Example_analisa Hidrologi.xlsx
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- Words: 2,611
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No 1 2 3 4 5 6 7 8 9 10
Tahun 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Sumber:
Januari Februari Maret
April
48
68
56
48
57
34
45
42
36 49 116 110 55 57 28 28
34 67 30 64 35 38 47 38
40 30 53 88 60 45 67 45
42 51 127 84 30 75 45 20
Mei
Juni
Juli
26
43
37 14 28 16 20 52 26 18
48 24 22 26
Agustus September Oktober
30 61
37 32 33
68 10
49
42 23
11 9
32
14 9 36
36 36 21
47 34 25
November Desember CH Max Rata-rata 68 44 45 36 72 54 72 64 54 37 54 38 28 53 67 36 39 68 127 58 49 60 110 56 11 64 64 39 52 32 75 44 65 40 67 38 58 48 58 33
S.Dev 12 13 10 18 33 32 19 15 16 13
No 1 2 3 4 5 6 7 8 9 10
Maximum Rerata Minimum Standar Deviasi
Curah Hujan Rata-Rata (mm) 44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
57.82 43.99 33.40 8.91
ANALISA FREKUENSI DENGAN DISTRIBUSI NORMAL No 1 2 3 4 5 6 7 8 9 10
Tahun
X
Xrangking
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
141.40 131.20
Jumlah Data Rerata Standar Deviasi
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
n `X Sx
Tr (tahun)
KTr
2 5 10 20 50 100
0.00 0.84 1.28 1.64 2.05 2.33
Probabilitas 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
Tr (tahun) 11.00 5.50 3.67 2.75 2.20 1.83 1.57 1.38 1.22 1.10
10.00
43.99 8.91
XTr (mm) Probabilitas 43.99 51.47 55.39 58.60 62.25 64.75
0.400 0.200 0.100 0.045 0.020 0.010
Xi 141.40 131.20 125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
P(Xi) 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
f(t) 10.93 9.79 9.09 8.64 6.47 6.32 5.86 4.38 4.04 4.04
P'(Xi) 0.0571 0.1292 0.1977 0.2514 0.5793 0.5987 0.6700 0.8485 0.8770 0.8770
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sumber :Bonnier, 1980 d
Interpolasi Tr 1
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI NORMAL
i 1 2 3 4 5 6 7 8 9 10
Nilai variabel reduksi Ga No
DP 0.03 0.05 0.08 0.11 0.12 0.05 0.03 0.12 0.06 0.03
2
3
4 Selisih Maksimum
DPmaks
0.12
Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
D kritis
0.41 Diterima
5
Nilai variabel reduksi Gauss KT Periode Ulang, T Peluang (tahun) 1.001 0.999 -3.05 1.005 0.995 -2.58 1.010 0.990 -2.33 1.050 0.950 -1.64 1.110 0.990 -1.28 1.250 0.800 -0.84 1.330 0.750 -0.67 1.430 0.600 -0.52 1.670 0.500 -0.25 2.000 0.400 0 2.500 0.300 0.25 3.330 0.250 0.52 4.000 0.250 0.67 5.000 0.200 0.84 10.000 0.100 1.28 20.000 0.050 1.64 50.000 0.020 2.05 100.000 0.010 2.33 200.000 0.005 2.58 500.000 0.002 2.88 1000.000 0.001 3.09 Sumber :Bonnier, 1980 dalam Suripin, 2003
Interpolasi Tr 20 0.09 10
1.64 0.92 1.28
6
2 0.64 1.67
0.00 -1.03 -0.25
10 0.18 5
1.28 0.42 0.84
7
1.67 0.73 1.43
-0.25 -1.31 -0.52
5 0.27 3.33
0.84 -0.07 0.52
8
1.43 1.38 1.33
-0.52 -0.60 -0.67
3.33 0.36 2.5
0.52 -0.44 0.25
9
1.25 0.91 1.11
-0.84 -1.91 -1.28
2.5 0.45 2
0.25 -0.77 0.00
10
1.11 0.00 1.05
-1.28 -7.94 -1.64
ANALISA FREKUENSI DENGAN DISTRIBUSI LOG NORMAL No 1 2 3 4 5 6 7 8 9 10
Tahun
X
Xrangking
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44 54 38 36 58 56 39 44 38 33
141.40 131.20
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
Jumlah Data Rerata Standar Deviasi
n Log`X Sx
Tr (tahun)
KTr
Log XTr
2 5 10 20 50 100
0.00 0.84 1.28 1.64 2.05 2.33
2.02 2.09 2.13 2.17 2.20 2.23
Log Xrangking Probabilitas 2.15 0.09 2.12 2.00 2.10 3.00 2.08 4.00 2.01 5.00 2.00 6.00 1.98 7.00 1.92 8.00 1.90 9.00 1.90 10.00
10.00
2.02 0.09 XTr (mm) Probabilitas 103.87 124.03 136.11 146.86 160.15 169.91
0.400 0.200 0.100 0.045 0.020 0.010
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI LOG NORMAL
i 1 2 3 4 5 6 7 8 9 10
Log Xi 2.15 2.12 2.10 2.08 2.01 2.00 1.98 1.92 1.90 1.90
P(Xi) 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
Selisih Maksimum Nilai Kritis 5% ditolak
f(t) 1.46 1.11 0.88 0.72 -0.10 -0.17 -0.36 -1.06 -1.24 -1.24
P'(Xi) 0.0722 0.1335 0.1894 0.2358 0.5398 0.5675 0.6406 0.8554 0.8925 0.8925 D maks Do
DP 0.019 0.048 0.083 0.128 0.085 0.022 0.004 0.128 0.074 0.017 0.13 0.41
Tr (tahun) 11.00 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
