Exercici Clima d'Onatge - Caglar Birinci

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Water Engineering

Master in Civil Engineering UPC

Course 10-11

CAGLAR BIRINCI

E01. Characterization of long-term wave

Our aim is to determine the scalar wave height associated with returning periods 5, 10, 20

years with having a wave forecast data set of 10 years.

The analysis focuses on the characterization of extreme events in the data provided. The

method used by the extreme characterization is the peak over threshold (POT) method.

To use this method we have to define some criteria for each temporal wave:

Extreme events must be independent; which means there should be at least 12-18hours of time after the last extreme event.

All events must correspond to likely extreme weather situations; All events must meet the condition of seasonality.

According to the ROM 03.91; the defined minimum threshold value of wave height is 2 m in

Catalan coast. (Whole table attached to the next page)


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The determination of the values of approximation functions may be performed as a least

square approximation, which requires assigning a approximation value or drawing position.

Extreme case of a scheme from the POT method generally uses the Grinorten - Gumbel

approximation, because of this reason we also use it:

()

Where i is the order of the selected data in arranged form from high to low and N is the

number of the selected data.

Return period also known as a recurrence interval is an estimate of the average recurrence

interval over a period of time (in years) between temporary events that have certain intensity

(value) of wave height. The relationship between the return period Tr and the approximation

probability F (Hs) is given by the following equation:

( ())

Where is the number of temporary half a year and therefore defined as

Nt being the number of temporary and N the number of years covered sample.

With the criteria described before it has found 176 temporary times in the period of the

sample. The total number of years covered by the sample is 10 years. The number of

temporary half a year is, = 17.6

To adjust the calculation function of reduced variable;

[ (())]


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With A = 2.2239 and B = 0.5966

Tr = 5 years ----> F(Hs) = 0.98864 ----> yr= 4.47163 ---->Hs = 4.89167m

Tr = 10 years ----> F(Hs) = 0.99432 ----> yr=5.16764 ---->Hs =5.30691m


As the return period increases this approximation will give the results lower than the real ones.

This approximation may get better if it is higher order approximation.

The extreme values are reduced by the linear approximation.

To approximate better we can use linear approximation between the first three values of the

following table.


Tr = 10 years ----> F(Hs) = 0.99432 ----> yr=5.16764 ---->Hs =7.33856m



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Year Month Day Hour Hm0 i F (Hs) y(reduced)

