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Jon M. Nese

Abstract

The authors demonstrate that manual observations of daily maximum and minimum temperature are strongly biased toward temperatures ending in certain digits. The nature and severity of these biases are quantified using standard statistical methods. Temperatures ending in “0”, “2”, “5”, and “8” are overrepresented in the data, with the bias toward multiples of ten being most statistically significant.

Inconsistencies in the distribution of the data by final digit suggest that biasing toward a temperature T may result not only from misobservations of temperatures T ± 1 but also from misobservations of temperatures T ± 2. Although changes adopted by the U.S. Weather Bureau in 1950 in the rules governing the rounding of temperature observations improved several of the biases, all biases remained statistically significant after the rule revision.

To estimate the potential effect of these biases on the mean and standard deviation of a temperature distribution, biasing simulations were performed on various normal distributions. In addition, it is shown that these biases can affect other relevant climatic statistics, such as the number of days that certain temperature thresholds are reached.

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Jon M. Nese and John A. Dutton

Abstract

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

Abstract

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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Jon M. Nese, John A. Dutton, and Robert Wells

Abstract

Advancing knowledge about the phase space topologies of nonlinear hydrodynamic or dynamical systems has raised the question of whether the structure of the attractors in which the solutions are eventually confined can be characterized rigorously and economically. It is shown by applying the Lyapunov exponents, Lyapunov dimension, and correlation dimension to several low-order truncated spectral models that these quantities give useful information about the phase space structure and predictability characteristics of such attractors. The Lyapunov exponents measure the average exponential rate of convergence or divergence of nearby solution trajectories in an appropriate phase space. The Lyapunov dimension d L incorporates the dynamical information of the Lyapunov exponents to give an estimate of the dimension of the system attractor, while the correlation dimension v is a more geometrically motivated measure that is simple to compute and related to more classical dimensions.

The Lyapunov exponents detect bifurcations between solution regimes and also subtle predictability differences between attractors. As measures of chaotic attractor dimension, v>d L in all cases, and the ratio v/d L is smallest at values of the forcing just above the transition to chaos. Changes in the Lyapunov dimension are concentrated in a small range of forcing values, while the correlation dimension varies more uniformly. The value of d L is tied closely to the number of positive Lyapunov exponents, while v is more sensitive to the magnitude of the chaotic component of the system. Variations in these measures for a hierarchy of convection models support the idea that the appearance of strong chaos in two-dimensional models is truncation-related, and can be delayed to arbitrarily large forcing if enough modes are included.

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Jon M. Nese, Raymond G. Najjar, and Joseph G. Murgo
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