P i l a r c z y k K . W . S e n i o r Eng i n e e r

IAHR Ice Symposium 1984 Hamburg

PREDICTION OF ICE FORMATION FOR THE EASTERN SCHELDT I N THE NETHERLANDS

SY NOP S I S

Delta Depar tment The N e t h e r l a n d s Hydr a u 1 ics D i v i s i o n Rijkswaterstaat

The E a s t e r n Sche ld t is t h e l a s t t i d a l e s t u a r y to be closed w i t h i n t h e scope o f t h e Delta P l a n i n t h e N e t h e r l a n d s . The r e s u l t w i l 1 be a s to rm- surge barrier a t t h e e n t r a n c e of t h e t i d a l b a s i n t o g e t h e r w i t h compar tment dams s e p a r a t i n g t h e t i d a l E a s t e r n Scheldt from a new f r e s h w a t e r lake. One o f t h e aspects s t u d i e d i n c o n n e c t i o n w i t h d e t e r m i n i n g t h e d e s i g n c o n d i t i o n s for t h e s to rm- surge barrier and t h e c o n s e q u e n c e s of c l o s u r e f o r t h e env i ronmen t and n a v i g a t i o n was t h e f o r m a t i o n and movement of ice. Because of t h e l a c k of data no s t a t i s t i ca l a n a l y s i s o f ice data was possible. The p r e d i c t i o n of ice f o r m a t i o n was based o n t h e a n a l y s i s of t h e a v a i l a b l e data on a i r and water t e m p e r a t u r e c h a n g e s d u r i n g t h e w i n t e r periods. For t h e ice- growth a fo rmula was d e r i v e d a n a l y t i c a l l y . The n u m e r i c a l c o n s t a n t s i n t h i s fo rmula were o b t a i n e d from a compar i son w i t h l i t e r a t u r e data and some p t e v i o u s l y o b s e r v e d data o n ice f o r m a t i o n i n t h e area c o n c e rned . . -.

1 HOEKVAN HOLLAND 2 ROTTERDAM

& 3 GORINCHEM N_O_ORO_H'N OER FROM 1859

10 St. ANNALAND 11 WISSEKERKE 12 VERE 13 WOLPHAARTSDIJK 14 KATSEVEER 15 LODIJKSECAT 16 VLISSINGEN 17 BATH

8 [ ~ ~ E ~ o ~ ~ ~ : ~ ~ ~ ~ ~ ~ ~ T l ~ ~ s

$j CLIMATOLOGICAL HEAD -STATION

& LIGHTSHIPS 18 WOENSDRECHT

A : STORM-SURCE BARRIER

6 : OESTERDAM c : PHILIPSDAM

Fig.1. E a s t e r n Scheldt and t h e dams under c o n s t r u c t i o n . Climatological s t a t i o n s i n t h e Delta area.

INTRODUCT ION b

The Eastern Scheldt is the largest and therefore the l a s t t ida l basin to be closed under the Delta Plan. As a resul t of the Delta Works the flow of the rivers Rhine and Maas through the southern part of the region was restricted: the Volkerakdam, completed i n 1969, c u t off southward flow almost completely. The Eastern Scheldt can therefore be regarded as an estuary subject to only very limited freshwater influence. The Eastern Scheldt has not only a v i t a l function i n nature conservation b u t also an important role w i t h regard to shipping. A large proportion of the shipping going t o Antwerp and other trade centres along the Western Scheldt passes through the Eastern Scheldt.

The execution of the present plan regarding the Eastern Scheldt w i l l result i n a storm-surge barrier a t the entrance of the t i d a l basin together w i t h two compartment dams (Philipsdam and Oesterdam) , separating the (reduced) t i d a l Eastern Scheldt from a new freshwater lake (see f i g . 1 ) .

