Table 1: Descriptive statistics (average (AVE) and standard deviation (SD)) of monthly rainfall at the twelve synoptic stations of Rwanda,
Station Name
|
Kanombe
|
Rubona
|
Gikongoro
|
Byimana
|
Rubengera
|
Gisenyi
|
Longitude [0,]
|
30.13
|
29.76
|
29.55
|
29.71
|
29.41
|
29.26
|
Latitude [0,]
|
-1.97
|
-2.46
|
-2.48
|
-2.16
|
-2.07
|
-1.68
|
Altitude [m]
|
1490
|
1706
|
1910
|
1750
|
1700
|
1554
|
Station ID
|
10306100
|
20411100
|
20503100
|
20602100
|
30109100
|
30304100
|
District
|
Kicukiro
|
Huye
|
Nyamagabe
|
Ruhango
|
Karongi
|
Rubavu
|
Province
|
Kigali City
|
Southern
|
Southern
|
Southern
|
Western
|
Northern
|
Period
|
1971-2018
|
1958-2018
|
1981-2018
|
1981-2018
|
1981-2018
|
1975-2018
|
Statistics [mm]
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
January
|
81.13
|
60.19
|
110.42
|
58.15
|
109.71
|
43.40
|
129.32
|
81.79
|
84.34
|
33.70
|
88.82
|
34.40
|
February
|
100.47
|
60.30
|
110.87
|
46.06
|
137.68
|
60.66
|
106.84
|
50.51
|
80.29
|
36.81
|
78.29
|
33.05
|
March
|
108.79
|
45.59
|
150.50
|
64.25
|
141.42
|
40.05
|
128.29
|
52.85
|
154.84
|
55.02
|
136.87
|
47.45
|
April
|
138.79
|
63.31
|
166.47
|
62.58
|
201.95
|
70.64
|
158.18
|
67.59
|
115.05
|
60.96
|
132.61
|
60.76
|
May
|
87.95
|
61.25
|
101.11
|
53.90
|
131.47
|
68.98
|
144.76
|
89.34
|
123.87
|
60.76
|
88.26
|
34.65
|
June
|
15.87
|
30.57
|
17.24
|
27.26
|
34.92
|
53.97
|
25.82
|
37.51
|
48.03
|
60.13
|
49.61
|
49.87
|
July
|
4.68
|
14.02
|
4.11
|
12.81
|
16.76
|
29.16
|
11.76
|
27.35
|
22.89
|
44.37
|
26.16
|
35.71
|
August
|
40.16
|
51.45
|
36.57
|
41.73
|
48.22
|
49.26
|
50.19
|
45.86
|
58.51
|
57.11
|
88.49
|
65.14
|
September
|
66.08
|
53.23
|
65.16
|
37.71
|
100.49
|
55.75
|
83.27
|
51.96
|
115.89
|
43.14
|
109.22
|
31.39
|
October
|
81.49
|
27.62
|
95.51
|
33.85
|
123.73
|
49.85
|
103.05
|
44.86
|
120.27
|
56.01
|
131.08
|
39.63
|
November
|
121.49
|
62.72
|
115.03
|
50.06
|
130.05
|
50.87
|
131.30
|
58.50
|
104.86
|
53.39
|
143.68
|
45.49
|
December
|
79.97
|
52.33
|
105.78
|
56.80
|
111.22
|
68.65
|
148.70
|
72.08
|
109.68
|
44.83
|
95.70
|
34.21
|
Station Name
|
Ruhengeri
|
Byumba
|
Nyagatare
|
Kawangire
|
Kibungo
|
Kamembe
|
Longitude [0,]
|
29.61
|
30.05
|
30.31
|
30.45
|
30.53
|
28.91
|
Latitude [0,]
|
-1.48
|
-1.60
|
-1.28
|
-1.81
|
-2.16
|
-2.46
|
Altitude [m]
|
1878
|
2235
|
1377
|
1473
|
1604
|
1591
|
Station ID
|
40303100
|
40503100
|
50210100
|
50410100
|
50604100
|
30606100
|
District Name
|
Musanze
|
Gicumbi
|
Nyagatare
|
Kawangire
|
Ngoma
|
Rusizi
|
Province Name
|
Northern
|
Northern
|
Eastern
|
Eastern
|
Eastern
|
Western
|
Period
|
1981-2018
|
1981-2018
|
1954-2918
|
1981-2018
|
1981-2018
|
1957-2018
|
Statistics [mm]
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
AVE
|
SD
|
January
|
88.53
|
62.82
|
56.50
|
36.54
|
37.13
|
24.15
|
64.95
|
41.31
|
80.97
|
46.79
|
135.05
|
37.38
|
February
|
91.45
|
41.71
|
74.18
|
36.76
|
46.74
|
29.34
|
78.03
|
47.04
|
78.32
|
44.28
|
132.26
|
38.64
|
March
|
138.55
|
43.69
|
150.47
|
46.05
|
108.13
|
38.91
|
119.00
|
51.40
|
138.84
|
51.44
|
162.66
|
55.20
|
April
|
198.32
|
51.78
|
175.79
|
55.49
|
96.97
|
35.56
|
145.16
|
48.05
|
144.05
|
38.65
|
138.47
|
45.73
|
May
|
137.00
|
53.12
|
114.84
|
52.98
|
125.32
|
66.88
|
90.45
|
54.80
|
110.13
|
63.10
|
87.11
|
33.17
|
June
|
52.50
|
45.16
|
28.63
|
34.33
|
25.50
|
27.60
|
19.00
|
24.60
|
9.58
|
15.60
|
30.39
|
29.19
|
July
|
11.62
|
15.65
|
10.27
|
17.05
|
6.27
|
14.86
|
17.32
|
44.30
|
9.22
|
22.44
|
15.68
|
25.69
|
August
|
47.92
|
35.71
|
48.70
|
37.35
|
22.70
|
20.22
|
25.16
|
23.42
|
31.27
|
39.16
|
42.43
|
38.54
|
September
|
125.59
|
41.96
|
114.14
|
49.88
|
70.14
|
28.33
|
82.70
|
61.72
|
72.68
|
62.24
|
105.43
|
32.11
|
October
|
175.92
|
46.24
|
121.86
|
43.94
|
100.70
|
46.90
|
152.16
|
74.11
|
105.49
|
47.16
|
161.27
|
47.44
|
November
|
167.11
|
44.41
|
121.32
|
46.64
|
94.70
|
31.11
|
148.14
|
48.39
|
170.05
|
55.62
|
164.00
|
38.39
|
December
|
89.22
|
30.14
|
69.14
|
32.39
|
66.00
|
27.46
|
139.30
|
89.24
|
108.65
|
54.94
|
126.46
|
38.63
|
Table 2: Summary statistics of the annual maximum of daily rainfall data (mm/day) for the twelve synoptic stations of Rwanda.
