The shallow water wave hindcast model: HISWA Part II: test cases

(1)

The shallow water wave hindcast model HISWA Part 11: test cases

N. Booij

L.H. Holthuijsen

T.H.C. Herbers Report No. 7-85

(2)

•

Delft University of Technology Department of Civil Engineering Group of Fluid Mechanics

•

The shallow water wave hindcast model HISWA Part 11: test cases

N. Booij

L.H. Holthuijsen

T.H.C. Herbers Report No. 7-85

(3)

•

PROJECT REPORT Delft University of Technology

Department of Civil Engineering

Group of Fluid Mechanics

•

Project title GEOMOR wave model (HISWA)

•

Project description Development of a two-dimensional model to

hindcast spectral wave parameters in an estuary with tidal flats on the basis of bottomtopography, current and wind data

•

Customer Rijkswaterstaat

Deltadienst, Afdeling Kustonderzoek

van Alkemadelaan 400

2597 AT THE HAGUE, the Netherlands

•

represented by J. v , Marle

•

Project leader dr.ir. L.H. Holthuijsen

•

work carried out by d rsLr , N. Booij

dr.ir. L.H. Holthuijsen ir. T.H.C. Herbers G. Marangoni

•

Conclusion Computational results of the HISWA model

with default parameter values are

compared with field observations in the Haringvliet and over the Galgenplaat. The results indicate that some tuning of the parameter values is required but not extensively.

•

Status of report confidential, final report, part 11

•

City/date: Delft, February 15, 1985

released for unlimited

(4)

•

Contents

•

page

l. Introduction 1

•

2. Test in the Haringvliet estuary 4

3. Test in the Galgenplaat region 20

•

4. Computer capacity 23 5. Conclusions 24

•

6. References 25

•

(5)

•

1. Introduction

•

To demonstrate that the basic concepts of the HISWA model and the

numerical implementation thereof provides realistic information in

complex geophysical conditions, two tests have been carried out

without turning the HISWA model. The following test should therefore

be considered as "blind" tests in the sense that all coefficients in

the HISWA model were either taken from literature or from arbitrary

choices and that no feed-back was used from the observations in these

tests to the model.

The first test was carried out

branches in the river Rhine

for the

delta).

Haringvliet (one of the

This situation can be

•

characterized as non-locally generated waves passing over a shoal

where breaking and refraction (and perhaps diffraction) are dominant.

Local wave generation was relevant only far behind the shoal and

currents were taken to be zero.

•

The second test was carried out for the Galgenplaat (on extensive

shoal surrounded by deep channels in one of the branches of the river

Rhine delta). This situation can be characterized as local wave

generation on a current with considerable current refraction. Over the

top of the shoal wave breaking is dominant and behind the shoal bottom

refraction is dominant.

•

• -1-•

(6)

•

2. Test in the Haringvliet estuary

•

In the mouth of the Haringvliet estuary (see fig. 1) a comprehensive

measurement campaign has been undertaken which is described by

Dingemans (1983). These measurements were carried out to verify the

refraction-diffraction computations with the CREDIZ-model (Booij and

Radder, 1981).

•

The computations have been carried out for a situation with low

current velocities which occurred during the measurement period on

October 1982 at 22.00 (M.E.T). The bottom topography on a large scale

is shown in fig. land the location of the area of computation is

shown in fig. 2. A more detailed topography in the computation area is

shown in fig. 3. The results of the computations are given in

figs. 4-7.

