Isopycnal averaging at constant height. Part I: The formulation and a case study

Simple Eulerian averaging of velocities, density, and tracers at constant position is the most natural way of averaging. However, Eulerian averaging gives incorrect watermass distributions and properties as well as spurious diabatic circulations such as the Deacon cell. Instead of averaging at constant height, averaging along isopycnals removes such fictitious mixing and diabatic circulations. Such isopycnal averaging is normally performed at constant latitude, that is, averaging along isopynals as they heave up and down. As a result, height information is lost and the sea surface becomes much warmer (or lighter) than with simple Eulerian averaging. In fact, averaging can be performed along arbitrarily aligned surfaces. This study considers a particular case in which isopycnal averaging is performed at constant height. Thus, this new isopycnal averaging follows isopycnals as they meander horizontally at constant z. Height information is now retained at the cost of losing latitudinal information. The advantage of this averaging is that it avoids the problem of giving a surface that is too warm. Associated with this new isopycnal averaging, a "vertical" transport streamfunction in (rho, z) space can be defined, in analogy to the conventional meridional overturning streamfunction in (y, rho) space. Here in Part I, this constant-height isopycnal averaging is explained and illustrated in an idealized zonal channel model. In Part II the relationship between the two different isopycnal averagings and the Eulerian mean eddy flux divergence is explored.