Nilai variabel reduksi Gauss No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sumber :Bonnier, 1980 dalam S
Korelasi hasil uji kecocokan
Diterima
ilai variabel reduksi Gauss Periode Ulang, T Peluang (tahun) 1.001 0.999 1.005 0.995 1.010 0.990 1.050 0.950 1.110 0.990 1.250 0.800 1.330 0.750 1.430 0.600 1.670 0.500 2.000 0.400 2.500 0.300 3.330 0.250 4.000 0.250 5.000 0.200 10.000 0.100 20.000 0.050 50.000 0.020 100.000 0.010 200.000 0.005 500.000 0.002 1000.000 0.001 umber :Bonnier, 1980 dalam Suripin, 2003
Interpolasi Tr 1
KT -3.05 -2.58 -2.33 -1.64 -1.28 -0.84 -0.67 -0.52 -0.25 0 0.25 0.52 0.67 0.84 1.28 1.64 2.05 2.33 2.58 2.88 3.09
20 12 10
1.64 1.35 1.28
6
2 0.64 1.67
0.00 -1.03 -0.25
2
10 0.18 5
1.28 0.42 0.84
7
1.67 0.73 1.43
-0.25 -1.31 -0.52
3
5 0.27 3.33
0.84 -0.07 0.52
8
1.43 1.38 1.33
-0.52 -0.60 -0.67
4
3.33
0.52
9
1.25
-0.84
5
0.36 2.5
-0.44 0.25
2.5 0.45 2
0.25 -0.77 0.00
10
0.91 1.11
-1.91 -1.28
1.11 0.00 1.05
-1.28 -7.94 -1.64
ANALISA FREKUENSI DENGAN DISTRIBUSI LOG PERSON III No
Tahun
X
Log X
1 2 3 4 5 6 7 8 9 10
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
35.70 39.29 53.57 33.40 56.33 38.00 37.67 44.44 57.82 43.67
1.55 1.59 1.73 1.52 1.75 1.58 1.58 1.65 1.76 1.64
(Log X - Log`X)2 0.00688 0.00171 0.00871 0.01251 0.01326 0.00312 0.00356 0.00015 0.01599 0.00002
n Log`X Sx Gs
1.6356 0.0856 0.429
Jumlah Data Rerata Standar Deviasi Koefisien Kemencengan
(Log X - Log`X)3 -0.00057 -0.00007 0.00081 -0.00140 0.00153 -0.00017 -0.00021 0.00000 0.00202 0.00000
10.00
Tr (tahun)
KTr
Log XTr
XTr (mm)
2 5 10 20 50 100
0.04 0.856 1.26 1.67 1.93 2.16
1.64 1.71 1.74 1.78 1.80 1.82
43.54 51.15 55.39 60.10 63.18 66.12
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI LOG PERSON III
i
Log Xi
P(Xi)
f(t)
P'(Xi)
DP
1 2 3 4 5 6
1.55 1.59 1.73 1.52 1.75 1.58
0.09 0.18 0.27 0.36 0.45 0.55
-0.97 -0.48 1.09 -1.31 1.35 -0.65
-0.014 -0.087 0.127 -0.341 0.320 0.712
0.11 0.27 0.15 0.70 0.13 0.17
7 8 9 10
1.58 1.65 1.76 1.64
0.64 0.73 0.82 0.91
-0.70 0.14 1.48 0.05
Selisih Maksimum Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
0.732 0.719 0.632 0.726
0.10 0.01 0.19 0.18
D maks
0.70 0.41 Ditolak
Do
Interval kejadian (Recurrence interval), tahun (periode ulang) 1.0101 1.25 2 5 10 25 50 Koef G Persentase peluang terlamapaui (Percent chance of being exceeded) 99 80 50 20 10 4 2 3.0 -0.667 -0.636 -0.396 0.420 1.180 2.278 3.152 2.8 -0.714 -0.666 -0.384 0.460 1.210 2.275 3.114 2.6 -0.769 -0.696 -0.368 0.499 1.238 2.267 3.071 2.4 -0.832 -0.725 -0.351 0.537 1.262 2.256 3.023 2.2 -0.905 -0.752 -0.330 -0.574 1.284 2.240 2.970 2 -0.990 -0.777 -0.307 0.609 1.302 2.219 2.192 1.8 -1.087 -0.799 -0.282 0.643 1.318 2.193 2.848 1.6 -1.197 -0.817 -0.254 0.675 1.329 2.163 2.780 1.4 -1.318 -0.832 -0.225 0.705 1.337 2.128 2.706 1.2 -1.449 -0.844 -0.195 0.732 1.340 2.087 2.626 1 -1.588 -0.852 -0.164 0.758 1.340 2.043 2.542 0.8 -1.733 -0.856 -0.132 0.780 1.336 1.993 2.453 0.6 -1.88 -0.857 -0.099 0.800 1.328 1.939 2.359 0.4 -2.029 -0.855 -0.066 0.816 1.317 1.880 2.261 0.2 -2.178 -0.850 -0.033 0.830 1.301 1.818 2.159 0.43 -2.495 -0.833 0.038 0.856 1.260 1.674 1.927 0.0 -2.326 -0.842 0.000 0.842 1.282 1.751 2.051 -0.2 -2.472 -0.830 0.033 0.850 1.258 1.680 1.945 -0.4 -2.615 -0.816 0.066 0.855 1.231 1.606 1.834 -0.6 -2.755 -0.800 0.099 0.857 1.200 1.528 1.720 -0.8 -2.891 -0.780 0.132 0.856 1.166 1.448 1.606 -1.0 -3.022 -0.758 0.164 0.852 1.128 1.366 1.492 -1.2 -2.149 -0.732 0.195 0.844 1.086 1.282 1.379 -1.4 -2.271 -0.705 0.225 0.832 1.041 1.198 1.270 -1.6 -2.388 -0.675 0.254 0.817 0.994 1.116 1.166 -1.8 -3.499 -0.643 0.282 0.799 0.945 1.035 1.069 -2 -3.605 -0.609 0.307 0.777 0.895 0.959 0.980 -2.2 -3.705 -0.574 0.33 0.752 0.844 0.888 0.900 -2.4 -3.80 -0.537 0.351 0.725 0.795 0.823 0.830 -2.6 -3.889 -0.490 0.368 0.696 0.747 0.764 0.768 -2.8 -3.973 -0.469 0.384 0.666 0.702 0.712 0.714 -3.0 -7.051 -0.420 0.396 0.636 0.660 0.666 0.666
Interpolasi 1
2
100 1 4.051 3.973 2.889 3.800 3.705 3.605 3.499 3.388 3.271 3.149 3.022 2.891 2.755 2.615 2.472 2.159 2.326 2.178 2.029 1.880 1.733 1.588 1.449 1.318 1.197 1.087 0.990 0.905 0.832 0.769 0.714 0.667
25 0.09 10
#REF! #REF! #REF!
