The scattering properties of natural waters

The scattering properties of pure water provide us with a suitable baseline from which to go on to the properties of natural waters. We shall make use here of a valuable review by Morel (1974) of the optical properties of pure water and pure sea water. For measurements of the scattering properties, water purified by distillation in vacuo or by repeated filtration through small-pore-size filters must be used: ordinary distilled water contains too many particles. Scattering by pure water is of the density fluctuation type, and so varies markedly with wavelength. Experimentally, scattering is found to vary in accordance with 2~4'32 rather than IT4 as predicted by density fluctuation theory alone: this is a result of the variation of the refractive index of water with wavelength. Pure sea water (35-38% salinity) scatters about 30% more intensely than pure water. Table 4.1 lists values of the scattering coefficient for pure water and pure sea water at a number of wavelengths. The volume scattering function of pure water or pure sea water has, as predicted by density fluctuation theory, its minimum at 90 ° and rises symmetrically towards greater or lesser angles (Fig. 4.8).

When water molecules scatter light, most of the scattered light undergoes no change in wavelength - so-called elastic scattering. A small proportion of the scattered photons, however, when they interact with the scattering molecule, lose or gain a small amount of energy corresponding to a vibrational or rotational energy transition within the molecule, and so after scattering are shifted in wavelength. This is inelastic scattering. These photons appear in the scattered light as emission bands at wavelengths other than that of the exciting light, and are referred to as Raman emission lines, after the Indian physicist who discovered this phenomenon. A particularly strong Raman emission in the case of water arises from the O-H vibrational stretching mode: this shows up as an emission band roughly 100 nm on the long-wavelength side of the exciting wavelength. For an incident wavelength of 488 nm the Raman scattering coefficient of pure water is 2.4 x 10 4m-1.75,307 Raman scattering of water exhibits a strong inverse dependence on wavelength: over the range 250 to 500 nm, Bartlett et al. (1998) found this to correspond to 2~5-5 when normalized to units of energy and to l-5 3 when normalized to units of photons. They found no significant difference between the Raman scattering coefficients of sea water and pure water.

The scattering coefficients of natural waters are invariably much higher than those of pure water. Table 4.1 lists a selection of values from the

Table 4.1 Scattering coefficient values for various waters.

Water body

Wavelength (nm)

Scattering coefficient, b (m^1)

Reference

Pure water

400

0.058

939

450

0.0035

939

500

0.0022

939

550

0.0015

939

600

0.0011

939

Pure sea water

450

0.0045

939

500

0.0019

939

Marine waters

Atlantic Ocean

Sargasso Sea

633

0.023

758

440

0.04

636

Caribbean Sea

655

0.06

636

3 oceanic stations

544

0.06-0.30

747

Bahama Islands

530

0.117

1051

Mauritanian upwellinga

550

0.4-1.7

942

Mauritanian coastalb

550

0.9-3.7

942

Iceland coastal

655

0.1-0.5

576

New England shelf, summer

440

0.312

1269

Coccolithophore bloom, North

440 & 550

1-3

65

Atlantic

New Jersey, 2-15 km offshore

532

~3.4

1262

Great Bay Estuary (New Jersey)

532

~3.3

1262

Rhode R. Estuary (Chesapeake Bay)

720

1.7-55.3

428

Northern Gulf of Mexico: inside

532

5.08 ± 2.69

428

coastal barrier islands

10-20 km outside coastal barrier

532

2.02 ± 1.55

428

islands

Pacific Ocean

Central (Equator)

440

0.05

636

Galapogos Islands

655

0.07

636

440

0.08

636

126 oceanic stations

544

0.18 (av.)

747

Kieta Bay (Solomon Is.)

544

0.54

747

Great Barrier Reef (Australia),

555

0.093 ± 0.036

126

~18° S

Mossman-Daintree estuarine (NE

555

0.780 ± 0.405

126

Australia) 16° S. Dry season

Wet season

555

5.005 ± 9.381

126

Fitzroy R./Keppel Bay system

555

>20

1025

(NE Australia), 23 °S. Dry

season. Estuary station 2

Offshore (28 km)

555

0.002

1025

Lagoon, Tarawa atoll (Gilbert Is.)