Station
|
Period
|
Minimum
|
1st Quantile
|
Median
|
Mean
|
3rd Quantile
|
Maximum
|
Kanombe
|
1971-2018
|
24.0
|
38.8
|
45.8
|
51.4
|
63.3
|
92.0
|
Rubona
|
1958-2018
|
26.0
|
47.5
|
54.0
|
56.4
|
65.0
|
90.4
|
Gikongoro
|
1981-2018
|
28.0
|
51.0
|
57.0
|
60.6
|
73.0
|
92.0
|
Byimana
|
1981-2018
|
26.0
|
50.0
|
59.5
|
59.0
|
67.5
|
84.0
|
Rubengera
|
1981-2018
|
31.0
|
46.8
|
55.0
|
58.9
|
73.0
|
94.0
|
Gisenyi
|
1975-2018
|
35.5
|
42.0
|
50.2
|
55.8
|
66.3
|
99.0
|
Ruhengeri
|
1981-2018
|
25.0
|
36.3
|
44.5
|
47.3
|
56.8
|
91.0
|
Byumba
|
1981-2018
|
24.0
|
38.5
|
48.0
|
50.2
|
57.8
|
81.0
|
Nyagatare
|
1954-2918
|
19.0
|
33.8
|
41.0
|
43.9
|
52.8
|
76.0
|
Kawangire
|
1981-2018
|
26.0
|
44.3
|
56.5
|
58.0
|
66.0
|
100.0
|
Kibungo
|
1981-2018
|
33.0
|
46.3
|
57.5
|
60.1
|
70.0
|
97.0
|
Kamembe
|
1957-2018
|
19.0
|
42.8
|
50.5
|
50.9
|
59.0
|
97.0
|
Table 3: Parameter estimates with their 95% confidence intervals of the fitted GEV distribution to AMS of daily rainfall at the twelve synoptic stations of Rwanda. LCI: low confidence interval; UCI: upper confidence interval.
Location parameter
|
|
|
|
|
|
|
|
|
|
|
|
Station
|
MLE-LCI
|
MLE
|
MLE-UCI
|
BAYE-LCI
|
BAYE
|
BAYE-UCI
|
LME-LCI
|
LME
|
LME-UCI
|
GMLE-LCI
|
GMLE
|
GMLE-UCI
|
Kanombe
|
38.44
|
43.11
|
47.78
|
39.52
|
42.68
|
46.06
|
38.07
|
43.13
|
47.96
|
38.39
|
43.13
|
47.87
|
Rubona
|
46.28
|
50.16
|
54.04
|
46.04
|
50.00
|
53.54
|
46.14
|
49.82
|
53.80
|
45.95
|
49.82
|
53.69
|
Gikongoro
|
37.69
|
43.21
|
48.73
|
40.58
|
43.70
|
46.72
|
38.06
|
43.10
|
48.71
|
37.54
|
43.10
|
48.65
|
Byimana
|
42.87
|
47.64
|
52.41
|
44.18
|
48.84
|
52.07
|
43.40
|
47.22
|
51.62
|
42.46
|
47.22
|
51.99
|
Rubengera
|
49.46
|
54.73
|
59.99
|
52.57
|
57.32
|
62.27
|
49.27
|
54.08
|
59.45
|
48.90
|
54.08
|
59.26
|
Gisenyi
|
42.93
|
46.50
|
50.07
|
42.61
|
48.67
|
53.17
|
43.56
|
47.25
|
51.29
|
42.79
|
46.32
|
49.85
|
Ruhengeri
|
43.07
|
46.75
|
50.43
|
45.51
|
47.86
|
51.20
|
44.07
|
47.63
|
51.77
|
43.02
|
46.67
|
50.32
|
Byumba
|
39.87
|
44.74
|
49.62
|
39.71
|
43.03
|
46.31
|
40.53
|
45.14
|
50.49
|
40.15
|
45.14
|
50.13
|
Nyagatare
|
34.27
|
38.11
|
41.96
|
35.02
|
38.65
|
42.07
|
34.30
|
37.70
|
41.82
|
33.90
|
37.70
|
41.51
|
Kawangire
|
39.85
|
44.47
|
49.09
|
40.33
|
44.05
|
47.11
|
39.40
|
44.10
|
48.86
|
39.48
|
44.10
|
48.73
|
Kibungo
|
35.04
|
39.21
|
43.39
|
40.34
|
43.55
|
48.70
|
34.75
|
38.99
|
43.27
|
34.81
|
38.99
|
43.18
|
Kamembe
|
41.27
|
45.21
|
49.14
|
37.11
|
42.33
|
47.37
|
41.48
|
45.57
|
49.97
|
41.57
|
45.57
|
49.57
|
Scale parameter
|
|
|
|
|
|
|
|
|
|
|
|
Station
|
MLE-LCI
|
MLE
|
MLE-UCI
|
BAYE-LCI
|
BAYE
|
BAYE-UCI
|
LME-LCI
|
LME
|
LME-UCI
|
GMLE-LCI
|
GMLE
|
GMLE-UCI
|
Kanombe
|
10.32
|
13.88
|
17.43
|
11.28
|
14.89
|
20.04
|
11.16
|
14.63
|
18.04
|
10.53
|
14.63
|
18.72
|
Rubona
|
10.72
|
13.53
|
16.33
|
11.10
|
14.16
|
18.47
|
10.94
|
13.70
|
16.69
|
10.82
|
13.70
|
16.59
|
Gikongoro
|
10.27
|
14.46
|
18.65
|
11.62
|
16.11
|
22.42
|
10.96
|
15.27
|
20.12
|
10.42
|
15.27
|
20.13
|
Byimana
|
9.59
|
13.06
|
16.53
|
10.57
|
14.37
|
19.84
|
9.67
|
13.35
|
16.78
|
9.69
|
13.35
|
17.00
|
Rubengera
|
10.86
|
14.64
|
18.42
|
11.89
|
16.08
|
22.00
|
11.44
|
14.53
|
18.77
|
10.93
|
14.53
|
18.13
|
Gisenyi
|
6.84
|
9.92
|
13.00
|
7.48
|
12.32
|
17.94
|
8.41
|
11.48
|
14.83
|
6.79
|
9.86
|
12.92
|
Ruhengeri
|
6.23
|
9.46
|
12.70
|
7.79
|
11.00
|
15.25
|
8.07
|
11.21
|
15.31
|
6.21
|
9.43
|
12.65
|
Byumba
|
10.76
|
14.07
|
17.37
|
11.29
|
14.85
|
20.06
|
10.76
|
14.41
|
18.21
|
10.82
|
14.41
|
18.00
|
Nyagatare
|
9.05
|
11.84
|
14.63
|
9.83
|
12.78
|
16.70
|
8.95
|
11.89
|
14.90
|
9.10
|
11.89
|
14.69
|
Kawangire
|
9.34
|
12.69
|
16.03
|
9.91
|
13.59
|
18.92
|
9.50
|
13.00
|
16.66
|
9.44
|
13.00
|
16.56
|
Kibungo
|
8.00
|
11.13
|
14.25
|
9.98
|
13.67
|
19.13
|
8.34
|
11.58
|
14.81
|
8.10
|
11.58
|
15.06