•

The wave situation can be characterized as one in which waves have

been generated by wind in deeper water and which penetrate the area

under consideration. There the waves break on a shoal with a minimum

depth of about 2 m. The wave height reduction over the shoal is

•

considerable: from

behind the shoal.

breaking over the

around the shoal.

about 3 m in front of the shoal to about 0.5 m

The situation is obviously dominated by wave

shoal and by refraction and possibly diffraction

•

At seven locations measurements were taken (see figs. 2 and 3):

•

a pitch-and-roll buoy providing not only the

significant wave height and mean wave period but also

the main direction and the directional energy

spreading. These measurements served as input at the

upwind boundary of the model

WR1, WR2, WR3 waverider buoys in front of the shoal giving

WA

WR4, WR5, WR6 E75

significant wave height and mean wave period waverider buoys behind the shoal

a wavestaff far behind the shoai

•

(7)

•

The results

(1983). They

of the measurements are taken from Dingemans

are given in figs. 3 through 15 together with relevant

•

HISWA results. It should be noted that two sets of analysis were

available: one labelled "Hellevoetsluis" and the other ..D.I.V ....The

former is based on a statistical analysis of the observed time series,

the latter is the result of aspectral analysis. Since the HISWA model

is based on energy (or action) considerations the "D.I.V." results are

the relevant observation results. The computations were carried out

for time 22.00 hr. (M.E.T.), the observations were taken mostly at

another time. The two nearest observations (nearest in time) are

indicated in the figures.

•

Additional information regarding the wind and the computation

•

parameters are given on the next page.

For convenience of comparison the following list gives the

time-interpreted observations at 22.00 hours M.E.T. and the

•

corresponding HISWA results.

•

location D.I.V. observation HISWA

H Tmean Hs Tmean s (m) (s) (s) (m) WA 3.23 T = 8.3 input input p WR-1 3.30 6.3 3.02 7.8 WR-2 2.36 6.3 2.58 7.0 WR-3 2.56 5.9 2.52 7.0 WR-4 0.61 2.6 0.46 3.7 WR-5 0.99 3.7 1.04 4.2 WR-6 1.47 5.1 1.34 4.6 E-75 0.89 2.8 0.77 3.6

•

(8)

-3-•

• TEST:

HARINGVLIET OCT. 14, 1982,

at

22.00

bottomgrid:

21750

m x

29000

m

87

x

116

computational grid:

15000

m x

15000

m x

120

0

225

x

60

x

15

•

boundary values incoming waves:

• H

=

3.285

m, s per

8.3

s, dir.

5.5

0, 2 cos distr.

.

'

wind:

UlO

=

16.5 mis dir

•

breaking on/~ frequency on/~ bottom friction on/~ frequency on/~

diffraction off

numeric diffusion on/~ (upstream scheme) wave blocking on/~

•

notes: in wind, breaking and friction only standard coefficients were used.

•

• -4-•

(9)

•

Fig. 1 Bathymetry of Haringvliet estuary, contourlines in m, interval is 2.0 m.

(10)

-5-•

• I

• r======"\\

"

~

\\ ~A

wR3

\\

~Rl

1

\\

~R2

~R4

\\

~~:5

Et~~

"

~

\\

\

• 2000

m ~

•

Fig. 2 Location of computation ar :

HaringvIi ea in

et area sh

with buoy 1 own in fig. 1

ocations.

(11)

•

1000 m land

•

Fig. 3 Detailed bathymetry in area of

computation. Contourlines in m,

interval is 2.0 m.

(12)

-7-•

•

land L() c

f.-75

o

Fig. 4 Significant waveheight in m,

contourline interval is O~5 m.

(13)

-8-•

•

land

tlR3

tlR2

• _~-75

0 0

.

v CC c

•

,...

.

•

Fig. 5 Mean wave period in s,

contourline interval is 1.0 s.

(14)

-9-•

•

~ !!JO I!l' ~

..

.-~R3

SI' !!JO lP I!l'

..

-tlR

1

ïlR4

SI'

,...

l\1R2

-

9'

....--

-~ ç;::

-

....

===;;:

_-

ilRS

!!JO !!JO ".

"""::IP'--tlR6

lP ~ BI _~

-land 3 2 m /s t----+

~-7S

Fig. 6 Energy transport vectors in 3

m Is.

(15)

-10-•

•

land '-'

•

10-3 m2/s2

_.

_~

--

!

