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Kevin E. Trenberth

Abstract

An analysis has been made of the means and variability of the 500 mb field in the Southern Hemisphere, with accent on the zonal means of geopotential height and westerly wind. Long-term means for May 1972-January 1978 are significantly different from previous analyses and reveal very large and significant trends in geopotential height, especially over Antarctica. Standard deviations of zonal winds and heights are larger than in the Northern Hemisphere and, in contrast to the Northern Hemisphere, are lowest in winter. Temporal variations in the zonal mean component of the flow are very pronounced and some aspects of the very anomalous flow in December 1976 are documented. Interannual variations show a remarkable quasi-biennial fluctuation in the zonal mean fields with a systematic progression of the anomalies from low to high latitudes. These are correlated with the quasi-biennial oscillation in the equatorial stratosphere.

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KEVIN E. TRENBERTH

Abstract

Numerical time integrations of a nine-layer, quasi-geostrophic, highly truncated spectral model of the atmosphere are used to study tropospheric-stratospheric interaction with particular regard to sudden stratospheric warmings. The model is global, extends to 0.05 mb (71 km) with roughly 10-km resolution in the stratosphere, and includes an annual heating cycle.

Model integrations simulating the months of December and January were made (1) without nonzonal forcing and (2) with nonzonal heating and orography included, to represent Southern Hemisphere and Northern Hemisphere winters, respectively. The presence of nonzonal heating in the winter hemisphere brought about an increase in circulation intensity and produced a stationary perturbation having a strong westward slope with height extending high into the stratosphere. This feature is similar to the Aleutian system. It was accompanied by considerably warmer temperatures in the polar night stratosphere and a weaker stratospheric westerly jet.

Sudden stratospheric warmings occurred as a result of large increases in the intensity of planetary scale waves in the troposphere, which in turn produced surges of upward propagating energy. The energetics of the warming occurred in two phases. A change from a baroclinically direct to a driven circulation occurred as the stratospheric temperature gradient reversed. This coincided with a change from enhancement to absorption of the vertical energy flux. The mechanism of the warming was similar to that described by Matsuno.

Nonlinear interactions between the progressive long wave and the nonzonal heating were primarily responsible for the tropospheric events that produced the transient upward flux of energy and thus the warmings. A seasonally coupled index cycle in the long waves was also of significance, while interactions with other waves and orographic forcing were of secondary importance in the long-wave energetics of sudden warmings.

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Kevin E. Trenberth

Abstract

Nearly eight years of daily Southern Hemisphere analyses at 500 mb have been used to define the spatial dependence of the variance fields of geopotential height and the two geostrophic wind components, the corresponding covariance fields, and the transient kinetic energy. The fields are further examined in the frequency domain by using Lorenz' (1979) “poor man's spectral analysis” technique. In view of the small variation in eddy statistics as a function of the time of the year in the SH, this study removes the first four harmonies of the annual cycle and then considers all data together, so that contributions from all time scales from 2 to 4096 days (∼11 years) can be resolved. The main results are based on analyses from May 1972–January 1978 but are verified with analyses from the relatively data-rich FGGE period.

Results for the zonal mean statistics are compared with those from previous studies. The zonal means of the geopotential height and westerly wind component have spectra which roughly follow that of red noise with an autocorrelation of about 0.5, whereas the northward wind component spectra closely resembles red noise with autocorretation of 0.2, resulting in considerable anisotropy in the wind fields. The northward component of transient kinetic energy is larger than the eastward component at high frequencies in middle latitudes but the reverse is true for periods of greater than two months. The westerly momentum flux by the transient eddies has a broad spectral peak at 8–32 days and is dominated by contributions from fluctuations of less than about two weeks period.

The geographical dependence of the eddy statistics is mapped for four broad frequency bands covering periods of roughly less than one week, one week to two months, two months to two years, and greater than two years, thereby separating out contributions from transient baroclinic eddies, episodes of blocking, and intermonthly and interannual variability. The spatial patterns of the statistics are interpreted in the light of synoptic behavior of systems and storm tracks as defined by synoptic studies and satellite observations in the Southern Hemisphere. For periods less than a week, variances are largest in the southern Indian Ocean and relationships between the storm tracks and eddy statistics are similar to those found in the Northern Hemisphere by Blackmon, Lau, Wallace and others. However, there also are differences associated with the differences in the mean flow in each hemisphere and these are discussed in the context of baroclinic theory. At periods longer than a week geopotential height variances are largest near southern New Zealand and, to a lesser extent, southeast of South America and appear to be related to the incidence of blocking in the Southern Hemisphere. The corresponding transient kinetic energy has a maximum further north in association with cutoff cold-centered lows. In general, the high-frequency transient eddies play a much larger role in the circulation of the Southern Hemisphere than is true for the winter circulation of the Northern Hemisphere, and the eddy statistics are more zonally symmetric.

