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Analysis Method

In order to isolate the response of the solar, QBO and ENSO forcings from a long-term linear trend in the monthly time series temperature data, we used a multiparameter least squares fit analysis (AMOUNTS, Adaptative Model for Unambiguous Trend Survey) developed by Hauchecorne et al., 1991; Keckhut et al. 1995 The regression model used is :

T(t) = m + S_t + A.trend + B.solar +C.QBO + D.ENSO + N_t       (Eq. 1)

where for each gridpoint, T(t) is the temperature of month t, m is a constant term, S_t is a seasonal component which includes annual, semi-annual and terannual terms of the form:

A and B terms include an annual and semi-annual variation, in contrast to the C and D terms which take into account only the annual cycle so that the total number of parameters to be fitted is 23.

The 10.7 cm solar radio flux, well correlated with the 11-year sunspot cycle, has been taken as an indicator of solar variability. The reference QBO time series is the monthly tropical wind at 45 hPa in m/s (negative when easterly). Concerning ENSO, the standardised Southern Oscillation Index (NCEP/NCAR data) was chosen. For isolating the stratospheric warming effect due to Pinatubo eruption, analyses have been performed on the whole dataset (8.5 years) and on a reduced dataset (where the period June '91-September '93 was omitted). Finally, in equation (1), N_t is the residual term. At this first stage we assume that it is a stationary first order autoregressive process AR(1), so that 

N_t = F.N_t-1 + e_t        (Eq. 3)

where e_t are independent random variables with mean zero and common variance s² . For the stationarity, we assume -1 < F < 1, where F is the autocorrelation whose positive value indicates a long-term natural variation in the time series data.