2001 11 15 12 10 1 0.99682 5.74939

2000 11 6 9 5.3 2 0.99114 4.72203

2001 11 11 0 4.6 3 0.98546 4.22385

2003 10 31 9 4.6 4 0.97979 3.891212003 12 8 0 4.5 5 0.97411 3.64076

1996 11 11 21 4.4 6 0.96843 3.43957

1997 4 8 21 4.3 7 0.96275 3.27126

1997 11 6 15 4.2 8 0.95707 3.12644

2003 12 4 6 4.2 9 0.95140 2.99926

1997 10 29 3 4.1 10 0.94572 2.88580

2002 5 8 3 4.1 11 0.94004 2.78334

2002 11 25 3 4.1 12 0.93436 2.68986

2001 12 15 3 4 13 0.92868 2.60388

1996 12 7 21 3.8 14 0.92301 2.524252003 10 18 6 3.7 15 0.91733 2.45005

1996 11 20 3 3.4 16 0.91165 2.38057

2002 1 4 12 3.4 17 0.90597 2.31521

1997 1 6 12 3.3 18 0.90030 2.25349

2004 4 16 9 3.3 19 0.89462 2.19499

1996 12 5 21 3.2 20 0.88894 2.13939

1997 1 4 0 3.2 21 0.88326 2.08639

1997 1 23 21 3.2 22 0.87758 2.03574

1998 1 20 15 3.2 23 0.87191 1.98723

2002 3 28 15 3.2 24 0.86623 1.940672003 4 3 15 3.2 25 0.86055 1.89589

1997 4 21 15 3.1 26 0.85487 1.85276

2002 11 21 15 3.1 27 0.84919 1.81114

2004 2 21 15 3.1 28 0.84352 1.77092

1997 4 18 3 3 29 0.83784 1.73200

1997 12 18 3 3 30 0.83216 1.69428

1996 2 1 0 2.9 31 0.82648 1.65770

1996 11 22 3 2.9 32 0.82080 1.62216

1997 1 3 21 2.9 33 0.81513 1.58762

2000 1 19 12 2.9 34 0.80945 1.553992001 3 2 21 2.9 35 0.80377 1.52124

2003 2 26 3 2.9 36 0.79809 1.48930

2004 3 29 21 2.9 37 0.79241 1.45813

1996 1 23 9 2.8 38 0.78674 1.42769

1996 1 24 9 2.8 39 0.78106 1.39794

1996 2 20 21 2.8 40 0.77538 1.36884

1996 4 21 21 2.8 41 0.76970 1.34036

1998 12 21 15 2.8 42 0.76402 1.31247

1999 1 31 9 2.8 43 0.75835 1.28513

2002 4 11 18 2.8 44 0.75267 1.25832

2002 11 14 3 2.8 45 0.74699 1.23202


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2004 5 3 12 2.8 46 0.74131 1.20620

2005 3 1 6 2.8 47 0.73563 1.18084

1996 5 18 15 2.7 48 0.72996 1.15591

1996 6 21 21 2.7 49 0.72428 1.13141

1996 6 22 21 2.7 50 0.71860 1.10730

1996 7 7 15 2.7 51 0.71292 1.08358

1996 12 28 21 2.7 52 0.70725 1.06022

1997 12 23 15 2.7 53 0.70157 1.03722

1996 2 7 15 2.6 54 0.69589 1.01455

1996 5 1 15 2.6 55 0.69021 0.99221

1996 9 21 15 2.6 56 0.68453 0.97017

1996 10 14 9 2.6 57 0.67886 0.94843

1997 12 5 15 2.6 58 0.67318 0.92698

1998 12 3 9 2.6 59 0.66750 0.90580

2000 10 24 6 2.6 60 0.66182 0.88489

2001 11 2 3 2.6 61 0.65614 0.86423

1996 7 26 15 2.5 62 0.65047 0.84381

1997 2 15 12 2.5 63 0.64479 0.82363

1997 6 29 15 2.5 64 0.63911 0.80368

1997 11 8 15 2.5 65 0.63343 0.78394

1997 11 22 15 2.5 66 0.62775 0.76441

1998 1 19 15 2.5 67 0.62208 0.74509

1999 12 28 3 2.5 68 0.61640 0.72595

2003 11 17 9 2.5 69 0.61072 0.70701

2004 11 14 0 2.5 70 0.60504 0.68824

1996 1 30 9 2.4 71 0.59936 0.66965

1996 2 18 21 2.4 72 0.59369 0.65123

1996 4 25 15 2.4 73 0.58801 0.63297

1996 5 19 15 2.4 74 0.58233 0.61486

1996 7 29 15 2.4 75 0.57665 0.59690

1997 1 1 3 2.4 76 0.57097 0.57908

1997 3 28 15 2.4 77 0.56530 0.56141

1997 5 4 15 2.4 78 0.55962 0.54387

1997 5 13 15 2.4 79 0.55394 0.52645

1997 5 14 15 2.4 800.54826 0.509162001 1 14 9 2.4 81 0.54258 0.49199

1996 2 6 21 2.3 82 0.53691 0.47493

1996 3 10 15 2.3 83 0.53123 0.45798

1996 7 8 3 2.3 84 0.52555 0.44113

1996 12 13 15 2.3 85 0.51987 0.42439

1997 5 6 15 2.3 86 0.51419 0.40774

2000 10 21 15 2.3 87 0.50852 0.39118

2001 1 26 21 2.3 88 0.50284 0.37471

2002 11 20 9 2.3 89 0.49716 0.35833

2002 12 28 0 2.3 90 0.49148 0.342032003 1 31 21 2.3 91 0.48581 0.32580


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2003 2 18 18 2.3 92 0.48013 0.30965

