northernmost region, and that most were juveniles (withL<L50).By comparison, Norway pout were present mainly in the north and northwest, with a population that was more evenly balanced between adults and juveniles.
4.2.2.3.2 Marine mammals
A biogeographical database, including information from marine mammal sightings, is available from the Ocean Biogeographic Information System (obis, www).The abundance of different species varies enormously.Global population estimates from Bowen and Siniff (1999) for various periods in the 1980s and 1990s include
— for pinnipeds, between 12 000 000 crabeater seals18 or 6 000 000 harp seals to fewer than 500 Mediterranean monk seals;
— for cetacea, between 2 000 000 sperm whales or 2 000 000 spinner dolphins19to 500 Indus river dolphins and fewer than 1000 northern right whales;
— for sirenians, between 100 000 dugongs or 100 000 sea otters to just 2500 Florida manatees.
12 m/s (for higher wind speeds, the opposite is true).Kent and Taylor (1997) compare various alternatives to WMO 1100 and show that, of the scales considered, those due to da Silvaet al.(1994) and to Lindau (1995) agree best with observation.Table 4.10 shows the revised Beaufort scale of da Silvaet al.(1994), preferred here over Lindau Figure 4.18. Geographical distribution in the North Sea by season, 1985–1987: herring . . . (reprinted from Knijnet al., 1993).
(1995) because, in addition to an average value ofvfor each wind force, an indication is given of the likelyspreadinv.The first column shows the Beaufort force number and corresponding WMO description.An alternative description used for the same scale, referred to by Bowditch (1966) as the ‘‘seaman’s term’’, is included for compar- 4.3 Properties of the sea surface 161 Sec.4.3]
Figure 4.18(cont.). . . .and Norway pout (reprinted from Knijnet al., 1993).
Table 4.10. WMO Beaufort wind force scale and estimated wind speedv20due to da Silvaet al.(1994) at a measurement height of 20 m.The final column shows the wind speedv10converted to a standard height of 10 m, assuming air temperature is equal to water temperature (see Figure 4.19).
Beaufort force Photograph Appearance at sea if fetch and duration of Estimated Wind speed WMO description reproduced the blow have been sufficient to develop wind speed at standard
Seaman’s term from the sea fully height
(Bowditch 1966) NOAA (http) (WMO, 1970) v20/m s1 v10/m s1
0 Sea like a mirror 0.0–1.0 0.0–1.0
Calm Calm
1 Ripples with the appearance of scales are 1.0–3.0 1.0–2.9 Light air formed, but without foam crests
Light air
2 Small wavelets, still short but more 3.0–4.6 2.9–4.3 Light breeze pronounced; crests have a glassy
Light breeze appearance and do not break
3 Large wavelets; crests begin to break; 4.6–6.8 4.3–6.4 Gentle breeze foam of glassy appearance; perhaps
Gentle breeze scattered white horses
4 Small waves, becoming longer; fairly 6.8–9.8 6.4–9.2 Moderate breeze frequent white horses
Moderate breeze
5 Moderate waves, taking a more 9.8–12.0 9.2–11.3
Fresh breeze pronounced long form; many white Fresh breeze horses are formed (chance of some spray)
6 Large waves begin to form; the white 12.0–15.0 11.3–14.1 Strong breeze foam crests are more extensive
Strong breeze everywhere (probably some spray)
4.3 Properties of the sea surface 163 Sec.4.3]
Beaufort force Photograph Appearance at sea if fetch and duration of Estimated Wind speed WMO description reproduced the blow have been sufficient to develop wind speed at standard
Seaman’s term from the sea fully height
(Bowditch 1966) NOAA (http) (WMO, 1970) v20/m s1 v10/m s1
7 Sea heaps up and white foam from 15.0–17.8 14.1–16.5
Near gale breaking waves begins to be blown in Moderate gale streaks along the direction of the wind
8 Moderately high waves of greater length; 17.8–21.0 16.5–19.5 Gale edges of crests begin to break into the
Fresh gale spindrift; the foam is blown in well- marked streaks along the direction of the wind
9 High waves; dense streaks of foam along 21.0–24.2 19.5–22.5 Strong gale the direction of the wind; crests of waves