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Kevin E. Trenberth

Abstract

A brief review and evaluation of various analyses of the Southern Hemisphere westerlies is given along with the presentation of some relent results. Several features characterize the westerlies of the Southern Hemisphere as quite different from those in the Northern Hemisphere and, in the past, thew have typically been difficult to reproduce well in general circulation modes. They are the double jet structure in winter, the stronger midlatitude tropospheric winds in summer than in winter, and the ensuing much smaller amplitude of the annual cycle which is associated with a maximum of global atmospheric angular momentum in January. New values for the hemispheric angular momentum integrals are than previously reported.

Two estimates of the distribution and strength of the southern westerlies that have been widely used are considered to be seriously biased. Factors contributing to discrepancies among different results am large natural variability, missing data and biases in observing systems, and methods of analysis. Over the sparsely observed Southern Hemisphere, the latter is the main reason why biases exist in analyses based only on mean station data, and the absence of imposed dynamical constraints has led to internally inconsistent fields. Even recent estimates of the southern westerlies from global operational analyses should be used judiciously with proper consideration given to reliability and biases.

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Kevin E. Trenberth

Abstract

Possible methods for estimating surface fluxes include (i) use of bulk fluxes and in situ observations, (ii) use of model parameterizations to interpret specified inputs and compute surface fluxes, and (iii) various indirect methods, which rely on the fact that the mass and surface heat, energy, and momentum budgets must balance and so, given computations of all the other components in the various budget equations applied to fields either within the ocean or the atmosphere, fluxes may be inferred as a residual. This paper reviews the third approach using indirect methods and outlines the advantages associated with the use of global atmospheric analyses from four-dimensional data assimilation (4DDA). The time mean increment required in producing analyses in 4DDA is identical to the systematic short-term (6 h) assimilating model forecast error and is most likely due to errors in the model physics. Therefore, the analyses include a desirable fix, which allows the sum of the “physics” to be deduced from “dynamics.” The focus is on the heat and moisture budgets to infer surface heat fluxes and freshwater fluxes, but with the recognition of the need to balance the mass budget as well. The diurnal cycle of the vertically integrated mass budget for July 1985 and January 1996 from National Centers for Environmental Prediction (formerly the National Meteorological Center) reanalyses is presented, revealing the strong semidiurnal tide and highlighting the need for at least four-times-daily data. The new results reveal that gross violations of the mass budget continue to be present, but these can be allowed for. A discussion is given of other sources of errors contributing to the heat and moisture budgets.

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Kevin E. Trenberth

Abstract

The distribution of the mean westerly wind over the globe is described for June, July and August, the southern winter, using analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) from 1979 to 1982. The tropospheric momentum budget is analyzed from both the traditional Eulerian and the transformed Eulerian perspectives. Thus an assessment is made of the Eliassen-Palm flux divergence and the diabatically driven residual mean circulation. The vertical mean budget is also analyzed to allow deductions about the mean surface torque by the atmosphere on the earth and the grow surface stress.

In the southern winter, transient eddies dominate the poleward momentum transports in both hemispheres, and total transports are somewhat larger than found in previous studies. Values of the deduced mean westerly surface stress are therefore larger than most previous estimates, but seem very reasonable and are probably more reliable in midlatitudes. A strange vertical structure analyzed to be present in the ECMWF zonal mean meridional wind is found to be inconsistent with the momentum budget, and the analyzed Hadley circulation is shown to be much too weak. The latter was expected since diabatic effects were not included in the initialization at ECMWF for this period. The total momentum budget is determined without including vertical eddy fluxes of momentum, but the residual is fairly small outside of the tropics and can probably be accounted for by fairly small errors in the analyzed divergent wind component.

The traditional Eulerian view reveals that the midlatitude westerlies are maintained mainly by convergence of westerly momentum by the transient eddies, while the induced Ferrel cell decelerates the westerlies aloft and transports momentum down to the surface to balance losses by surface friction. The transformed Eulerian view shows that the net effect of the eddies in the upper troposphere, above 300 mb, is small, but there is a marked net deceleration by the transient eddies between 700 and 300 mb, and the westerlies there are maintained by the Coriolis torque acting on the diabatically driven residual mean circulation. The observed Ferrel cell is thus revealed to be a fairly small residual of the direct diabatically driven cell and the eddy-induced indirect cell. However, the vertical mean budget clearly shows that it is the meridional transport of westerly momentum by the eddies that is primarily acting to maintain the midlatitude westerlies against losses by surface friction.