Much research has also been done to determine the design conditions for the storm-surge barrier and the consequences of closure for the environment. ûne of the aspects studied was the formation and movement of ice. I n order t o solve the various problems of interaction of ice w i t h engineering structures, it is necessary to have some basic knowledge of the formation and types of ice i n the area under consideration. However, data on ice formation and movement i n the Western and Eastern Scheldt are rather scarce. The reason for t h i s is that ice is not normally considered to be a dominant problem i n the South-West Netherlands, where the probability of having a severe winter is about 1/10 per-year. However, it has to be taken into account i n t h e design process regarding the possible ice forces which w i l l be exerted on structures, especially when a design load w i t h a probability of exceeding of 2.5 x 10°4 per year is chosen as a design cr i ter ion, as it is a case for the storm-surge barrier. Moreover, the forming of a freshwater lake behind the the compartment dams w i l l have a very significant influence on the ice regime and t h u s on the duration of the hindrances t o navigation caused by ice.

Because of the lack of the proper data no s t a t i s t i c a 1 analys'is of ice data was possible. Therefore, the prediction of ice formation was based on the analysis of the data on a i r temperatures for t h i s area and restr ic ted data on water temperature changes during some winter periods. For the ice-growth a formula was derived analytically.

I n t h i s paper the present situation w i t h regard to the formation and movement of floating ice i n the Eastern Scheldt and the influence of the damming up of t h i s t i da l estuary w i l l be discussed.

CLIMATOLOGICAL CONDITIONS

The region of t h e large estuaries i n the south-west is favourably affected by the G u l f Stream whose influence reaches inland. I n addition the existence of sea and/or brackish water there reduces the occurrence of ice. Consequently, ice is not a very common occurrence i n t h e Du tch estuaries. Most winters i n the south-western part of the Netherlands are characterised by short periods of moderate f ros t , alternatecl by thaw w i t h l i t t l e or no ice a t a l l .

The genera1 annual-cycle of the average monthly (1961-'70)air- and water temperatures for s tat ion Vlissingen and t h e temperatures for seawater (Goeree) and for the western part of the Eastern Scheldt (Zierikzee) are given i n figure 2.

x _ . - . ~. " . I _ _ - -- - . - - _ - _ _ _ . .^__ _ _ _ _ -

E cr

1

u 20

z

2 - 15-

ï-4 -

I - -

5 10

I

w a -

4

a -

---- - AIR TEMPERATURE VLISSINGEN (TA ) - WATER TEMPERATURE VLISSINGEN ( TW )

0 WATER TEMPERATURE ZIERIKZEE

O WATER TEMPERATURE LIGHT-SHIP GOEREE

ûccasionally winters are very severe. The winter 1962/63 is an example of a very severe winter. Its characteristics including the mean air temperatures at reference station Vlissingen and the water temperatures stations mentioned

\. above are presented in figure 3. \

Fig.2 Year-cycle of the monthly air-and water temperatures. (Period 1961-1970).

( 7 ) + max individual ico - poriod

'I + - I i- max. ico - growth poriod ( 70 days

- 11 J

Fig.3. Characteristics of the winter 1962/63. South-West Netherland. . - ~ .-- - I . - - ~- - __

1

5

f - . . . _ . . .. . - . . .. . , .

I

EQUATION FOR PREDICTING ICE THICKNESS

I f t h e d a t a on r e p r e s e n t a t i v e ice t h i c k n e s s are n o t a v a i l a b l e , a less a c c u r a t e estimate c a n be o b t a i n e d from c l i m a t o l o g i c a l d a t a for a g i v e n r e g i o n , which are u s u a l l y a c c e s s i b l e . The f i r s t approach i n t h i s d i r e c t i o n was made by S t e f a n i n 1881 ( 7 ) - H i s e q u a t i o n h a s been u s e d w i t h c o n s i d e r a b l e s u c c e s s i n t h e m o d i f i e d form