|
Kamembe
|
10.66
|
13.32
|
15.99
|
11.07
|
14.06
|
18.07
|
10.57
|
13.51
|
16.34
|
10.71
|
13.51
|
16.31
|
Shape parameter
|
|
|
|
|
|
|
|
|
|
|
|
Station
|
MLE-LCI
|
MLE
|
MLE-UCI
|
BAYE-LCI
|
BAYE
|
BAYE-UCI
|
LME-LCI
|
LME
|
LME-UCI
|
GMLE-LCI
|
GMLE
|
GMLE-UCI
|
Kanombe
|
-0.280
|
0.014
|
0.308
|
-0.266
|
0.041
|
0.423
|
-0.230
|
-0.010
|
0.190
|
-0.333
|
-0.010
|
0.312
|
Rubona
|
-0.356
|
-0.145
|
0.066
|
-0.366
|
-0.130
|
0.119
|
-0.317
|
-0.111
|
0.064
|
-0.345
|
-0.111
|
0.123
|
Gikongoro
|
-0.388
|
-0.045
|
0.298
|
-0.369
|
-0.027
|
0.380
|
-0.336
|
-0.056
|
0.155
|
-0.441
|
-0.056
|
0.329
|
Byimana
|
-0.404
|
-0.128
|
0.148
|
-0.392
|
-0.111
|
0.235
|
-0.334
|
-0.091
|
0.125
|
-0.404
|
-0.091
|
0.222
|
Rubengera
|
-0.479
|
-0.224
|
0.031
|
-0.548
|
-0.241
|
0.082
|
-0.432
|
-0.151
|
0.069
|
-0.434
|
-0.151
|
0.132
|
Gisenyi
|
-0.031
|
0.321
|
0.673
|
-0.141
|
0.277
|
0.786
|
-0.120
|
0.145
|
0.360
|
0.000
|
0.363
|
0.725
|
Ruhengeri
|
-0.033
|
0.355
|
0.743
|
-0.052
|
0.332
|
0.811
|
-0.152
|
0.146
|
0.365
|
-0.016
|
0.375
|
0.766
|
Byumba
|
-0.322
|
-0.162
|
-0.001
|
-0.280
|
-0.102
|
0.130
|
-0.490
|
-0.227
|
-0.022
|
-0.337
|
-0.227
|
-0.116
|
Nyagatare
|
-0.353
|
-0.109
|
0.135
|
-0.354
|
-0.093
|
0.222
|
-0.279
|
-0.060
|
0.137
|
-0.327
|
-0.060
|
0.206
|
Kawangire
|
-0.428
|
-0.158
|
0.112
|
-0.408
|
-0.112
|
0.247
|
-0.364
|
-0.126
|
0.091
|
-0.435
|
-0.126
|
0.184
|
Kibungo
|
-0.366
|
-0.047
|
0.271
|
-0.461
|
-0.120
|
0.302
|
-0.300
|
-0.037
|
0.184
|
-0.395
|
-0.037
|
0.320
|
Kamembe
|
-0.296
|
-0.166
|
-0.035
|
-0.263
|
-0.115
|
0.095
|
-0.447
|
-0.225
|
-0.025
|
-0.307
|
-0.225
|
-0.143
|
Table 4: Augmented Dickey-Fuller (ADF) stationary test applied to POT rainfall data series for the period of study of each station. Lag selection achieved according to the Akaike information
criteria (AIC)
.
Station 's name
|
Test's critical values
|
Test statistic
|
p-value
|
1%
|
5%
|
10%
|
Kanombe
|
-3.99
|
-3.43
|
-3.13
|
-6.7329
|
1.647e-15
|
Rubona
|
-3.99
|
-3.43
|
-3.13
|
-9.8293
|
< 2.2e-16
|
Gikongoro
|
-3.99
|
-3.43
|
-3.13
|
-6.2023
|
3.605e-14
|
Byimana
|
-3.99
|
-3.43
|
-3.13
|
-7.4032
|
1.071e-15
|
Rubengera
|
-3.99
|
-3.43
|
-3.13
|
-6.8743
|
6.905e-14
|
Gisenyi
|
-3.99
|
-3.43
|
-3.13
|
-9.0938
|
< 2.2e-16
|
Ruhengeri
|
-3.99
|
-3.43
|
-3.13
|
-7.7259
|
3.512e-16
|
Byumba
|
-3.99
|
-3.43
|
-3.13
|
-6.4693
|
4.574e-15
|
Nyagatare
|
-3.99
|
-3.43
|
-3.13
|
-9.0619
|
< 2.2e-16
|
Kawangire
|
-3.99
|
-3.43
|
-3.13
|
-7.3338
|
< 2.2e-16
|
Kibungo
|
-3.99
|
-3.43
|
-3.13
|
-7.3996
|
8.681e-14
|
Kamembe
|
-3.99
|
-3.43
|
-3.13
|
-10.0425
|
< 2.2e-16
|
Table 5: Kwiatkowski-Phillips-Schmidt-Shin (KPSS) stationary test applied to POT rainfall data series for the period of study of each station.
Station's name
|
Test's critical values
|
Test statistic
|
p-value
|
10%
|
5%
|
2%
|
1%
|
Kanombe
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0761
|
>0.1
|
Rubona
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0743
|
>0.1
|
Gikongoro
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0812
|
0.09586
|
Byimana
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0834
|
0.06304
|
Rubengera
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0752
|
>0.1
|
Gisenyi
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0506
|
>0.1
|
Ruhengeri
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0453
|
>0.1
|
Byumba
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0448
|
>0.1
|
Nyagatare
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0691
|
>0.1
|
Kawangire
|
0.119
|
0.146
|
0.176
|
0.216
|
0.109
|
0.07046
|
Kibungo
|
0.119
|
0.146
|
0.176
|
0.216
|
0.1051
|
0.0604
|
Kamembe
|
0.119
|
0.146
|
0.176
|
0.216
|
0.0634
|
0.06568
|
Table 6: Threshold rainfall (mm/day) calculated with different rules of thumb for the twelve stations of the study.
Station
|
90% quantile
|
95% quantile
|
99% quantile
|
|
.
|
Kanombe
|
9
|
15
|
32
|
35
|
27
|
Rubona
|
10
|
17
|
36
|
42
|
31
|
Gikongoro
|
12
|
19
|
36
|
39
|
29
|
Byimana
|
12
|
19
|
36
|
38
|
29
|
Rubengera
|
11
|
16
|
33
|
35
|
27
|
Gisenyi
|
10
|
15
|
32
|
36
|
26
|
Ruhengeri
|
12
|
17
|
30
|
31
|
24
|
Byumba
|
10
|
16
|
31
|
33
|
24
|
Kawangire
|
10
|
19
|
39
|
40
|
31
|
Nyagatare
|
7
|
13
|
28
|
30
|
23
|
Kibungo
|
10
|
18
|
39
|
42
|
31
|
Kamembe
|
12
|
18
|
34
|
37
|
28
|
Table 7: Parameter estimates with their 95% confidence intervals of the fitted GP distribution to PDS of daily rainfall at the twelve synoptic stations of Rwanda. LCI: low confidence interval; UCI: upper confidence interval.
Scale parameter
|
|
|
|
|
|
|
|
|
|
|
|
Station
|
MLE-LCI
|
MLE
|
MLE-UCI
|
BAYE-LCI
|
BAYE
|
BAYE-UCI
|
LME-LCI
|
LME
|
LME-UCI
|
GMLE-LCI
|
GMLE
|
GMLE-UCI
|
Kanombe
|
9.38
|
12.26
|
15.15
|
9.05
|
12.09
|
15.74
|
9.38
|
11.51
|
14.52
|
9.76
|
12.75
|
15.74
|
Rubona
|
12.89
|
15.81
|
18.74
|
12.52
|
15.50
|
18.78
|
12.30
|
15.08
|
18.39
|
12.15
|
15.08
|
18.01
|
Gikongoro
|
11.35
|
14.82
|
18.30
|
11.06
|
14.62
|
18.88
|
12.19
|
15.51
|
19.90
|
12.00
|
15.51
|
19.01
|
Byimana
|
13.78
|
18.14
|
22.50
|
13.81
|
18.02
|
22.95
|
13.80
|
17.53
|
22.64
|
13.21
|
17.53
|
21.85
|
Rubengera
|
9.98
|
13.84
|
17.69
|
9.75
|
13.61
|
18.29
|
9.95
|
13.01
|
16.96
|
11.02
|
14.78
|
18.54
|
Gisenyi
|
11.01
|
14.41
|
17.80
|
10.93
|
14.37
|
18.40
|
11.23
|
14.06
|
17.76
|
10.72
|
14.06
|
17.40
|
Ruhengeri
|
7.70
|
10.44
|
13.17
|
7.58
|
10.26
|
13.56
|
8.01
|
10.38
|
13.50
|
6.40
|
8.93
|
11.47
|
Byumba
|
8.41
|
11.35
|
14.28
|
8.37
|
11.20
|
14.78
|
8.14
|
10.97
|
14.07
|
6.74
|
9.41
|
12.08
|
Nyagatare
|
8.24
|
11.06
|
13.88
|
8.09
|
10.86
|
14.14
|
7.99
|
10.26
|
12.88
|
8.25
|
10.80
|
13.36
|
Kawangire
|
6.89
|
9.41
|
11.93
|
6.77
|
9.24
|
12.15
|
7.04
|
9.27
|
11.96
|
6.10
|
8.50
|
10.91
|
Kibungo
|
12.69
|
16.70
|
20.72
|
12.89
|
16.71
|
21.22
|
12.66
|
16.31
|
20.99
|
12.33
|
16.31
|
20.30
|
Kamembe
|
9.24
|
11.26
|
13.28
|
9.09
|
11.10
|
13.39
|
9.25
|
11.92
|
14.46
|
10.02
|
11.92
|
13.83
|
Shape parameter
|
|
|
|
|
|
|
|
|
|
|
|
Station
|
MLE-LCI
|
MLE
|
MLE-UCI
|
BAYE-LCI
|
BAYE
|
BAYE-UCI
|
LME-LCI
|
LME
|
LME-UCI
|
GMLE-LCI
|
GMLE
|
GMLE-UCI
|
Kanombe
|
-0.161
|
0.021
|
0.204
|
-0.134
|
0.060
|
0.299
|
-0.104
|
0.082
|
0.231
|
-0.179
|
0.000
|
0.179
|
Rubona
|
-0.279
|
-0.148
|
-0.017
|
-0.249
|
-0.118
|
0.048
|
-0.270
|
-0.097
|
0.048
|
-0.253
|
-0.097
|
0.060
|
Gikongoro
|
-0.279
|
-0.116
|
0.048
|
-0.258
|
-0.077
|
0.151
|
-0.391
|
-0.167
|
0.033
|
-0.304
|
-0.167
|
-0.031
|
Byimana
|
-0.457
|
-0.283
|
-0.109
|
-0.426
|
-0.253
|
-0.040
|
-0.500
|
-0.247
|
-0.064
|
-0.439
|
-0.247
|
-0.056
|
Rubengera
|
-0.183
|
0.039
|
0.260
|
-0.147
|
0.087
|
0.365
|
-0.141
|
0.095
|
0.268
|
-0.207
|
0.000
|
0.207
|
Gisenyi
|
-0.207
|
-0.030
|
0.146
|
-0.186
|
-0.005
|
0.209
|
-0.221
|
-0.006
|
0.168
|
-0.191
|
-0.006
|
0.180
|
Ruhengeri
|
-0.174
|
0.019
|
0.212
|
-0.128
|
0.066
|
0.311
|
-0.219
|
0.023
|
0.200
|
-0.084
|
0.214
|
0.512
|
Byumba
|
-0.225
|
-0.031
|
0.164
|
-0.190
|
0.012
|
0.261
|
-0.206
|
0.003
|
0.188
|
-0.110
|
0.199
|
0.509
|
Nyagatare
|
-0.217
|
-0.017
|
0.183
|
-0.187
|
0.027
|
0.279
|
-0.132
|
0.057
|
0.239
|
-0.194
|
0.000
|
0.194
|
Kawangire
|
-0.080
|
0.126
|
0.332
|
-0.028
|
0.174
|
0.440
|
-0.091
|
0.138
|
0.302
|
-0.017
|
0.255
|
0.527
|
Kibungo
|
-0.324
|
-0.151
|
0.021
|
-0.295
|
-0.125
|
0.083
|
-0.337
|
-0.126
|
0.063
|
-0.311
|
-0.126
|
0.059
|
Kamembe
|
-0.197
|
-0.090
|
0.018
|
-0.165
|
-0.058
|
0.089
|
-0.336
|
-0.152
|
0.036
|
-0.207
|
-0.152
|
-0.097
|
Table 8: Kolmogorov-Smirnov (K-S) goodness-of-fit test applied to the BM series of daily rainfall and the GEV distribution at each station with the four methods of parameterization. Underlined values correspond respectively to lowest KS statistics and highest p-values.