Strong gale begin to topple, tumble and roll over;
spray may affect visibility
10 Very high waves with long overhanging 24.2–27.8 22.5–25.9 Storm crests; the resulting foam, in great
Whole gale patches, is blown in dense white streaks along the direction of the wind; on the whole, the surface of the sea takes a white appearance; the tumbling of the sea becomes heavy and shock-like; visibility affected
11 Exceptionally high waves (small and 27.8–31.4 25.9–29.0 Violent storm medium sized ships might be for a time
Storm lost to view behind the waves); the sea is completely covered with long white patches of foam lying along the direction of the wind; everywhere the edges of the wave crests are blown into froth; visibility affected
12 The air is filled with foam and spray; sea >31.4 >29.0 Hurricane completely white with driving spray;
Hurricane visibility very seriously affected
ison.Some of these descriptions are ambiguous unless the Beaufort force is also quoted.For example, the same word ‘‘storm’’ can mean either force 10 or force 11 depending on whether the WMO or seaman’s term is intended.A more complete physical description is provided in columns 2 and 3 in the form of an image (NOAA, http) and text (WMO, 1970).Finally, columns 4 and 5 contain the likely spread of wind speeds (at two different measurement heights of 20 and 10 m, denotedv20 and v10respectively, and averaged over 10 min in time) associated with these conditions.
Figure 4.19 shows the conversion factors between these two measurement heights.
The definingcharacteristics of the Beaufort scale are the physical descriptions under the heading ‘‘appearance at sea’’.All other parameters, including quoted wind speed values, have the status of derived or likely parameters for the stated appear- ance.Wind speed is given here in units of meters per second, in keeping with the adoption of SI units throughout this book.For wind speed values reported in knots (kn), the conversion is (see Appendix B)
1 kn¼ ð1852=3600Þm=s0:5144 m=s:
In an attempt to address the shortcomings of code 1100, which is based on measure- ments made in the late 19th and early 20th centuries, in 1970 the WMO published an updated Beaufort Scale (dubbed ‘‘proposed new Code 1100’’ and referred to by Kent Figure 4.19. Wind speed scaling factors to convert from a 20 m reference height to the standard reference height of 10 m (Dobson, 1981).The legend shows the temperature difference jTairTwaterjinC.Red curves indicate stable conditions (Tair>Twater); blue curves indicate unstable conditions (Tair<Twater).
and Taylor, 1997 as CMM IV21), intended for scientific use (WMO, 1970).Wind speed estimates based on the WMO 1100 and WMO CMM-IV scales are compared in Table 4.11 with those of the modern values of da Silva from Table 4.10. Treating da Silva’s scale as a reference, WMO 1100 underestimates wind speed by up to 1 m/s for Beaufort force 1–5, and overestimates it by up to 3 m/s for force 7-11, while the CMM-IV scale generally tends to underestimate wind speed.This bias (the difference between columns 5 and 6 of Table 4.11) increases with increasing wind force up to a maximum of about 1.8 m/s for force 9 and above. Kent and Taylor conclude that
‘‘the operationally used WMO1100 seemed to be better than the CMM-IV scale recommended for scientific use.’’
Another widely used measure of sea surface conditions issea state, which is a measure of the height of surface waves rather than wind speed, although the two are related.As with the Beaufort scale, there is no single, universally accepted definition, but the one known as WMO code 3700 is in widespread use (see Table 4.12).
4.3 Properties of the sea surface 165 Sec.4.3]
Table 4.11. Comparison of wind speed estimates for Beaufort force 1–11 based on WMO code 1100 and CMM-IV with those of da Silva.All are average values in meters per second except the shaded column, which shows wind speed ranges in knots for the original WMO code 1100.
