Long term pressure gradients along the Belgian and Dutch coast

(1)

(2)

Ministry of Transport. PublicWorks and Water Management

Directorate-General of Public Works and Water Management

Tidal Waters Oivision

Nationallnstitute for Coastal and Marine Management/RIKl

Long term pressure

gradients along the

Belgian and Dutch coast

Rapport DGW - 93.045

september 1993

MaST*G8M

P.A.J. Verlaan

F

.

C. Groenendijk

(3)

Tidal Waters Division

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1 Introdudion 5 2 Theoretical Background 6 3 Measuring Method 9

4 Results of the analysis 12

5 Dlscussion 21

6 Conclusion 25

7 References 26

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(5)

1 Introduction

Many of the currently used flow models are based upon the depth -integrated momentum equations. This type of modelling is characterized by a fixed relation between the depth-integrated velocity and the bottom shear stress, the parameter which mainly determines the transport of sediment. In reality, however, the bottom shear stress depends on the current velocity in the vicinity of the seabed.This means that if the velocity profile deviates from the assumed shape, e.g due to wind-induced upwelling or downwelling, the depth-integrated flow model can no longer be applied. In such a case, the structure of the vertical velocity profile has to be taken into account in order to calculate a more realistic value for the bottom shear stress.

The vertical velocity profile may be implemented by using the so-called Quasi-3D approach. In this approach, the vertical flow structure is determined locally,thereby assuming a horizontal uniform flow structure. The relationship between the bottom shear stress and the depth-integrated velocities is derived from the so obtained vertical flow structure. The vertical flow structure can be determined by making use of a modified version of Davies shapefunction [2,12]. It is therefore necessary to have accurate information on driving forces such as the wind stress,density gradients and the sea surface slope. However, there isn't any reliable information on the sea surface slope obtained from observations. Along prismatic coasts,a zero longshore sea surface slope is often adopted [6,11]. Sea Surface Slopes produced by 2DH-models are not accurate enough for a precise calculation of the bottom shear stress.

This report will provide us valuable information on the sea level gradient needed to come to an improved computation of the vertical flow structure which in turn wililead to a more accurate calculation of the bottom shear stress.

Aims of the investigation

The aim of the investigation is to quantify the long shore and cross shore Sea Surface Slope (SSS)along the Dutch and Belgian coast. We have to pay particular attention to the influence of the river Rhine, the windeffect, the seasonal influence and finally the effect of Dover Strait on the Mean Sea Level. Furthermore, these investigations provide an improved view of the Sea Surface Slope and can be important for the calibration of modeis. The Mean Sea Level and Sea Surface Slope can be derived from waterlevel recordings [3].

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2 Theoretical background

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The equations governing the dynamics of water movement on a time scale of the residual circulation and on length scales of several hundred of kilometers are given below. A redangular coordinate system is chosen with the z-axis direded vertically upwards. The x-axis is chosen normal to the coast

and

the y-axis parallel to the coastline.

The equations are:

Du

1 aPa

dt

-

fv

=

-p

ax

-Dv

dt

+

fu

=

g~

+

ax

g~

+

ay

+

gz.È..e_

p

ay

(1)

for momentum inthe x and y direction and for continuity

au

+

ov

+

àw

=

0 ax

ay az

(2)

In these equations ~is the surface elevation, u arrd v the velocity components in the x and y direction. f the Coriolis parameter, K the eddy viscosity, g the gravity,

Pa

the atmospheric pressure and p the density of seawater.

By integrating through a vertical column of water from the bottorn (z=-H) to the surface (z=!;) and defining the component U en

V

by :

(

U

=

J

udz

-H (

V

=

J

vdz

-H

(3)

the depth-integrated momentum equations and continuity equation may, after negleding the non-linear advedive terms, be written as :

iJu _ rv

= _

(H+() oP. _g(H+~) iJ~ + T_-TJor _ g(H' -(') ~

Tt

p OX iJx p 2p iJ)f

iJv + fU = _ (H+() iJP. _g(H+~) iJ~ + ~ _ g(H'-~') ~

iJt; p oy iJy fl 2p iJy

iJu + iJv + iJ~ '" 0

iJx ay at;

(4)

where U and Vare the vertical averaged veleeltles and 'tsand'tbthe shear stress due to the wind and the bottorn friction respedively. The time variation of the surface elevation ~is'ignored since we are only interested in processes occuring on a time scale of the residual circulation.

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Figure 2.1

Seasurfaceelevation due to the pressureeffect (a) and windeffect (b) respectively[I].

To get some idea about the magnitude of the 555 we deal with the pressure and wind stress effect seperately. The y-axis is considered to be parallel to the coastline, so that it is assumed that

U=O.

