The MK trend, with the ss estimator, and SQMKT results are presented here for 1841–1899, then 1933–2020, and finally 1841–2020 (Fig. 2, 3, 4, 5, Table 1). Overall, 30 trends were calculated for these periods, with three significant trends quantified for 1841–1899 (Fig. 2), six for 1933–2020 (Fig. 4) and one for 1841–2020 (Fig. 5). The SQMKT results reveal complex and varying patterns of change for the rainfall seasonality variables, demonstrating why relatively few significant trends exist (Fig. 3). For 1841–1899 and 1933–2020, nine abrupt change points exist overall, with five during 1841–1899 and four during 1933–2020 (Table 1, Fig. 3). Accounting for these, a further 18 trends were quantified and among these ten significant trends exist (Table 1).
Table 1
Statistically significant change points, detected using the sequential Mann-Kendall (SQMKT) test, for the various rainfall seasonality variables for 1841–1899 and 1933–2020. Here, ss represents the Sen’s slope, z represents the Mann-Kendall statistic and p represents the Mann-Kendall test p value. Statistically significant p values (p < 0.05) are denoted in bold.
Variable
|
Statistically significant change point(s) (Y/N)
|
Year of change point(s)
|
Trend before change point(s)
|
Trend after change point(s)
|
Seasonality score
|
N
|
-
|
-
|
-
|
Wet-season start-date (Julian day)
|
N
|
-
|
-
|
-
|
Wet-season end-date (Julian day)
|
Y
|
1879
|
ss = 0.8, z = 1.74, p = 0.082
|
ss = -0.6, z = -0.56, p = 0.576
|
Wet-season length (days)
|
N
|
-
|
-
|
-
|
Wet-season total rainfall (mm)
|
Y
|
1879
|
ss = 2.3, z = 1.74, p = 0.082
|
ss = -3.5, z = -0.22, p = 0.827
|
Number of wet-season rain days
|
N
|
-
|
-
|
-
|
Wet-season daily rainfall rate (mm.d− 1)
|
Y
|
1879
|
ss = 0.1, z = 2.47, p = 0.013
|
ss = -0.2, z = -1.74, p = 0.081
|
1982
|
ss = 0.1, z = 2.78, p = 0.005
|
ss = -0.1, z = -2.83, p = 0.005
|
Dry-season total rainfall (mm)
|
Y
|
1879/80
|
ss = 0.7, z = 1.87, p = 0.062
|
ss = -2.2, z = -1.74, p = 0.081
|
1955/56
|
ss = 1.6, z = 2.03, p = 0.042
|
ss = -0.3, z = -2.03, p = 0.042
|
Number of dry-season rain days
|
Y
|
1949/50
|
ss = 1.3, z = 1.44, p = 0.149
|
ss = -0.1, z = -2.34, p = 0.019
|
Dry-season daily rainfall rate (mm.d− 1)
|
Y
|
1879/80
|
ss = 0.1, z = 2.22, p = 0.026
|
ss = -0.1, z = -2.73, p = 0.006
|
1996/97
|
ss = 0.1, z = 3.82, p = 0.0001
|
ss = -0.1, z = -3.75, p = 0.0002
|
The very weak insignificant score trend of -0.0020.yr− 1 (z = -0.87, p = 0.385) for 1841–1899 indicates a tendency towards a stronger degree of seasonality as scores tend away from zero, towards more unevenly distributed rainfall (Fig. 2a). The SQMKT results reflect strong variability, evident from numerous insignificant change points and the highly variable nature of U(t), thus indicating no clear score trend (Fig. 3a). A reduction (an increase) in the wet-season (dry-season) length similarly reflects a tendency towards a stronger degree of seasonality. This trend of -0.1d.yr− 1 (z = -0.34, p = 0.734) is similarly weak and insignificant, and numerous insignificant change points with a highly variable nature of U(t) also indicates strong variability and no clear trend (Fig. 2d, 3d). This is the case for the very weak insignificant wet-season start- (0.1d.yr− 1, z = 0.35, p = 0.724) and end-date (0.1d.yr− 1, z = 0.81, p = 0.420) trends, reflecting later start- and end-dates (Fig. 2b, c, 3b, c). However, the wet-season end-dates were characterised by a significant change point for 1879 (Fig. 3c). Despite being weaker than the trend prior to 1878 (given 1878–1880 missing data), the trend towards earlier end-dates (-0.6d.yr− 1, z = -0.56, p = 0.576) from 1881, may have, together with the overall later start-date trend, contributed to driving the shorter wet-season trend until 1899 as this trend is more pronounced from ~ 1881 (Fig. 3c, d, Table 1).