Beaufort WMO 1100 WMO 1100 da Silva da Silva WMO CMM-IV force (NOAA, http) (Table 4.10) (Table 4.10) (WMO, 1970)
spread/kn av./m s1 av./m s1 av./m s1 av./m s1 meas.
height: 10 m 10 m 10 m 20 m 20 m
1 1–3 1.0 2.0 2.0 2.0
2 4–6 2.6 3.6 3.8 3.6
3 7–10 4.4 5.4 5.7 5.6
4 11–16 6.9 7.8 8.3 7.9
5 17–21 9.8 10.3 10.9 10.2
6 22–27 12.6 12.7 13.5 12.6
7 28–33 15.7 15.3 16.4 15.1
8 34–40 19.0 18.0 19.4 17.8
9 41–47 22.6 21.0 22.6 20.8
10 48–55 26.5 24.2 26.0 24.2
11 56–63 30.6 27.5 29.6 28.0
21CMM IV stands for ‘‘Commission for Maritime Meteorology IV’’.
4.3.2 Surface roughness
Sea surface roughness is determined by the spectrum of surface waves propagating along it.An overview of surface waves and associated spectra, including the effect of wind fetch, is provided by Robinson (2004).Two surface roughness spectra are described in Sections 4.3.2.1 and 4.3.2.2, both applicable to open ocean conditions.
Of these, the Pierson–Moskowitz spectrum is in modern use, while the Neumann–
Pierson spectrum is needed for comparison with results from older literature.
The RMS slope of the sea surface has been measured optically by Cox and Munk (1954) and related empirically to the wind speed.Their equation relating these two parameters is22
2¼ ð3þ5:12^vv10Þ 103: ð4:58Þ
4.3.2.1 Pierson–Moskowitz spectrum
The statistics of sea surface waves can be represented by a spectrum due to Pierson and Moskowitz (1964).The Pierson–Moskowitz (PM) wave height spectral density
Table 4.12. Definition of sea state (WMO code 3700).
Sea state code WMO code 3700(NODC, www) Description Significant wave heighta
in meters (exact)
0 Calm (glassy) 0
1 Calm (rippled) 0–0.1
2 Smooth (wavelets) 0.1–0.5
3 Slight 0.5–1.25
4 Moderate 1.25–2.5
5 Rough 2.5–4
6 Very rough 4–6
7 High 6–9
8 Very high 9–14
9 Phenomenal >14
aSee Equation (4.65).
22The actual measurement height for wind speed was 12.5 m (41 ft). For simplicity, it is assumed here that the difference between the wind speeds at 10 m and 12.5 m may be neglected.
(of squared displacement from the mean surface)vs.surface wave frequencyO, for wind speed between 0 m/s and 20 m/s, is of the form
SðOÞ ¼CPMg2
O5exp BPM
g Ov20
4
; ð4:59Þ
where23v20is the wind speed at an anemometer height of 20 m;gis acceleration due to gravity; andBPMandCPMare dimensionless constants given by
BPM¼0:74 ð4:60Þ
and
CPM¼0:0081: ð4:61Þ
The RMS roughness is the square root of the variance of the sea surface elevation about its mean value.Thus (Chapman, 1983)
2PM¼ CPM 4BPM
v420
g2: ð4:62Þ
Substituting for numerical values, this becomes
2PM¼DPMv420; ð4:63Þ where
DPM¼2:85105 m2s4: ð4:64Þ A common descriptor of the sea surface issignificant wave height Hsig, often referred to simply as ‘‘wave height’’.This parameter is historically defined as the average peak-to-trough height of the highest third of all waves.With this definitionHsig is given to a good approximation by four times the RMS roughness, whereas the American Meteorological Societydefines Hsig as precisely this value, that is,
Hsig4: ð4:65Þ
Another descriptor sometimes used is the mean peak-to-trough wave heightHH, given approximately by
H
H2:5: ð4:66Þ
Using Equation (4.62) one can estimate the RMS roughness and hence the wave height for each Beaufort force, shown in Table 4.13 for Beaufort force 0 to 7. The inverse operation converts wave height to wind speed, as shown in Table 4.14 for sea states 0 to 6.
4.3.2.2 Neumann–Pierson spectrum
An alternative spectrum that is of historical importance, as it is used in much early theoretical work on surface wave scattering, is the Neumann–Pierson (NP) spectrum, 4.3 Properties of the sea surface 167 Sec.4.3]
23The actual wind speed measurement height of 19.5 m is rounded here to 20 m.
Table 4.13. Beaufort wind force: relationship between wind speed and wave height.
