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Jeffrey L. Anderson

Abstract

The unstable normal modes of the barotropic vorticity equation, linearized around an observed zonally varying atmospheric flow, have been related to patterns of observed low-frequency variability. The sensitivity of this problem to changes in the model truncation and diffusion and to details of the basic state flow are examined. Normal modes that are highly sensitive to these changes are found to be of minimal relevance to the low-frequency variability of the atmosphere.

A new numerical method capable of efficiently finding a number of the most unstable modes of large eigenvalue problems is used to examine the effects of model truncation on the instability problem. Most previous studies are found to have utilized models of insufficiently high resolution. A small subset of unstable modes is found to be robust to changes in truncation. Sensitivity to changes in diffusion in a low-resolution model can partially reproduce the truncation results.

Sensitivity to the basic state is examined using a matrix method and by examining the normal modes of perturbed basic states. Again, a small subset of unstable normal modes is found to be robust. These modes appear to agree better with observed patterns of low-frequency variability than do less robust unstable modes.

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Jeffrey L. Anderson

Abstract

An extremely simple chaotic model, the three-variable Lorenz convective model, is used in a perfect model setting to study the selection of initial conditions for ensemble forecasts. Observations with a known distribution of error are sampled from the “climate” of the simple model. Initial condition distributions that use only information about the observation and the observational error distribution (i.e., traditional Monte Carlo methods) are shown to differ from the correct initial condition distributions, which make use of additional information about the local structure of the model's attractor. Three relatively inexpensive algorithms for finding the local attractor structure in a simple model are examined; these make use of singular vectors. normal modes, and perturbed integrations. All of these are related to heuristic algorithms that have been applied to select ensemble members in operational forecast models. The method of perturbed integrations, which is somewhat similar to the “breeding” method used at the National Meteorological Center, is shown to be the most effective in this context. Validating the extension of such methods to realistic models is expected to be extremely difficult; however, it seems reasonable that utilizing all available information about the attractor structure of real forecast models when selecting ensemble initial conditions could improve the success of operational ensemble forecasts.

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Jeffrey L. Anderson

Abstract

Nearly stationary states (NSSs) of the barotropic vorticity equation (BVE) on the sphere that are closely related to observed atmospheric blocking patterns have recently been derived. Examining the way such NSSs affect integrations of the BVE is of interest. Unfortunately, the BVE rapidly evolves away from the neighborhood of blocking NSSs due to instability and never again generates sufficient amplitude to return to the vicinity of the blocking NSSs. However, forced versions of the BVE with both a high amplitude blocking NSS and more zonal low amplitude NSSs can be constructed. For certain parameter ranges, extended integrations of these forced BVFs exhibit two “regimes,” one strongly blocked and the other relatively zonal. Somewhat realistic simulators of low and high frequency variability and individual blocking event life cycles are also produced by these forced barotropic models. It is argued here that these regimes are related to “attractor-like” behavior of the NSSs of the forced BVE. Strong barotropic short waves apparently provide the push needed to cause a transition to or from the blocked regime. In the purely barotropic model used here, there is a rather delicate balance required between the forcing strength for different spatial scales in order to produce regimelike behavior. However, the mechanism proposed appears to be a viable candidate for explaining the observed behavior of blocking events in the atmosphere.

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Jeffrey L. Anderson

Abstract

A robust algorithm, capable of finding nearly stationary solutions of the unforced barotropic vorticity equation near to observed atmospheric streamfunctions, is presented. When applied to observed persistent anomaly patterns, the nearly stationary states (NSSs) produced by the algorithm usually have a distinctive appearance. NSSs produced for observed blocks tend to have even stronger blocks, and NSSs for intense jet anomaly patterns have intense jets. When applied to observed patterns that are not associated with persistent anomalies, the algorithm produces low-amplitude relatively zonal NSSs. The blocking and intense jet anomaly NSSs bear a striking resemblance to previously derived analytic stationary solutions of the vorticity equation. In particular, NSS blocking states are similar to certain types of modons.The algorithm is applied to a number of modified observed flows to better document what features of an observed pattern determine the nature of the resulting NSS. The short-wave components of an observed pattern need not be present in order for the algorithm to find interesting zonally varying NSSs. However, short waves play an essential part in the resulting NSSs by balancing the long-wave time tendencies. All the NSSs discovered are unstable to the introduction of small perturbations in the barotropic vorticity equation. Despite this instability, the NSSs still persist for many days when integrated in time. The existence of these persistent NSSs may play a significant role in the appearance and subsequent longevity of persistent anomaly patterns in the atmosphere.

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Sukyoung Lee and Jeffrey L. Anderson

Abstract

A forced, nonlinear barotropic model on the sphere is shown to simulate some of the structure of the observed Northern Hemisphere midlatitude storm tracks with reasonable accuracy. For the parameter range chosen, the model has no unstable modes with significant amplitude in the storm track regions; however, several decaying modes with structures similar to the storm track are discovered. The model's midlatitude storm tracks also coincide with the location of a waveguide that is obtained by assuming that the horizontal variation of the time-mean flow is small compared with the scale of the transient eddies. Since the model is able to mimic the behavior of the observed storm tracks without any baroclinic dynamics, it is argued that the barotropic waveguide effects of the time-mean background flow acting on individual eddies are partially responsible for the observed storm track structure.

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Jeffrey L. Anderson, Bruce Wyman, Shaoqing Zhang, and Timothy Hoar

Abstract

An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation’s prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined.

The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model’s spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the results also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.

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Thomas M. Hamill, Jeffrey S. Whitaker, Jeffrey L. Anderson, and Chris Snyder
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