Let us first consider the pressure effect.

The 555 induced by the gradient in atmospheric pressure can be written as:

(5)

Eq (5) may in case of a finite horizontal distance also be written as:

1 =

--àp

pg

a

(6)

Thus, an increased atmospheric pressureis accompanied by a decrease in sea level. This is called the "inverted barometer effect". If the barometric pressure is expressedin millibars and ,the sea level in cm, it can be seen that a pressure fall of 1 mbar corresponds to 1 cm sea level

.

'

nse

.

It is assumed here that a change in sea level due'to a change in atmospheric pressure occurs sufficiently slowly for a steady state to be achieved. In the case of a fast moving

disturbance

,

as a depression, this will not be the case and the inverted barometer effect is only a rough approximation of the actual change in sea level.

(al

(b)

w

)Ir

(8)

Secondly, we consider the windeffect

on

the sea level. In that case equation (4)

becornes

after neglecting the acceleration term and Coriolis

effect: .

'tsy - 'tby

pg(H+~ )

(7)

This equation can be

apolied

in case of a nearly half closed

basin

like the southern North Sea where the acceleration terms are generally small and y-coordinate is direeted parallel to the length axis of the basin. In such a basin, the bottom shear stress is only a fraction of the wind shear stress and

directed

in the

opposite

direction [5] (see Fig. 2.1).

Equation (7) can

therefore

be

wntten

as:

c3~

=

c3y

C

'tSy

pg(H+O

'tsy

C--pgH

if

~<H (8)

De

constant

C

hes

between 1 and 1.5. In practice,

ho

we

ver

,

1 is more likely than 1.5.

For the wind

shear

stress1:5can

be derived

:

(9)

where

P

a

is the

densityof

air (=1.25.~g/11il3),

W

~h~ wind

speed

.and

Cl? the drag coefficient

dependlag

Qr;J

the

wind

speed accordmg

to :

CD :::: (0 .

,

63 + 0 .

06

6

W)

1 0

-3

(10)

Comb

i

ning

equation

(9) and

(10) indicates that the

wind

shear stress is not

exactlyquadratically

dependent on

the wind

speed.

Setting W=10

mis,

H=20 m,g=9.81 m/s>, C=1, p=.1Q25

kg/m

3, Co becomes 1.29 10-3. The wind shear stress and the

Sea

Surface Slope can

now be calculated.

'ts

=

O.16N/m

2

,

oE

(11 )

c3y

=

8.10-

7

In case of a depression traveling on mid-lattitudes-over an area such as the North Sea,the windstress.effect usually exceeds the pressure

effect

,

One must realize that this arialysis is only validin case of

a

half closed

basin. The actual Sea Surface Slope wi.1Iusually be smaller.

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3 Measuring method

Figure 3.1

Tidal stationsalong theBelgian and Dutch coast.

The waterlevel measurements are performed by using a gauge. In the Netherlands the waterlevel values are given with respect to N.A.P (Nieuw Amsterdams Peil):In Belgium the waterlevel values are given

with respect to T.A.W. (Tweede Algemene Waterpassing). The

distinction between these two reference levels is:NAP-TAW=232 cm. Thus, we have converted the Belgian levels to NAP by subtracting 232 cm.

The absolute value of a single measurement is quaranteed with an accuracy of 2 cm. A recent analysis revealed that some of the tidal gauges have risen or sinken somewhat. This rising or sinking can amount up to 10 cm/century. In our analysis, we only make use of a three year time sequence making that sueh variations are negligible. The water level recordings of 8 Dutch locations and 3 Belgian locations (see Fig.3.1) are used.The Dutch locations deliver 10 minute values with a precision of 1 cm and the Belgian locations only give hourly values but the precision is 0.1 cm for each measurment.

5ince we are only interested in processes happening on time scales greater than one day the time sequences are filtered. We have used the

weil known Godin-filter [4]. ,

This filter applies three times the moving ave rage over 1440,1490 and 1500 minutes respectively if 10 minute values were available. If only hourly values were available we have taken the moving average over 24, 24 and 25 hours respectively. The Godin filter has the property that the main tidal frequences (M2 and 52) along with their higher harmonies

are completely filtered out. Moreover, only 1

%

of the frequences with a period smaller than 30 hours will remain.

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It is necessary to make a few notes about this filtering process. 1 By taking for

instanee

the moving average of 1440 minutes, 145

water level (10 minute) values are averaged. This is not exactly correct. A

better

alternative should be :

i-144

[0.5 (~l + ~14S) +

E ~)

i-2

~ =

₁₄₄

Nevertheless, the distinction between these formulations is fairly

srnall

.

2

The filter we used doesn't only filter out the tidal variations but all variations on time scales smaller than one day. However, we have to

realize

that sea level variations on a time scale of the residual circulation is our primary interest.