B h = asg

where Sg known as t h e f r e e z i n g e x p o s u r e , is t h e cum o f n a g e t i v e d a i l y a i r t e m p e r a t u r e s i n c e f r e e z e- u p (below f r e e z i n g p o i n t ) , h is t h e ice t h i c k n e s s , Q is an empirica1 c o ë f f i c i e n t c o n s i d e r i n g snow c o v e r , stream flow, and o t h e r local c o n d i t i o n s , and B is a n o t h e r empirica1 c o ë f f i c i e n t e q u a l to a b o u t 0,5. It is recommend t h a t = 2,7 be used f o r f r e s h w a t e r- l a k e ice and a = 2- 2 . 4 f o r sea-ice ( 2 , 4 ) . I f Sg is i n deg ree- days ( C e l s i u s scale) and t h e s e v a l u e s of a and B are u s e d , h w i l 1 be i n cm..

a c c o u n t is t a k e n o f c o n v e c t i v e h e a t t r a n s f e r a t t h e ice-air i n t e r f a c e . I n t h i s case, t h e b a s i c h e a t t r a n s f e r e q u a t i o n becomes

Another more a c c u r a t e form of ice g rowth e q u a t i o n may be o b t a i n e d when

o d h e K i d t e h + K i L.p- =

where L is t h e l a t e n t h e a t , K i is t h e mean t h e r m a l c o n d u c t i v i t y , O is t h e t e m p e r a t u r e d i f f e r e n c e be tween t h e top s u r f a c e o f a n ice c o v e r and t h e water under it a t a t i m e t , a n d ' e is t h e overall c o ë f f i c i e n t of s u r f a c e h e a t t r a n s f e r . I n t e g r a t i o n w i t h respect to h g i v e s

t

h 2

or A e h2 + - h - 24BSg = O

where A = 2 K i r B = 2 Ki/L.t, and c

- sg - 2 ( i n " C x d a y s )

( O - h o u r l y mean a i r t e m p e r a t u r e s ) . F i n a l l y

h =J(d(:)2 + 96BSg'- ") e

For sea-ice w i t h s a l i n i t y of a b o u t 4 o / o o t h e f o l l o w i n g c h a r a c t e- r i s t i c v a l u e s may be assumed used as r e p r e s e n t a t i v e :

- t h e r m a l c o n d u c t i v i t y of ice : K i = 2 W/m/'C =

- l a t e n t h e a t of ice : L = 300 kJ/kg - d e n s i t y o f ice : p = 920 kg/m3 +

0,072 kJ/hr/cm/"C

920.1 0'6kg/cm3

ü s i n g t h e s e v a l u e s and d e f i n i n g h i n cm. and Sg i n "C x days t h e f o r m u l a for ice t h i c k n e s s ( w i t h o u t snow c o v e r ) is m o d i f i e d to

,-

where 'e ' is the coefficient of surface heat transfer expressed i n w/m2/ o c , The values of 'e'equal t o 6 W/m2/'C for a calm weather and about 26 W/m2/'C for wind-speed of 10 m / s are often mentioned as representative ones(5). I n the case of t h i s s t udy the value of 'e ' equal to 13,3 W/m2/'C has been applied. I n t h i s case the formula can be rewritten as

h = % ( \/go0 + 50 Sg'- 30)

where h is i n cm and Sg i n "C x days. I n figure 4 both the modified formula of Stefan and the l a s t

formula are compared w i t h l i t e ra tu re data and some previously observed indicative data of ice thickness for the area concerned. The l a t e s t were observed a t shallow locations and are not therefore very representative for the whole area. Because of better agreement w i t h prototype data and because of safety reasons the l a s t formula has been chosen as the most representative one,

GROWTH N a C l - C E [i1

X 29.61 NO SNOW

- CEA-CE i THULE , GREENLAND 9 1 j 1 1 1 0 NO CNOW

3 I I j l 8 7.6 cm POWDERSNOW ON IC€

I I I I I I I I

Fig.4. Growth of ice, hice = f(Sg) ,

i n the formulas discussed above the parameter Sg is defined as accumulated degree-days of frost below the freezing point of water since f i r s t freeze-up. The point of the f i r s t freeze-up depends to a great extent on local conditions. I n the case of inlets/estuaries sa l in i ty and the exchange of heat w i t h warmer seawater is mostly much higher a t t h e mouth (entrance) than inside. Moreover, i n larger areas, the local a i r temperatures may d i f fer from each other a t the Same time. Thus, for practica1 application, it is suitable to define Sg as

f

where: )o - correction factor of 10-cal air-temperature related to reference station where Smax

hax - sum of negative daily air temperature since the first moment that air temperature falls below the freezing point of water.

