Overview

The Lorenz Energy Cycle (LEC), introduced by Edward Lorenz in 1965, is an analytical framework used to estimate atmospheric energy. It categorizes energy into zonal and eddy components of Kinetic Energy (Kz and Ke, respectively) and Available Potential Energy (Az and Ae, respectively). The LEC also quantifies conversions between these forms (Ca, Ce, Cz, and Ck), along with generation and dissipation terms (Gz, Ge, Dz, and De). Originally developed for global energetics, the framework has been adapted for regional studies, incorporating calculations for energy transport across boundaries (BAz, BAe, BKz, BKe).

The LEC budget is described by the following equations:

\begin{align*} \frac{\partial A_Z}{\partial t} &= -C_Z - C_A + G_Z + B A_Z \\ \frac{\partial K_Z}{\partial t} &= -C_Z + C_K - D_Z + B K_Z + B \Phi_Z \\ \frac{\partial A_E}{\partial t} &= C_A - C_E + G_E + B A_E \\ \frac{\partial K_E}{\partial t} &= C_E - C_K - D_E + B K_E + B \Phi_E \end{align*}

Due to the difficulty in measuring friction terms for dissipation, both dissipation and generation are often computed as residuals from the budget equations:

\begin{align*} RG_Z &= G_Z + \varepsilon_{AZ} \\ RG_E &= G_E + \varepsilon_{AE} \\ RK_Z &= B \Phi_Z - D_Z + \varepsilon_{KZ} \\ RK_E &= B \Phi_E - D_E + \varepsilon_{KE} \end{align*}

Where ε represents numerical errors. The complete cycle, assuming all terms are positive, is depicted below: