Physical Properties of Seawater

CHAPTER 3

3.1. MOLECULAR PROPERTIES in the oceans, because water is such an effective OF WATER heat reservoir (see Section S15.6 located on the textbook Web site Many of the unique characteristics of the ; “S” denotes supplemental ocean can be ascribed to the nature of water material). itself. Consisting of two positively charged As seawater is heated, molecular activity hydrogen ions and a single negatively charged increases and thermal expansion occurs, oxygen ion, water is arranged as a polar mole- reducing the density. In freshwater, as tempera- cule having positive and negative sides. This ture increases from the freezing point up to about molecular polarity leads to water’s high dielec- 4C, the added heat energy forms molecular tric constant (ability to withstand or balance an chains whose alignment causes the water to electric ﬁeld). Water is able to dissolve many shrink, increasing the density. As temperature substances because the polar water molecules increases above this point, the chains break align to shield each ion, resisting the recombina- down and thermal expansion takes over; this tion of the ions. The ocean’s salty character is explains why fresh water has a density maximum due to the abundance of dissolved ions. at about 4C rather than at its freezing point. In The polar nature of the water molecule seawater, these molecular effects are combined causes it to form polymer-like chains of up to with the inﬂuence of salt, which inhibits the eight molecules. Approximately 90% of the formation of the chains. For the normal range of water molecules are found in these chains. salinity in the ocean, the maximum density Energy is required to produce these chains, occurs at the freezing point, which is depressed which is related to water’s heat capacity. Water to well below 0C (Figure 3.1). has the highest heat capacity of all liquids Water has a very high heat of evaporation (or except ammonia. This high heat capacity is the heat of vaporization) and a very high heat of primary reason the ocean is so important in fusion. The heat of vaporization is the amount the world climate system. Unlike the land and of energy required to change water from a liquid atmosphere, the ocean stores large amounts of to a gas; the heat of fusion is the amount of heat energy it receives from the sun. This heat energy required to change water from a solid is carried by ocean currents, exporting or to a liquid. These quantities are relevant for importing heat to various regions. Approxi- our climate as water changes state from a liquid mately 90% of the anthropogenic heating in the ocean to water vapor in the atmosphere associated with global climate change is stored and to ice at polar latitudes. The heat energy

Salinity FIGURE 3.1 Values of density st 0 10 20 30 40 (curved lines) and the loci of maximum 30 density and freezing point (at atmospheric pressure) for seawater as functions of temperature and salinity. The full density r 3 is 1000 þ st with units of kg/m .

0 5

10 15 20 25

30 10 90% of ocean Temperature (°C) Temperature

Temp. of max. density Mean T&S Freezing point Most 0 abundant –2

involved in these state changes is a factor in pressure is the Pascal, where 1 Pa ¼ 1 N/m2. weather and in the global climate system. Atmospheric pressure is usually measured in Water’s chain-like molecular structure also bars where 1 bar ¼ 106 dynes/cm2 ¼ 105 Pa. produces its high surface tension. The chains Ocean pressure is usually reported in decibars resist shear, giving water a high viscosity for where 1 dbar ¼ 0.1 bar ¼ 105 dyne/cm2 ¼ its atomic weight. This high viscosity permits 104 Pa. formation of surface capillary waves, with wave- The force due to pressure arises when there is lengths on the order of centimeters; the restoring a difference in pressure between two points. The forces for these waves include surface tension as force is directed from high to low pressure. well as gravity. Despite their small size, capil- Hence we say the force is oriented “down the lary waves are important in determining the pressure gradient” since the gradient is directed frictional stress between wind and water. This from low to high pressure. In the ocean, the stress generates larger waves and propels the downward force of gravity is mostly balanced frictionally driven circulation of the ocean’s by an upward pressure gradient force; that is, surface layer. the water is not accelerating downward. Instead, it is kept from collapsing by the upward pressure gradient force. Therefore pressure 3.2. PRESSURE increases with increasing depth. This balance of downward gravity force and upward pres- Pressure is the normal force per unit area sure gradient force, with no motion, is called exerted by water (or air in the atmosphere) on hydrostatic balance (Section 7.6.1). both sides of the unit area. The units of force The pressure at a given depth depends on the are (mass length/time2). The units of pressure mass of water lying above that depth. A pressure are (force/length2) or (mass/[length time2]). change of 1 dbar occurs over a depth change of Pressure units in centimeters-gram-second (cgs) slightly less than 1 m (Figure 3.2 and Table 3.1). are dynes/cm2 and in meter-kilogram-second Pressure in the ocean thus varies from near (mks) they are Newtons/m2. A special unit for zero (surface) to 10,000 dbar (deepest). Pressure PRESSURE 31

is usually measured in conjunction with other 6000 seawater properties such as temperature, salinity, and current speeds. The properties are often presented as a function of pressure rather than depth.

