:

' h (8) I % * 1 1

- $- hw ='fx - . In- h 2 c 1;; . 1112- ZO k: zo

31

Since the r a t i o h / k , i n t h i s equation is f a i r l y constant (both

inc rease wi th increas ing rate of tu rbulen t exchange), we may take t o

approximation h / k , = a, where a is a constant c o e f f i c i e n t .

k, and h f i r s t

The r e s u l t s of ca l cu la t ions based on (8) show t h a t f o r l i n e a r growth of

h (h = a k , ) , t h e r a t i o v l v increases i n s i g n i f i c a n t l y , whereas f o r h = akt t he t h e o r e t i c a l dependence of v / V on v

dependence (Fig. 3).

between t h e ca l cu la t ed and the observed dependence of t he angle a on t h e wind

speed (see Table 3).

and equation (l),

h g q u a l i t a t i v e l y f i t s t h e empir ical

h g 9 I n t h e l a t te r case, however, t h e r e is a discrepancy

The empir ical dependence w a s computed us ing Figure 2

om which 21 w a s obtained making u s e of t h e known value g

of r.

The above t h e o r e t i c a l equ s c o r r e t o instantaneous wind speeds, but t he r e s u l t s

da t a which conta r e s s u r e grad ien t . The conclusions der ived from observat ions, us

and the r e s u l t a n t wind speeds with monthly o r ten-day average pressure gradi-

comparison w i t h empirical

tantaneous d a t a

. 2 , Table 2 , equat ions (5) and ( 6 ) l .

V g vs. v computed from equat ion (8) f o r g wz = 7010'~ l/sec, z o = 5*10F4 m.

1--for h = const = 50 m; 2--for h = ak, = 500k,; &-for h = ak: = 500k: ; &-from observat ions.

32

Changes i n t h e due t o f luc tua t ions i n 8tmo-

sphe r i c st show t h a t

f o r s t a b l e str

Romanov [7] proce

polar s t a t i o n s (n = 6000) and obtained a l i n e a r r e l a t i o n between t h e verti-

cal temperature grad ien t and t h e r a t i o v / v For nea r ly isothermal condi t ions, t h e r a t i o v / u i s 0.65-0.70 191. These

conclusions based on observat ion da ta are i n q u a l i t a t i v e agreement wi th the

r e s u l t s of t h e o r e t i c a l computations [5]. * from 0.32 f o r s t a b l e s t r a t i f i c a t i o n t o 0.40 f o r uns tab le s t r a t i f i c a t i o n .

( c o r r e l t i o n c o e f f i c i e n t r = 0 . 6 8 ) . 9

9

Thus, t he r a t i o v / v increases

Let us consider t h e dependence of t h e monthly average r e s u l t a n t wind

speed on the pressure grad ien t and the v a r i a t i o n of t h e angle a i n t he spring-

summer period (March-September) along the Chukchi coas t from Chetyrekhstolbovoi

I s land t o Cape Shmidt. This region is covered by t h e r e s u l t s of [ Z ] , where

ind iv idua l measurements on Chetyrekhstolbovoi I s land and Cape Vankarem were

processed t o y i e ld t w O s i g n i f i c a n t l y d i f f e r e n t equations f o r t h e wind speed

(see Table 1). The v a r i a t i o n of the angle u was not considered by t h e 1

author , d e s p i t e i ts considerable p r a c t i c a l importance.

To f i n d the dependence of t he wind speed on the pressure g rad ien t , w e

used t h e monthly average r e s u l t a n t wind da ta (according t o po la r s t a t i o n s

on Chetyrekhstolbovoi I s l and , Aion I s l and , Cape Valkarai , and Cape B i l l i ngs )

and t h e corresponding pressure grad ien ts frQm the monthly average cha r t s .

The observat ions were grouped f o r each month sepa ra t e ly and according t o

lm/ sec gradat ions of wind speed.

observat ions are l i s t e d i n Tables 5 and 6.

The r e s u l t s of t h e processing of c o a s t a l

We see from Table 5 t h a t the r a t i o v/U increases with increas ing g pressure grad ien t (or wind speed) i n any month. I n the major i ty of observa-

t i o n s f o r each month, t h e r a t i o of wind speed t o t h e pressure grad ien t

*In t h e diagrams included i n [ 5 ] , it i s shown t h a t v Calculat ions are performed f o r with an inc rease i n turbulen t f l u x P.

v = 10 m/see, z o = 1.8 cm. 9

March 1.0 5.2 192 20

5.9 339 1 $1 6.8 427 14

4.1 7.9 $20 7 4,s 9.2 S22 4 6.0 10.5 571 1 7.2 11.7 615 2

‘

0.3 0; 9 2.0 2.9 4.0

t 4;9 6-7

2.14

3.14

A p r i l 3.7 - 5.5 5.6 ti.!) 8 , .4 8.8

10.4

81 16.3 358 420 477’ 557 645

3 24 16 13 4 4 2

5.4 185 13 I

7-0 286 14 7.8 397 23 8-9 450 11 9.2 532 8

10.3 533 3 13.6 513 2 13.0 . 557 1

7.9 I 370 12 n=75

June

Sep temijer 0.3 3.5 86 1.0 4.4 2.50 1.9 5.3 35s

, 2.9 6.4 4.5.3 4.0 8.0 0 4.8 I ”8.5 J 6.2 9.5 2

1.85 5.3 :E k

4 14 27 : 16 n

7 32 20 9 4

3 > I

The l a s t row f o r each month is t h e monthly averagq.

i ncse from spr ing t o s u m m e r , reaching i t s max5mum i n June (v /X = 447) and

a g a i n b n September, v/J? - 250). This seasonal v a r i a t i o n of U / r

is c l e a r l y assoc ia ted mainly with t h e inc rease of wind speed, which i s observed

f o r most observat ions i n each month, and a l s o with the inc rease of atmospheric

i n s t a b i l i t y t rd t h e summer.

34

TABLE 6

0.18 0,41 0.61 0.76 0,86 0.94 1,OO

19 66 135 119 49 33 17

(based on t h e d a t a of Table 5.and equa- t i o n (1) from which vg w a s determined.

The r e s u l t s gave t h e following average r e l a t i o n of wind speed t o t h e

p re s su re g rad ien t :

For Narch-June v = 855 r - 3 . 2 4

For July-September v = 855 I' - 2 . 9 0

It is only f o r May t h a t t he equation has a somewhat d i f f e r e n t f r e e

I n de r iv ing t h e r e l a t i o n of v t o r , t h e pressure g rad ien t . as t h e dependent v a r i a b l e and t h e r e s u l t a n t wind speed as

independent v a r i a b l e ( t h e lat ter being t h e more accu ra t e of t h e two).

From (1) f o r t h e r e l evan t reg ion ( 0 - 70'N) w e have

1 9 P

v = 0 . 7 2 2 - r \

(10)

This r e l a t i o n was used t o compute t h e r a t i o v /r f o r each month as a 9 func t ion of the many-year average air temperature (average for t he fou r

s t a t i o n s ) and t h e many-year average pressure f o r t hese month8 (Table 7 ) . The va lue of p f a r each month w a s computed from the equation

where P is t h e monthly average and Po = 1000 mb.

Month

March

Apr i l

May June

Ju ly August

We see from Table 7 t h a t the r a t i o u / u increases from sp r ing t o summer, 9 reaching i t s maximum i n May and June, when t h e r e s u l t a n t wind speed is a l s o

maximal.

Sea i n 1922-1924 [12], i n d i c a t e t h a t t he annual maximum f o r the wind speed

r a t i o a t a l t i t u d e s of 8 and 80 m is a t t a i n e d in Apr i l and May r a t h e r than i n

May and June, whereas the minimum f a l l s in J u l y and August. A Secondary maxi-

mum i s noted i n September and October. A similar annual v a r i a t i o n i s observed

f o r t h e temperature l apse rate y. However, as t h e author i s t h e f i r s t t o

admit, t hese indi.ces are not p a r t i c u l a r l y accura te f o r t h e summer months,

s ince the t o t a l number of observat ions i s f a i r l y small; moreover, t h e observa-

t i ons were c a r r i e d out i n t h e c e n t r a l p a r t of t h e sea. It the re fo re seems

t h a t t h e maximum value of u / u

t h e minimum f a l l i n g i n February and March.

be observed i n autumn, with a corresponding secondary m i n i m u m i n summer.

no te t h a t t he r a t i o U/U

basin.

Observations on board R/V Maud, whlch d r i f t e d i n the East S ibe r i an

i n t h i s area is a t t a i n e d i n May and June, with 9 A secondary maximum should apparent ly

Also

f o r t h e E a s t S iber ian Sea i s higher than f o r t h e Arctic 9 Thus, i n summer (May-September), t h i s r a t i o is 0.66 and 0.54, respec t ive ly .

- t P(mb) p * 1 0 ~ ( ~ / ~ ~ ~ ~ ) vg/r u/r m u/ug -

-26.0' 1021 1.44 500 265 39 0.53

-17.7 1017 1.39 518 241 40 0.46

- 6.3 1017 1.32 542 397 23 0.73

2.0 1012 1.28 565 447 20 0.82

3.4 1010 1.27 570 350 24 0.61

3.0 1010 1.27 570 344 27 0.60

TABLE 7

THE RATIO Vg/r COMPUTED FROM EQUATION ( io ) AND THE RATIO u i r OBTAINED FROM OBSERV~TION RESULTS IN THE SOUTHEASTERN PART OF THE EAST SIBERIAN SEA

1.5

1.5 3 . 1

3.0 2.0 2.1

1.0

36 ,

Let us cons ider t h e dependence of t h e wind d i r e c t i o n on t h e d i r e c t i o n

of t h e i s o b a r s over a number of years.

I n processing t h e observation r e s u l t s , a l l d i r e c t i o n da ta for t h e

monthly average r e s u l t a n t wind Dv and f o r t he i soba r s D, were grouped

according t o wind grada t ions i n 40' i n t e r v a l s (0-40- , 40-80°, 80-120°, etc. , up t o 320-360'). computed the average va lues of Dv and D, f o r each month sepa ra t e ly .

r e s u l t s are l i s t e d i n Table 8 .

Then, using a l l the observations i n each i n t e r v a l , w e

The

> TABLE 8

THE WIND DIRECTION Dv AS A FUNCTION OF THE DIRECTION OF THE I S 0 Du I N THE SOUTHEASTERN PART OF THE EAST SIBERIAN SEA

300 3.38

56 101 143 210 257 306

2% 333

251@ -37' 297 - 35 310 -6 + 18 320

z == --2' -

4-4 +5

=-16

J u l y 70 -48 85 -38

132 +9 230 -50 253 -37 2!J1 -32

4- 3 295 - a =--3

11 3

r n z 6 4

August 79 -23

1 OG -6 "of ! -59 247 -37 286 -29 312 -6 -

a -28

September

lumber If cases

4 4a a

Zn=& 1

3 5 3 1

14 31 4

X n = G l

2 6 3

14 33

& - 6 2 4

G8 I 11i 1 0 2 117

21 1 1-13 SO 1 1 : " *PLk

June 22 - 38 1

127 i 3 1 1

37

We see from Table 8 t h a t t h e angle a between t h e wind and t h e i soba r s

v a r i e s between wide l i m i t s (from +35' t o -60") depending on the time of year

and the d i r e c t i o n of t h e i sobars . The smallest angles of wind devia t ion t o

t h e l e f t of the i soba r s are observed with the i sobars s t r e t c h i n g t o t h e north-

w e s t (300-335' ) .

c o a s t a l l i n e . The average of 62 observat ions gave a = -3'.

devia t ion angles i n March-August were observed with the Isobars s t r e t c h i n g

t o the w e s t , southwest, and south (200-270'). The average of 4 1 observat ions

is a = -43'.

This is apparent ly associated with the d i r e c t i o n of t h e

The l a r g e s t

A s i g n i f i c a n t f a c t o r i s the considerable s t a b i l i t y of the wind d i r e c t i o n

during t h e e n t i r e re levant period. WSW winds prevai led (260'). The negat ive

values of i soba r s increased from March t o June (from 15' t o 35' i n absolu te

value) and then decreased ( t o 26') i n September. Note t h a t t he wind ve loc i ty

varies i n the same sequence ( see Table 7 ) . The seasonal v a r i a t i o n of a i n

t h e East S iber ian Sea d i f f e r s from the earlier r e s u l t s f o r t h e Kara Sea and

the Arctic bas in (see Table 2) . One of t h e reasons f o r t h e unusual seasonal

v a r i a t i o n of a, i n our opinion, is t h e increase of wind speed from winter t o

summer i n t h i s region (see Table 7 ) .

i n s t a b i l i t y i n the su r face l a y e r on the v a r i a t i o n of a, no d e f i n i t e conclusions

can be reached i n t h i s case. I n summer, both i n t h e Central Arctic and i n

t h e per iphera l seas [8 ] , t h e atmospheric s t a b i l i t y decreases , whereas i n

winter i t increases . Y e t the annual v a r i a t i o n of a f o r t he Kara Sea and

I f w e consider t h e e f f e c t of atmospheric

the Arctic bas in follows an opposi te t rend t o i t s v a r i a t i o n i n the East

S iber ian Sea. This i nd ica t e s t h a t the annual v a r i a t i o n i n the Arctic is

apparent ly more s e n s i t i v e t o the wind speed than t o changes i n atmospheric

s t a b i l i t y . This conclusion does not cont rad ic t r e l a t i o n (2) .

Our study l eads t o a number of important conclusions.

1. The r a t i o of t he wind speed t o the pressure grad ien t shows a d i s t i n c t

annual va r i a t ion . I n t h e E a s t S iber ian Sea and i n the Arc t ic basin, t h e

maximum i s observed i n summer and the minimum i n winter .

2. The r a t i o v /vg increases with increas ing wind speed.

38

3. Among t h e d i f f e r e n t regions considered, t h e East S iber ian Sea is

charac te r ized by t h e h ighes t values of v/Vg, followed by the Kara Sea and

the Arctic basin i n t h a t o rder .

4 , The angle ct shows an annual variation: i n the Arctic bas in and

and i n t h e Kara Sea, t h e maximum values of ct are observed i n winter and t h e

minimum i n summer; i n t h e E a s t S ibe r i sn Sea, conversely, the annual curve

has a maximum ( i n absolu te value) i n summer and a minimum i n winter .

5. The absolu te va lue of cx i nc reases with the inc rease i n wind

speed.

BIBLIOGRAPHY

1. Kare l in , D. B. Re la t ion of wind t o pressure grad ien t i n t h e a r c t i c seas. ProbZemy Arkt iki , No. 2 , 1941.

2 . Kuznetsov, I. M. Computation of wind speed from pressure grad ien t f o r t he po la r s t q t i o n s on Chetyrekhstolbovoi I s land and Cape Vankarem. I n ProbZemy A r k t i k i , No. 4 . Leningrad: Morskoi Transport , 1958.

3. Tverskoi, P. N., e d i t o r . A Cowse i n MeteoroZogy: Physics of the Atmosphere. Leningrad: Gidrometeoizdat, 1951.

4. Labzovskii, N. A. The dev ia t ion of the wind i n the su r face l a y e r from t h e d i r e c t i o n of t he grad ien t . ProbZery Arktiki , No. 2 , 1944.

5. Laikhtman, D. L. Physics of the Boundary Layer of the Atmosphere. Leningrad: Gidrometeoizdat, 1961.

6. Nikolae.va, A. Y a . Using the r e s u l t a n t wind for t h e cons t ruc t ion of pressure c h a r t s . I n ProbZermj A r k t i k i i Antarktiki, No. 12. Leningrad: Morskoi Transport , 1963.

7 . Romanov, Yu. A. Re la t ion of su r face wind t o geostrophic wind. Proc. In t . Oceanogr. Congress, 31 Aug. -12 Sept. 1959. Washington, 1959.

8. Smetanriikova, A. V. Heat exchange between the ocean and the atmosphere i n t h e Arctic i n win ter . Ins t i tu tu , Vol. 229. Leningrad, 1961.

Trudy Arkticheskogo i Antarkticheskogo

9. Sorkina, A. I . Construction of wind f i e l d c h a r t s f o r seas and oceans. Trudy Gosudurstvennogo Okeanograficheskogo Inskituta I No. 4 4 , 1958.

