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Initial Conditions for Optimal Growth in a Coupled Ocean–Atmosphere Model of ENSO

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  • 1 Joint Institute for the Study of the Atmosphere and Ocean and Department of Applied Mathematics, University of Washington, Seattle, Washington
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Abstract

Several studies have examined the conditions in the equatorial Pacific basin that lead to the maximum growth over a fixed time period, τ. These studies have the purpose of finding the characteristic precursor to an ENSO warm event, or more generally to explore error growth and predictability of the coupled ocean–atmosphere system. This paper develops a linearized version of the Battisti model (similar to the Zebiak–Cane model) with a time-invariant background state. The optimal initial conditions for time period τ (τ-optimals) were computed for a range of τ and for a selection of background states.

A number of interesting characteristics of the τ-optimals emerged: 1) The τ-optimals grow more quickly than even the most unstable mode (the ENSO mode) of the system. 2) The τ-optimals develop quickly into the ENSO mode—in around 90 days. 3) The ENSO mode produced by a given τ-optimal does not in general peak at time τ. For τ less than 360 days the ENSO modes peak after time τ, and for τ greater than 360 days the ENSO mode first peaks before τ. At 360 days, designated τmax, the ENSO mode peaks at τ: this is also the τ-optimal, which produces the most growth. 4) Optimals were produced that used the SST only (T-optimals) and that used only the ocean dynamics (r-optimals). It is shown that for τ greater than 60 days, these two optimals both produce ENSO modes (of the same phase). This result makes a comparison of the relative importance of the SST versus the ocean dynamics straightforward: A T-optimal pattern with a 0.1 degree anomaly produces the same size ENSO as an r-optimal pattern with 1.2-m thermocline anomaly. 5) It is shown that the full optimal is the linear combination of these two suboptimals, where their relative sizes are determined by their relative weights (in the norm used).

The paper also experiments with a neutral and a damped version of the model and shows that their optimals have similar properties to those listed above; in particular, the shape of the optimal patterns is not overly sensitive to stability. The physical mechanisms for optimal growth are explored in depth.

Corresponding author address: Chris Thompson, University of Washington, JISAO, Box 354235, Seattle, WA 98195-4235.

Email: thompson@amath.washington.edu

Abstract

Several studies have examined the conditions in the equatorial Pacific basin that lead to the maximum growth over a fixed time period, τ. These studies have the purpose of finding the characteristic precursor to an ENSO warm event, or more generally to explore error growth and predictability of the coupled ocean–atmosphere system. This paper develops a linearized version of the Battisti model (similar to the Zebiak–Cane model) with a time-invariant background state. The optimal initial conditions for time period τ (τ-optimals) were computed for a range of τ and for a selection of background states.

A number of interesting characteristics of the τ-optimals emerged: 1) The τ-optimals grow more quickly than even the most unstable mode (the ENSO mode) of the system. 2) The τ-optimals develop quickly into the ENSO mode—in around 90 days. 3) The ENSO mode produced by a given τ-optimal does not in general peak at time τ. For τ less than 360 days the ENSO modes peak after time τ, and for τ greater than 360 days the ENSO mode first peaks before τ. At 360 days, designated τmax, the ENSO mode peaks at τ: this is also the τ-optimal, which produces the most growth. 4) Optimals were produced that used the SST only (T-optimals) and that used only the ocean dynamics (r-optimals). It is shown that for τ greater than 60 days, these two optimals both produce ENSO modes (of the same phase). This result makes a comparison of the relative importance of the SST versus the ocean dynamics straightforward: A T-optimal pattern with a 0.1 degree anomaly produces the same size ENSO as an r-optimal pattern with 1.2-m thermocline anomaly. 5) It is shown that the full optimal is the linear combination of these two suboptimals, where their relative sizes are determined by their relative weights (in the norm used).

The paper also experiments with a neutral and a damped version of the model and shows that their optimals have similar properties to those listed above; in particular, the shape of the optimal patterns is not overly sensitive to stability. The physical mechanisms for optimal growth are explored in depth.

Corresponding author address: Chris Thompson, University of Washington, JISAO, Box 354235, Seattle, WA 98195-4235.

Email: thompson@amath.washington.edu

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