Geoscience Reference
In-Depth Information
x
x
ij
È
Ø
igk
jgk
Median
E
gk
=
for all
i
<
j
(68)
É
Ù
Ê
Ú
where
E
gk
= slope between data points
x
igk
and
x
jgk
,
x
igk
= data measurement
at time
i
,
x
jgk
= data measurement at time
j
; and
j
= time after time
i
;
g
= season; and
k
= site. It is defined as the estimator E is the median overall
combination of record pairs for the whole dataset, and is resistant/robust to the
extreme observations or outliers. The positive value of the E
connotes the
slope of the upward trend and negative value for the downward trend.
4.3.15 Trend-Homogeneity Test
The trend results of the seasonal data are assumed to be homogeneous to find
the overall trend by summing the trends over the seasons for a given station
(Hirsch and Slack, 1984). However, presence of noticeable upward and
downward seasonal trends may even result in an overall no trend in the series
due to summing (Van Belle and Hughes, 1984). Hence, the test of homogeneity
is conducted to interpret the seasonal and spatial variability of trend results
and also their interactions. The F
2
-based homogeneity test partitions the total
sum of square (F
2
Total
) into F
2
Homogeneity
and F
2
Trend
(e.g., Van Belle and Hughes,
1984; Gan, 1998; Kahya and Kalayci, 2004). The F
2
Homogeneity
is further
partitioned into F
2
Season
, F
2
Station
and F
2
Season-Station
, and are used to test the
significance of heterogeneity of season, station and their interactions,
respectively. The F
2
-based test statistics to carry out homogeneity test are
given below:
pq
ÇÇ
2
st
Z
F
2
Total,
pq
=
(69)
st
11
pq
ÇÇ
2
(
ZZ
)
F
2
Homogeneity,
pq
-1
=
(70)
st
st
11
Ç
p
s
2
qZZ
(
)
F
2
Season,
p
-1
=
(71)
s
1
Ç
q
t
2
F
2
Station,
q
-1
=
pZZ
(
)
(72)
t
1
Ç
pq
st
2
(
ZZZZ
)
F
2
Season-Station, (
p
-1)(
q
-1)
=
(73)
st
s
t
11
2
F
2
Trend, 1
=
pqZ
(74)
Search WWH ::
Custom Search