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KEVIN E. TRENBERTH

Abstract

The development of a nine-layer, quasi-geostrophic, highly truncated spectral model of the atmosphere is described. The model is global, extends to 0.05 mb (71 km) with roughly 10-km resolution in the stratosphere, and includes an annual heating cycle. Preliminary integrations without eddies reveal the seasonal variation of a thermally driven circulation.

A model integration was made to simulate the months of December and January without nonzonal forcing, thus being more representative of a Southern Hemisphere winter. The overall features of the atmosphere were well simulated. A midlatitude temperature maximum was produced in the winter mesosphere of the model, which was driven in the manner of the lower stratosphere. With the inclusion of the annual heating cycle, the model successfully reproduced a more intense circulation in January than existed in December. This caused the maximum tropospheric meridional temperature gradient in the winter hemisphere to occur weeks prior to the maximum in the external heating field. A seasonally coupled index cycle in the very long waves was of significance in producing transient upward energy propagation and, as such, may be the source of sudden stratospheric warming events.

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Kevin E. Trenberth

Abstract

Potential predictability of a meteorological time series can be estimated from the ratio of the actual interannual variability to the natural variability associated with climatic noise. The extent to which this ratio is larger than one is taken as a measure of the climatic signal-to-noise variance ratio. However, there are major problems in separating out the signal from the noise which are compounded by persistence in the time series, the presence of an annual cycle and the effects of finite sample size.

An F test may be used to deduce that a signal is present by rejecting the null hypothesis of no signal. However, it is shown that, generally, the null hypothesis should not be accepted just because it cannot be rejected. Confidence limits can be very large when a signal is present in a finite sample since the signal will be fictitiously correlated with the noise due to sampling in a manner that is unknown. Although the correlation coefficient is statistically not significant, there is a large impact on the confidence limits of the F ratio. A case is presented using many artificially generated, and thus known, time series that include a signalcombined with a first order autoregressive process (red noise). With a signal-to-noise ratio of 1 (<F) = 2) only about half of the time could the null hypothesis be rejected at the 5% level and 5% of the time the sample F ratio was found to be less than I.

The problem of assessing potential predictability is analyzed in detail in the time domain. The presence of any low frequency signal can lead to overestimates of the level of climatic noise since the signal will add to the persistence of the time series. A method is devised to adjust the statistics and remove the effects of the signal and thus obtain a more accurate signal-to-noise ratio.

The results are compared with the alternative approach of Jones and of Madden in the frequency domain. The latter uses a low frequency white noise extension of the power spectrum to estimate the climatic noise. The method is shown to work quite well, with minimal impact of a low frequency signal on results, but the confidence limits were very large. It is necessary to greatly increase the degrees of freedom of the spectral estimates before the results can be considered reliable; even then they are still subject to the inherent uncertainty associated with the unknown correlation between signal and noise.

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Kevin E. Trenberth

Abstract

The utility of a simple index for monitoring the Southern Oscillation signal is explored in detail. Based upon sea level pressure data at the two stations Tahiti (T) and Darwin (D), an optimal index, in the sense that it combines the Southern Oscillation variance into one series is the combination [Tn + Dn] where the subscript n denotes normalization by the overall standard deviation of each series. A direct measure of the noise due to small-scale or transient phenomena that are not a part of the large-scale coherent Southern Oscillation fluctuations is the index [Tn + Dn]. It is recommended that this index of noise also should be monitored in order to determine the representativeness of the Southern Oscillation index.

The signal-to-noise ratio is shown to depend upon the cross correlation between Darwin and Tahiti, and can be increased by applying weighted moving average low-pass filters to the data. Monthly data exhibit a signal-to-noise ratio, defined as the ratio of the standard deviations, of 1.44 and this increases to 1.97 for seasonal data. An 11-term low-pass filter is designed that increases the signal-to-noise ratio to 2.70 without adversely reducing the variance in frequencies that are important in the Southern Oscillation. Resulting time series plots are presented.

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Kevin E. Trenberth

Abstract

The zonally asymmetric component of the 500 mb flow in the Southern Hemisphere has been analyzed into wavenumber space, and the annual cycle and interannual variability are documented for the period May 1972–January 1978. The planetary waves 1–3 account for most of the variance and all three waves make important contributions, especially to the interannual variability, although the mean fields are dominated by wave 1. The seasonal variation in all fields is small compared with that in the Northern Hemisphere. In the subtropics, the interannual fluctuations in the planetary waves are mainly coupled to the Southern Oscillation and the wave fluctuations are coupled to those in the mean zonal westerlies.

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