254 100 1892 233 0146 0340 2232 170585 200 1892 258

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155.254 100 1.892 2.33 0.146 0.340 2.232 170.585 200 1.892 2.58 0.146 0.377 2.268 185.548 1000 1.892 3.09 0.146 0.451 2.343 220.267 Contoh : Tabel 4.6.d Simpangan Metode Log Normal No Tahun X X’ Log X Variabel Reduksi (r) Peluang (P) Simpangan (∆) 1 1999 57.25 170.00 2.2304 9.09 14.87 5.78 2 2000 65.00 102.00 2.0086 18.18 24.35 6.16 3 2001 65.00 92.50 1.9661 27.27 37.40 10.12 4 2002 170.00 81.00 1.9085 36.36 48.85 12.48 5 2003 73.00 73.00 1.8633 45.45 59.44 13.98 6 2004 92.50 65.00 1.8129 54.55 74.34 19.80 7 2005 62.50 65.00 1.8129 63.64 74.34 10.71 8 2006 81.00 62.50 1.7959 72.73 74.93 2.20 9 2007 57.50 57.50 1.7597 81.82 86.23 4.42 10 2008 102.00 57.25 1.7578 90.91 86.36 4.55 Maks 19.80 ̅
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50 c) Metode distribusi Gumbel Langkah perhitungan distribusi Gumbel adalah sebagai berikut di bawah ini. Tabel 4.7.a Perhitungan Metode Gumbel No 1 2 3 4 5 6 7 8 9 10 R S X 57 65 65 170 73 93 63 81 58 102 83 34.163 ̅ Tabel 4.7.b Tabel Hasil Hujan Rancangan Metode Gumbel T (Tahun) t Yt Q (m 3 /dt) 2 2 0.367 76.960 5 1.250 1.500 107.166 10 1.111 2.250 127.165 25 1.042 3.199 152.434 50 1.020 3.902 171.180 100 1.010 4.600 189.788 200 1.005 5.296 208.327 1000 1.001 6.907 251.273 Contoh : ( ) ( )
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51 Tabel IV.7.c Simpangan Metode Gumbel No Tahun X X’ Variabel Reduksi (r) Peluang (P) Simpangan (∆) 1 1999 57.25 170.00 9.09 2.66 6.43 2 2000 65.00 102.00 18.18 24.67 6.49 3 2001 65.00 92.50 27.27 37.21 9.94 4 2002 170.00 81.00 36.36 48.48 12.12 5 2003 73.00 73.00 45.45 58.70 13.24 6 2004 92.50 65.00 54.55 68.98 14.43 7 2005 62.50 65.00 63.64 68.98 5.34 8 2006 81.00 62.50 72.73 69.92 2.81 9 2007 57.50 57.50 81.82 79.44 2.37 10 2008 102.00 57.25 90.91 79.49 11.42 Maks 14.43 d) Metode distribusi Log Pearson Type III Langkah perhitungan distribusi Log Pearson Type III adalah sebagai berikut di bawah ini. Pada tabel IV.8 di bawah ini akan diperoleh harga rata- rata hitung dari log x sebagai berikut : Contoh perhitungan Log Person type III ̅
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52 Tabel 4.8.a Perhitungan Metode Log Pearson Type III No X Log X 1 57 1.76 -0.13 0.02 0.00 2 65 1.81 -0.08 0.01 0.00 3 65 1.81 -0.08 0.01 0.00 4 170 2.23 0.34 0.11 0.04 5 73 1.86 -0.03 0.00 0.00 6 93 1.97 0.07 0.01 0.00 7 63 1.80 -0.10 0.01 0.00 8 81 1.91 0.02 0.00 0.00 9 58 1.76 -0.13 0.02 0.00 10 102 2.01 0.12 0.01 0.00 18.92 0.00 0.19 0.03 - Menghitung standar deviasi ∑( ̅ ) - Menghitung Koefisien Asimetris ∑( ̅ ) ( )( ) ( )( ) Maka harga - harga G (Koefisien Pearson) di dapat dari tabel untuk harga Cs = 0.2, sehingga diperoleh nilai nilai G untuk rencana periode ulang tertentu seperti tertera pada tabel di bawah ini : ( 𝑋 𝑋 ̅ ) ( 𝑋 𝑋 ̅ ) 𝑋 𝑋 ̅
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53 Tabel IV.8.b Harga harga G ( Koefisien Pearson) untuk Periode Ulang Tertentu T 2 5 10 25 50 100 200 1000 G -0.033 0.830 1.301 1.818 2.152 2.472 2.763 3.380 Table V.8.c Tabel Hasil Hujan Rancangan Metode Log Pearson Type III T (Tahun) G S G.S Q (m 3 /dt ) 2 1.892 -0.033 0.15 -0.005 1.887 77.054 5 1.892 0.830 0.15 0.121 2.013 103.002 10 1.892 1.301 0.15 0.190 2.082 120.682 25 1.892 1.818 0.15 0.266 2.157 143.601 50 1.892 2.159 0.15 0.315 2.207 161.051 100 1.892 2.472 0.15 0.361 2.253 178.930 200 1.892 2.763 0.15 0.404 2.295 197.327 1000 1.892 3.380 0.15 0.494 2.385 242.833 Contoh perhitungan : ̅ Tabel 4.8.d Simpangan Metode Log Pearson III No Tahun X X’ Log X Variabel Reduksi (r) Peluang (P) Simpangan (∆) 1 1999 57.25 170.00 2.2304 9.09 2.32 7.65 1.44 2 2000 65.00 102.00 2.0086 18.18 0.80 18.10 0.09 3 2001 65.00 92.50 1.9661 27.27 0.51 36.33 9.06 4 2002 170.00 81.00 1.9085 36.36 0.12 78.39 42.03 5 2003 73.00 73.00 1.8633 45.45 -0.19 92.22 46.77 6 2004 92.50 65.00 1.8129 54.55 -0.54 107.66 53.11 7 2005 62.50 65.00 1.8129 63.64 -0.54 113.41 49.77 8 2006 81.00 62.50 1.7959 72.73 -0.66 119.14 46.42 9 2007 57.50 57.50 1.7597 81.82 -0.90 131.34 49.52 10 2008 102.00 57.25 1.7578 90.91 -0.92 131.98 41.07 Maks 53.11 𝑋 ̅ 𝑋 𝑇
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54 Tabel 4.9 Rangkuman Analisis Frekuensi Curah Hujan Rencana Perioda Ulang (Tahun) t Distribusi Probabilitas Normal Log Normal 2 Parameter Gumbel Log Pearson III 2 0.0000 82.58 77.91 76.96 71.73 5 0.8400 111.27 103.35 107.42 100.27 10 1.2800 126.30 119.83 127.12 125.64 20 1.6400 138.60 135.26 146.29 151.56 25 1.7083 140.94 138.40 150.42 166.46 50 2.0500 152.61 155.25 171.06 203.26 100 2.3300 162.17 170.59 189.70 246.98 200 2.5800 170.72 185.55 208.07 299.22 1000 3.0900 188.14 220.27 250.94 352.94 Penympangan Max 15.58 19.80 14.43 53.11 kitis (Sig. Level 5%) 39.6 39.6 39.6 39.6 Berdasarkan hasil perhitungan pada table diatas maka distribusi Gumbel yang dipilih karena mengalami deviasi yang paling kecil.
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