Station
|
Size
|
CV
|
GEV K-S TEST Statistics
|
p-value
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
36
|
0.221
|
0.139
|
0.111
|
0.139
|
0.139
|
0.885
|
0.982
|
0.885
|
0.885
|
Rubona
|
48
|
0.192
|
0.063
|
0.063
|
0.063
|
0.063
|
1.000
|
1.000
|
1.000
|
1.000
|
Gikongoro
|
26
|
0.259
|
0.115
|
0.115
|
0.115
|
0.115
|
0.997
|
0.997
|
0.997
|
0.997
|
Byimana
|
24
|
0.269
|
0.083
|
0.125
|
0.083
|
0.083
|
1.000
|
0.994
|
1.000
|
1.000
|
Rubengera
|
38
|
0.215
|
0.115
|
0.115
|
0.115
|
0.115
|
0.997
|
0.997
|
0.997
|
0.997
|
Gisenyi
|
44
|
0.201
|
0.088
|
0.088
|
0.088
|
0.088
|
1.000
|
1.000
|
1.000
|
1.000
|
Ruhengeri
|
29
|
0.246
|
0.069
|
0.103
|
0.069
|
0.138
|
1.000
|
0.998
|
1.000
|
0.951
|
Byumba
|
30
|
0.242
|
0.100
|
0.133
|
0.100
|
0.100
|
0.999
|
0.958
|
0.999
|
0.999
|
Nyagatare
|
34
|
0.227
|
0.088
|
0.059
|
0.059
|
0.059
|
1.000
|
1.000
|
1.000
|
1.000
|
Kawangire
|
33
|
0.231
|
0.061
|
0.091
|
0.061
|
0.061
|
1.000
|
0.999
|
1.000
|
1.000
|
Kibungo
|
28
|
0.250
|
0.107
|
0.179
|
0.071
|
0.071
|
0.998
|
0.773
|
1.000
|
1.000
|
Kamembe
|
43
|
0.203
|
0.070
|
0.116
|
0.070
|
0.070
|
1.000
|
0.938
|
1.000
|
1.000
|
Table 9: Cramer Von Mises (CVM) goodness-of-fit test applied to the BM series of daily rainfall and the GEV distribution at each station with the four methods of parameterization. Underlined values correspond respectively to lowest CVM statistics and highest p-values.
Station
|
Size
|
CV
|
GEV CVM TEST Statistics
|
p-value
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
36
|
0.218
|
0.198
|
0.151
|
0.201
|
0.201
|
0.728
|
0.813
|
0.701
|
0.706
|
Rubona
|
48
|
0.218
|
0.095
|
0.090
|
0.085
|
0.085
|
0.945
|
0.952
|
0.965
|
0.970
|
Gikongoro
|
26
|
0.218
|
0.092
|
0.151
|
0.098
|
0.098
|
0.942
|
0.836
|
0.942
|
0.947
|
Byimana
|
24
|
0.218
|
0.104
|
0.097
|
0.097
|
0.097
|
0.931
|
0.948
|
0.946
|
0.951
|
Rubengera
|
38
|
0.218
|
0.139
|
0.121
|
0.104
|
0.104
|
0.853
|
0.893
|
0.936
|
0.934
|
Gisenyi
|
44
|
0.218
|
0.099
|
0.061
|
0.102
|
0.088
|
0.946
|
0.990
|
0.935
|
0.966
|
Ruhengeri
|
29
|
0.218
|
0.087
|
0.101
|
0.077
|
0.106
|
0.959
|
0.946
|
0.978
|
0.924
|
Byumba
|
30
|
0.218
|
0.087
|
0.211
|
0.091
|
0.091
|
0.965
|
0.684
|
0.959
|
0.965
|
Nyagatare
|
34
|
0.218
|
0.092
|
0.061
|
0.074
|
0.074
|
0.950
|
0.994
|
0.983
|
0.979
|
Kawangire
|
33
|
0.218
|
0.071
|
0.093
|
0.067
|
0.067
|
0.987
|
0.962
|
0.989
|
0.988
|
Kibungo
|
28
|
0.218
|
0.097
|
0.531
|
0.077
|
0.077
|
0.945
|
0.252
|
0.977
|
0.975
|
Kamembe
|
43
|
0.218
|
0.082
|
0.220
|
0.069
|
0.069
|
0.970
|
0.658
|
0.988
|
0.989
|
Table 10: Kolmogorov-Smirnov (K-S) goodness-of-fit test applied to the PDS series of daily rainfall and the GP distribution at each station with the four methods of parameterization. Underlined values correspond respectively to lowest KS statistics and highest p-values.
Station
|
SIZE
|
CV
|
GPD K-S TEST Statistics
|
p-value
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
111
|
0.129
|
0.054
|
0.054
|
0.063
|
0.054
|
0.997
|
0.997
|
0.980
|
0.997
|
Rubona
|
113
|
0.128
|
0.088
|
0.088
|
0.097
|
0.097
|
0.768
|
0.768
|
0.658
|
0.658
|
Gikongoro
|
35
|
0.224
|
0.114
|
0.086
|
0.114
|
0.114
|
0.979
|
1.000
|
0.979
|
0.979
|
Byimana
|
106
|
0.132
|
0.111
|
0.083
|
0.083
|
0.083
|
0.982
|
1.000
|
1.000
|
1.000
|
Rubengera
|
111
|
0.129
|
0.135
|
0.108
|
0.135
|
0.108
|
0.894
|
0.985
|
0.894
|
0.985
|
Gisenyi
|
150
|
0.111
|
0.059
|
0.068
|
0.059
|
0.059
|
0.986
|
0.949
|
0.986
|
0.986
|
Ruhengeri
|
109
|
0.130
|
0.097
|
0.065
|
0.097
|
0.097
|
0.999
|
1.000
|
0.999
|
0.999
|
Byumba
|
103
|
0.134
|
0.118
|
0.118
|
0.118
|
0.059
|
0.976
|
0.976
|
0.976
|
1.000
|
Nyagatare
|
135
|
0.117
|
0.075
|
0.075
|
0.057
|
0.057
|
0.999
|
0.999
|
1.000
|
1.000
|
Kawangire
|
110
|
0.129
|
0.065
|
0.065
|
0.065
|
0.065
|
1.000
|
1.000
|
1.000
|
1.000
|
Kibungo
|
112
|
0.128
|
0.081
|
0.108
|
0.081
|
0.081
|
1.000
|
0.985
|
1.000
|
1.000
|
Kamembe
|
174
|
0.103
|
0.073
|
0.073
|
0.056
|
0.056
|
0.900
|
0.900
|
0.989
|
0.989
|
Table 11: Cramer Von Mises (CVM) goodness-of-fit test applied to the PDS series of daily rainfall and the GP distribution at each station with the four methods of parameterization. Underlined values correspond respectively to lowest CVM statistics and highest p-values.
