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Qihang Li, Rafael L. Bras, and Shafiqul Islam

Abstract

The behavior of a numerical cloud model is investigated in terms of its sensitivity to perturbations with two kinds of lateral boundary conditions: 1) with cyclic lateral boundary conditions, the model is sensitive to many aspects of its structure, including a very small potential temperature perturbation at only one grid point, changes in time step, and small changes in parameters such as the autoconversion rate from cloud water to rainwater and the latent heat of vaporization; 2) with prescribed lateral boundary conditions, growth and decay of perturbations are highly dependent on the flow conditions inside the domain. It is shown that under relatively uniform (unidirectional) advection across the domain, the perturbations will decay. On the other hand, convergence, divergence, or, in general, flow patterns with changing directions support error growth. This study shows that it is the flow structure inside the model domain that is important in determining whether the prescribed lateral boundary conditions will result in decaying or growing perturbations. The numerical model is inherently sensitive to initial perturbations, but errors can decay due to advection of information from lateral boundaries across the domain by uniform flow. This result provides one explanation to the reported results in earlier studies showing both error growth and decay.

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Shafiqul Islam, Rafael L. Bras, and Kerry A. Emanuel

Abstract

A general framework has been developed to study the predictability of space–time averages of mesoscale rainfall in the tropics. A comparative ratio between the natural variability of the rainfall process and the prediction error is used to define the predictability range. The predictability of the spatial distribution of precipitation is quantified by the cross correlation between the control and the perturbed rainfall fields. An upper limit of prediction error, called normalized variability, has been derived as a function of space–time averaging. Irrespective of the type and amplitude of perturbations, a space–time averaging set of 25 km2–15 min (or larger time averaging) is found to be necessary to limit the error growth up to or below the prescribed large-scale mean rainfall.

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Shafiqul Islam, Rafael L. Bras, and Ignacio Rodriguez-Iturbe

Abstract

There have been numerous attempts to detect the presence of deterministic chaos by estimating the correlation dimension. The values of reported correlation dimension for various geophysical time series vary between 1.3 and virtually infinity (i.e., no saturation). It is pointed out that analyzing variables that depend on physical constraints and thresholds, like precipitation, may lead to underestimation of the correlation dimension of the underlying dynamical system.

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