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Abstract: We present a metriplectic formulation of a reduced model for the upper ocean. The model is valid at low frequencies, includes a single layer with lateral inhomogeneity and uniform stratification, and is thermodynamically consistent - that is, it conserves energy while producing entropy. The evolution of any functional of the model variables (horizontal velocity, layer thickness, and buoyancy's vertical average and gradient) is governed by its (Lie-)Poisson bracket with the Hamiltonian, plus a symmetric bracket with a Casimir that incorporates dissipation. The symmetric bracket is constructed in two ways: algebraically and using the metric on the flow domain, the latter justifying the term 'metriplectic bracket.' This is joint work with Erwin Luesink (University of Amsterdam).