Beaufort WMO description Wind speed Wave height Approximate
force (Table 4.10) (Pierson–Moskowitz sea state
spectrum) equivalent v10=m s1 v20=m s1 =m Hsig=m
0 Calm 0–1.0 0–1.0 0.000–0.006 0.000–0.024 0–1
1 Light air 1.0–2.9 1.0–3.0 0.006–0.050 0.024–0.20 1–2 2 Light breeze 2.9–4.3 3.0–4.6 0.050–0.11 0.20–0.44 2 3 Gentle breeze 4.3–6.4 4.6–6.8 0.11–0.24 0.44–0.97 2–3 4 Moderate breeze 6.4–9.2 6.8–9.8 0.24–0.51 0.97–2.03 3–4 5 Fresh breeze 9.2–11.3 9.8–12.0 0.51–0.77 2.03–3.10 4–5 6 Strong breeze 11.3–14.1 12.0–15.0 0.77–1.19 3.10–4.77 5–6 7 Near gale 14.1–16.5 15.0–17.8 1.19–1.68 4.77–6.72 6–7
Table 4.14. Sea state: relationship between wave height and wind speed.
Sea state Description Significant RMS Wind speed of Approximate (WMO code wave roughness corresponding Pierson–Beaufort
3700) height Moskowitz spectrum force
equivalent Hsig/m /m v10=m s1 v20=m s1
0 Calm (glassy) 0.00 0 0.0 0.0 0
1 Calm (rippled) 0.00–0.10 0–0.025 0.0–2.1 0.0–2.2 0–1 2 Smooth (wavelets) 0.10–0.50 0.025–0.12 2.1–4.6 2.2–4.8 1–2
3 Slight 0.50–1.25 0.12–0.31 4.6–7.2 4.8–7.7 3–4
4 Moderate 1.25–2.50 0.31–0.62 7.2–10.2 7.7–10.8 4–5
5 Rough 2.50–4.00 0.62–1.00 10.2–12.9 10.8–13.7 5–6
6 Very rough 4.00–6.00 1.00–1.50 12.9–15.7 13.7–16.8 6–7
given by (Neumann and Pierson, 1957, 1966) SðOÞ ¼ANP 1
O6exp 2 g Ov5
2
; ð4:67Þ
whereANP is a constant equal to 2.4 m2s5; and v5 is the wind speed at an anem- ometer height24of 5 m.
The RMS wave height roughness corresponding to the NP spectrum is given by (Ainslie, 2005)
2NP¼ANP31=2 211=2
v5 g
5
: ð4:68Þ
Substituting for numerical values yields
2NP¼DNPv55; ð4:69Þ where
DNP¼3:11106 m3s5: ð4:70Þ
4.3.3 Wind-generated bubbles
Wind-generated bubbles close to the sea surface are caused primarily by breaking waves.The number of whitecaps, and hence the bubble population density, is highly correlated with wind speed.Bubble density is highest close to the sea surface and decreases with increasing depth away from the sea surface.Some measurements of bubble population density, from Trevorrow (2003), are shown in Figure 4.20.
The calculation of sound speed and attenuation (see Chapter 5) requires as input the bubble population densitynðaÞas a function of wind speed, depth, and bubble radius, in principlevs.position in three-dimensional (3D) space.A detailed 3D model of near-surface bubble distribution, including the bubble plumes, is given by Novarini et al.(1998).A range-averaged model, retaining only depth dependence, is described below.
The following recipe, based on measurements by Johnson and Cooke (1979), is due originally to Hall (1989) and modified by Novarini as described by Keifferet al.
(1995).The resulting bubble population model, referred to henceforth as the
‘‘Hall–Novarini’’ model, is
nða;zÞ ¼n0uðv10ÞDðz;v10ÞGða;zÞ; ð4:71Þ wheren0 is a constant equal to
n0 ¼1:61010 m4: ð4:72Þ The other factors are uðv10Þ,Dðz;v10Þ, and Gða;zÞwhich describe the dependence, respectively, on wind speed at 10 metersv10, depth from the surface z, and bubble 4.3 Properties of the sea surface 169 Sec.4.3]
24The wind speed measurement height is not specified explicitly by Neumann and Pierson (1957), but the implied value is approximately 5.5 m, rounded here to 5 m.