39

10. Yudin, M. I. and M. E , Shvets S ta t ionary model of ver t ical wind d i s t r i b u - t i o n i n a turbulen t atmosphe No. 8 (31), Leningrad, 1940,

GZmnoi Geofizicheskoi Observatorii ,

11. Fundamentals of Dynumical MeteoroZogy. Leningrad: Gidrometeoizdat, 1955.

12. Sverdrup, H. The wind-drift of t h e i c e of the North S iber ian Sbel f . The Norwegian North Polar Expedition with t h e Maud, 1918-1925. Sei . Res . , Vol. 4, No. 1, Bergen, 1928.

40

EXPERIMENTAL DETE ION OF THE WIND DRAG ON AN &ET

I. D. KapeZin and L. A . T<mokhov

The f i r s t measurements of the shear ing wind stresses i n na ture were

c a r r i e d out by Y . Suzuki i n 1963 [4]. e performed two series of observations

of 10 and 12 minutes, respec t ive ly .

dynamometers, readings being taken v i s u a l l y a t 5-second i n t e r v a l s .

forces were measured with spr ing

The authors c a r r i e d out similar measurements on Lake Ladoga between

Continuous recording was ensured and a wider 29 March and 10 Apr i l 1969.

range of grad ien t observat ions w a s covered,

p r o p e r t i e s of t h e measuring system were a l s o conducted.

T e s t s of the na tu ra l o s c i l l a t o r y

A c i r c u l a n diameter w a s sawn from the f a s t i c e i n the lake

The sawn-out f l o e was separated from the f a s t ice by a 400 m from the shore.

c i r c u l a r channel 35 c m wide, A s h a f t with a b a l l b

a t the cen te r of t h e f l o e (Fig. 1 ) . Steel cables 1.2 m i n diameter and

7.0 m long were s t r e t ched from th ree loops soldered t o the ou te r sur face of

t he b a l l bear ing with 120' spacing.

a bracket f rozen i n t o the f a s t ice. One cab le ppinted nor th , and the o ther

two cables w e r e spaced a t 120* and 240°, respectively.

ing on top was mounted

The o the r end of each cab le w a s t i e d t o

The wind fo rce w a s measured with s t r a i n gauges held by turnbuckles

between the end of t he cable and the f i x i n g bracket .

a s tee l r i n g with a 200 ohm r e s i s t o r element bonded on the in s ide .

l i n e a r deformation of the r ing , which w a s proport ional ' t o t he stress i n the

cable , was converted by t h e s t r a i n gauges i n t o e l e c t r i c s i g n a l s , and these

were then t raced on tape by an N-105 loop osc i l lograph . Before each series

of observat ions, a l l t h ree gauges were ca l ib ra t ed with the a id of standard

weights suspended on a s p e c i a l c a l i b r a t i n g s tand. The c a l i b r a t i o n r e s u l t s w e r e a l s o t raced on the osc i l lograph tape.

The s t r a i n gauge is

The

4 1

Fig. 1. Schematic diagram of the measuring system.

p of t h e s h a f t ; 2-steel $--strain gauge r ing ;

5--brackets frozen i n t o f a s t ice.

Before t h e beginning of the measurements, t h e i c e f l o e w a s propped up with

wooden wedges, so t h a t t he c i r c u l a r channel was of uniform width a l l around.

Each cable w a s tensioned with the turnbuckle t o 2-5 kg, and the wedges were

then removed.

were recorded from t.he measurements of t he th ree s t r a i n gauges.

e s t ab l i shed absence of sea cu r ren t s under the f loe .

The osc i l lograph tape d r i v e w a s switched on and the cable stresses

Sea vanes

Every 10 minutes, reading were taken of the wind speed, a i r temperature,

and air humidity using cup anemometers and Assman psychrometers a t he ights of

0.5, 1.0, and 2.0 m; wind d i r e c t i o n at 2 m he ight w a s a l s o measured. An M-12

anemograph mounted a t a he ight of 6 . 5 m recorded wind d i r e c t i o n and t h e wind

ve loc i ty averaged over 10 min i n t e r v a l s .

instruments w a s mounted north of t he f l

gauge w a s mounted a t a he ight of 1 m, recording the wind speed on osc i l lograph

A meteorological mast with grad ien t

, 4 m from i ts edge. A wind speed

42

chnica l reasons, however, the wind speed d e r was not C a l i -

bratecl.

ve loc i ty spectrum, but not t h e magnitude of wind speed.

The readings t h e r e f o t e could be used t o cha rac t e r i ze the wind

The recording equipment w a s housed i n a heated shed 80 m from t h e f l o e .

The f i e l d instruments were connected t o the recording instruments by mult i -

conductor cables about 100 m long.

ment

with

w e r e

from

Continuous recordings of the wind fo rce were obtained f o r 21 measure-

series.

an o v e r a l l du ra t ion of 8.5 hours.

r e j e c t e d for a v a r i e t y of reasons: considerable snow d r i f t and t h e top water l a y e r f roze ; i n the remaining

The r e s u l t s of 10 series were used f o r f u r t h e r computations,

The r e s u l t s of t he remaining series

i n t h r e e cases, the channel suf fe red

cases , near-resonance c i t i o n s were observed. The r e s u l t i n g o s c i l l a c i o n s

of the cable stresses were so l a r g e t h a t t he taped recording was d i f f i c u l t

t o process , and i n a number of cases t h e curve a c t u a l l y jumped of f the

osc i tape.

The measuting system cons i s t ing 9f t h e ice f l o e , t he cable l i n e s , and

the s t r a i n gauge r ings has c e r t a i n n a t u r a l o s c i l l a t i o n frequencies because

of the e l a s t i c i t y of t h e cables and r ings .

system exc i ted and sus ta ined by the wind pay d i s t o r t t he r e s u l t s of the

ex te rna l d i s turbame t o a certain ex ten t . It should be es tab l i shed t o whar-

ex ten t t h i s d i s t o n interferes with the determinat ion of t he wind force

ac t ing on the ice f l o e .

The natural o s c i l l a t i o n s of t he

The wind-generated motion of the constrained ice f l o e , wTth allowance

fo r the cable r e s i s t a n c e and water drag, is descr ibed by the vec tor e q v a t j o n

-z 3- j .

where TI, T,, T, are the tens ion fo rces i n cables 1, 2 , 3 , respec t ive ly ;

Fr is t h e resistance and drag fo rces ; and Fa i s the wind f o r c e on the f l o e . -h -+

+ The res is tance fo rce F, i s the sum of water drag and the reSis tance

r e s u l t i n g from the elastic p rope r t i e s o f the cab le and s t r a i n gauge r ing .

Assuming t h a t both components of the r e s i s t a n c e fo rce are propor t iona l t o

43

t h e rate of displacement of t h e f l o e , with a p ropor t iona l i t y c o e f f i c i e n t v, f o r

water and v, f o r t he cables and t h e s t r a i n gauge r i n g s ( i d e n t i c a l e l a s t i c

p r o p e r t i e s are assumed f o r t h e cables and the r i n g s ) , we w r i t e

The cable tens ion recorded on the osc i l lograph t a p e i n weight u n i t s is

propor t iona l t o the l i n e a r deformation of ' the r i n g and hence t o t h e displace-

ment vec tor of the cen te r of g r a v i t y of the f loe . Therefore,

-c -+ -* -* .. I I + 7; + I;= P , ~ z , , -1- P2ge2 + ~Sgq,= ~g- l i - - cr *

+ + + + where e , , e,, e 3 are the u n i t vec tors f o r t he forces; y ' is t h e u n i t vec tor

f o r t h e r e s u l t a n t force; c is the e l a s t i c i t y c o e f f i c i e n t of t h e cables and

s t r a i n gauge r ings ; and g is t h e g r a v i t a t i o n a l acce le ra t ion . I I

The equation of motion of t he ice f l o e , taking the x and Y components

of t h e above fo rces , thus takes t h e form

I l P y , riy '"id12 -1- Y 7 4- cy -= (IT,,

I n (2) t h e wind fo rce components e n t e r via the p ro jec t ions of t h e wind

shear ing stress :

F0.r = 9 T . c

F , , =

where oi is t h e f l o e area.

Suppose t h a t t he components of t he f r i c t i o n a l stresses can be represented

f o r t h e t i m e 0 4 t 4 T as the expansions

I I = -- m

- where = (2n/T)n, -rX = const , and 7 = const.. Y

44

f o r equations ( 2 ) , we obtagn the so lu t ion i n the form

c-r -2 - - P,g cos r, -- P2g cos & -- P,.g cos c3 I'

where t 9 c - <.I-

sin ,*I,$ -i- ' , , cos taJ - (c * - w y $- ",, '6 , ,

W e see from (3) ) t h a t t he insfantaneous values of t h e cable

9' up of the mean shear ing stresses yz and 7 tensions P,, P,, P, are

o s c i l l a t i o n s of frequency % generated by the wind fo rce f l u c t u a t

na tu ra l o s c i l l a t i o n s of frequency 1.1 which are damped exponent ia l ly with time as exp ( - u k t / 2 ) .

The parameters v* and p w e r e determined experimentally by the au thors ,

I n calm windless weather, an impulsive f o r c e of 1.5 kg w a s applied t o the

i c e f l o e and the loads P,, P,, P, w e r e recorded on the osc i l lograph tape.

The period of n a t u r a l o s c i l l a t i o n s Tr increased by 10-15 pe r cent of i t s

i n i t i a l va lue during t h e damping s t a g e (Table 1).

computed from the decrease of t he amplitude, and t h e e l a s t i c i t y c o e f f i c i e n t c was obtained from t h e formula

The c o e f f i c i e n t V" w a s

Ca4xln2j 3 \ T'?r -t- 4

The f l o e mass a t t h e t i m e of t h e experiment was m i = 57*103 kg.

TABLE 1

NUMERICAL VALUES OF THE PARAMETERS OF NATURAL OSCILLATIONS OF THE MEASURING SYSTEM

T ( sec) ( l /sec) p (1/ sec) v (kg/ sec) c (kg / sec 2, --

Cable-ring 2.7 15.8 1 . 6 0 1 0 - ~ 0.34 19*102 8*103 2.9 14.7 1 . 4 0 1 0 - ~ 0.40 16*102 10.6*103 4.4 13.3 1 . 7 0 1 0 - ~ 0.42 2 2 0 1 0 ~ 3;1.8*103 5 .1 12.0 1 . 6 0 1 0 - ~ 0.46 18*102 13.2-103 5 .1 12.4 1.5*10-2 0.45 1 8 0 1 0 ~ 12.7*103

5.1 69 0.29*10-2 0.091 3. 3*102 0 .473010~ Cable-spring-ring

The e l a s t i c i t y c o e f f i c i e n t of t h e cables and the r ings w a s found t o depend

on t h e mean cable tension:

D = (P,+P2+P3)/3 (Fig. 2).

e, a spr ing of known e las t ic p rope r t i e s w a s i n se r t ed i n the cable-ring

c i r c u i t .

t h e curve i n Figure 2 t o 1.5 kg load gives e -N 6 . 8 0 1 0 ~ kg/sec2 f o r t h e elas-

t i c i t y c o e f f i c i e n t of t h e cable and t h e r ing .

p rope r t i e s of the spr ing , we ob ta in for t h e cable-spring-ring c i r c u i t

c = 0.495*103 kg/sec2.

the n a t u r a l o s c i l l a t i o n s was found t o be 0.473*103 kg/sec2, i.e., a relative

i t increased with increas ing cable tens ion

To check t h e v a l i d i t y of t h e r e s u l t s obtained f o r

A load of 3 kg produced an extension of 55 mm. I n t e rpo la t ion of

Making allowance f o r t h e elastic

The same coe f f i c i en t computed from the frequency of

e r r o r of 4 pe r cent i n computations.

46

1 3 -

1 2 .

Fig. 2. E l a s t i c i t y coef 11 .

cient of t he cable an 1 0 -

s t r a i n gauge r i n g c vs. 9 -

- - - 8 -

7,

t h e average cable tension D = (P1+P21-F , ) /3 .

ze r e l a t i o n s (3) and (4). When the period of the na tura l

of t h e ice f l o e is equal t o the period of t he wind stress

f l u c t u a t i o n s .(e* = ui) , the amplitude of the cable tens ion o s c i

markedly increases and a near-resonance e f f e c t i s observed.

If the s p e c t r a l pos i t i on of the wind f r i c t i o n stresses is s w h

t h a t the frequency of t he wind fo rce pulsa t ions is s u b s t a n t i a l l y higher

than the frequency of the n a t u r a l o s c i l l a t i o n s (c* < &$), the instantaneous

fQrce w i l l f l u c t u a t e i n counterphase t o the wind' shear ing stress f l u c t u a t i o n

Indeed, the f a c t o r before s i n w f i t i n (3) and (4) can be ignored, U* being

small , and the f a c t o r before cos unt w i l l be negat ive, s ince Q* < 0:.

i n d i c a t e s t h a t t o the n-th shear ing stress harmonic of p o s i t i v e amplitude

corresponds the same n-th harmonic i n the instantaneous recorded force ,

but of negat ive amplitude.

T h i s

Let us consider t he t i m e averaging of equations (3) and (4). Seeing

that v* i s an order of magnitude less than 11, averaging between 0 and T gives

/

P' O J

/ /

/ o # /

h , , ,. i z g P ( W

T J*

1 -- A*-e sin pT where TP

C*1(E* - 0;) + 'm sin.wJ' +

+ e sin p T . Y*

c* (c* - u2,) -T r ,

I n der iv ing (5 ) and (6), we ignored t h e changes i n t h e anglea E l , E 2 , c3 , as they are s m a l l ,

L e t u s estimate t h e parameters A and 6 f o r an averaging per iod of

T = 5 min (300 sec) , borrowing the parameters v * ~ The cor rec t ion A 4 7*10'5 is very small, so t h a t f o r l a r g e averaging p,eriods

i t i s of no kmportance.

pu lsa t ions .

and p from Table 1.

6 ( n ) depends on the spectrum of wind fo rce

For t h e harmonics u i =

and f o r ut < c*, 6 ( n ) < 1.6*10m2.

we f i n d 6(n) 4 lo-', f o r (A$ > e*, 6 ( n ) c: l o m 2 ,

I f e of t h e harmonics of t h e shear ing wind stress with

l a r l y l a r g e compared t o t h e amplitude of the mean f r i c -

T (n? /%O. 2) the' cor rec t ions 6 (n) should be taken a$

zero,, We then f ind f o r t h e shear ing stress

- v;: + ;; = g v+ (F2 - F3)2 + [F, - + (F-+ p8,I2 0 ; (7)

and the angle between t h e mean shear ing wind stress and the

Equa l i t i e s (7) and (8) i n d i c a t e t h a t t h e mean value of t h e shear ing

wind stress can be computed from the cab le tension recordings i f t h e instan-

taneous tension values are replaced by averages over a c e r t a i n length of t i m e ,

48

Continuous cab le tens ion recordings on osc i l l og raph tapes yere weraged

and the averaged f i w r e s were i n s e r t e d i n (7) and (8) t o determine the

a c t u a l values of t h e shear ing stresses r, applied t o the ice f l o e s and the

corresponding angles aT. between the d i r e c t i o n of t h e wind v e l o c i t y vec to r a t 2 m and 6.5 m heighfs

(a,) and the angJe a t which the shear ing stress a c t 6 oq t h e ice f l o e 9, for var ious averaging tiwes.

The d i r e c t i o n of t h e shear ing wind stress c l e a r l y does not co inc ide

Table 2 lists t h e va lyes of Ta and t h e d i f f e rence

with t h e d i r e c t i o n of t h e wind v e l o c i t y vec tor e igher a t 2 m o r 6 . 5 m

height. The wind f o r c e applied t o the f l o e can be uted from t h e

r e l a t i o n

where p is the air dens i ty , Ch

wind speed,

From kpown va lues of t he

is the f r i c t i o n c o e f f i c i e n t , and uh i s t h e

f r i c t i o n a l stresses and wind speeds a t

he ight h , w e computed the f r i c t i o n c o e f f i c i e n t q ch using the re la t ion I_- -

=.' - 2 . - Ta (10) P

and t h e r e s u l t s are l i s t e d i n Table 2.

c o e f f i c i e n t co inc ides with t h e va lues of ch computed by Y. Suzuki

To o rde r s of magnitude, t h e f r i c t i o n

(ch*102 = 1.18, 1.01) [ 4 ) and obtained from wind-tunnel tests of i c e f l o e

models (Ch'lo' = 0.45) [I].

