Earth Atmosphere

Description: Model of an Atmospheric Storm Track

This benchmark models the track of an atmospheric storm track. More details can be found in and , .

Origin

This benchmark is part of the SLICOT Benchmark Examples for Model Reduction.

Data

The system matrices $A$, $B$, $C$ are available from the SLICOT benchmarks page: eady.zip and are stored as MATLAB .mat file.

Here is Python code for loading the matrices ($B$ and $C$ are stored as arrays of 8-bit unsigned integers):

import numpy as np
from scipy.io import loadmat

mat = loadmat('eady.mat')
A = mat['A']
B = mat['B'].astype(np.float64)
C = mat['C'].astype(np.float64)

Dimensions

System structure:

$\begin{align} \dot{x}(t) &= A x(t) + B u(t) \\ y(t) &= C x(t) \end{align}$

System dimensions:

$A \in \mathbb{R}^{598 \times 598}$, $B \in \mathbb{R}^{598 \times 1}$, $C \in \mathbb{R}^{1 \times 598}$.

Citation

To cite this benchmark, use the following references:

• For the benchmark itself and its data:

Niconet e.V., SLICOT - Subroutine Library in Systems and Control Theory, http://www.slicot.org

@MANUAL{slicot_cdisc,
 title =        {{SLICOT} - Subroutine Library in Systems and Control Theory},
 organization = {Niconet e.V.}
 address =      {\url{http://www.slicot.org}},
 key =          {SLICOT}
}

• For the background on the benchmark:

@ARTICLE{FarI95,
 author =       {B.F. Farrell and P.J. Ioannou},
 title =        {Stochastic Dynamics of the Midlatitude Atmospheric Jet},
 journal =      {Journal of the Atmospheric Sciences},
 volume =       {52},
 number =       {10},
 pages =        {1642--1656},
 year =         {1995},
 doi =          {10.1175/1520-0469(1995)052<1642:SDOTMA>2.0.CO;2}
}