Smin - cum of negative daily air-temperatures since a first freeze-up.

is defined.

The final form of the ice-growth (thickness) formula becomes

h = +(t/900 + 30)

To calculate the ice thickness at different locations inside the sea-estuaries parameters ‘9, Sma, and Smin must be determined. This can

. be done through the elaboration of available air-temperatures for frost periods ( p , Smax) and available water temperatures and ice formation data (+Smin) . If the latest data are not available, the best possible estimate (quess) has to be made.

THE CONDITIONS UNDER WHICH ICE FORMATION TAKES PLACE (Smin).

Surface water temperature change parallels air-temperature change during the first stage of cooling of freshwater and during the whole stage of cooling of seawater. Because of that it should be possible to ectablish a relationship between air and water temperature. (10, 1 1 , 12). The simplified mathematica1 expression, based on the assumption that the rate of heat loss from water surface depends on air water temperature difference is:

dTw = Tw - Ta dt A -

where: Tw = surface water temperature, which is assumed to remain essentially constant to depth d (depth of convective mixing), and Ta= air temperature.

Parameter A defines the retardation phase difference in the adjustment of water temperature to ambient air temperature. The procedure is to determine that value of A which reduces a weighteä air temperature sequence to the freezing point of water.

The relationship between air temperature and surface water temperature has been succesfully applied to predict ice formation in areas with relatively stable winter periods ( 8 ) . The sensitivity of surface ice formation to var iable weather conditions during the f inal stage of cooling is one reason why freeze-up data fluctuate within rather wide limits. In milder regions, an ice cover may freeze, then melt under milder conditions, before freezing into a permanent ice cover. That makes the applicability of this method to milder (unstable) regions i.e. the Netherlands difficult and/or questionable. However, even in the last case, this method may be a useful tool in understanding a problem.

In the present study the background data needed to calculate the parameter A were not available. Therefore a simple linear approximation was applied and the following average values of A (= retardation time) were roughly established: Goeree (seawater, close to the coast) : A- 35 days Vlissingen (mouth Western Scheldt) Zierikzee (western part of Eastern _ _ _ - _ - .

: A 4 9 days Scheldt) : A 4 2 days . ._ I - -- - - _ - r -

a . ..

i

The values of Sminr referred to two freezing points (Tv = O" C and Tv= -1.5O C ) , defined both by the linear approximation (a i r water temp. relationship) and by the real values for the winter period 1962/63 are given i n table 1 for different locations i n the Western and Eastern Scheldt.

Table 1: Sm;* - values for locations i n the Delta area.

Station

L i g h t s h ip Goes ee (seawater) Vlissingen Western Bath Scheldt Zier ikzee (west part) Eastern

Scheldt Lodijkse Gat (east part)

Tv

-1,s

-1,6

-1,6 -015

-1,5

Date for

Tw = Tv

18-01-63 03-01-63 11-01-63

27-1 2-62

l inear aPPr . 180

66

40 -

7

rea l 62/63

240")

113 53 79

23

NB. Date for Ta ,< Tv: 23/12/1962; * ) estimated values.

l inear aPPr . 1 O0

30

12 -

O

- real 62/63

170*)

71 33 45

-

15

-

The Smin,ValUeS for Goeree (seawater) are only roughly estimated because freezing point was not reached during the cooling period i n 1962/63; the decrease i n the water temperature stopped a t about O' C when t h e negative a i r temperatures became less than -5" C. That means that the growth of Sg-values only does not quarantee a decrease i n water temperature; a certain m i n i m u m difference is also needeà between a i r and water temperature which compensates for the locally present influx of heat by heat transfer into the atmosphere.

