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RINGKASAN KULIAH

HIDROLOGI

S1 TL -FTSL,ITB

Minggu 1 Sem 1 09/10

Oleh: Dr. Ir.Arwin ,MS

FTSL-ITB

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Kota

Kab.

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Variabel Acak/stokastik

Variabel Acak/stokastik

INPUT

OUTPUT

PROSES

Curah Hujan

(P)

Debit

(Q)

Kualitas Ruang DAS

Tata Guna Lahan

Topografi

Morfologi

Sifat Batuan

Sistem Dalam DAS Model Fisik Hidrologi

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Pola Distribusi Hujan

DAS

P

Q

Siklus Hidrologi

Konsep Dasar Hidrologi

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Water Supply General

KAWASAN PELAYANAN

(Kepuasan Konsumen )

Kualitas Air

Kwantitas Air

Kontinuitas air

Harga jual kompetitif

Laju Kebutuhan Air

RESPON TEKNOLOGI PENGOLAHAN AIR

Respon Teknologi Air Bersih

Biaya Operasi

SUMBER AIR BAKU

Fresh water (Gol A/B)

Randow variabel

Keandalan Sumber Air( Kuantitas & Kualitas Air )

11.bin

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Besaran Input

Variabel Acak/Stokastik

Besaran Out put

Variabel Acak/Stokastik

Sifat tanah, batuan,

Morfologi, topografi

Tutupan lahan

PROSES

INPUT

Curah hujan)

Muka air tanah

Debit sungai

OUTPUT

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Ketersediaan Data Curah Hujan di DAS Jeneberang- waduk Bili-Bili SULSEL

