**Statistical Methods for the Analysis of Wave Video
Data**

Waves play an extremely important role in air-sea interaction and contribute significantly to weather and climate dynamics. In the air-sea interaction context the role of wind waves is primarily two-fold: (i) wave dynamics to a large extent control exchange of gas, heat and momentum at the air-sea interface; (ii) most of remote sensing methods employed to monitor physical processes on ocean surface or/and in the ocean interior require knowledge of specific properties of the waves.

Experimental techniques for studying these processes have improved dramatically in the past few years, along with the computer power available to analyze the resulting data; statistical techniques to analyze this data, though, have lagged behind. The aim of this research is to develop new statistical approaches for analyzing wave field video data.

To date, we have:

i) Developed a measure of regularity for wave patterns in terms of a decomposition of the wave field into a sum of non-linear plane waves (1).

i) Developed methods for the reconstruction of wave height and slope fields from refraction and reflection based imaging (2,3).

Figure (a),(b)*: Images of the
wave tank at IRPHE, Marseille. *(a)* shows a typical wave pattern, *(b)*
shows the evolution of breaking waves. *(c)* is a schematic of the wave
tank. Waves are generated either by controlled wind or by a paddle.
Overhead video camera records slopes of the waves present over a 1 square metre
light box. These are then reconstructed to obtain a wave height field as
shown in *(d)*.*

**Researchers: **Finbarr
O'Sullivan, Kingshuk
Roy Choudhury

Students: Mayukh Samanta (Ph.D. submitted 2009)

**Collaborators:** G.** **Caulliez
(IRPHE),
V.I. Shrira
(Mathematics Department, Keele University)

1) O’Sullivan,
F., Roy Choudhury, K, 2006, A Statistical Measure of Regularity
for the Study of Wind-Generated Wave Field Images, *J.American Statist.Assoc.*, 101, 475, 1119 – 1131

2) O’Sullivan,
F., Huang, J., Roy Choudhury, K., Caulliez, G., Shrira, V., 2008, Regularized Reconstruction of Water
Surfaces from Noisy Gradient Information using Plane Wave Superposition, *Inverse Problems, *24, 034016

3) Roy
Choudhury, K., O’Sullivan, F., Samanta, M., Caulliez, G., Shrira, V., 2009,
Reconstruction of wave height and slope fields from refracted images of water, *Journal of the American Statistical
Association,* in press* *

**Funding:**

Irish Research Council for Science Engineering and Technology, Basic Research Grant: 2004-2007

INTAS (EU): 2006-2008