Bottom Topography as a Control Parameter in an
    Ocean Circulation Model
    
Martin Losch and Carl Wunsch

  Bottom topography is a major factor in determining the general
  circulation of the ocean. It is, however, inaccurately known in many
  regions, and even where accurately known, the best way to represent 
  (parameterize) it in models is obscure. To begin to understand the  
  influence of errors in topography and of misrepresentations of both 
  resolved and sub-grid scale structures, a linear barotropic shallow 
  water model and its adjoint are developed in which depth is used as 
  a control variable. Simple basin geometries are employed to explore 
  the extent to which topographic structure determines the sea-surface
  elevation in a steady flow and, more directly, the information
  content about the bottom contained in elevation measurements. 
  Experiments show that even perfect measurements of sea-surface
  elevation in a steady state cannot, by themselves, uniquely
  determine the full structure of the bottom topography. (There is a
  null space.) As in most control problems, a priori knowledge of its
  structure is useful in the best topographic determination.
  Resolution of the bottom topography as a function of position is
  greatest where the flow velocities are greatest. Spatial correlation
  between the resolution of the bottom topography and the flow field  
  is weaker (as expected) when noise with realistically large variance
  is introduced into the data. Ultimately, bottom topography will
  likely be included generally as a control variable in GCMs of  
  arbitrary complexity along with other controls such as friction and
  lateral boundary conditions.