On the Errors of Estimating Oceanic Eddy Kinetic Energy
Guidi Zhou, Xuhua Cheng
Abstract
Abstract When evaluating the kinetic energy of the eddy field, using a flow‐decomposition method to split the eddies from the mean‐flow is often necessary. However, the kinetic energies of the eddy and mean‐flow may not sum up to the total energy, because of the existence of a third term, the residual kinetic energy (RKE). This paper attempts to thoroughly assess the RKE from both theoretical and observational perspectives. It is shown that the instantaneous RKE can be quite large, therefore should not be ignored in the time‐varying energetics. The Reynolds decomposition, however, eliminate the time‐mean RKE. It is thus a good practice to study the energy budget in the sense of time‐mean. A running piece‐wise Reynolds decomposition is proposed to allow for choosing the scales of interest while retaining the feature of zero mean RKE. Another decomposition method, the temporal filtering using spectral truncation, are inspected in detail. Based on 26‐years realistic ocean observations, it is found that the ratio between the mean RKE and mean total energy (the Mean Residual Energy Error [MREE]) depends on the spectral shape, the cutoff period, and the available data length. Maximum MREE for cutoff period of 1 year is about 20%. Spatially, the MREE concentrates in zonal bands migrating poleward with increasing cutoff period. MREE from the temporal and spatial coarse‐graining filters with the boxcar and Gaussian kernels are also evaluated. The necessity to estimate the MREE before analyzing the energy budget is emphasized, lest the RKE takes up a non‐negligible portion.