Relaxation toward observations in level and isopycnic models

Relaxation toward observed values is frequently undertaken in ocean models for numerous reasons. In level models, relaxation of some quantity takes th e form of a linear "nudging" term proportional to the difference between ob served and computed value of that quantity. In isopycnic models, relaxation of tracers and/or layer depth toward observed values is often employed as an equivalent. This note shows that relaxation of temperature and salinity- and hence density-in a level model is not equivalent to relaxation either o f those tracers or of layer thickness in an isopycnic model. Comparison of layer thickness tendencies in the two model types shows that these differ b y the ratio of observed Vertical density gradient to model vertical density gradient. Only in the special case where the model remains close to observ ations are the two methods the same to leading order. It is not obvious whe ther isopycnic or level relaxation is to be preferred.