-E>

• WR3

_-

_~

IIR

1 ,WR4

-

,WR2

-•

<,

--

ilR5-.-~-75

I

---WR6

• -

.__--

<,

-,

.

---

-•

--\.

-

-•

•

2 2

Fig. 7 Wave induced stress in m /s •

(16)

-ll-•

SENSOR

WA

14 October

1982

•

811014 :!20C.U\,;!l IlVEt. ID energy spectrum IS

T

If~E : 22.00

• Hs (m)

3.23

'(:0 l!:: .1. ~ flll 014 2:!crj l''':!l lS

e

q .2 .a

_.'

.'J 16 .(1;2!

main direct ion

•

11

12

•

.1 .•1 '.J .4 .5

&.!1 014 2:!0C. UiJR IIflt,

•

12 0

~

.

12 6 .6 directional spreading lHl! .~_'--~~--~~ .i .2 .l .' .j.

•

2

• Hs

=

significant

wave height

Tp

=

peak period

SPR=

.

standard

deviation

of direct

.

ional

energy

distribution

•

Fig. 8 Measurements at location WA.

(17)

-12-•

SENSOR

WR-l

14-0ctober-1982

• MEASUREMENTS

:

lIf:1:Q 12 ~_~

...

lil 1I

•

• ,

1)2 101 4 21 00 UUR HWIII WST: 30 Wil: 330 WSN= 12 HS: 249 TH5: '.40

Time:

21.00 Hellevoetsluis

D.I.V •

Hs(m)

3.22 Tm(s)

6.1 Hs(m)

2.49 Tm(s)

6.0

•

• Time:

22.30 Hellevoetsluis

D.I.V.

Hs(m)

Tm(s)

Hs(m)

Tm(s)

4.81

6.5 3.71+

6 .+

•

.4

+from Hellevoetsluis measurements with

same ratios as at 21.00

•

• HISWA

Time:

22.00

Fig. 9 Measurements at location

WR-l.

Hs(m)

3.02 Tm(s)

7.8

•

• Hs

=

significant wave height

Tm

=

mean wave period

(18)

-13-SENSOR

_WR-2

• MEASUREMENTS

~Z1014 2100 UUR HWftlt WST: 30 WR: 330 WSN: U HS= U7 TH!;'; '1.40

"

•

6 2

•

L-~ .1__ ~~.2 .3 .' F~!.5

•

1E1 i(i 12 ~

-u.. lil

"

• ,

•

2 2 101 4 2230 UUR HWft2 liST: 120 Wit: 300' WSN_ IS HS: 240 THS: '1.70

•

• HISWA

Time:

22.00 Hs(m)

2.58 Tm(s)

7.0

•

• Hs

=

significant wave height

Tm

=

mean wave period

I

.

I

Time:

14-0ctober-1982

Hellevoetsluis

21.00 Hs(m)

2.89 Time:

T

m(s)

6.2 Hellevoetsluis

22.30 Hs(m)

3 .

57 Tm(s)

6.5 O. I.V •

Hs(m)

2.27 '

Hs(m)

2.40 O.l.V.

Tm(s)

6.1 Tm(s)

6.4

Fig. 10 Measurements at location WR-2.

(19)

-14-•

•

• SENSOR

WR-3

MEASUREMENTS

11(4 ::;; 12 ~ 8;!101422::;0 UUR HIII!3' o/:>T- I~O IIR- $00 W~N· I ~ H~· ~II)I') TH:;- 7,70 IB 2

HISWA

Time:

22.00 Hs(m)

Tm(s)

2.52

7.0 Hs

=

significant wave height

Tm

=

mean wave period

14-0ctober-1982

Time:

21.20 Hellevoetsluis

O.l.V.

Hs(m)

2.54 Tm(s)

5.9 Hs(m)

2 5

• j

~ +

Time:

22.50 Hellevoetsluis

O.l.V.