Station
|
SIZE
|
CV
|
GPD CVM TEST Statistics
|
p-value
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
111
|
0.22
|
0.109
|
0.082
|
0.170
|
0.075
|
0.918
|
0.966
|
0.761
|
0.987
|
Rubona
|
113
|
0.22
|
0.379
|
0.387
|
0.468
|
0.468
|
0.425
|
0.392
|
0.303
|
0.306
|
Gikongoro
|
35
|
0.218
|
0.113
|
0.084
|
0.117
|
0.117
|
0.913
|
0.962
|
0.913
|
0.909
|
Byimana
|
106
|
0.22
|
0.111
|
0.077
|
0.093
|
0.093
|
0.925
|
0.979
|
0.957
|
0.948
|
Rubengera
|
111
|
0.22
|
0.202
|
0.135
|
0.208
|
0.188
|
0.721
|
0.852
|
0.677
|
0.739
|
Gisenyi
|
150
|
0.22
|
0.122
|
0.128
|
0.117
|
0.117
|
0.892
|
0.883
|
0.901
|
0.897
|
Ruhengeri
|
109
|
0.22
|
0.091
|
0.057
|
0.091
|
0.053
|
0.959
|
0.992
|
0.959
|
0.997
|
Byumba
|
103
|
0.22
|
0.220
|
0.137
|
0.209
|
0.092
|
0.638
|
0.865
|
0.667
|
0.955
|
Nyagatare
|
135
|
0.22
|
0.074
|
0.072
|
0.056
|
0.066
|
0.978
|
0.986
|
0.997
|
0.990
|
Kawangire
|
110
|
0.22
|
0.041
|
0.036
|
0.041
|
0.041
|
1.000
|
1.000
|
0.999
|
1.000
|
Kibungo
|
112
|
0.22
|
0.100
|
0.129
|
0.080
|
0.080
|
0.947
|
0.875
|
0.968
|
0.976
|
Kamembe
|
174
|
0.22
|
0.182
|
0.200
|
0.118
|
0.118
|
0.751
|
0.695
|
0.907
|
0.892
|
Table 12: Root mean square error (RMSE), mean absolute error (MAE) and R-Square between empirical quantiles and estimated quantiles using the four methods of parameterization for GEV distribution at each station. Underlined values correspond to lowest values, and italic values correspond to highest values of RMSE and MAE, the opposite is for R-Square.
|
RMSE
|
MAE
|
R-Square
|
Station
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
8.019
|
11.034
|
7.566
|
7.566
|
3.431
|
3.937
|
3.263
|
3.263
|
0.866
|
0.826
|
0.886
|
0.886
|
Rubona
|
2.936
|
3.790
|
3.654
|
3.654
|
1.683
|
1.860
|
1.723
|
1.723
|
0.966
|
0.957
|
0.955
|
0.955
|
Gikongoro
|
4.034
|
5.796
|
6.008
|
6.008
|
2.633
|
3.380
|
2.973
|
2.973
|
0.955
|
0.950
|
0.921
|
0.921
|
Byimana
|
2.498
|
2.795
|
2.842
|
2.842
|
2.120
|
2.197
|
2.206
|
2.206
|
0.982
|
0.978
|
0.974
|
0.974
|
Rubengera
|
5.960
|
9.110
|
7.067
|
7.067
|
3.610
|
4.226
|
3.709
|
3.709
|
0.911
|
0.884
|
0.898
|
0.898
|
Gisenyi
|
30.598
|
37.706
|
13.024
|
38.505
|
6.659
|
7.794
|
3.807
|
8.034
|
0.537
|
0.515
|
0.763
|
0.488
|
Ruhengeri
|
8.958
|
16.824
|
7.190
|
29.427
|
3.399
|
4.783
|
3.020
|
7.386
|
0.854
|
0.767
|
0.900
|
0.627
|
Byumba
|
3.251
|
5.201
|
4.131
|
4.131
|
1.933
|
3.533
|
2.043
|
2.043
|
0.959
|
0.957
|
0.946
|
0.946
|
Nyagatare
|
3.346
|
4.664
|
4.561
|
4.561
|
1.913
|
1.803
|
1.954
|
1.954
|
0.951
|
0.931
|
0.927
|
0.927
|
Kawangire
|
8.019
|
11.034
|
7.566
|
7.566
|
2.522
|
3.539
|
2.725
|
2.725
|
0.927
|
0.908
|
0.906
|
0.906
|
Kibungo
|
2.936
|
3.790
|
3.654
|
3.654
|
3.076
|
6.712
|
3.068
|
3.068
|
0.859
|
0.906
|
0.870
|
0.870
|
Kamembe
|
4.034
|
5.796
|
6.008
|
6.008
|
1.620
|
3.027
|
1.441
|
1.441
|
0.983
|
0.979
|
0.986
|
0.986
|
Table 13: Root mean square error (RMSE), mean absolute error (MAE) and R-Square between empirical quantiles and estimated quantiles using the four methods of parameterization for GP distribution at each station. Underlined values correspond to lowest values, and italic values correspond to highest values for RMSE and MAE, the opposite is for R-Square.