Sheet1358123c1001249.18602752678400333.709928028667.4198560561298.5235878321813.6599097269d9.32260.8729052419200333.709928028631.103731776812.4443189949594.7452360504l3003192.32986928572678400315.551865888515.1363218949297.4372389504188.71099416k0.0010334114.7021593752592000315.551865888297.3079971108.26467776986.3524798228k 1060.001297577.7754562678400257.5681609474208.3137813504207.985671216634.384052592000257.568160947489.1234576858.8131250068726.035742678400148.6539985569.734126016814.385662678400148.6539985538.530551744931.03638752592000104.156890675280.44631641047.617742678400104.1568906752127.53935481611107.939025259200044.5617288279.777952812216.1869669231267840044.5617288579.0351722068134.867063008234.867063008319.265275872419.265275872540.2231582640.2231582763.769677408863.7696774089139.888976410139.888976411289.517586103412289.5175861034HEADA205.00650566991JanFebMaretAprilMeiJuniJuliAgustSeptOktNovDesJanB10.0235154083885871Input667.419856056631.103731776515.1363218949297.3079971208.313781350489.123457669.73412601638.53055174480.4463164127.539354816279.7779528579.0351722068667.419856056B2(0.00000604874644313077)NP91098754446789B30.0000000022361343794144TAIL103EFF0.98Sheet7DiskritDiskritisasi periode pengoperasian tiga bulananInputDiskritisasiNP(hm3)200100402010BervariasiTetap1813.661800.001800.001800.001800.0018109.336.25594.75600.00600.00600.00600.006006.676.25188.712002002002001904.006.25986.35100010009609809807.006.253583.473600.003600.003560.003580.003580.00k =0.001013Diskritisasi periode pengoperasian dua bulananInputDiskritisasiNP(hm3)200100402010BervariasiTetap1298.52120013001280130012909.506.25812.448008008408208108.506.25297.444003002803003006.006.25108.262001001201001104.006.25207.992002002002002105.006.25858.818009008408608607.506.253583.4736003600356035803580Diskritisasi periode pengoperasian satu bulananInputDiskritisasiNP(hm3)200100402010BervariasiTetap667.426007006806606709.006.25631.1060060064064063010.006.25515.146005005205205109.006.25297.314003002803002908.006.25208.312002002002002107.006.2589.1201008080905.006.2569.7301008080704.006.2538.53004040404.006.2580.4501008080804.006.25127.542001001201201306.006.25279.784003002802802807.006.25579.046006005605805808.006.253583.4736003600356035803580Diskritisasi periode pengoperasian setengah bulananInputDiskritisasiNP(hm3)200100402010BervariasiTetap333.714003003203403309.006.25333.714004003203403309.006.25315.5540030032032032010.006.25315.5540030032032032010.006.25257.572003002402602609.006.25257.572003002402602609.006.25148.652002001601601608.006.25148.652002001601401608.006.25104.16200100801001007.006.25104.162001001201001007.006.2544.56004040405.006.2544.56004040405.006.2534.87004040304.006.2534.87004040304.006.2519.2700020204.006.2519.27004020204.006.2540.22004040404.006.2540.22004040404.006.2563.7701008060606.006.2563.7701008060606.006.25139.892001001201401407.006.25139.892002001201401407.006.25289.522003002802802908.006.25289.522003003202802908.006.25358336003600356035803580K5005010015020025030034635040065.0070.1475.5581.2287.1593.3599.82106.00106.55113.54Debit NormalPenentuan harga energi listrik tanpa adanya waduk periode pengoperasian tiga bulananInputTurbinTurbinVolumeStockHPVNPGain(hm3)(m)(m)(GWh)BervariasiTetapBervariasiTetap1813.66895.87353.0188.90214.3355.8947.269.336.25440.89295.35594.75895.87353.0186.34193.2953.3345.096.676.25300.75281.81188.71895.87353.0173.3079.5240.2934.064.006.25136.25212.90986.35895.87353.0165.000.0031.9927.057.006.25189.33169.04895.871067.22959.10k =0.001297Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian dua bulananInputTurbinTurbinVolumeStockHPVNPGain(hm3)(m)(m)(GWh)BervariasiTetapBervariasiTetap1298.52368.13235.3482.36159.7649.3427.819.506.25264.22173.83812.44368.13235.3490.32225.7957.3032.308.506.25274.56201.88297.44368.13235.3486.34193.2953.3330.066.006.25180.36187.87108.26368.13235.3477.71119.3344.6925.194.006.25100.77157.46207.99368.13235.3469.2241.1936.2020.415.006.25102.04127.55858.81368.13235.3465.000.0031.9918.037.506.25135.23112.69368.12517823331057.19961.29Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian satu bulananSumber : Proyek Pengembangan PSDA JeneberangInputTurbinTurbinVolumeStockHPVNPGain(hm3)(m)(m)(GWh)BervariasiTetapBervariasiTetap667.42667.42117.6771.0258.3038.0110.719.006.2596.4166.95631.10631.10117.6782.67162.4749.6614.0010.006.25139.9687.47515.14515.14117.6790.03223.4757.0116.079.006.25144.63100.43297.31297.31117.6792.09239.9759.0716.658.006.25133.20104.06208.31208.31117.6792.60244.0359.5816.797.006.25117.55104.9689.1289.1289.1289.40218.3956.3912.045.006.2560.1975.2469.7369.7369.7385.60187.0952.598.784.006.2535.1454.9038.5338.5338.5381.65153.6848.644.494.006.2517.9628.0680.4580.4580.4577.74119.5744.738.624.006.2534.4853.87127.54127.54117.6773.9985.8540.9811.556.006.2569.2972.18279.78279.78117.6771.1259.2438.1110.747.006.2575.1867.13579.04579.04117.6770.7255.4437.7010.638.006.2585.0166.42266.69969905571008.99881.67Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian setengah bulananInputTurbinTurbinVolumeStockHPVNPGain(hm3)(m)(m)(GWh)BervariasiTetapBervariasiTetap333.71214.7058.8467.6425.9634.624.889.006.2543.9130.50333.71214.7058.8470.3551.9237.335.269.006.2547.3532.88315.55214.7058.8476.20105.8443.186.0910.006.2560.8538.03315.55214.7058.8482.36159.7649.346.9510.006.2562.5843.46257.57214.7058.8485.59187.0452.577.419.006.2566.6846.31257.57214.7058.8488.90214.3355.897.889.006.2563.0149.22148.65214.7058.8489.61220.0656.597.988.006.2563.8049.85148.65214.7058.8490.32225.7957.308.088.006.2556.5350.47104.16214.7058.8490.24225.1657.228.067.006.2556.4550.40104.16214.7058.8490.16224.5357.158.057.006.2540.2750.3344.56214.7058.8488.24208.9155.227.785.006.2538.9148.6444.56214.7058.8486.34193.2953.337.515.006.2530.0646.9734.87214.7058.8484.19175.3251.177.214.006.2528.8545.0734.87214.7058.8482.07157.3449.066.914.006.2527.6543.2119.27214.7058.8479.87138.3446.866.604.006.2526.4141.2719.27214.7058.8477.71119.3344.696.304.006.2525.1939.3640.22214.7058.8475.4999.4242.475.984.006.2523.9437.4140.22214.7058.8473.3079.5240.295.684.006.2534.0635.4863.77214.7058.8471.2460.3538.225.396.006.2532.3233.6763.77214.7058.8469.2241.1936.205.106.006.2535.7131.89139.89214.7058.8467.5525.0834.534.877.006.2534.0730.42139.89214.7058.8465.918.9732.894.647.006.2537.0828.97289.52214.7058.8465.454.4932.444.578.006.2536.5728.57289.52214.7058.8465.000.0031.994.518.006.2536.0628.17214.70328125171008.32960.54V106.0Debit