Physical Oceanography, Vol.
STATISTICAL CHARACTERISTICS OF THE MODULI
OF SLOPES OF THE SEA SURFACE
A. S. Zapevalov
On the basis of data of measurements carried out on an oceanographic platform, we study the
variability of statistical characteristics of the modulus of slopes of the sea surface under various
hydrometeorological situations. We show that the law of distribution of the modulus of slopes of
the sea surface depends on the velocity of the wind and note that the empirical distribution dif-
fers considerably from the approximation proposed by Longuet-Higgins for it by the results of
analysis of a Gauss random moving surface. The possible reasons for the difference in model
and empirical distributions are discussed.
The roughness of the water–air interface influences any process where electromagnetic waves interact with
the sea surface, which explains the timeliness of studying its characteristics for problems of remote sensing.
Slopes of the sea surface are among the main parameters characterizing its roughness.
Studies of slopes of the sea surface were carried out by contact and remote methods [1
5]. The difference
in the characteristics of gages in use became the reason for a significant difference in results derived by many
authors . Most efficient for measurement of slopes are optical methods with the use of laser gages [6, 7].
Their use is not accompanied by a local disturbance of the wave field as occurs with contact gages. Moreover,
the laser gages allow one to measure slopes on the scale of capillary waves, which is impossible if one uses me-
ters coming into contact with the surface.
Field observations showed that the distribution of probabilities for the orthogonal components of slopes is
well described by the Gram
Charlier two-dimensional distribution [1, 2, 5]. Coefficients of Gram
series are such that, in essence, the distribution of the components of slopes is close to the Gauss one and can be
identified with it in some problems. However, slight deviations and the dependence of one of the third-order
moments on the wind velocity [1, 2, 5] may turn out to be significant in the simulation of the distribution of the
modulus of slopes of the sea surface.
It was historically established that the study of variability in the modulus of slopes of the sea surface re-
ceived much less attention than the investigation of variability in their components. At the same time, this pa-
rameter is of importance for a number of problems related to remote sensing. In particular, it is one of the main
parameters defining the character of a lidar signal on sounding in the nadir.
The goal of the present work is to study the variability in the statistical characteristics of the modulus of
slopes of the sea surface under various hydrometeorological conditions.
Measuring Instruments and Conditions of Measurements
Investigations were carried out on the oceanographic platform of the Marine Hydrophysical Institute of the
Ukrainian Academy of Sciences on the Black Sea in summer of 1991 and 1992. The platform was situated at a
distance of 650
m from the seashore, and the depth at the place where the platform was mounted was about 30
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
36, January–February, 2002. Original article submitted November 10, 1999.
24 0928–5105/02/1201–0024 $27.00 © 2002 Plenum Publishing Corporation