|
RMSE
|
MAE
|
R-Square
|
Station
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
MLE
|
BAYE
|
LME
|
GMLE
|
Kanombe
|
1.226
|
1.059
|
1.339
|
1.046
|
0.762
|
0.676
|
0.914
|
0.625
|
0.995
|
0.993
|
0.992
|
0.996
|
Rubona
|
1.722
|
1.628
|
1.775
|
1.775
|
1.340
|
1.288
|
1.431
|
1.431
|
0.996
|
0.995
|
0.993
|
0.993
|
Gikongoro
|
1.572
|
1.271
|
1.779
|
1.779
|
1.051
|
0.958
|
1.022
|
1.022
|
0.989
|
0.990
|
0.986
|
0.986
|
Byimana
|
1.206
|
1.084
|
1.145
|
1.145
|
0.862
|
0.784
|
0.804
|
0.804
|
0.992
|
0.992
|
0.992
|
0.992
|
Rubengera
|
3.665
|
2.921
|
3.544
|
3.318
|
2.465
|
2.019
|
2.444
|
2.323
|
0.982
|
0.978
|
0.978
|
0.984
|
Gisenyi
|
1.495
|
1.300
|
1.387
|
1.387
|
0.928
|
0.862
|
0.892
|
0.892
|
0.990
|
0.991
|
0.991
|
0.991
|
Ruhengeri
|
1.532
|
1.116
|
1.513
|
2.246
|
1.052
|
0.802
|
1.042
|
0.993
|
0.991
|
0.990
|
0.991
|
0.978
|
Byumba
|
1.507
|
1.140
|
1.470
|
1.581
|
0.960
|
0.771
|
0.988
|
1.097
|
0.994
|
0.994
|
0.994
|
0.982
|
Nyagatare
|
0.976
|
1.174
|
1.114
|
0.962
|
0.717
|
0.781
|
0.601
|
0.653
|
0.992
|
0.990
|
0.988
|
0.991
|
Kawangire
|
2.237
|
1.375
|
2.142
|
1.578
|
1.188
|
0.732
|
1.165
|
1.077
|
0.990
|
0.992
|
0.990
|
0.991
|
Kibungo
|
1.842
|
1.821
|
1.687
|
1.687
|
1.382
|
1.464
|
1.240
|
1.240
|
0.988
|
0.989
|
0.989
|
0.989
|
Kamembe
|
0.826
|
1.108
|
0.639
|
0.639
|
0.672
|
0.833
|
0.505
|
0.505
|
0.995
|
0.994
|
0.995
|
0.995
|
Table 14: Parameter estimates with their 95% confidence intervals of the selected parameterization method for the fitted GEV distribution to AMS of daily rainfall at the twelve synoptic stations of Rwanda. LCI: low confidence interval; EST: estimates; UCI: upper confidence interval.
GEV distribution
|
Station
|
Method
|
Location
|
Scale
|
Shape
|
|
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
Kanombe
|
LME
|
38.39
|
43.13
|
47.87
|
10.53
|
14.63
|
18.72
|
-0.333
|
-0.010
|
0.312
|
Rubona
|
MLE
|
46.28
|
50.16
|
54.04
|
10.72
|
13.53
|
16.33
|
-0.356
|
-0.145
|
0.066
|
Gikongoro
|
MLE
|
37.69
|
43.21
|
48.73
|
10.27
|
14.46
|
18.65
|
-0.388
|
-0.045
|
0.298
|
Byimana
|
MLE
|
42.87
|
47.64
|
52.41
|
9.59
|
13.06
|
16.53
|
-0.404
|
-0.128
|
0.148
|
Rubengera
|
MLE
|
49.46
|
54.73
|
59.99
|
10.86
|
14.64
|
18.42
|
-0.479
|
-0.224
|
0.031
|
Gisenyi
|
LME
|
43.56
|
47.25
|
51.29
|
8.41
|
11.48
|
14.83
|
-0.120
|
0.145
|
0.360
|
Ruhengeri
|
LME
|
44.07
|
47.63
|
51.77
|
8.07
|
11.21
|
15.31
|
-0.152
|
0.146
|
0.365
|
Byumba
|
MLE
|
39.87
|
44.74
|
49.62
|
10.76
|
14.07
|
17.37
|
-0.322
|
-0.162
|
-0.001
|
Nyagatare
|
BAYE
|
35.02
|
38.65
|
42.07
|
9.83
|
12.78
|
16.70
|
-0.354
|
-0.093
|
0.222
|
Kawangire
|
MLE
|
39.85
|
44.47
|
49.09
|
9.34
|
12.69
|
16.03
|
-0.428
|
-0.158
|
0.112
|
Kibungo
|
LME
|
34.75
|
38.99
|
43.27
|
8.34
|
11.58
|
14.81
|
-0.300
|
-0.037
|
0.184
|
Kamembe
|
LME
|
41.48
|
45.57
|
49.97
|
10.57
|
13.51
|
16.34
|
-0.447
|
-0.225
|
-0.025
|
Table 15: Parameter estimates with their 95% confidence intervals of the selected parameterization method for the fitted GP distribution to PDS of daily rainfall at the twelve synoptic stations of Rwanda. LCI: low confidence interval; EST: estimates; UCI: upper confidence interval.
GP distribution
|
Station
|
Method
|
Location
|
Scale
|
Shape
|
|
|
|
|
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
Kanombe
|
GMLE
|
-
|
-
|
-
|
9.76
|
12.75
|
15.74
|
-0.179
|
0.000
|
0.179
|
Rubona
|
BAYE
|
-
|
-
|
-
|
12.52
|
15.50
|
18.78
|
-0.249
|
-0.118
|
0.048
|
Gikongoro
|
BAYE
|
-
|
-
|
-
|
11.06
|
14.62
|
18.88
|
-0.258
|
-0.077
|
0.151
|
Byimana
|
BAYE
|
-
|
-
|
-
|
13.81
|
18.02
|
22.95
|
-0.426
|
-0.253
|
-0.040
|
Rubengera
|
BAYE
|
-
|
-
|
-
|
9.75
|
13.61
|
18.29
|
-0.147
|
0.087
|
0.365
|
Gisenyi
|
BAYE
|
-
|
-
|
-
|
10.93
|
14.37
|
18.40
|
-0.186
|
-0.005
|
0.209
|
Ruhengeri
|
BAYE
|
-
|
-
|
-
|
7.58
|
10.26
|
13.56
|
-0.128
|
0.066
|
0.311
|
Byumba
|
BAYE
|
-
|
-
|
-
|
8.37
|
11.20
|
14.78
|
-0.190
|
0.012
|
0.261
|
Nyagatare
|
GMLE
|
-
|
-
|
-
|
8.25
|
10.80
|
13.36
|
-0.194
|
0.000
|
0.194
|
Kawangire
|
BAYE
|
-
|
-
|
-
|
6.77
|
9.24
|
12.15
|
-0.028
|
0.174
|
0.440
|
Kibungo
|
GMLE
|
-
|
-
|
-
|
12.33
|
16.31
|
20.30
|
-0.311
|
-0.126
|
0.059
|
Kamembe
|
BAYE
|
-
|
-
|
-
|
9.09
|
11.10
|
13.39
|
-0.165
|
-0.058
|
0.089
|
Table 16: Return level estimates (mm/day) with their 95% confidence intervals corresponding to return periods (years) 10, 20, 50, 75, 100, 150, 200 for GEV distribution fit of AMS of daily rainfall data with the selected parameterization method for each station. LCI: low confidence interval; EST: estimates; UCI: upper confidence interval.