It v a r i e s from one series of observqtions t o t h e nex t , and s i g n i f i c q p t l y

depends on t h e p a r t i c u l a r he igh t h a t which the wind speed was measured.

Yet the f r i c t i o n c o e f f i c i e n t i s no t cons tan t .

For low Richardson numbers, t he d i s t r i b u t i o n of t h e wind speed u in t h e ground l a y e r is c l o s e t o logarit tunic [ 2 ] :

where x" is a qumerical c o e f f i c i e n t and z g is a roughness parameter.

49

cn 0

TABLE 2

ACTUAL VALUES OF THE SHEARING WIND STRESS AND THE MEAN WIND SPEEDS u AT VARIOUS HEIGHTS (Time is Moscow local time.)

L e t U h be t h e wind speed

(11) y i e l d s a r e l a t i o n f o r t he

a t he ight z=h. shear ing wind stress ac t ing on the ice f l o e

Then a f t e r some manipulations,

and a r e l a t i o n f o r t h e time-average f r i c t i o n a l stresses

we reduce (12) t o (9). This tmpl ies t h a t t he f r i c t i o n c o e f f i c i e n t should

f l o e and the numerical co

we can now compute z o .

The most s t a b l e r e s u l t s were obtained us ing t h e wind observat ions from he igh t s of 0.5 m and 1.0 m (see Table 2) . The rough parameter var ied

o 3.3 cm. A f a i r l y c l o s e dependence of the roughness Parameter

(Fig. 3) : t h e rou ess c o e f f i c i e n t decreases

approaching asymp t

The r e s u l t s obtained f o r z g from wind speed me@

of 0.5 and 2.0 m and he igh t s of 1.0 and 2.0 m showed

from 0 t o 6.7 c m and from 0 t o 12.2 cw, respec t ive ly .

n i f i c a n t scatter:

The numerical c o e f f i c i e n t x" from (11) can be computed from wind observat ion d a t a and the a c t u a l stressee using t h e r e l a t i o n

51

2 Pig. 3, The roughness

parameter zo vs. wind speed uh a t h=1 m.

0 , I I I 1 uh(mlsec) 2 3 4 5 6

Table 2 lists t h e values of xo which were computed from wind speed

observat ions a t he igh t s of 0.5 and 1 .0 m.

The c o e f f i c i e n t xo f o r a logari thmic wind speed p r o f i l e i s p rec i se ly

equal t o t h e von Karman constant xo = x = 0.4. than n e u t r a l , w e have i n the l inear- logari thmic approximation [2 ]

For a i r s t r a t i f i c a t i o n o ther

I

where (3 is a un ive r sa l constant and L is t he v e r t i c a l scale dependent on

the s t r a t i f i c a t i o n of t he medium ( f o r n e u t r a l s t r a t i f i c a t i o n , Z F ~ ) 121.

Comparing t h e last r e l a t i o n with ( l l ) , w e see t h a t the v a r i a t i o n of

t h e numerical c o e f f i c i e n t

i s assoc ia ted wi th changes in air s t r a t i f i c a t i o n .

Let us estimate the e r r o r i e shear ing wind stresses as ca lcu la ted

from (9) . The i n i t i a l values of z o and xlf are thos Table 2. The

f r i c t i o n c o e f f i c i e n t s for h=1 m are obtained from (13).

Calculat ions made f o r wind speeds a t 1 m height show t h a t the shear ing

wind stress ~~~l~ may d i f f e r from t h e t r u e va lue by as much as 25 per cent .

When T is computed from the wind speeds a t he ights of 2.0 and 6.5 m, the

percentage e r r o r is higher , A more promising approach i s thus t o determine

52

the shearing wind stress as a fuwtion of the gewfrophic wind,

f i sat ion, an4 the rougFness coeffic$eqt by solving a sianyftaneow s y s t w

of dynamics equqtions [3 J

BIBLIOGRAPHY

1. Gudkovich, 2, M . , G . I. Melkopyan, and I$. G . Nikiforov. Wind-tunqel f l o e models. Tmdy Arktichesko i Anfarktichsskogo 1. 253, Leningrad, 1963.

2. Matveev, L. T. PrindpZes of Geneml MetqoroZogy. Physicg of the Atmosphere. Leningrad: Gidrometeoizdat, 1965.

tman, a. L. Nonlinear theory of w$nd d r i f t . Iapes$2ya AN SSSR, z3ka atmosfery $ okeancz, Vol. ZV, No. $1, 1968.

4. Susuki, Y. On the measurement of $he wind drag on an ice sheet. Lad TempezwWre Science, Ser. A, 22, 1964.

STATISTICAL CHARACTERISTICS OF SOME ICE COVER PARAMETERS IN THE ARCTIC

A . Ya. Buzueu and V. F. DLlbovtseO

One of t h e main parameters r e f l e c t i n g t h e s ta te of t h e ice cover

ickness .

h, and fhey can be roughly divided i n t o two groups:

Numerous s t u d i e s have d e a l t with t h e processes of

1. Studies i n which ice growth processes are analyzed as a funct ion

of a i r tempersture , snow cover he igh t , and o the r f a c t o r s proceeding from a c t u a l measurements o r computations a t po in t [7]. Although several

poin t readings are genera l ly a v a i l a b l e f o r t h e a

area, the space c h a r a c t e r i s t i c s of ice th ickness d i s t r i b u t i o n cannot be

recovered by t h i s method.

2.

analyzed.

c a r r i e d out a long s p e c i a l p r o f i l e s o r Over a test area, wi th a f ixed

spacing between success ive measurement po in t s . Because of t h e f ixed

spacing, modern s ta t i s t ica l methods can be appl ied t o process t h e obser-

va t ion d a t a ( ca l cu la t ing the c o r r e l a t i o n and s t r u c t u r a l funct ions,

s p e c t r a l dens i ty , etc.).

S tudies i n which the s p a t i a l d i s t r i b u t i o n of ice t h i c

These s t u d i e s are based on s p e c i a l ice th ickness measurements

Knowledge of t he s p a t i a l d i s t r i b u t i o n of i c e ickness is necessary

f o r computing both t h e r e s i s t a n c e of t h e ice cover t o t h e motion of sh ips

and i t s car ry ing capac i ty .

th ickness are h ighly inadequate.

o r d r i l l i n g h a l e s i s a tedious process , SO chat la rge-sca le observat ions

Over ex tens ive areas are unfeas ib le .

determining ice thickness is a l s o fa r from pe r fec t a t t h i s s tage . ch i s reason, observat ions of ice th ickness i n t h e c o i s t a l seas and i n

Unfortunately, t he methods of measuring ice

Measuring the i ce thickness by boring

The electromagnet ic method of

For

t o measurements along ind iv idua l p r o f i l e s .

55

Most of the available ice thickness data correspond to fast ice, since since the many hydrographic expeditions working on fast ice in springtime often perform incidental ice thickness measurements. Generalization of these data indicates that nonuniform distribution of ice thickness prevails

in all the regions of the arctic seas.

ness cannot be used to solve various applied problems; it is therefore essential to have detailed pictures of the distribution of ice thickness in space.

As a result, the average ice thick-

In our study, we generalized the results of special observations of drift-ice thickness, snow-cover height, top-surface level (from the data of drifting stations), and fast-ice thickness (from incidential measurements

of hydrographic expeditions in winter). problems :

We tried to solve the following

1. Elucidate the main features of the d ribution of ice thickness and snow cover height in space.

2. Investigate the relationship between the individual measurements, depending on the time interval between them. The structural and the corre- lation functions for the thickness of old and one-year ice were determined in previous studies based on the restricted material of special ice surveys

[1,2]. data of special observations.

In this paper the statistical analysis was based on more extensive

3. Analyze the relationship between ice-thickness distribution and

top-surface level, ice thickness, and snow-cover height.

4 . Estimate individual parameters characterizing the state of the ice cover (hummocking, deterioration, etc.) and their contribution to the equiva- lent ice thickness.

The problems did not include the relationship between ice thickness at the polar stations and in the navigable parts of the arctic seas, as it has been considered elsewhere.

The observation results were subjected to statistical processing on the URAL-2 computer, using programs of L. P. Borisova and Yu. V. Nikolaev.

56

Statistical imates o f the Distribution o f the Main State Parameters o f the Ice Cover

Arctic ice i s h ighly nonuniform with regard t o the d i s t r i b u t i o n of

such main parameters as th ickness , hummocking, and snow height . This

nonuniformity i s due t o t h e combined e f f e c t of a v a r i e t y of hydrmeteoro-

logical and hydrographic f a c t o r s . Since i t is impossible t o sepa ra t e

t h e r e spec t ive con t r ibu t ions of t hese f a c t o r s t o i c e cover formation, we

can only observe the r e s u l t a n t e f f e c t of a l l t h e f a c t o r s a t any given

t i m e . S t a t i s t i c a l methods the re fo re have t o be appl ied t o i n v e s t i g a t e

the genera l f e a t u r e s r e f l e c t i n g t h e s ta te of the ice cover. The s ta te parameters of t he ice cover are t r e a t e d as random va r i ab le s .

1

The d i s t r i b u t i o n func t ion of a random va r i ab le F ( z ) represents the

cumulative frequency of t he va r i ab le . For p r a c t i c a l purposes, w e o f t e n

use t h e d e r i v a t i v e of t h e d i s t r i b u t i o n func t ion @(z) = dF(z) /d tc , which

corresponds t o t h e p robab i l i t y dens i ty .

Thickness measurements of f a s t ice i n d i c a t e t h a t t h e th ickness is

not d i s t r i b u t e d normally. We the re fo re used t h e Char l ie r d i s t r i b u t i o n

i n our a n a l y s i s , as i t i s appl icable t o any q u i t e a r b i t r a r y d i s t r i b u t i o n

[a] . second, t h i r d , and fou r th moments ( t h e a r i t hme t i c mean, t he var iance, t he skewness, and t h e k u r t w i s ) . The Char l i e r i n t e g r a l d i s t r i b u t i o n funct ion

i s expressed by t h e r e l a t i o n

To compute t h e Char l ie r d i s t r i b u t i o n func t ions , we r equ i r e t h e f i r s t ,

where F o ( - t ) is the i n t e g r a l normal d i s t r i b u t i o n func t ion , @,(t) is the

second d e r i v a t i v e of t h e normal d i s t r i b u t i o n funct ion, $,(t) is t h e t h i r d

d e r i v a t i v e of t h e normal d i s t r i b u t i o n func t ion , Sk i s the skewness, Ex i s

the k u r t o s i s , and t = (z - zo)/o is t h e random

Here Q i s t h e r m s devia t ion , zo is the a r i t hme t i c mean, and x i s the ran-

dom va r i ab le .

r i a b l e (normalized).

57

e

The probability distribution density is expressed by

where $,(t) is the normal distribution function and O b ( & ) is the fourth derivative of the normal distribution function.

The values of the functions E , , $,, $ 2 , $ 3 , and c $ ~ are tabulated [8], so the distribution functions can be computed without much difficulty once the first four moments have been determined.

The obseryations results were processed to yield th bution functions for the state parameters of the ice cover. then used to find the theoretical distribution (1). The fit between the theoretical and the empirical distribution was quantitatively assessed using Kolmogorov's test. of the theoretical distribution function from the empirical distribution. The starting equation has the form

These data,were

To apply this test, we require the maximum deviation D,

where n is the number of observations and An is the threshold value corre-

sponding to a given significance level P.

If the probability (1 - P ) \< 0.05-0.10, the deviation between t ordinates of. the theoretical and the empirical distribution is apparently not random and the fit is inadequate; fo r (1 - P ) > 0 . 3 0 - 0 . 4 0 , good fit is observed between the theoretical and the empirical distribution. Mitropol'skii [8] indicates that if (1 - P ) > 0.05, the theoretical and the empirical distribution match. The values of P and the corresponding values of An are tabulated in [8], and the goodness-of-fit test is also computed without difficulty. parameters of the theoretical distribution are assumed known when Kodmogorov's test is applied. distribution were obtained using the same data, the goodness of fit

We will use this test in our computations.

The

Since the parameters of the theoretical and the empirical

apparently came out too high.

58

Using equat ions (4) and (5) and tabula ted d a t a , w e can f ind t h e

confidence l i m i t s of the unknown funct ion Ft(z) from the da t a of the

enrpirical funct ion :

Lower l i m i t . , . 1" I: ( \ . ) - ; F (x)--- 9, ' f n (4)

( 5 ) A,,

Upper l i m i t . - ru ( x ) - z F (XI + 7~ 1

Since always Fg(z) b 0, F,@) 4 1, t h e r e s u l t s obtained from (4) and (5) are set equal t

be less than one o r g rea t e r than Z e r O .

a b i l i t y of each type of i ce , we a l s o computed the v a r i a t i o n c a e f f i c i e n t s

zero and one, r e s p e c t i v e V , if they come *ut t o

To permi$ comparing the var i -

L e t us now consider the r e s u l f s obtained by s ta t is t ical processing

of the observat ion da ta .

of group types.

f a s t i ce ) were used i n the ana lys i s .

observat ions of the authors c a r r i e d out on the Severmy< poeyus-33 d r i f t i n g

s t a t i o n i q 1964-65.

The s p e c i a l o b s e r v a t i w s covered a wide range

The da ta of 14,258 thickness measurements ( d r i f t and

This sample a l s o includes the s p e c i a l

The v a r i a t i o n of ice th ickness , expressed i n terms of t he rms devi-

a t i o n , i s a func t ion of i c e age, a i1 o ther condi t ions being equal (Fig. l).

Using t h i s dependence, w e can estimate appraximately the m s devia t ion 0

from the computed average ice thickness .

the nonuni fomi ty of t h e i c e cover thickness .

Given u , we can form an idea Of

d

0 2

- H

Fig. 1. Rms devia t ion 0 versus average i c e

1--winter and one-year i c e 2--old ice

0 0

___-e

59

In some regions this dependence is less pronounced: it breaks down for small cf and for comparatively large average ice thickness (210-290 cm). The low value of (T points to "quiet" conditions of ice formation. average Xce thickness in these regions therefore is unsuitable even for rough estimates of the rms deviation.

The

BO-

I 40-

The variation coefficient v y which provides'an indication of the rela- tive changes in ice thickness, also depends on the average ice thickness,

* I - 0 * A 3

A

although this relationship is less pronounced.

To assess the general features of the variation of these characteristics,

we divided all the available observations according to age groups. Th variation coefficients were computed in order to estimate the variatio ice thickness within each group. variation coefficients were found to remain fairly constant for the different

The maximum, the minimum, and the average

age groups (Fig. 2 ) .

The Charlier distribution was found to fit in most cases the thickness of old and one-year ice and the snow cover height on old ice (the Kolmogorov test is greater than 0.05 in all cases). and the theoretical distribution.

Figure 3 compares the empirical

60

Fig. 3 . Comparison of t h e o r e t i c a l and empirical d i s t r i b u t i o n functions using Kolmogorov's tes t f o r t he thickness of o ld i c e . I--empirical po in t s , 2--theoretical d i s t r i b u t i o n , 3--maximum devia t ion of t h e o r e t i c a l d i s t r i b u t i o n from t h e empirical func t ion .

The thickness of young o r win ter i c e and the snow he ig

ice are found t o remain constant wi th in the margin of measuremegt error.

The d i s t r i b u t i o n of f a s t - i c e thickness i n space does not f i t t he

Char l ie r curve i n some regions, s ince Kolmogorov' est is less than t h e

cr i t ical value. This may be due t o the s p e c i a l conditions of f a s t - i c e

formation mentioned before .

The d i s t r i b u t i o n of t he thickness of o ld and one-year ice and of

snow he ight on o ld ice thus revea ls c e r t a i n common fea tu res and may be

adequately expressed by the Char l ie r d i s t r i b u t i o n . It seems t h a t t he

thickness of two-year ice a l s o follows t h e same s p a t i a l d i s t r i b u t i o n

a t t e rn .

The d i s t r i b u t i o n func t ion , wever, does not i n d i c a t e the mutual

dependence of the ord ina tes of the corresponding random functions. Y e t

t h i s po in t i s important f o r studying t h e s p a t i a l d i s t r i b u t i o n of t h e

state parameters of t h e ice cover and f o r planning i c e surveys. To

so lve t h i s problem, we computed the s t r u c t u r a l and c o r r e l a t i o n func t ions

61

and the s p e c t r a l d e n s i t i e s of t h e re levant elements. These funct ions are

used i n a number of works dea l ing with the s p a t i a l nonuniformity i n t h e

d i s t r i b u t i o n of i ce thickness and snow height [1,2,7].