544

1.04

747

Offshore, Southern California

530

0.275

1051

Monterey Bay, California

532

0.52 ± 0.31

1262

Table 4.1 (cont.)

Water body

Wavelength (nm)

Scattering coefficient, b (m-1)

Reference

San Diego Harbour, California

530

1.21-1.82

1051

Chatham Rise (East of New Zealand),

493

0.246

1218

av. of 17 stations

Indian Ocean

164 oceanic stations

544

0.18 (av.)

747

Tasman Sea

Australia

Jervis Bay, NSW

Entrance, 30 m depth

450-650

0.25

1053

Inshore, 15m depth

450-650

0.4-0.6

1053

New Zealand

North Island, 9 estuaries, mouth

400-700

1.1-4.8

1401

sites, low water

Mediterranean Sea

Tyrrhenian Sea (1000 m depth)

546

0.016

938

Western Mediterranean

655

0.04

569

Bay of Villefranche

546

0.1

938

North Sea

Fladen Ground

655

0.07-0.13

571

English Channel

546

0.65

938

Baltic Sea

Kattegat

655

0.15

636

South Baltic

655

0.20

636

Bothnian Gulf

655

0.28

636

Black Sea

33 stations

544

0.41 (av.)

747

Inland waters

North America

L. Pend Oreille

480

0.29

1076

L. Ontario, coastal

530-550

1.5-2.5

183

L. Ontario, Irondequoit

400-700

1.9-5.0

1445

Bay

Otisco L., N.Y.

400-700

0.9-4.6

347,1446

Onondaga L., N.Y.

400-700

2.2-11.0

348

Owasco L., N.Y.

400-700

1.0-4.6

347

Seneca R., N.Y.

400-700

3.1-11.5

347

Woods L., N.Y.

300-770

0.13-0.20

184

Dart's L., N.Y.

300-770

0.19-0.25

184

China

Lake Taihu

532

20.2 (3.3-48.1) 1325

Australia

(a) Southern tablelands

Corin Dam

400-700

1.5

703

Water body

Wavelength (nm)

Scattering coefficient, b (m-1)

Reference

Burrinjuck Dam

400-700

2.0-5.5

703

L. Ginninderra

400-700

4.4-21.6

703

L. Burley Griffin

400-700

2.8-52.6

703

L. George

400-700

55.3, 59.8

703

(b) Murray-Darling system

Murrumbidgee R., Gogeldrie

400-700

9-58

1014

Weir

Murray R., upstream of Darling

400-700

13.0

1014

confluence

Darling R., above confluence with

400-700

27.8-90.8

1014

Murray R.

(c) Northern Territory (Magela Creek

billabongs)

Mudginberri

400-700

2.2

725

Gulungul

400-700

5.7

725

Georgetown

400-700

64.3

725

(d) Tasmania (lakes)

Perry

400-700

0.27

152

Risdon Brook

400-700

1.8-2.7

152

Barrington

400-700

1.1-1.4

152

Pedder

400-700

0.6-1.3

152

Gordon

400-700

1.0

152

(e) Southeast Queensland, coastal

dune lakes

Basin

400-700

0.6

151

Boomanjin

400-700

1.1

151

Wabby

400-700

1.5

151

(f) South Australia

Mount Bold Reservoir

400-700

5.7-6.8

433

New Zealand

Waikato R. (330 km, L. Taupo to

the sea):

L. Taupo (0 km)

400-700

0.4

282

Ohakuri (77 km)

400-700

1.0

282

Karapiro (178 km)

400-700

1.2

282

Hamilton (213 km)

400-700

1.9

282

Tuakau (295 km)

400-700

6.3

282

Lakes:

Rotokakahi

400-700

1.5

1402

Rotorua

400-700

2.1

1402

D

400-700

3.1

1402

a Waters rich in phytoplankton. b High concentration of resuspended sediments.

