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John A. Dutton


An analytical model of the globally averaged surface temperature response to changes in radiative forcing induced by greenhouse gases is developed from a time-dependent version of the global energy budget. The model clarifies the role of feedback and system heat capacity in controlling the magnitude and rate of response.

Observed seasonal changes in surface temperature, radiative fluxes, and planetary albedo are combined to estimate the atmospheric feedback and the net gain of the system. A simple model of ocean upwelling and diffusion then yields an estimate of the heat capacity and thus the time constant of the system. The observed global temperature change from 1900 to 1990 is used to calibrate the model and refine the estimate of the time constant. The model provides a framework for comparing numerical models, including time-dependent ocean-atmosphere models used by the Intergovernmental Panel on Climate Change to estimate expected global temperature changes.

When integrable analytical approximations to greenhouse-forcing scenarios are combined with the model, completely analytical representations of the global temperature change are readily obtained, yielding numerical estimates that agree with those of more complex models.

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Jon M. Nese and John A. Dutton


A dynamical systems approach is used to quantify the predictability of weather and climatic states of a low order, moist general circulation model. The effects on predictability of incorporating a simple oceanic circulation are evaluated. The predictability and structure of the model attractors are compared using Lyapunov exponents, local divergence rates, and the correlation and Lyapunov dimensions.

Lyapunov exponents quantify global, or time-averaged predictability, by measuring the mean rate of growth of small perturbations on an attractor, while local divergence rates quantify temporal variations of this error growth rate and thus measure local, or instantaneous, predictability.

Activating an oceanic circulation increases the average error doubling time of the atmosphere and the coupled ocean-atmosphere system by 10% while decreasing the variance of the largest local divergence rate by 20% . The correlation dimension of the attractor decreases slightly when an oceanic circulation is activated, while the Lyapunov dimension decreases more significantly because it depends directly on the Lyapunov exponents.

The average predictability of annually averaged states is improved by 25% when an oceanic circulation develops, and the variance of the largest local divergence rate also decreases by 25%. One-third of the yearly averaged states have local error doubling times larger than 2 years, indicating that annual averages may, at times, be predictable, even without predictable variations in external forcing. The dimensions of the attractors of the yearly averaged states are not significantly different than the dimensions of the attractors of the original model.

Arguably the most important contribution of this article is the demonstration that the local divergence rates provide a concise quantification of the variations of predictability on attractors and an efficient basis for comparing their local predictability characteristics. From a practical standpoint, local divergence rates might he computed to provide a real-time estimate of local predictability to accompany an operational forecast.

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Jon M. Nese, Arthur J. Miller, and John A. Dutton


A low-order moist general circulation model of the coupled ocean-atmosphere system is reexamined to determine the source of short-term predictability enhancement that occurs when an oceanic circulation is activated. The predictability enhancement is found to originate predominantly in thermodynamic processes involving changes in the mean hydrologic cycle of the model, which arise because the mean sea surface temperature is altered by the oceanic circulation. Thus, time-dependent sea surface temperature anomalies forced by anomalous geostrophic currents in the altered mean conditions do not contribute to the dominant ocean-atmosphere feed-back mechanism that causes the predictability enhancement in the model.

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