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Computers & Geosciences Vol. 13, No. 4, pp. 409--416, 1987 Printed in Great Britain. All rights reserved

0098-3004/87 $3.00 + 0.00 Copyright © 1987 Pergamon Journals Ltd

S H O R T N O T E

H P 67/97 C A L C U L A T O R W A V E S A P P L I C A T I O N P R O G R A M S

NI~STOR W. LANFREDI t and MARIANA B. FRAMII~INAN 2

tDcpartment of Oceanography, Naval Hydrographic Service and 2National Research Council, Ave. Montes de Oca 2124, 1271 Buenos Aires, Argentina

(Received 7 March 1986; revised 11 August 1986)

INTRODUCTION Case L The fetch is > 16km:

The purpose of this note is to provide three different Uw = hand-held calculator programs related to coastal Uw --- morphology and shoreline protection, and the prin- cipal objective is to obviate to the coastal geologist, where oceanographer, or engineer engaged in field opera- Uw tions or surveys, the use of charts or nomograms of the Shore Protection Manual (US Army, 1984). Even UL though these topics are interrelated, the following RL three steps present simplified models for:

(1) Computing adjusted windspeed, (2) Wave forecasting, and (3) Statistical approximation of extreme wave con-

ditions.

COMPUTING ADJUSTED WINDSPEED

This program is designed to calculate a windspeed for use in equations for wave predictions. One thous- and meters above the surface, winds are driven mainly by geostrophic balance between the Coriolis and the atmosheric pressure; in the lower region, the oceans distort wind by friction. Windspeed and direction therefore become a function of the height above the mean surface, roughness, and air-sea temperature differences.

To make the necessary wind transformations, combinations of four adjustment factors will be used.

Elevation The windspeed must be adjusted at 10m above

mean sealevel, using the approximation if Z < 20 m:

U(IO) = U(Z)(IO/Z) t/7 (m/s) (1)

U = windspeed, and

Z -- measurement elevation.

where

Location effects If the wind data are only available from nearby

land sites, open-marine velocity can be approximated with a knowledge of fetch.

RLU z if UL < 18.5 (m/s) (2)

0.9 UL if UL > 18.5 (m/s) (3)

= windspeed total,

= windspeed in lower zone, and

-- lower zone correction

( U L - 1~ 0.5~t2 Rz = 1.95 - \ ~ ] . (4)

Equation (4) corresponds to the curve of figures 3-15, of the SPM (U.S. Army, 1984), developed from Resio and Vincent (1977).

Case IL The fetch is < 16km:

U~ ffi 1.1UL. (5)

Stability correction The air-sea temperature differences may be avail-

able, and the following equation can be used:

u'~ = RTU,~ (6)

where

u ~ =

Rr =

air temperature corrected windspeed, and

temperature correction

_ ( A T ~ °''5 = l \6-~.5/ forAr > 0 (7)

(fATl o.''' R~-) = l + \g~-A/ AT < 0. (8)

Equations (7) and (8) were taken from curves of figure 5 of Resio and Vincent 0977).

A T = - T o - T ~

To = air temperature (°C)

1", = sea temperature (°C).

If the air-sea temperature differences is unknown, but the boundary layer can be characterized, then an assumed correction factor may be used:

409

410 Short Note

stable Rr = 0.9

neutral Rr = 1.0

unstable Rr = 1.1.

In absence of all information of temperature, Rr = 1.1 should be assumed.

Coefficient o f drag The windspeed should be converted to wind stress

factor by the formula:

Ua = 0.71 UA 1'23 (m/s). (9)

Figure 1 shows the flowchart for computing adjusted windspeed.

PROGRAM USER INSTRUCTIONS

Load card (side I and side 2) (Appendix I)

Input data Keys Output

U (m/s) STO 0 Z (m) STO I F (m) STO 2

if: U (overwater) = 1 STO 3 U (overland) = 0 STO 3 AT (known) = 1 STO 4

AT (unknown) = 0 STO 4 Tai r STO 5 T_ STO 6

boundary layer: Stable 1 STO 7 Neutral 0 STO 7 Unstable - 1 STO 7 Press A Press R/S

U (m/s) U (kts)

WAVE FORECASTING

The process of wave forecasting was described by Sverdrup and Munk (1947) by introducing the new concept of wave height. This wave forecasting method was revised by Bretsehneider (1952, 1958) using empirical data, usually termed the SMB method. Spectral analysis, another statistical concept, was introduced to the study of sea waves by Pierson, Neumann , and James (1955). Hasselmann and others (1976), have demonstrated that the spectrum of an actively growing sea wind can be represented reason- ably by one family of spectral shapes. The program which developed the spectral shapes was termed the Joint North Sea Waves Project (JONSWAP).