An alternative approach instead of the used filter could be :

Mean Sea level = Observed Sea Level - Predicted Sea Level

One of the major problems arising in this procedure is that the predicted values are not always available and if they are

available

they can not be obtained

easily.

The Godin filter is a relatively simple method to obtain the Mean Sea Level in examining all kinds of processes occuring on timescales greater than one day.

The obtained Mean Sea Level only depends on the density of sea water, the atmospheric pressure and the wind shear stress. Non-linear effects are ignored in this study since they are of minor importance

atthe

Dutch coast [7].

Before the results of the analysis are presented, let us first consider the effect of density differences on the Mean

Sea

Level (MSL). If the density variation with respectto z is zero (no stratification) we find by assuming a hydrostatic balance at the botlom between two regions with density P1 and P2 (see Fig.3.2) :

In the Dutch coastal zone, the spatial differences in sea water density are mainly determined by the salinity. A salinity difference of 4%0 results in a density difference of about 3

kg/m',

Setting P1=1025, P2=1022, H=20 and Ç1=0 results in: Ç2= 5.87 cm. Thus, a decrease in water density of 3

kg/rn"

gives a

6

cm rise of the MSL. If stratification is

adopted

P

l (z)

=

P

'

l

=

P

a

-

«

(1

+

2 z )

H

(13)

then, integration from z=-H to

z=ç

yields :

~1 ~2

!Plgdz

=

![P2-«

.

(1+

2:)]gdZ

-H -H

(14)

(11)

where

P1

and

P

2

are the vertical-averaged water densities.

(15) Setting

a

=0 in (15) we obtain eq.(12). Using the same sea water density and waterdepth values along with

a=3

we find :

<;

2 =

5.88 cm. It can be concluded that the effect of stratification on the sea level can be ignored. The surface elevation therefore depends on the vertical

-...averaged water density. Figure 3.2

The assumptionof a hydrostatic balanceat the bottom between two regions with density

P1

and

P

2

leadsto a differencein mean sea

level.

r---...,. ---

----

__

----r:---,

_.

'

_.

.

ç

2 .

.

0...

.

Ä

:·

· .

_.

.

_.

...

'. -- '0,"• .. 0, '

.

_{. .}

_.

.

_.

.

_.

.

_.

...

.

L- .... ..__ ---''-''

.

..

....

. .

_.

.

_{. .}

.

...

.

..

...

.

_..

_....

.

. .

_{. .}

>

(12)

4 Results of the analysis

...................................................................................................................................................................................................

This Chapter will give the results of the Mean Sea Level (MSL) as weil as

the Sea Surface Slope (SSS)in all kind of circumstances.

Subsequently, we examine the effect of

the

river Rhine on the MSL,

the

windeffect on the MSL and SSS,the seasonal variatien and the effect of

Dover Strait.

The wind data of Meetpost Noordwijk

(denoted as

MPN in Fig.3

.

1) is

used to examine the windeffect. To get an indication of the amoun

t

of

Rhine water flowing out into the North Sea

,

the Rhine discharge at

Lobith

i

s taken.

4.1 The effect of the river Rhine

Fig.4.1 gives the MSL of all coastal stations at different Rhine

discharges

.

We have only considered cases with

a

wind speed smaller

than 5

mis

to filter out a possible w

i

nd effect on

the

MSt. Fig.4.1

demonstrates that variations on a short length scale often appear to be

much greater than the long distance variation in MSl. We always

observe that the MSL at Hoek van Holland and

llrnuiden exceeds

the

MSL of Scheveningen and Petten

.

These differences are caused by

location factors

such

as the salinity of the sea water, the distance

from

the coast of the gauges etc .. At Hoek van Holland the water has a

remarkable lower salinity and thus a lower density than at Scheveningen

making that the MSL is higher. Measurement of the

sea

level at

Petten

occurs 800 meter offshore resulting in a lower MSt due to the absence

of some wave-upset. Moreover, FigA

.1

indicates an overal decreasing

MSL towards the north along the Belgian coast, We wil! deal with this

observation in section 4.3

.

From the MSL of all stations

,

the longshore S5Salong the Dutch and

Belgian coast can be determined by applying a linear regression

,

The

results are presented in Table 4.1.

Similarly

,

the cross shore SSSis obtained

by

subtracting the MSL of

Meetpost Noordwijk

trom

the average MSt of llmuiden and

Scheveningen

.

Fig.4.2 demonstrates the effect of the Rhine discharge on

this waterlevel difference. Table 4

.

1 presents the averaged cross shore

and longshore SSSfor the three Rhine discharge interva

1 sde

ri

ved

trom

Fig. 4.2

Table4.1

The cross shore SSSand longshore SSStordifferent Rhinedischarges.

