1GR Esercizio Gumbel (Fatto)

Anno Q(m3/s) i1928 16.40 11929 77.30 21930 100.90 31932 19.70 41933 31.20 51934 17.30 61935 53.30 71936 24.20 81937 40.60 91938 35.50 101939 51.80 111940 47.30 121960 96.70 131961 119.10 141962 66.10 151963 107.90 161965 113.90 171966 137.00 181967 41.50 191968 160.90 201969 180.90 Nc 21

Nc+1 22

prob. di NON superamentotempo di ritorno

N α1 0.03

20 0.0360 0.0380 0.03

120 0.03160 0.03200 0.03

Q P(Q)20 yP(q)20 P(Q)6016.40 0.00 -3.91 0.0017.30 0.00 -3.88 0.0019.70 0.00 -3.82 0.0024.20 0.00 -3.70 0.0031.20 0.00 -3.52 0.0035.50 0.00 -3.41 0.0040.60 0.00 -3.27 0.0041.50 0.00 -3.25 0.0047.30 0.00 -3.10 0.0051.80 0.00 -2.98 0.0053.30 0.00 -2.94 0.0066.10 0.00 -2.61 0.0077.30 0.00 -2.31 0.0096.70 0.00 -1.81 0.00

100.90 0.00 -1.70 0.00107.90 0.01 -1.51 0.00113.90 0.02 -1.36 0.00119.10 0.03 -1.22 0.00137.00 0.12 -0.75 0.00160.90 0.32 -0.13 0.03180.90 0.51 0.40 0.13

20 288.80 0.96 3.22 0.8960 330.80 0.9680 341.79

120 357.29160 368.29200 376.82

Q F(Q) Q-Qm (Q-Qm)^2 P(Q) yF(q) yP(q)16.40 0.05 -56.91 3238.69 0.08 -1.13 -0.9117.30 0.09 -56.01 3137.07 0.09 -0.87 -0.8919.70 0.14 -53.61 2873.98 0.10 -0.69 -0.8324.20 0.18 -49.11 2411.75 0.13 -0.53 -0.7131.20 0.23 -42.11 1773.21 0.18 -0.39 -0.5235.50 0.27 -37.81 1429.56 0.22 -0.26 -0.4140.60 0.32 -32.71 1069.91 0.27 -0.14 -0.2841.50 0.36 -31.81 1011.85 0.28 -0.01 -0.2547.30 0.41 -26.01 676.50 0.33 0.11 -0.1051.80 0.45 -21.51 462.66 0.37 0.24 0.0153.30 0.50 -20.01 400.38 0.39 0.37 0.0566.10 0.55 -7.21 51.98 0.51 0.50 0.3977.30 0.59 3.99 15.92 0.60 0.64 0.6896.70 0.64 23.39 547.11 0.74 0.79 1.19

100.90 0.68 27.59 761.23 0.76 0.96 1.30107.90 0.73 34.59 1196.50 0.80 1.14 1.48113.90 0.77 40.59 1647.59 0.82 1.36 1.64119.10 0.82 45.79 2096.77 0.84 1.61 1.78137.00 0.86 63.69 4056.48 0.90 1.92 2.24160.90 0.91 87.59 7672.09 0.94 2.35 2.87180.90 0.95 107.59 11575.71 0.97 3.07 3.39

48106.94Q media Varianza

73.31 2405.35Scarto quadratico medio

49.04 49.04

Nc+1 22.00Q media 73.31SQM 49.04α 0.03ξ 51.24R 0.04P(x) 0.96T 25.00K' 1.72 Qt R P(Q)Qt 174.28 174.28 0.04 0.96

x yQt 174.28 3.20 T 25 anni

400.00 3.20

x y174.28 0.00174.28 3.20

H4

Pino: In questa colonna sono state riordinate le portate in ordine crescente

I4

Pino: Frequenza di non superamento secondo Weibull : i/(N+1)

L4

Pino: Probabilità di non superamento secondo Gumbel NOTA: i parametri α ed ξ della legge dipendono dalla media e dallo scarto quadratico medio