2003 3 15 21 2.3 93 0.47445 0.29357

2003 4 14 15 2.3 94 0.46877 0.27755

2006 2 19 9 2.3 95 0.46309 0.26159

1997 4 30 15 2.2 96 0.45742 0.24569

1997 8 28 15 2.2 97 0.45174 0.22985

1998 1 2 15 2.2 98 0.44606 0.21406

1999 3 3 21 2.2 99 0.44038 0.19831

1999 4 28 9 2.2 100 0.43470 0.18261

1999 12 15 3 2.2 101 0.42903 0.16695

2000 4 3 9 2.2 102 0.42335 0.15133

2000 12 22 3 2.2 103 0.41767 0.13575

2000 12 25 3 2.2 104 0.41199 0.12019

2003 9 14 15 2.2 105 0.40631 0.10466

2004 5 6 9 2.2 106 0.40064 0.08916

2006 1 30 21 2.2 107 0.39496 0.07367

1996 1 17 21 2.1 108 0.38928 0.05821

1996 2 2 15 2.1 109 0.38360 0.04275

1996 4 2 12 2.1 110 0.37792 0.02731

1996 4 3 21 2.1 111 0.37225 0.01187

1996 4 16 15 2.1 112 0.36657 -0.00356

1996 4 21 3 2.1 113 0.36089 -0.01900

1996 6 28 15 2.1 114 0.35521 -0.03444

1996 8 10 15 2.1 115 0.34953 -0.04989

1996 9 11 15 2.1 116 0.34386 -0.06535

1996 10 2 21 2.1 117 0.33818 -0.08083

1996 12 29 21 2.1 118 0.33250 -0.09632

1997 1 7 3 2.1 119 0.32682 -0.11184

1997 1 9 15 2.1 120 0.32114 -0.12739

1997 1 21 21 2.1 121 0.31547 -0.14298

1997 4 26 15 2.1 122 0.30979 -0.15860

1997 5 8 0 2.1 123 0.30411 -0.17426

1997 6 21 15 2.1 124 0.29843 -0.18997

1997 11 11 15 2.1 125 0.29275 -0.20573

1997 12 27 21 2.1 1260.28708 -0.221551998 4 10 21 2.1 127 0.28140 -0.23743

1998 11 22 12 2.1 128 0.27572 -0.25337

1999 3 24 21 2.1 129 0.27004 -0.26940

1999 10 23 3 2.1 130 0.26437 -0.28550

1999 11 29 21 2.1 131 0.25869 -0.30169

2000 4 9 3 2.1 132 0.25301 -0.31797

2000 12 23 3 2.1 133 0.24733 -0.33435

2001 1 28 15 2.1 134 0.24165 -0.35083

2002 4 4 3 2.1 135 0.23598 -0.36744

2003 4 7 9 2.1 136 0.23030 -0.384162003 5 6 21 2.1 137 0.22462 -0.40102


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2004 3 11 3 2.1 138 0.21894 -0.41802

1996 2 8 9 2 139 0.21326 -0.43517

1996 2 15 15 2 140 0.20759 -0.45248

1996 4 22 21 2 141 0.20191 -0.46997

1996 5 3 15 2 142 0.19623 -0.48764

1996 5 12 21 2 143 0.19055 -0.50551

1996 5 15 15 2 144 0.18487 -0.52359

1996 11 28 15 2 145 0.17920 -0.54190

1996 11 30 21 2 146 0.17352 -0.56046

1996 12 9 21 2 147 0.16784 -0.57927

1997 1 28 21 2 148 0.16216 -0.59837

1997 4 25 15 2 149 0.15648 -0.61778

1997 7 15 21 2 150 0.15081 -0.63751

1997 9 29 15 2 151 0.14513 -0.65759

1997 11 20 15 2 152 0.13945 -0.67806

1998 12 1 18 2 153 0.13377 -0.69894

1999 11 13 3 2 154 0.12809 -0.72027

2000 4 2 21 2 155 0.12242 -0.74209

2000 10 22 15 2 156 0.11674 -0.76445

2000 11 23 12 2 157 0.11106 -0.78740

2000 12 23 15 2 158 0.10538 -0.81100

2000 12 29 15 2 159 0.09970 -0.83532

2001 3 4 15 2 160 0.09403 -0.86043

2001 8 16 21 2 161 0.08835 -0.88643

2001 10 20 21 2 162 0.08267 -0.91344

2002 2 6 12 2 163 0.07699 -0.94158

2002 4 2 21 2 164 0.07132 -0.97102

2002 12 10 9 2 165 0.06564 -1.00196

2003 4 16 6 2 166 0.05996 -1.03464

2003 11 23 21 2 167 0.05428 -1.06938

2003 12 1 3 2 168 0.04860 -1.10660

2003 12 16 9 2 169 0.04293 -1.14686

2003 12 22 21 2 170 0.03725 -1.19094

2003 12 24 9 2 171 0.03157 -1.23999

2004 3 31 3 2 1720.02589 -1.295782004 12 2 6 2 173 0.02021 -1.36134

2004 12 9 3 2 174 0.01454 -1.44248

2005 11 10 3 2 175 0.00886 -1.55318

2005 12 10 15 2 176 0.00318 -1.74937

Exercici Clima d'Onatge - Caglar Birinci

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