4000 Horizontal pressure gradients drive the horizontal flows in the ocean. For large-scale currents (of horizontal scale greater than a kilo- meter), the horizontal flows are much stronger Depth (m) than their associated vertical flows and are 2000 usually geostrophic (Chapter 7). The horizontal pressure differences that drive the ocean currents are on the order of one decibar over hundreds or thousands of kilometers. This is much smaller than the vertical pressure 0 0 2000 4000 6000 gradient, but the latter is balanced by the down- Pressure (dbar) ward force of gravity and does not drive a flow. Horizontal variations in mass distribution FIGURE 3.2 The relation between depth and pressure, using a station in the northwest Pacific at 41 53’N, 146 create the horizontal variation in pressure in 18’W. the ocean. The pressure is greater where the water column above a given depth is heavier either because it is higher density or because it is thicker or both. TABLE 3.1 Comparison of Pressure (dbar) and Depth Pressure is usually measured with an elec- (m) at Standard Oceanographic Depths tronic instrument called a transducer. The accu- Using the UNESCO (1983) Algorithms racy and precision of pressure measurements is high enough that other properties such as Pressure (dbar) Depth (m) Difference (%) temperature, salinity, current speeds, and so 000forth can be displayed as a function of pressure. 100 99 1 However, the accuracy, about 3 dbar at depth, is not sufficient to measure the horizontal pressure 200 198 1 gradients. Therefore other methods, such as the 300 297 1 geostrophic method, or direct velocity measure- 500 495 1 ments, must be used to determine the actual flow. Prior to the 1960s and 1970s, pressure 1000 990 1 was measured using a pair of mercury ther- 1500 1453 1.1 mometers, one of which was in a vacuum 2000 1975 1.3 (“protected” by a glass case) and not affected by pressure while the other was exposed to the 3000 2956 1.5 water (“unprotected”) and affected by pressure, 4000 3932 1.7 as described in the following section. More 5000 4904 1.9 information about these instruments and methods is provided in Section S6.3 of the 6000 5872 2.1 supplementary materials on the textbook Web Percent difference ¼ (pressure depth)/pressure 100%. site. 32 3. PHYSICAL PROPERTIES OF SEAWATER 3.3. THERMAL PROPERTIES OF A change of 1C is the same as a change of 1 K. A SEAWATER: TEMPERATURE, temperature of 0C is equal to 273.16 K. The HEAT, AND POTENTIAL range of temperature in the ocean is from the TEMPERATURE freezing point, which is around 1.7C (depending on salinity), to a maximum of around 30C One of the most important physical charac- in the tropical oceans. This range is considerably teristics of seawater is its temperature. Temper- smaller than the range of air temperatures. As ature was one of the first ocean parameters to be for all other physical properties, the tempera- measured and remains the most widely ture scale has been refined by international observed. In most of the ocean, temperature is agreement. The temperature scale used most the primary determinant of density; salinity is often is the International Practical Temperature of primary importance mainly in high latitude Scale of 1968 (IPTS-68). It has been superseded regions of excess rainfall or sea ice processes by the 1990 International Temperature Scale (Section 5.4). In the mid-latitude upper ocean (ITS-90). Temperatures should be reported in (between the surface and 500 m), temperature ITS-90, but all of the computer algorithms is the primary parameter determining sound related to the equation of state that date from speed. (Temperature measurement techniques 1980 predate ITS-90. Therefore, ITS-90 tempera- are described in Section S6.4.2 of the supple- tures should be converted to IPTS-68 by multi- mentary materials on the textbook Web site.) plying ITS-90 by 0.99976 before using the 1980 The relation between temperature and equation of state subroutines. heat content is described in Section 3.3.2. As The ease with which temperature can be a parcel of water is compressed or expanded, measured has led to a wide variety of oceanic its temperature changes. The concept of “poten- and satellite instrumentation to measure ocean tial temperature” (Section 3.3.3) takes these temperatures (see supplementary material in pressure effects into account. Section S6.4.2 on the textbook Web site). Mercury thermometers were in common use from the late 1700s through the 1980s. Reversing 3.3.1. Temperature (mercury) thermometers, invented by Negretti and Zamba in 1874, were used on water sample Temperature is a thermodynamic property of bottles through the mid-1980s. These thermom- a fluid, due to the activity or energy of mole- eters have ingenious glasswork that cuts off the cules and atoms in the fluid. Temperature is mercury column when the thermometers are higher for higher energy or heat content. Heat flipped upside down by the shipboard observer, and temperature are related through the specific thus recording the temperature at depth. The heat (Section 3.3.2). accuracy and precision of reversing thermome- Temperature (T) in oceanography is usually ters is 0.004 and 0.002C. Thermistors are now expressed using the Celsius scale (C), except used for most in situ measurements. The best in calculations of heat content, when tempera- thermistors used most often in oceanographic ture is expressed in degrees Kelvin (K). When instruments have an accuracy of 0.002C and the heat content is zero (no molecular activity), precision of 0.0005e0.001C. the temperature is absolute zero on the Kelvin Satellites detect thermal infrared electromag- scale. (The usual convention for meteorology is netic radiation from the sea surface; this radia- degrees Kelvin, except in weather reporting, tion is related to temperature. Satellite sea since atmospheric temperature decreases to surface temperature (SST) accuracy is about very low values in the stratosphere and above.) 