The JONSWAP program developed new equations for predicting wind generated waves. The cases presented in these programs are:

Case L Fetch limited waves, when the wind duration ta is:

8.933 x 10-3F 2/3 t d > (U A X 0.515) 1/3

where

F = fetch.

Case H. Durat ion limited waves, if:

8.933 x 10-3F 2/3 t d < (UA × 0.515) 1/3 "

Case I lL Fully developed waves, when:

ta > 1.5815 (UA x 0.515)

ta: in hours F: in meters UA: in knots (1 knot = 0.515m/s).

In the situation of fetch limited waves the parameters required are the fetch (F) and the windspeed (UA), where UA has been adjusted in Equat ion (9), (g) is the gravitational acceleration. The following equations are dimensionless:

= 1.6 × l 0 -3

'13

U2 2.857 x lO- ' ~,~-]) (11)

T, : peak spectral period. If the situation is durat ion limited, use:

gH, f gtd~ TM U~ = 6.698 x 10 -s ~ - ] ) (12)

gT= = 3As.s × 10_ 2 (13) v ̂ \vAj

For the situation of fully developed waves:

tr/-/, U2 = 2.433 x 10 -1 (14)

trT. - - = 8.134 (15) UA

T, = 0.95 Tm (where T, is the significant period). Figure 2 is the flowdiagram for wave forecasting.

PROGRAM USER INSTRUC lIONS

Load card (side 1 and side 2) (Appendix 2)


U A (kts) STO 1 t d (h) STO 2 F (m) STO 3 Press A Hj (m)

T (s)

Note: operation of the calculator is simple and straightforward, the program determines and resolves the case. If the fetch is unknown, enter in F f f i 3 x 10 6.

STATISTICAL APPROXIMATION OF EXTREME WAVE CONDITIONS

It is may be necessary to make estimates of the highest waves likely to occur in the lifetime of a shore protection structure. Estimating wave condit ions for

Short Note 411

SEA

© [::':::::°1

LAND

K ~ UNKNOWN

I R,=o.9 [

T

Ju:=R~u. I I

L I i

I

~ L E

I i t,~ :4.t : ol I

Figure 1, Flowchart for computing adjusted windspeed.

100 years, based upon one year of data is obviously hazardous, but the statistic of extreme values provides a theoretical basis from which an estimate can be made. For sea waves, it has been shown that the double exponential distribution is appropriate (Petruaskas and Aagaard, 1970).

Accordingly the Gumbell distribution is appropriate to predict the highest wave value.

(a) first determine the observation period. (b) select N highest waves which exceed a thres-

hold for the period, (c) arrange the N highest waves according to their

value, (d) give the order m for N highest waves after

arranging, and calculate the probabilities that they will not exceed a given value by the following equation:

F t l - - e t

P=(H < xr,.v) = 1 N + # (16)

where xm,t~ represents mth highest wave of N

highest waves, and = and/~, are the parameters determined for the distribution, (,, = 0.44 and

= 0.12), (e) examine the ntness for the Oum~l l distri-

bution,

(17)

in fitting the distribution, the regression coef- ficients A and B are estimated from the following linear equation:

x = A~. + B, (18)

(f) the return period Rp for each highest wave is determined by the following equation:

K 1 R, = N 1 - P , ( H < x,.,~) (19)

where K is the effective period,

CAGZO IB=t-G

412 Short Note

NON

JK 8933 I0"3F 2/3 ( U A x 0.515 ) I ts

/UA Input ,F,t~ /

YES

YES

DURATION LIMITED WAVES

H$ [ Equation(12)]

T$ I" Equation (13)3

FETCH. LIMITED WAVES

H s [ Equotion (10)'1

Ts [ Equotion (11) ]

FULLY DEVELOPED WAVES

H s [ Equation (14 )3

Ts [ Equation ( 15 )3 /

Figure 2. Flowchart for wave forecasting.

(g) the probable wave height for a given return period is calculated as follows:

(1) from Equation (19), the probability that the wave will not exceed the probable height is calculated,

(2) by substituting the probability into Equa- tion 07) , the probable wave height for a given return period is derived.

Figure 3 gives the flowchart for the statistic of extreme wave conditions

PROGRAM USER INSTRUCTIONS

Load card (side 1) (Appendix 3)


Rp (years) STO A K (years) STO B N STO C Press A (program execution will begin) H t (wave data)

After the input of the N wave data, the probable wave height for a period Rp is displayed:

"Rp Remarks: If the period of return is a different

number of years, use the same

Rp (years) STO A

Press fLBL a.