NormalPenentuan harga energi listrik tanpa adanya waduk periode pengoperasian tiga bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap1813.661813.66353.01106.0071.5360.489.336.25564.30378.02594.75594.75353.01106.0071.5360.486.676.25403.42378.02188.71188.71188.71106.0072.5432.794.006.25131.15204.93986.35986.35353.01106.0071.5360.487.006.25423.38378.02k =0.0012971522.251338.97Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian dua bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap1298.521298.52235.34106.0071.5340.329.506.25383.06252.01812.44812.44235.34106.0071.5340.328.506.25342.73252.01297.44297.44235.34106.0071.5340.326.006.25241.93252.01108.26108.26108.26106.0072.6518.844.006.2575.36117.75207.99207.99207.99106.0071.8335.785.006.25178.92223.65858.81858.81235.34106.0071.5340.327.506.25302.41252.011524.421349.45Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian satu bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap667.42667.42117.67106.0071.5320.169.006.25181.45126.01631.10631.10117.67106.0071.5320.1610.006.25201.61126.01515.14515.14117.67106.0071.5320.169.006.25181.45126.01297.31297.31117.67106.0071.5320.168.006.25161.29126.01208.31208.31117.67106.0071.5320.167.006.25141.13126.0189.1289.1289.12106.0072.1215.405.006.2576.9896.2269.7369.7369.73106.0072.4412.104.006.2548.4075.6338.5338.5338.53106.0072.816.724.006.2526.8842.0080.4580.4580.45106.0072.2713.934.006.2555.7187.04127.54127.54117.67106.0071.5320.166.006.25120.96126.01279.78279.78117.67106.0071.5320.167.006.25141.13126.01579.04579.04117.67106.0071.5320.168.006.25161.29126.011498.261308.93Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian setengah bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap333.71333.7158.84106.0071.5310.089.006.2590.7263.00333.71333.7158.84106.0071.5310.089.006.2590.7263.00315.55315.5558.84106.0071.5310.0810.006.25100.8063.00315.55315.5558.84106.0071.5310.0810.006.2590.7263.00257.57257.5758.84106.0071.5310.089.006.2590.7263.00257.57257.5758.84106.0071.5310.089.006.2580.6463.00148.65148.6558.84106.0071.5310.088.006.2580.6463.00148.65148.6558.84106.0071.5310.088.006.2570.5663.00104.16104.1658.84106.0071.5310.087.006.2570.5663.00104.16104.1658.84106.0071.5310.087.006.2550.4063.0044.5644.5644.56106.0072.127.705.006.2538.4948.1144.5644.5644.56106.0072.127.705.006.2530.7948.1134.8734.8734.87106.0072.446.054.006.2524.2037.8134.8734.8734.87106.0072.446.054.006.2524.2037.8119.2719.2719.27106.0072.813.364.006.2513.4421.0019.2719.2719.27106.0072.813.364.006.2513.4421.0040.2240.2240.22106.0072.276.964.006.2527.8543.5240.2240.2240.22106.0072.276.964.006.2541.7843.5263.7763.7758.84106.0071.5310.086.006.2560.4863.0063.7763.7758.84106.0071.5310.086.006.2570.5663.00139.89139.8958.84106.0071.5310.087.006.2570.5663.00139.89139.8958.84106.0071.5310.087.006.2580.6463.00289.52289.5258.84106.0071.5310.088.006.2580.6463.00289.52289.5258.84106.0071.5310.088.006.2580.6463.001474.251308.93V65Debit NormalPenentuan harga energi listrik tanpa adanya waduk periode pengoperasian tiga bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap1813.661813.66353.0165.0030.5325.819.336.25240.85161.34594.75594.75353.0165.0030.5325.816.676.25172.18161.34188.71188.71188.7165.0031.5414.264.006.2557.0289.10986.35986.35353.0165.0030.5325.817.006.25180.70161.34k =0.001013650.76573.12Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian dua bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap1298.521298.52235.3465.0030.5317.219.506.25163.49107.56812.44812.44235.3465.0030.5317.218.506.25146.28107.56297.44297.44235.3465.0030.5317.216.006.25103.26107.56108.26108.26108.2665.0031.658.214.006.2532.8351.30207.99207.99207.9965.0030.8315.365.006.2576.8095.99858.81858.81235.3465.0030.5317.217.506.25129.07107.56651.73577.54Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian satu bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap667.42667.42117.6765.0030.538.609.006.2577.4453.78631.10631.10117.6765.0030.538.6010.006.2586.0553.78515.14515.14117.6765.0030.538.609.006.2577.4453.78297.31297.31117.6765.0030.538.608.006.2568.8453.78208.31208.31117.6765.0030.538.607.006.2560.2353.7889.1289.1289.1265.0031.126.645.006.2533.2241.5269.7369.7369.7365.0031.445.254.006.2521.0132.8238.5338.5338.5365.0031.812.944.006.2511.7418.3580.4580.4580.4565.0031.276.034.006.2524.1037.66127.54127.54117.6765.0030.538.606.006.2551.6353.78279.78279.78117.6765.0030.538.607.006.2560.2353.78579.04579.04117.6765.0030.538.608.006.2568.8453.78640.79560.60Penentuan harga energi listrik tanpa adanya waduk periode pengoperasian setengah bulananInputTurbinTurbinVolumeHPVNPGain(m)(m)(GWh)BervariasiTetapBervariasiTetap333.71333.7158.8465.0030.534.309.006.2538.7226.89333.71333.7158.8465.0030.534.309.006.2538.7226.89315.55315.5558.8465.0030.534.3010.006.2543.0226.89315.55315.5558.8465.0030.534.3010.006.2538.7226.89257.57257.5758.8465.0030.534.309.006.2538.7226.89257.57257.5758.8465.0030.534.309.006.2534.4226.89148.65148.6558.8465.0030.534.308.006.2534.4226.89148.65148.6558.8465.0030.534.308.006.2530.1226.89104.16104.1658.8465.0030.534.307.006.2530.1226.89104.16104.1658.8465.0030.534.307.006.2521.5126.8944.5644.5644.5665.0031.123.325.006.2516.6120.7644.5644.5644.5665.0031.123.325.006.2513.2920.7634.8734.8734.8765.0031.442.634.006.2510.5016.4134.8734.8734.8765.0031.442.634.006.2510.5016.4119.2719.2719.2765.0031.811.474.006.255.879.1819.2719.2719.2765.0031.811.474.006.255.879.1840.2240.2240.2265.0031.273.014.006.2512.0518.8340.2240.2240.2265.0031.273.014.006.2518.0818.8363.7763.7758.8465.0030.534.306.006.2525.8126.8963.7763.7758.8465.0030.534.306.006.2530.1226.89139.89139.8958.8465.0030.534.307.006.2530.1226.89139.89139.8958.8465.0030.534.307.006.2534.4226.89289.52289.5258.8465.0030.534.308.006.2534.4226.89289.52289.5258.8465.0030.534.308.006.2534.4226.89630.58560.60

