GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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132 Q c Code figure Quadrant of the globe Latitude Longitude 1 North East 3 South East 5 South West 7 North West 3333 Q c = 7 N Q c = 1 Equator W E Q c = 5 S Q c = 3 Note: The choice is left to the observer in the following cases: — When the ship is on the Greenwich meridian or the 180th meridian (L oL oL oL o = 0000 or 1800 respectively): Q c = 1 or 7 (northern hemisphere) or Q c = 3 or 5 (southern hemisphere); — When the ship is on the Equator (L aL aL a = 000): Q c = 1 or 3 (eastern longitude) or Q c = 5 or 7 (western longitude). x Exponent for spectral wave data GUIDE TO WAVE ANALYSIS AND FORECASTING 4800 Code Code figure figure 0 10 –5 5 10 0 1 10 –4 6 10 1 2 10 –3 7 10 2 3 10 –2 8 10 3 4 10 –1 9 10 4 Greenwich meridian
The following distributions are briefly described in the order shown (see Johnson and Kotz, 1970, inter alia, for further details): • Normal or Gaussian • Log-normal • Gamma • Weibull • Exponential • Rayleigh • Generalized extreme value (GEV) • Fisher-Tippett Type I or Gumbel • Fisher-Tippett Type III • Generalized Pareto The symbols – x and s are used for the mean and standard deviation of the series x i (i = 1, n), i.e.: x where Σ indicates summation over i (i = 1, n). The symbol Γ has its usual meaning as the gamma function: Values are widely tabulated. 1. Normal or Gaussian distribution Probability paper Moments estimators α˜ = x ˜ β = s s 2 x = n ∑ x x = n ∑( i – ) – 1 ∞ z– 1 – t dΓ Γ() z = ∫ t e dt; Γ′ () z = t = 0 dz f (x) = 1 2π β mean = α variance = β 2 x =Φ –1 ⎡ ( p) ⎢Φ(x)= ∫ ⎣⎢ y = (h) Maximum likelihood estimators αˆ = x ˆ ( – ) β = ∑ xix n i 2 2 ⎡ ⎣ (x – α )2 exp – 2β 2 ⎢ x –∞ 1 2π ANNEX III PROBABILITY DISTRIBUTIONS FOR WAVE HEIGHTS ⎤ ⎥ – ∞
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WORLD METEOROLOGICAL ORGANIZATION G
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© 1998, World Meteorological Organ
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IV Chapter 7 - WAVES IN SHALLOW WAT
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ACKNOWLEDGEMENTS The revision of th
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VIII has been included particularly
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X considerable attention. Annex III
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2 η Crest Zero level a H = 2a a Tr
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4 Figure 1.5 — Paths of the water
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6 When waves propagate into shallow
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8 1.3.2 Wave groups and group veloc
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10 wavelengths in a given sea state
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12 for instance, a frequency of 0.1
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14 in which E(f) is the variance de
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16 2.1.1 Wind and pressure analyses
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18 GUIDE TO WAVE ANALYSIS AND FOREC
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20 Figure 2.2(a) (right) — Usual
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22 As a quick approximation of ocea
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24 GUIDE TO WAVE ANALYSIS AND FOREC
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26 Gr G Gr ∇p C Cnf ∇p C Cnf
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28 POINT C — The effect of warm a
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30 a general sense, and can be appl
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32 Free atmosphere Ekman layer Cons
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3.1 Introduction This chapter gives
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ange of directions. Also, waves at
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small enough that swell can survive
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Figure 3.7 — Structure of spectra
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4.1 Introduction CHAPTER 4 WAVE FOR
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necessary to forecast waves for a p
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TABLE 4.4 Additional wave informati
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TABLE 4.6 Ranges of swell periods a
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this situation, the angular spreadi
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the energy flux is c gH 2 . This is
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α0, degrees Solution: 80° 70° 60
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5.1 Introduction National Meteorolo
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only once, since it is usual to sto
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Frequency 0.050 0.067 0.083 0.100 0
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The models may differ in several re
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The CH class may include many semi-
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6.1 Introductory remarks Since the
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in some applications, the zero up/d
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OPERATIONAL WAVE MODELS 71 Figure 6
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give large differences in the compa
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Wind (m/s) Waves (m) Buoy/GSOWM Wav
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TABLE 6.2 Numerical wave models ope
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TABLE 6.2 (cont.) Country Name of m
Page 91 and 92: 7.1 Introduction The evolution of w
Page 93 and 94: water boundary into shallow water.
Page 95 and 96: eflected waves, although the latter
Page 97 and 98: Energy (cm 2 /Hz) Energy (cm 2 /Hz)
Page 99 and 100: 8.1 Introduction Wave data are ofte
Page 101 and 102: matter and timing the intervals bet
Page 103 and 104: a Directional Waverider (Barstow et
Page 105 and 106: 80°N 60°N 40°N 20°N 0° -20°S
Page 107 and 108: a combination of sea-surface temper
Page 109 and 110: 8.7.1 Digital analysis of wave reco
Page 111 and 112: 9.1 Introduction Chapter 8 describe
Page 113 and 114: Presentation of data and wave clima
Page 115 and 116: the monsoon season of June to Septe
Page 117 and 118: Probability of non-exceedance case
Page 119 and 120: individual wave height derived usin
Page 121 and 122: emote, data-sparse areas. However,
Page 123 and 124: TABLE 9.2 (cont.) Country Source of
Page 125 and 126: For a storm hindcast, select the mo
Page 127 and 128: TABLE 9.3 (cont.) Country Model use
Page 129 and 130: ANNEX I ABBREVIATIONS AND KEY TO SY
Page 131 and 132: Abbreviation/ Definition Symbol MOS
Page 133 and 134: CODE FORM: D . . . . D or IIiii* SE
Page 135 and 136: sensors, spectral peak wave period
Page 137 and 138: cs1cs1 The ratio of the spectral de
Page 139 and 140: M jM j n mn m n smn sm n bn bn b P
Page 141: 1744 Im Indicator for method of cal
Page 145 and 146: 4. Weibull distribution Probability
Page 147 and 148: 8. Fisher-Tippett Type I (FT-I) (or
Page 149 and 150: ANNEX IV THE PNJ (PIERSON-NEUMANN-J
Page 151 and 152: ANNEX IV 141 Duration graph. Distor
Page 153 and 154: REFERENCES Abbott, M. B., H. H. Pet
Page 155 and 156: REFERENCES 145 Carter, D. J. T., P.
Page 157 and 158: REFERENCES 147 Gumbel, E. J., 1958:
Page 159 and 160: REFERENCES 149 Maat, N., C. Kraan a
Page 161 and 162: Slutz, R. J., S. J. Lubker, J. D. H
Page 163 and 164: SELECTED BIBLIOGRAPHY CERC, 1984: C
Page 165 and 166: 156 Energy . . . . . . . . . . . .
Page 167 and 168: 158 steepness . . . . . . . . . . .
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