0.5e0.8 K, plus an additional error due to the THERMAL PROPERTIES OF SEAWATER: TEMPERATURE, HEAT, AND POTENTIAL TEMPERATURE 33 presence or absence of a very thin (10 mm) skin Maps of heat flux are based on measurements layer that can reduce the desired bulk (1e2m) of the conditions that cause heat exchange observation of SST by about 0.3 K. (Section 5.4). As a simple example, what heat loss from a 100 m thick layer of the ocean is needed to change the temperature by 1Cin30 3.3.2. Heat days? The required heat flux is rcpDTV/Dt. Typical values of seawater density and specific The heat content of seawater is its thermody- heat are about 1025 kg/m3 and 3850 J/(kg C). namic energy. It is calculated using the V is the volume of the 100 m thick layer, which measured temperature, measured density, and is 1 m2 across, and t is the amount of time the specific heat of seawater. The specific heat D (sec). The calculated heat change is 152 W. The is a thermodynamic property of seawater heat flux through the surface area of 1 m2 is expressing how heat content changes with thus about 152 W/m2. In Chapter 5 all of temperature. Specific heat depends on tempera- the components of ocean heat flux and their ture, pressure, and salinity. It is obtained from geographic distributions are described. formulas that were derived from laboratory measurements of seawater. Tables of values or computer subroutines supplied by UNESCO 3.3.3. Potential Temperature (1983) are available for calculating specific Seawater is almost, but not quite, incom- heat. The heat content per unit volume, Q, is pressible. A pressure increase causes a water computed from the measured temperature parcel to compress slightly. This increases the using temperature in the water parcel if it occurs without exchange of heat with the surrounding Q ¼ rcpT (3.1) water (adiabatic compression). Conversely if a water parcel is moved from a higher to a lower where T is temperature in degrees Kelvin, r is pressure, it expands and its temperature the seawater density, and cp is the specific heat decreases. These changes in temperature are of seawater. The mks units of heat are Joules, unrelated to surface or deep sources of heat. It that is, units of energy. The rate of time change is often desirable to compare the temperatures of heat is expressed in Watts, where 1 W ¼ 1 of two parcels of water that are found at J/sec. The classical determinations of the different pressures. Potential temperature is specific heat of seawater were reported by defined as the temperature that a water parcel Thoulet and Chevallier (1889). In 1959, Cox would have if moved adiabatically to another and Smith (1959) reported new measurements pressure. This effect has to be considered estimated to be accurate to 0.05%, with values when water parcels change depth. 1 to 2% higher than the old ones. A further study The adiabatic lapse rate or adiabatic temperature (Millero, Perron, & Desnoyers, 1973) yielded gradient is the change in temperature per unit values in close agreement with those of Cox change in pressure for an adiabatic displace- and Smith. ment of a water parcel. The expression for the The flux of heat through a surface is defined lapse rate is as the amount of energy that goes through the vT surface per unit time, so the mks units of heat ðS; T; pÞ¼ (3.2) G p flux are W/m2. The heat flux between the atmo- v heat sphere and ocean depends in part on the where S, T, and p are the measured salinity, temperature of the ocean and atmosphere. temperature, and pressure and the derivative 34 3. PHYSICAL PROPERTIES OF SEAWATER is taken holding heat content constant. Note that surface pressure, potential temperature must both the compressibility and the adiabatic lapse also be referenced to the same pressure; see rate of seawater are functions of temperature, Section 3.5.) salinity, and pressure. The adiabatic lapse rate As an example, if a water parcel of temper- was determined for seawater through labora- ature 5C and salinity 35.00 were lowered adia- tory measurements. Since the full equation of batically from the surface to a depth of 4000 m, state of seawater is a complicated function of its temperature would increase to 5.45C due these quantities, the adiabatic lapse rate is also to compression. The potential temperature a complicated polynomial function of tempera- relative to the sea surface of this parcel is ture, salinity, and pressure. In contrast, the lapse always 5 C, while its measured, or in situ, rate for ideal gases can be derived from basic temperature at 4000 m is 5.45C. Conversely, physical principles; in a dry atmosphere the if its temperature was 5C at 4000 m depth lapse rate is approximately 9.8C/km. The lapse and it was raised adiabatically to the surface, rate in the ocean, about 0.1 to 0.2C/km, is much its temperature would change to 4.56C due smaller since seawater is much less compress- to expansion. The potential temperature of ible than air. The lapse rate is calculated using this parcel relative to the sea surface is thus computer subroutines based on UNESCO 4.56C. Temperature and potential temperature (1983). referenced to the sea surface from a profile in The potential temperature is (Fofonoff, 1985): the northeastern North Pacific are shown in Figure 3.3. Compressibility itself depends on Z pr temperature (and salinity), as discussed in qðS; T; pÞ¼T þ GðS; T; pÞdp (3.3) p Section 3.5.4. where S, T, and p are the measured (in situ) salinity, temperature, and pressure, G is the 3.4. SALINITY AND adiabatic lapse rate, and q is the temperature CONDUCTIVITY that a water parcel of properties (S, T, p) would have if moved adiabatically and without Seawater is a complicated solution contain- change of salinity from an initial pressure p ing the majority of the known elements. Some to a reference pressure pr where pr may be of the more abundant components, as percent greater or less than p. The integration above of total mass of dissolved material, are chlorine can be carried out in a single step (Fofonoff, ion (55.0%), sulfate ion (7.7%), sodium ion 1977). An algorithm for calculating q is given (30.7%), magnesium ion (3.6%), calcium ion by UNESCO (1983), using the UNESCO adia- (1.2%), and potassium ion (1.1%) (Millero, Feis- batic lapse rate (Eq. 3.2); computer subroutines tel, Wright, & McDougall, 2008). While the total in a variety of different programming concentration of dissolved matter varies from languages are readily available. The usual place to place, the ratios of the more abundant convention for oceanographic studies is to components remain almost constant. This “law” reference potential temperature to the sea of constant proportions was first proposed surface. When defined relative to the sea by Dittmar (1884), based on 77 samples of surface, potential temperature is always lower seawater collected from around the world than the actual measured temperature, and during the Challenger Expedition (see Chapter only equal to temperature at the sea surface. S1, Section S1.2, on the textbook Web site), (On the other hand, when calculating potential confirming a hypothesis from Forchhammer density referenced to a pressure other than sea (1865). SALINITY AND CONDUCTIVITY 35

