GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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118 be computed; the bias, RMS (root-mean-square) error and scatter index (ratio of RMS error to mean measured value) are particularly useful as measures of performance. Continuous hindcasts typically show scatter indices for significant wave height in the range of 0.25–0.30, while for peak-to-peak comparisons of storm hindcasts they are often in the range of 0.12–0.16. In addition, it is useful to construct 1-D spectral plots of the respective observed and modelled spectra, e.g. at peak wave height or within three hours. For continuous wave measurements, an appropriate moving average should be used on the recorded data (e.g. 6 or 7 point moving average). It is instructive to represent the data with error bars indicating appropriate confidence limits (for instance 95 per cent). See, for example, Figure 5.4, where the 90 per cent confidence limits are shown. If 2-D spectral measurements are available, they should be used to evaluate the model predicted values. 9.6.7 Extremal analysis From the wave hindcast model, the following quantities are available at all points and at each time step: • H s — significant wave height; • T p — spectral peak period; • θ d — vector mean wave direction; • W s — average wind speed; • W d — wind direction. The objective of the extreme analysis is to describe extremes at all contiguous grid locations for the following variables: • H s versus annual exceedance probability or inverse return period; • W s versus annual exceedance probability; • H m (maximum individual wave height) versus annual exceedance probability. Techniques for extremal analysis of these quantities are described in preceding sections. 9.6.7.1 Extreme wave/crest height distribution For the points at which a detailed extremal analysis is performed, the maximum individual wave height may GUIDE TO WAVE ANALYSIS AND FORECASTING be estimated in each storm from the hindcast zeroth and first spectral moments following Borgman’s (1973) integral expression, which accounts for storm build-up and decay. The integral may be computed for two assumed maximum individual wave height distributions: (a) Rayleigh (as adapted by Cartwright and Longuet- Higgins, 1956); (b) Forristall (1978). The same approach may be used to estimate the maximum crest height at a site in a storm using the empirical crest-height distribution of Haring and Heideman (1978). The median of the resulting distributions of H m, H c may be taken as the characteristic maximum single values in a storm. The mean ratios of H m/H s and H c/H s should be calculated and used to develop a mean ratio to provide extremes of H m and H c from fields of extreme H s. 9.6.7.2 Presentation of extremes Fields of extremes of H s, H m, W s should be tabulated and displayed as field plots (contour plots if necessary) of numerical values. Results of detailed extremal analysis at selected grid locations should be presented in tabular form for each analysed point and in graphical form. The graphical display of extrapolations shall include the fitted line, the confidence limits on the fit and the fitted points. 9.6.8 Available hindcast databases Several hindcast databases have been created covering a wide range of ocean basins. Most of these are continuous hindcasts, a few are storm hindcasts. There are no hybrid hindcast databases presently available. A list of available hindcast databases, with their characteristics, is shown in Table 9.3. These databases cover periods of three years or longer (continuous) or 40 storms or more (storm). It is not possible to include the many other hindcasts, related to short periods for verification purposes or to studies of particular events, in this publication.
ANNEX I ABBREVIATIONS AND KEY TO SYMBOLS (Preferable units are shown with alternatives in brackets) Abbreviation/ Definition Symbol a Wave amplitude — m (ft) ASCE American Society of Civil Engineers ∆b Distance between two wave rays CERC Coastal Engineering Research Center (US) c; cphase Phase speed; the speed of propagation of a wave — m/s (kn) cg; cg –c g Group speed, velocity. The speed (velocity) of propagation of a wave group — m/s (kn) Effective group velocity for total energy — m/s (kn) cθ Speed of directional change — rad/s (deg/s) Cd; C10 Drag coefficient; drag coefficient at the 10 m level. CD Coupled discrete — model class CH Coupled hybrid — model class CMC Canadian Meteorological Center deg Measure of angle, degree Dp Duration of wave generation — h DNMI The Norwegian Meteorological Institute DP Decoupled propagation — model class e, exp Exponential constant ≅ 2.71828 E, Etotal Wave energy (variance) per unit area — m2 per area E∞ Energy of fully developed wave field — m2 per area E(f) Wave spectral energy density as a function of frequency — m2/Hz E(f,θ) Wave spectral energy density as function of frequency and direction — m2/Hz /rad E[ ] Expected value of variable in brackets ECMWF European Centre for Medium-range Weather Forecasts ESA European Space Agency f Wave frequency — Hz – f Coriolis parameter — s Mean wave frequency — Hz fp Wave frequency corresponding to the peak of the spectrum — Hz ft Unit of length, foot FFT Fast-Fourier transform F(H) Probability of not exceeding the wave height H FNMOC Fleet Numerical Meteorology and Oceanography Centre (USA) FT Fisher-Tippett distribution g Acceleration due to gravity — m/s2 G, (ug, vg); G Geostrophic wind velocity; speed — m/s (kn) GD Groen and Dorrestein Gr; Gr Gradient wind velocity; speed — m/s (kn) GTS Global Telecommunications System h Unit of time, hour h Water depth — m
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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-
Page 77 and 78: 6.1 Introductory remarks Since the
Page 79 and 80: in some applications, the zero up/d
Page 81 and 82: OPERATIONAL WAVE MODELS 71 Figure 6
Page 83 and 84: give large differences in the compa
Page 85 and 86: Wind (m/s) Waves (m) Buoy/GSOWM Wav
Page 87 and 88: TABLE 6.2 Numerical wave models ope
Page 89 and 90: 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: TABLE 9.3 (cont.) Country Model use
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 and 142: 1744 Im Indicator for method of cal
Page 143 and 144: The following distributions are bri
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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GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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