6
2 0.64 1.25
#REF! #REF! #REF!
10 0.18
#REF! #REF!
7
2 0.73
#REF! #REF!
5
#REF!
1.25
#REF!
3
5 0.27 2
#REF! #REF! #REF!
8
2 0.82 1.25
#REF! #REF! #REF!
4
5 0.36 2
#REF! #REF! #REF!
9
1.25 0.91 1.0101
#REF! #REF! #REF!
5
5 0.45 2
#REF! #REF! #REF!
10
1.25 0.00 1.0101
#REF! #REF! #REF!
ANALISA FREKUENSI DENGAN DISTRIBUSI GUMBEL No
Tahun
X
Xrangking
Probabilitas
Tr (tahun)
1 2 3 4 5 6 7 8 9 10
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
141.40 131.20
0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
11.00 5.50 3.67 2.75 2.20 1.83 1.57 1.38 1.22 1.10
Jumlah Data Rerata Standar Deviasi Reduced mean Reduced standard deviation
YTr
Tr (tahun) 2 5 10 25 50 100
0.3668 1.5004 2.2510 3.1993 3.9028 4.5012
3x= x=
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
n `X Sx Yn Sn
43.99 8.91 0.4952 0.9496
KTr
XTr (mm)
-0.14 1.06 1.85 2.85 3.59 4.22
42.78 53.42 60.46 69.36 75.96 81.58
10.00
1.13 4.5344 4.5012 -0.0332 -0.011067
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI GUMBEL
i 1 2 3
Xi 141.40 131.20 125.00
P(Xi) 0.09 0.18 0.27
f(t) Ln(Ln T/T-1) 10.93 13.44362 9.79 11.97549 9.09 11.08310
Ln T/T-1 689429.4337 158814.3864 65062.2486
4 5 6 7 8 9 10
121.00 101.60 100.30 96.20 83.00 80.00 80.00
0.36 0.45 0.55 0.64 0.73 0.82 0.91
8.64 6.47 6.32 5.86 4.38 4.04 4.04
10.50736 7.71504 7.52793 6.93780 5.03787 4.60606 4.60606
36583.8882 2241.8147 1859.2465 1030.4971 154.1407 100.0894 100.0894
Selisih Maksimum Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
0.521428 3.03014
Reduced N
0
1
2
10
0.4952
0.4996
0.5035
20 30 40 50 60 70 80 90 100
0.5236 0.5362 0.5436 0.5485 0.5521 0.5548 0.5569 0.5586 0.5600
0.5252 0.5371 0.5442 0.5489 0.5524 0.5550 0.5570 0.5587 0.5602
0.5268 0.5380 0.5448 0.5493 0.5527 0.5552 0.5572 0.5589 0.5603
Reduce Standa N 10 20 30 40 50
0 0.9496 1.0628 1.1124 1.1413 1.1607
1 0.9697 1.0696 1.1159 1.1436 1.1623
2 0.9833 1.0754 1.1193 1.1458 1.1638
60 70 80 90 100
1.1747 1.1854 1.1938 1.2007 1.2065
1.1759 1.1863 1.1945 1.2013 1.2069
1.1770 1.1873 1.1953 1.2020 1.2073
Reduced variate. Ytr sebagai Periode ulang Reduced variate Tr (tahun) Ytr 2 0.3668 5 1.5004 10 2.2510 20 2.9709 25 3.1993 50 3.9028 75 4.3117
T/T-1 #NUM! #NUM! #NUM!
T #NUM! #NUM! #NUM!
P'(Xi) #NUM! #NUM! #NUM!
DP #NUM! #NUM! #NUM!
Interpolasi 1
25 0.09 10
ih Maksimum Kritis 5% ditolak lasi hasil uji kecocokan
#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! ### 1.00000 ### 1.00000 ### 1.00000
#NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00
#NUM! #NUM! #NUM! #NUM! 0.73 0.82 0.91
D maks
#NUM! 0.41 #NUM!