For 1841–1899, the wet-season totals increased significantly (2.2mm.yr− 1, z = 2.38, p = 0.017; Fig. 2e). A significant change point was detected for 1879, and a decreasing trend of -3.5mm.yr− 1 (z = -0.22, p = 0.827) was calculated thereafter, despite the significant increasing trend, until 1892, demonstrated by the U(t) line (Fig. 3e, Table 1). A decline of -0.2d.yr− 1 (z = -1.56, p = 0.118) was quantified for the rain day counts (Fig. 2f). However, this series demonstrates much variability, reflected by numerous insignificant change points and the highly variable nature of U(t), indicating no clear trend (Fig. 3f). A significant increase of 0.1mm.d− 1.yr− 1 (z = 2.76, p = 0.006) was quantified for the wet-season daily rainfall rate (Fig. 2g). Though, a significant change point was detected for 1879, and from 1881–1899 a near-significant (i.e. p < 0.10) decreasing trend of -0.2mm.d− 1.yr− 1 (z = -1.74, p = 0.081) was calculated, despite the significant increasing trend until 1892 (Table 1, Fig. 3g).
For 1841/42-1898/99, the dry-season totals increased at a near-significant rate of 0.4mm.yr− 1 (z = 1.85, p = 0.064; Fig. 2h), however, a significant change point was detected for 1879/80 (Fig. 3h). From 1881/82-1898/99, a near-significant decreasing trend (-2.2mm.yr− 1, z = -1.74, p = 0.081) was calculated (Table 1), despite the significant increasing trend until 1892/93 (Fig. 3h). A near-significant decline of -0.1d.yr1 (z = -1.65, p = 0.099) was quantified for the dry-season rain day counts (Fig. 2i). Numerous insignificant change points and high variability in the U(t) line suggests no clear trend, despite a relatively strong p value (Fig. 2i, 3i). A significant increase of 0.1mm.d− 1.yr− 1 (z = 2.42, p = 0.016) was calculated for the dry-season daily rainfall rate (Fig. 2j). Though, from 1881/82-1898/99, following a significant change point during 1879/80, a significant decreasing trend of -0.1mm.d− 1.yr− 1 (z = -2.73, p = 0.006) persisted (Table 1), despite a significant increasing trend until 1886/87 (Fig. 3j).
For 1933–2020, the scores consistently tended away from zero, towards more unevenly distributed rainfall and a stronger degree of seasonality, evident from low variability in the SQMKT results and the significant trend of -0.0038.yr− 1 (z = -3.41, p = 0.001; Fig. 3a, 4a). While the trend for the wet-season length demonstrates notable variability (Fig. 3d), the near-significant decreasing trend of -0.3d.yr− 1 (z = -1.66, p = 0.097; Fig. 4d), which indicates a shorter (longer) wet-season (dry-season) duration trend, corresponds to the score trend. The later wet-season start-date trend of 0.3d.yr− 1 (z = 2.88, p = 0.004) is significant, and is stronger and varies less than the later end-date trend of 0.1d.yr− 1 (z = 0.70, p = 0.484), thus the start-date trend was a stronger driver of the declining wet-season duration trend (Fig. 3b, c, 4b, c).
