GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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72 GUIDE TO WAVE ANALYSIS AND FORECASTING Figure 6.5 — Wave directional spectra at 12 selected locations in the seas adjacent to Japan for the 24-hour forecast valid at 00 UTC, 27 September 1991. The directional spectra are presented in polar plots with concentric circles representing wave frequencies (in Hz) and isopleths of spectral energy in units of m 2 /Hz/rad. Isopleths are labelled by order of magnitude (–1 means 10 –1 m 2 /Hz/rad) and indicate the direction from which waves are coming. Also depicted on the perimeters are the wind speed and direction at each location. The values of peak period (s) and significant wave height (m) are shown at the centre of each spectrum plot (source: Tadashi Asoh, JMA)
give large differences in the comparisons. Further, it must be remembered that in situ measurements are only estimates and individual spectral components may have quite large uncertainty due to high sampling variability in the estimates. For these reasons, model validation studies are usually performed in a statistical sense using all available data, and are based on comparisons of derived parameters. A common approach is to perform a regression analysis on a set of important parameters such as H s, T – z (or T p) and, if directional wave data are available, the mean direction (for different frequency bands). In addition, it may be useful to compare mean wave spectra or cumulative distributions (of, for example, H s) for simultaneous model results and measurements. Since the wind field that drives the model is intimately related to the model wave field, most evaluation studies also include verification of wind speed and direction. An important requirement for evaluation of a wave model is the availability of reliable sea-state measurements and related weather data. Most of the evaluation studies reported in the last 15 years have used buoy data for wind and wave measurements and have occasionally used analysed weather maps for additional wind information. A few earlier studies (e.g. Feldhausen et al., 1973) have used visual ship reports for wave height to make a qualitative evaluation of several wave hindcasting procedures. More recently, satellite altimeter data have been used to validate wave model results. For example, Romeiser (1993) validated the global WAM model (WAMDI Group, 1988; Komen et al., 1994) for a one-year period using global data from the GEOSAT altimeter. Most verification studies have attempted to calculate several statistical parameters and analysed the magnitude and variation of these parameters to determine the skill of a wave model. Among the parameters that are most commonly used are: • The mean error (ME) or bias; • The root-mean-square error (RMSE); • The Scatter Index (SI) defined as the ratio of RMSE to the mean observed value of the parameter; and • r, the sample linear correlation coefficient between the model and the observed value. A few studies have considered other statistical measures to evaluate wave model performance such as the slope of the regression line between model and observed values or the intercept of the regression line on the y axis. The four parameters as listed above are the best indicators of the performance of a wave model. Verification of operational wave models at national Services of many countries is an ongoing activity. At most Services, the initial verification of a wave model is performed during the implementation phase and the verification statistics are updated periodically so as to monitor the model’s performance. Table 6.1 shows the performance of a few wave models which are presently in operational use at various OPERATIONAL WAVE MODELS 73 national (international) organizations in different parts of the world. The table presents verification statistics for wind speed, wave height and peak period (where available) in terms of four statistics, namely: ME, RMSE, SI and r as defined above. The table includes a variety of models developed over the last twenty years, ranging from first generation (1G) to the recent third generation (3G) models (see Section 5.5 for a discussion of model classifications). Verification statistics for many more models have been summarized elsewhere by Khandekar (1989). Based on these statistics, it may be concluded that a firstgeneration wave model driven by winds obtained from a weather prediction model can provide wave height simulations with an RMS error of about 1.0 m and a scatter index of around 35 per cent. The second- and third-generation wave models, driven by winds from operational weather prediction models, can provide wave height simulations with RMS errors of about 0.5 m and scatter indices of about 25 per cent. The third-generation WAM model (see Section 5.5.4), which has run operationally since early 1992 at the European Centre for Medium-Range Weather Forecasts (ECMWF) in the United Kingdom, generates wave height values with RMS errors ranging from 0.4 m to 0.7 m in different parts of world oceans, while the bias (or mean error) ranges from 0.05 m to 0.2 m. Since these statistics were generated further improvements have been made both to the determination of wind fields and the wave models themselves, so it is expected that the results of the verifications will also be continually improving. A sample wave height plot generated by the US Navy’s GSOWM at a buoy location in the Gulf of Alaska is shown in Figure 6.6. The figure shows wave height variation in the Gulf of Alaska as measured by the buoy and as modelled by the GSOWM. The GSOWM was driven by winds from the GSCLI (Global Surface Contact Layer Interface) boundary-layer model. The figure also shows wave height variation simulated by the WAM model, which was configured to run on a 1° x 1° grid and was driven by surface wind stress fields generated by the Navy Operational Global Atmospheric Prediction System (NOGAPS). Also shown along with the wave plots are wind and wave error statistics covering the one-month period from 20 February to 20 March 1992. The GSOWM has a high bias of about 1 m in its wave height simulation on the US west coast. This bias is due to the model’s tendency to retain excess low-frequency energy from swell waves which often travel from the central Pacific to the US west coast. Figure 6.7 shows the verification of the global wave height field generated by the WAM model at ECMWF against wave heights measured by the radar altimeter aboard the satellite ERS-1 (see Section 8.5.2). The altimeter wave heights plotted along the sub-satellite tracks cover a six-hour window centred around the time for which the model wave height field is valid. In general, the model wave heights show an excellent agreement with
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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
Page 31 and 32: 20 Figure 2.2(a) (right) — Usual
Page 33 and 34: 22 As a quick approximation of ocea
Page 35 and 36: 24 GUIDE TO WAVE ANALYSIS AND FOREC
Page 37 and 38: 26 Gr G Gr ∇p C Cnf ∇p C Cnf
Page 39 and 40: 28 POINT C — The effect of warm a
Page 41 and 42: 30 a general sense, and can be appl
Page 43 and 44: 32 Free atmosphere Ekman layer Cons
Page 45 and 46: 3.1 Introduction This chapter gives
Page 47 and 48: ange of directions. Also, waves at
Page 49 and 50: small enough that swell can survive
Page 51 and 52: Figure 3.7 — Structure of spectra
Page 53 and 54: 4.1 Introduction CHAPTER 4 WAVE FOR
Page 55 and 56: necessary to forecast waves for a p
Page 57 and 58: TABLE 4.4 Additional wave informati
Page 59 and 60: TABLE 4.6 Ranges of swell periods a
Page 61 and 62: this situation, the angular spreadi
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: OPERATIONAL WAVE MODELS 71 Figure 6
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
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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
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Page 123 and 124: TABLE 9.2 (cont.) Country Source of
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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
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CODE FORM: D . . . . D or IIiii* SE
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sensors, spectral peak wave period
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cs1cs1 The ratio of the spectral de
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M jM j n mn m n smn sm n bn bn b P
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1744 Im Indicator for method of cal
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The following distributions are bri
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4. Weibull distribution Probability
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8. Fisher-Tippett Type I (FT-I) (or
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ANNEX IV THE PNJ (PIERSON-NEUMANN-J
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ANNEX IV 141 Duration graph. Distor
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REFERENCES Abbott, M. B., H. H. Pet
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REFERENCES 145 Carter, D. J. T., P.
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REFERENCES 147 Gumbel, E. J., 1958:
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REFERENCES 149 Maat, N., C. Kraan a
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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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