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Karakteristik Sumber Air

Randow variable Kejadian dan besaran Komponen Siklus Hidrologi (sumber air ) tidak menentu dalam proses waktuUrutan berturut -turut , sumber air dari rentang independent ke dependent : Air Hujan ,Air permukaan ,Air tanah dan mata air (Karakter air hujan lebih independent dari air permukaan atau air permukaan lebih dependent dari air hujan atau air tanah/mata air lebih dependent dari air permukaan).

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Gamb. Fluktuasi Hujan Wilayah Mintakat Ciremai Utara

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Model Kontinu Hujan-Debit
Metode Regresi Ganda

Debit hasil peramalan dengan metode regresi linier ganda dapat mengikuti fluktuasi debit historis yang ada. Peramalan debit metode regresi linier ganda dapat digunakan sebagai alat untuk memperkirakan debit yang akan datang.

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Data debit aliran minimum periode kemarau 1970-2003

*

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View Mintakat Ciremai ,Up Stream Sumber sumber Mata Air Mandirancan Cibulakan,Cikepel dan Cigorowong (Rando Bawagirang Minggu, 25 jul 04)

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*

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Model Deterministik
Aliran Permukaan Bebas

B

Dx

R(t)

0

t

0

t

H(t)

Dx

B

H

Volume Kontrol

L

HULU

HILIR

B

*

Kondisi alam dari ilustrasi tersebut kemudian disederhanakan untuk dapat dimodelkan menurut hipotesa Saint-Venant. Saluran dibuat tunggal dan prismatik rectangular dengan panjang L dan lebar B. (klik) Asumsi input aliran hanya berasal dari hulu, yaitu limpasan hujan sebagai kondisi batas hulu, dan output aliran berada di hilir yang berupa berbagai bentuk muara, misalnya laut, danau, dll yang memiliki parameter2 yang dapat menjadi kondisi batas hilir. (klik) Untuk menghitung pergerakan fluida, diperlukan volume kontrol yang dibuat dengan membagi panjang saluran ke dalam ruas-ruas dengan besar delta x. (klik) Apabila diambil satu ruas, maka diperoleh (klik) satu buah volume kontrol dengan panjang delta x, lebar B, dan tinggi sesuai ketinggian muka air atau H.

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Perhitungan Curah Hujan Rata-rata Wilayah

Metode Aljabar/Aritmatika

dengan :

= Curah hujan daerah (mm)

n = Jumlah titik-titik (stasiun-stasiun) pengamat hujan

R1, R2,, Rn = Curah hujan di tiap titik pengamatan

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Gambar Pembagian Wilayah Hujan dengan Metode Thiessen

dimana :

Ai = luas masing-masing poligon

Pi = tinggi hujan pada stasiun A

*

dimana :

Pw= curah hujan wilayah

A1,A2,...An= luas bagian-bagian antara garis-garis isohiet

P1,P2,...Pn= curah hujan rata-rata pada bagian A1,A2,...An

Gambar Pembagian Wilayah Hujan dengan Metode Isohiet

*

Q = C (P x A ) + b

Q = debit sungai, C = koefisien limpasan (run off), P = curah hujan, A = luas DAS, b = aliran dasar (base flow)

DS = P-R-E-B**-B*

R = Limpasan; E= Evaporasi;

B = Aliran Air Tanah

Keseimbangan Air di DAS

*

*

Keseimbangan Masa Air Waduk

Keseimbangan masa : St+1 = St + Qin Qout - E

S : Variabel ditentukan

Qin : debit input air ( variabel acak) Prakiraan debit input ,simulasi debit air : Metode Kontinu dan metode Diskret (Arwin ,1992)

Q out : Keandalan air baku

E : evaporasi fungsi komponen meteorologi

T : Waktu ( time step)

Q out

Q In

E

Smaks ( 11 m)

Smin (+ 7 m )

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Model Kontinu
Metode Regresi Linier Ganda

Dibangun berdasarkan korelasi antara dua variabel acak, yaitu :

* Stasiun pengamat hujan (P )

* Stasiun pengamat debit (Q )

Model dengan nilai koefisien Korelasi (R) terbesar dipilih sebagai model yang paling baik untuk membangun data debit.

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Korelasi 2 variabel

= Koefisien korelasi 2 variabel xy

= nilai Variabel X atau Ykei

= Simpangan baku variabel X dan Y

n = Jumlah populasi ,bila n

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REGRESI LINAIR

Y = a + b . X

dimana:

n = jumlah pasangan observasi atau pengukuranb = koefisien regresi, kemiringan grafik

r = koefisien korelasi ( -1 < r < 1 )

r < 0 korelasi berlawanan arah

r> 0 korelasi searah

*

Tabel 4.1 Penyusunan Koefisien Korelasi Antar Pos Hujan
( pengisian atau perpanjangan data hujan )

NilaiP1P2P3P4PnP11 1nP2211 2nP3 31 321 3nP4 41 42 431 4nPm m1 m2 m3 m4 mn

*

Tabel 4.2 Koefisien Korelasi Spartial Pos Hujan dan Debit

( Pembangunan Prakiraan Debit dgn Metode Kontinu

NilaiP1P2P3QtQt+1Qt-1P11P2 P2P11P3 P3 P1 P3 P21Qt Qt P1 Qt P2 Qt P31Qt+1 Qt+1 P1 Qt+1 P2 Qt+1 P3 Qt+1 Qt1Qt-1 Qt-1 P1 Qt-1 P2 Qt-1 P3 Qt-1 Qt Qt-1 Qt+11

*

4 Variabel

(Kuaterner)

3 Variabel

(Terner)

2 Variabel

(Biner)

R >>>

MODEL PEMBANGKITAN DEBIT

TERPILIH

Korelasi

Regresi Ganda

*

Persamaan Regresi Linier Model Biner :

x1 = r2x2 +

Koefisien Determinasi Dinyatakan sbb :

R = 12

2 = 1 R2

(Q1)P

(Q1)Q

Model 2 Variabel (Biner)

12

X1

X2

*

Persamaan Regresi Linier Model Terner :

x1 = r2x2 + r3x3 +

Koefisien Determinasi Dinyatakan sbb :

(Q1)PP

(Q1)QP

(Q1)QQ

Model 3 Variabel (Terner)

12

X1

X2

X3

13

23

*

Koefisien Korelasi Parsiil Dinyatakan sbb

Model 3 Variabel (Terner) (Lanjutan)

*

Persamaan Regresi Linier Model Kuaterner :

x1 = r2x2 + r3x3 + r4x4 +

Koefisien Determinasi Dinyatakan sbb :

2 = 1 R2

= 1 + r22 + r32 + r42 2(r212 + r313 + r414) + 2(r2r323 + r2r424 + r3r434)

(Q1)PPP

(Q1)QPP

(Q1)QQP

(Q1)QQQ

Model 4 Variabel (Kuaterner)

X1

X3

X4

14

34

X2

12

23

24

24

*

Koefisien Korelasi Parsiil Dinyatakan sbb

= 1 (232 + 242 + 342) + 22324 34

2 = 12(1- 342) 13(23 24 34) 14(24 - 23 34)

3 = 13(1- 242) 12(23 24 34) 14(34 - 23 24)

4 = 14(1- 232) 12(24 23 34) 13(34 - 23 24)

Model 4 Variabel (Lanjutan)

*

Analisis Korelasi & Regresi

Model Terpilih

R >>>

Model Hujan-Debit Model HePQQ(Q1)

*

Matrik

Perbandingan Model Pembangkitan Debit
Model Kontinu Model Diskrit Waduk Saguling

Debit hasil peramalan dengan model kontinu dan model diskrit dapat mengikuti fluktuasi debit historis yang ada.