(a) (b) (c) 0 5 10 15 20 30 35 40 33.5 34.0 34.5 0 0 0

1000 1000 1000

2000 0 2000 2000 1000

2000 3000 3000 3000 3000

4000

Pressure (decibar) θ T 4000 5000 4000 4000

0 1 2 3 T 5000 5000 5000 θ

0 5 10 15 20 30 35 40 33.5 34.0 34.5 Temperature/potential temperature (°C) Conductivity (mmho) Salinity FIGURE 3.3 (a) Potential temperature (q) and temperature (T) (C), (b) conductivity (mmho), and (c) salinity in the northeastern North Paciﬁc (36 30’N, 135W).

The dominant source of the salts in the ocean salinity of ocean water is about 35 grams of salts is river runoff from weathering of the continents per kilogram of seawater (g/kg), written as (see Section 5.2). Weathering occurs very slowly “S ¼ 35 &”oras“S¼ 35 ppt” and read as over millions of years, and so the dissolved “thirty-five parts per thousand.” Because evap- elements become equally distributed in the oration measurements are cumbersome, this ocean as a result of mixing. (The total time for definition was quickly superseded in practice. water to circulate through the oceans is, at In the late 1800s, Forch, Knudsen, and Sorensen most, thousands of years, which is much shorter (1902) introduced a more chemically based defi- than the geologic weathering time.) However, nition: “Salinity is the total amount of solid there are significant differences in total concen- materials in grams contained in one kilogram tration of the dissolved salts from place to place. of seawater when all the carbonate has been These differences result from evaporation and converted to oxide, the bromine and iodine from dilution by freshwater from rain and river replaced by chlorine, and all organic matter runoff. Evaporation and dilution processes completely oxidized.” occur only at the sea surface. This chemical determination of salinity was Salinity was originally defined as the mass in also difficult to carry out routinely. The method grams of solid material in a kilogram of used throughout most of the twentieth century seawater after evaporating the water away; was to determine the amount of chlorine ion this is the absolute salinity as described in (plus the chlorine equivalent of the bromine Millero et al. (2008). For example, the average and iodine) referred to as chlorinity, by titration 36 3. PHYSICAL PROPERTIES OF SEAWATER with silver nitrate, and then to calculate salinity in terms of the ratio of the electrical conductivity by a relation based on the measured ratio of of the sample at 15C and a pressure of one stan- chlorinity to total dissolved substances. (See dard atmosphere to that of a potassium chloride Wallace, 1974, Wilson, 1975, or Millero et al., solution in which the mass fraction of KCl is 2008 for a full account.) The current definition 32.4356 103 at the same temperature and of salinity, denoted by S &, is “the mass of silver pressure. The potassium chloride solutions required to precipitate completely the halogens used as standards are now prepared in a single in 0.3285234 kg of the seawater sample.” The laboratory in the UK. PSS 78 is valid for the current relation between salinity and chlorinity range S ¼ 2 to 42, T ¼2.0 to 35.0C and pres- was determined in the early 1960s: sures equivalent to depths from 0 to 10,000 m. The accuracy of salinity determined from Salinity ¼ 1:80655 Chlorinity (3.4) conductivity is 0.001 if temperature is very accurately measured and standard seawater is These definitions of salinity based on chemi- used for calibration. This is a major improve- cal analyses were replaced by a definition based ment on the accuracy of the older titration on seawater’s electrical conductivity, which method, which was about 0.02. In archived depends on salinity and temperature (see Lewis & data sets, salinities that are reported to three Perkin, 1978; Lewis & Fofonoff, 1979; Figure 3.3). decimal places of accuracy are derived from This conductivity-based quantity is called prac- conductivity, while those reported to two places tical salinity, sometimes using the symbol psu are from titration and usually predate 1960. for practical salinity units, although the preferred The conversion from conductivity ratio to international convention has been to use no units practical salinity is carried out using a computer for salinity. Salinity is now written as, say, subroutine based on the formula from Lewis S ¼ 35.00 or S ¼ 35.00 psu. The algorithm that is (1980). The subroutine is part of the UNESCO widely used to calculate salinity from conduc- (1983) routines for seawater calculations. tivity and temperature is called the practical In the 1960s, the pairing of conductivity salinity scale 1978 (PSS 78). Electrical conduc- sensors with accurate thermistors made it tivity