3.0

i.a

1.6

1 ^

b

X.

i.a

'a

IjO

Z

0.6

04

0.2

Fig. 4.8 Volume scattering function of pure water for light of wavelength 550 nm. The values are calculated on the basis of density fluctuation scattering, assuming that b(90°) = 0.93 x 10 4 m"1 sr"1 and that P(6) = b(90°) (1 + 0.835 cos20) (following Morel, 1974).

literature. Even the lowest value — 0.016 m"1 at 546 nm for water from 1000 m depth in the Tyrrhenian Sea938 - is ten times as high as the value for pure water at that wavelength. Unproductive oceanic waters away from land have low values. Coastal and semi-enclosed marine waters have higher values due to the presence of resuspended sediments, river-borne terrigenous particulate material and phytoplankton. Resuspension of sediments is caused by wave action, tidal currents and storms. High levels of phytoplankton can give rise to quite high values of the scattering coefficient in oceanic upwelling areas, such as the Mauritanian upwelling off the west coast of Africa.942 In arid regions of the continents large amounts of dust are carried up into the atmosphere by wind, and when subsequently redeposited in adjoining areas of the ocean, can substantially increase scattering in the water.746 Scattering coefficient values are on average higher in inland and estuarine waters than in the open sea. Indeed the very high values that can occur in some turbid inland waters (Table 4.1) are unlikely to be equalled in the sea because high ionic strength promotes the aggregation and precipitation of colloidal clay minerals. Resuspension of sediments by wind-induced turbulence, especially in shallow waters, can substantially increase scattering in inland water bodies.995 Filter-feeding zooplankton, by packaging suspended clay particles into more rapidly settling faecal pellets, can substantially increase the rate of clearing of turbid lake water.463

Water in its solid form - snow or ice - is a highly scattering medium. On the basis of their measurements of spectral irradiance within, and transmittance through, sea ice in the Beaufort Sea (Arctic Ocean), Light et al. (2008) estimated that the scattering coefficient at 600 nm was 500 to 1100 m-1 in the surface layer, and 8 to 30 m-1 in the ice interior. Ehn et al. (2008) measured irradiance spectra at a series of increments within the bottom-most layers of landfast sea ice in Franklin Bay, Canada. On the basis of inverse radiative transfer modelling they estimated that for light at 400 nm, b was ~400m-1 in the bottom 0.1m of the ice, decreasing to 165m-1 in the 0.1 to 0.2m layer.

Volume scattering functions for natural waters differ markedly in shape from that of pure water. They are invariably characterized, even in the clearest waters, by an intense concentration of scattering at small forward angles. This, as we saw earlier, is typical of scattering by particles of diameter greater than the wavelength of light, and scattering in natural waters is primarily due to such particles. Figure 4.9 shows the volume scattering functions for a clear oceanic water and a moderately turbid, harbour water. They are quite similar in shape but there is a noticeable difference at angles greater than 90 °: scattering by the oceanic water shows a greater tendency to increase between 100 ° and 180 °. This is because at these larger angles density fluctuation scattering (which exhibits this kind of variation in this angular range - Fig. 4.8) becomes a significant proportion of the total in the case of the clear oceanic water (see below), but remains insignificant compared to particle scattering in the case of the harbour water.

A knowledge of the shape of the volume scattering function is essential for calculations on the nature of the underwater light field. Table 4.2 lists values for the normalized volume scattering function ¡3(9) = ¡(9)/b, and the cumulative scattering (between 0 ° and 0, as a proportion of the total) at a series of values of 0, for Tongue-of-the-Ocean (Bahamas) and San Diego Harbour water.1051 It will be noted that backscattering (0 > 90 °) constitutes 4.4% of total scattering in the case of the clear oceanic water but only 1.9% in the turbid harbour water. At a Crimean coastal water station, 600 m offshore in the Black Sea, Chami et al. (2005) from a large

Scattering angle, 6

Fig. 4.9 Volume scattering functions for a clear, and a moderately turbid, natural water. The curves for the clear ocean water (b = 0.037m-1) of Tongue-of-the-Ocean, Bahama Islands, and the somewhat turbid water (b = 1.583 m-1) of San Diego Harbour, have been plotted from the data of Petzold (1972).

