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Elizabeth A. Barnes
and
Randal J. Barnes

Abstract

Two common approaches for estimating a linear trend are 1) simple linear regression and 2) the epoch difference with possibly unequal epoch lengths. The epoch difference estimator for epochs of length M is defined as the difference between the average value over the last M time steps and the average value over the first M time steps divided by NM, where N is the length of the time series. Both simple linear regression and the epoch difference are unbiased estimators for the trend; however, it is demonstrated that the variance of the linear regression estimator is always smaller than the variance of the epoch difference estimator for first-order autoregressive [AR(1)] time series with lag-1 autocorrelations less than about 0.85. It is further shown that under most circumstances if the epoch difference estimator is applied, the optimal epoch lengths are equal and approximately one-third the length of the time series. Additional results are given for the optimal epoch length at one end when the epoch length at the other end is constrained.

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Elizabeth A. Barnes
and
Dennis L. Hartmann

Abstract

The persistence of the North Atlantic Oscillation (NAO) is studied using observations of the three-dimensional vorticity budget in the Atlantic sector. Analysis of the relative vorticity tendency equation shows that convergence of eddy vorticity flux in the upper troposphere counteracts the effect of anomalous large-scale divergence at the upper level. At low levels, the convergence associated with this large-scale vertical circulation cell maintains the relative vorticity anomaly against frictional drag. The eddy vorticity flux convergence thus acts to sustain the vorticity anomaly associated with the NAO against drag and increases the persistence of the NAO vorticity anomaly. The adiabatic cooling associated with the rising motion in the vorticity maximum sustains the thermal structure of the NAO anomaly, enhancing the baroclinicity, and thus eddy generation. This constitutes a positive eddy feedback that helps maintain the NAO. The positive eddy feedback occurs only in the midlatitude region and is strongest during the negative phase of the NAO when the Atlantic jet is displaced toward the equator, with a high pressure anomaly to the north and a low pressure anomaly to the south. The stronger feedback demonstrated during the negative phase is consistent with the greater persistence observed for this phase of the NAO. The positive feedback appears to be associated with anomalous northward eddy propagation away from the jet.

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Elizabeth A. Barnes
and
Dennis L. Hartmann

Abstract

The persistence of the southern annular mode (SAM) is studied during austral winter (June–September) and summer (December–March) using observations of the three-dimensional vorticity budget. Analysis of the relative vorticity tendency equation shows that convergence of eddy vorticity flux in the upper troposphere, coupled with a secondary circulation, constitutes a positive eddy feedback that acts to sustain the vorticity anomaly associated with the jet shift against drag. The feedback exhibits a strong seasonality, with summer months revealing a positive feedback through much of the hemisphere and winter months showing a positive feedback over the Indian Ocean but not over the western Pacific. Results suggest that the lack of wintertime feedback over the western Pacific is due to the weakness of the eddy-driven midlatitude jet in that region.

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Elizabeth A. Barnes
and
Dennis L. Hartmann

Abstract

The eddy-driven jet is located in the midlatitudes, bounded on one side by the pole and often bounded on the opposite side by a strong Hadley-driven jet. This work explores how the eddy-driven jet and its variability persist within these limits. It is demonstrated in a barotropic model that as the jet is located at higher latitudes, the eddy length scale increases as predicted by spherical Rossby wave theory, and the leading mode of variability of the jet changes from a meridional shift to a pulse. Looking equatorward, a similar change in eddy-driven jet variability is observed when it is moved equatorward toward a constant subtropical jet. In both the poleward and equatorward limits, the change in variability from a shift to a pulse is due to the modulation of eddy propagation and momentum flux. Near the pole, the small value of beta (the meridional gradient of absolute vorticity) and subsequent lack of wave breaking near the pole account for the change in variability, whereas on the equatorward side of the jet the strong subtropical winds can affect eddy propagation and restrict the movement of the eddy-driven jet or cause bimodal behavior of the jet latitude. Barotropic quasilinear theory thus suggests that the leading mode of zonal-wind variability will transition from a shift to a pulse as the eddy-driven jets move poleward with climate change, and that the eddy length scale will increase as the jet moves poleward.

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Elizabeth A. Barnes
and
Chaim I. Garfinkel

Abstract

As the surface drag is increased in a comprehensive general circulation model (GCM), the upper-level zonal winds decrease and eddy momentum flux convergence into the jet core increases. Globally averaged eddy kinetic energy decreases, a response that is inconsistent with the conventional barotropic governor mechanism whereby decreased barotropic shears encourage baroclinic wave growth. As the conventional barotropic governor appears insufficient to explain the entire response in the comprehensive GCM, the nondivergent barotropic model on the sphere is used to demonstrate an additional mechanism for the effect of surface drag on eddy momentum fluxes and eddy kinetic energy. Analysis of the pseudomomentum budget shows that increased drag modifies the background meridional vorticity gradient, which allows for enhanced eddy momentum flux convergence and decreased eddy kinetic energy in the presence of a constant eddy source. This additional feedback may explain the changes in eddy momentum fluxes observed in the comprehensive GCM and was likely present in previous work on the barotropic governor.

