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Characteristics of the temperature variations

The results of the regression model terms are presented for the regions where the significance is the 95%. In addition, all the results presented here have been obtained excluding the Pinatubo period.

Seasonal components

The seasonal components (not shown) exhibit, as expected, an annual signature with the amplitude decreasing with height up to 10 hPa in the extra-tropics and 30 hPa in the Tropics. In agreement with Reid (1994), a significant semi-annual signal is observed in the tropical stratosphere for the 30-10 hPa layer with two maxima in April and October.   

QBO signal

It is for the highest layer (Figure 2, bottom) that the QBO signature (constant part of term C in Eq. 1), symmetrical to the equator, is the strongest, with temperatures warmer during the eastern phase of the QBO. The amplitude of this term indicates that 30-10 hPa tropical temperatures are dominated by the QBO oscillation.

Figure 2 : Calculated latitude-longitude patterns of QBO temperature variability in Kelvin per QBO cycle (constant part of term C in Eq. 1) for the 70-50 (top) and 30-10 (bottom) hPa layers in the regions where it's 95% significant.

In the 100-70 hPa layers (not shown) and 70-50 hPa, a signature is found at higher latitudes (20-30 °) in both the hemispheres and a dipolar structure at latitudes higher then 60°N, the amplitude of which depends on the terms considered in Equation 1.

No significant annual variation of the QBO term is observed.

ENSO signal

The ENSO signal (D term in Eq.1) as well as its seasonal dependence which, contrary to the QBO, is not negligible, are now examined.

Figure 3 shows the 95% significant ENSO pattern with its annual amplitude and phase for the 100-70 hPa layer (Kelvin per normalized SOI index).

Figure 3: Top: Calculated ENSO pattern (D term in Eq. 1) for the 100-70 hPa layer in Kelvin per standardized SOI index and amplitude of annual oscillation of the ENSO pattern for the 100-70 hPa layer . Bottom: Phase of the annual ENSO oscillation [months].

The latitude-longitude structure over the globe of the ENSO term (figure 3a) consists of two positive centres symmetric to the equator and a negative one at higher latitudes in the Southern Hemisphere (at about 45° S).

The annual oscillation, whose amplitude and phase are given in figure 3b and 3c respectively, give a positive/negative contribution near to the Equator on February/July between 20°N-20°S and a reversed one (positive in August) at high latitudes in the southern hemisphere.

The ENSO effect diminishes with increasing height and vanishes above 30 hPa.

Trend and solar signal

We performed two different analyses including and excluding the solar term to avoid introducing errors due to the shortness of the period which does not include a complete solar cycle. Comparing the results we conclude that our record is far too short to isolate trend term from solar forcing because the trend and solar terms are spatially and temporally related (Randel, and Cobb, 1994).

Study of the residual term

To study the residual term we performed the statistical analysis of monthly time series data using first a simpler model which accounts for the constant, seasonal, trend and residual terms only. The idea is that the influence of the other factors (i.e. ENSO, QBO and solar cycle) on trend estimation is accounted for the residual term N_t.

Following the works of Tiao et al. (1990) and Weatherhead et al. (1998), we can evaluate the standard error of the trend estimate, in the hypothesis the residual term is AR(1). The standard error is highly dependent on the variance and autocorrelation of noise  N_t. Adopting the rule that a trend is real or significantly different from zero at the 95% level if its absolute value is greater than 2 times its standard deviation, Tiao et al. and Weatherhead et al. estimated the minimum number of years of data required to detect a real trend of specified magnitude. In figure 4 (top) we show the estimated number of years necessary to detect a trend (of magnitude of 0.3% per year) plotting  residual autocorrelation versus noise standard deviation for different latitudes in the 30-10 hPa layer.

Contour curves indicate the number of years of data needed to detect a 0.3% per year trend; the coloured points are the real variance s_N (in percent) and F at different latitudes for the northern hemisphere; similar results are found for the southern hemisphere. The latitudinal dependence is obvious: low latitude data have positive F and lower sigma then high latitude points.

In a second experiment, the QBO term was considered (Figure 4, bottom: as expected, for low latitudes, we need less years to detect a significant trend. From this graph, we can expect to be able to determine a trend for all latitudes, once all the NOAA/TOVS (available since 1979) will be reanalyzed.

Figure 4: Residual autocorrelation versus variance [%] for points at different latitudes. Contour curves are the estimated number of years of data required to detect a 0.3% per year trend with the 95% of significance. Points are residual latitudinal average for autocorrelation and variance with their standard deviation at 5 different latitudes.

Top: using a simpler model which accounts for the constant, seasonal, trend and residual term only. Bottom: including the QBO term.