The probability that a wave crest in a random sea will exceed a specified height has long been recognized as important statistics in practical work, e.g., in predicting green water load and volume on a ship. Nonlinear probability density functions for predicting green water load and volume are presented. The models are based on the parametric model of Ogawa (2003, “Long-Term Prediction Method for the Green Water Load and Volume for an Assessment of the Load Line,” J. Marine Sci. Technol., 7, pp. 137–144) combined with transformation of a second order wave crest height model. The wave crest height model is obtained from second order wave theory for a narrow-banded sea state in combination with transformation of the Rayleigh distribution. Results from the second order models are compared with model tests of a cargo ship presented in Ogawa (2003, “Long-Term Prediction Method for the Green Water Load and Volume for an Assessment of the Load Line,” J. Marine Sci. Technol., 7, pp. 137–144) and the Ogawa models.

1.
Ogawa
,
Y.
, 2003, “
Long-Term Prediction Method for the Green Water Load and Volume for an Assessment of the Load Line
,”
J. Mar. Sci. Technol.
0948-4280,
7
, pp.
137
144
.
2.
Stansberg
,
C. T.
, and
Karlsen
,
S. I.
, 2001, “
Green Sea and Water Impact on FPSO in Steep Random Waves
,”
Proc. of the Eighth Int. Symp. on Practical Design of Ships and Other Floating Structures
,
Shanghai, China, pp.
593
601
.
3.
Stansberg
,
C. T.
, and
Nielsen
,
F. G.
, 2001, “
Nonlinear Wave-Structure Interaction on Floating Production Systems
,”
Proc. 11th ISOPE Conference
, Stavanger, Norway, pp.
363
372
.
4.
Greco
,
M.
, 2001, “
A Two-Dimensional Study on Green-Water Loading
,” Dr.ing. thesis, Norwegian University of Science and Technology, Faculty of Marine Technology, Trondheim, Norway.
5.
Stansberg
,
C. T.
,
Hellan
,
Ø.
,
Hoff
,
J. R.
, and
Moe
,
V.
, 2002, “
Green Sea and Water Impact on FPSO: Numerical Predictions Validated Against Model Tests
,”
Proc. of the 21st Int. Conf. on Offshore Mechanics and Arctic Engineering
, Oslo, Norway, Paper No. OMAE2002-28562.
6.
Faltinsen
,
O. M.
,
Greco
,
M.
, and
Landrini
,
M.
, 2002, “
Green Water Loading on a FPSO
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
124
(
2
), pp.
97
103
.
7.
Kriebel
,
D. L.
, and
Dawson
,
T. H.
, 1993, “
Nonlinearity in Wave Crest Statistics
,”
Proc. of the 2nd Int. Symp. on Ocean Wave Measurement and Analysis ASCE Waves ’93
,
New Orleans, LA, pp.
61
75
.
8.
Forristall
,
G. Z.
, 1998, “
Wave Crest Distributions: Observations and Second-Order Theory
,”
Ocean Wave Kinematics, Dynamics and Load on Structures, Proc. of 1998 Int. OTRC Symposium
,
Houston, TX, pp.
372
395
.
9.
Tayfun
,
M. A.
, 1980, “
Narrow-Band Nonlinear Sea Waves
,”
J. Geophys. Res.
0148-0227,
85
(
C3
), pp.
1548
1552
.
10.
Tung
,
C.-C.
, and
Huang
,
N. E.
, 1985 “
Peak and Trough Distributions of Nonlinear Waves
,”
Ocean Eng.
0029-8018,
12
(
3
), pp.
201
209
.
11.
Kriebel
,
D. L.
, and
Dawson
,
T. H.
, 1991, “
Nonlinear Effects on Wave Groups in Random Seas
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
113
(
2
), pp.
142
147
.
12.
Forristall
,
G. Z.
, 2000, “
Wave Crest Distributions: Observations and Second-Order Theory
,”
J. Phys. Oceanogr.
1520-0485,
30
(
8
), pp.
1931
1943
.
13.
Prevosto
,
M.
,
Krogstad
,
H. E.
, and
Robin
,
A.
, 2000, “
Probability Distributions for Maximum Wave and Crest Heights
,”
Coastal Eng.
0378-3839,
40
, pp.
329
360
.
14.
Longuet-Higgins
,
M. S.
, 1963, “
The Effect of Non-Linearities on Statistical Distributions in the Theory of Sea Waves
,”
J. Fluid Mech.
0022-1120,
17
(
3
), pp.
459
480
.
15.
Sharma
,
J. N.
, and
Dean
,
R. G.
, 1981, “
Second-Order Directional Seas and Associated Wave Forces
,”
SPEJ
0197-7520,
21
, pp.
129
140
.
16.
Wist
,
H. T.
,
Myrhaug
,
D.
, and
Rue
,
H.
, 2002, “
Joint Distributions of Successive Wave Crest Heights and Successive Wave Trough Depths for Second-Order Nonlinear Waves
,”
J. Ship Res.
0022-4502,
46
(
3
), pp.
175
185
.
17.
Marthinsen
,
T.
, and
Winterstein
,
S. R.
, 1992, “
On the Skewness of Random Surface Waves
,”
Proc. of the Second Int. Offshore and Polar Engineering Conference
,
San Francisco, Vol.
3
, pp.
472
478
.
18.
Myrhaug
,
D.
,
Stansberg
,
C. T.
, and
Wist
,
H. T.
, 2002, “
Aspects of Nonlinear Random Wave Kinematics
,”
Proc. of OMAE’02, 21th Int. Conf. on Offshore Mechanics and Arctic Engineering
, Oslo, Norway, Paper No. OMAE2002-28205.
19.
Wist
,
H. T.
, 2003, “
Statistical Properties of Successive Ocean Wave Parameters
,” Dr.ing. thesis, Norwegian University of Science and Technology, Faculty of Engineering Science and Technology, Trondheim, Norway.
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