Elastisitas debit antisipasi terbaik Metode Diskrit Chain Markov.

Metode peramalan terpilih Pengelolaan Waduk Aktual

*

Korelasi & Regresi

Perbandingan Model Pembangkitan Debit
Model Kontinu Model Diskrit Waduk Cirata

Debit hasil peramalan dengan model kontinu dan model diskrit dapat mengikuti fluktuasi debit historis yang ada.

Elastisitas debit antisipasi terbaik Metode Regresi Linier Ganda.

Metode peramalan terpilih Pengelolaan Waduk Aktual

Metode Regresi Linier Ganda Model Heterogen Q(1)QQP

*

Kriteria Desain Air Baku Multisektor

Sumber: Modifikasi BMA ,Cipta karya -PU ,1994

Sumber Air Permukaan Kriteria disain Perencanan Air baku Debit Air Suksesif KeringDomestikIrigasiIndustri1 - 7 hariR=10 - 20 tahun15 - 30 hariR=5 tahun1 - 2 hariR=20 tahun

*

Uji Chi-kuadrat

Penentuan distribusi Terpilih

Seleksi Data Debit Harian

Pengelompokkan Data Debit

(Durasi 1,2,7,15,30 dan 60 hari)

Pengurutan Data

Uji K-S

Penentuan distribusi Terpilih

Pembuatan Kurva Debit Andalan

Penentuan Debit Andalan 5, 10, 20, 50 tahun untuk berbagai durasi.

Perbandingan Debit Andalan dengan Kebutuhan Air

*

KAJIAN SUMBER AIR SUNGAI

Q = C (P.A)+ b

C= f( P,I,f, Tutupan lahan)

P : variabel bebas ( Randown variabel)

A : Luas tanggapan hujan

Q: variabel tergantung( Randown variabel)

b : aliran dasar ( tutupan lahan, batuan )

Diagram Alir Analisis Peluang Debit Air musim kering (Ekstrim Kering) Seleksi data & urutan data debit air 1,2,7,15,30 dan setengah bulanan kalender Pemilihan distribusi teoritis ( Normal, Gumbel dan log Person III) yang cocokdengan Uji Goodness-of-fit Hitung debit air minum Periode Ulang 5, 10, 20, 50 tahun dengan distribusi teoritis terpilih Debit air minimum dengan Periode Ulang 5,10,20 dan 50 tahunKurva peluang debit air minimum ekstrem keringKeandalan Debit Air Baku

Kawasan Hulu

Boundary Hilir

Q

Boundary Hulu

*

sebuah test yang menentukan tingkat kesesuaian antara distribusi sampel dengan distribusi teoritis.

Bila Fo(X) adalah suatu fungsi distribusi frekuensi kumulatif yang ditentukan atau distribusi kumulatif teoritis dan SN(x) merupakan frekuensi kumulatif sampel maka diharapkan dengan uji ini selisih antara Fo(X) dan SN(X) adalah sesedikit mungkin atau nilai dari Fo(X) mendekati nilai dari SN(X) yang masih dalam batas-batas kesalahan random. Sehingga kedua distribusi frekuensi tersebut bisa dikatakan identik.

Uji kecocokan Smirnov Kolmogorov, sering juga disebut uji kecocokan non-parametrik (non-parametrik test) karena pengujiannya tidak menggunakan fungsi distribusi tertentu. Prosedurnya adalah sebagai berikut:

TEST GOODNESS-OF-FIT

*

*

Analisis Peluang Debit

Untuk memahami karakteristik debit sebagai variabel acak, dituntut pencocokan distribusi teoritis tertentu pada nilsi-nilsi observasi acak yang ada (Chow, 1964).Jenis Distribusi yang banyak digunakan untuk menganalisis debit ekstrim kering, yaitu (Lindsley, 1969 dan Soewarno, 1995):

- Distribusi ekstrim tipe III (Weibull atau Gumbel tipe III)

Distribusi Log-Pearson tipe III

Distribusi Log-Normal

Uji Goodness-of-fit

Berfungsi untuk memilih fungsi distribusi yang sesuai dengan sampel dengan cara menentukan kesesuaian antara sampel dengan distribusi teoritis tertentu.

Ket: Penentu lain, Data

Distribusi Debit

Jenis DistribusiParameter SampelUji yang DigunakanDiskritDiketahui2DiskritDiperkirakan2KontiniuDiketahuiK-SKontiniuDiperkirakan2

*

Urutkan data (dari besar ke kecil atau sebaliknya) dan tentukan besarnya peluang dari masing-masing data tersebut.

2.Tentukan nilai masing-masing peluang teoritis dari hasil penggambaran data (persamaan distribusinya).

3. Dari kedua nilai peluang tersebut tentukan selisih terbesarnya antara peluang pengamatan dengan peluang teoritis. D = Maksimum [ Fo(Xm) SN(Xm)]

4. Berdasarkan tabel nilai kritis(Kolmogorov - Smirnov test) tentukan harga Do.

Apabila nilai D lebih kecil dari Do maka distribusi teoritis yang digunakan untuk menentukan persamaan distribusi dapat diterima, apabila D lebih besar dari Do maka distribusi teoritis yang digunakan untuk menentukan persamaan distribusi sampel tidak dapat diterima.

Langkah Langkah Test K -S.

*

Distribusi Debit

Distribusi Debit

Distribusi Normal

Distribusi Log-Normal

Distribusi Gumbel

Distribusi Log-Pearson III

*

Uji K-S

Uji Goodness-of-fit

Uji 2

Menetapkan suatu titik dimana terjadi simpangan terbesar antara distribusi teoritis dan sampel.

Mengukur perbedaan relatif antara

Frekuensi hasil pengamatan

Dengan frekuensi yang diharapkan

Dn = Maksimum IFo(X)-Sn(X)I

Dimana,

Dn: Penyimpangan Terbesar

Fo(X): Suatu fungsi distribusi

kumulatif yang ditntukan

Sn(X): Distribusi Kumulatif

Sampel

Dimana,

k: Jumlah variabel

Oi: Frekuensi hasil pengamatan

Ei: Frekuensi distribusi teoritis

n: jumlah data

Pi: Peluang dari distribusi teoritis

2 =

Distribusi Normal

Distribusi Log-Normal

Distribusi Gumbel

Distribusi Log-Normal

Distribusi Normal

Distribusi Log-Normal

Distribusi Gumbel

Distribusi Log-Normal

*

Uji Goodness-of-Fit X2

2

Grafik Distribusi Teoritis (expected)

Distribusi Frekuensi Data (observed)

*

Q (debit)

Distribusi Normal

P (Probabilitas)

Hasil Pengamatan

= 2

= Dn

2

5

8

frekuensi

No.Qf15.55226.55139.143413.501514.581618.481721.631824.981925.7421028.8611133.4311233.7311336.3311437.2021538.6311665.8011766.5611885.9211994.511

