Lorenz95 model

Introduction

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

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

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, $x_{41} = x_{1}$.

YAML parameters

The configurable Lorenz95 model parameters are as follows:

• geometry: define grid parameters

  • resol: define the number of variables $I$

• model: define model parameters

  • f: define the constant $F$

  • name: define the model

  • tstep: define the time step

• forecast length: define the length of the forecast

• initial condition: define initial condition parameters

  • date: define the initial date to issue a forecast

  • filename: define the name of the file to be used as initial condition

• output: define output parameters

  • datadir: define the directory to save files

  • date: define the output date

  • exp: define an experiment identification

  • frequency: define the frequency to save output files

  • type: define the type of output file

Note

Although the YAML parameters are defined using real time quantities for dates and time intervals (e.g., date, tstep, forecast length, frequency), the actual equivalence between real time and the time considered for this model is defined as a combination of the number of variables $I$ and the constant $F$. See details in Lorenz (1996) and Lorenz and Emanuel (1998).

References

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.