Hs(m)

2.61 Tm(s)

5.8 Hs (m)

2.60 +from Hellevoetsluis measurements with

same ratios as at 22.50

Tm(s)

5.9 +

Tm(s)

5.8

(20)

-15-•

SENSOR

WR-4

• MEASUREMENTS

•

1E2 _~ 8210142140 UU!! ~ HNU 31 "Sh 60

-

.lIh 320

...

~ IISN: 14 25 _KSo: SB TKS: 2.20 21

•

15

I'

A

5 F !HZ!

•

.1 .2 .3.4 .5 .G.7 .8 .91.1

•

1E2 ;;; .

1~

1121014 USO UUII Hf.R4 31 - liST: ISO Wil: 300 IISN:: IS ·.. S= 64 THSo: 3.110

•

• HISWA

Time:

22.00 Hs{m)

Tm{s)

•

0.46

3.7

• Hs

=

significant wave height

Tm

=

rneanwave period

• 14-0ctober-1982

Time:

21.40 He11evoets1uis

Hs

(m)

0.58 Tm{s)

2.1 Time:

22.50 Hellevoetsluis

Hs{m)

0.61 Tm{s)

3.2 n.i.v.

Hs{m)

0.58 Hs{m)

0.64

0.1. V.

Tm{s)

2.1 Tm{s)

3.2

(21)

-16-•

•

II{') ~ 38

§

~ lilt 25 2t 15 11 5

•

• SENSOR

WR-5

MEASUREMENTS

1121014 2140 UUR HII"5 IISI: 60 1111: 320 IIS"= 14 HSc 87 THh 4.110 .1 .2 .3 .~ .5 821014 2230 UUR UII'!S liST: 120 IIR: 300 liS"" 15 HS: 112 T"S: 5.10 ·25 2t 15 11 5

HISWA

Time:

22.00 Hs(m)

Tm(s)

1.04

4.2 Hs

=

significant wave height

Tm

=

mean wave period

14-0ctober-1982

Time:

21.40 Hellevoetsluis

Hs(m)

0.86 Time:

Tm(s)

3.6 Hellevoetsluis

22.30 Hs(m)

1.10 Tm(s)

3.6

0.1. V.

Hs(m)

0.87 Hs(m)

1.12 O.l.V.

Tm(s)

3.6 Tm(s)

3.8

Fig. 13 Measurements at location WR-S.

(22)

-17-•

SENSOR

~R-6

• MEASUREMENTS

•

!¬ ii~. , . ~ 821014 2HO' UUR HWR6 S - W5T: 60 Wil,. 320 W6W: 14 "5= 131 T"5:6.80

Time:

3

Hs(m)

1.36 14-0ctober-1982

Hellevoetsluis

21.40

2

•

821014 2110uu~ HWR6 liST: 185 WR= 300 IISN: 14 H5= 179 T"5= 1.60

Time:

-...

l1i

Tm(s)

5.1 Hellevoetsluis

23.10 Hs(m)

1. 79

•

2

•

• HISWA

Time:

22.00 Hs(m)

Tm(s)

•

1.34

4.6

• Hs

=

significant wave height

Tm

=

mean wave period

Tm(s)

5.7

D.

I.

V.

Hs(m)

1.37 Hs(m)

1. 79

0.1. V.

Tm(s)

5.1 Tm(s)

5.7

•

I

(23)

-18-•

SENSOR

E-75

14-0ctober-1982

• MEASUREMENTS

•

IEl ëQ 821014 2200 UUR

§

E15 . 12 N$Ta: iO

u:

IIh 300

Time:

22.00

~

..

IISH:

"

Ha. 89

Hellevoetsluis

O.l.V.

•

• ,

Hs(m)

Tm(s)

Hs(m)

Tm(s)

0.90

2.8

0.89

2.8

2 F D!Z!

•

.1 .2 .3

••

.5

,

• Time:

Hellevoetsluis

O.l.V.

Hs(m)

Tm(s)

Hs(m)

Tm(s)

•

• HISWA

Time:

22.00 Hs(m)

Tm(s)

•

0.77

3.6

• Hs

=

significant wave height

Tm

=

mean wave period

Fig. 15 Measurements at location E-75.