methods were first introduced in the possible to collect continuous profiles of salinity 1930s (see Sverdrup, Johnson, & Fleming, 1942 in the ocean. Because the geometry of the for a review). Electrical conductivity depends conductivity sensors used on these instruments strongly on temperature, but with a small change with pressure and temperature, calibra- residual due to the ion content or salinity. There- tion with water samples collected at the same fore temperature must be controlled or time is required to achieve the highest possible measured very accurately during the conduc- accuracies of 0.001. tivity measurement to determine the practical An example of the relationship between salinity. Advances in the electrical circuits and conductivity, temperature, and salinity profiles sensor systems permitted accurate compensa- in the northeastern North Pacific is shown in tion for temperature, making conductivity- Figure 3.3. Deriving salinity from conductivity based salinity measurements feasible (see requires accurate temperature measurement supplemental materials in Chapter S6, Section because the conductivity profile closely tracks S6.4.3 on the textbook Web site). temperature. Standard seawater solutions of accurately The concept of salinity assumes negligible known salinity and conductivity are required variations in the composition of seawater. for accurate salinity measurement. The practical However, a study of chlorinity, density relative salinity (SP) of a seawater sample is now given to pure water, and conductivity of seawater DENSITY OF SEAWATER 37 carried out in England on samples from the (2010) manual strongly recommends that obser- world oceans (Cox, McCartney, & Culkin, vations continue to be made based on conduc- 1970) revealed that the ionic composition of tivity and PSS 78, and reported to national seawater does exhibit small variations from archives in those practical salinity units. For place to place and from the surface to deep calculations involving salinity, the manual indi- water. It was found that the relationship cates two corrections for calculating the absolute between density and conductivity was a little salinity SA from the practical salinity SP: closer than between density and chlorinity. 1 This means that the proportion of one ion to SA ¼ SR þ dSA ¼ð35:16504gkg =35ÞSP þ dSA another may change; that is, the chemical (3.5) composition may change, but as long as the total weight of dissolved substances is the same, the The factor multiplying SP yields the conductivity and the density will be unchanged. “reference salinity” SR, which is presently the Moreover, there are geographic variations in most accurate estimate of the absolute salinity the dissolved substances not measured by the of reference Atlantic surface seawater. A conductivity method that affect seawater geographically dependent anomaly, dSA,is density and hence should be included in abso- then added that corrects for the dissolved lute salinity. The geostrophic currents computed substances that do not affect conductivity; this locally from density (Section 7.6.2), based on the correction, as currently implemented, depends use of salinity PSS 78, are highly accurate. on dissolved silica, nitrate, and alkalinity. The However, it is common practice to map proper- mean absolute value of the correction globally ties on surfaces of constant potential density or is 0.0107 g/kg, and it ranges up to 0.025 g/kg related surfaces that are closest to isentropic in the northern North Pacific, so it is significant. (Section 3.5). On a global scale, these dissolved If nutrients and carbon parameters are not constituents can affect the definition of these measured along with salinity (which is by surfaces. far the most common circumstance), then The definition of salinity is therefore under- a geographic lookup table based on archived going another change equivalent to that of measurements is used to estimate the anomaly (McDougall, Jackett, & Millero, 2010). It is 1978. The absolute salinity recommended by the IOC, SCOR, and IAPSO (2010) is a return to understood that the estimate (Eq. 3.5) of abso- the original definition of “salinity,” which is lute salinity could evolve as additional measure- required for the most accurate calculation of ments are made. density; that is, the ratio of the mass of all dis- All of the work that appears in this book solved substances in seawater to the mass of predates the adoption of the new salinity scale, the seawater, expressed in either kg/kg or g/kg and all salinities are reported as PSS 78 and all (Millero et al., 2008). The new estimate for abso- densities are calculated according to the 1980 lute salinity incorporates