Methodology - Response of Flood Events to Land Use and Climate Change - page 87

3.12.1 Detection of Randomness

One of the problems in detecting trends in hydrologic time series is the effect of
serial correlation. If there is a positive serial correlation in a time series, the non-
parametric test will suggest a significant trend in the time series [ 107 - 110 ]. To
avoid this problem, the autocorrelation structure of the time series should be
investigated. If the time series is random, the autocorrelation coefficients are not
statistically different from zero. In other words, the autocorrelation coefficients do
not cut the confidence interval (CI) at any desired level of significance, i.e., 95 %.
The CIs are given by

CIs ¼ Z / /= 2

p n

ð 3 : 40 Þ

where:
Z is defined as the percent point function of the normal distribution; n is the
sample size and / is the significance level.

3.12.2 Detection of Homogeneity

Different methods and tests have been introduced to test the homogeneity of
hydroclimatic variables [ 111 , 112 ]. A climatic variable is said to be ''homoge-
neous'' when its variations are caused only by fluctuations in weather and climate
[ 113 ]. In order to detect homogeneity in monthly precipitation, maximum dis-
charge series, and monthly temperature, the ''run test'' is applied in this study
because it is a common and valid method suggested by many investigators [ 110 ].
In this test, time series of length n and x med or the median of the time series are
considered. A code called ''a'' was considered for any value x j [ x med and a code
called ''b'' was considered for any value x j \ x med . Each uninterrupted series of
''a'' and ''b'' codes is called a ''run''. The distribution of the number of runs (N)
approximates a normal distribution with the following average (E) and variance
(Var):

E ðÞ¼ N þ 2
2

Var ðÞ¼ N ð N 2 Þ
4 ð N 1 Þ

ð 3 : 41 Þ

The Z statistic is defined as:

Z ¼ R E ð R Þ p

Var ð R Þ

ð 3 : 42 Þ

For significance level of a = 0.01 and a = 0.05, the null hypothesis of homoge-
neity is verified if |Z| B 2.58 and |Z| B 1.96, respectively.