GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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Pp 0 Pp 1 D f G In reality, since surface friction turns the flow towards low pressure, confluence will increase the inflow angle over the effect of friction alone, and difluence will decrease the inflow angle, with the result that flow towards high pressure will seldom exist. Figure 2.6 illustrates the modification to geostrophic wind due to effects by difluence and confluence. 2.3.6 Surface friction effects u Figure 2.6 — Examples of difluent/confluent wind fields (p 0 and p 1 are isobars. D f and C f are the difluent and confluent wind components, respectively, and G and u are the geostrophic and surface winds) p 0 p 1 The effect of friction is to reduce the speed of the free air flow. As a result of the balance of forces this will turn the direction of flow toward lower pressure, which is to the left in the northern hemisphere and to the right in the southern hemisphere. As one approaches the surface of the Earth the wind speed tends to zero, and the inflow angle tends to reach a maximum. A simple balance between the pressure gradient, Coriolis and frictional forces (Figure 2.7) describes this effect through the well-known Ekman spiral. The lower part of the atmosphere in which this effect is prominent is called the Ekman layer. In nature the predicted 45° angle of turning at the surface is too large, and predicted speeds near the surface are too low. These effects of friction on the geostrophic flow in the Ekman layer are further influenced by the thermal wind discussed above. Studies have shown the importance of the thermal wind in explaining deviations from the typical Ekman spiral (Mendenhall, 1967). A result of the thermal wind influence is larger surface cross-isobaric (inflow) flow angles during cold advection, and smaller inflow angles during warm advection, as described above. An illustration of the effect of thermal wind on the wind in the Ekman layer is shown for a low pressure system in Figure 2.8. In order to represent the effects of friction in a more realistic manner several approaches have been developed that relate the free atmospheric wind to a stress at the ocean surface. These often use the concept of a two-regime boundary layer; a constant flux layer at the surface, and the Ekman layer (spiral) above. Observations fit much better with this representation of C f u G OCEAN SURFACE WINDS 27 the planetary boundary layer, with a turning angle of 10–15° predicted over the ocean for a neutrally stable atmosphere in contact with the ocean. 2.3.7 Stability effects Stability within the boundary layer is important in determining the wind speed near the ocean surface. Over much of the oceans, the surface air temperature is in equilibrium with the sea-surface temperature so that near-neutral stability dominates. Under these conditions the structure of the wind profile in the constant flux layer is dominated by friction and can be described by a logarithmic profile. For unstable cases (air temperature colder than the water temperature) convection becomes active and the higher wind speeds aloft are brought to the surface quickly, reducing dissipation by friction, and increasing the stress on the ocean surface. A stable atmosphere (warm air over cold water) acts to increase the friction forces in the boundary layer, resulting in lighter winds and a weaker wind stress. Table 2.6 shows the effects of stability on wind profiles above the ocean. Stability effects are most important for ocean areas near large land masses, which act as source areas for air masses with very different physical properties from oceanic air masses. An expanded discussion of the theory of friction and stability in the boundary layer is presented in the next section. 2.4 A marine boundary-layer parameterization The boundary layer of the atmosphere is that region which extends from the surface to the free atmosphere (at approximately 1 km height). At the surface frictional forces dominate. In the free atmosphere frictional forces become less important and, to a first order of approximation, the atmospheric flow is close to being in geostrophic balance. Because all flows in nature are turbulent, the frictional forces we are concerned with are those arising from turbulent fluctuations — the so-called Reynolds stresses. A fundamental difficulty of the turbulence theory is to relate these turbulent stresses to the properties of the mean flow. Through extensive research some insights into these relationships have evolved, at least in ∇p u G F C Figure 2.7 — Balances of friction, pressure gradient and Coriolis forces (northern hemisphere) (u = surface wind; G = geostrophic wind, ∇p = pressure gradient force; C = Coriolis force and F = friction)
28 POINT C — The effect of warm air advection in decreasing cross-isobar flow for the surface wind POINT B — The effect of a cold low in increasing the speed of the surface wind C G (SURFACE ) z G (SURFACE ) EKMAN PLUS THERMAL B z z z EKMAN EKMAN GUIDE TO WAVE ANALYSIS AND FORECASTING EKMAN PLUS THERMAL A KEY G POINT A — The effect of cold air advection in increasing cross-isobar flow for the surface wind SURFACE G GRADIENT WIND LEVEL THERMAL WIND G (SURFACE ) z ACTUAL WIND AT z EKMAN PLUS THERMAL ACTUAL WIND AT z WITHOUT THERMAL EFFECT z EKMAN Figure 2.8 — The thermal wind. Sketch of surface winds, surface isobars (solid contours) and a constant pressure surface (dashed contours) for an extra-tropical cyclone (after Pierson, 1979)
Page 1 and 2: WORLD METEOROLOGICAL ORGANIZATION G
Page 3 and 4: © 1998, World Meteorological Organ
Page 5 and 6: IV Chapter 7 - WAVES IN SHALLOW WAT
Page 7 and 8: ACKNOWLEDGEMENTS The revision of th
Page 9 and 10: VIII has been included particularly
Page 11 and 12: X considerable attention. Annex III
Page 13 and 14: 2 η Crest Zero level a H = 2a a Tr
Page 15 and 16: 4 Figure 1.5 — Paths of the water
Page 17 and 18: 6 When waves propagate into shallow
Page 19 and 20: 8 1.3.2 Wave groups and group veloc
Page 21 and 22: 10 wavelengths in a given sea state
Page 23 and 24: 12 for instance, a frequency of 0.1
Page 25 and 26: 14 in which E(f) is the variance de
Page 27 and 28: 16 2.1.1 Wind and pressure analyses
Page 29 and 30: 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: 26 Gr G Gr ∇p C Cnf ∇p C Cnf
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 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
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TABLE 6.2 (cont.) Country Name of m
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7.1 Introduction The evolution of w
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water boundary into shallow water.
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eflected waves, although the latter
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Energy (cm 2 /Hz) Energy (cm 2 /Hz)
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8.1 Introduction Wave data are ofte
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matter and timing the intervals bet
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a Directional Waverider (Barstow et
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80°N 60°N 40°N 20°N 0° -20°S
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a combination of sea-surface temper
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8.7.1 Digital analysis of wave reco
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9.1 Introduction Chapter 8 describe
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Presentation of data and wave clima
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the monsoon season of June to Septe
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Probability of non-exceedance case
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individual wave height derived usin
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emote, data-sparse areas. However,
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TABLE 9.2 (cont.) Country Source of
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For a storm hindcast, select the mo
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TABLE 9.3 (cont.) Country Model use
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ANNEX I ABBREVIATIONS AND KEY TO SY
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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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GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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