Weather & Climate Services for the Energy Industry by Alberto Troccoli

Author:Alberto Troccoli
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

where α, β and γ are constant parameters, subscripts denote time-steps, and δt is the interval between adjacent time-steps. Following Palmer (1999), ϵ is used to denote a small external forcing (for the initial discussion it is assumed that ϵ = 0).

The time evolution of the Lorenz system can be represented as a trajectory (or path) in phase space.1 Figure 6.2a shows a short section of a trajectory as an example: from an initial state near (U, X, Y) = (33, 15, 18), the model evolves to a state (24,-12,-18) over a ‘time’ interval ∑δt = 0.7. If the model is allowed to evolve for a longer period to produce a more extended trajectory (referred to as an attractor), a fuller view of the system’s properties emerges (Fig. 6.2b). The attractor clearly shows two lobes, with the system preferring to occupy states in one or the other of the lobes.

Fig. 6.2The Lorenz model and initial condition problems, using α = 10, β = 28, γ = 8/3 and ϵ = 0. See text for discussion

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