The case of a homogeneous and i s o t r o p i c f i e l d is of t h e g r e a t e s t

practical i n t e r e s t , as the computation and the app l i ca t ion of t h e var ious

func t ions become very simple.

of hydrometeorological elements are genera l ly not i so t rop ic .

t h e func t ions of t he elements are replaced by t h e funct ions of t he devia-

t i o n s of t h e corresponding elements from the norm [3]. t h e p a r t i c u l a r case of thickness d i s t r i b u t i o n of o ld i c e t h a t t h e r e s u l t i n g

f i e l d , t o f i r s t approximation, is c lose t o homogeneous and i s o t r o p i c [l].

The s t r u c t u r a l and c o r r e l a t i o n funct ions

Therefore,

It was shown f o r

L e t us consider t o what ex ten t t h e condi t ion of a homogeneous and

i s o t r o p i c d i s t r i b u t i o n is s a t i s f i e d i n our case.

func t ion is given by

The normalized s t r u c t u r a l

and the normalized co r re l a t ion funct ion by

where p is the c o r r e l a t i o n coe f f i c i en t between t h e values of t h e element a t

two po in t s d i s t a n t p from each other .

I f the f i e l d i s homogeneous and i s o t r o p i c , t h e s t r u c t u r a l and correla- >

t i on . func t ions of the element are r e l a t e d by the simple equa l i ty

Pf(p)= 1 - P f ( P ) (8)

Thus, i f t h e s t r u c t u r a l and co r re l a t ion funct ions have been determined

from the observat ion da ta , we can i n s e r t t h e i r values i n (8) t o check whether

o r no t t he f i e l d is homogeneous and i s o t r o p i c . This check was appl ied t o a l l our observat ion data. Table 1 lists t h e r e s u l t of t he tests, i n the form of

a "residue" averaged by groups.

We see from Table 1 t h a t t o f i r s t approximation the f i e l d s indeed may

be t r ea t ed as homogeneous and i s o t r o p i c . The normalized c o r r e l a t i o n funct ions

62

TABLE 1

I -0.04 VI 0.05 I1 0.15 VI1 0.03 111 0.01 VI1 0.23

IV 0.02 IX 0.01

Y 0.00

of ice thickness for different age groups, of SQOW height, and of top surface level were averaged by groups and plotted graphical form

s of basically e. Figure 4 sh f ,

Each curve wa an

expression (Table 2)

Fig. 4 . Normalized correlation functions ss distribution devia- norm ~ ( p ) . p is

distance between the points. I--one-year ice, 2--old ice, 3--winter and white ice

6 3

TABLE 2

ANALYTICAL EXPR2SSIONS =FOR THE NORMALIZED CORRELATION FUNCTION BY GROUPS

Measured Element Group Formula

-0. l o p Thickness of o ld ice I Vn(P) = e

- winter and white ice 11 -0.056P

-0.132P Thickness of one-year ice I11 v,(P) = e

Snow height . *; d i s t r i b u t i o n on o ld i c e I V vn(p) = e Snow he ight d i s t r i b u t i o n on

one-year ice V Un(P) - - ,-O.OSp

Top su r face l e v e l of old ice V I

Top su r face l e v e l of one-year ice V I I

V I , and V I 1 t h e curves could not be with ana ly t i -

s changes of win t h e top su r face level

e ice

and one-year ice

(groups V I and V I I ) f a l l wi thin t h e margin of measurement

The co r re l a t ion funct ions make i t poss ib le t o compute the s p e c t r a l

dens i ty of t he sample. The corresponding r e l a t i o n has t h e form

where S(w) is the s p e c t r a l densi ty .

For c o r r e l a t i o n funct ions f i t t e d with equations of the form ?

-a(P> k(p) = e

t h e s p e c t r a l dens i ty (9) is

(10) 0%

S(4== 7 * u2 p, (12

For the normalized c o r r e l a t i o n funct ion i t takes the form

a (11) x (3-+ (12) S (4 =

64

where w = (2Tr/L)p, a is t h e coe f f i c i en t charac te r iz ing the rate of

deerease of t h e c o r r e l a t i o n between the measurements as t h e separa t ion

p increases , and L i s t h e length of the p r o f i l e over which t h e measure-

ments are made.

' Since t h e area under the curve S(w) is always equal t o un i ty , t he

curve should approach t h e ho r i zon ta l axis as a increases . For each of

t h e elements f i t t e d with an a n a l y t i c a l expression (see Table 2 ) , equation

(11) was used t o compute the s p e c t r a l dens i ty and the corresponding curves

ed. A l l t h e curves were similar, and Figure 5 shows only one of

them as a t y p i c a l example.

"white noise" spec t ra ; i .e . , they have a constant dens i ty i n t h e e n t i r e

re levant frequency range. This leads t o the conclusion t h a t t h e d i s t r ibu -

t i o n of ice thickness i n space is governed by random, and not by

per iodic , forces .

The s p e c t r a l dens i ty curves are c l o s e t o the

S W

Fig. 5. Spec t r a l dens i ty S(w) of t h e thickness d i s t r i b u t i o n of one-year ice vs. d i s t ance between measure- ment points .

Le t us consider t he cross-correlat ion funct ions f o r t he ice thick-

ness , t h e top su r face level, and t h e snow cover height . Because of t h e

considerable d i f f i c u l t i e s i n determining ice thickness , i n d i r e c t methods

have t o be devised, perhaps approximate, f o r es t imat ing t h e s p e c i f i c f e a t u r e s of thickness d i s t r i b u t i o n f o r ice o f d i f f e r e n t age groups.

65

I f i s o s t a t i c equi l ibr ium of ice is assumed, a convenient index of i c e

thickness is provided by t h e level Qf t h e top su r face of ice r e l a t i v e to the

water edge (o r t h e r e l a t i v e l e v e l ) ; unfortunately, no simultaneous measure-

ments of ice thickness and top su r face level are ava i lab le .

Visual r e s u l t s and a b s t r a c t reasoning seem t o suggest a c e r t a i n i n t e r -

dependence between ice thickness , snow he ight , and top su r face level f o r

old ice. The snow cmer levels the sur face , f i l l i n g a l l t he depressions

which form mainly as a r e s u l t of uneven melting of d i f f e r e n t s ec t ions .

Cross-correlat ion funct ions r e f l e c t t o a c e r t a i n ex ten t t h i s f e a t u r e

of snow d i s t r i b u t i o n on old ice ( t h e cross-correlat ion c o e f f i c i e n t between

ice thickness and snow height a t a poin t i s 0.40).

observed between' the top su r face l e v e l of old ice and the height of t h e snow

cover (c ross -cor re la t ion coe f f i c i en t a t a poin t as high as 0.80).

A c lose r c o r r e l a t i o n is

Thus the snow height da t a , which are very easy t o c o l l e c t , provide

l i t t l e i n d i r e c t information about ice thickness , but they adequately r e f l e c t

t he unevenness of t h e top sur face of old ice.

and t o render more accura te t h e very general f e a t u r e s of thickness d i s t r ibu -

t i o n f o r ice of d i f f e r e n t age groups, which are the following:

Our work helped t o e luc ida te

1. The nonuniform d i s t r i b u t i o n of i ce thickness i n space is assoc ia ted

with t h e e f f e c t of random f a c t o r s ;

2 . The s p a t i a l thickness d i s t r i b u t i o n of o ld , one-year, and, apparent ly ,

two-year i ce may be f i t t e d with the Char l ie r d i s t r i b u t i o n funct ion.

3. The unevenness of t h e top su r face of o ld ice is adequately represented

by t h e thickness of t he snow cover.

Combined Analysis o f the State Parameters o f I c e Cover (Equivalent I c e Thickness)

Measurements of i c e thickness f o r d e t e r i o r a t i o n index of 2/10-3/iO and

higher were ca r r i ed out i n regions without snow s lush o r water channels.

66

I so l a t ed r e s u l t s of t hese measurements i n d i c a t e t h a t t he general

f e a t u r e s of thickness d i s t r i b u t i o n are also observed i n t h i s per iod, but

f u r t h e r s t u d i e s of t h i s quest ion are needed, We w i l l t e n t a t i v e l y assume

t h a t t h e previous r e s u l t s are appl icable t o a l l s t ages of ice

de te r io ra t ion .

L e t us consider t he app l i ca t ion of our ice thickness r e s u l t s t o t h e

ana lys i s of nav igab i l i t y .

of the state of t he ice cover which determines the rate of progress 0 f . a

vessel through ice [4]. Our ana lys i s of a l a r g e volume of ice thickness

measurements revealed the d i f f i c u l t i e s which are involved i n the quanti-

ta t ive determinat ion of t h i s i c e c h a r a c t e r i s t i c , even before the onse t

of ice melt ing.

Ice thickness i s one of the bas i c parameters

I n sp r ing and summer, as t h e ice cover begins t o d e t e r i o r a t e

through meJting, t he very concept of "ice thickness" lo ses much of i t s

meaning.

channels are formed i n t h e ice cover, so t h a t t h e ice thickness may

f l u c t u a t e from near ly zero t o i t s maximum wintertime value ( i n hummocks).

Thus f o r ice d e t e r i o r a t i o n index of 2/10-3/10, i s o l a t e d through

At present , s t u d i e s of ice navigabi l i ty* pursue two sepa ra t e courses :

(1) e luc ida t ion of q u a n t i t a t i v e r e l a t ionsh ips between the sh ip parameters

(dimensions, h u l l s t r eng th , engine power) and the allowed speed of s a f e

s a i l i n g i n ice of known c h a r a c t e r i s t i c s [5] ( the r e s u l t s of these s tud ie s

are appl ied i n a c t u a l sh ip design); and (2) determination of technica l

(or ac tua l ) ice s a i l i n g speeds of sh ips of var ious classes from n a t u r a l

da t a (the r e s u l t s of these s tud ie s are used i n inves t iga t ing the s a i l i n g

condi t ions in various geographical regions and i n planning marine and

arctic operat ions, e t c . ) [ 4 ] .

One of t he most d i f f i c u l t a spec t s i n these problems is es t imat ing

t h e a c t u a l i ce condi t ions. Various authors t r i e d t o f ind methods of

allowing f o r the b a s i c parameters charac te r iz ing t h e s ta te of t h e ice

*The a b i l i t y of a sh ip t o overcome t h e r e s i s t a n c e of i ce and t o advance through ice with a certain ve loc i ty , corresponding t o t h e power r a t i n g of the engine and t h e s t r eng th and shape of t h e h u l l .

67

cover. Churkina and Sergeev, i n t h e i r ca l cu la t ions of t h e s a i l i n g speeds of

sh ips , estimated the s ta te of t he ice cover i n terms of var ious combinations

of thickness , hummocking index, and o ther parameters. Kashtelyan and Ryvlin

[ S ] proposed a method f o r s epa ra t e ca l cu la t ion of the hummocking and d e t e r i -

o r a t i o n ind ices of ice f o r purposes of computing the nav igab i l i t y of s o l i d

i ce from the AANII Navigation Research Laboratory formula,

Spichkin [6] proposed a method f o r es t imat ing the ind iv idua l components of

t h e r e s i s t ance of t he ice cover t o navigat ion and derived an empir ical

r e l a t ionsh ip between the t o t a l ice r e s i s t ance , the ice s ta te parameters,

and the i c e breaker dimensions. Their formula comprises 1 2 c o e f f i c i e n t s

which should be determined from n a t u r a l empir ical da ta : some of the coe f f i c i -

e n t s are determined with the previously mentioned Navigation Laboratory

formula, and o the r s are determined using boundary condi t ions, l o g i c a l

considerat ions, and the r e s u l t s of i s o l a t e d observations of a Moskua-type

ice breaker i n d r i f t ice.

formula corresponds t o the physics of the i n t e r a c t i o n between t h e ' s h i p and

t h e ice cover, t h i s approach t o es t imat ing the a c t u a l s t a t e of t h e ice cover

seems q u i t e leg i t imate .

*

K i r i l l o v and

Regardless of whether or not K i r i l l o v and Spichkin 's

A common f e a t u r e of the var ious methods f o r es t imat ing ice nav igab i l i t y

is t h a t they a l l use the average thickness as a bas i c parameter of state,

without c l e a r l y s t r e s s i n g the fundamental importance of t h i s c h a r a c t e r i s t i c .

Af te r a l l , besides the nonuniform d i s t r i b u t i o n of ice thickness i n nonhummocky

regions, navigable ice a l s o shows hummocks, inc lus ions of ice of var ious

ages, snow s lush , water channels, and thawed patches.

One of t he methods which i n e f f e c t allows f o r a l l t he p a r t i c u l a r

f e a t u r e s of t he s ta te of ice is described i n [4], This method determines

t h e so-called "equivalent" ice thickness , i . e . , t he hypothe t ica l thickness

t h a t t h e ice cover would have i f a l l t he humps and hummocks were leveled ou t

and t h e depressions, channels, and thawed patches f i l l e d with ice.

The equivalent ice thickness thus automatical ly allows f o r hummocking

and d e t e r i o r a t i o n of t h e ice cover and f o r the presence of ice of d i f f e r e n t

age groups.

r equ i r e the compaction and the s i z e of t he ice formations. Our r e s u l t s

With d r i f t i ce , bes ides the equivalent thickness , w e a l s o

i n ' e th ickness o u t s i d e

channels (thawed patches) should be computed using the Char l ie r

d i s t r i b u t i o n .

l o allow f o r t he e f f e c t of hummocking on the equivalent thi'ckness

of ice, w e can use q u a n t i t a t i v e r e l a t ionsh ips between the average ice

thickness and t h e hummocking ( t h e higher the hummocking, t h e higher

t he equivalent ice th ickness) .

equivalent thickness r e f l e c t the reduct ion i n s a i l i n g speed as a r e s u l t

of t h e increase i n hummocking?

The quest ion t o consider is, does the

Sergeev compared the s a i l i n g da ta of i d e n t i c a l sh ips i n ice of

d i f f e r e n t hummocking ind ices and derived t h e c o e f f i c i e n t s of average

thickness increase due t o humnocking. Comparison of these r e s u l t s with

the da t a of observat ions i n na tu re revea ls good f i t .

ice nav igab i l i t y , hummocking thus can be t r ea t ed as an increase i n the

'average, and hence t h e equiva len t , i ce thickness.

I n connection with

Similar comparison could e s t a b l i s h t h e e f f e c t of d e t e r i o r a t i o n

and old ice inc lus ions on changes i n the equivalent thickness .

tuna te ly , t he observat ion da ta are inadequate f o r t h i s purpose.

Unfor-

The use of t he equivalent ice thickness f o r es t imat ing i c e

nav igab i l i t y has c e r t a i n shortcomings. F i r s t , the s a i l i n g speed of

sh ips of var ious i ce classes is estimated by a s ta t is t ical method,

ignoring t h e a c t u a l fo rces which c o n s t i t u t e t he t r u e t o t a l r e s i s t a n c e

of i ce and thus the physics of t h e i n t e r a c t i o n between the sh ip and the

ice cover. Second, t he approach is based on a somewhat i dea l i zed ice

I model which does not f u l l y correspond t o the real ice conditions.

These shortcomings, however, are o f f s e t by the f a c t t h a t the i c e

condi t ions along the sh ip ' s course are expressed v i r t u a l l y i n terms of

a s i n g l e parameter, which is moreover based on f a i r l y de t a i l ed s t u d i e s

of the a c t u a l state of t he ice cover. P r a c t i c a l appl ica t ion of the

equivalent i ce thickness w i l l t he re fo re s t imula te f u r t h e r study of those

phys ica l processes which are responsible f o r t h e formation and the changes of t he i c e cover i n the a rc t ic seas. Wide use of t h e equivalent

69

ice thickness for estimating ice navigability requires actual observations in nature of the rate of progress of ice breakers in drift ice with various equivalent thicknesses.

BIBLIOGWHY

1. Buzuev, A. Ya. Application of structural functions to the determhation of the space distribution of ice thickness. Antarkticheskogo Ins t i tu ta , Vol. 277, Leningrad, 1966.