The trend of -0.5mm.yr− 1 (z = -0.90, p = 0.368) reflects a decline in wet-season totals for 1933–2020, despite being weak overall with notable variability in the U(t) line (Fig. 3e, 4e). The wet-season rain day counts demonstrate little variability and declined at a significant rate of -0.3d.yr− 1 (z = -4.32, p < 0.0001; Fig. 3f, 4f). The wet-season daily rainfall rate increased at significant rate of 0.1mm.d− 1.yr− 1 (z = 2.39, p = 0.017), however, three significant change points exist from 1975–1982 (Fig. 3g, 4g). Considering the last change point, the wet-season daily rainfall rate decreased at a significant rate of -0.1mm.d− 1.yr− 1 (z = -2.83, p = 0.005) for 1982–2020 (Table 1), despite a significant increasing trend, reflected by the U(t) line for much of 1982–2009 (Fig. 3g).
Although the dry-season totals decreased significantly (-0.3mm.yr− 1; z = -2.27, p = 0.023) for 1933/34-2019/20 (Fig. 4h), according to the SQMKT results, this significant decreasing trend only persisted from 1955/56 at rate of -0.3 mm.yr− 1 (z = -2.03, p = 0.042), following a significant increasing trend (1.6mm.yr− 1; z = 2.03, p = 0.042; Fig. 3h, Table 1). Similarly, while the dry-season rain day counts decreased significantly (-0.1d.yr− 1; z = -3.43, p = 0.001), this significant decreasing trend only occurred from 1949/50 at a rate of -0.1d.yr− 1 (z = -2.34, p = 0.019; Fig. 3i, 4i, Table 1). The dry-season daily rainfall rate increased at a near-significant rate of 0.1mm.d− 1.yr− 1 (z = 1.91, p = 0.057), however, three significant change points were detected from 1990/91-1996/97 (Fig. 3j, 4j). Again, considering the last change point for 1996/97, the dry-season daily rainfall rate decreased at a significant rate of -0.1mm.d− 1.yr− 1 (z = -3.75, p = 0.0002) for 1996/97-2019/20 (Table 1), despite the significant increasing trend evident from the U(t) line until 2001/02 (Fig. 3j).
Consistent with the score trends detected for 1841–1899 and 1933–2020, the trend for 1841–2020 reflects a decreasing trend of -0.0006.yr− 1 (z = -1.25, p = 0.212; Fig. 5a), indicating that since 1841 the scores have generally tended towards stronger WRZ conditions. The near-significant decreasing trend (-0.1d.yr− 1; z = -1.72, p = 0.085) for the wet-season length for 1841–2020 is similarly consistent with the decreasing trends for 1841–1899 and 1933–2020 (Fig. 5d). Together with an increasing dry-season length, this also reflects a trend towards stronger WRZ conditions. Notably, the SQMKT results for the scores and wet-season length appear to broadly track each other in direction throughout 1841–2020 (Fig. 3a, d), thus highlighting good agreement between the two methods (Roffe et al. 2021a). The U(t) line reflects cyclic patterns, with periods of stronger and weaker seasonality (Fig. 3a, d); though further analysis in terms of length and drivers of cycles is beyond this papers scope. The near-significant later wet-season start-date trend of 0.1d.yr− 1 (z = 1.82, p = 0.068) for 1841–2020 also corresponds to the trends quantified for 1841–1899 and 1933–2020 (Fig. 5b). No trend exists in the wet-season end-dates for 1841–2020 (Fig. 5c), which corresponds to large variability in the end-dates for 1841–1899 and 1933–2020 (Fig. 3c). This highlights that since 1841, and particularly from 1933, the later start-date trend has primarily driven the shorter wet-season trend. Given this, it is notable that the cyclic patterns reflected by the start-date U(t) line broadly supports later (earlier) start-dates for periods with shorter (longer) wet-seasons, while relatively little correspondence exists between the end-dates and wet-season length (Fig. 3b, c, d).
