## 1. Introduction

[2] *Egbert and Ray* [2001; see also *Egbert and Ray*, 2000] presented empirical maps of tidal dissipation in the global ocean based on TOPEX/Poseidon (T/P) altimeter data, demonstrating that a significant fraction (25–35%) of barotropic tidal energy is lost in the deep ocean over rough topography. Although the T/P data only directly constrain the spatial pattern of open ocean dissipation, this pattern, and other evidence [*Ray and Mitchum*, 1997; *Egbert and Ray*, 2001] support the inference that energy losses from the surface tides in the deep ocean must result from conversion into internal tides. The analysis of *Egbert and Ray* [2001] was restricted to the dominant semi-diurnal M_{2} constituent, which accounts for roughly 2/3 of all tidal dissipation. In this paper we present estimates of dissipation computed for seven additional tidal constituents, both semi-diurnal and diurnal. The largest of these dissipate almost an order of magnitude less energy than M_{2}, so we can anticipate significantly greater difficulties with noise.

[3] As in *Egbert and Ray* [2001] the dissipation rate is estimated as the balance between work done by tidal forces and the divergence of tidal energy flux

Here ζ and **U** are tidal elevations and volume transports, ζ_{EQ} is the equilibrium tide, ζ_{SAL} accounts for ocean self-attraction and loading, and the brackets 〈 〉 denote time averages. T/P directly constrains ζ, and from this ζ_{SAL} can be readily calculated [*Ray*, 1998]. *Egbert and Ray* [2001] estimated **U** by fitting altimetrically constrained elevations and the shallow water equations (SWE) with two different least squares (LS) procedures. In the first approach, the variational data assimilation scheme of *Egbert et al.* [1994] was used to estimate both ζ and **U** by minimizing a weighted misfit to the T/P data and the SWE. In the second approach, gridded tidal elevation fields ζ estimated empirically from T/P altimeter data were substituted into the SWE, and the volume transports **U** were estimated by weighted LS, minimizing residuals in the dynamical equations. Provided mass conservation was strongly enforced, similar dissipation maps for M_{2} were obtained with both approaches. For the additional constituents considered here dissipation maps obtained by the two approaches are similar for S_{2} and K_{1}, but for the smaller constituents maps derived from the empirical solution are rather noisy. We thus focus on the generally cleaner results obtained with the variational assimilation approach.