Trudy Arkticheskogo i

2. Buzuev, A. Ya. Some statistical features of the distribution of old ice thickness. Vol. 284, Leningrad, 1968,

Trudy Arkticheskogo i Antarkticheskogo Irwbituta,

3. Gandin, L. S . Objective Analysis of MeteoroZoghaZ Fields. Leningrad: Gidrometeoizdat, 1963.

4 . Gordienko, P. A., A . Ya. Buzuev, and G. N. Sergeev. Studies of the sea ice cover as a navigable medium. No. 27. Leningrad: Gidrometeoizdat, 1967.

In ProbZemy A r k t i k i i Antarktiki,

5. Kashtelyan, V. I. and A. Ya. Ryvlin. Allowance for the natural charac- teristics of solid ice in estimating its navigability to ice breakers. In Problemy A r k t i k i i Antarktiki, No. 22. Leningrad: Gidrometeoizdat, 1966.

6. Kirillov, A. A. and V. A . Spichkin. Approximate computation of the beginning of movement of ice breakers in ice cover. i Antarktieheskogo Insti tuta, Vol. 257 , Leningrad , 1967 b

Trudy Arkticheskogo

7. Laikhtman, D. L. and R. L. Kagan. Some aspects of snow survey moderni- zation. 1960.

Trudy Glavnoi Geofizieheskoi ObservatoKi , N o . 108 , Leningrad ,

8 . Mitropol'skii, A. K. Stat is t ical Techniques. Moscow: Fizmatgiz, 1961.

70

ESTIMATING THE LATERAL MELTING OF DRIFT ICE

Yu. L, Nazintsev

e summer d e t e r i o r a t i o n of t h e ice cover, t h e

d r i f t ice provides an important fo recas t ing

A quanti- parameter f o r es t imat ing t h e n a v i g a b i l i t y of ice-covered seas,

tative estimate of t h e lateral melt ing can be obtained using t h e t h e o r e t i c a l

models from [1,2].

measurement d a t a are a v a i l a b l e on t h e turbulence parameters and t h e hydro-

l o g i c a l f i e l d s near t h e edge of t h e melt ing ice f loe . So f a r no d i r e c t

measurements of t h e lateral melt ing of ice have been made, and t h e r e is no t o o l f o r assess ing t h e r e l i a b i l i t y of t h e computations.

This l eads t o c e r t a i n d i f f i c u l t i e s , however, as no

Observations of t h e small-scale oceanological processes near t h e edge

of a d r i f t i n g f l o e and measurements of t h e lateral melt ing are the re fo re of

considerable i n t e r e s t . Such observations were c a r r i e d ou t by t h e author i n

cooperation wi th S. E. Nikolaev and G. K. Rudenya on t h e Seoemyi poZyus-I3 d r i f t i n g s t a t i o n i n 1966.

ice melt ing period, a long narrow l ane formed along t h e break l i n e i n t h e

ice, which p e r s l s t e d a l l through t h e summer u n t i l t h e autumn cold.

"breathed," changing i ts width from 20 t o SO m.

During t h e observations a t t h e beginning of t h e

The l ane

ateral melt ing w a s measured i n two sec t ions using s p e c i a l equip-

f ixed t o bracke ts f rozen i n t o t h e edge of t h e ice f loe . Ice thickness w a s about 2.5 m.

wi th a thermis tor gauge.

and water temperature p r o f i l e s were taken under t h e ice, near t h e edge,

and a t var ious d i s t ances from t h e lane.

su r f ace of i c e i n t h e summer was a l s o determined a t t h e same points .

Temperature p r o f i l e s i n t h e ice l ane w e r e taken

S a l i n i t y d i s t r i b u t i o n i n t h e l ane was measured,

The amount of mel t ing at t h e bottom

Measurements of t h e water temperature and s a l i n i t y f i e l d s i n a number

of s ec t ions showed t h a t t h e m e l t water running off t h e ice spreads over t h e

71

su r face of t h e l a n e forming a r e l a t i v e l y t h i n (0.5-1.0 m) l aye r of low-salinity

water wi th a sharp temperature and s a l i n i t y d i scon t inu i ty relative t o t h e under-

l y i n g sea water.

from -0.5 t o + l . O ° C and t h e s a l i n i t y from 1 7 t o 19O/,,, whereas below t h e i n t e r -

f a c e these parameters var ied from -1.4 t o -1.5OC and from 28 t o 2go/oo.

temperature f i e l d a l s o showed small ho r i zon ta l g rad ien t s , wi th t h e temperature

decreasing from midlane t o t h e ice edge. The g rad ien t s were s t e e p e s t near t h e

ice. As expected, t h e h ighes t water temperature w a s observed i n t h e su r face

l a y e r a t t h e middle of t h e lane.

Above t h e d i scon t inu i ty l a y e r , t h e w a t e r temperature var ied

The

This s t r u c t u r e of t h e temperature f i e l d accounts f o r t h e nonuniform v e r t i c a l

It leads t o t h e formation of i c e overhangs, which are danger- mel t ing of t h e ice.

ous t o walk on. Figure 1 shows t h e v a r i a t i o n of t h e lateral ice p r o f i l e during

melting.

lane i s double t h e melt ing a t t h e bottom of t h e ice f l o e ,

numerical va lues are 130 and 70 cm.

edge gradually drops as t h e i c e f l o e f l o a t s up. The mean in t eg ra t ed la teral

melt ing is 77 cm.

We see t h a t t h e lateral melt ing wi th in the low-salinity l aye r of t h e

The corresponding

The peak melt ing value a t t h e lane water

The cont r ibu t ion of t h i s process t o t h e o v e r a l l melting of ice can be

assessed by comparing t h e volumes of i c e removed as a r e s u l t of mel t ing by a i r

and water h e a t from t h e top and t h e s i d e sur faces .

l a y e r on t h e top su r face is 30 cm thick.

t h e volume of mel t ing i c e from t h e s i d e su r face is 8000 m3, and t h e volume of

mel t ing ice from t h e top is 288,000 m3.

whereas f o r a s m a l l f l o e of 10x10 m i t would be 3: l .

f o r t he two sur faces are observed f o r a 27x27 m floe.* These r e l a t i o n s i n d i c a t e

t h a t t h e cont r ibu t ion of la teral melting r ap id ly increases as t h e f l o e dimensions

drop t o a few t ens of meters.

I n our example, t h e mel t ing

For an i c e f l o e measuring 1200x800 m,

The r a t i o of t h e two volumes i s 1:36,

Equal mel t ing volumes

It is worth t ry ing t o e s t a b l i s h the e f f e c t of t h e l a n e on i c e melt ing a t

t h e bottom sur face , s i n c e t h e t h e o r e t i c a l estimates [1,2], cont ra ry t o accepted

opinion, seem t o i n d i c a t e , t h a t t h e hea t absorbed by l anes from t h e atmosphere

is not e n t i r e l y expended i n la teral melt ing of ice [ l ] .

*It is assumed t h a t t he r e l a t i v e l ane area remains fixed.

72

5 Distance (m)

3 4 2 I

Fig. 1. Temperatu s i d e p r o f i l e p r o f i l e , 8 J u

Careful regular measurements of ice melt ing from

su r face (Table 1) show t h a t bottom melt ing a t t h e

a t a d i s t ance of 10 m from t h e l ane it w a s 1 4 em; l ane i t w a s 8-10 cm. These f igu res r evea l t h a t bo i nc reases only a t t h e very edge of t h e ice . I f t h

i n terms of t h e volume of ice, we f i nd t h a t most o

t h e l ane w a t e r is used up i n la teral melt ing and does 'no t con t r ibu te much

t o the melt ing of t h e bottom su r face of ice.

73

TABLE 1

140

39 46

47 52 59 63 63

ICE MELTING ( in cm) FOR VARIOUS POINTS OF AN ICE FLOE I N 1966

-

160

0 0 0 0

38 44

76 53 60 61 62

DATE

51 59 80 80 78

- J u l y

8 1 2 20 24

Augus

1 7

16 20 27

8 9

14 1 7 19

Lateral sur face a t a t h e v -

0 - 0 0

14 55

95 100 158 172 1 7 0

- 20 -

0 4

48 61

69 73

127 130 129 -

-ti

40 - -

0 1

47 55

61 66 82 83 83 -

t 1 down - 60 - 0 0

38 45

49 55 67 80 80 -

- 80

0 0

40 45

47 49 58 59 60

- 100

I -

O 0

36 44

46 50 65 66 66

- 120

0 1 40 45

45 51 62 63 64

given d i s t ance (cm) along Erom t h e water edge

in sur f e v n $Eo a t m e from

2

dl 11 t 1 2

- COP pur- €ace

3 6

12 15

20 26 30 31 31 -

More r e l i a b l e r e l a t i o n s can be obtained by considering t h e quant i ty of

heat absorbed by t h e l ane f r o m t h e atmosphere. Taking t h e l a n e half-width

(30 m on t h e average) , t h e absorpt ion of r ad ia t ion , and t h e re-emission of

hea t i n t o t h e a phere during t h e melting per iod, w e f ind t h a t t h e t o t a l

quant i ty of hea t h e lane from t h e atmosphere is 1,200,000 kcal/m.

The melting ice volume per 1 m along t h e s i d e su r face was 1.77 2 , and 120,000

kca l of hea t were needed t o m e l t t h i s volume of ice.

f igu res shows t h a t only 10 per cent of t h e hea t absorbed by t h e l ane w a t e r

from air w a s us era1 melting of ice,

al ler f r a c t i o n of hea t is used up i n lateral melting

according t o Nikolaev [2J, t h i s f r a c t i o n is 10 per

about 25 per cent f o r a 30 m lane. Our measurements

than ha l f of t hese f igu res . The reason f o r t h i s

i n t h e crude approximation of t h e numerical values

Comparison of t h e two

discrepancy i

assumed f o r t h e i n i t i a l physical parameters, r a t h e r than i n t h e s p e c i f i c fea-

t u r e s of t h e t h e o r e t i c a l so lu t ion .

74

f r a c t i o n of h e a t expended i n lateral i

e rate of l a t

urement r e s u l t s r l t i n g i s c o r r e l a t e d wi th t h e

changes i n l a n e width

l ane ; t h e c o r r e l a t i o n may break down below t h e temperature d i scon t inu i ty

l e v e l (Figure 2). If t h i s f a c t ( i s o l a t e d so f a r ) is not a c c i d e n t a l , t h e

above discrepancy may be a t t r i b u t e d t o t h e spreading of t h e low-sa l in i ty

m e l t water over t h e s u r f a c e of t h e l a n e and t h e r i s i n g of co lder s a l i n e

water from g r e a t e r depths. Despi te t h e tremendous a b s o r p t i f atmospheric

h e a t by l ane water, t h e o v e r a l l thermal p o t e n t i a l of t h i s water inc reases

q u i t e i n s i g n i f i c a n t l y .

provided by t h e surrounding ice.

su r face l a y e r of water i n t h e

\

This is due t o t h e e f f e c t of t h e cold r e s e r v o i r s

J u l y August

Fig. 2. Variation of t h e rate of lateral ice melt ing V and ice l ane width 1. edge, 2--rate of mel t ing a t 1-2 m depth, 3--lane width.

l--rate of mel t ing at water

I n conclusion, we should stress t h a t t h e con t r ibu t ion from lateral

melt ing markedly inc reases f o r smaller f l o e s and i t can no longer be ignored

i n estimates of t h e o v e r a l l ice melting.

l o g i c a l c h a r a c t e r i s tics i n ice l anes and of turbulence parameters now

one of t h e press ing problems of modern ice physics.

Detailed measurements of t h e

BIBLIOGRAPHY

1. Doronin, Yu. P., and A. S. Grushkina. The e f f e c t of thermal f a c t o r s i n ice compaction, Insti tuta, Vol. 271, No. 1, Moscow Leningrad, 1964.

Antarktiki, No. 12.

Trudy Arktioheskogo i Antarkticheskogo

2. Nikolaev, Yu. V. Ice melt ing i n l anes . I n ProbZemy A r k t i k i i Leningrad: Morskoi Transport , 1963.

1. SNOW ACCUMULATION ON KARA SEA

Yu. L. Nazintsev

One of the significant factors both in forecasting the growth, melting, and strength of ice and in estimating the navigability of ice-covered seas

is correct dete on sea ice. Snow, with i a considerable effect on the rate of growth and melting of ice, its physical

characteristics, and the temperature conditions of ice formations [l-51.

ation of the quantity and the physical p

However, very little has been published on the quantities and physical properties of snow on arctic sea ice in relation to the climatic cond and the properties of the ice cover. The main reason for this is insuffi- ciency of snow data.

Recent snow surveys on fast and drift ice can be compared with

stal observations of polar stations; the information resulting from the comparison can be used to estimate snow accumulation on ice of varioue types.

We will first indicate the basic fsc and the distribution of the snow cover on of the ice formations. autumn ice will have accumulated a fairly thick snow layer by spring.

accumulation is largely responsible for the fact that the snow cover is thicker on fast ice than on drifting ice.

major factor is the age Young ice generally carries very little snow, whereas

This

Jutting hummocks also enhance snow accumulation, In most areas, hummocks are much more numerous on drift ice than on fast ice. therefore seem that more snow should accumulate on drift ice than, say, on autumn ice. In fact, however, drift ice shows poorer snow accumulation, mainly because the incessant shifts and cracks between the floes produce

It would

clear water lanes, which act as snow traps under snowdrift conditions,

Year-to-year f l u c t u a t i o n s i n p r e c i p i t a t i o n a l s o play a c e r t a i n r o l e . They exceed the changes i n snow d i s t r i b u t i o n on sea ice, as can be seen i n t h e Cent ra l Arctic [23.

Snow on f a s t ice. The mass of snow dep i t e d on fast ice reaches i ts maximum i n the second ten-day period i n May. accumulation during t h e month of May, assuming smooth ice s e c t i o n s (without hummocks).* average of 0.30-0.34 g/cm3). used as an i n d i c a t o r of snow mass f o r general estimates.

We w i l l now consider snow

I c e dens i ty changes f a i r l y l i t t l e from year t o year (with an The he igh t of t h e snow cover will t h e r e f o r e be

Comparison of t h e yea r ly snow cover th ickness f i g u r e s f o r d i f f e r e n t po lar s t a t i o n s r evea l s a genera l ly good fit . This is important f o r fo recas t ing , as i t impl ies t h a t t h e yea r ly f l u c t u a t i o n s of snow accumulation depend on la rge- scale atmospheric processes which are common over the e n t i r e sea area.

Snow surveys c a r r i e d out over t h e e n t i r e f a s t i c e area show t h a t t h e quan t i ty of snow on ice is highly v a r i a b l e from year t o year. p reva i l i ng snow he igh t s reached 15-20 cm, whereas i n 1967 they were 40-50 cm, i.e., almost t h r e e t i m e s as high. The snow cover cha r t s f o r f a s t ice a l s o r e v e a l year-to-year changes i n t h e geographical d i s t r i b u t i o n of snow on ice.

I n 1960, t h e

To e l u c i d a t e t h e reasons f o r t h e nonuniform d i s t r i b u t i o n of snow over t h e yea r s , t h now cover c h a r t s were compared with t h e ice hummocking cha r t s . The two sets of ch surveys had o r i g i n a l l y been performed on smooth ice s t r e t c h e s , ignor ing t h e snow d r i f t s near t he hummocks.

The f i t between t h e

ts revealed many f e a t u r e s i n common, although the snow

t iona ry c o a s t a l observations of p o l a r s t a t i o n s and t h e d e t a i l e d f i e l d snow surveys over t h e f a s t ice area is demonstrated by curves 1 and 2 i n Figure 1, but t h e s i g n d i f f e r s from year t o yea r , d a t a of po la r s t a t i o n s the re fo re can be extended t o t h e e n t i r e f a s t i c e zone.

The divergence is genera l ly small (5-10 a), For background estimates, t h e average

h (cm) Fig, 1. Year-to-year f luc tu - 40

a t i o n s of snow accumulation ast i c e . I--coastal

observations, 2--field sur- 20-

veys of t h e e n t i r e f a s t i c e area,

1964 1965 I966 1967 I968 I S 6 9 0 1963

- _ . ~.

*There are very few measurements of t h e snow mass i n hummocks, and no unique methodology is a v a i l a b l e f o r these measurements.