A comparison of the real and l inearly approximated values of Smin allows the conclusion t o the dram that the h i g h fluctuations i n the a i r temperature changes during a cooling period resul t i n h igher S,in-values than i n the case of gradually decreasing air-temperatures.

Because the purpose of the present s tudy was to predict ice formation and ice growth during very severe winters w i t h a low probability of occurence, it was reasonable to assume that during future severe winters there w i l 1 be a real chance of a winter w i t h a nearly linear (gradual) decrease i n a i r temperature during a cooling period. I t was therefore decided to use t h e Smin-vâlues obtained throughout the l inear approximat ion for the winter 1962/63 as representative (i.e. on the safe s ide) for f u t u r e severe winters.

FREQUENCY ANALYSIS.

The quantity Sg representing the accumulated degree-days of frost below freezing point is the main factor governing the formation and growthof ice. T h i s quantity may be also used for the classif icat ion of w i n t e r s . As mentioned before, most winters i n the south-western part of the Netherlands are characterized by short periods of moderate f ros t alternating w i t h shorter or longer periods of thaw. It is therefore d i f f i cu l t to define the representative f ros t perioä w i t h respect to

~ "- - _ _

r e p r e s e n t a t i v e ice growth. To a v o i d t h i s problem t h e f o l l o w i n g d e f i n i t i o n was a p p l i e d : i f t h e cum of p o s i t i v e a i r t e m p e r a t u r e s ( r e f e r r e d to f r e e z i n g p o i n t ) d u r i n g thaw p e r i o d ( s d ) which takes place between t w o f r o s t p e r i o d s , is equal or l a r g e r t h a n h a l f o f t h e cum of t h e n e g a t i v e t e m p e r a t u r e s (Sg) o f t h e p r e c e d i n g f r o s t p e r i o d , t h e n these t w o f r o s t p e r i o d s are c l a s s i f i e d as independen t ( i n d i v i d u a l ) p e r i o d s . I n such a case, t h e p e r i o d w i t h a l a r g e r Sg w a s t a k e n as t h e r e p r e s e n t a t i v e one f o r a g i v e n w i n t e r . When t h e opposite was t r u e , b o t h f r o s t p e r i o d s ( i n c l u d i n g thaw perioä) were t a k e n t o g e t h e r as t h e r e p r e s e n t a t i v e f rost period ( b o t h n e g a t i v e and p o s i t i v e t e m p e r a t u r e s were added t o g e t h e r ) . It is known t h a t t h e i n f l u e n c e of p o s i t i v e t e m p e r a t u r e s c a n n o t be l i n e a r l y compensated f o r by n e g a t i v e t e m p e r a t u r e s . I t was, however, a safe assumpt ion i n a l i g h t of t h e purpose of t h e s t u d y d i s c u s s e d .

The q u a n t i t i e s Sg were c a l c u l a t e d for e a c h w i n t e r w i t h r e f e r e n c e to t w o f r e e z i n g p o i n t s : Tv = O" C and Tv = -1,5" C. The f r e e z i n g p o i n t o f f r e s h water was of i n t e r e s t because o f t h e p l a n s to form f r e s h w a t e r lake behind t h e compartment dams i n t h e e a s t e r n part of t h e E a s t e r n S c h e l d t . The Sg-values were c a l c u l a t e d f o r t h e p e r i o d 1876-1975 ( V l i s s i n g e n as a r e f e r e n c e s t a t i o n ) . To o b t a i n c u r v e shoa ing t h e p r o b a b i l i t y of Sg-values be ing exceeded, t h e normal p r o b a b i l i t y paper was used (Fig.5) .

0,Of QOS OJ 42 6$ 1 2 5 l0 20 30 4û 50 - EXCEEDANCE PERCENTAGE ( * I e )

F i g . 5 . Exceedance of Sg-values . RESULTS.