Scattering angle, 6

Fig. 4.9 Volume scattering functions for a clear, and a moderately turbid, natural water. The curves for the clear ocean water (b = 0.037m-1) of Tongue-of-the-Ocean, Bahama Islands, and the somewhat turbid water (b = 1.583 m-1) of San Diego Harbour, have been plotted from the data of Petzold (1972).

number of measurements, found for the particulate fraction (which accounted for nearly all the scattering) an average backscattering ratio of -1.9%, at all three wavelengths used (443, 490 and 555nm), but the results did show high intrinsic variability (1.2 to 3.2%). Waters of a given broad optical type appear, on the basis of published measurements to date, to have ¡3(9) curves of rather similar shape. We may therefore take the data sets in Table 4.2 as being reasonably typical for clear oceanic, and moderately/highly turbid waters, respectively. Above a certain minimum level of turbidity, such that particle scattering is dominant at all angles, we would not expect the normalized volume scattering function to alter its shape with increasing turbidity, since the shape of the ¡3(9) curve is determined by the intrinsic scattering properties of the particles, not by their concentration. This is why the San Diego Harbour data may reasonably be applied to much murkier water. Indeed the ¡3(9) data in Table 4.2(b) are applicable to the majority of natural waters other than the very clear oceanic ones: Timofeeva (1971) has presented evidence that ¡3(9) is virtually the same for most natural waters. However, in the specialized

Table 4.2 Volume scattering data for green (530 nm) light for a clear and a turbid natural water. ~ (0)= normalized volume scattering function (p(0)/6). Cumulative scattering = 2^J0 ~(0) sin 0d0. Data from Petzold (1972).

(b) San Diego Harbour, California, USA, b = 1.583 m-1.

Table 4.2 Volume scattering data for green (530 nm) light for a clear and a turbid natural water. ~ (0)= normalized volume scattering function (p(0)/6). Cumulative scattering = 2^J0 ~(0) sin 0d0. Data from Petzold (1972).

(b) San Diego Harbour, California, USA, b = 1.583 m-1.

(a)

(b)

Cumulative

Cumulative

Angle 6 (°)

0(0) (sr-1)

scattering 0°!$

p(0) (sr-1)

scattering 0°!$

1.0

67.5

0.200

76.4

0.231

2.0

21.0

0.300

23.6

0.345

3.16

9.0

0.376

10.0

0.431

5.01

3.91

0.458

4.19

0.522

6.31

2.57

0.502

2.69

0.568

7.94

1.70

0.547

1.72

0.616

10.0

1.12

0.595

1.09

0.664

15.0

0.55

0.687

0.491

0.750

20.0

0.297

0.753

0.249

0.806

25.0

0.167

0.799

0.156

0.848

30.0

0.105

0.832

0.087

0.877

35.0

0.072

0.857

0.061

0.898

40.0

0.051

0.878

0.0434

0.916

50.0

0.0276

0.906

0.0234

0.940

60.0

0.0163

0.925

0.0136

0.956

75.0

0.0093

0.943

0.0073

0.971

90.0

0.0066

0.956

0.00457

0.981

105.0

0.0060

0.966

0.00323

0.987

120.0

0.0063

0.975

0.00276

0.992

135.0

0.0072

0.984

0.00250

0.995

150.0

0.0083

0.992

0.00259

0.997

165.0

0.0110

0.997

0.00323

0.999

180.0

0.0136

1.000

0.00392

1.000

situation of scattering being dominated by organic particles with a low refractive index, as might be the case in oceanic upwelling areas or eutrophic inland waters, a somewhat different set of ¡3(9) data might be appropriate.

Since the scattering effects of water itself are the same for every location, it is sometimes considered useful to subtract the contribution of the water so as to more clearly reveal the characteristics of the scattering by particles. In such cases we may refer to bp for the scattering coefficient, and bp($) for the volume scattering function, of the particu-late fraction on its own.

Agrawal (2005) has used the LISST-100 particle size analyzer (see above) to measure the volume scattering function over the range 0.1 to 20° in shallow (15m) water off the New Jersey (USA) coast. Time-averaged (one week duration) scattering phase functions were calculated for 2, 4, 6 and 8 m depth. Agreement with the Petzold phase function was fair at 2 m but less good at the other depths. These results suggest that, at least at small angles, scattering phase functions may be somewhat more variable in shape than earlier data have seemed to imply.