Although the wet-season totals trend for 1841–2020 indicates a near-significant decline of -0.4mm.yr− 1 (z = -1.67, p = 0.096; Fig. 5e), this trend has only persisted since 1881, or more likely since 1892 (Fig. 3e, Table 1). The significant decreasing trend of -0.1d.yr− 1 (z = -2.52, p = 0.012) calculated for the wet-season rain day counts for 1841–2020 corresponds to the decreasing trends quantified for 1841–1899 and 1933–2020 (Fig. 5f). No trend was detected for the wet-season daily rainfall rate for 1841–2020 (Fig. 5g), despite significant increasing trends quantified for 1841–1899 and 1933–2020. This is primarily because the series was characterised by relatively high variability, as is evident from the U(t) line and numerous significant and non-significant change points (Fig. 3g, Table 1).
While the trend for 1841/42-2019/20 indicates a near-significant decline of -0.1mm.yr− 1 (z = -1.91, p = 0.056) for the dry-season totals (Fig. 5h), this trend has only persisted at a significant rate of -0.3mm.yr− 1 (z = -2.03, p = 0.042) since 1955/56 (Fig. 3h, Table 1). No trend was calculated for 1841/42-2019/20 for the dry-season rain day counts and daily rainfall rate (Fig. 5i, j). Despite a significant decreasing trend of -0.1d.yr− 1 (z = -2.34, p = 0.019) from 1949/50 for the dry-season rain day counts, the no trend result broadly corresponds to relatively high variability evident from the U(t) line for 1841/42-1898/99 and the significant change point detected (Fig. 3i, Table 1). For the dry-season daily rainfall rate, this corresponds to high variability throughout 1841–2020, evident from the U(t) line and numerous significant and non-significant change points (Fig. 3j).
Although we do not further explore cyclic patterns for the various rainfall seasonality variables, it is worth noting similarity in trend evolution. This exists between the wet- and dry-season totals (Fig. 3e, h), the wet- and dry-season rain day counts (Fig. 3f, i), and the wet- and dry-season daily rainfall rate (Fig. 3g, j); though there appears to be stronger, more distinct cyclicity for the wet- and dry-season totals. The structure, and specifically the timing, of cyclicity appears to change from the earlier (1841–1899) to later period (1933–2020); a result which is similarly evident for SAAO annual and seasonal rainfall totals (Ndebele et al. 2020). As such, the similarity in trend structure across the wet- and dry-seasons highlights that despite differences in their timing, there is much similarity in their rainfall characteristics and trends.
4.2 Statistically comparing historical (1841–1899) and recent (1962–2020) period rainfall seasonality characteristics
Significant mean and data distribution differences in the various rainfall seasonality variables for 1841–1899 (HP) and 1962–2020 (RP) were calculated, using the WPST, for the wet-season rainfall totals and rain day counts and the dry-season rainfall totals (Fig. 6e, f, h). For the remaining variables, the differences are insignificant (Fig. 6a, b, c, d, g, i, j). Despite this, data distribution differences exist between the HP and RP for most variables – evident from visual inspection of the boxplots, focusing mainly on the interquartile range (IQR), representing the behaviour and spread of most data values, and mean and median values (Fig. 6). Notwithstanding the statistical significance level, the differences detected generally agree with trend results for 1841–2020 (Fig. 5, 6, Table 2), reflecting that the mean and data distribution differences broadly represent the results of these trends.
Table 2
Descriptive statistics of rainfall seasonality characteristics for the historical (1841–1899) and recent (1962–2020) periods. HP and RP denote statistics for the historical and recent periods, respectively.