Do
2
10 0.18 5
3
5 0.27 2
4
5 0.36 2
5
5 0.45 2
3
Reduced Mean. Yn. 4 5
6
7
8
9
0.5070
0.5100
0.5128
0.5157
0.5181
0.5202
0.5220
0.5283 0.5288 0.5453 0.5497 0.5530 0.5555 0.5574 0.5591 0.5604
0.5296 0.8396 0.5458 0.5501 0.5533 0.5557 0.5576 0.5592 0.5606
0.5309 0.5403 0.5463 0.5504 0.5535 0.5559 0.5578 0.5593 0.5607
0.5320 0.5410 0.5468 0.5508 0.5538 0.5561 0.5580 0.5595 0.5608
0.5332 0.5418 0.5473 0.5511 0.5540 0.5563 0.5581 0.5596 0.5609
0.5343 0.5424 0.5477 0.5515 0.5543 0.5565 0.5583 0.5598 0.5610
0.5353 0.5436 0.5481 0.5518 0.5545 0.5567 0.5585 0.5599 0.5611
6 1.0316 1.0961 1.1313 1.1538 1.1696
7 1.0411 1.1004 1.1339 1.1557 1.1708
8 1.0493 1.1047 1.1363 1.1574 1.1721
9 1.0565 1.1080 1.1388 1.1590 1.1734
1.1814 1.1906 1.1980 1.2044 1.2087
1.1824 1.1915 1.1987 1.2049 1.2090
1.1834 1.1923 1.1994 1.2055 1.2093
1.1844 1.1930 1.2001 1.2060 1.2096
Reduce Standard Deviation. Sn 3 4 5 0.9971 1.0095 1.0206 1.0811 1.0864 1.0915 1.1226 1.1255 1.1285 1.1480 1.1499 1.1519 1.1658 1.1667 1.1681 1.1782 1.1881 1.1959 1.2026 1.2077
1.1793 1.1890 1.1967 1.2032 1.2081
1.1803 1.1898 1.1973 1.2038 1.2084
duced variate. Ytr sebagai fungsi periode ulang Reduced variate Periode ulang Reduced variate Ytr Tr (tahun) Ytr 0.3668 100 4.5012 1.5004 200 5.2969 2.2510 250 5.5206 2.9709 500 6.2149 3.1993 1000 6.9087 3.9028 5000 8.5188 4.3117 10000 9.2121
3.199 1.625 2.251
6
2 0.55 0
0.367 0.100 0.000
2.251 0.777 1.500
7
2 0.64 0
0.367 0.117 0.000
1.500 -0.286 0.367
8
2 0.73 0
0.367 0.133 0.000
1.500 -0.252 0.367
9
2 0.82 0
0.367 0.150 0.000
1.500 -0.217 0.367
10
2 0.91 0
0.367 0.167 0.000
11
2 0.00 0
0.367 0.000 0.000
RESUME ANALISA FREKUENSI CURAH HUJAN 1 HARIAN
Periode Ulang 2 5 10 25 50 100
Analisa Frekuensi Curah Hujan Rencana (mm) Log Normal Log Pearson III Normal Gumbel 43.99 103.87 43.54 42.78 51.47 124.03 51.15 53.42 55.39 136.11 55.39 60.46 58.60 146.86 60.10 69.36 62.25 160.15 63.18 75.96 64.75 169.91 66.12 81.58
RESUME SMIRNOV-KOLMOGOROV Nilai kritis Smirnov-Kolmogorov (a)
No.
n 0.2
0.1
0.05
0.01
5
0.45
0.51
0.56
0.67
10
0.32
0.37
0.41
0.49
15
0.27
0.30
0.34
0.40
20
0.23
0.26
0.29
0.36
25
0.21
0.24
0.27
0.32
30
0.19
0.22
0.24
0.29
35
0.18
0.20
0.23
0.27
40
0.17
0.19
0.21
0.25
45
0.16
0.18
0.20
0.24
50
0.15
0.17
0.19
0.23
1.07
1.22
1.36
1.63
n0.5
n0.5
n0.5
n0.5
n>50
1 2 3 4 5 6 7 8 9 10
Selisih Maksimal Uji Kecocokan Korelasi
Selisih Untuk Nilai Kritis 5 % Log Normal Normal
0.03 0.05 0.08 0.11 0.12 0.05 0.03 0.12 0.06 0.03
0.019 0.048 0.083 0.128 0.085 0.022 0.004 0.128 0.074 0.017
0.12
0.13
0.41 Diterima Diterima
lisih Untuk Nilai Kritis 5 % Log Pearson III
Gumbel
0.11 0.27 0.15 0.70 0.13 0.17 0.10 0.01 0.19 0.18
#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.73 0.82 0.91
0.70
#NUM!
0.41 Ditolak
#NUM!
