The results of the analysis are divided into five sections corresponding to each statistical method applied in this study along with a discussion.
2.2.2 CS results
The results based on CS are summarized in Table 43. For quarter DJF, it is possible to see that, as in the MK test, a single gauge (1547020), had a decreasing trend. For quarter MAM, gauge 1547013 presented a decreasing trend, different from the MK results, where a trend was not identified in this period for any gauge. Quarter JJA also presented multiples gauges, 1547014, 1547019, 1547020, 1547021, 1548008, and 1548010, describing decreasing trends. The last four replicated behavior described in MK. Stations 1547021 and 1548006 were identified as having trends for the Water Year, and the first also repeated the classification obtained by the MK.
Table 43 brings together the number of positive and negative differences, making it possible to see the magnitude of the trends. Chen and Huang (2020) presented an analysis based on these values, and the p-value to identify the degree of a trend. In this way, using the definition proposed by Chen and Huang (2020), some gauges that presented trends for MK could also be identified presenting some level of a trend for CS. Despite the null hypothesis being rejected, these gauges showed a high number of Positive Differences compared to Negative Differences in the CS as well as significant p-value (0.05 < p-value < 0.1). Following the classification proposed by Chen and Huang (2020), Table 44 depicts the gauges classified as “Strong”, where most could be classified as trending by MK. Gauge 1548005 was an exception, and did not present a tendency for MK, displaying significant contrast between positive and negative differences.
Table 3
CS Results for gauges rejected by the null hypothesis
Period
|
Rain Gauge Code
|
n
|
p-value
|
Trend
|
Positive Differences
|
Negative Differences
|
DJF
|
1547020
|
39
|
0.032
|
increasing
|
5
|
14
|
MAM
|
1547013
|
46
|
0.047
|
decreasing
|
16
|
7
|
JJA
|
1547014
|
39
|
0.048
|
decreasing
|
13
|
5
|
JJA
|
1547019
|
39
|
0.010
|
decreasing
|
15
|
4
|
JJA
|
1547020
|
39
|
0.048
|
decreasing
|
13
|
5
|
JJA
|
1547021
|
39
|
0.015
|
decreasing
|
14
|
4
|
JJA
|
1548008
|
39
|
0.010
|
decreasing
|
15
|
4
|
JJA
|
1548010
|
39
|
0.032
|
decreasing
|
14
|
5
|
WY
|
1547021
|
39
|
0.032
|
decreasing
|
14
|
5
|
WY
|
1548006
|
47
|
0.047
|
decreasing
|
16
|
7
|
Table 4
CS results for gauges accepted by the null hypothesis and Mann-Kendal results.
Rain Gauge Code
|
Period
|
n
|
Mann-Kendall
|
p-value
|
Positive Differences
|
Negative Differences
|
1547003
|
DJF
|
38
|
decreasing
|
0.084
|
13
|
6
|
1548001
|
JJA
|
45
|
decreasing
|
0.058
|
14
|
6
|
1548005
|
JJA
|
47
|
no trend
|
0.067
|
15
|
7
|
1548007
|
JJA
|
47
|
decreasing
|
0.067
|
15
|
7
|
1547020
|
WY
|
39
|
increasing
|
0.084
|
6
|
13
|
1547003
|
WY
|
38
|
decreasing
|
0.084
|
13
|
6
|
Following the classification proposed by Chen and Huang (2020), a “Weak” trend can be identified if 0.1 < p-value < 0.25. Six gauges presented a “Weak” trend for quarter DJF, three for quarter MAM, four for JJA, three in SON, and three for the WY. Gauge 158007 showed a weak trend for quarters DJF and JJA, and for the WY. This gauge is located in the watershed used for water supply. The overall results indicate that the percentage of gauges/periods displaying a trend by CS was 9.52%.
2.2.5 Water management from the perspective of a trending scenario
The spatial distribution of all analyses can be observed in Fig. 3 and Fig. 4. The first one shows the concentration of trend points in the JJA period, where it is possible to identify a clusterization among the trending points. Figure 4 aggregates all the trending results by season periods, where a point was classified as trending if it was identified by at least one test. JJA period is once more identified as a trending season for multiple points, and WY also presents three decreasing gauges.
It can be seen that for all analyses described in the previous topics, there were mixed results. In order to group the statistics obtained by MK, CS, and SP, Table 47 was built. To help with visualization, WW statistics were not included. The only gauge classified as having a trend was also classified in the same way by WW. The percentage of gauges/periods identified as having a trend by at least one test was approximately 10%. From the trending points, 54% presented trends with only one method, 27% with two methods, and 19% with three methods. Hipel and McLeod (1994) suggested that non-parametric tests were not developed to show the magnitude of a certain statistical characteristic, but to indicate if there is some type of behavior. That is, non-parametric tests are considered to be exploratory data analysis procedures and can be a powerful tool for environmental analysis (Goossens and Berger 1987; WMO 2009; Rao and Hamed 2019). The results here, especially those depicted in Table 47, presented just one gauge with decreasing trends during quarter DJF, the most important quarter for water management in your region of study, and it was identified by more than one test (MK and SP). As observed in the MK test, the site of this gauge is outside the watershed of the water supply reservoirs. Analyzing the WY, three gauges presented decreasing trends. All of them are located in urban areas that are not used for water supply.