78

Local r e l a t ionsh ip can a l s o be observed f o r d i f f e r e n t p a r t s of the

The p l o t i n Figure 2 is based on f a s t ice zone (Fig. 2) .

f o r an i c e cover 170-190 cm th ick .

of c o a s t a l observat ions g ive too low values f o r

i n the f a s t - i c e p a r t . A co r rec t ion coe f f i c i en t of 1 .5 sho

f o r proper conversion. This c r l y s t a b l e , and i n t h i s sense

t h e r e s u l t s of coastal observat ions are f u l l y representa t ive .

t i o n s are as low as l t2 cm, which is c lose t o the accuracy of t he snow surveys.

We see from t h e f i g u r e t h a t the r e s u l t s

a c t u a l snow accumulation

The r m s devia-

- __ -

hc (cm)

coas t hc VS. snow he ight i n of fshore f a s t i c e z. ,o 2:LLL.lL 20 30 4F-(cm) 10

Fig. 2. Snow height near t he

Ice th ickness

Nevertheless , i n i nd iv idua l years i n which t h e i c e thickness d i f f e r s markedly

r t a i n co r rec t ion should be introduced i n t o the observed

r e l a t i o n s h i p , using the s t a t i s t i c a l c o r r e l a t i o n between snow accumulation

and the i c e thickness (Table' 1 ) .

Using the l i n e a r approximation, we ob ta in the mean deeendence

Snow height ---- -. -- - I minimum" maximum* mean I

h = 0.W - 10

where h i s t h e snow he ight i n cm and H i s the i c e thickness i n cm.

TABLE 1

!OO - 1 ' 1 0 13 3 1 1 ::o -- 1 00 160 -- 190 27 I3 3 4 1 IN) -- 220 27 13

23

I I

.-

I ' G3

*Average f o r i nd iv idua l s e c t i o n s o r t r ave r ses .

7 9

pendence, w e can propose t h e following method f o r computing

t h e average snow height on i c e i n t h e open sea (from the r e s u l t s of coas t a l

ns). F i r s t t h e measurement r e s u l t s are processed t o determine t h e

Then t h e p l o t i n Figure 2 is used t o average snow height near t h e coas t hc. determine t h e snow he ight f o r sea ice z f o r average condi t ions

The co r rec t ion Ah f o r t h e t r u e ice thickness H i n t hese regions, according

t o (1) , has t h e form

(3) Ah = 0.2(180 - H)

W e thus ob ta in f o r t he snow he ight KH on fast ice

- hH z - 0.2(180 - H) (4)

n e r a l i z a t i o n of extens ive s t a t i s t i ca l d a t a w i l l enable us t o improve

t h e r e l i a b i l i t y of t h e resu l t s .

Snow on d r i f t ice. Corre la t ion wi th c o a s t a l observat ions and correc-

t i o n f o r ice age ( th ickness) a l s o provide a s u i t a b l e method f o r es t imat ing

t h e snow accumulation on d r i f t ice.

adversely a f f ec t ed by our i n a b i l i t y , a t t h i s s t age , t o allow f o r t h e dynamics

and morphology of t h e ice cover, as these f a c t o r s are much more s i g n i f i c a n t

here than f o r f a s t i c e .

year-to-year f l u c t u a t i o n

e n t i r e sea are f a i r l y cons is ten t .

The r e l i a b i l i t y of t h e procedure is

Analysis of snow surveys (Table 2) shows t h a t t h e f snow a c c m u l a t i o n on fast and d r i f t i c e f o r t h e

To some approximation, t h i s r e l a t ionsh ip can be expressed i n t h e l i n e a r

form

where xd is t h e mean snow he ight on d r i f t ice and Xc is t h e mean snow height

f r o m c o a s t a l observat ions.

80

TABLE 2 I

SNOW ACCUMULATION ON FAST AND DRIFT ICE ( i n cm)

1963 1969 1!66 1066 1!167 1- 1969

8

12 5

13 7

-

-

'Average i c e th ickness c l o s e to 120 em.

i n spr igg on em sec t ions of

d r i f t i c e is approximately one t h i r d of t he corresponding f i g u r e f o r . f a S t

e observed snow height .

ice thickness . The same f i g u r e p l o t s t he mult iy

he ight vs. i c e thickness .

t h i n ice are l a r g e r f o r t h i c k ice.

from 5 t o 34 cm. This po i

The maximum "devia t io

h t greater than

Thus f o r 160-196 cm i c e the mean snow height varies

e v a r i e t y i n the general p a t t e r n

o s i t i o n sn d r i f t , i c e . It is s i g n i f i c a n t t h a t the minimum snow

he ight (3-5 cm t h e same f o r almost a l l age groups of i c e (Fig. 3).

To determine t h e snow height on d r i f t i c e , w e should f i r s t use (5) t o

f i n d xd corresponding t o

ing t o H = 1.2 m and the

poin t A f o r i;d = 10 cm).

d r i f t i c e thickness H = 1 . 2 m. The po in t correspond-

r e s u l t i n g r d is then located on Figure 3 (e .g . ,

Drawing an i n t e r p o l a t i o n curve aa through t h i s

* According t o t e n t a t i v e estimates, hummocks r e t a i n almost ha l f of t h e

e n t i r e snow m a s s accumulating on d r i f t i c e .

81

h lcul

Fig. 3. Average snow height h vs. d r i f t ice thickness H and nus devia t ions of snow he ight $E averaged over t he ind iv idua l surveys.

This procedure, however, is st i l l highly approximate, s i n c e it uses

on H a m i t m e r g e s after mult iyear averaging, whereas the dependence of

t h e year-to-year var iance i n the Qbserved values of snow a c c d u l a t i o n on ice is f a i r l y l a rge .

To improve t h i s meth

i n paral le l wi th erttensive a l l po la r s t a t i o n s .

, we need mor- d e t a i l e d S n m surveys on sea ice, eterminat ions of h and @ f o r ice i n

Other methods of ca l cu la t ion of snow accumulation on ice are a l s o

available.

N. P. Shesterikov, who determined t h e snow l a y e r on i c e using age ind ices

( thickness) and hydrometeorological condi t ions t o which t h e ice w a s subjected

during the e n t i r e growth phase.

In our opinion, t he most promising approach w a s suggested by

BIBLIOGRAPHY

1, Doronin, Yu. P. The growth of sea ice, Xn ProbZemy A r k t i k i i Antark t i k i , No. 1. Leningrad: Morskoi Transport , 1959.

82

2. Zoshchilov, V. S. Snow cover Qn Cenfral Arctic ice. In Problemy A r k t i k i t i k i No. 17. Lenhgrad : Gidrometeoizdat , 1964.

3. Smetannikova, A. V. Heat transfer between ocean and the atmosphere In RadiaOsionnyi i tepZov& b a l m A r k t i k i . e Arctic in winter.

h k t i c h e a k o g o i Antarktioheskogo Imtituta, Vol. 229, Leningrad,

4. Yakovlev, G, N. S cover on dr;ift ice in Central Arctic. In Problemy A r k t i k i 5 Antark , No. 3 . Leningrad: Morskoi Transport, 1960.

5. Holtsmark, B. E. Insulating qffect os snow cover on the growth of young sea ice. A r c t i c , Vol. 8, No. 1, 1955.

# I

SHEAR E A NT5 OF NATURAL ICE WITH OPT LITES

A . P. Legen'kov, Y. D. UgZev, and N. I, BZinov

t r i angu la t ion

been c a r r i e d out bef

e. The i c e su r face he tr izingle w a s h ighly uneven. g t o a height of 2-3 m

ve ocean level. Slush f i e l d s of var ious dimensions were loca ted between

these ranges.

taneous measurement

er and 8 October w i ed by fhe c i r c u l a r method

l u e of t h e angle ,

One t h i r d of the t r i a n g l e e r r o r , i .e . , on

W = a + f4 + y - 180'

w a s s u b t r

were computed from the relat3ala-s

rom each measured angle 121. The rms e r r o r s of t h e angles

where m i.s t he rms e r r o r of the measured angle and M is the rms e r r o r of t h e cor rec ted angle .

85

Calcula t ions show t h a t m l ies between +0".3 and k3Il.6, with an arithmetic

mean of 11'.6. The range of M is between ?0",2 and +2",8, with a mean of

i t y of t h e observat ions is als

= 1".6; EBA =2 EBC = 1".4; ECA -i ECB - 1".6 'AB --if 'AC

uted from the standard r e l a t i o n s of geodesy us ing t h e co l l imat ion

ing t o t h e e r r o r s E , t h e rms e r r o r s f o r t h e angles Aa, AB, k2Il.3, t2".0, a 22". 3, respec t ive ly .

Table 1 lists t h e d

success ive observat ion se

rence i n t h e cor rec ted angles a, B , y between

a l s o t h e air temperature d i f -

A t which charac te e r a t u r e between

ve series. If t h he ice floe were i n a l l d i r e c t i o n s

erences Aa, A @ , A

ment e r r o r s i n t h e angles .

TEWE At BETWEEN

2-3 -2 .2

3-4 2 .o 4-5 3 .9

5- 6 -0 .2

6- 7 2 .4

7-8 3 .2

8- 9 -2 .o 9-10 -1 .2

-3 .2

1 .5 3 . 2

-1 .4

3 .6

-9 .4

5 .o -1 .2

4".2 -3.7" 5 .4 -2.2

-3 .5 3.1

0 .7 -1.3

1 .6 0.7 -6 .O -1.9

6 .2 2.4

-3 .o 1 . 7

2 ;.4] 2.4

No. of I I

11-12 -2 .o -1 .o 12-13 2 .2 0 .6 13-14 -0 .8 0 . 2

14-15 -4 .4 -0 .4 15-16 0 .5 -1 . 5

16-17 1 .3 -0 .1

+ 3 .O -1.4

-2 .8 1.6

0 .6 0

4 .8 -3.9

1 .o -3.9

-1 . 2 -4.2 I -3 .71 3.6

Natural ice f l o e s , however, are always ac ted upon by fo rces which

d i f f e r both i n magnitude and i n d i r e c t i o n ; t h e thermal expansion c o e f f i c i e n t s

of ice d i f f e r i n d i f f e r e n t d i r e c t i o n s ; an iso t ropy of s t r u c t u r e and t e x t u r e

and th ickness f a c t o r s render the f l o e r e s i s t a n c e inhomogeneous i n space.

The r e l a t i v e l i n e a r deformation of ice f l o e s i s the re fo re d i f f e r e n t i n

d i f f e r e n t d i r e c t i o n s , so t h a t a n e t shear should occur.

The q u a n t i t i e s Aa, AB, Ay i n Table 1 thus represent t h e f l o e shear , as

The shea r , as w e see from w e l l as t h e measurement e r r o r s of t h e angles.

Table 1, does no t exceed a few seconds i n ice f l o e s .

Note t h a t t h i s conclusion is v a l i d f o r t h i c k mul t iyear f l o e s i n autumn

Younger and th inne r s a l i n e and for measurement p l o t s f a r from t h e ice edge.

ice under t h e same condi t ions should e x h i b i t a higher shear (because of lower

i n t r i n s i c r e s i s t a n c e , h igher s p a t i a l inhomogeneity of s t r u c t u r e and t e x t u r e ,

aqd h igher thermal expansion c o e f f i c i e n t s ) .

s e l e c t e d close t o t h e i c e edge, t h e shear under t h e same condi t ions w i l l a l s o

be l a r g e r than i n Table 1, s i n c e t h e s t r a i n due t o the p re s su re of t h e

ad jo in ing f l o e s cancels ou t as i t propagates f a r t h e r i n t o each f l o e .

I f t h e measurement t r i a n g l e i s

The p a r t i c u l a r t i m e of year is of cons iderable importance. Our observa-

t i o n s were performed i n autumn.

p o s i t i v e thermal s t r a i n i n summer and t h e nega t ive thermal s t r a i n i n win ter .

I n autumn the thermal s t r a i n is n a t u r a l l y less than e i t h e r i n summer o r i n

win ter .

r e s u l t of t h e h igher thermal s t r a i n , t he win te r and summer shear w i l l be

h igher than t h e va lues l i s t e d i n Table 1.

This i s a t r a n s i t i o n a l period between t h e

A similar p a t t e r n should be observed i n sp r ing . Therefore, as a

BIBLIOGRAPHY

1. Graur, A. V. AppZied Geodesy. Moscow-Leningrad: Glavnaya redakts iya geologo-razvedochnoi i geodezicheskoi l i t e r a t u r y , 1934.

2. Iordan, V, Handbook of Geodesy. Moscow: Redbyruo GUGK, 1939.

Fig. 1. P o s i t i o n of f l o e s and po le s relative t o t h e base lYne TIT,.

Once t h e pole coo

can f i n d t h e i c e compac

s; (2) t h e chaa i n d i s t a n c e between t h e f l o e cen te r s ; (3) angle

of t h e f l o e s ; and (5) v e l o c i t i e s of t h e ice f l o e s relative t o t h e base l i n e ,

r e l a t i v e t o one another, e t c .

of the f l o e s r e l a t i v e t o the base l i ne ; (4) cen te r s of r o t a t i o n

If strong t i d a l motion of ice is observed i n the r e l evan t region, t h e

angles a and f.3 should p re fe rab ly be measured a t one-hour intervals. If no

t i d a l motion is observed, a and 6 may be measured every four t o s i x hours,

o r more f requent ly i n cases of i n t e n s i v e motion.

c a r r i e d out simultaneously wi th d r i f t and azimuth observations of t h e base

f l o e .

bution, conf igura t ions , compaction, and re ive of the ice floes

and t h e i r c e n t e r s of g rav i ty . Without t h i

impossible t o r econs t ruc t c o r r e c t l y t h e ice motion and changes i n compaction.

These observations can be

A t least: one aerial photograph is needed t o determine t h e s i z e d i s t r i -

information, i t will be

>

90

OBSERVATIONS OF I C E MOTION WITH OPTICAL THEODOLITES

(METHODOLOGY AND ACCURACY)

A . P. Legen’kou and V. D. UgZev

ON THE SEWRNYI POLYUS-I7 D R I F T I N G STATION

Ice motion i n the context of t h i s paper i s t o be i n t e r p r e t e d as t h e

mutual displacement of t h e f l o e s r e s u l t i n g i n compaction and opening of i c e .

I c e motion has been t r a d i t i o n a l l y regarded as a highly important t o p i c , bu t

t h e observations of t h i s phenomenon have been made sporad ica l ly And mostly

by v i s u a l methods.

sys temat ic r e s u l t s .

l a rge-sca le observations conducted according t o a s p e c i a l program wi th

s u i t a b l e ins t rumenta t ion (air surveys, o p t i c a l t heodo l i t e s , o p t i c a l range

meters, e t c . )

This approach n a t u r a l l y f a i l e d t o y i e l d s i g n i f i c a n t

E f f e c t i v e study of ice motion i s p o s s i b l e only by using

I n 1968, Blinov, Legen’kov, Rusanov, and Uglev conducted observations

of ice motion wi th o p t i c a l t heodo l i t e s on t h e Sevemyi pozyus-17 d r i f t i n g

s t a t i o n .

i n t h i s paper.

The methodology and accuracy of t h e i r observations are discussed

For observa t ions with o p t i c a l t h e l i tes , a t least f o u r i c e f l o e s have

t o be chosen, wi th t h e i r c e n t e r s preferab ly a t t h e corners of a r ec t ang le , a

square, o r a rhombus 3-5 km on a s ide .

t hese f l o e s from a h e l i c o p t e r o r r egu la r a i rcraf t (Fig. 1 ) . A base l i n e

T I T P = a of accu ra t e ly measured l eng th is marked on t h e f l o e on which t h e

s t a t i o n is loca ted , wi th the two t heodo l i t e s T, and T 2 a t i t s ends.

wi th t h e base l i n e (we w i l l c a l l i t t h e base f l o e ) may be loca ted i n s i d e o r

ou t s ide t h e quadrangle formed by t h e poles 1, 2, 3, etc. measure the two angles a and B.