Rhine discharge(m3/s) cross shore 555 longshore 55·5(W < 5mis)

0-1500

1500 - 3000

>

3000

1 .

410 .

6

2 .

2 1.0

.

6

4.1 10

.

6

9.5 10

.

8

2.310 .

8

8.0

1

0 .

8

(13)

The influence of the Rhine discharge on the MSL is fairly smal

I.

It may be anticipated that a higher Rhine discharge leads to higher Mean Sea Levels.The observations (Fig.4.1), however, show that the MSL is lower at higher discharges. It appears that other effe cts overrule the river Rhine effect on the MSL. In fact, periods of a high Rhine discharge

usually happen in spring. It is known that the ave rage air pressure is

usually higher in spring which results in a lower MSL. This issue is

discussed further in section 4.4. Nevertheless, we observe that the sea

level difference between Hoek van Holland and its neighbouring

locations is substantially higher at an increasing Rhine discharge.

The longshore SSSwithout any wind israther small and doesn't have

any significant effect on the coastal dynamics. In other words :The tidal

current alone doesn't cause any substantial SSS.Nevertheless, a small

positive longshore SSSis observed regardless the magnitude of the river

Rhine discharge. It is not evident whether this small SSSis generated by

the tidal current orjust by the weak south-westerly winds in the

measurements Thisproblem is discussed in Chapter 5.

Figure4.1 Rhine Discharge: 0-1500 m'/s

MSL for low windconditions along

theBelgianandDutch coastfor three

1:-;-

-p

~---'--~~--

~

--

--~~

--

---~

differentRhinedischarges. ~

~

· -

·'-t'I

'--

7 -

~

'---

T-"fY-

-~

~f'--

--

~:__

-

---:~

--

..s:..

--I

Ê

~

_...._-tO+_----""'_....,-_-_-:Jh,L- ---en :::E

-

.,~-

--

--_r----_,--

₁₀ _too

-

----

r_

---;_---._---_1

110 100

Diafane. 'rom NI.uwpaort (km)

--"i~

---

-

---

_1

-Rhine Discharge 1500-3000 m'/s

-

"

_•

~

---'---'---r_----'---'_----_1

50 100 110 zoo

Diafane. from NI.uwpoort (km)

-Rhine Discharg. > 3000 m'/s

~

.

Ê

~

_-_tO

-....

~

-

.'~----

.

-

_..

_r---'---~r---.-

_'00 ₁₁₀ ₂₀₀

--

---

._

----~

Diafane. lrom NIeuwpoort (km)

(14)

Figure 4.2

Crossshore 555 at Meetpost

Noordwijk as a function of the Rhine discharge.

Cross shore SSS versus Rhine discharge

0.80 0.70 0.60

~

₀_.₅₀ Qj~

~~

0040 VI

8

0.30 .... 0 0.20 0.10 0.00 2 3 4 5 6 7 8 9 10 11 12 Rhine discharge (*500 m3/sl

The cross shore SSS,on the other hand, exceeds in situations without any wind the longshore SSSby at least one order of magnitude and is clearly related to the Rhine discharge as can be seen in Fig.4.2. Figure 4.2 shows that an increasing Rhine discharge is associated with a higher cross shore SSS.A complementary conclusion followed from the work done by Groenendijk [5]. He found a clear relation between the Rhine discharge and the cross shore density gradient.

4.2 The Windeffect

To examine the wind effect, the wind data of Meetpost Noordwijk is divided in 16 direction intervals and 5 windspeed intervals. For each wind interval the average of the MSL values is determined. Thus, we obtain for each location an averaged value for the MSL for each of the 80 windconditions. Fig.4.3 depiets the.longshore SSSfor all

windconditions. The MSL value of Hoek van Holland is omitted because of its diverging value. A few of the windconditions didn't occur during the three years considered which makes that at high windspeeds for some winddirection (e.g. south-easterly wind) there is no information available on the long shore SSS.

Fig.4.3 shows that the longshore SSSreaches its maximum positive value during westerly winds and is maximum negative during a north

-easterly wind. The picture of the SSSis not entirely symmetrical, in other words :the SSSis almost the same for all winddirections between south

-southwest and northwest while a clear negative maximum is found at a north-easterly wind. This asymmetrical behaviour is probably related to the (asymmetrical) shape of the Southern Bight.

(15)

Figure 4.3

Longshore555for 5 windspeeds categoriesand 16 winddirection intervals.

