## 1. Introduction

[2] The breaking of ocean surface waves is an important mechanism for air-sea interaction and for controlling wave growth, yet field quantification of breaking is limited [*Banner and Peregrine*, 1993; *Melville*, 1996]. Lack of breaking quantification thus limits global air-sea exchange estimates and operational wave predictions [*Jensen et al.*, 2002]. Remote sensing is a promising approach to fill this data gap, but the extent to which remote signals can be related to dynamic quantities remains largely unknown. Here we use field observations to successfully validate a relationship between the distribution of breaking waves and the energy dissipation rate, and then examine the scale dependence of the breaking activity.

[3] *Phillips* [1985] introduced Λ(*c*), the distribution of total breaking crest lengths per unit area in bands of speed *c* + *dc*, defined by

where *L*_{total} is the average total length of breaking crests per unit area. The distribution is useful as a spectral description of wave-breaking kinematics, with potential extension to wave-breaking dynamics. In particular, the first moment of Λ(*c*) is directly equivalent to the breaking rate at a point,

Higher moments of Λ(*c*) are indirectly related to the dynamics. Since energy dissipation is proportional to *c*^{5} [*Duncan*, 1981], *Phillips* [1985] hypothesized that the total energy dissipation rate would be

where *g* is gravity, *ρ*_{w} is the density of water, and *b* is a numerical constant predicted to be small. This so-called “breaking parameter” *b* is necessary to complete the conceptual model of a breaking crest extracting a fraction of the available wave energy by exerting a stress on the front face of the wave (and against the background orbital motion). As detailed by *Gemmrich et al.* [2008], the breaking parameter *b* thus incorporates the wave slope, the density anomaly of the foam, the ratio of crest to wavelength, and the ratio of orbital velocity to phase speed.

[4] Practical application of Λ(*c*) observations requires in situ measurements of the dissipation rate to validate equation (3) and estimate the breaking parameter *b*, but such in situ measurements have been missing from previous Λ(*c*) studies [*Gemmrich et al.*, 2008; *Melville and Matusov*, 2002; *Phillips et al.*, 2001]. Rather, previous studies have compared *E*_{Λ} with the energy input by the wind [*Gemmrich et al.*, 1994; *Terray et al.*, 1996], assuming a local equilibrium between the wind input and the dissipation due to breaking. Published values for *b* vary from *O*(10^{−4}) [*Gemmrich et al.*, 2008] to *O*(10^{−2}) [*Melville and Matusov*, 2002]. Recent work by *Drazen et al.* [2008] reviews these values, as well as laboratory estimates, and incorporates new data to suggest that *b* is of order (2*ak*)^{5/2}, where *ak* is the wave steepness given by the wave amplitude *a* and wavenumber *k*.