The contribution of density fluctuation scattering to total scattering varies not only with the type of water body but also with the angular range of scattering and wavelength of light under consideration. In the moderately or very turbid waters such as are typically found in inland, estuarine and some coastal water bodies, scattering at all angles and all visible wavelengths is predominantly due to the particles present. In contrast, in the very clear waters of the least fertile parts of the ocean, density fluctuation scattering can be a significant component of total scattering at short wavelengths and the major component at large scattering angles. In the Sargasso Sea, for example, Kullenberg (1968) found that density fluctuation scattering accounted for 3% of the total scattering coefficient at 655 nm and11% at 460 nm. For scattering angles from 60-75 to 180 °, however, the greater part of the scattering at both wavelengths was due to density fluctuation: in the case of blue (460 nm) light it accounted for only 0.3% of the scattering at 1 °, but contributed 89% at 135 °. Because of its importance as a component of backscattering in oceanic waters, density fluctuation scattering makes a disproportionately large contribution to the upwelling light stream. Morel and Prieur (1977) pointed out that even for a water with a total scattering coefficient of 0.29 m"1 (rather turbid by oceanic standards), while density fluctuation scattering accounts for only 1% of the total scattering coefficient, it contributes about 33% of the backscattering. Thus, even in the not-so-clear oceanic waters, density fluctuation scattering initiates a substantial proportion of the upwelling light flux.

Compared with density fluctuation scattering by pure water itself, particle scattering is less sensitive to wavelength. Since, even in a very clear oceanic water, density fluctuation scattering makes up only a small proportion of the total scattering coefficient, the dependence of this scattering on I"4'3 does not by itself bring about a marked variation of the value of b for natural waters with wavelength. There is, however, some evidence that in particle-dominated natural waters, the value of b varies inversely with wavelength. For 63 stations in the Arabian Sea, Northern Gulf of Mexico and coastal North Carolina, Gould et al. (1999) obtained spectral scattering data over the range 412 to 715 nm, by difference between beam attenuation coefficient and absorption coefficient measurements made with an ac-9 instrument. Scattering coefficients at 412 nm ranged from 0.2 to 15.1 m-1. The value of b(l) was found to decrease in an approximately linear manner with wavelength, but the slope of the spectral scattering relationship decreased progressively from high-scattering turbid waters dominated by suspended sediments to lower-scattering clear waters dominated by phytoplankton.

Using the same technique, Blondeau-Patissier et al. (2009) measured b(l) at a number of locations in the Great Barrier Reef region (Australia), covering inshore, estuarine, lagoonal and reef waters. Scattering decreased with wavelength approximately in conformity with b(l) / l-7b where the average values of gb for seven sites ranged from ^0.43 to 0.75, although highly variable at each site. In a variety of stations within the large (670 km2) and deep (av. 44 m) Lake Biwa in Japan, Belzile et al. (2002a) found, using the ac-9 difference method, that b decreased approximately linearly with wavelength. Expressed as a power law, the exponent gb varied from 0.50 to 1.06 (mean 0.78). For the turbid waters of Lake Taihu (China), dominated by inorganic suspended matter, Sun et al. (2009) found, using the ac-9 difference method, a decrease of b(l) with wavelength, expressible as a power law with gb = 0.729.

By contrast, in shallow (10-30 m) inshore waters in Jervis Bay (SE Australia), Phillips and Kirk (1984) found little variation in scattering coefficient over the spectral range, 450 to 650 nm. A similar finding was made by Roesler and Zaneveld (1994) in the waters of East Sound, Washington. Also, for Case 2 (coastal) waters around Europe, Babin et al. (2003a) found only a slight tendency for bp(l) to decrease towards longer wavelengths. For Case 1 (oceanic, phytoplankton-dominated) waters they found a somewhat greater tendency for scattering to decrease towards longer wavelength, but the scattering spectra were clearly affected by absorption, with significant minima being evident in the main phyto-plankton absorption bands in the blue and the red wavebands. For the specific scattering coefficient (scattering per unit mass) at 555 nm, average values of 1.0 and 0.5 m2 g-1 were found for Case 1 and Case 2 waters, respectively.51

The general behaviour of total scattering with respect to wavelength, as just described, can conceal somewhat different patterns of the wavelength variation of scattering at certain specific angles. When backscattering alone is considered, then in oceanic waters, in which as we saw above density fluctuation scattering is a major contributor for 0 > 90 a more marked inverse dependence on wavelength is to be expected. In the Great Barrier Reef region (Australia, see above) Blondeau-Patissier et al. (2009) found that backscattering (determined directly) decreased with wavelength with an average value of the exponent, gbb, of — 2.0 for the reef and open waters, but in the range —0.65 to 0.95 for the other locations (inshore, estuarine, lagoonal). For a large number of US near-shore coastal waters, Snyder et al. (2008) found that particulate backscattering varied inversely with wavelength, clustered around a power-law exponent of —0.94.