*

KOLMOGOROV-SMIRNOV

Uji Goodness-of-Fit
Kolmogorov-Smirnov

Grafik Distribusi Frekuensi Teoritis

Distribusi Frekuensi Kumulatif Data

Dn

GRAFIK FREKUENSI KUMULATIF

108.unknown

*

Grafik Debit Andalan Mata air Paniis

Chart1111112222277777151515151530303030306060606060TR 2 thnTR 5 thnTR 10 thnTR 20 thnTR 50 thnDurasi (hari)Debit (L/det)Grafik Debit air andalan mata air Paniiis652.7994442.2399310.1465189.079139.1467661.9494450.4728318.7062198.577850.6913672.2851441.5734307.6979192.203658.5503676.8207449.9796321.4623212.623989.2522681.9049464.6931344.074243.4942131.439743.1659.238596046615.415084999579.22258315538.47737738uji distribudiDistribusi Peluang untuk Debit Suksesif Ektrim Kering 1 Harino. datatahun1 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996460.3382.10.1000382.1-1.770.03840.06165.9458-1.920.02730.0727382.10.15880.14680.064421997382.1460.30.2000460.3-1.260.10300.09706.1318-1.220.11070.0893460.30.24620.21820.098331998568.6568.60.3000568.6-0.560.28610.01396.3431-0.430.33420.0342568.60.44380.35840.019141999649.3649.30.4000649.3-0.040.48270.08276.47590.070.52810.1281649.30.67980.49330.072852000719.4719.40.5000719.40.410.65890.15896.57840.460.67580.1758719.40.97610.62320.150162001819.8731.00.6000731.00.480.68590.08596.59440.520.69710.0971731.01.03550.64490.077972002789.5784.10.7000784.10.830.79610.09616.66460.780.78230.0823784.11.35420.74180.093382003731.0789.50.8000789.50.860.80570.00576.67140.810.78970.0103789.51.39090.75110.003592004784.1819.80.9000819.81.060.85500.04506.70910.950.82820.0718819.81.61750.80160.0440n9Dn =0.1589n9Dn =0.1758n91/ =0.0589478079jumlah5904.1 =0.05jumlah58.11 =0.05jumlah5904.1Ao =0.4400434936rata-rata656.0111D0 =0.375rata-rata6.4571D0 =0.375rata-rata656.0111Bo =21.4916617959varian23963.776varian0.07076varian23963.776S154.80238S0.2660SE154.80238 =16.9642CS-0.83CS-1.112S-0.83CK-0.603CK0.144CK-0.603Dn =0.1501 =724.1309D0 =0.375 =-2602.8295 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 2 Harino. datatahun2 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996467.5432.30.1000432.3-1.680.04686075540.00206.0690-1.780.03780.0482432.30.20130.18230.000521997432.3467.50.2000467.5-1.430.07640.07896.1473-1.440.07450.1251467.50.24490.21720.077431998615.6615.60.3000615.6-0.390.34800.10376.4226-0.270.39300.0275615.60.54440.41980.097341999653.9653.90.4000653.9-0.120.45130.08206.4830-0.010.49420.2559653.90.66490.48570.088452000728.4728.40.5000728.40.400.65530.04016.59090.440.67170.2025728.40.97340.62220.045362001828.7733.10.6000733.10.430.66730.00266.59730.470.68150.1488733.10.99670.63090.008372002795.6787.30.7000787.30.810.79180.00666.66860.780.78100.1095787.31.30710.72940.005382003733.1795.60.8000795.60.870.80810.00906.67910.820.79400.0690795.61.36220.74390.008592004787.3828.70.9000828.71.100.86490.00966.71990.990.83980.0334828.71.60270.79870.0054n9Dn =0.1037n9Dn =0.2559n91/ =0.0661jumlah6042.4 =0.05jumlah58.38 =0.05jumlah6042.4Ao =0.4371rata-rata671.3778D0 =0.375rata-rata6.4864D0 =0.375rata-rata671.3778Bo =21.0091varian20352.6920varian0.0552varian20352.6920S142.6629S0.23495S142.6629 =15.1217CS-0.804CS-1.037CS-0.804CK-0.652CK-0.23CK-0.652Dn =0.0973 =733.7412D0 =0.375 =-838.1797 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 7 Harino. datatahun7 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996570.4553.30.1000553.3-1.560.05980.01996.3159-1.620.05250.0440553.30.39470.32610.019021997553.3570.40.2000570.4-1.390.08220.05706.3463-1.420.07780.1209570.40.42900.34890.057931998689.6659.70.3000659.7-0.520.30130.09296.4919-0.450.32520.0494659.70.65430.48020.085641999659.7689.60.4000689.6-0.230.40900.04066.5361-0.160.43680.2242689.60.74930.52730.060452000741.2741.20.5000741.20.270.60690.02896.60820.320.62530.1483741.20.94130.60990.009662001833.7757.00.6000757.00.430.66480.06416.62940.460.67730.1099757.01.00840.63520.045872002817.9796.70.7000796.70.810.79160.07046.68050.800.78810.0832796.71.19430.69710.054382003757.0817.90.8000817.91.020.84570.00256.70680.970.83500.0831817.91.30500.72880.011792004796.7833.70.9000833.71.170.87930.04436.72591.100.86450.0200833.71.39300.75170.0392n9Dn =0.0929n9Dn =0.2242n91/ =0.1410jumlah6419.5 =0.05jumlah59.04 =0.05jumlah6419.5Ao =0.4069rata-rata713.2778D0 =0.375rata-rata6.5601D0 =0.375rata-rata713.2778Bo =15.9798varian10567.004varian0.02268varian10567.004SE102.79594S0.15058SE102.79594 =7.0927CS-0.533CS-0.694CS-0.533CK-1.062CK-0.853CK-1.062Dn =0.0856 =755.1011D0 =0.375 =-887.5583 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 15 Harino. datatahun15 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996590.9569.70.1000569.7-1.540.06190.05026.3451-1.610.05400.0314569.70.41640.34060.031321997569.7590.90.2000590.9-1.320.09280.02676.3816-1.350.08880.1083590.90.46210.37000.045731998692.4662.00.3000662.0-0.600.27480.07936.4953-0.540.29410.1037662.00.64760.47670.084241999662.0692.40.4000692.4-0.290.38640.01156.5402-0.220.41190.1724692.40.74390.52480.062652000741.9741.90.5000741.90.220.58530.04746.60920.270.60530.1194741.90.92600.60390.007162001835.4768.50.6000768.50.490.68660.06026.64450.520.69740.1060768.51.03830.64600.002072002824.0802.20.7000802.20.830.79670.12176.68740.820.79440.0408802.21.19680.69790.063582003768.5824.00.8000824.01.050.85340.05586.71411.010.84410.0654824.01.30930.73000.003092004802.2835.40.9000835.41.170.87840.02956.72791.110.86630.0434835.41.37180.74630.0059n9Dn =0.1217n9Dn =0.1724n91/ =0.1661jumlah6487 =0.05jumlah59.14 =0.05jumlah6487Ao =0.3967rata-rata720.7778D0 =0.375rata-rata6.5716D0 =0.375rata-rata720.7778Bo =14.2910varian9637.3844varian0.01986varian9637.3844SE98.17018S0.14092SE98.17018 =6.0194CS-0.442CS-0.588CS-0.442CK-1.245CK-1.053CK-1.245Dn =0.0842 =759.7208D0 =0.375 =-643.2284 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 30 Harino. datatahun30 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996603.0584.70.1000584.7-1.490.06760.08426.3711-1.560.05990.0114584.70.42990.34950.045621997584.7603.00.2000603.0-1.300.09690.00736.4020-1.330.09260.0883603.00.47210.37630.031331998693.2663.20.3000663.2-0.660.25390.06236.4970-0.610.26950.1439663.20.63470.46990.093841999663.2693.20.4000693.2-0.340.36560.01516.5414-0.280.38870.1485693.20.73160.51890.091152000747.4747.40.5000747.40.230.59120.04006.61660.280.61020.1074747.40.93640.60790.046862001837.2771.10.6000771.10.480.68510.09836.64790.510.69610.0545771.11.03950.64640.009072002826.4804.70.7000804.70.840.79890.17536.69050.830.79730.0225804.71.20120.69920.085682003771.1826.40.8000826.41.070.85720.08356.71711.030.84870.0618826.41.31630.73190.011592004804.7837.20.9000837.21.180.88140.06686.73011.130.87030.0434837.21.37660.74760.0094n9Dn =0.1753n9Dn =0.1485n91/ =0.1871jumlah6530.9 =0.05jumlah59.21 =0.05jumlah6530.9Ao =0.3882rata-rata725.6556D0 =0.375rata-rata6.5792D0 =0.375rata-rata725.6556Bo =12.8806varian8905.5703varian0.01789varian8905.5703SE94.36933S0.13376SE94.36933 =5.3441CS-0.366CS-0.499CS-0.366CK-1.401CK-1.253CK-1.401Dn =0.0938 =762.2895D0 =0.375 =-453.2395 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 60 Harino. datatahun60 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996611.9593.10.1000611.9-1.510.06610.07466.3853-1.570.05810.0163611.90.46810.3738-0.273821997593.1611.90.2000593.1-1.320.09390.00236.4165-1.340.08930.0932593.10.42740.3478-0.147831998701.0689.10.3000701.0-0.540.29380.06976.5354-0.490.31380.1374701.00.70620.5065-0.206541999689.1701.00.4000689.1-0.420.33610.02956.5525-0.360.35890.1763689.10.66970.4881-0.088152000772.0772.00.5000772.00.290.61410.04006.64900.340.63200.1114772.00.95970.6170-0.117062001860.8780.40.6000860.80.370.64580.10586.65980.420.66090.0465860.81.37590.7474-0.147472002850.1829.50.7000850.10.870.80700.17536.72080.860.80410.0186850.11.31940.7327-0.032782003780.4850.10.8000780.41.070.85860.05976.74541.030.84950.0716780.40.99390.62990.170192004829.5860.80.9000829.51.180.88120.09366.75781.120.86960.0234829.51.21510.70330.1967n9Dn =0.1753n9Dn =0.1763n91/ =0.1855jumlah6687.9 =0.05jumlah59.42 =0.05jumlah6687.9Ao =0.3889rata-rata743.1D0 =0.375rata-rata6.6024D0 =0.375rata-rata743.1Bo =12.9919varian9924.45varian0.0191varian9924.45SE99.62153S0.13821SE99.62153 =5.3919CS-0.372CS-0.516CS-0.372CK-1.32CK-1.153CK-1.32Dn =0.1967 =781.8396D0 =0.375 =-512.4335 =0.05Gemma:dah oke!!!Gemma:SN(X)=m/(n+1)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:dah di sortGemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:dah di sortGemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Hasil Uji DistribusiHasil uji K-S debit suksesif minimum (1, 2, 7, 15, 30 & 60 hari)Durasinormallog normalextreme value type 31 hari0.13660.25220.13782 hari0.10370.25590.09737 hari0.12880.22420.120015 hari0.12170.17240.084230 hari0.17530.14850.093860 hari0.17530.17630.5007Gemma:yang di pilih yang memiliki nilai terkecilPeriode ulangDEBIT EKSTRIM HARIAN MATA AIR PANIIS YANG DIMANFAATKAN PDAM (L/DET)DurasiPeriode Ulang (tahun)251020501652.7994442.2399310.1465189.079139.14672661.9494450.4728318.7062198.577850.69137672.2851441.5734307.6979192.203658.550315676.8207449.9796321.4623212.623989.252230681.9049464.6931344.074243.4942131.43960743.1659.238596046615.415084999579.22258315538.47737738grafikgrafik111112222277777151515151530303030306060606060TR 2 thnTR 5 thnTR 10 thnTR 20 thnTR 50 thnDurasi (hari)Debit (L/det)Grafik Debit Ekstrim Harian Minimum Paniiis652.7994442.2399310.1465189.079139.1467661.9494450.4728318.7062198.577850.6913672.2851441.5734307.6979192.203658.5503676.8207449.9796321.4623212.623989.2522681.9049464.6931344.074243.4942131.439743.1659.238596046615.415084999579.22258315538.47737738