|
Method
|
10
|
20
|
50
|
75
|
100
|
150
|
200
|
Station
|
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
Kanombe
|
LME
|
66
|
76
|
86
|
72
|
86
|
102
|
80
|
99
|
124
|
83
|
105
|
136
|
85
|
109
|
146
|
87
|
115
|
161
|
88
|
119
|
171
|
Rubona
|
MLE
|
70
|
76
|
82
|
75
|
83
|
91
|
78
|
90
|
103
|
79
|
94
|
108
|
80
|
96
|
112
|
80
|
98
|
117
|
80
|
100
|
120
|
Gikongoro
|
MLE
|
74
|
81
|
88
|
78
|
86
|
95
|
80
|
93
|
105
|
81
|
95
|
109
|
81
|
97
|
112
|
81
|
99
|
116
|
81
|
100
|
119
|
Byimana
|
MLE
|
72
|
77
|
81
|
75
|
80
|
85
|
77
|
84
|
90
|
78
|
85
|
92
|
78
|
85
|
93
|
78
|
86
|
94
|
78
|
87
|
95
|
Rubengera
|
MLE
|
72
|
81
|
91
|
76
|
90
|
103
|
77
|
99
|
121
|
77
|
103
|
129
|
76
|
106
|
135
|
75
|
109
|
144
|
74
|
112
|
150
|
Gisenyi
|
LME
|
67
|
78
|
91
|
74
|
90
|
110
|
82
|
107
|
142
|
85
|
116
|
161
|
87
|
122
|
177
|
90
|
132
|
201
|
92
|
139
|
222
|
Ruhengeri
|
LME
|
58
|
67
|
79
|
64
|
77
|
93
|
70
|
89
|
116
|
72
|
94
|
129
|
73
|
98
|
139
|
76
|
104
|
153
|
77
|
108
|
164
|
Byumba
|
MLE
|
61
|
68
|
76
|
65
|
75
|
84
|
67
|
81
|
95
|
68
|
84
|
100
|
68
|
86
|
104
|
68
|
88
|
109
|
67
|
90
|
113
|
Nyagatare
|
BAYE
|
57
|
64
|
77
|
62
|
72
|
94
|
68
|
82
|
119
|
69
|
87
|
132
|
71
|
90
|
142
|
72
|
94
|
157
|
73
|
97
|
169
|
Kawangire
|
MLE
|
71
|
81
|
92
|
76
|
90
|
105
|
80
|
102
|
123
|
81
|
106
|
132
|
81
|
109
|
138
|
81
|
114
|
147
|
80
|
117
|
153
|
Kibungo
|
LME
|
73
|
84
|
95
|
78
|
94
|
108
|
84
|
106
|
131
|
86
|
112
|
142
|
87
|
116
|
150
|
88
|
121
|
162
|
89
|
125
|
171
|
Kamembe
|
LME
|
64
|
69
|
75
|
67
|
75
|
82
|
71
|
81
|
90
|
72
|
83
|
94
|
73
|
84
|
96
|
74
|
86
|
100
|
74
|
87
|
103
|
Table 17: Return levels estimates with their 95% confidence intervals corresponding to return periods (years) 10, 20, 50, 75, 100, 150, 200 for GP distribution fit of PDS of daily rainfall data with the selected parameterization method for each station. LCI: low confidence interval; EST: estimates; UCI: upper confidence interval.
GP distribution
|
Method
|
10
|
20
|
50
|
75
|
100
|
150
|
200
|
|
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
LCI
|
EST
|
UCI
|
Kanombe
|
GMLE
|
67
|
87
|
106
|
70
|
103
|
135
|
71
|
128
|
186
|
69
|
141
|
213
|
66
|
151
|
235
|
62
|
166
|
270
|
57
|
177
|
297
|
Rubona
|
BAYE
|
73
|
79
|
88
|
78
|
86
|
100
|
84
|
95
|
116
|
86
|
99
|
124
|
87
|
101
|
129
|
89
|
105
|
137
|
90
|
108
|
144
|
Gikongoro
|
BAYE
|
74
|
81
|
93
|
79
|
89
|
106
|
85
|
98
|
125
|
87
|
102
|
134
|
88
|
105
|
140
|
90
|
109
|
150
|
91
|
111
|
157
|
Byimana
|
BAYE
|
73
|
78
|
88
|
77
|
83
|
97
|
80
|
89
|
108
|
81
|
91
|
113
|
82
|
92
|
117
|
83
|
94
|
122
|
83
|
96
|
125
|
Rubengera
|
BAYE
|
77
|
90
|
116
|
84
|
104
|
148
|
93
|
125
|
204
|
96
|
135
|
236
|
98
|
143
|
259
|
101
|
154
|
298
|
103
|
163
|
331
|
Gisenyi
|
BAYE
|
74
|
84
|
100
|
81
|
94
|
120
|
89
|
109
|
150
|
92
|
115
|
165
|
94
|
120
|
177
|
96
|
127
|
195
|
98
|
132
|
210
|
Ruhengeri
|
BAYE
|
62
|
70
|
86
|
67
|
80
|
105
|
74
|
94
|
138
|
76
|
100
|
156
|
78
|
105
|
169
|
81
|
112
|
192
|
82
|
118
|
209
|
Byumba
|
BAYE
|
64
|
72
|
86
|
69
|
80
|
103
|
75
|
92
|
130
|
77
|
98
|
145
|
78
|
102
|
156
|
80
|
108
|
173
|
82
|
112
|
187
|
Nyagatare
|
GMLE
|
58
|
66
|
74
|
60
|
74
|
88
|
64
|
84
|
104
|
66
|
88
|
110
|
65
|
102
|
156
|
66
|
96
|
125
|
64
|
99
|
133
|
Kawangire
|
BAYE
|
73
|
85
|
109
|
80
|
99
|
139
|
89
|
121
|
195
|
93
|
133
|
227
|
95
|
142
|
253
|
99
|
156
|
296
|
102
|
167
|
334
|
Kibungo
|
GMLE
|
76
|
76
|
86
|
96
|
93
|
106
|
83
|
101
|
119
|
84
|
104
|
125
|
84
|
107
|
129
|
85
|
110
|
135
|
85
|
112
|
139
|
Kamembe
|
BAYE
|
66
|
71
|
80
|
71
|
78
|
91
|
77
|
87
|
106
|
79
|
90
|
113
|
81
|
93
|
118
|
83
|
96
|
126
|
84
|
99
|
131
|