Table 6
SP Results for gauges rejected by the null hypothesis
Period
|
Rain Gauge Code
|
n
|
ρ
|
p-value
|
Direction
|
DJF
|
1547020
|
39
|
0.32
|
0.049
|
increasing
|
DJF
|
1547003
|
38
|
-0.35
|
0.029
|
decreasing
|
JJA
|
1547013
|
46
|
-0.29
|
0.047
|
decreasing
|
JJA
|
1547018
|
40
|
-0.37
|
0.019
|
decreasing
|
JJA
|
1547020
|
39
|
-0.38
|
0.019
|
decreasing
|
JJA
|
1547021
|
39
|
-0.40
|
0.014
|
decreasing
|
JJA
|
1548006
|
47
|
-0.30
|
0.043
|
decreasing
|
JJA
|
1548007
|
47
|
-0.37
|
0.012
|
decreasing
|
JJA
|
1548008
|
39
|
-0.49
|
0.00
|
decreasing
|
JJA
|
1548010
|
39
|
-0.47
|
0.00
|
decreasing
|
JJA
|
1548001
|
45
|
-0.35
|
0.020
|
decreasing
|
WY
|
1547021
|
39
|
-0.41
|
0.010
|
decreasing
|
WY
|
1547003
|
38
|
-0.47
|
0.003
|
decreasing
|
Understanding the exploratory characteristic of these tests, and their results could be a suitable condition for the study area related to the water supply. As mentioned in the introduction, a water scarcity event occurred in DF between 2016 and 2018. Lima et al. (2018) highlight the fact that during these three years, the gauge (1548007) located inside the basin most important for water supply, registered an average of 75% of the historic average. The cited gauge presented a decreasing trend behavior in JJA period for the MK, SP and the CS, the latter considering the approach proposed by Chen and Huang (2020). It presented the same behavior in DJF period for the WW.
As observed by Alves et al. (2015), Anunciação, Walde, et al., 2014, Borges et al. (2016), and Costa et al. (2012), DF presents high spatial heterogeneity for rainfall data. These variations may also be present within the series as observed in the cited triennium. Moreover, the fact that the study area is located within a monsoon region can explain these variations (Deng et al. 2018). Yue et al. (2002), analyzing the power of MK and SP, identified that variations within a series mask the existence of a trend. They suggest that as variations increase, the power of the test reduces. Likewise, as skewness coefficient increases, trend detection rates also increase (Yue et al. 2002). In order to corroborate this point of view, skewness verification was performed (D’Agostino et al. 2020). From the analyzed gauges/periods, 70% were classified as highly skewed, 10% as moderately skewed, and 20% as symmetric (Bulmer 1979). Gauge 1548007, for instance, presented moderate and high γ values (0.836, 0.537, 5.210, 1.659, and 0.886 for the periods DJF, MAM, JJA, SON, and WY, respectively). Yue et al. (2002) suggest that the power of the test is affected by the site’s characteristics when a trend exists, and this skewness can affect the results. Hamed and Ramachandra Rao (1998) also observe influences related to the autocorrelation factor throughout the data series, where positive/negative autocorrelations increase/decrease rejection of the Null hypothesis.
As WW verifies variations around the median, results can indicate great disparities throughout the series which may affect trend analysis. The definition used for a climatic trend based on Micthell (1966), and supported by Goossens and Berger (1987), points out that this type of trend is identified by a smooth and monotonic alteration of average value for the analyzed period. Therefore, instead of presenting a climatic trend condition, expected oscillations in the rainfall amounts can be suggested instead. As commented by WMO (2009), statistical tests serve to point to the significance of results but do not supply indubitable conclusions. So, it is recommended to search for other additional types of information in order to shed more light on the results. These considerations should be analyzed by decision-makers in order to effectively manage the water supply as significant variations in future years, especially for the trending sites, can be expected.
Table 7
gauges/periods identified as trending sites for MK, CS, and SP. The * means the only gauge which was classified as a trending site by WW.
Period
|
Rain Gauge Code
|
MK
|
CS
|
SP
|
DJF
|
1547003
|
decreasing
|
No
|
decreasing
|
WY
|
1547003
|
decreasing
|
No
|
decreasing
|
JJA
|
1547013
|
No
|
No
|
decreasing
|
MAM
|
1547013
|
No
|
decreasing
|
No
|
JJA
|
1547018
|
decreasing
|
No
|
decreasing
|
JJA
|
1547019
|
No
|
decreasing
|
No
|
DJF
|
1547020
|
No
|
increasing
|
increasing
|
JJA
|
1547020
|
decreasing
|
decreasing
|
decreasing
|
WY
|
1547020
|
increasing
|
No
|
No
|
JJA
|
1547021
|
decreasing
|
decreasing
|
decreasing
|
WY
|
1547021
|
decreasing
|
decreasing
|
decreasing
|
JJA
|
1548001
|
decreasing
|
No
|
decreasing
|
JJA
|
1548006
|
No
|
No
|
decreasing
|
WY
|
1548006
|
No
|
decreasing
|
No
|
JJA
|
1548007
|
decreasing
|
No
|
decreasing
|
JJA
|
1548008
|
decreasing
|
decreasing
|
decreasing
|
JJA
|
1548010
|
decreasing
|
decreasing
|
decreasing
|
JJA
|
1547014 *
|
No
|
decreasing
|
No
|
Studies point out a decreasing trend in the duration of the rainy season in monsoon region of South America (Carvalho et al. 2011; Zilli et al. 2019) and a decreasing in the volume of rainfall in the Amazônia in the last five decades (e.g., Agudelo et al. 2019). In addition, Prado et al. (2021) identified changes in the variability of precipitation in Central Brazil associated with the influence of the Pacific Ocean. These observations may affect the amount of rain in FD.