Longshore Sea Surface Slope

related to windconditions

1.5E-<J6.---, Ê

~

5E-07 :§_ <I> 0. 0 ü'i 0 <I> 0 <ti 't: :::> _-_5E-07 Cl) <ti <I> Cl) -1E-<J6 -1.5E-<J6 1E-<J6 . . . ... . ... .. .. . ... ...•. . . ... . ... ... . .. . ... -.... N NNE NE ENE E ESE SE SSE S SSW SW WSW W WNW NW NNW winddirection

02.5-5 mis

0

5-7.5mis .7.5-10 mis GSll0-15 mis CSl15-20 mis

To obtain more insight in the behaviour of the MSL, we have also plotted (for 8 windconditions) the MSL distribution along the coast (FigAA). It is shown that the MSL reaches its maximum during north -westerly winds and its minimum during easterly winds.

Besides the longshore 555 we also examined the windinfluence on the cross shore 555.The wind data at MPN is again devided in 16 direction intervals and 5 windspeed intervals (if available). FigA.5 gives the results of the analysis.

It appears that the cross shore SSSis nearly always positive (the MSL increases towards the coast). This is due to both a lower salinity and a higher wave setup at the coastal stations Scheveningen and Urnulden, thus causing a higher MSL there.

The winddirection associated with the highest cross shore 555 depends on the windspeed. If the windspeed ranges from 15 to 20

mis,

an onshore directed wind (west-northwesterly) gives the maximum cross -shore SSS.This result was expected. At lower windspeeds, however, the cross shore SSSreaches its maximum during a south-southwesterly wind. This is probably due to the river Rhine effect. The amount of fresh Rhine water off the coast at Meetpost Noordwijkis controled by the winddirection. The observations indicate that at lower windspeeds, the windsetup is dominated by the river Rhine effect which elevates the sea level at the coast leading to a greater cross shore 555.With a south -southwesterly wind the relatively fresh water is forced to remain in a smal! strip near the coast.

(16)

TidalWaters Division

Figure 4.4

MSL along the Belgian and Dutch coastfor awindspeed between 10

and15mis. t.4SLfor c windspu() belween lOene 15

mis

.- "onh ~ nol'1"-IO" ~.o.t ... sov1hl0r1

.!

"

...-1.

~

I

~

-

..

~

..J I ~ ! -JO .

I

-..-I i -JO~ .; 0

-

+---

--~---~

---

-

--

-

--

_

.

• ..

.• 1t1 _ HO

::>;.tanc. Iram N;.uwpoan (km)

-USL for o windspeed belween 10 end 15

mis

.- sO\.o1h

a+&eO tout"-.... t G4HHHl •• ,, ... nonh- ....t

-••.f-.---

..

---,_ ---tM --..,..---,---_

-O;stanc. Irom N;ou.. poon (km)

,

..

-Finally we examine how the MSL (the average of the MSL of 10 coastal stations, without Hoek van Holland) and the longshore SSSrespond to a change in windspeed from a certain direction. To examine the sea level respons to a varying windspeed, the ave rage MSL and longshore SSSare plotted for some selected periods of a two day duration. Fig.4.6a gives the sea level respons in case of an increasing north-easterly wind. The MSL decreases significantly as the windspeed increases.The longshore SSSbecomes increasingly negative. This result corresponds to the ave rage longshore SSSin case of a north-easterly wind as indicated in Fig.4.3. The longshore SSScan amount up to -1.4 10-6

mlm

ata north-easterly wind of about 15

mis

.

The results for an increasing south-westerly wind are given in Fig.4.6b. Although the respons is reversed, the pattern is similar to that of a north-easterly wind. During a south-westerly wind, the average longshore SSSis substantially smaller than that in case of the two day period which is seen by comparing Fig.4.6b and Fig.4.3.

It's not possible to derive a value for the respons time from these Figures.In fact, the depicted MSL values were calculated by applying a Godin filter which makes that a

suddert

change in sea level is smoothed out over at least one day. This explains the rather smoothed CUNe of the longshore SSSand MSL.

(17)

Figure4.5

Cross shore SSSatMeetpost

Noordwijk for 5 windspeed categories and 16 direction intervals.

Figure 4.6

Longshore SSSandMSL along with the windspeed in case of a northeasterly wind (al and southwesterly wind (b).

Cross-shore Sea Surface Slope

re

l

ated

1 0w

i

ndconditions

6E~

!.

3E~ .2 .(1)

8

2E~ '_..

