139
Spatial Patterns of Temporal Trends in Precipitation
Positive or negative autocorrelation affects the variance (S). Positive autocorrelation
increases the variance (S) and negative autocorrelation decreases the variance (S).
Thereby, positive autocorrelation overestimates the significance of both positive and
negative trends, and negative autocorrelation underestimates the significance
(Dinpashoh et al. 2013). It is important to check the autocorrelation in a given series
and to adjust the test if necessary, as often the trend of precipitation autocorrelation
receives little attention.
We calculated the coefficient of autocorrelation lag-1 as significant (positive or
negative) autocorrelation coefficient (r1) for the 12 months of the year, in 117 CFSR
grid point locations. Table 8.2 lists the results of autocorrelation lag-1 in the monthly
time series. The autocorrelation close to zero is observed in the time series January–
April and October–December. For April, May, June, July, and September, a few
locations showed a positive correlation. This pattern can be due to the shaping effect
of the monsoon season in the occurrence of precipitation in the state of Durango. In
contrast, during winter the unpredictable phenomena like ENSO and PDO influence
precipitation in the northwest of Mexico (Magaña et al. 2003). The scarce autocorrelation found in winter and part of spring for the analyzed locations suggests an
increased randomness in the occurrence of the precipitation during those months.
Temporal trends in monthly and annual precipitation and their respective change
values (mm/year) for each 117 localizations were obtained by the modified Mann–
Kendall test (modMK1) (Hamed and Rao 1998) and the Theil–Sen’s estimator
(Fig. 8.4). The temporal trends were mapped to identify their spatial distribution
across all months of the year. The standard test statistic Z was used as the criterion
to identify temporal trends; Z < −1.96 indicated a significant decreasing trend,
−1.96 < Z < 0 indicated a no significant decreasing trend, 0 < Z < 1.96 indicated a
not significant increased trend, Z > 1.96 indicated a significant increased trend.
Table 8.2 Number of locations showing significant and not-significant lag-1 autocorrelation and
significant and not significant trends throughout the state of Durango
+
–
Increasing
Decreasing
Increasing
Decreasing
January
0
0
117
0
2
0
115
February
0
0
117
0
0
18
98
March
0
2
115
0
0
33
84
April
9
0
108
7
110
0
0
May
37
0
80
2
0
10
101
June
6
0
111
1
4
38
60
July
27
0
90
3
1
114
7
August
8
0
109
0
14
26
86
September
14
0
103
4
2
82
23
October
2
2
113
0
0
52
67
November
0
2
115
0
1
21
90
December
0
3
114
0
42
0
64
8 Spatial and Temporal Analysis of Precipitation and Drought Trends Using…
Spatial Patterns of Temporal Trends in Precipitation
Positive or negative autocorrelation affects the variance (S). Positive autocorrelation
increases the variance (S) and negative autocorrelation decreases the variance (S).
Thereby, positive autocorrelation overestimates the significance of both positive and
negative trends, and negative autocorrelation underestimates the significance
(Dinpashoh et al. 2013). It is important to check the autocorrelation in a given series
and to adjust the test if necessary, as often the trend of precipitation autocorrelation
receives little attention.
We calculated the coefficient of autocorrelation lag-1 as significant (positive or
negative) autocorrelation coefficient (r1) for the 12 months of the year, in 117 CFSR
grid point locations. Table 8.2 lists the results of autocorrelation lag-1 in the monthly
time series. The autocorrelation close to zero is observed in the time series January–
April and October–December. For April, May, June, July, and September, a few
locations showed a positive correlation. This pattern can be due to the shaping effect
of the monsoon season in the occurrence of precipitation in the state of Durango. In
contrast, during winter the unpredictable phenomena like ENSO and PDO influence
precipitation in the northwest of Mexico (Magaña et al. 2003). The scarce autocorrelation found in winter and part of spring for the analyzed locations suggests an
increased randomness in the occurrence of the precipitation during those months.
Temporal trends in monthly and annual precipitation and their respective change
values (mm/year) for each 117 localizations were obtained by the modified Mann–
Kendall test (modMK1) (Hamed and Rao 1998) and the Theil–Sen’s estimator
(Fig. 8.4). The temporal trends were mapped to identify their spatial distribution
across all months of the year. The standard test statistic Z was used as the criterion
to identify temporal trends; Z < −1.96 indicated a significant decreasing trend,
−1.96 < Z < 0 indicated a no significant decreasing trend, 0 < Z < 1.96 indicated a
not significant increased trend, Z > 1.96 indicated a significant increased trend.
Table 8.2 Number of locations showing significant and not-significant lag-1 autocorrelation and
significant and not significant trends throughout the state of Durango
+
–
Increasing
Decreasing
Increasing
Decreasing
January
0
0
117
0
2
0
115
February
0
0
117
0
0
18
98
March
0
2
115
0
0
33
84
April
9
0
108
7
110
0
0
May
37
0
80
2
0
10
101
June
6
0
111
1
4
38
60
July
27
0
90
3
1
114
7
August
8
0
109
0
14
26
86
September
14
0
103
4
2
82
23
October
2
2
113
0
0
52
67
November
0
2
115
0
1
21
90
December
0
3
114
0
42
0
64
8 Spatial and Temporal Analysis of Precipitation and Drought Trends Using…