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Chengji Liu
and
Elizabeth A. Barnes

Abstract

Isentropic mixing is an important process for the distribution of chemical constituents in the mid- to high latitudes. A modified Lagrangian framework is applied to quantify the mixing associated with two distinct types of Rossby wave breaking (i.e., cyclonic and anticyclonic). In idealized numerical simulations, cyclonic wave breaking (CWB) exhibits either comparable or stronger mixing than anticyclonic wave breaking (AWB). Although the frequencies of AWB and CWB both have robust relationships with the jet position, this asymmetry leads to CWB dominating mixing variability related to the jet shifting. In particular, when the jet shifts poleward the mixing strength decreases in areas of the midlatitude troposphere and also decreases on the poleward side of the jet. This is due to decreasing CWB occurrence with a poleward shift of the jet. Across the tropopause, equatorward of the jet, where AWB mostly occurs and CWB rarely occurs, the mixing strength increases as AWB occurs more frequently with a poleward shift of the jet. The dynamical relationship above is expected to be relevant both for internal climate variability, such as the El Niño–Southern Oscillation (ENSO) and the annular modes, and for future climate change that may drive changes in the jet position.

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Bryn Ronalds
and
Elizabeth A. Barnes

Abstract

Previous studies have suggested that, in the zonal mean, the climatological Northern Hemisphere wintertime eddy-driven jet streams will weaken and shift equatorward in response to Arctic amplification and sea ice loss. However, multiple studies have also pointed out that this response has strong regional differences across the two ocean basins, with the North Atlantic jet stream generally weakening across models and the North Pacific jet stream showing signs of strengthening. Based on the zonal wind response with a fully coupled model, this work sets up two case studies using a barotropic model to test a dynamical mechanism that can explain the differences in zonal wind response in the North Pacific versus the North Atlantic. Results indicate that the differences between the two basins are due, at least in part, to differences in the proximity of the jet streams to the sea ice loss, and that in both cases the eddies act to increase the jet speed via changes in wave breaking location and frequency. Thus, while baroclinic arguments may account for an initial reduction in the midlatitude winds through thermal wind balance, eddy–mean flow feedbacks are likely instrumental in determining the final total response and actually act to strengthen the eddy-driven jet stream.

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Marie C. McGraw
and
Elizabeth A. Barnes

Abstract

In climate variability studies, lagged linear regression is frequently used to infer causality. While lagged linear regression analysis can often provide valuable information about causal relationships, lagged regression is also susceptible to overreporting significant relationships when one or more of the variables has substantial memory (autocorrelation). Granger causality analysis takes into account the memory of the data and is therefore not susceptible to this issue. A simple Monte Carlo example highlights the advantages of Granger causality, compared to traditional lagged linear regression analysis in situations with one or more highly autocorrelated variables. Differences between the two approaches are further explored in two illustrative examples applicable to large-scale climate variability studies. Given that Granger causality is straightforward to calculate, Granger causality analysis may be preferable to traditional lagged regression analysis when one or more datasets has large memory.

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Elizabeth A. Barnes
and
Isla R. Simpson

Abstract

Near-surface Arctic warming has been shown to impact the midlatitude jet streams through the use of carefully designed model simulations with and without Arctic sea ice loss. In this work, a Granger causality regression approach is taken to quantify the response of the zonal wind to variability of near-surface Arctic temperatures on subseasonal time scales across the CMIP5 models. Using this technique, a robust influence of regional Arctic warming on the North Atlantic and North Pacific jet stream positions, speeds, and zonal winds is demonstrated. However, Arctic temperatures only explain an additional 3%–5% of the variance of the winds after accounting for the variance associated with the persistence of the wind anomalies from previous weeks. In terms of the jet stream response, the North Pacific and North Atlantic jet streams consistently shift equatorward in response to Arctic warming but also strengthen, rather than weaken, during most months of the year. Furthermore, the sensitivity of the jet stream position and strength to Arctic warming is shown to be a strong function of season. Specifically, in both ocean basins, the jets shift farthest equatorward in the summer months. It is argued that this seasonal sensitivity is due to the Arctic-warming-induced wind anomalies remaining relatively fixed in latitude, while the climatological jet migrates in and out of the anomalies throughout the annual cycle. Based on these results, model differences in the climatological jet stream position are shown to lead to differences in the jet stream position’s sensitivity to Arctic warming.

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Elizabeth A. Barnes
and
Dennis L. Hartmann

Abstract

The correlation lengths of vorticity anomalies from temporal averages are examined in the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis dataset. It is shown that, in the annual mean, eddies in the Southern Hemisphere are significantly larger than those in the Northern Hemisphere. The eddy vorticity lengths exhibit a strong seasonal cycle, with the largest scales occurring in the winter season. The maximum zonal eddy lengths closely follow the contours of the strong upper-level winds, while the maximum meridional lengths are found in jet exit regions and in the stratosphere.

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