(24)

-19-•

3. Test in the Galgenplaat region

•

The Galgenplaat is located in the Oosterschelde estuary. The

Galgen-plaat is a shoal surrounded by deep channels, with depths up to 50 m.

•

In contrast with the Haringvliet test, measurements are scarce. Wave

gauges were instalIed in two places, indicated in fig.

16

as 'GALA'

and 'GAHO'. The test was carried out for a situation on March 30,

1983, at 13:00 (M.E.T.).

•

The wind was coming from the South-West, so the waves were primarily

locally generated. Thus wave frequencies are rather high, and the

velocities of the currents around the Galgenplaat cannot be neglected

in this test. Current velocities were determined by the 2-dimensional

unsteady flow model' WAQUA. The station can be characterized as local

wave generation on a current upwind from the shoal, wave breaking over

the shoal and refraction around the shoal. At the location of

observation the situation seems to be dominated by the breaking of

locally generated waves.

•

Details of the parameters of the computations are on the next page.

The following figures are provided:

fig.

16:

Location of the area.

fig. 17: Depths and current vectors in parts of the computational

region.

fig. 18: Significant wave height and energy transport vector in the

same region.

fig. 19: Mean wave period in the same region.

•

The results of the mean wave period were unreliable in part of the

area (the shaded region in fig. 19). It is the region downwave of a

dry part of the shoal, where the action densities are small; the mean

wave period is there obtained as the ratio of two small quantities, so

that small errors deteriorate the results.

•

Because the wave gauge 'GARO' was not flooded at the time of

observation, comparison with measurement can only be based on the

gauge 'GALA'. These measurements are: H

=

0.33 m, and Tmean

=

•

s

1.82 sec; the computation gave: H

=

0.15 mand T

=

2.2 sec.

s mean

(25)

-20-•

•

The differences are considerable, but it must be stressed that

1) the model has been run with default parameter values which have not

been tuned;

2) the current field was not observed but has been computed, thus

introducing differences between the actual situation and the input

current field for the HISWA model;

3) the significant wave height and period are very low in the

measurements. The effects of instrument noise and the reliability

of these measurements is not known to the present authors. Some

caution seems to be called for considering the quality of some of

the observations in the tests described in the previous section

(Har Lngv l.fe t )•

•

To estimate the effect of the spatial resolution of the computation

grid, the computations were repeated for a sub-region of the region

considered above with a mesh of 50 m x 124 mand with a directional

resottition of 8°. The result at the location GALA is for the

signifi-cant wave height 0.15 mand for the mean wave period 2.6 s. This is

slightly better than the results of the large grid computations

compared with the observations. Possible causes for the discrepancies

between observations and computational results are a) wave generation on a current is too slow

b) wave dissipation on a current is too high

c) up-stream boundary effects penetrate deep into the area under

consideration

d) breaking at the shoal is overestimated e) wave set-up is not taken into account

•

• -21-•

(26)

• TEST:

GALGENPLAAT MARCH 14, 1983

•

bottomgrid:

7950

m x

159

x

7950

m x 100 x

12400

m

248 12400

m x

50

x computational grid:

•

boundary values

incoming waves: absent

•

H

=

s

o

m, per

=

s, dir.

=

dspr.

=

•

wind: South-West

UlO

=

9. mis dir

breaking on/-&# frequency on/~

•

bottom friction on/~ frequency on/~ diffraction off

numeric diffusion on/~ wave blocking on/~

•

notes: in wind, breaking and friction only standard coefficients were used.

•

• -22-•

(27)

•

• N

• _{The Netherlands}

•

Oostersehelde ~

•

• DuiveLand

• Noord

a

e

veland

Thol

e

n

• Zuid

a.ve-land

•

Fig. 16 Location of the Galgenplaat shoal in the Oostersehelde tidal basin.