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Perbandingan Kurva Debit Andalan air permukaan (Mata air Paniis & Sungai Cisadane)

Chart11111222277771515151530303030606060605 tahun10 tahun20 tahun50 tahunDurasi (hari)Debit (l/s)Kurva Debit Andalan S. Cisadane Pos Legokmuncang5.50000935224.63598900284.02577553323.43450990575.65187506934.74297375234.10366267053.48659562497.30304775826.48640031845.88130837715.26752833178.08713254887.3032750366.71356384776.10660637578.5640250897.72831765867.92572727686.4537548459.43818617398.57720456997.92572727687.2514886192Sheet1Tabel Debit Andalan Sungai Cisadane Pos BatubeulahBerdasarkan Uji x2Durasai KeringDistribusiPeriode Ulang (Tahun)(Hari)Terpilih510205015.50000935224.63598900284.02577553323.434509905725.65187506934.74297375234.10366267053.486595624977.30304775826.48640031845.88130837715.2675283317158.08713254887.3032750366.71356384776.1066063757308.5640250897.72831765867.92572727686.453754845609.43818617398.57720456997.92572727687.2514886192Sheet10000000000000000000000005 tahun10 tahun20 tahun50 tahunDurasi (hari)Debit (m3/hari)Kurva Peluang Debit Andalan Sungai Cisadane Pos Legokmuncang000000000000000000000000Sheet2Sheet3Chart1111112222277777151515151530303030306060606060TR 2 thnTR 5 thnTR 10 thnTR 20 thnTR 50 thnDurasi (hari)Debit (L/det)Grafik Debit Ekstrim Harian Minimum Paniiis652.7994442.2399310.1465189.079139.1467661.9494450.4728318.7062198.577850.6913672.2851441.5734307.6979192.203658.5503676.8207449.9796321.4623212.623989.2522681.9049464.6931344.074243.4942131.439743.1659.238596046615.415084999579.22258315538.47737738uji distribudiDistribusi Peluang untuk Debit Suksesif Ektrim Kering 1 Harino. datatahun1 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996460.3382.10.1000382.1-1.770.03840.06165.9458-1.920.02730.0727382.10.15880.14680.064421997382.1460.30.2000460.3-1.260.10300.09706.1318-1.220.11070.0893460.30.24620.21820.098331998568.6568.60.3000568.6-0.560.28610.01396.3431-0.430.33420.0342568.60.44380.35840.019141999649.3649.30.4000649.3-0.040.48270.08276.47590.070.52810.1281649.30.67980.49330.072852000719.4719.40.5000719.40.410.65890.15896.57840.460.67580.1758719.40.97610.62320.150162001819.8731.00.6000731.00.480.68590.08596.59440.520.69710.0971731.01.03550.64490.077972002789.5784.10.7000784.10.830.79610.09616.66460.780.78230.0823784.11.35420.74180.093382003731.0789.50.8000789.50.860.80570.00576.67140.810.78970.0103789.51.39090.75110.003592004784.1819.80.9000819.81.060.85500.04506.70910.950.82820.0718819.81.61750.80160.0440n9Dn =0.1589n9Dn =0.1758n91/ =0.0589478079jumlah5904.1 =0.05jumlah58.11 =0.05jumlah5904.1Ao =0.4400434936rata-rata656.0111D0 =0.375rata-rata6.4571D0 =0.375rata-rata656.0111Bo =21.4916617959varian23963.776varian0.07076varian23963.776S154.80238S0.2660SE154.80238 =16.9642CS-0.83CS-1.112S-0.83CK-0.603CK0.144CK-0.603Dn =0.1501 =724.1309D0 =0.375 =-2602.8295 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 2 Harino. datatahun2 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996467.5432.30.1000432.3-1.680.04686075540.00206.0690-1.780.03780.0482432.30.20130.18230.000521997432.3467.50.2000467.5-1.430.07640.07896.1473-1.440.07450.1251467.50.24490.21720.077431998615.6615.60.3000615.6-0.390.34800.10376.4226-0.270.39300.0275615.60.54440.41980.097341999653.9653.90.4000653.9-0.120.45130.08206.4830-0.010.49420.2559653.90.66490.48570.088452000728.4728.40.5000728.40.400.65530.04016.59090.440.67170.2025728.40.97340.62220.045362001828.7733.10.6000733.10.430.66730.00266.59730.470.68150.1488733.10.99670.63090.008372002795.6787.30.7000787.30.810.79180.00666.66860.780.78100.1095787.31.30710.72940.005382003733.1795.60.8000795.60.870.80810.00906.67910.820.79400.0690795.61.36220.74390.008592004787.3828.70.9000828.71.100.86490.00966.71990.990.83980.0334828.71.60270.79870.0054n9Dn =0.1037n9Dn =0.2559n91/ =0.0661jumlah6042.4 =0.05jumlah58.38 =0.05jumlah6042.4Ao =0.4371rata-rata671.3778D0 =0.375rata-rata6.4864D0 =0.375rata-rata671.3778Bo =21.0091varian20352.6920varian0.0552varian20352.6920S142.6629S0.23495S142.6629 =15.1217CS-0.804CS-1.037CS-0.804CK-0.652CK-0.23CK-0.652Dn =0.0973 =733.7412D0 =0.375 =-838.1797 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 7 Harino. datatahun7 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996570.4553.30.1000553.3-1.560.05980.01996.3159-1.620.05250.0440553.30.39470.32610.019021997553.3570.40.2000570.4-1.390.08220.05706.3463-1.420.07780.1209570.40.42900.34890.057931998689.6659.70.3000659.7-0.520.30130.09296.4919-0.450.32520.0494659.70.65430.48020.085641999659.7689.60.4000689.6-0.230.40900.04066.5361-0.160.43680.2242689.60.74930.52730.060452000741.2741.20.5000741.20.270.60690.02896.60820.320.62530.1483741.20.94130.60990.009662001833.7757.00.6000757.00.430.66480.06416.62940.460.67730.1099757.01.00840.63520.045872002817.9796.70.7000796.70.810.79160.07046.68050.800.78810.0832796.71.19430.69710.054382003757.0817.90.8000817.91.020.84570.00256.70680.970.83500.0831817.91.30500.72880.011792004796.7833.70.9000833.71.170.87930.04436.72591.100.86450.0200833.71.39300.75170.0392n9Dn =0.0929n9Dn =0.2242n91/ =0.1410jumlah6419.5 =0.05jumlah59.04 =0.05jumlah6419.5Ao =0.4069rata-rata713.2778D0 =0.375rata-rata6.5601D0 =0.375rata-rata713.2778Bo =15.9798varian10567.004varian0.02268varian10567.004SE102.79594S0.15058SE102.79594 =7.0927CS-0.533CS-0.694CS-0.533CK-1.062CK-0.853CK-1.062Dn =0.0856 =755.1011D0 =0.375 =-887.5583 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 15 Harino. datatahun15 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996590.9569.70.1000569.7-1.540.06190.05026.3451-1.610.05400.0314569.70.41640.34060.031321997569.7590.90.2000590.9-1.320.09280.02676.3816-1.350.08880.1083590.90.46210.37000.045731998692.4662.00.3000662.0-0.600.27480.07936.4953-0.540.29410.1037662.00.64760.47670.084241999662.0692.40.4000692.4-0.290.38640.01156.5402-0.220.41190.1724692.40.74390.52480.062652000741.9741.90.5000741.90.220.58530.04746.60920.270.60530.1194741.90.92600.60390.007162001835.4768.50.6000768.50.490.68660.06026.64450.520.69740.1060768.51.03830.64600.002072002824.0802.20.7000802.20.830.79670.12176.68740.820.79440.0408802.21.19680.69790.063582003768.5824.00.8000824.01.050.85340.05586.71411.010.84410.0654824.01.30930.73000.003092004802.2835.40.9000835.41.170.87840.02956.72791.110.86630.0434835.41.37180.74630.0059n9Dn =0.1217n9Dn =0.1724n91/ =0.1661jumlah6487 =0.05jumlah59.14 =0.05jumlah6487Ao =0.3967rata-rata720.7778D0 =0.375rata-rata6.5716D0 =0.375rata-rata720.7778Bo =14.2910varian9637.3844varian0.01986varian9637.3844SE98.17018S0.14092SE98.17018 =6.0194CS-0.442CS-0.588CS-0.442CK-1.245CK-1.053CK-1.245Dn =0.0842 =759.7208D0 =0.375 =-643.2284 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 30 Harino. datatahun30 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996603.0584.70.1000584.7-1.490.06760.08426.3711-1.560.05990.0114584.70.42990.34950.045621997584.7603.00.2000603.0-1.300.09690.00736.4020-1.330.09260.0883603.00.47210.37630.031331998693.2663.20.3000663.2-0.660.25390.06236.4970-0.610.26950.1439663.20.63470.46990.093841999663.2693.20.4000693.2-0.340.36560.01516.5414-0.280.38870.1485693.20.73160.51890.091152000747.4747.40.5000747.40.230.59120.04006.61660.280.61020.1074747.40.93640.60790.046862001837.2771.10.6000771.10.480.68510.09836.64790.510.69610.0545771.11.03950.64640.009072002826.4804.70.7000804.70.840.79890.17536.69050.830.79730.0225804.71.20120.69920.085682003771.1826.40.8000826.41.070.85720.08356.71711.030.84870.0618826.41.31630.73190.011592004804.7837.20.9000837.21.180.88140.06686.73011.130.87030.0434837.21.37660.74760.0094n9Dn =0.1753n9Dn =0.1485n91/ =0.1871jumlah6530.9 =0.05jumlah59.21 =0.05jumlah6530.9Ao =0.3882rata-rata725.6556D0 =0.375rata-rata6.5792D0 =0.375rata-rata725.6556Bo =12.8806varian8905.5703varian0.01789varian8905.5703SE94.36933S0.13376SE94.36933 =5.3441CS-0.366CS-0.499CS-0.366CK-1.401CK-1.253CK-1.401Dn =0.0938 =762.2895D0 =0.375 =-453.2395 =0.05Distribusi Peluang untuk Debit Suksesif Ektrim Kering 60 Harino. datatahun60 hariXSN(X)distribusi normaldistribusi log normaldistribusi gumbel tipe 3/extreme value type 3XZF0(X)Dln XkF0(X)DxyF0(X)D11996611.9593.10.1000611.9-1.510.06610.07466.3853-1.570.05810.0163611.90.46810.3738-0.273821997593.1611.90.2000593.1-1.320.09390.00236.4165-1.340.08930.0932593.10.42740.3478-0.147831998701.0689.10.3000701.0-0.540.29380.06976.5354-0.490.31380.1374701.00.70620.5065-0.206541999689.1701.00.4000689.1-0.420.33610.02956.5525-0.360.35890.1763689.10.66970.4881-0.088152000772.0772.00.5000772.00.290.61410.04006.64900.340.63200.1114772.00.95970.6170-0.117062001860.8780.40.6000860.80.370.64580.10586.65980.420.66090.0465860.81.37590.7474-0.147472002850.1829.50.7000850.10.870.80700.17536.72080.860.80410.0186850.11.31940.7327-0.032782003780.4850.10.8000780.41.070.85860.05976.74541.030.84950.0716780.40.99390.62990.170192004829.5860.80.9000829.51.180.88120.09366.75781.120.86960.0234829.51.21510.70330.1967n9Dn =0.1753n9Dn =0.1763n91/ =0.1855jumlah6687.9 =0.05jumlah59.42 =0.05jumlah6687.9Ao =0.3889rata-rata743.1D0 =0.375rata-rata6.6024D0 =0.375rata-rata743.1Bo =12.9919varian9924.45varian0.0191varian9924.45SE99.62153S0.13821SE99.62153 =5.3919CS-0.372CS-0.516CS-0.372CK-1.32CK-1.153CK-1.32Dn =0.1967 =781.8396D0 =0.375 =-512.4335 =0.05Gemma:dah oke!!!Gemma:SN(X)=m/(n+1)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:dah di sortGemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:dah di sortGemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Gemma:okGemma:okGemma:okGemma:fixGemma:fixGemma:fixGemma:max(D)Gemma:max(D)Hasil Uji DistribusiHasil uji K-S debit suksesif minimum (1, 2, 7, 15, 30 & 60 hari)Durasinormallog normalextreme value type 31 hari0.13660.25220.13782 hari0.10370.25590.09737 hari0.12880.22420.120015 hari0.12170.17240.084230 hari0.17530.14850.093860 hari0.17530.17630.5007Gemma:yang di pilih yang memiliki nilai terkecilPeriode ulangDEBIT EKSTRIM HARIAN MATA AIR PANIIS YANG DIMANFAATKAN PDAM (L/DET)DurasiPeriode Ulang (tahun)251020501652.7994442.2399310.1465189.079139.14672661.9494450.4728318.7062198.577850.69137672.2851441.5734307.6979192.203658.550315676.8207449.9796321.4623212.623989.252230681.9049464.6931344.074243.4942131.43960743.1659.238596046615.415084999579.22258315538.47737738grafikgrafik111112222277777151515151530303030306060606060TR 2 thnTR 5 thnTR 10 thnTR 20 thnTR 50 thnDurasi (hari)Debit (L/det)Grafik Debit Ekstrim Harian Minimum Paniiis652.7994442.2399310.1465189.079139.1467661.9494450.4728318.7062198.577850.6913672.2851441.5734307.6979192.203658.5503676.8207449.9796321.4623212.623989.2522681.9049464.6931344.074243.4942131.439743.1659.238596046615.415084999579.22258315538.47737738

