Analysis of Trend and Periodicity in Long-Term Annual Rainfall Time Series of Nigeria - Hydrologic Time Series Analysis: Theory and Practice - page 258

deviation is within the range of what can be expected. The sample size is only
100 in this case study, thus only one of such outliers seems not to be out of
place, and hence, the statistical tests accepted the null hypothesis that the data
with inclusion of the one extreme value can still be approximated with a
normal distribution.
2. Parametric and nonparametric trends : The parametric Least Square
Regression test and nonparametric Mann-Kendall test were performed on the
annual rainfall time series with and without outlier flagged in Fig. 12.4. The
Kolmogorov-Smirnov test revealed presence of normality for linear regression
in the annual rainfall time series (test-statistic value 0.071 at 0.68 significance
level). The annual rainfall time series passed the constant variance test ( p =
0.92) verifying the assumption that variance of the annual rainfall in source
population is constant. The Durbin-Watson test-statistic value is computed to
be 1.56, which does not deviate from 2 by more than 0.50. This indicates that
the linear regression assumption of independent residuals is true. Thus, all the
three assumptions of the linear regression hold true, and therefore, the
parametric trend test, i.e. least square regression test, can be applied to the
annual rainfall time series in this study. The results of the parametric and
nonparametric trend tests for the four annual rainfall time series are summarized
in Table 12.3. The linear regression lines depicting trends in the annual rainfall
time series for the Guinea, Savannah and Sahel zones, and Nigeria over the
last century are shown in Fig. 12.5.
Both the graphical and statistical methods (Table 12.3 and Fig. 12.5)
detected negative trends, i.e., decreasing rainfall in all the zones and in entire
Nigeria. The results of the parametric trend test were significantly affected by
the presence/removal of the outlier. For example, a trend of -0.90 mm/year,
which translate to a reduction of about 90 mm, was observed in Guinea for the
1901-2000 period, while the removal of the outlier changed this trend to -0.71
mm/year, which translate to a reduction of about 71 mm for the same time
series. This observed variation was common to all the time series examined.
However, the nonparametric tests are less sensitive to the outliers as compared
to the parametric tests and also do not require the knowledge of the data
distribution a priori . For example, a trend of -1.07 mm/year, which translate
to a reduction of about 107 mm, was observed in Guinea for the 1901-2000
periods, while the removal of the outlier changed this trend slightly to -0.98
mm/year, which translate to a reduction of about 98 mm. For the parametric
test, a relative change of about 21% was observed as against 8% in the
nonparametric test. This may be one of the reasons that many researchers as
well as the WMO have recommended the use of the nonparametric methods
for trend detection in hydroclimatological time series (Mitchell et al., 1966;
Liu et al., 2008). It should be noted that, in the above example, both the
magnitude and direction of the outlier's departure from the sample mean
contribute significantly to the overall trend estimated.