To c a l c u l a t e t h e local i c e- t h i c k n e s s t h e local Sg- value h a s to be used. The mean a i r t e m p e r a t u r e s i n t h e c e n t r a 1 part of t h e E a s t e r n S c h e l d t i n t h e w i n t e r p e r i o d s are abou t 0,5' C lower t h a n t h e s e a t V l i s s i n g e n . The c o r r e l a t i o n between t h e e q u i v a l e n t Sg-values a t V l i s s i n g e n and t h o s e a t t h e s t a t i o n i n t h e e a s t e r n part of t h e E a s t e r n S c h e l d t y ie lds .

Sg(E .Sche ld t ) 1.20 Sg (Vlis- s i n g e n )

Factor 1.2 is t h e c o r r e c t i o n factor ( 9 ) i n t h e formula on ice growth when applied to t h e e a s t e r n part of t h e E a s t e r n S c h e l d t .

1

The f o r e g o i n g c h a p t e r s have shown how t h e d a t a needed for t h e p r e d i c t i o n o f ice f o r m a t i o n and ice growth have been collected. By combining t h e c a l c u l a t e d d a t a w i t h a n a v a i l a b l e q u a l i t a t i v e d e s c r i p t i o n of d i f f e r e n t ice s t a g e s a t c e r t a i n d a t e s d u r i n g v a r i o u s w i n t e r s i n t h e Delta area, a comprehensive p i c t u r e of ice f o r m a t i o n and ice movement i n t h e area concerned may be ach ieved . Using t h e s e d a t a , an approach h a s been made to c l a s s i f y i n g t h e w i n t e r s i n t h i s area i n terms of Sg q u a n t i t y (Fig .6) . -. - - -

3

I WINTERS WARM MILD MODERATE

DRIFT ICE

LIGHT ICE s - 2 cm

RATHER HEAVY CE

VERY SEVERE ( EXTREME) ir! SEVERE

HHEAVY ICE

EXCEE0ANCE:Ib

b! HARBOURS FROZEN I I

O O 5 4 2: 2 0 b, fi (o in c) 9

NO NAVIGATION OR HEAVY OBSTRUCTED

- .-

Fig .6 . Expected ice s t a g e s as f u n c t i o n o f Sg f o r v a r i o u s l o c a t i o n s i n t h e Delta area,

.-

The f u t u r e s i t u a t i o n i n t h e E a s t e r n S c h e l d t depends l a r g e l y upon t h e method o p e r a t i o n of t h e g a t e s . However, t h e open ing of t h e s to rm- surge barrier is so l a r g e t h a t t h e s e is a r e d u c t i o n o f less t h a n 20% i n t h e t ide . Moreover, t h e g a t e s w i l l be closeä o n l y i n t h e e v e n t of a v e r y s e v e r e storm b e i n g predicted ( n o t u s u a l d u r i n g f r e e z i n g period), Because of t h a t , t h e change i n h y d r o l o g i c a l c o n d i t i o n s r e g a r d i n g i n p a r t i c u l a r t h e factors i m p o r t a n t f o r ice f o r m a t i o n ( s a l i n i t y , i n t r u s i o n of warmer seawater, etc.) w i l l be r a t h e r smal1 i n compar i son to t h e p r e s e n t s i t u a t i o n . T h a t means t h a t t h e i n f l u e n c e of t h e damming up of t h e t i d a l E a s t e r n S c h e l d t on t h e f o r m a t i o n and movement of f l o a t i n g ice i n t h e s e waters w i l l be n e g l i g i b l e .