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ALAT UKUR THOMPSON & CIPOLETTI

Tahap pekerjaan pengukuran debit air

- Literatur alat ukur ambang tajam dan syarat berlaku formula

-Menentukan lokasi pengukuran debit air dan penafsiran dimensi alat ukur

- Pembuatan alat ukur

-Test pengukuran di lapangan

-Revisi alat ukur

-Penempatan alat ukur

-Pengukuran

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Sumber : Proyek Pengembangan PSDA Jeneberang

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4

4

r

=

0,609

0,688

0,77

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

P(Q1)HePP(Q1)HePQQ(Q1)He

Kawasan Hulu

Boundary Hilir

Q

Boundary Hulu

=

-

k

i

i

i

i

E

E

O

1

2

)

(

Variable:

gdk_Jan

, Distribution: Normal

Chi-Square test = 8.76148, df = 2, p = 0.01252

0.0

1.5

3.0

4.5

6.0

7.5

Category (upper limits)

0

10

20

30

40

50

60

70

80

90

100

110

Relative Frequency (%)

Grafik Debit air andalan mata air Paniiis

0

100

200

300

400

500

600

700

800

0102030405060

Durasi (hari)

Debit (L/det)

TR 2 thn

TR 5 thn

TR 10 thn

TR 20 thn

TR 50 thn

Kurva Debit Andalan S. Cisadane Pos Legokmuncang

0,000

2,000

4,000

6,000

8,000

10,000

0102030405060

Durasi (hari)

Debit (l/s)

5 tahun

10 tahun

20 tahun

50 tahun

Grafik Debit Ekstrim Harian Minimum Paniiis

0

100

200

300

400

500

600

700

800

0102030405060

Durasi (hari)

Debit (L/det)

TR 2 thn

TR 5 thn

TR 10 thn

TR 20 thn

TR 50 thn

0

100

200

300

400

500

600

700

JanFebMarAprMeiJunJulAgstSeptOktNovDes

Bulan

hujan (mm/bl)

Rata-rata BulananRata-rata Tahunan

Gamb. 4.1. Data Debit Harian Minimum Sungai Cisadane Pos

Batubeulah

0,000

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

19701975198019851990199520002005

Tahun

Debit ekstim minimum

(m3/det)

1 hari

2 hari

7 hari

15 hari

30 hari

60 hari

Gambar 3.4 : Penyelamatan Air & Tanah

C hutan =0,1-0,2

C budidaya = 0,5-0,6

C permukiman pedesaan

= 0,4-0,5

C Urban metro = 0,9-1,0

Neraca Air:

P = I + R

I/P + R/P= 1

Ik + C = 1

Gambar 3.5. : NERACA KESEIMBANGAN AIR TANAH

P = I +R , Ik+C =1

S = P R E-B** -B*

E = 1250 1500 mm/tahun(Evapotranspirasi

potensial)

S < 0 terjadi pada musim kemarau kering

S > 0 terjadi pada musim hujan basah

Kawasan pengunungan:

Hujan wilayah = 3000 mm

C= 0,5 maka I = 1500 dan E=1500 & S =0

.bila muka air diatas permukaan tanah

maka B * > 0 bila tidak B = 0 ( nihil)

Nilai C = nilai rata-rata

C=1-Ik = F (P,jenis tanahTutupan lahan)

0

100

200

300

400

500

600

700

800

0

6

12

18

24

30

36

42

48

54

60

Bulan

Juta m

3

HISTORIS

NORMAL

REGRESI

MARKOV

0

100

200

300

400

500

600

700

0

6

12

18

24

30

36

42

48

54

60

Bulan

Juta m

3

HISTORIS

NORMAL

REGRESI

MARKOV

Pengukuran debit air

1.Pengukuran tak langsung (current meter)

2.Pengukuran langsung ambang tajam

-Alat Ukur Thompson

-Alat Ukur Cipoletti

Alat ukur debit tidak langsung (Current Meter)

Alat Ukur ambang tajam : Thompson & Cipoletti

Current Meter

Kecepatan air V didapatkan dari pengukuran Current Meter ( Propeller atau tipe Price)

dinyatakan sebagai berikut :

V = a + b.N

N = banyaknya perputaran propeller atau kerucut kecil (baling -baling) per-detik.

a = kecepatan awal yang diperlukan untuk mengatasi g esekan mekanis

a & b = merupakan konstanta yang didapat dari kalibrasi alat

Formula Alat Ukur Ambang Tajam

2/5

.hKQ

2

)09.0)(

12

4.8(

24.0

2.81

B

h

D

h

K

Alat Ukur Thompson

hghbQ 2..42,0

2/3

..86,1hbQ

Alat ukur Cipoletti

Gamb. Fluktuasi debit Mandirancan Kemarau 2004

0

20

40

60

80

100

120

140

160

6/17/047/1/047/15/047/29/048/12/048/26/049/9/049/23/0410/7/0410/21/0411/4/0411/18/0412/2/0412/16/0412/30/0

Debit (Lt/dt)

Waktu

Cig-sedaIrigasi-Cig-SedaCibulakanCikepelRaksabaya