~

"

(1) .1E~ l.-.L--L_.o.__....L.--'I_....L..--'_..L__L_.o.__....L..--l_..L____l_.L-_L_J N NNE NE ENE E ESE SE SSE S ssw SW WSw W WNWNWNNW winddirection

o

z.s-sevs

0

S·7.Smls • 7.S·10mls

IJ

lQ..1Smis

!SJ

lS·20mls

Northeastetfy wind

lSSSnn'\o'"

r---

----

---

--

---

----

--

----

-,

MSI." .... 0 ('0) (201 (30) '0 1CP,.01",~ 250 200 '50 '00 50 00 '0 1olSI." .... '0 ('0) (201 (30) (40)0 '0 ~,..oIIhtWll'1O'o'lllOdl 250 200 '50 (2E<>71 South-'ertywind

~~

I

--

---

----

---~--~======

==

L~~sn""m

UIE..08 I12E.06

~

--

----

---

--

---

--~

~~

---

----~

....

"_

40 50

(18)

4.3 Tbe effect of Dover Strait

The Southern Bight can be considered as a semi closed basin.This makes that the windeffect is not isotropie in all directlens. A northeasterly wind induces a larger longshore SSSthan a southwesterly wind as indicated in Fig.4.3. This effect is supposed to be due to the narrowing effect of the North Sea in the vicinity of Dover Strait.

We have [ust discussed the SSSalong the entire Belgian and Dutch coast, If we only consider the longshore SSSalong the Belgian coast between Nieuwpoort and Zeebrugge. we neariy always dbserve a decreasing MSL towards the north except tor wind directions between west and north (see Fig.4.4). The observed longshore SSSoff the Belgian coast is usually quite large and approximatelyequal to

1 .

10 .

6

m/m. This feature has earlier been observed

b

y

varrous authors

'[10]

.

Prandle [9] has to incorporate a negative SSSin his model to explain the observed SSS

[10]

along the Belgian and Dutch coast. This negative SSS contributes to the nearly always north-eastward directed mass transport through Dover Strait.

Figure 4.7.

Monthly averaged MSL of 12 locations reflecting a seasonal influence.

Mean Sea Level Mean Sea Level

Texel Petten _ '990 c::J '99' ffiIIllI '992 _ '990 c:::J

'

99'

mrrm

'992 40,---~----, '0 40 30 TI 20 ~

~

_..

t 0

Ih_

;0

~

-'0 -20 -30 30 <'0 -'0 -20

)8n t~ I'TYt epr rnay ~ ~I lIIUQseo oet nov dec

-30 ~---.----

----Jan feb nY t apr may ',.,.. ~r avo sep eet -ov dec

Mean Sea Level _ 1990

_c::J

'991 D]]] 1992 _ 1990 Mean Sea Level Noordwijk

c::J

'991 ~ 1992 IjmUiden 40,---, 30 -10 ..~()-_._--_._---- ._..----_._.._-_

}

.

ft

~

.:

~

fl'n

~--

feb ITYt apr mt'I

-

y

--

.,..,

-

.~I

-

&UQ

-

S~

-

---

oct nov dec

(19)

Tidal Waters Division _ 1990

Me

an Se

a Leve

l

Scheveningen c::J 1991 0]]] 1992 30,--- ---20 LO .-3L...0 _J

)C\n feb ITYt apr r-ev ,._" ~I 8UQ sec oct riO.... dec

M

e

a

n Sea Level

8 G

8

_ 1990

mmn

1992 30 20

~

10

~

_•

0

~

_~

-20 -30L--- _ ,an feb tTYt apr may ,... ~r aug sec oct nov dec

_ 1990

M

e

an S

e

a

L

eve

l

Westkapelle c::::J 1991 0]]] 1992 30r---, 20 -10 -JoL--- ___

ItIn 'eb nyt ePI" lT\ê:Iy,.." ~I ftug sec oer nov dec

_ 1990

Mean Sea Leve

l

Oostende

c::J

1991 ITDllD 1992 20,--- -10 -20 -JoL---~

Long term pressuregradients alongtheBelgianand Dutch coast 19

Mean Sea Level

Hoel~ van Holland

_ 1990

0]]] 1992

4 0,---

--

---

--

--.

30

-2

0~---

---

_

jan feb nlfl ltopr n'lëlV il.n IJl i'lUO Sep 011'1IV.)\I dp.t~

Mean Sea Level

Roompot

_ 1990 c::J 1991

mmn

1992

30,---

---20

--

J

,an feb mrt apr may J,ll ,..,1 C!lLMJ sec oei na", oec

_ 1990

Mean

S

e

a

L

e

v

e

l

Zeebrugge c::J 1991 ITITTID 1992 -JO ----.

_

.---_._--_. --,.---.--- ----_ 1990

Mean

Sea

Level

r-~Ieuwpoort c::J 199 1 (]]]JJ] 1992 JO 20

E

10 0 -10 -20

,---

----

-

----

-

----

-

1 I

~~

~

I

ru~~~

~---_.