Variable
|
Minimum
|
First Quartile
|
Median
|
Mean
|
Third Quartile
|
Maximum
|
Interquartile range
|
Range
|
Standard deviation
|
Coefficient of variation (%)
|
Skewness
|
HP seasonality score
|
-2.00
|
-1.39
|
-1.16
|
-1.21
|
-1.02
|
-0.56
|
0.37
|
1.44
|
0.28
|
23.1
|
-0.27
|
RP seasonality score
|
-2.17
|
-1.35
|
-1.19
|
-1.23
|
-1.06
|
-0.46
|
0.29
|
1.71
|
0.30
|
24.3
|
-0.77
|
HP start-date (Julian day)
|
4 January (4)
|
20 March (79)
|
11 April (101)
|
3 April (93)
|
23 April (113)
|
25 May (145)
|
34
|
141
|
30
|
32.0
|
-1.32
|
RP start-date (Julian day)
|
5 February (36)
|
24 March (83)
|
17 April (107)
|
11 April (101)
|
18 April (118)
|
26 May (146)
|
35
|
110
|
27
|
26.6
|
-0.59
|
HP end-date (Julian day)
|
8 September (251)
|
28 September (271)
|
10 October (283)
|
12 October (285)
|
23 October (296)
|
30 November (334)
|
25
|
83
|
21
|
7.5
|
0.50
|
RP end-date (Julian day)
|
10 August (222)
|
23 September (266)
|
11 October (284)
|
10 October (283)
|
1 November (305)
|
8 December (342)
|
39
|
120
|
28
|
9.9
|
-0.08
|
HP wet-season length (days)
|
139
|
168
|
192
|
194
|
218
|
294
|
50
|
155
|
33
|
17.1
|
0.49
|
RP wet-season length (days)
|
115
|
159
|
184
|
183
|
209
|
240
|
50
|
125
|
32
|
17.5
|
-0.15
|
HP wet-season total rainfall (mm)
|
387.2
|
460.7
|
518.2
|
536.9
|
598.0
|
871.8
|
137.3
|
484.6
|
106.4
|
19.8
|
0.83
|
RP wet-season total rainfall (mm)
|
282.1
|
387.5
|
486.9
|
481.8
|
558.5
|
793.5
|
171.0
|
511.4
|
118.8
|
24.6
|
0.43
|
HP number of wet-season rain days
|
50
|
61
|
68
|
70
|
75
|
105
|
14
|
55
|
12
|
16.9
|
0.79
|
RP number of wet-season rain days
|
43
|
57
|
63
|
64
|
72
|
92
|
15
|
49
|
11
|
16.6
|
0.14
|
HP wet-season daily rainfall rate (mm.d− 1)
|
4.1
|
6.4
|
7.6
|
7.9
|
9.0
|
12.9
|
2.6
|
8.8
|
2.0
|
25.3
|
0.61
|
RP wet-season daily rainfall rate (mm.d− 1)
|
4.4
|
6.2
|
7.3
|
7.7
|
8.8
|
13.7
|
2.6
|
9.3
|
2.1
|
26.7
|
0.75
|
HP dry-season total rainfall (mm)
|
37.1
|
99.1
|
110.6
|
113.2
|
126.4
|
161.8
|
27.3
|
124.7
|
24.1
|
21.3
|
-0.42
|
RP dry-season total rainfall (mm)
|
59.6
|
87.6
|
103.0
|
104.2
|
120.3
|
156.9
|
32.7
|
97.3
|
22.3
|
21.4
|
0.20
|
HP number of dry-season rain days
|
12
|
24
|
30
|
29
|
36
|
49
|
12
|
37
|
9
|
30.0
|
0.11
|
RP number of dry-season rain days
|
12
|
23
|
27
|
27
|
33
|
43
|
10
|
31
|
7
|
26.1
|
0.09
|
HP dry-season daily rainfall rate (mm.d− 1)
|
2.0
|
3.2
|
3.8
|
4.2
|
5.0
|
9.3
|
1.8
|
7.3
|
1.7
|
40.3
|
1.22
|
RP dry-season daily rainfall rate (mm.d− 1)
|
2.0
|
3.2
|
3.7
|
4.1
|
4.6
|
9.2
|
1.4
|
7.2
|
1.4
|
34.7
|
1.42
|
