GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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102 H s (m) GUIDE TO WAVE ANALYSIS AND FORECASTING DATE FEB 1979 DATE JAN 1979 H s (m) H s (m) H s (m) DATE APR 1979 DATE MAR 1979 9.3 Figure 9.1 — Time series of significant wave height measurements at Ocean Weather Ship “Lima” (57°30'N, 20°W), January–April 1979. Gaps indicate calms (from HMSO, 1985)
Presentation of data and wave climate statistics 9.3.1 Plot of the data Having obtained a data set of wave parameters over, say, a year, it is important to plot the results to obtain an overall view of the range of values, the presence of any gaps in the data and any outliers suggesting errors in the data, etc. Figure 9.1 shows an example, in the form of a “comb” plot, which provides a good visual impact. 9.3.2 Plotting statistical distributions of individual parameters Estimates from the data set of the parameter’s probability distribution can be obtained by plotting a histogram. Given, for example, T – z measurements for a year (2 920 values if a recording interval of three hours is used), then a count of the number of measurements T – z in, say, 0.5-s bins (i.e. 0.0–0.5 s, 0.5–1.0 s, ...) is made and estimates of the probability of a value in each bin is obtained by dividing the total in the bin by 2 920. Such a plot, as shown in Figure 9.2, is called a histogram. The bin size can, of course, be varied to suit the range of data — one giving a plot covering 5–15 bins is probably most informative. Note that a histogram or comb plot of the spectral peak period, Tp, may give additional information to a T – z plot. Over large expanses of the world’s oceans long swells commonly coincide with shorter wind seas, leading to wave spectra which are bimodal (double-peaked form). Over a long measurement series the histogram distribution may also be bimodal. Wave height data may also be presented in a histogram, but it is more usual to give an estimate of the cumulative probability distribution, i.e. the probability that the wave height from a randomly chosen member of the data set will be less than some specified height. Figure 9.2 — Histogram of zeroupcrossing period measurements (12 520 valid observations, including six calms), at three-hour intervals at OWS “Lima”, December 1975 to November 1981 (from HMSO, 1985) Percentage occurrence WAVE CLIMATE STATISTICS 103 Estimates are obtained by adding the bin totals for increasingly high values and dividing these totals by the number of data values. Sometimes, to emphasize the occurrence of high waves, the probability of waves greater than the specified height is plotted — see Figure 9.3. 9.3.3 Plotting the joint distribution of height and period A particularly useful way of presenting wave climate data, combining both height and period data in one figure, is an estimate from the data of the joint distribution of Hs and T – z (often called the joint frequency table or scatter table). Data are counted into bins specified by height and period and the totals divided by the grand total of the data to give an estimate of the probability of occurrence. In practice — see for example Figure 9.4 — the estimates are usually multiplied by 1 000, thus expressing the probability in parts per thousand (‰), and rounded to the nearest whole number, but with a special notation to indicate the bins with so few values that they would be lost by rounding. It is sometimes more convenient for further analysis to plot the actual bin totals. In any case, the grand total should be given with the scatter plot together with the number of calms recorded. It is also useful to draw on the scatter plot lines of equal significant steepness (2πHs/gT – z 2 — see Section 1.3.5). The line representing a significant steepness of one-tenth is particularly useful, since this seems in practice to be about the maximum value found in measurements from open waters. Any records indicating steeper waves should therefore be checked for possible errors. 9.3.4 Checks on the data sets As mentioned above, the various plots of the data and the estimates from the data of probability distributions
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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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Page 63 and 64: the energy flux is c gH 2 . This is
Page 65 and 66: α0, degrees Solution: 80° 70° 60
Page 67 and 68: 5.1 Introduction National Meteorolo
Page 69 and 70: only once, since it is usual to sto
Page 71 and 72: Frequency 0.050 0.067 0.083 0.100 0
Page 73 and 74: The models may differ in several re
Page 75 and 76: 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: 9.1 Introduction Chapter 8 describe
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 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
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SELECTED BIBLIOGRAPHY CERC, 1984: C
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156 Energy . . . . . . . . . . . .
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158 steepness . . . . . . . . . . .
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GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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