(20)

4.4 Seasonal Influence

Fig.4.7 depiets the MSL during all months of the year. It's striking that the MSL is highly variabie during January and February but on the other hand relatively constant in April and May. Moreover, the MSL usually

reaches its minimum during May and its maximum during November.

The question arises what the origin is of the differences in the MSL during the year. Prandle [9] demonstrated that yearly variations in

longshore density differences or the M2-tide are of negligible

importance. As indicated in Chapter 2, the MSL is affected by both the atmospheric pressure and the wind. It is found that the average air

pressure reaches its maximum in April/May and its minimum in

November. This explains the variations in the monthly mean MSL during a year.

The differences in the monthly mean MSL from year to year are

probably caused by the current windconditions. In winter, the

windspeed is usually greater than in summer which makes that a change

in winddirection will have significantly more effect on the MSL than in

summer and therefore makes that the MSL is highly variabie during January and February but relatively constant in April and May.

(21)

5 Discussion

Figure 5.1

The difference in MSL due to the M2tide only as computed

by Prandl [9].

In this Chapter we shall make a comparison between the observed sea level recordings analysed in this report, and the model results of Prandle [9] and Davies [2].

Prandle solved the depth-integrated momentum equations numerically. He neglected the spatial variability of the atmospheric pressure and water density but took into account the non-linear adveetion terms.

The initial condition is taken as a constant waterlevel with zero current velocities. The boundary conditions along the open boundaries were specified as a sinusoidal-shaped surface elevation. The phase and amplitude of the elevation were obtained from observations.

Fig.5.1 depiets the calculated mean sea level due to the M2 tide only.

As we can see, this picture deviates substantially from our mean sea level calculations carried out in a situation without any significant wind stress (Fig.5.1). The results do agree in the sense that the mean sea level increases towards the north. In contrast, the computed increase in sea level along the Belgian coast is not confirmed by our observations.

Our results demonstrate that the wind shear stress mainly determines the magnitude of the 555. We compare our results with the model calculation of Davies [2] and other observations in the southern North Sea and the English Channel. Fig.5.2 shows the model results of the MSL during a typical summer and winter condition. In winter, Davies imposed a southwesterly wind of 7

mis

while in summer he took a southwesterly wind of 3

mis

over the Southern Bight. For the longshore 555 along the Dutch and Belgian coast he found :

4.10 -

7

m/m

in winter and

1 .

10 -

7

m/m

in summer. These values are in

agreement with our results.

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Table 5.1

Acomparison between theSSS

estimated from thesealevel difference (óG)andthelongshore

SSSfound in this study.

Prandle also gave values for the observed sea level difference

(AG)

between the southern North Sea and the English Channel at a specific windspeed of 7.5

mis

for 8 directions. The sea level difference was obtained from 4 coastal stations (Fig.5.3) according to :

Table 5.1 represents a comparison between the SSSderived from these and our values as weil as the longshore SSScomputed in Fig.4.3.

winddirection

AG(cm)

estimated SSS*

(x 10

.

7)

SSS from our

observations (x 10

-

7)

N

NE

E

SE S SW

W

NW -0.8 0.33 2.8 -1.16 4.6 -1.91 4.4 -1.83 3.6 -1.50 -0.4 0.16 -4.9 2.04 -5.0 2.09 -3.84 -2.23 -3.21 -2.15 1.41 3.12 3.96 2.87

*

An estimation of the distance is 240 km.

Although the SSS,obtained by Prandle,cannot be really compared to the SSSfound in this study since they concern a different area, they are of the same order of magnitude.

Besides the spatial variations in MSL due to the M2-tide and the wind

stress,Prandle has to incorporate a negative longshore SSSto get agreement between his model results and observational data from Rossiter [10]. He found that a sea level difference of approximately 5 cm between the southern North Sea and the English Channel is sufficient to get agreement with the observations of Rossiter.The sea level

recordings of Rossitercorrespond roughly to our observations. This confirms that the imposed negative SSSin Prandl's model is really necessary. In fact, an imposed negative SSSis necessary to correct for the observed dynamical inbalance at the boundaries of Prandle's model. lt's also possible to explain the difference concerning the SSSin cases without any windstress by comparing Fig.5.1 with Fig.4.1. Prandle didn't impose a negative SSSin that case although it appeared to be necessary to make a comparison with our observations. Nevertheless, the observed strong negative SSSalong the Belgian coast cannot be fully confirmed by his model, even if sueh a negative gradient was imposed.

Probably, local effects seem to play an important role to explain entirely the observed negative SSSalong the Belgian coast.

Finally, we look more closely at the observed longshore SSSduring strong wind conditions. If a state of equilibrium is established, formula (8) may be applied to calculate the longshore SSS.Setting H=30 and W=12.5, the longshore SSSbecomes :9.41O-7

m/m.