Poles 1, 2, 3, etc., are s tuck i n

The f l o e

The theodo l i t e s

These angles and t h e base l eng th a permit

The f l o e on which t h e Severnzji pozzjus-17 s t a t i o n was located'was an

g approximately 8x10 km2 and

en:

ec t ions ; enormous hummocks up t o 8-10 m -3 m above ocean l e v e l stood o u t among t h e s e forma-

r idges of hummocks p a r t i a l l y smoothed by melt ing

l a t areas were observed between t h e r9dges.

f which were 5-7 m The f l o e was f r inged by old and f r e s h hummocks, so

high.

rrounding i c e ha It cons is ted of indi-

v i d u a l ice s h e e t s and t h e i r fragments, and of o l d , one-year, and young cake

i c e . This area i n May and June c o n s t i t u t e d an ice mosaic wi th t h i n ,

p laces akmtost i n v i s i b l e , cracks. When t h e snow and ice melted, exposing

component f l o e s of t h e mosaic became c l e a r l y

v i s i b l e , bu t t h e d i s t a n c e between t h e f l o e s genera l ly $ id no t exceed 1-5 m.

A narrow lead would occas iona l ly ope e w e e n t h e base f l o e and t h e

surrounding i c e , i t s width not exceeding 50 m (with t h e except ion of one

t h e surrounding ice receded t o a d i s t a n c e of 150-200 m from

t h e base f l o e ) . Because these open l eads were usua l ly q u i t e narrow, i t was le t o s t e p from the base f l o e to t h e ad jacent ice and s t always poss

f i x t h e r e fe rence po le s without a i rbo rne help.

t h e f l o e s could no t b e ph graphed and measured, no exac t

d a t a are a v a i l a b l e on f l o e sizes and conffgura t ion of the base f l o e

drawing).

of po les I , 11, ..., V I .

F igure 1 shows a p a r t

t h e surrounding ice w i t h t h e ference pole (a v i s u a l

The edge of t h e base f l o e is marked from t h e o d o l i t e observations

s t e d of t h r e e co enat p a r t s : (1) a p ine

i n cross s e c t i o n and 3 m long; (2) ralumin tube 32 mm i n diameter and 3 m long;

high and 30 ctn wide, made

t h e top of t h e pole. t he ice sur face .

t o prevent mel t ing .

t a r g e t (of varying shapes) SO cm

steel rods o r duralumin

The poles were allowed t o f r e e z e in holes d r i l l e d i n

The ice a t t h e base of each pole was covered with sawdust

91

The theodo l i t e s were mounted on ice hummocks r i s i n g t o a he ight of

about 3 m above t h e ocean level.

of 120-130 cm i n t o t h e ice. each theodol i te .

relative t o t h e head of t h e n a i l . The na i lheads thus n s t i t u t e d t h e t r u e

end p o i n t s of t h e TIT, base l i n e (Fig. 1).

pyriod, t h e theodo l i t e s rem adequate p ro tec t ion from s o l a r r a d i a t i o n .

They were set on poles f rozen t o a depth

A po le wi th a n a i l w a s s tuck i n t o t h e ice under

The theodo l i t e s were centered wi th an o p t i c a l plumbline

During t h e e n t i r e observat ion

e l y f i r m su r face , thanks t o

Since t h e r e fe rence poles moved incessan t ly , t h e angles 01 and f3 were

measured simultaneously with a f ixed circle. a t t h e o the r end of t h e base l i n e was observed wi th t h e c i r c l e turned t o t h e

r i g h t (CR), and then wi th t h e circle t o t h e l e f t (CL), most po le on ice was observed f o r t h e two pos i t i ons of t h e circle, then t h e

next po le , and so on from l e f t t o r i g h t up t o t h e f a r t h e s t r i g h t pole.

F ina l ly , a f t e r t h e r e fe rence poles , t h e t h e o d o l i t e rod w a s again observed

with CR and CL.

F i r s t t h e rod Qf t h e t h e o d o l i t e

After t h a t , t h e l e f t -

was no telephone communication, v i s u a l s i g n a l s w e r e used

The t i m e d i f f e r e n c e between observations made wi th t h e two i n observations.

t heodo l i t e s w a s sometimes as long as a few minutes. t a b l e f o r l a r g e ice displacements.

This is

I

According t o t h e program, t h e angles a and f3 were measured c l o s e to

t h e standard meteorological obs

Moscow time).

10 September, whe

r d l y be seen.

va t ion times (0300, 0900, 1500, and 2100 h r s

The pole observatlons were begun on 8 June and f in i shed on

the poles had receded t o such a d i s t ance t h a t they could

The base length t h d * A po le D with

a n a i l was f ixed appro l i n e us ing the

(Fig. 1). Using t h e theodo l i t e C' , PO

one length of t h e i ar w i r e . Bra

i t h two c ross l i n e s marked on t h e i r heads. The I

d i s t ances between t h e c e n t e r s of t he n a i l s i n

inva r w i r e backward and forward. The d i f f e r e n c e between the backward and

92

forward measurements of t he d i s t ance DC w a s 0.6 mm. was found t o be 168,357.8 m.

The mean length of DC

We may thus take

DC = 168,357.8 3 0.3-snm

The angles T,CD and DCT, were then measured i n six r e p e t i t i o n s f o r

d i f f e r e n t pos i t i ons of t he circle: & T I C , LTIDC, LDCT,, LCT,D. The

t r i a n g l e T,CT, w a s .' \V =: TZTl C -t L T1CT2 -t L CG TI .- 180" -3".35

and the m s e r r o r f o r each angle [2]

-- - -t- 1".9 v - One t h i r d of t he e r r o r of t he t r i a n g l e T',CT,, i .e, , W / 3 = 1".12, w a s

added t o each angle. The corrected angles were found t o be

L 7; r, c = y = 2 101 8'02".7; L T2 c7-1 =E = 13 IO01 '38'': L C r , =A=27°40'19''.3

with m s e r r o r f o r each corrected angle

W fi = f 1".6 -3-

H a l f of t h e co r rec t ion W / 3 was subtracted from each of t h e meaeured

/ a , C D andLDCT2 t o obta in

L TI CD E I 67'29'04" and DCq == c2 = 63'32'34'

with t h e respec t ive e r r o r 1 ".G -- f1".12

which correspo

E, and c p measured with the same accuracy,

t o f ind the lengths T,D, DT2 i n t h e t r i a n g l e s T,CD and DCT,:

s t o t he e r r o r of an angle equal t o the 8- of t h e angles

The s i n e theorem was then applied

-. -

(2) CD T,D =sin E, - =- 425,995.7 mm SI11 1

CD DT2 = sin - = 324,551.8 mm sin k

93

Hence

a = 21,D + DT, = 750,547.5 mm

Differentiating (2) we find

Replacing the differentials by the rms errors, the length T,D [2]

M T I D = 2 1/ (Gr+ (A, ctgE;)' + (mzctg r)2

where m, m,, m 2 are the nns errors in CD, E,, and y, respectively.

Plugging the numerical values

CD = 168,357.8 m = k0.3 mm El = 67"29'oq' = & l'l.12 ~0.0000056

m, =z= k 1".6= +0.0000085 7 =ZT 2 1 18'02".7

lar computat ns for the length DT, will give us

The absolute nus error in the base length is thus

and the relative nus error is

= + -

We thus have a = 750,547.5 * 7 mm

In what follows we are assuming a = 750.55 m

94

1

L e t us now t r y t o estimate t h e e r r o r s i and 6. The determination

of e r r o r s of hor i zon ta l angles i n geodesy follows a e l e a r c u t procedure.

Geodesy, however, dea l s with f ixed objects,where t h e angles are f ixed and

t h e measurements can be repeated as o f t e n as needed t o ensure t h e des i red

Moreover, i n geodesy, t h e angles i n t r i a n g u l a t i o n

a l l t h e vertices of every t r i a n g l e . As a result, t h e e r r o r s of

angle measurements can be found wi th f a i r c e r t a i n t y ,

I n ice motion observa t ions , we are dea l ing with v a r i a b l e angles a and

t h r e e t r i a n g l e angles are meas ed, as the t h i r d angle

d measurements are e fo re meaningless,

and t h e t r i a n g l e e r r o r cannot be found,

It is thus clear t h a t t h e e r r o r s i n t h e angles a and 6 i n ice motion

s i n tr iangula-

Moreover, t h e e n t i r e problem of angle e r r o r es t imat ion becomes much

measurements w i l l be e s s e n t i a l l y l a r g e r t ha

t i o n .

mre involved, a h o two of t h e t h r e e t r i a n g l

es t imat ion apparent ly r equ i r e s special methods.

Without attempting t o develop new r igorous methods, w e w i l l use t h e

t r a d i t i o n a l methods i n order t o obtain some rough estimates of t h e e r r o r s

i n a and 8 . Before proceeding wi th t h e a c t u a l estimates, however, let us

r e c a l l t he law of e r r o r s of a genera l func t ion [2]. A genera l function$'

of t h e measured v a r i a b l e s Z,, Z,, ..., Z,, i .e. , t h e func t ion

, mn &re t he m s measurement e r r o r s i n Z,, Z,, ..., 2,. (3) to determine e r ~ s e r r o r of base

again i n the following.

are measured with t h e e o d o l i t e T, as t h e

o t h e poles 1, 2, ..., n and t h e d i r e c t i o n

t h e angles a1,2,,..,n according

95

t o (3) t h e r e f o r e may- be "wri t ten i n t h e form

2 ax,, 2 . 3 , . . , , n v - = k v ~ ? , 2 , 3 , ..., . + E T 2 (4)

a1 15".6 14 .5

a3 18 .9 a4 21 .4 "5 9 .7 a6 12 .6

where Aa1,2 ,*..,n is t h e rms e r r o r of t h e angles a1 2,, . . ,n; &1,2,. . . ,n is t h e rms e r r o r i n the d i r e c t i o n s to the poles 1, 2, ..., n from t h e t

81

82

B3

P4

8s PS

'T, is t h e rms e r r o r i n t h e d i r e c t i o n t o t h e rod of t heodo l i t e T, from Tl.

"A

"E

ar a2

a3

"4

"5'

'6'

The e r r o r s i n t h e angles @1,2,,,,,n are s i m i l a r l y obtained.

11".9

14 .4

22 .2

16 .4

7 .5

27 .7

17 .4

9 .o 8 .9 '

The r e s u l t s of computations using (4) are arranged i n Table 1. The

e r r o r s &l,2y...,x and &y2 col l imat ion e r r o r s [l].

were obtained using t h e standard r e l a t i o n s f o r 3 1

A t o t a l of 166 observation series were conducted.

10 .5 @ A aA 12 .8 PE. =E

32 9 .4 82

23 23 .6 P3 . 34 14 .1 84

"5' 7 .8 $5

'6' 7 .8 Bo'

6 .8 7 .4 4 .2 8 .1 9 .1 4 .5 4 $ 5

11".5 1'6 .8 23 .4 18 .4 7 .8 7 .1

Series 136-166

7".6

6 .8

8 .8

8 .5

4 .o 9 .5

9 .9

4 .2

4 .3

We see from Table 1 t h a t t h e e r r o r s in t h e angles ci and $ are from 4 t o 28".

observatipns do not exceed 1".

accurate.

atmospheric condi t ions , and t h e motion of t h e poles. The co l l imat ion e r r o r s

used i n these computations n a t u r a l l y changed from one pole t q another i n each

For comparison we recall t h a t the same e r r o r s i n geodetic t h e o d o l i t e

The i c e observations are thus n Q t p a r t i

This may be due t o i n s u f f i c i e n t experience of t h e ope ra to r s ,

96

series and from series t o series f o r each po le ,

imperfections and because of po le motion.

po le w a s observed only once, in order t o f

which took one t o two minutes.

Under t h e s e condi t ions , each

t h e "instantaneous" pos i t i on ,

Once t h e e r r o r s Aa and AB have been found, w e can compute t h e e r r o r s

e na te s as w e l l as i n any o t h e r chara t ics of ice

motion. F i r s t l e t us f i n d t h e e r r o r s i n t h e caord s. We d i f f e r e n t i a t e

nd s u b s t i t u t e t he e r r o r s for fhe d i f f e r e n t i a l s . Th ing t h e g th , we f i n d by (3)

(5) I -- cos2 @ ( A u ) ~ sin2 a (dp)2

sl i i2psln2 ( a +- p) Ax ?-: 1- ,y .{- - .- I/ cos:!a . sln2 (u 1 8)

where Ax, A 9 are the rms e r r o r s i n t h e coordinates Ax an

Taking t h e err nd y from Table 1, w e compute t h e e r r o r s Az and

used in observations. The r e s u l

g l e s c1 and 0 f o r po les 5 and 6 are

se f o r t he o t h e r poles correspond t

are ind ica t ed i n Table 2. The e r r o r s Ax and Azj

e discussed la te r on) f o r a l l po les , except 5 a

ted as ind iv idua l terms, a r b i t r a r i l y ex t r ac t ed from

a t i v e l y l a r g e series and varying wi th t h e v a r i a t i o n of t h e angles a and 8 . Taken on t h e i r own, of course, they do not represent t he series t o which

they belopg . he v a r i a t i o n of Ax and A 3 i n these series, however, i s r e l a t i v e l y s m a l l . This can be seen by comparing t h e values of AL an

t r y t o analyze t h e s i t u a t i o n . On each f l o e t h e r e are two poles. l e coord ina tes , w e can compute t h e d i s t ance between t h

I f z,,zjl and z2,y2 are the coordinates of po les 1 and 2, r e s p e c t i v

length of t h e segment L,,, between these poles is given by

L , - 2 z1 V ( X 2 - x , ) 2 + (y, --- (6)

This is a constant f i gu re . Computing t h i s length f o r each series, we f i n d a number of va lues of L,,, which d i f f e r from one another because of e r r o r s

97

i n t h e angles

given by

a and 6. The rms e r r o r f o r each member of t h i s series is

/- n

where n is t h e number of terms i n the series, i is t h e index of each term,

and Lm i s t h e mean length.

The same quant i ty can be found by a d i f f e r e n t method. We d i f f e r e n t i a t e

(6) by tak ing x1,2 and y1,2 as va r i ab le s ,

rms e t r o r s , w e f i nd from (3) the rms e r r o r i n L l m 2 , i . e . ,

Replacing the d i f f e r e o t i a l s w i th

where h=cl ,2 and Ay ,2 are t h e r m s e r r o r s of t h e coordinates of po les 1 and 2.

Equations (7) and (8) thus y i e l d t h e same r e s u l t , t h e rms e r r o r of t h e

d i s t ance between t h e poles (Table 2 ) .

ably c l o s e t o m (although i t has been computed from a r b i t r a r i l y chosen

observat ion series). This i nd ica t e s t h a t t h e v a r i a t i o n of AL(z,y)in e

series i s r e l a t i v e l y small, except f o r those i s o l a t e d cases which correspond

t o l a r g e devia t ions of the angles ci and @ from the mean.

Table 2 thus provide a f a i r l y f a i t h f u l representa t ion of t he e r r o r s Ax and

We see from Table 2 t h a t AL i

The d a t a of

L e t us a l s o consider the e r r o r s i n t h e areas between t h e poles and the

angles 9, nates . Consider t he t r i a n g l e with vertices YII, 4, and 3 (Fig. 2). L e t

t h e coordinates of these vertices be xvI144,3 and yyII,4,3, respec t ive ly ,

The area of t h e t r i a n g l e s with vertices a 1 , 4 , 3 is given by

The area between the poles can be computed from t h e po le coordi-

1 $- - I - -- 2 I(-%, - "a) (y.I -- Y J -. (XI - x:,) (Yv,, -- Y J I

Here t h e p lus and minus

i n bracke ts is p o s i t i v e

s igns are taken according t o whether t h e expression

o r negat ive, so as t o make t h e area A always pos i t i ve .

