Evaluation of the Temperature Trend and Climate Forcing in the Pre- and Post Periods of Satellite Data Assimilation - Satellite-based Applications on Climate Change - page 52

4.2.5 Methodology

It is obvious that the two analysis periods have an important difference: the lack of
satellite data prior to November 1978 and the use of assimilated satellite data after
1978. The MSU-retrieved temperature data is available for the period of 1978
through 2006. Based on the whole publicly available data from ERA-40 for
1958-2002, two data periods in the present study were chosen: 1979-2002 and
1958-1978. All three datasets will be used in the 1979-2002 period; the two
reanalysis datasets used in the earlier period did not contain satellite data. The
winter season was defined as December through February in this study. A multiple
linear regression analysis was used in this study to ascertain the linear impacts for
the selected set of forcing parameters.

4.2.5.1 Multiple Linear Regression Analysis

For a limited selection of atmospheric variables ( Y ), a multiple linear regression
equation can be expressed as follows:

Y ¼ a 0 þ a 1 TRD þ a 2 F10 þ a 3 ENSO þ a 4 QBO þ a 5 AOD þ E

: 7 (4.1)

where a 0 is the long-term mean for a particular variable (in this case, temperature),
TRD is the linear trend, and F10.7 represents the solar forcing quantified by the
solar 10.7-cm radio flux. ENSO is the El Ni˜o index, QBO is the equatorial zonal
wind at 30 hpa from the Free University of Berlin (K. Labitzke, 2009, private
communication), AOD is the global stratospheric aerosol optical depth, and

is
a residual error term. The coefficients a 0 , a 1, a 2, a 3 , a 4 , and a 5 are determined by
least squares regression. Note that each forcing term index was normalized before
the calculation.
This global analysis will be completed in steps. First, a reference baseline will be
established by reviewing the trends in the global temperatures and the resulting
pattern. This baseline provides insight into the consistency of the datasets prior to
performing any additional analysis. Next a multiple regression analysis that
accounts for the selected forcing factors is performed.

E

4.3 Trend of Global Temperature

Before discussing the impacts of climate forcing on the temperature anomalies, it is
important to first review the preliminary features of the DJF temperature trends in
the two periods as a baseline. The trend was calculated by the term a 1 TRD in
Eq. ( 4.1 ).