The s i t u a t i o n w i l l be q u i t e d i f f e r e n t o n t h e f r e s h w a t e r lake (Zoommeer Lake) b e h i n d t h e compartment dams. Because it w i l l c o n s i s t of f r e s h water w i t h o n l y s e c o n d a r y c u r r e n t s ( r e f r e s h i n g d i s c h a r g e ) , a solid ice cover w i l l form r a t h e r q u i c k l y once f r e e z i n g c o n d i t i o n s have set i n , T h i s w i l l r e s u l t i n a c o n s i d e r a b l e change i n t h e d u r a t i o n of t h e h i n d r a n c e to n a v i g a t i o n c a u s e d by ice on t h i s i m p o r t a n t n a v i g a t i o n way be tween Ro t t e rdam and t h e W e s t e r n S c h e l d t (e.g. from Antwerpen) , The p r o b a b i l i t y o f o b s t r u c t i o n to n a v i g a t i o n w i l l i n c r e a s e from a b o u t 10% i n t h e p r e s e n t s i t u a t i o n to a b o u t 20% i n t h e f u t u r e . The d u r a t i o n of t h e h i n d r a n c e w i l l be d o u b l e its p r e s e n t d u r a t i o n n o t o n l y b e c a u s e of t h e l o n g e r l i f e t i m e of f r e s h w a t e r ice b u t also b e c a u s e no effect w i l l be f e l t from e a s t e r n winds ( t h e p r e s e n t r o u t e f o r d r i f t ice to t h e sea w i l l be b locked by f u t u r e compartment dams).

For d e s i g n p u r p o s e s of t h e s to rm- surge barrier a t h i c k n e s s of 4 5 cm. h a s been chosen as r e p r e s e n t a t i v e . The diameter of ice-floes is m o s t l y r e s t r i c t e d b e c a u s e of t h e i n f l u e n c e o f t h e t i d a l flow (based o n past o b s e r v a t i o n s ) and h a s been assumed e q u a l to a b o u t 15 m, By d e f i n i n g t h e d r i f t v e l o c i t y of ice floes (velocities of t i d a l flow and s u p e r p o s e d w i n d- d r i f t effect) and t a k i n g i n t o a c c o u n t t h e above men t ioned d i m e n s i o n s of t h e ice-floes t h e forces r e s u l t i n g from

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interaction with the structure (i.e. piers) have been calculated. Static ice thrust due to jamming has alco been considered. None off these forces, however, were of primairy importance to design in comparison with other design hydraulic loads (water levels and waves) . REFERENCES .

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ASSUR, A. and WEEKS, W.F., 1964, Growth, Structure and Strength of Sea 1ce.U.S. Army, Cold Regions Research & Engng.Laboratory, Research Report 135, ûctober 1964. ANONWOUS, 1972, Guide to World Inventory of Sea, Lake and River-Ice, UNESCO/IAHS, Paris 1972. BILELLO, M.A., 1961, Formation, Growth, and Decay of Sea-Ice in the Canadian Arctic Archipelago, Arctic 14(1) , 1961. NEMEC, A., MILLS, D., LANGFORD, C. and JESSEAU, S., 1973, Lake Melville Ice Investigation, Labrador..2nd. 1nt.Conf. on Port and Ocean Engng. under Arctic Conditions, Reykjavik, 1973. NEUMANN, K., 1948, The Growth Velocity of Ice Sheets as a Function of Air Temperatures and Wind Velocity (text in German). Annalen der Meterologie, Vo1.2, 1948. PILARCZYK, K.W., 1977, Formation and Movement of Ice in the EasternScheldt (in Dutch) Delta Department, Report W-76.033,1977. POUNDER, E.R., 1965, Physics of Ice Pergamon Press, 1965. RODHE, B., 1952, On the Relation Between Air Temperatures and Ice Formation in the Baltic Geografiska annaler 34, 1952. WEEKS, W.F. and LEE, O.S., 1962, The Salinity Dictribution in Young Sea Ice, U.S. Army Cold Regions Research Report 98, 1962. WILLIAMS, G.P., 1965, Correlating Freeze-Up and Break-Up with Weather Conditions Canadian Geotechnical Journal, Vo1.2, nr.45, 1965. WILLIAMS, G . P . , 1966, Freeze-Up and Break-Up of Fresh-Water Lakes. Proc. Conf. on Ice Pressures Against Structures, Quebec, 1966. YAMAOKA, I., 1970, Estimation of Incipient Ice Cover Formation Date of Reservoirs in Hokkaido by Use of a Time Series of Daily Accumulated Air Temperatures IAHR. Ice Svmmsium. Revkiavik 1970-

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