7A suite of idealized models is used to evaluate and compare several previously proposed scalings for the 8 eddy transport coefficient in downgradient mesoscale eddy closures. Of special interest in this comparison 9 is a scaling introduced as part of the eddy parameterization framework of Marshall et al. (2012), which is 10 derived using the inherent geometry of the Eliassen-Palm eddy flux tensor. The primary advantage of using 11 this coefficient in a downgradient closure is that all dimensional terms are explicitly specified and the only 12 uncertainty is a nondimensional parameter, α, which is bounded by one in magnitude. 13 In each model a set of passive tracers is initialized, whose flux statistics are used to invert for the eddy-14 induced tracer transport. Unlike previous work, where this technique has been employed to diagnose the 15 tensor coefficient of a linear flux-gradient relationship, the idealization of these models allows the lateral 16 eddy transport to be described by a scalar coefficient. The skill of the extant scalings is then measured by 17 comparing their predicted values against the coefficients diagnosed using this method. The Marshall et al.
18(2012) scaling is shown to scale most closely with the diagnosed coefficients across all simulations. It is 19 shown that the skill of this scaling is due to its functional dependence on the total eddy energy, and that 20 this scaling provides an excellent match to the diagnosed fluxes even in the limit of constant α. Possible 21 extensions to this work, including how to incorporate the resultant transport coefficient into the Gent and 22 McWilliams parameterization, are discussed.23 large-scale circulation requires model grid spacings at least an order of magnitude finer than the dominant 33 energy-containing scales. Even in the mid-latitudes, where the dominant eddy scale is approximately 100 34 km (Stammer, 1997; Chelton et al., 1998), for a model to be considered "mesoscale eddy-resolving" requires 35 a grid spacing of less than 10 km (Hecht and Smith, 2008; Hallberg, 2013), beyond the capability of current 36 climate-scale ocean models.
37A longstanding approach to the eddy parameterization problem is to consider the resolved flow as an 38 averaged or filtered representation of the true flow field. For a Cartesian-coordinate model, after applying 39 the standard Reynolds averaging axioms to the primitive equations the resulting equation set contains an eddy 40 flux divergence in each of the constituent equations, each of which must be parameterized. It has heretofore 41 been common to develop parameterizations for each eddy flux individually, rather than developing a single, 42 unified parameterization for the full set of eddy fluxes. The downside of this approach is that a model may 43 feature several potentially inconsistent eddy parameterizations, where answers to practical questions such as 44 how these parameterizations interact are often unknown. 45 Because of these difficulties, it is advantageous to try to reduce the number of ...
