Geoscience Reference
In-Depth Information
Spatial annual rainfall time series were examined for presence of trends
by using one of the World Meteorological Organization (WMO) recommended
nonparametric tests, i.e. Mann-Kendall test. The Mann-Kendall test is often
used to explore trends in hydroclimatological time series (Salmi et al., 2002;
Tosic and Unkasevic, 2005, Oguntunde et al., 2006). Details about the Mann-
Kendall test can be found in Chapter 4. It should be noted that the Mann-
Kendall test is non-dimensional and does not quantify the scale or the magnitude
of the trend in the units of the time series under study, but is rather a measure
of the correlation of variable with time and, as such, simply offers information
as to the direction and a measure of the significance of the observed trends. To
estimate the true slope of an existing trend, the nonparametric Sen's slope
estimation method was used (Salmi et al., 2002). The Sen's slope estimation
method can be used in cases where the trend can be assumed to be linear. The
details about the Sen's slope estimation method can be found in Chapter 4.
Generally, before embarking on the parametric trend test or least-squares
(regression) analysis, the time series data are checked for its suitability for
regression analysis by checking the three assumptions of the linear regression
(Montgomery et al., 2006; Kleinbaum et al., 2007): (i) the source population
is normally distributed, (ii) the variance of the dependent variable in the
source population is constant regardless of the value of the independent
variable(s), and (iii) the residuals are independent of each other. In this study,
the normality assumption for linear regression was tested using the
Kolmogorov-Smirnov test (details can be found in Chapter 3). Constant
variance was tested by computing the Spearman rank correlation between the
absolute values of the residuals and the observed value of the dependent
variable and the Durbin-Watson statistic was used to test residuals for their
independence to each other. The Durbin-Watson statistic is a measure of serial
correlation between the residuals. If the residuals are not correlated, the Durbin-
Watson statistic will be 2 (Montgomery et al., 2006; Kleinbaum et al., 2007).
To estimate the true slope of an existing trend, the parametric method or
least-squares regression analysis was used (Liu et al., 2008). This method can
be used in cases where the trend can be assumed to be linear. This means that
slope ( Q) and intercept ( B) in linear equation f(t) = Qt + B are estimated by
minimizing the sum of square errors between predicted and observed values.
Thus, the mean values of Q and B that yield the least error of estimate for the
model are selected. A t -statistic is then computed to measure the significance
of the independent variable in predicting the dependent variable. The regression
module of SigmaPlot 10.0 software was used in this analysis, including the
verification of the assumptions.
Finally, autocorrelation and spectral methods were used to analyze periodic
signals in the annual rainfall time series of three zones, namely Guinea, Savanna
and Sahel. Autocorrelation is the correlation of a time series dataset signal
with itself at different time lags (Phillips et al., 2008). Theoretical details
about autocorrelation analysis are presented in Chapter 4. Spectral analysis,
on the other hand, is a procedure for decomposing a complex time series
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