Hujan harian maximum metode Normal Periode Ulang T 2 5 Hujan (mm) 43.99 51.47
25 146.86
50 62.25
100 64.75
300 250
5 93.53 58.92 44.97 37.12 21.62 17.84 11.24 8.58 7.08 6.10
10 100.66 63.41 48.39 39.95 23.26 19.20 12.10 9.23 7.62 6.57
25 266.87 168.12 128.30 105.91 61.68 50.92 32.07 24.48 20.21 17.41
50 113.12 71.26 54.38 44.89 26.15 21.58 13.60 10.38 8.57 7.38
100 117.66 74.12 56.56 46.69 27.19 22.45 14.14 10.79 8.91 7.68
Intensitas Hujan (mm/jam)
Hasil Hitungan IDF Mononobe Durasi (menit) 2 5 79.93 10 50.35 15 38.43 20 31.72 45 18.47 60 15.25 120 9.61 180 7.33 240 6.05 300 5.22
10 55.39
200 150 100 50 0
0 20 40 60 80 100120
Durasi H
Intensitas Hujan (mm/jam)
300 250 200 I2 I5 I10 I25 I50 I100
150 100 50 0 0 20 40 60 80 100120140160180200220240260280300 Durasi Hujan (menit)
Tahun 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Sumber:
Januari Februari Maret
April
48
68
56
48
57
34
45
42
36 49 116 110 55 57 28 28
34 67 30 64 35 38 47 38
40 30 53 88 60 45 67 45
42 51 127 84 30 75 45 20
Mei
Juni
Juli
26
43
37 14 28 16 20 52 26 18
48 24 22 26
Agustus September Oktober
30 61
37 32 33
68 10
49
42 23
11 9
32
14 9 36
36 36 21
47 34 25
November Desember CH Max Rata-rata 68 44 45 36 72 54 72 64 54 37 54 38 28 53 67 36 39 68 127 58 49 60 110 56 11 64 64 39 52 32 75 44 65 40 67 38 58 48 58 33
S.Dev 12 13 10 18 33 32 19 15 16 13
No 1 2 3 4 5 6 7 8 9 10
Maximum Rerata Minimum Standar Deviasi
Curah Hujan Rata-Rata (mm) 44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
57.82 43.99 33.40 8.91
ANALISA FREKUENSI DENGAN DISTRIBUSI NORMAL No 1 2 3 4 5 6 7 8 9 10
Tahun
X
Xrangking
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
141.40 131.20
Jumlah Data Rerata Standar Deviasi
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
n `X Sx
Tr (tahun)
KTr
2 5 10 20 50 100
0.00 0.84 1.28 1.64 2.05 2.33
Probabilitas 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
Tr (tahun) 11.00 5.50 3.67 2.75 2.20 1.83 1.57 1.38 1.22 1.10
10.00
43.99 8.91
XTr (mm) Probabilitas 43.99 51.47 55.39 58.60 62.25 64.75
0.400 0.200 0.100 0.045 0.020 0.010
Xi 141.40 131.20 125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
P(Xi) 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
f(t) 10.93 9.79 9.09 8.64 6.47 6.32 5.86 4.38 4.04 4.04
P'(Xi) 0.0571 0.1292 0.1977 0.2514 0.5793 0.5987 0.6700 0.8485 0.8770 0.8770
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sumber :Bonnier, 1980 d
Interpolasi Tr 1
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI NORMAL
i 1 2 3 4 5 6 7 8 9 10
Nilai variabel reduksi Ga No
DP 0.03 0.05 0.08 0.11 0.12 0.05 0.03 0.12 0.06 0.03
2
3
4 Selisih Maksimum
DPmaks
0.12
Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
D kritis
0.41 Diterima
5
Nilai variabel reduksi Gauss KT Periode Ulang, T Peluang (tahun) 1.001 0.999 -3.05 1.005 0.995 -2.58 1.010 0.990 -2.33 1.050 0.950 -1.64 1.110 0.990 -1.28 1.250 0.800 -0.84 1.330 0.750 -0.67 1.430 0.600 -0.52 1.670 0.500 -0.25 2.000 0.400 0 2.500 0.300 0.25 3.330 0.250 0.52 4.000 0.250 0.67 5.000 0.200 0.84 10.000 0.100 1.28 20.000 0.050 1.64 50.000 0.020 2.05 100.000 0.010 2.33 200.000 0.005 2.58 500.000 0.002 2.88 1000.000 0.001 3.09 Sumber :Bonnier, 1980 dalam Suripin, 2003
Interpolasi Tr 20 0.09 10
1.64 0.92 1.28
6
2 0.64 1.67
0.00 -1.03 -0.25
10 0.18 5
1.28 0.42 0.84
7
1.67 0.73 1.43
-0.25 -1.31 -0.52
5 0.27 3.33
0.84 -0.07 0.52
8
1.43 1.38 1.33
-0.52 -0.60 -0.67
3.33 0.36 2.5
0.52 -0.44 0.25
9
1.25 0.91 1.11
-0.84 -1.91 -1.28
2.5 0.45 2
0.25 -0.77 0.00
10
1.11 0.00 1.05
-1.28 -7.94 -1.64
ANALISA FREKUENSI DENGAN DISTRIBUSI LOG NORMAL No 1 2 3 4 5 6 7 8 9 10
Tahun
X
Xrangking
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44 54 38 36 58 56 39 44 38 33
141.40 131.20
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
Jumlah Data Rerata Standar Deviasi
n Log`X Sx
Tr (tahun)
KTr
Log XTr
2 5 10 20 50 100
0.00 0.84 1.28 1.64 2.05 2.33
2.02 2.09 2.13 2.17 2.20 2.23
Log Xrangking Probabilitas 2.15 0.09 2.12 2.00 2.10 3.00 2.08 4.00 2.01 5.00 2.00 6.00 1.98 7.00 1.92 8.00 1.90 9.00 1.90 10.00
10.00
2.02 0.09 XTr (mm) Probabilitas 103.87 124.03 136.11 146.86 160.15 169.91
0.400 0.200 0.100 0.045 0.020 0.010
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI LOG NORMAL
i 1 2 3 4 5 6 7 8 9 10
Log Xi 2.15 2.12 2.10 2.08 2.01 2.00 1.98 1.92 1.90 1.90
P(Xi) 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
Selisih Maksimum Nilai Kritis 5% ditolak
