Metode Gumbel

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    Data Rata-Rata Curah Hujan Bulanan

    Kota Makassar Tahun 2009-2014

    No

    .

    Bulan Curah

    Hujan

    Rata-Rata

    Rata-Rata Curah

    Hujan

    1 Januari 788

    255.3875

    2 Februari 466.83

    3 Maret 32.83

    4 !"ril 21.67

    5 Mei 134.33

    6 Juni 1#2.16

    7 Juli 55.83

    8 !$u%tu% 1#.67

    &e"te'b

    er

    38.83

    1# ()tober 52.33

    11 No*e'be

    r

    155.17

    12 +e%e'be

    r

    648

    Rata-Rata 255.3875

    Diketahui:

    1. X=255.3875mm

    2. n=12

    Ditanyakan:

    1. Ym

    2. YT

    3. S ' ,&tanar +e*ia%iYm

    4. S " ,&tanar +e*ia%i Curah Hujan

    5. XT ,Curah Hujan "aa

    Ti

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    Penyelesaian:

    1 Ym

    Ym=ln(ln((n+1 )m(n+1 ) ))

    ( (n+1 )m ) ((n+1

    )m

    (n+1 ) ) ln

    ((n+1

    )m

    (n+1 ) ) ln

    (ln((

    n+1

    )m(n+1) ))1 12 #.23#77 #.#8##43 2.5251441

    2 11 #.846154 #.167#54 1.7843765

    3 1# #.76231 #.262364 1.338#21418

    4 #.623#8 #.367725 1.###42#5#1

    5 8 #.615385 #.4855#8 #.7225583

    6 7 #.538462 #.61#3 #.47586667

    7 6 #.461538 #.7731 #.25723#61

    8 5 #.384615 #.55511 #.#455#8537

    4 #.3#762 1.178655 -#.1643735

    1

    # 3 #.23#76 1.466337 -#.3827675

    1

    1 2 #.153846 1.8718#2 -#.626#17

    1

    2 1 #.#7623 2.5644 -#.413873

    ln(ln((n+(n 6.#4178

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    YM=

    ln(ln((n+1 )m(n+1 ) ))n

    YM=6.041978

    12

    YM= 0!0"49#

    2 YT

    YT=ln(ln((T1 )T ))/10 3 /20 6 /30

    T

    ,/ahun ((T1 )

    T

    ) (ln

    ((T1)

    T

    )) ln

    (ln

    ((T1 )

    T

    ))3

    #.666667 #.4#5465 #.#272

    6#.83333

    3 #.182322 1.7#183

    #.88888

    #.117783 2.13811

    YT1=0,90272

    YT2=1.701983

    YT3=2.138911

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    " S $ %&tan'ar De(iasiYm )

    Sm= (Ym (i)Ym )

    2

    (n1 )

    Ym (n ) Ym (Ym (n)Ym ) (Ym(i)Ym )2

    2.5251441

    #.5#34822.#2167 4.#87258

    1.7843765 1.2853 1.65364

    1.338#21418 #.834523 #.66421.###42#

    5#1 #.4622 #.24632#.72255

    83 #.21#62 #.#4788#.47586

    667 -#.#231 #.###572#.25723#

    61 -#.24627 #.#6#648#.#455#8

    537 -#.457 #.2#755

    -#.164373

    -#.66787 #.446#53

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    5-

    #.3827675 -#.88627 #.785467

    -#.626#1

    7 -1.13#4 1.2778#4-

    #.413873 -1.44544 2.#8288

    (Ym(i)Ym)2

    11.6#183

    Sm=

    (Ym (i)Ym )2

    (n1 )

    Sm=11.6018311Sm=0.966819

    Sm=0.98327

    4 S * %&tan'ar De(iasi Curah Hujan)

    Sp= (P(i )P)

    2

    (n1)

    Bulan P( i) P (P(i )P ) (P(i )P )2

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    Januari 788

    255.3875

    532.6125 283676.#752Februari 466.83 211.4425 447#7.3#81Maret 32.83 137.4425 188#.44#81!"ril 21.67 -35.7175 1275.738#6

    Mei 134.33 -121.#58 14654.1831Juni 1#2.16 -153.228 23478.66676Juli 55.83 -1.558 3823.1581

    !$u%tu% 1#.67 -244.718 5886.65481&e"te'

    ber38.83

    -216.558 4687.15#81()tober 52.33 -2#3.#58 41232.34831No*e'b

    er155.17

    -1##.218 1##43.54731+e%e'b

    er

    648

    32.6125 154144.5752 (P(i) P )2

    738711.2438

    Sp= (P(i )P)

    2

    (n1)

    Sp=738711.243811Sp=67155.56762

    Sp=259.143913mm

    ! XT %Curah Hujan *a'a

    Ti )

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    XT=P+((YTYm )Sm )SP

    YT P Sm Ym Sp

    XT1#.#272

    255.3875 #.8327 #.5#348 25.1431

    3

    XT21.7#183

    255.3875 #.8327 #.5#348 25.1431

    3

    XT32.13811

    255.3875 #.8327 #.5#348 25.1431

    3

    YTYm(YTYm )

    Sm ((YTYm )

    Sm )SP

    P+(

    (YTYm )Sm )

    SP

    #.322

    #.4#6#1251 1#5.2157268 36#.6#32

    1.17583

    1.2175462 315.6268868 571.#144

    1.635411

    1.66323654 431.#178773 686.4#54