98

TABLE: 2

IN THE POLE COORDINATES OF KCJTATION OF THE

S REIATTVE T - b t (R

- I I -

1.31

0.56

0.25

0.46

0.78

0.86

Segment between poles Number

2 I 3 -

12 -

1.15

0.75

0.30

0.23

1 .a3

0.40

7 - 0.99

0.23

0.23

0.08

0 ,, 65

0.80

8 I 4

I 6

1-2 10

5

0.87

0.24

0.11

0,07

O S Q

0.59

138O29'53" x 15".6

94O 19'30" - +18" .Y

0.72

0.87

0.18

0,32

0.59

0.64

0.74

0.89

0.13

0.37

0.44

0.56

3-4

5-6

70@11'50°" & 18". 4

1-106

1 24

42@2P43" i 7 " . 1

51-61 77O31'33" - -r5".O

37010145" *7".0

39@00?22" . 2 Y . O

129 A-6

B-r 1 12

3 Writing f o r t he coordinates of poles 2,

1, and 111, respec t ive ly , x2 and y2, x1 and yl, zIII and yIII, w e ob ta in

similar expressions f o r t h e areas of

t Y

... r x

01

Fig. 2 , Area between poles .

t h e t r i a n g l e s with vertices VII, 3, 2; VII, 2, 1; and VII, 1, 111, which are

designated A2, A 3 , and A,, respec-

t i v e l y :

1 A4= Zk ICXVII -- #TIH)(Yl -- Y, , , ) - (XI - X,,,) iYv

Adding up these areas, w e f i n d t h e area of the poly We d i f f e r e tices VII, 4 , 3, 2, 1, 111, which we denote S.

tak ing t h e coordinates x ~ , ~ , ~ , , and y1,2,3,4 as the v a r i a b l e s and s u b s t i t u t e

t he m s e r r o r . for t h e d i f f e r e n t i a l s , Then, using (3 ) , we f i n d t h e rms e r r o r

i n t h e area of t h e polygon with vertices VII, 4, 3, 2, 1, 111, i .e. ,

Ls = F I (Yl, I - YJ2 (AX,), + (y, - yJ2 (Ax,)? +- (yz - y4) + 0’3 - YVll )? (AX,)” + (x^? - Xl1J2 (AY,)? + (.% - x^? ( (9)

-+ (-q - x*)? (Ay,)? + (XVII -- x3)*(Ay4)2p

Table 3 lists S f o r var ious observat ion series. following coordi-

na t e s were assumed i n t h e computations:

zIII = -485 m, yvII = yIII = 1350 m, xvII

Besides t h e area S , Table 3 a l s o gives t h e d i f f e rence As i n t h e areas between successive observat ion series, t h e e r r o r m i n s d i f f e rence , and

the e r r o r AS computed from (9) f o r t he e r r o r s i n t h e coordinates x~,~,~,,,

100

I

$1 9 2 9 394, l i s t e d i n Table 2.

= f V(LS# + (AS, + $2

where AS$ and AS$+l are successive e r r o r s AS from Table 3.

We see from Table 3 t h a t t h e e r r o r m is s i g n i f i c a n t l y less than the

d i f f e rence fb. As is s u f f i c i e n t l y high t o be considered r e l i a b l e ,

re fore , t he accuracy i n t h e determination of t h e d i f fe rence

TABLE 3

COMPUTED AREA s (m2) B VII, I11 FOR VARIOUS OB

.- -

Series I S 1 As I bS number , I I 1

1 2 3 4 5 7 8

12 I :3 14 16 17 20 21 22 39 40 48 54 59 70 74

+60 183 -65 178 -11 167 +29 665 - 220 52 1 -34 SO!) - 14 0#'$3 - - - e 3 1 5.16 - 20 4 1 I -59 153 1- 26 m 5 t 21 977 4-2,: 654 -21 355 +44 663 +I2 461 - 13 2%) -9 0G9

+69 -188 -9 8'24 +7 468 695

72 1

1 430 1435 1 470

I

I I

Fina l ly , l e t us consider t h e e r r o r i n t h e angle t h a t t h e se

1-2, 3-4, 5-6, e t c , , these angles from d i f f e r e n t observation seri

t i m e between the corresponding series, The angle $J f o r t h e segment 1-2 is

e

101

The same formula n a t u r a l l y a p p l i e s t o any o the r segment, provided t h a t t h e

coordinates C C ~ , ~ and y 1 , 2 a r e replaced appropr ia te ly .

r e l a t i o n and s u b s t i t u t i n g rm8 e r r o r s f o r t h e d i f f e r e n t i a l s , we o b t a i n by (3) D i f f e r e n t i a t i n g t h i s

The r m s e r r o r s i n $ computed from t h i s r e l a t i o n f o r d i f f e r e n t segments are l i s t e d i n Table 2. We see t h a t t h i s e r r o r , l i k e t h e e r r o r s Ax, Ay, and AL v a r i e s from segment t o segment between f a i r l y wide l i m i t s , depending on t h e

angle $, t h e e r r o r s Ax, Ay, and t h e d i f f e rences i n t h e PO

I n conclusion, no te t h a t i n observations of ice motion wi th theodo l i t e s

and similar survey instruments, t h e c a l c u l a t i o n of t h e angles Act and AB is of paramount importance, s i n c e they permit computing t h e e r r o r s Ax, AZJ, AL, A$, AS, e t c , , and thus enable us t o determine t h e accuracy of t h e method.

ca l cu la t ed t h e e r r o r s Aa and AB from (4) using t h e e r r o r s i n d i r e c t i o n which

i n t u r n had been computed from the standard r e l a t i o n s f o r co l l imat ion e r r o r s

[ l ] . cons tan t lengths L. The errors i n L were a l s o computed from ( 7 ) . Comparison

of AL and m shows t h a t t hese two are c l o s e t o each o the r . This i n d i c a t e s t h a t

t h e method of determinat ion of t h e e r r o r s Aa and AB t h a t w e borrowed from

geodesy (where i t is genera l ly used f o r f ixed ob jec t s ) is a l s o app l i cab le t o

moving poles .

e r r o r s i n t h e angles a and B . r e s u l t s by using r e l a t i o n s ( 7 ) and (8).

We

The e r r o r s Act and AB were appl ied i n (8) t o f i n d t h e e r r o r s AL i n t h e

W e t he re fo re recommend t h i s method f o r t h e determinat ion of

I f is of course d e s i r a b l e t o doublecheck t h e

Note t h a t t h e accuracy i n determining x,y and the main elements of i c e

motion can be impro d several t i m e s over by t i n g t h e observa t ion r e s u l t s

wi th p a r t i c u l a r l y 1 ge e r r o r s . These are ea de tec ted by examining t h e

series of L va lues .

The computations w e r e performed on t h e URAZ-2 computer us ing t h e pro-

grams of E. s. Mednikova.

102

BIBLIOGRAPHY

1. Gram, A. V. Applied Geodesy. Leningrad-Moscow: Glavnaya redakts$ya geologicheskoi i geodezicheskoi l i teratury, 1934.

2. Iordan, W. Randbook of Geodesy, Vol. 1. Moscow: Redbyuro GUKG, 1939.

I

Yu. R. Nowikov

The possibilities 1 of processing aerial ice surveys by automation are being investigated in Computer Laboratory and the Laboratory of Instru- mental Ice-Survey Meth at the Arctic and Antarctic Institute. Automated

processing would both d up the treatment and yield an objective quanti- - tative analysis of the cover which is not dependent on the individual qualifications and exp ce of the operator.

Aerial ice surve e used to determine a whola range of ice-cover characteristics which eded for compiling ice charts. From the point of view of automation two groups, The first of the ice age, i.e., one has only to distin

the camera or other su includes those charact knowledge of the age p certain definite concl characteristics, we th tiating ice formations analysis of ice of var for age differentiation,

ements, the characteristics can be divided into includes those which do not require knowledge

tion and size distribution of ice, Technically, etween ice and water surface in this case, if

instrument saw clear water. n e second group s which cannot be determined without proper s of particular ice floes, since ice age gives bout the thickness of ice. To determine these

re certain quantitative indices for differen- This paper presents the results of a computer

groups intended to extract stable indices

The analysis was out using aerial photographs of arctic ice which were scanned by Laboratory. In the fi e of recognition algorithm development, we

worked with photograph by age by ice survey specialists. density readings runs into a difficulty which is associated with the

nonuniform illumination in the focal plane of the camera.

atic microphotometer developed at the Computer

ad been definitely identified and classified The processing of the microphotometer

This difficulty

105

a

can be overcome i n several ways,

t i v e mask taken wi th the same camera from a uniformly i l lumina ted smooth

surface. This method, however, r equ i r e s knowledge of t he f i l m y. No sens i to-

met r ic c o n t r o l was attempted f o r t h e f i lms used i n t h e surveys, so t h a t t h i s method could not be used.

One i s t o cover the nega t ive wi th a posi-

Another method uses the a n a l y t i c a l expression f o r t h e nonuniform

i l l umina t ion i n t h e f o c a l p lane t o in t roduce co r rec t ions i n t o t h e measure-

ments.

nonuniformity i s propor t iona l t o cos3 a, where a is t h e d e f l e c t i o n angle of

t h e ray from the o p t i c a l axis of t h e l ens . This method, however, a l s o r equ i r e s

knowledge of y,

For t h e p a r t i c u l a r l e n s used i n t h e surveys, t h e i l l umina t ion

We used a d i f f e r e n t method which, i n s t ead o f measuring t h e abso lu te

photographic d e n s i t i e s , measured t h e d i f f e r e n c e s i n dens i ty between two

near po in t s .

of t h e camera l e n s , t h e nonuniform i l l umina t ion can be ignored.

t he e r r o r due t o d i f f e rences i n y of var ious f i lms , t h e dens i ty d i f f e r e n c e s

on each microphotometer t r a c i n g were normalized t o a mean average dens i ty

d i f f e rence f o r a given photograph. This approach adequately r e f l e c t s t h e

t r u e condi t ions of an aerial survey, when t h e b r igh tness of t h e s u r f a c e

o b j e c t s may vary between wide l i m i t s . Our problem was t o determine s t a b l e

c h a r a c t e r i s t i c s of t he dens i ty d i f f e r e n c e elements which would be s u i t a b l e

I f t h e po in t s epa ra t ion is s m a l l compared t o t h e f o c a l d i s t a n c e

To reduce

f o r i d e n t i f y i n g ice age under real conditions.

Stat is t ical Charactefistbs of Densi ty Elements. The computer w a s used t o analyze t h e mean dens i ty d i f f e r e n c e c\Dx102, t h e var iance G, t h e

k u r t o s i s a , and t h e skewness E [ 3 , 4 ] , Table 1 lists these parameters f o r

two i c e groups: Most of t h e observa t ion

material r e f e r r e d t o these p a r t i c u l a r age groups. We see from t h e t a b l e

t h a t t h e mean dens i ty d i f f e r e n c e i s c l o s e t o zero.

fe rences are taken wi th t h e i r proper s ign , t h e zero mean p o i n t s t o a

symmetrical d i s t r i b u t i o n on t h e photograph,

by t h e skewness c o e f f i c i e n t .

young ice is more peaked than t h a t f o r o ld i c e .

t h i c k one-year ice and o ld ice.

Since t h e dens i ty d i f -

This conclusion is borne ou t

The k u r t o s i s shows t h a t t h e d i s t r i b u t i o n f o r

W e see from Table 1

106

T A B U 1

TERISTICS OF THE DENSITY DIFFERENCE RIAL PHOTOGRAPHS OF ICE

Thick one-year i c e 11 Old i c e

-1.68 - 0.5.5 -0.68 -2.10 -2.12 --1.81 -1.64 -0.74 -1.27 -2.07

5.62 2.75 3.56

16.86 12.75 8.29 7.50 5.21 4.71

i2.77

67.00 51.00 46.00 82.00 75.00 52.00 74.00 69.00 &3.00 89.00

t h a t t h e va r i ance o r t he rms dev ia t ion of t

as an i ~ d e x of i c e age determination. t y elements may be used

Figure 1 shows t h e histogram d i s t r i b u t i o n of t h e var iances f o r two

series of microphotometer t r a c i n g s ,

one-year ice and o the r 25 photographs of old ice. grams t h a t t h i c k o

dens i ty elements than t h e o ld ice, b u t t he two d i s t r i b u t i o n s neve r the l e s s

overlap a t p r o b a b i l i t y d e n s i t i e s of P(0.7) = 0.05.

One series contained 25 photographs of

W e see from t h e h i s to -

ar ice is charac te r ized by a smaller va r i ance of

~.

A N N’

02 i - 7 ’ ,-,

“1-1 “:i I 0

O’\ J’, , , 2 ,

ograms of 0 f o r t h i c k one-year (I) and o ld (2) ice.

0.4 0.8 0.8 1.0

W e know from s t a t i s t i c a l theory [3,4] t h a t c o r r e l a t i o n func t ions

provide va luable information on t h e mutual d i s t r i b u t i o n and r e l a t i o n s h i p s

f o r t h e elements of s ta t i s t ica l series. c o r r e l a t i o n func t ions of the dens i ty elements f o r our microphotmeter

t r a c i n g s - i g u r e 2 shows t h e averaged auto-

Analysis of t hese func t ions r i n g s o u t t h e s t a b l e mechanism of

107

formation of ice profiles; the basic element on photographs of thick one- year ice is smaller than on photographs of old ice, and its recurrence period is smaller. of the two ice groups (Fig. 3 ) . For one-year ice, the spectrum has a maximum for elements of about 10 m, whereas for old ice the peak is shifted to sizes of 14-15 m.

This difference is even more conspicuous

IO2

Fig. 2. Normalized auto- Fig. 3. Statistical spectra correlation functions of density difference elements for one-year ( 2 ) and old and old (2) ice. (2) ice.

of density difference elements of one-year ( I )

The calculations thus show that the statistical characteristics of ice

density elements, in particular the variance and the autocorrelation function, permit classifying ice formations by age.

Stat is t ical Characteristics of Microphotometer Tracings. Fast compu- tation of statistical characteristics and autocorrelation functions is possible only with the help of modern camputers. One of our tasks was t o develop sufficiently simple algorithms for these computations. We therefore investigated of the microphotometer was defined as the

another algorithm, one which computes the wavelength tracing and its amplitudes [2,5]. The wavelength distance between two successive maxima and the

108

amplitude wa

values of t he wave.

puted, i.e., t he mean, t he var iance, etc.

shows t h a t the m e

most s t a b l e chara

&en as t he d i f f e rence between the peak and va l l ey dens i ty

The s t a t i s t i c a l moments o hese variables were co

Analysis of t h e n u e r i c a l results

elength 7 and t h e m a n amplitude

ties of t h e t r ac ing ,

are among t he

Figure 4 shows t h e d i s t r i b u t i o n of and f o r the same series of

photographs f o r which the s ta t i s t ica l c h a r a c t e r i s t i c s and the autocorrela-

t i o n func t ions of t he dens i ty elements have been computed.

histograms t h a t x and z a l s o c o n s t i t u t e s u f f i c i e n t l y s t a b l e age charac te r i s -

t ics of ice. Figure 5 a two-dimensional d i s t r i b u t i o n of x and r, We see

t h a t the d i f f e r e n t age groups f a l l i n d i s t i n c t s epa ra t e regions according

to these ind ices . Further i d e n t i f i c a t i o n i n t h i s case may be c a r r i e d out by

W e see from the

Fig. 4. Histograms of z (a) and x (b) f o r one- year (I) and old (2) ice.

the method of c u t t i n g planes. f o r t h i c k young

i c e and o ld i c e never the less overlap f o r P(z+ 0.05 and P(h) - 0.05.

Further refinement of these c h a r a c t e r i s t i c s may thus i n d i c a t e t h a t t he two-

dimensional regions defined by these parameters a l s o overlap.

recogni t ion should the re fo re be conducted by one of t he p robab i l i t y methods,

using a given e r r o r [l].

The d i s t r i b u t i o n s of 'i; and

) The a c t u a l

-

1 (m)

Fig, 5. Two-dimensional d i s t r i b u t i o n of one-year (I) and o ld (2) ice according to and x.

109

-

The results of our study show that stable characteristics for age differentiation of ice formations can be determined from aerial survey photo- graphs. given error. have to be improved using a larger sample and similar indices have to be derived for other ice groups.

From these age characteristics, ice thickness can be found with a For further application of our results, the quantitative indices

BIBLIOGRAPHY

1. Barabash, Yu. L, B. V. Varskii, et alb EZements of the S ta t i s t ica l Recognition Theory. Moscow: "Sovetskoe 0 ," 1967.

for Interpretation of Sea Ice AerYial S w e y Photographs. Leningrad: AN SSSR, 1963.

3 . Romanovskii, V. I. Elementary Cowse i n Mathematical S ta t i s t ics .

2 . Gonin, G. B. and D. A . Yanutsh. Microphotometyiy as un Objective Method Moscow-

Moscow-Leningrad: Gosplanizdat, 1939,

4 . Smirnov, N. V, and I. V. Dunin-Barkovskii, Probability Theory and Mathemtical S ta t i s t ics . Moscow: "Nauka , I 1 1965.

5. Yanutsh, I). A. photographs, obrabotki aerosnimkov.

Microphotometry as a method of interpretation of aerial In Voprosy deshifrirovaniya i fotograrmnetr4cheskoi

Moscow-Leningrad: AN SSSR, 1963.