(28)

-23-•

•

/

1 mis 1000 m ~

•

land

\

•

\

"

\

<,

,

_\.

<, 'I. _\.

•

F;i.g.17 Bathymetry and current pattern in the area of

the Galgenplaat. Contourlines are in m, interval is 10.0 m.

(29)

•

wind 9 mis 1000 m 0.01 m /s3 ) ~

• "

...

-

-land

-

-•

0

o

-

--

....

-

--

<,

"

...

..

... _\

,

•

I

0 ..

.,..

•

_...

_..

"

•

• ..

-..

-•

-

--

--land

-•

Fig. 18 Contourlines of significant wave height and

energy transport vectors in the Galgenplaat

area; values are in m, interval is 0.1 m. Wind

is south~west, 9 mis; direct ion as indicated

above.

(30)

-25-I

.

•

Fig. ]9 Contourlines of the average wave pe~, values are in seconds, the interval 1S

0.5 s. In the shaded area the results are truncated at 3.0 s.

(31)

-26-•

4. Computer capacity

•

The computer capacity required for running HISWA is estimated from

some runs with the Galgenplaat model.

•

As a general rule it can be stated that the amount of CPU-time

required for a HISWA computation is roughly proportional to the total

number of points in the computational grid, i.e. the product of N ,

x the number of points in

in x-direction,

•

the number of points

y-direction, and Ne'

illustrated by table 2.

the number of

N ,

y

points in e-direction. This is

•

N_x

*

_N_y

_*

_Ne CPU-time UNIVAC 1100

part of region 6000 44 sec

whole Galgenplaat

region (coarse grid) 40000 319 sec

•

Table 2. Relation of gridsize and computer time for the Galgenplaat

test.

•

The computer storage required is a more complicated matter; this

depends on the number of points in the bottom grid and on the number

of points

points in

preparation

in the computational grid. If M

*

M is the number of

x

y

the bottom grid, the number of data to be stored during the

phase is a few thousand

+

3

*

M

*

M if currents are

x y

•

taken into account, or M

*

M if currents are absent. During the

x

y

computational phase the number of data is roughly 30

*

Ny Ne; Nx

does not influence the required storage because a stepping procedure

is employed in x-direction.

•

• -27-•

(32)

•

5. Conclusions

•

The HISWA model has been run in two regions: the Haringvliet and the

Galgenplaat without any tuning.

•

The agreement between the observations and the computational results

is fair for the Haringvliet situation with differences in significant

wave height of typically 5%-20% (HISWA results too low) and in mean

period of 10%-30% (HISWA results too high) over a range of 0.5-3.0 m

and 6-2 s respectively.

•

The is -50%

agreement between the observations and the computational results

not good for the Galgenplaat situation. The difference is about

for the observed significant wave height of 0.33 mand about +20%

for the observed mean wave period of 1.82 s.

•

Other wave parameters produced by the HISWA model, such as the

directional energy distribution or the radiation stress gradient have

not been observed and the HISWA results could therefore not be

validated for these parameters.

•

The main conclusion is that the HISWA model produces realistic values

for the wave field in complex geophysical situations but some tuning

is required especially in the presence of a current.

•

• -28-•

(33)

•

6. References

•

Booij, N., Gravity waves on water with non-uniform depth and current.

Dissertation, Delft University of Technology, 1981.

Booij, N. and A.C. Radder, CREDIZ, a refraction-diffraction model for

sea waves. DIVISIE, Data Processing Division of Rijkswaterstaat,

1981.

•

Dingemans, M.W., Verification of numerical wave propagation models

with field measurements; CREDIZ verification Haringvliet. Delft

Hydraulics Lab., report W488 part 1, 1983.

Radder, A.C., On the parabolic equation method for water wave

propa-gation. J. Fluid Mech. vol. 95, 1979, 159-176.

•

Stelling, G.S., On the construction of computational methods for

shallow water flow problems. Dissertation, Delft University of

Technology, 1983.

•

(34)

• '

.

•