f(t) 1.46 1.11 0.88 0.72 -0.10 -0.17 -0.36 -1.06 -1.24 -1.24
P'(Xi) 0.0722 0.1335 0.1894 0.2358 0.5398 0.5675 0.6406 0.8554 0.8925 0.8925 D maks Do
DP 0.019 0.048 0.083 0.128 0.085 0.022 0.004 0.128 0.074 0.017 0.13 0.41
Tr (tahun) 11.00 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
Nilai variabel reduksi Gauss No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sumber :Bonnier, 1980 dalam S
Korelasi hasil uji kecocokan
Diterima
ilai variabel reduksi Gauss Periode Ulang, T Peluang (tahun) 1.001 0.999 1.005 0.995 1.010 0.990 1.050 0.950 1.110 0.990 1.250 0.800 1.330 0.750 1.430 0.600 1.670 0.500 2.000 0.400 2.500 0.300 3.330 0.250 4.000 0.250 5.000 0.200 10.000 0.100 20.000 0.050 50.000 0.020 100.000 0.010 200.000 0.005 500.000 0.002 1000.000 0.001 umber :Bonnier, 1980 dalam Suripin, 2003
Interpolasi Tr 1
KT -3.05 -2.58 -2.33 -1.64 -1.28 -0.84 -0.67 -0.52 -0.25 0 0.25 0.52 0.67 0.84 1.28 1.64 2.05 2.33 2.58 2.88 3.09
20 12 10
1.64 1.35 1.28
6
2 0.64 1.67
0.00 -1.03 -0.25
2
10 0.18 5
1.28 0.42 0.84
7
1.67 0.73 1.43
-0.25 -1.31 -0.52
3
5 0.27 3.33
0.84 -0.07 0.52
8
1.43 1.38 1.33
-0.52 -0.60 -0.67
4
3.33
0.52
9
1.25
-0.84
5
0.36 2.5
-0.44 0.25
2.5 0.45 2
0.25 -0.77 0.00
10
0.91 1.11
-1.91 -1.28
1.11 0.00 1.05
-1.28 -7.94 -1.64
ANALISA FREKUENSI DENGAN DISTRIBUSI LOG PERSON III No
Tahun
X
Log X
1 2 3 4 5 6 7 8 9 10
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
35.70 39.29 53.57 33.40 56.33 38.00 37.67 44.44 57.82 43.67
1.55 1.59 1.73 1.52 1.75 1.58 1.58 1.65 1.76 1.64
(Log X - Log`X)2 0.00688 0.00171 0.00871 0.01251 0.01326 0.00312 0.00356 0.00015 0.01599 0.00002
n Log`X Sx Gs
1.6356 0.0856 0.429
Jumlah Data Rerata Standar Deviasi Koefisien Kemencengan
(Log X - Log`X)3 -0.00057 -0.00007 0.00081 -0.00140 0.00153 -0.00017 -0.00021 0.00000 0.00202 0.00000
10.00
Tr (tahun)
KTr
Log XTr
XTr (mm)
2 5 10 20 50 100
0.04 0.856 1.26 1.67 1.93 2.16
1.64 1.71 1.74 1.78 1.80 1.82
43.54 51.15 55.39 60.10 63.18 66.12
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI LOG PERSON III
i
Log Xi
P(Xi)
f(t)
P'(Xi)
DP
1 2 3 4 5 6
1.55 1.59 1.73 1.52 1.75 1.58
0.09 0.18 0.27 0.36 0.45 0.55
-0.97 -0.48 1.09 -1.31 1.35 -0.65
-0.014 -0.087 0.127 -0.341 0.320 0.712
0.11 0.27 0.15 0.70 0.13 0.17
7 8 9 10
1.58 1.65 1.76 1.64
0.64 0.73 0.82 0.91
-0.70 0.14 1.48 0.05
Selisih Maksimum Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
0.732 0.719 0.632 0.726
0.10 0.01 0.19 0.18
D maks
0.70 0.41 Ditolak
Do
Interval kejadian (Recurrence interval), tahun (periode ulang) 1.0101 1.25 2 5 10 25 50 Koef G Persentase peluang terlamapaui (Percent chance of being exceeded) 99 80 50 20 10 4 2 3.0 -0.667 -0.636 -0.396 0.420 1.180 2.278 3.152 2.8 -0.714 -0.666 -0.384 0.460 1.210 2.275 3.114 2.6 -0.769 -0.696 -0.368 0.499 1.238 2.267 3.071 2.4 -0.832 -0.725 -0.351 0.537 1.262 2.256 3.023 2.2 -0.905 -0.752 -0.330 -0.574 1.284 2.240 2.970 2 -0.990 -0.777 -0.307 0.609 1.302 2.219 2.192 1.8 -1.087 -0.799 -0.282 0.643 1.318 2.193 2.848 1.6 -1.197 -0.817 -0.254 0.675 1.329 2.163 2.780 1.4 -1.318 -0.832 -0.225 0.705 1.337 2.128 2.706 1.2 -1.449 -0.844 -0.195 0.732 1.340 2.087 2.626 1 -1.588 -0.852 -0.164 0.758 1.340 2.043 2.542 0.8 -1.733 -0.856 -0.132 0.780 1.336 1.993 2.453 0.6 -1.88 -0.857 -0.099 0.800 1.328 1.939 2.359 0.4 -2.029 -0.855 -0.066 0.816 1.317 1.880 2.261 0.2 -2.178 -0.850 -0.033 0.830 1.301 1.818 2.159 0.43 -2.495 -0.833 0.038 0.856 1.260 1.674 1.927 0.0 -2.326 -0.842 0.000 0.842 1.282 1.751 2.051 -0.2 -2.472 -0.830 0.033 0.850 1.258 1.680 1.945 -0.4 -2.615 -0.816 0.066 0.855 1.231 1.606 1.834 -0.6 -2.755 -0.800 0.099 0.857 1.200 1.528 1.720 -0.8 -2.891 -0.780 0.132 0.856 1.166 1.448 1.606 -1.0 -3.022 -0.758 0.164 0.852 1.128 1.366 1.492 -1.2 -2.149 -0.732 0.195 0.844 1.086 1.282 1.379 -1.4 -2.271 -0.705 0.225 0.832 1.041 1.198 1.270 -1.6 -2.388 -0.675 0.254 0.817 0.994 1.116 1.166 -1.8 -3.499 -0.643 0.282 0.799 0.945 1.035 1.069 -2 -3.605 -0.609 0.307 0.777 0.895 0.959 0.980 -2.2 -3.705 -0.574 0.33 0.752 0.844 0.888 0.900 -2.4 -3.80 -0.537 0.351 0.725 0.795 0.823 0.830 -2.6 -3.889 -0.490 0.368 0.696 0.747 0.764 0.768 -2.8 -3.973 -0.469 0.384 0.666 0.702 0.712 0.714 -3.0 -7.051 -0.420 0.396 0.636 0.660 0.666 0.666
Interpolasi 1
2
100 1 4.051 3.973 2.889 3.800 3.705 3.605 3.499 3.388 3.271 3.149 3.022 2.891 2.755 2.615 2.472 2.159 2.326 2.178 2.029 1.880 1.733 1.588 1.449 1.318 1.197 1.087 0.990 0.905 0.832 0.769 0.714 0.667
25 0.09 10
#REF! #REF! #REF!
