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Lai-Yung Leung
and
Gerald R. North

Abstract

Atmospheric variability an a zonally symmetric planet in the absence of external forcing anomalies is studied. With idealized boundary conditions such as the absence of ocean and topography, and by using perpetual equinox solar forcing, a 15-year long stationary time series of the atmosphere is simulated with the NCAR Community Climate Model (CCM0). This provides sufficient time samples for realistic study of the properties of the atmosphere. Zonally averaged and space-time statistics for the surface air temperature field on this planet are presented. Such statistics can serve as noise climatologies for climate sensitivity experiments, allowing the effects of changes of external forcing on the atmosphere to be asssessed.

In search of a simple statistical model for atmospheric variability, the space-time spectra obtained from the CCM simulation are fitted statistically with a stochastic energy balance model. The space-time spectra for three zonal wavenumbers are found to be fitted satisfactorily by the stochastic model with only five parameters (a heat diffusion coefficient, a constant zonal advection speed, a radiative damping constant and two parameters for blue spatial noise amplitudes). The estimated parameters agree with previously obtained values. This suggests that useful statistics for large-scale atmospheric variability may be obtained from simple statistical models. With the method of analysis provided in this study, the ability of the stochastic model for describing atmospheric variability on a more realistic planet (including geography and seasonal cycle) can be tested. This may involve comparing space-time statistics from the stochastic model with observed quantities and by using empirical orthogonal functions as a basis set for expansion.

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Lai-Yung Leung
and
Gerald R. North

Abstract

This paper introduces the use of information theory in characterizing climate predictability. Specifically, the concepts of entropy and transinformation are employed. Entropy measures the amount of uncertainty in our knowledge of the state of the climate system. Transinformation represents the information gained about an anomaly at any time t with knowledge of the size of the initial anomaly. It has many desirable properties that can be used as a measure of the predictability of the climate system. These concepts when applied to climate predictability are illustrated through a simple stochastic climate model (an energy balance model forced by noise). The transinformation is found to depict the degradation of information about an anomaly despite the fact that we have perfect knowledge of the initial state. Its usefulness, especially when generalized to other climate models, is discussed.

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Gerald R. North
,
Kuor-Jier Joseph Yip
,
Lai-Yung Leung
, and
Robert M. Chervin

Abstract

The concept of “forced” and “free” variations of large-scale surface temperature is examined by analyzing several long runs of the Community Climate Model (CCMO) with idealized boundary conditions and forcing. 1) The planet is all land with uniform sea-level topography and fixed soil moisture. 2) The planetary surface and prescribed ozone are reflection symmetric across the equator and there is no generation of snow. 3) The obliquity is set to zero so that the climate is for a perpetual equinox solar insolation (i.e., sun fixed over the equator). After examining some relevant aspects of the undisturbed climate (surface temperature field) such as temporal and spatial autocorrelations and the corresponding spectra, two types of changes in external forcing are imposed to study the model response: 1) sinusoidal changes of the solar constant (5%, 10%, 90%, and 40% amplitudes) at periods of 15 and 30 days (the latter is the autocorrelation time for the global average surface temperature) and 20% at 60 days and 2) insertion of steady heat sources (points and zonal bands) of variable strength at the surface. Then the temporal spectra of large scales for the periodically forced climate and the ensemble-averaged influence functions are examined for the point source disturbed climates. In each class of experiments the response of ensemble-averaged amplitudes was found to be proportional to the amplitude of the forcing. These results suggest that the lowest moments of the surface temperature field have a particularly simple dependence on forcing. Furthermore, the apparent finiteness of the variance spectrum at low frequencies suggests that estimates of long-term statistics are stable in this type of atmospheric general circulation model.

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