two corrections over equation of state using PSS 78. PSS 78: (1) representation of improved information about the composition of the Atlantic 3.5. DENSITY OF SEAWATER surface seawater used to define PSS 78 and incorporation of 2005 atomic weights, and (2) Seawater density is important because it corrections for the geographic dependence of determines the depth to which a water parcel the dissolved matter that is not sensed by will settle in equilibrium d the least dense on conductivity. To maintain a consistent global top and the densest at the bottom. The distribu- salinity data set, the IOC, SCOR, and IAPSO tion of density is also related to the large-scale 38 3. PHYSICAL PROPERTIES OF SEAWATER circulation of the oceans through the The relationship between the density of geostrophic/thermal wind relationship (see seawater and temperature, salinity, and pres- Chapter 7). Mixing is most efficient between sure is the equation of state for seawater. The waters of the same density because adiabatic equation of state stirring, which precedes mixing, conserves ðS; T; pÞ¼ ðS; T; 0Þ=½l p=KðS; T; pÞ (3.7) potential temperature and salinity and conse- r r quently, density. More energy is required to was determined through meticulous laboratory mix through stratification. Thus, property distri- measurements at atmospheric pressure. The butions in the ocean are effectively depicted by polynomial expressions for the equation of state maps on density (isopycnal) surfaces, when r(S, T, 0) and the bulk modulus K(S, T, p) contain properly constructed to be closest to isentropic. 15 and 27 terms, respectively. The pressure (See the discussion of potential and neutral dependence enters through the bulk modulus. density in Section 3.5.4.) The largest terms are those that are linear in S, Density, usually denoted r, is the amount of T, and p, with smaller terms that are propor- mass per unit volume and is expressed in kilo- tional to all of the different products of these. grams per cubic meter (kg/m3). A directly Thus, the equation of state is weakly nonlinear. related quantity is the specific volume anomaly, Today, the most common version of Eq. (3.7) is usually denoted a, where a ¼ 1/r. The density “EOS 80” (Millero & Poisson, 1980; Fofonoff, of pure water, with no salt, at 0C, is 1000 kg/m3 1985). EOS 80 uses the practical salinity scale at atmospheric pressure. In the open ocean, PSS 78 (Section 3.4). The formulae may be found density ranges from about 1021 kg/m3 (at the in UNESCO (1983), which provides practical sea surface) to about 1070 kg/m3 (at a pressure computer subroutines and are included in of 10,000 dbar). As a matter of convenience, it various texts such as Pond and Pickard (1983) is usual in oceanography to leave out the first and Gill (1982). EOS 80 is valid for T ¼2to two digits and use the quantity 40C, S ¼ 0 to 40, and pressures from 0 to 10,000 dbar, and is accurate to 9 103 kg/m3 or better. ¼ ðS; T; pÞ1000 kg=m3 (3.6) sstp r A new version of the equation of state has been where S ¼ salinity, T ¼ temperature (C), and introduced (IOC, SCOR, and IAPSO, 2010), based p ¼ pressure. This is referred to as the in situ on a new definition of salinity and is termed density. In earlier literature, ss,t,0 was commonly TEOS-10. Only EOS 80 is used in this book. used, abbreviated as st. st is the density of the Historically, density was calculated from water sample when the total pressure on it has tables giving the dependence of the density been reduced to atmospheric (i.e., the water on salinity, temperature, and pressure. Earlier pressure p ¼ 0 dbar) but the salinity and determinations of density were based on temperature are as measured. Unless the anal- measurements by Forch, Jacobsen, Knudsen, ysis is limited to the sea surface, st is not the and Sorensen and were presented in the Hydro- best quantity to calculate. If there is range of graphical Tables (Knudsen, 1901). Cox et al. pressures, the effects of adiabatic compression (1970) found that the s0 values (at T ¼ 0 C) in should be included when comparing water “Knudsen’s Tables” were low by about 0.01 (on parcels. A more appropriate quantity is potential average) in the salinity range from 15 e 40, and density, which is the same as st but with temper- by up to 0.06 at lower salinities and temperatures. ature replaced by potential temperature and To determine seawater density over a range pressure replaced by a single reference pressure of salinities in the laboratory, Millero (1967) that is not necessarily 0 dbar. Potential density is used a magnetic float densimeter. A Pyrex glass described in Section 3.5.2. float containing a permanent magnet floats in a DENSITY OF SEAWATER 39