EXAMPLE PROBLEM 1

In a meteorological station located within the coastal area an 20 m/s wind velocity was registered at a 6m height. The air temperature was 10°C and the water's, 16°C. Considering:

(a) a 10kin fetch,

(b) a 100kin fetch,

which is the wind factor UA?

Short Note

* Load the wind adjustment program (Appendix 1)

Input data Output (units) Keys (units)

U = 20m/s STO 0 20.00 Z = 6 m STO 1 6.00 F = 10,000m STO 2 10,000.00 U (overland) 0 STO 3 0.00 AT (known) 1 STO 4 1.00 Tair = 10°C STO 5 10.00 T~ = 16°C STO 6 16.00 Press A 41.08 m/s Press R/S 79.77 kts

U = 20m/s STO 0 20.00 Z = 6 m STO 1 6.00 F-- I00,000 m STO 2 100,000.00 U (overland) 0 STO 3 0.0¢ AT (known) 1 $TO 4 1.00 T.;r = IO°C STO 5 10.00 T~ = 16°C STO 6 16.00 Press A 32.09 m/s Press R/S 62.33 kts

EXAMPLE PROBLEM 2

Given the wind cond i t ions o f the f o r m e r example ,

which are the H~ and the T, w h e n the d u r a t i o n td is 3 h?

• Load the wave forecasting program (Appendix 2)

Input data Output (units) Keys (units)

U a = 79.77 kts STO 1 79.77 t# = 3.0hs STO 2 3.00 F = 10,000m STO 3 10,000.00 Press A 2.10m

4.39 s U a = 32.09m/s STO I 32.09 t,~ = 3.0hs STO 2 100,000.00 F = 100,000m STO 3 100,000.00 Press A 1.34 m

4.41 s

EXAMPLE PROBLEM 3

W h i c h is the m o s t p r o b a b l e wave he ight to be

a t ta ined in 10 years in a site whe re the fo l lowing

m a x i m u m wave heights were registered: 5.0 m, 4.8 m,

7 .0m, and 3 .5m, in a 5 year effective per iod?

* Load the extreme wave conditions program (Appendix 3)

Input data Output (units) Key (units)

Rp = 10 years STO A K = 5 years STO B N = 4 S T O C Press A H I = 7.0m ENTER H I = 5.0m ENTER H 3 = 4.8m ENTER H 4 = 3.5m ENTER

10.00 5.00 4.00 1.00 7.00 5.00 4.80 3.50

6.99m

413

Iooo,/ ,K,~ /

l CLear

memor ies

Re. Rs,-,-R,,

I ~'=I 1 I-

Inpul' x. / I

[compu,e ~ I I

I Y.X=; Z r m

~ X,, T=; Y-T,~ 2

NON~ m =

ResoLves [ A 8 8 by Least

squares

t 1

I

I (o,.o,o..)

°.,]

Figure 3. Flowchart for statistic of extreme wave conditions

R E F E R E N C E S

Bretschneider, C. L., 1952, Revised wave forecasting rela- tionships: Proc. Second Conf. on Coastal Engineering (Houston, Texas), ASCE, Council on wave research, p. 1-5.

Bretschneider, C. L., 1958, Revisions in wave forecasting"

414 Short Note

deep and shallow water: Proc. Sixth Conf. on Coastal Engineering (Gainsville, Florida), ASCE, Council on wave research, p. 30-67.

Hasselman, K., Ross, D. B., Miiller, P., and Sell, W., 1976, A parametric wave prediction model: Jour. Physical Oceanography, v. 6, no. 2, p. 200-228.

Petruaskas, C., and Aagaard, P. M., 1970, Extrapolation of historical storm data for estimating design wave heights: Proc. Offshore Technology Conf. (Houston, Texas), Paper No. OCT 1190, p. 409-427.

Pierson, W. J., Ncuman, J. R., and James, R.W., 1955, Practical methods for observing and forecasting ocean wave by means of wave spectra and statistics: U.S. Navy

Hydrographic Office (Washington, D.C.), Publ. No. 603, 284 p.

Resio, D. T., and Vincent, C. L., 1977, Estimation of winds over the Great Lakes: Jour. Waterways, Ports, Coastal and Ocean Division, ASCE, v. 103, no. WW2, p. 265-283.

Sverdrup, H. U., and Munk, W. H., 1947, Wind, sea, and swell: theory of relations for forecasting: U.S. Navy Hydrographic Office (Washington, D.C.), Publ. No. 601, 47 p.

US Army, 1984, Shore protection manual: Coastal Engi- neering Research Center, Corps of Engineers, v. 1, p. 3-51.

APPENDIX 1

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APPENDIX 2

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APPENDIX 3

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