6
2 0.64 1.25
#REF! #REF! #REF!
10 0.18
#REF! #REF!
7
2 0.73
#REF! #REF!
5
#REF!
1.25
#REF!
3
5 0.27 2
#REF! #REF! #REF!
8
2 0.82 1.25
#REF! #REF! #REF!
4
5 0.36 2
#REF! #REF! #REF!
9
1.25 0.91 1.0101
#REF! #REF! #REF!
5
5 0.45 2
#REF! #REF! #REF!
10
1.25 0.00 1.0101
#REF! #REF! #REF!
ANALISA FREKUENSI DENGAN DISTRIBUSI GUMBEL No
Tahun
X
Xrangking
Probabilitas
Tr (tahun)
1 2 3 4 5 6 7 8 9 10
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
44.44 53.57 38.00 35.70 57.82 56.33 39.29 43.67 37.67 33.40
141.40 131.20
0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
11.00 5.50 3.67 2.75 2.20 1.83 1.57 1.38 1.22 1.10
Jumlah Data Rerata Standar Deviasi Reduced mean Reduced standard deviation
YTr
Tr (tahun) 2 5 10 25 50 100
0.3668 1.5004 2.2510 3.1993 3.9028 4.5012
3x= x=
125.00 121.00 101.60 100.30 96.20 83.00 80.00 80.00
n `X Sx Yn Sn
43.99 8.91 0.4952 0.9496
KTr
XTr (mm)
-0.14 1.06 1.85 2.85 3.59 4.22
42.78 53.42 60.46 69.36 75.96 81.58
10.00
1.13 4.5344 4.5012 -0.0332 -0.011067
SMIRNOV-KOLMOGOROV UNTUK DISTRIBUSI GUMBEL
i 1 2 3
Xi 141.40 131.20 125.00
P(Xi) 0.09 0.18 0.27
f(t) Ln(Ln T/T-1) 10.93 13.44362 9.79 11.97549 9.09 11.08310
Ln T/T-1 689429.4337 158814.3864 65062.2486
4 5 6 7 8 9 10
121.00 101.60 100.30 96.20 83.00 80.00 80.00
0.36 0.45 0.55 0.64 0.73 0.82 0.91
8.64 6.47 6.32 5.86 4.38 4.04 4.04
10.50736 7.71504 7.52793 6.93780 5.03787 4.60606 4.60606
36583.8882 2241.8147 1859.2465 1030.4971 154.1407 100.0894 100.0894
Selisih Maksimum Nilai Kritis 5% ditolak Korelasi hasil uji kecocokan
0.521428 3.03014
Reduced N
0
1
2
10
0.4952
0.4996
0.5035
20 30 40 50 60 70 80 90 100
0.5236 0.5362 0.5436 0.5485 0.5521 0.5548 0.5569 0.5586 0.5600
0.5252 0.5371 0.5442 0.5489 0.5524 0.5550 0.5570 0.5587 0.5602
0.5268 0.5380 0.5448 0.5493 0.5527 0.5552 0.5572 0.5589 0.5603
Reduce Standa N 10 20 30 40 50
0 0.9496 1.0628 1.1124 1.1413 1.1607
1 0.9697 1.0696 1.1159 1.1436 1.1623
2 0.9833 1.0754 1.1193 1.1458 1.1638
60 70 80 90 100
1.1747 1.1854 1.1938 1.2007 1.2065
1.1759 1.1863 1.1945 1.2013 1.2069
1.1770 1.1873 1.1953 1.2020 1.2073
Reduced variate. Ytr sebagai Periode ulang Reduced variate Tr (tahun) Ytr 2 0.3668 5 1.5004 10 2.2510 20 2.9709 25 3.1993 50 3.9028 75 4.3117
T/T-1 #NUM! #NUM! #NUM!
T #NUM! #NUM! #NUM!
P'(Xi) #NUM! #NUM! #NUM!
DP #NUM! #NUM! #NUM!
Interpolasi 1
25 0.09 10
ih Maksimum Kritis 5% ditolak lasi hasil uji kecocokan
#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! ### 1.00000 ### 1.00000 ### 1.00000
#NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00
#NUM! #NUM! #NUM! #NUM! 0.73 0.82 0.91
D maks
#NUM! 0.41 #NUM!