The mean (HP = -1.21, RP = -1.23) and median (HP = -1.16, RP = -1.19) score values reflect slightly stronger RP scores (Fig. 6a, Table 2), indicating a shift towards a slightly stronger degree of seasonality for the RP. This corresponds to a shorter (longer) RP wet-season (dry-season) length, supported by the plotted IQR and smaller RP minimum (HP = 139 days, RP = 115 days), mean (HP = 194 days, RP = 183 days), median (HP = 192 days, RP = 184 days) and maximum (HP = 294 days, RP = 240 days) values (Fig. 6d, Table 2). Although notable differences exist in the distribution of the HP and RP wet-season end-date datasets, particularly reflected by larger interannual variability (HP coefficient of variability [CV] = 7.5%, RP CV = 9.9%) and larger IQR (HP = 25 days, RP = 39 days) values for the RP, the mean (HP = 12 October, Julian day [JD] = 285, RP = 10 October, JD = 283) and median (HP = 10 October, JD = 283, RP = 11 October, JD = 284) values are very similar and reflect little to no end-date shift (Fig. 6c, Table 2). This confirms that the wet-season (and dry-season) duration shift is primarily due to later RP wet-season start-dates, evident from the plotted IQR, and later RP mean (HP = 3 April, JD = 93, RP = 11 April, JD = 101) and median (HP = 11 April, JD = 101, RP = 17 April, JD = 107) values (Fig. 6b, Table 2).
Besides the wet-season timing shifts, changes occurred in the magnitude and intensity of wet-season rainfall, and rain day counts. The HP wet-season was wetter than the RP wet-season (Fig. 6e, f, g, Table 2). Most (~ 70%) annual HP wet-season totals were higher than for the RP, evident from the plotted IQR, and the minimum (HP = 387.2mm, RP = 282.1mm), mean (HP = 536.9mm, RP = 481.8mm), median (HP = 518.2mm, RP = 486.9mm) and maximum (HP = 871.8mm, RP = 793.5mm) values (Fig. 6e, Table 2). The wet-season rain day counts were lower for the RP compared to the HP, as demonstrated by the plotted IQR, and the minimum (HP = 50 days, RP = 43 days), mean (HP = 70 days, RP = 64 days), median (HP = 68 days, RP = 63 days) and maximum (HP = 105 days, RP = 92 days) values (Fig. 6f, Table 2). Compared to the HP, the RP wet-season daily rainfall rate was slightly reduced, evident from the plotted IQR, and the mean (HP = 7.9mm.d− 1, RP = 7.7mm.d− 1) and median (HP = 7.6mm.d− 1, RP = 7.3mm.d− 1) values (Fig. 6g, Table 2).
Changes also occurred in the magnitude and intensity of dry-season rainfall, and the rain day counts, with the HP dry-season wetter than the RP dry-season (Fig. 6h, i, j, Table 2). The plotted IQR, and mean (HP = 113.2mm, RP = 104.2mm) and median (HP = 110.6mm, RP = 103.0mm) values reflect lower RP dry-season totals (Fig. 6h, Table 2). The RP dry-season rain day counts are marginally lower than those for the HP, reflected by the plotted IQR (Fig. 6i), and mean (HP = 29 days, RP = 27 days) and median (HP = 30 days, RP = 27 days) values (Table 2). The HP dry-season daily rainfall rate was only slightly higher than that for the RP, as demonstrated by the plotted IQR, and mean (HP = 4.2 mm.d− 1, RP = 4.1 mm.d− 1) and median (HP = 3.8 mm.d− 1, RP = 3.7 mm.d− 1) values (Fig. 6j, Table 2).