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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

An analysis has been made of the interseasonal and interannual variability of mean circulation and eddy statistics for both summer and winter in the Southern Hemisphere. Total variance fields of geopotential height, the noith-wuth and east-west wind components and poleward transient eddy momentum fluxes at 500 mb are analyzed along with their contributions from two broad frequency bands covering 2-8 day and 8-64 day period fluctuations. Largest interannual variability occurs between 40-60°S in association with the main jet stream in summer or the polar jet stream in winter and the main belt of eddy activity within each season.

The circulation and eddy statistics during the year of the Global Weather Experiment (GWE) are compared with the means and standard deviations over all years from 1972–80, and contrasted with individual years The GWE summer of 1978–79 is contrasted with 1976–77, and the 1979 winter is contrasted with 1980. The year of the GWE was charactrized by an exceptionally deep circumpolar trough, an increase in westerlies between 45–70°S and a decrease to the north, with a southward shift in the main westerly jet during summer 1978–79 and a considerably enhanced and southward shifted polar jet but weaker subtropical jet in winter 1979. Associated with these changes was a southward shift in storm tracks and high frequency eddy activity throughout the year. In both seasons anomalous convergence of momentum by the eddies into the jets was such that it would have helped sustain the abnormal distribution of westerlies against surface friction.

Many of the anomalies in the circulation statistics during the GWE are statistically significant. most notably in winter, and their reality is supported by station data and the dynamical consistency of the relationships between the anomalous mean flow and storm tracks. In addition, the deficit of mass over the Southern Hemisphere revealed by sea level pressures in April-July 1979 is compensated by the surfeit that occurred in the North Hemisphere. Although the vastly improved observations during the GWE may have contributed to the size of the anomaly, they cannot account for the systematic change in location of the features of the flow. The circulation during the GWE appears to have been at one extreme of the large natural interannual variability that is so much a feature of the Southern Hemisphere flow. The atypical nature of the circulation should be borne in mind in analyses based solely on the GWE over the Southern Hemisphere.

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Kevin E. Trenberth

Abstract

Time series of meteorological variables typically exhibit a pronounced annual cycle and persistence and samples are of finite size. This paper analyses the impact of these complicating features on certain statistics computed from the time series. The presence of an annual cycle means that statistics are nonstationary unless computed from multiyear samples of limited duration. Persistence leads to lack of independence of observations. Large amplitude weather (high frequency) events induce natural variability at low frequencies, known as climatic noise, that is enhanced by the presence of persistence. This natural variability should be, taken into account when estimating population statistics from a finite sample, but generally this has not been done in meteorology.

A number of studies in meteorology have computed statistics from daily data by 1) removing the annual cycle; 2) computing second moment statistics over each individual season; and 3) averaging the second moment statistics over all years. This procedure fails to take into account the natural interannual variability that should be present and results in biased estimates of certain statistics. In particular, autocorrelations that lag are systematically negatively biased. It is shown for first order autoregressive (AR) time series that theautocorrelations computed in this way become negative after just a few days lag. Consequently, several studies have drawn doubtful conclusions about the stochastic character of meteorological time series, and a few reported results are questionable. A brief discussion of some papers adversely affected by the methodology is given.

The effects of the statistical methodology are illustrated with simulated, and thus known, time series. It is shown that the best possible estimate of autocorrelations for stationary time series is obtained by subtraction of the mean of all available data, rather than subtracting a different mean for each subsample (season) in order to compute the anomalies. Appropriate methods for computing the statistics are discussed.

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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 [T n + D n ] 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 [T n + D n ]. 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

An analysis has been made of the persistence of geopotential heights at 1000 and 500 mb over the Southern Hemisphere for both summer and winter seasons. The focus is on lagged autocorrelation T 0 the effective time between independent samples and low order autoregressive (AR) models fit to the data.

A red noise AR(1) model provides the best fit to the data over most of the domain, especially in midlatitudes. However, there are substantial areas where AR(2) and AR(3) processes provide the best fit and these areas are much the same at both levels and for both seasons. Over Antarctica low-frequency trends appear to provide persistence exceeding that of the red noise process and contribute to the higher order AR processes there. However, over Austalasia the AR(2) processes fit to the data imply a damped quasi-periodicity and T 0 values less than for the corresponding red noise process. Such behavior may be linked to the 40–50 day oscillation of Madden and Julian.

Smallest T 0 values are found over the southern oceans and especially in the main storm track regions where developing synoptic systems and rapid advection contribute to reduce the autocorrelations and T 0 values. Largest persistence is found over Antarctica, in low latitudes and across Australasia Persistence in these regions is greatly enhanced by interannual variability. In part, such low frequency variability over Australasia and in the tropics is associated with the Southern Oscillation, and is thus linked to low frequency coupling between the atmospheric circulation and sea surface temperatures. The overall meridional profile of autocorrelations is similar to that in the Northern Hemisphere but persistence is less in the Southern Hemisphere in both seasons. Factors contributing to the differences are discussed.

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Kevin E. Trenberth

Abstract

An analysis of variance approach is used to estimate the potential predictability of interannual fluctuations of the seasonal mean flow over the Southern Hemisphere. The potential predictability of the 1000 and 500 mb geopotential height fields for both summer and winter is assessed. Daily variances at 500 mb are roughly double those at 1000 mb, but otherwise the patterns are quite similar in both seasons. The level of climatic noise is estimated from the daily variances and compared with the actual interannual variances under a null hypothesis that no signal exists. Results reveal that interannual or longer-term variability clearly exceeds the noise level at both levels and in both seasons over Antarctica and in the tropics No clear statement can be made one way or the other in midlatitudes. The methodology appears to fail over the Australia-New Zealand region where clear interannual signals associated with the Southern Oscillation and a quasi-biennial oscillation have previously been found. However, the noise in this region appears to include the 40–50 day oscillation which may be organized by or systematically contribute to the interannual variability. The implied correlation between signal and noise voids a basic assumption of the methodology.

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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

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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Kevin E. Trenberth

Abstract

Studies of the interannual variability of the 500 mb flow in the Southern Hemisphere for 1972–78 have revealed 1) a quasi-biennial fluctuation in the zonal mean geopotential height and westerly wind fields where there is a systematic poleward progression of anomalies, and 2) a longer period fluctuation, primarily in Wave 1, which has been identified with the Southern Oscillation. These phenomena are further studied regionally by considering four 90° sectors. Results show the dominant contributions to the fluctuations in the zonal mean fields come from the Australasian and South Pacific sectors. Only in the Australasian region is the quasi-biennial poleward progression of anomalies strongly evident. The South Pacific is dominated by lower frequency fluctuations associated with the Southern Oscillation. However, the sequences in all four sectors are correlated with those in the zonal mean fields. When the flow is stronger than normal in mid-latitudes it tends to be weaker than normal in low and high latitudes, and vice versa, in all sectors and in the zonal mean.

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