250 ml cell that contains the seawater and is sur- marginal seas). The ocean’s temperature range rounded by a solenoid, with the entire apparatus produces more of the ocean’s density variation sitting in a constant temperature bath. The float is than does its salinity range. In other words, slightly less dense than the densest seawater and temperature dominates oceanic density varia- is loaded with small platinum weights until it just tions for the most part. (As noted previously, sinks to the bottom of the cell. A current through an important exception is where surface waters the solenoid is then slowly increased until the are relatively fresh due to large precipitation or float just lifts off the bottom of the cell. The ice melt; that is, at high latitudes and also in the density of the seawater is then related to the tropics beneath the rainy Intertropical Conver- current through the solenoid. The relation gence Zone of the atmosphere.) The curvature between current and density is determined by of the density contours in Figure 3.1 is due to carrying out a similar experiment with pure the nonlinearity of the equation of state. The water in the cell. The accuracy of the relative curvature means that the density change for density determined this way is claimed to a given temperature or salinity change is be 2 106 (at atmospheric pressure). But as different at different temperatures or salinities. the absolute density of pure water is known to To emphasize this point, Table 3.2 shows the 6 be only 4 10 , the actual accuracy of seawater change of density (Dst) for a temperature density is more limited. The influence of change (DT) of þ1 K (left columns) and the pressure was determined using a high pressure value of Dst for a salinity change (DS) of þ0.5 version of the previously mentioned densimeter (right columns). These are arbitrary choices for to measure the bulk modulus (K). K has also been changes in temperature and salinity. The most determined from measurements of sound speed important thing to notice in the table is how in seawater because sound speed depends on density varies at different temperatures and the bulk modulus and seawater compressibility. salinities for given changes in each. At high The following subsections explore how temperatures, st varies significantly with T at seawater density depends on temperature, all salinities. As temperature decreases, the salinity, and pressure, and discusses concepts rate of variation with T decreases, particularly (such as potential and neutral density) that at low salinities (as found at high latitudes or reduce, as much as possible, the effects of in estuaries). The change of st with DS is about compressibility on a given analysis. the same at all temperatures and salinities, but is slightly greater at low temperature. 3.5.1. Effects of Temperature and Salinity on Density 3.5.2. Effect of Pressure on Density: Potential Density Density values evaluated at the ocean’s surface pressure are shown in Figure 3.1 (curved Seawater is compressible, although not contours) for the whole range of salinities and nearly as compressible as a gas. As a water temperatures found anywhere in the oceans. parcel is compressed, the molecules are pushed The shaded bar in the figure shows that most closer together and the density increases. At of the ocean lies within a relatively narrow the same time, and for a completely different salinity range. More extreme values occur only physical reason, adiabatic compression causes at or near the sea surface, with fresher waters the temperature to increase, which slightly outside this range (mainly in areas of runoff or offsets the density increase due to compression. ice melt) and the most saline waters in relatively (See discussion of potential temperature in confined areas of high evaporation (such as Section 3.3.) 40 3. PHYSICAL PROPERTIES OF SEAWATER