Do
2
10 0.18 5
3
5 0.27 2
4
5 0.36 2
5
5 0.45 2
3
Reduced Mean. Yn. 4 5
6
7
8
9
0.5070
0.5100
0.5128
0.5157
0.5181
0.5202
0.5220
0.5283 0.5288 0.5453 0.5497 0.5530 0.5555 0.5574 0.5591 0.5604
0.5296 0.8396 0.5458 0.5501 0.5533 0.5557 0.5576 0.5592 0.5606
0.5309 0.5403 0.5463 0.5504 0.5535 0.5559 0.5578 0.5593 0.5607
0.5320 0.5410 0.5468 0.5508 0.5538 0.5561 0.5580 0.5595 0.5608
0.5332 0.5418 0.5473 0.5511 0.5540 0.5563 0.5581 0.5596 0.5609
0.5343 0.5424 0.5477 0.5515 0.5543 0.5565 0.5583 0.5598 0.5610
0.5353 0.5436 0.5481 0.5518 0.5545 0.5567 0.5585 0.5599 0.5611
6 1.0316 1.0961 1.1313 1.1538 1.1696
7 1.0411 1.1004 1.1339 1.1557 1.1708
8 1.0493 1.1047 1.1363 1.1574 1.1721
9 1.0565 1.1080 1.1388 1.1590 1.1734
1.1814 1.1906 1.1980 1.2044 1.2087
1.1824 1.1915 1.1987 1.2049 1.2090
1.1834 1.1923 1.1994 1.2055 1.2093
1.1844 1.1930 1.2001 1.2060 1.2096
Reduce Standard Deviation. Sn 3 4 5 0.9971 1.0095 1.0206 1.0811 1.0864 1.0915 1.1226 1.1255 1.1285 1.1480 1.1499 1.1519 1.1658 1.1667 1.1681 1.1782 1.1881 1.1959 1.2026 1.2077
1.1793 1.1890 1.1967 1.2032 1.2081
1.1803 1.1898 1.1973 1.2038 1.2084
duced variate. Ytr sebagai fungsi periode ulang Reduced variate Periode ulang Reduced variate Ytr Tr (tahun) Ytr 0.3668 100 4.5012 1.5004 200 5.2969 2.2510 250 5.5206 2.9709 500 6.2149 3.1993 1000 6.9087 3.9028 5000 8.5188 4.3117 10000 9.2121
3.199 1.625 2.251
6
2 0.55 0
0.367 0.100 0.000
2.251 0.777 1.500
7
2 0.64 0
0.367 0.117 0.000
1.500 -0.286 0.367
8
2 0.73 0
0.367 0.133 0.000
1.500 -0.252 0.367
9
2 0.82 0
0.367 0.150 0.000
1.500 -0.217 0.367
10
2 0.91 0
0.367 0.167 0.000
11
2 0.00 0
0.367 0.000 0.000
RESUME ANALISA FREKUENSI CURAH HUJAN 1 HARIAN
Periode Ulang 2 5 10 25 50 100
Analisa Frekuensi Curah Hujan Rencana (mm) Log Normal Log Pearson III Normal Gumbel 43.99 103.87 43.54 42.78 51.47 124.03 51.15 53.42 55.39 136.11 55.39 60.46 58.60 146.86 60.10 69.36 62.25 160.15 63.18 75.96 64.75 169.91 66.12 81.58
RESUME SMIRNOV-KOLMOGOROV Nilai kritis Smirnov-Kolmogorov (a)
No.
n 0.2
0.1
0.05
0.01
5
0.45
0.51
0.56
0.67
10
0.32
0.37
0.41
0.49
15
0.27
0.30
0.34
0.40
20
0.23
0.26
0.29
0.36
25
0.21
0.24
0.27
0.32
30
0.19
0.22
0.24
0.29
35
0.18
0.20
0.23
0.27
40
0.17
0.19
0.21
0.25
45
0.16
0.18
0.20
0.24
50
0.15
0.17
0.19
0.23
1.07
1.22
1.36
1.63
n0.5
n0.5
n0.5
n0.5
n>50
1 2 3 4 5 6 7 8 9 10
Selisih Maksimal Uji Kecocokan Korelasi
Selisih Untuk Nilai Kritis 5 % Log Normal Normal
0.03 0.05 0.08 0.11 0.12 0.05 0.03 0.12 0.06 0.03
0.019 0.048 0.083 0.128 0.085 0.022 0.004 0.128 0.074 0.017
0.12
0.13
0.41 Diterima Diterima
lisih Untuk Nilai Kritis 5 % Log Pearson III
Gumbel
0.11 0.27 0.15 0.70 0.13 0.17 0.10 0.01 0.19 0.18
#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.73 0.82 0.91
0.70
#NUM!
0.41 Ditolak
#NUM!
Hujan harian maximum metode Normal Periode Ulang T 2 5 Hujan (mm) 43.99 51.47
25 146.86
50 62.25
100 64.75
300 250
5 93.53 58.92 44.97 37.12 21.62 17.84 11.24 8.58 7.08 6.10
10 100.66 63.41 48.39 39.95 23.26 19.20 12.10 9.23 7.62 6.57
25 266.87 168.12 128.30 105.91 61.68 50.92 32.07 24.48 20.21 17.41
50 113.12 71.26 54.38 44.89 26.15 21.58 13.60 10.38 8.57 7.38
100 117.66 74.12 56.56 46.69 27.19 22.45 14.14 10.79 8.91 7.68
Intensitas Hujan (mm/jam)
Hasil Hitungan IDF Mononobe Durasi (menit) 2 5 79.93 10 50.35 15 38.43 20 31.72 45 18.47 60 15.25 120 9.61 180 7.33 240 6.05 300 5.22
10 55.39
200 150 100 50 0
0 20 40 60 80 100120
Durasi H
Intensitas Hujan (mm/jam)
300 250 200 I2 I5 I10 I25 I50 I100
150 100 50 0 0 20 40 60 80 100120140160180200220240260280300 Durasi Hujan (menit)
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