Only in case of a

northeasterly wind, the observed and theoretically derived SSS'sare almost the same, meaning that the southern border of the North Sea can almost be considered

closed

,

This is an important result for modelling the water movement in the southern North Sea.

(23)

Figure 5.2

Wind-inducedseasurfaceelevation

for the period Decemberto February

(a)and the period June to August

(b) as computed by Davies[2].

(24)

Figure 5.3

A map of the EnglishChannel and the Southern Bight[9].

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(25)

6 Conclusions

The following conclusions can be derived:

1 A clear relation between the longshore 555 and the windvector is found. The longshore 555 reaches its maximum positive value during north-easterly winds and its maximum negative value during a westerly wind. In case of astrong northeasterly wind, a state of equilibrium

between the 555 and the wind stress is almost established.

2 In the absence of any wind, only a small positive (increasing sea level towards the north) longshore 555 remains (2.10-8 - 8.10-8 rn/rn) if the water level recordings of all coastal stations are taken into account. The

influence of the river Rhine on this longshore 555 can be neglected.

3 The longshore 555 is allways negative along the Belgian coast except for strong north-easterly winds. This 555 is generared by a structural difference in MSL between the southern North Sea and the English

Channel. This negative 555 amounts up to 1.10-6rn/rn.

4 The cross shore 555 between Meetpost Noordwijk and the coast reaches at high windspeeds its maximum during an on-shore directed wind. At a lower windspeed, on the other hand, the cross shore 555

reaches its maximum during a south-southwesterly wind.

In general, the cross shore 555 becomes increasingly more positive with

an increasing Rhine discharge.

Acknowledgements

We would like to thank the "Dienst der Kusthavens" of the Ministry of the Flemish Community in Belgium for supplying the waterlevel

recordings of the coastal stations Nieuwpoort, Oostende and

Zeebrugge, especially Ir. B de Putter and ing. C van Cauwenberghe. We

also thank Ir. Zitman from Delft Hydraulics for his helpful discussions.

This work was carried out as part of the MAST*G8M Coastal

Morphodynamics programm. It was funded jointly by the National

Institute for Coastal and Marine Management/RIKZ of the Dutch

Ministry of Transport, Public Works and Water Management, Directorate General Rijkswaterstaat and The Commission of the

European Communities, Directorate General

tor

Science,Research and

Developement under contract no. MAS2-CT92-0027

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7 References

.............................................................................................................................................................................

1:BOWDEN, K.F. (1983) Wind-driven currents and surges

In :Physical Oceanography of Coastal Waters

Ellis Horwood Limited, 302 pp

2: DAVlES,AM. (1983) Application

of

a Three Dimensional Shelf

Model to the Calculatian of North Sea Currents.

In :North Sea Dynamics. Editors: J.Sünderman and W.Lenz

Springer-Verlag, Berlin, pp 44-62

3:FANG,G. and B.ZHAO (1988) A note on the main forcing of the

Northeastward Current oft the South East China Coast.

Prog. Oceanogr. Vol.21 pp 363-372

4: GODIN, G (1972) The analyses of Tides.

Liverpool University Press, 264 pp

5: GROENENDIJK F.C. (1988) Residual Current structure in the

Netherlands coastal zone. Master Thesis (in Dutch). University of

Utrecht, Inst. of Marien and and Atmospheric Research. Report IMAU

V88-6, 94 pp

6:HEAPS,N.S.(1972) Estimation of density currents in the Liverpool

Bay area of the Irisch Sea.

Proceedings of the Royal Astronomical Society, nO.30 pp 415-432

7: NIHOUL, J.S.J.and F.C.RONDAY (1975)

The influence of tidal stress on the residual circulation.

Tellus 27 pp 484-489

8: PRANDLE, D.(1975)

Proceedings of the Royal Society London A344 pp 509-539

9: PRANDLE,D.(1978) Residual flows and elevations in the Southern

North Sea.

Proceedings of the Royal Society London A359 pp 189-228

10: ROSSITER,J.R. (1967) An analysis of annual sea level variations in

European Waters

Geophys. J.R. astro. Soc. 12 pp 259-299

11: VISSER,M. and W.P.M. DE RUIJTERand L.POSTMA (1'991) The

Distribution of suspended matter in the Dutch coastal zone.

Netherlands Joumal of Sea Research 27 (2) pp 127-143

12: ZITMAN, T.J. (1992) Quasi-3 dimensional current modellingby

applying a rncdified version of 'Davies' Shapefundion approach.

Continental ShelfResearch. vol.12 no 1 pp 143-158

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(28)

Long term pressure gradients along the Belgian and Dutch coast

Directorate-General of Public Works and Water Management

Tidal Waters Oivision