If the scattering particles have significant light absorption, this can affect the wavelength dependence of scattering. With increasing wavelength the real part of the refractive index undergoes a dip and then an increase as it passes through an absorption band,1395 and associated with the dip there is a decrease in the scattering coefficient. In their studies on light scattering in coastal Crimean waters, Chami et al. (2006b) found that as the concentration of particles absorbing strongly in the blue region increased, the ratio of bp(140 °) at 443 nm to that at 555 nm decreased from —1.2 to —0.7.

McKee and Cunningham (2005) measured the backscattering ratio (bb/b) at 470 and 676 nm at 120 stations in the Irish Sea. If the shape of the scattering phase function in this oceanic region is the same at all wavelengths, then the backscattering ratio should everywhere be the same in the blue as it is in the red, i.e. (bb/b)470/(bb/b)676 (which they indicated by B) should be —1.0. In fact in less than 5% of stations was this function between 0.9 and 1.1. At most stations the backscattering ratio was greater in the blue than in the red. About 53% of stations had B « 1.2, and the rest had greater values. Clearly, then we must expect some variation in the shape of the scattering phase function with wavelength, and the extent to which this occurs will not be the same at all points in the ocean. From the data of Petzold (1972) in Table 4.2 it can be seen that the backscattering ratio at 530 nm was 0.044 for the clear ocean water (Bahama Islands), and 0.019 for the turbid (San Diego) harbour water. In the Oslo Fjord, Aas et al. (2005) found, on the basis of a large number of measurements, a backscattering ratio (for the particulate fraction) of 0.018 to 0.022 for wavelengths from 412 to 665 nm. For the turbid waters of Chesapeake Bay (USA) Tzortziou et al. (2006) found the backscattering ratio at 530 nm to have an average value of 0.0128 ± 0.0032. For the turbid, inorganic particle-dominated, waters of Lake Taihu (China), Sun et al. (2009) found the backscattering ratio at 532 nm to have an average value of 0.013, but with a range of 0.005 to 0.027.

Since total light scattering in natural waters is dominated by the par-ticulate contribution, it increases broadly in proportion to the concentration of suspended particulate matter. For example, Jones and Wills (1956), using suspensions of kaolin (which would scatter but not significantly absorb light), found a linear relation between the beam attenuation coefficient (approximately equal in this system to the scattering coefficient) for green (550 nm) light and the concentration of suspended matter. Approximately linear relations between scattering coefficient and concentration of suspended matter have been observed for natural aquatic particulates by other workers.119,1301 The constant of proportionality can, however, vary from one kind of suspended matter to another:333 the refractive index and the size distribution of the particles both influence the relation between b and sediment concentration.

The concentration of particulate matter, and therefore the intensity of scattering, in inland and estuarine waters, and to some extent in coastal waters, is strongly influenced, not only by the nature of the physical environment (climate, topography, soil type, etc.) but also by the uses to which the land is put. The more thickly the ground is covered with vegetation, the less erosion and so the less transference of soil particles to surface waters occurs. Erosion is very low under undisturbed forest and is generally not high from permanent grassland. Logging activities and overgrazing of pastures can cause serious erosion even in these environments. Ground that is broken up for crop planting is susceptible to erosion until such time as the crop canopy is established. The extent to which erosion occurs in these different terrestrial systems depends not only on the extent to which the ground is protected by vegetation, but also on the nature of the soil (some types being more easily eroded than others), the average slope (the greater the slope, the greater the erosion) and the intensity of the rainfall (a short torrential downpour causes more erosion than the same amount of rain falling over a longer period). The average lifetime of the soil particles in suspension once they have been transferred into the aquatic sphere is quite variable and depends on their size and mineral chemistry, and on the ionic composition of the water: some fine clay particles for example, particularly in waters of low electrolyte content, can remain in suspension for long periods with drastic consequences for light attenuation in the water bodies that contain them.

It is clear that to understand the underwater light field, we must know not only about the water itself but also about the surrounding land forms, which to a large degree confer upon the aquatic medium the particular optical properties it possesses.

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