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A Stochastic-Dynamical Approach to the Study of the Natural Variability of the Climate

David M. StrausLaboratory for Atmospheric Sciences, NASA Goddard Space Flight Center, Greenbelt, Greenbelt, MD 20771

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Milton HalemLaboratory for Atmospheric Sciences, NASA Goddard Space Flight Center, Greenbelt, Greenbelt, MD 20771

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Abstract

We investigate here the statistical effects of changing boundary conditions on the daily fluctuations of the atmosphere. Weather fluctuations obtained from simulations with the GLAS general circulation model (GCM) and from observed station data are stochastically modeled over the continental United States. Eleven model January integrations with randomly perturbed initial conditions for three different years were carried out with identical climatological boundary conditions. These integrations are considered as independent realizations of an unchanging climate, whose statistical properties represent the natural variability (i.e., the unpredictable component) of the atmosphere.

Finite autoregressive processes (zeroth order or white noise, first order and second order) are used to model the behavior of the surface temperature and sea level pressure at 54 surface stations distributed over the continental United States. It is found that white noise and first-order processes are inconsistent with both the model and the observational data but that for many regions (in particular the midwest United States) a second-order process is consistent with the data. A comparison of the autocovariance functions (acfs) with those of the “best-fit” first- and second-order autoregressive processes indicates that the calculated acfs become negative after a few days, a feature that a first-order process cannot reproduce. Limitations to the statistical confidence of all these results were the fact that the integrations were only 31 days long and the initial conditions were not as independent as randomly chosen states.

Comparisons of model results with those from observations indicate that the changing boundary conditions do not affect the sea level pressure fluctuations on time scales less than one month, but that this assumption may not be true for surface temperature. This suggests an intrinsic limitation for inferring monthly or seasonal estimates of natural fluctuations of surface temperature from the observed daily statistics. Two further results suggested by the study are (i) that modeling climate noise at a station may require higher order autoregressive processes or must take into account spatial correlations, and (ii) that the applicability of stochastic processes may be geographically dependent.

Abstract

We investigate here the statistical effects of changing boundary conditions on the daily fluctuations of the atmosphere. Weather fluctuations obtained from simulations with the GLAS general circulation model (GCM) and from observed station data are stochastically modeled over the continental United States. Eleven model January integrations with randomly perturbed initial conditions for three different years were carried out with identical climatological boundary conditions. These integrations are considered as independent realizations of an unchanging climate, whose statistical properties represent the natural variability (i.e., the unpredictable component) of the atmosphere.

Finite autoregressive processes (zeroth order or white noise, first order and second order) are used to model the behavior of the surface temperature and sea level pressure at 54 surface stations distributed over the continental United States. It is found that white noise and first-order processes are inconsistent with both the model and the observational data but that for many regions (in particular the midwest United States) a second-order process is consistent with the data. A comparison of the autocovariance functions (acfs) with those of the “best-fit” first- and second-order autoregressive processes indicates that the calculated acfs become negative after a few days, a feature that a first-order process cannot reproduce. Limitations to the statistical confidence of all these results were the fact that the integrations were only 31 days long and the initial conditions were not as independent as randomly chosen states.

Comparisons of model results with those from observations indicate that the changing boundary conditions do not affect the sea level pressure fluctuations on time scales less than one month, but that this assumption may not be true for surface temperature. This suggests an intrinsic limitation for inferring monthly or seasonal estimates of natural fluctuations of surface temperature from the observed daily statistics. Two further results suggested by the study are (i) that modeling climate noise at a station may require higher order autoregressive processes or must take into account spatial correlations, and (ii) that the applicability of stochastic processes may be geographically dependent.

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