Lorenz95 model


The Lorenz95 model is an application of the Lorenz (1996) chaotic dynamics. This model is governed by \(I\) equations:

(11)\[\frac{dx_i}{dt} = -x_{i-2} x_{i-1} + x_{i-1} x_{i+1} - x_{i} + F,\]

where \(i = 1, 2, \ldots, I\), with cyclic boundary conditions, and the constant \(F\) is independent of \(i\). The variables of this model may be thought of as values of some atmospheric quantity in \(I\) locations of a latitude circle. The so-called 40-variable version of this model assumes \(I=40\), with \(i = 1, 2, \ldots, 40\), which implies to the cyclic boundary conditions being defined as: \(x_{0} = x_{40}\); \(x_{-1} = x_{39}\); and, \(x_{41} = x_{1}\).


This model was first presented at a Seminar on Predictability at ECMWF in 1995, with the seminar paper published in 1996. The model is also often referred to as the Lorenz96 model (for the year of publication).


Gaspari, G. and Cohn, S.E. (1999), Construction of correlation functions in two and three dimensions. Q.J.R. Meteorol. Soc., 125: 723-757. https://doi.org/10.1002/qj.49712555417

Lorenz, E. N., 1996: Predictability: a problem partly solved. Seminar on Predictability, 4-8 September 1995, volume 1, pages 1–18, European Centre for Medium Range Weather Forecasts, Reading, England. ECMWF.

Lorenz, E. N. and Emanuel, K. A. (1998). Optimal sites for supplementary weather observations: Simulation with a small model. J. Atmos. Sci., 55(3):399–414.