On the Errors of Estimating Oceanic Eddy Kinetic Energy

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. Plain Language Summary Eddy kinetic energy is an important quantity in ocean energetics. It is estimated from the current velocity of eddies, which is extracted from the background mean-flow field by some kind of flow-decomposition methods. These methods, however, usually cannot guarantee that the eddy and mean-flow kinetic energies sum up to the total energy. The part that is left over is called the residual energy. This paper evaluates the residual energy thoroughly and quantitatively. It is shown that the residual energy can be quite large, therefore it should not be ignored. Averaging the energy terms over a time window is useful to reduce or even eliminate the residual energy. The ratio between the time-mean residual and total energies is called the Mean Residual Energy Error (MREE), and it depends on the shape of the spectra of the current velocity, the critical period that defines the eddy and mean-flow (called the cutoff period), and the available data length. For ocean eddies on the time scales of a month, a season, a year, and several years, the MREE can reach up to 3%, 10%, 20%, and 20%, estimated using 26 years of data. Shorter data length would increase the MREE. Different methods are used and compared.

Automated summary

This paper evaluates the importance of residual kinetic energy (RKE) in ocean energetics, proposing methods for its assessment and handling, including Reynolds decomposition and spectral truncation. Through practical ocean observations, variations in MREE under different conditions were identified, highlighting the necessity of estimating MREE before analyzing energy budgets.