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
HP 67/97 CALCULATOR WAVES APPL ICAT ION PROGRAMS
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-
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.
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)
air temperature corrected windspeed, and
_ ( AT~ ''5 = l \6-~.5/ fo rAr > 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).
AT=- To -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:
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 of 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 adjus- ted 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)
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 equa- tions for predicting wind generated waves. The cases presented in these programs are:
Case L Fetch limited waves, when the wind dura- tion ta is:
8.933 x 10-3F 2/3 t d > (U A X 0.515) 1/3
F = fetch.
Case H. Duration 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 par- ameters required are the fetch (F) and the windspeed (UA), where UA has been adjusted in Equation (9), (g) is the gravitational acceleration. The following equa- tions are dimensionless:
= 1.6 l0 -3
U2 2.857 x lO-' ~,~-]) (11)
T,: peak spectral period. If the situation is duration 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)
Input data Keys Output
U A (kts) STO 1 t d (h) STO 2 F (m) STO 3 Press A Hj (m)
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 i3 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 conditions for
Short Note 411
K ~ UNKNOWN
I R,=o.9 [
L I i
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 appro- priate 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 fol- lowing equation:
Ft 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~ll distri-
in fitting the distribution, the regression coef- ficients A and B are estimated from the follow- ing 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,
412 Short Note
JK 8933 I0"3F 2/3 ( U A x 0.515 ) Its
/UA Input ,F,t~ /
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)
Input data Keys Output
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: I f 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 10C and the water's, 16C. Considering:
(a) a 10kin fetch,
(b) a 100kin fetch,
which is the wind factor UA?
* Load the wind adjustment program (Appendix 1)
Input data Output (units) Keys (units