H30

Pino: Scarto quadratico medio ottenuto utilizzando il comando deviazione standard

ξn K Q yP(Q)51.24 1.72 174.28 3.20

165.76 0.53 288.80 3.20207.75 0.42 330.80 3.20218.75 0.40 341.79 3.20234.25 0.38 357.29 3.20245.24 0.36 368.29 3.20253.77 0.35 376.82 3.20

yP(q)60 P(Q)80 yP(q)80 P(Q)120 yP(q)120 P(Q)160 yP(q)160-5.01 0.00 -5.29 0.00 -5.70 0.00 -5.99-4.98 0.00 -5.27 0.00 -5.68 0.00 -5.96-4.92 0.00 -5.21 0.00 -5.61 0.00 -5.90-4.80 0.00 -5.09 0.00 -5.49 0.00 -5.78-4.62 0.00 -4.91 0.00 -5.31 0.00 -5.60-4.51 0.00 -4.79 0.00 -5.20 0.00 -5.49-4.37 0.00 -4.66 0.00 -5.07 0.00 -5.35-4.35 0.00 -4.64 0.00 -5.04 0.00 -5.33-4.20 0.00 -4.49 0.00 -4.89 0.00 -5.18-4.08 0.00 -4.37 0.00 -4.77 0.00 -5.06-4.04 0.00 -4.33 0.00 -4.73 0.00 -5.02-3.71 0.00 -3.99 0.00 -4.40 0.00 -4.69-3.41 0.00 -3.70 0.00 -4.11 0.00 -4.39-2.91 0.00 -3.19 0.00 -3.60 0.00 -3.89-2.80 0.00 -3.08 0.00 -3.49 0.00 -3.78-2.61 0.00 -2.90 0.00 -3.31 0.00 -3.59-2.46 0.00 -2.74 0.00 -3.15 0.00 -3.44-2.32 0.00 -2.61 0.00 -3.01 0.00 -3.30-1.85 0.00 -2.14 0.00 -2.54 0.00 -2.83-1.23 0.01 -1.51 0.00 -1.92 0.00 -2.21-0.70 0.07 -0.99 0.02 -1.40 0.00 -1.682.12 0.85 1.83 0.79 1.43 0.73 1.143.22 0.95 2.93 0.92 2.53 0.90 2.24

0.96 3.22 0.94 2.81 0.92 2.530.96 3.22 0.95 2.93

0.96 3.22

x y0.00 3.20

400.00 3.20

yP(Q),N)3.20

T 25 anni

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.000.00

0.20

0.40

0.60

0.80

1.00

1.20

Column IP(q)

α=1,283/σ(x)ξ=μ(X)-0,45σ(x)

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

yF(q)yP(Q)

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

3.20

yF(q)yP(Q)rettalettura qt

P(Q)200 yP(q)2000.00 -6.210.00 -6.190.00 -6.120.00 -6.010.00 -5.820.00 -5.710.00 -5.580.00 -5.550.00 -5.400.00 -5.280.00 -5.240.00 -4.910.00 -4.620.00 -4.110.00 -4.000.00 -3.820.00 -3.660.00 -3.520.00 -3.050.00 -2.430.00 -1.910.67 0.920.88 2.010.90 2.300.94 2.710.95 3.000.96 3.22

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

3.20

yF(q)yP(Q)rettalettura qt

0 50 100 150 200 250250.00

270.00

290.00

310.00

330.00

350.00

370.00

390.00

Column J

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.000.00

0.20

0.40

0.60

0.80

1.00

1.20

Column IP(q)

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

yF(q)yP(Q)

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

3.20

yF(q)yP(Q)rettalettura qt

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

3.20

yF(q)yP(Q)rettalettura qt

0 50 100 150 200 250250.00

270.00

290.00

310.00

330.00

350.00

370.00

390.00

Column J

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.000.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.002.102.202.302.402.502.602.702.802.903.003.103.203.303.403.50

yF(q)yP(Q)20 anni60 anni80 anni120 anni160 anni200 anniretta 1

stima dei valori di portata di piena pluriennale Qn,n per

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