TABLE 3.2 Variation of Density (Dst) with Variations of Temperature (DT) and of Salinity (DS) as Functions of Temperature and Salinity

Salinity 0 20 35 40 0 20 35 40 Ds D [ D Ds D [ D Temperature ( C) t for T 1 C t for S 0.5 30 0.31 0.33 0.34 0.35 0.38 0.37 0.37 0.38 20 0.21 0.24 0.27 0.27 0.38 0.38 0.38 0.38 10 0.09 0.14 0.18 0.18 0.39 0.39 0.39 0.39 0 þ0.06 0.01 0.06 0.07 0.41 0.40 0.40 0.40

Density is primarily a function of pressure density is the density that a parcel would have (Figure 3.4) because of this compressibility. Pres- if it were moved adiabatically to a chosen refer- sure effects on density have little to do with the ence pressure. If the reference pressure is the sea initial temperature and salinity of the water surface, then we first compute the potential parcel. To trace a water parcel from one place temperature of the parcel relative to surface to another, the dependence of density on pres- pressure, then evaluate the density at pressure sure should be removed. An early attempt was 0 dbar.1 We refer to potential density referenced to use st, defined earlier, in which the pressure to the sea surface (0 dbar) as sq, which signifies effect was removed from density but not from that potential temperature and surface pressure temperature. It is now standard practice to use have been used. potential density, in which density is calculated The reference pressure for potential density using potential temperature instead of tempera- can be any pressure, not just the pressure at ture. (The measured salinity is used.) Potential the sea surface. For these potential densities, potential temperature is calculated relative to 0 the chosen reference pressure and then the potential density is calculated relative to the 1000 same reference pressure. It is common to refer to potential density referenced to 1000 dbar as 2000 s1, referenced to 2000 dbar as s2, to 3000 dbar as and so on, following Lynn and Reid (1968). 3000 s3

Pressure (dbar) 4000 3.5.3. Specific Volume and Specific 5000 Volume Anomaly 1030 1035 1040 1045 1050 Density (kg m–3) The specific volume (a) is the reciprocal of 3 FIGURE 3.4 Increase in density with pressure for density so it has units of m /kg. For some a water parcel of temperature 0C and salinity 35.0 at the purposes it is more useful than density. The in sea surface. situ specific volume is written as as,t,p. The

1 The actual pressure at the sea surface is the atmospheric pressure, but we do not include atmospheric pressure in many applications since pressure ranges within the ocean are so much larger. DENSITY OF SEAWATER 41 specific volume anomaly (d) is also sometimes across such a surface (quasi-vertical mixing) convenient. It is defined as: is much less important (Montgomery, 1938). However, because seawater density depends ¼ (3.8) d as;t;p a35;0;p on both salinity and temperature, the actual surface that a water parcel moves along in the The anomaly is calculated relative to , a35,0,p absence of external sources of heat or freshwater which is the specific volume of seawater of depends on how the parcel mixes along that salinity 35 and temperature 0C at pressure p. surface since its temperature and salinity will With this standard is usually positive. The d be altered as it mixes with adjacent water equation of state relates (and ) to salinity, a d parcels on that surface. This quasi-lateral mix- temperature, and pressure. Originally all calcu- ing alters the temperature (and salinity) and lations of geostrophic currents from the distri- therefore, the compressibility of the mixture. bution of mass were done by hand using As a result, when it moves laterally, the parcel tabulations of the component terms of , d will equilibrate at a different pressure than if described in previous editions of this book. there had been no mixing. This means that there With modern computer methods, tabulations are no closed, unique isentropic surfaces in the are not necessary. The computer algorithms for ocean, since if our water parcel were to return dynamic calculations (Section 7.5.1) still use to its original latitude and longitude, it will specific volume anomaly , computed using d have moved to a different density and hence subroutines, rather than the actual density , r pressure because its temperature and salinity to increase the calculation precision. will have changed due to mixing along that surface. Note that these effects are important 3.5.4. Effect of Temperature and even without diapycnal mixing between water Salinity on Compressibility: Isentropic parcels on different isentropic surfaces (quasi- Surfaces and Neutral Density vertical mixing), which also can change temperature, salinity, and compressibility. Cold water is more compressible than warm The density differences associated with these water; it is easier to deform a cold parcel than differences in compressibility can be substantial a warm parcel. When two water parcels with (Figure 3.5). For instance, water spilling out of the same density but different temperature and the Mediterranean Sea through the Strait of salinity characteristics (one warm/salty, the Gibraltar is saline and rather warm compared other cold/fresh) are submerged to the same with water spilling into the Atlantic from the pressure, the colder parcel will be denser. If Nordic Seas over the Greenland-Iceland ridge there were no salt in seawater, so that density (Chapter 9). The Mediterranean Water (MW) depended only on temperature and pressure, density is actually higher than the Nordic Sea then potential density as defined earlier, using Overflow Water (NSOW) density where they any single pressure for a reference, would be flow over their respective sills, which are at about adequate for defining a unique isentropic surface. the same depth. However, the warm, saline MW An isentropic surface is one along which water (13.4C, 37.8 psu) is not as compressible as the parcels can move adiabatically, that is, without much colder NSOW (about 1C, 34.9 psu; Price & external input of heat or salt. Baringer, 1994). The potential density relative to When analyzing properties within the ocean 4000 dbar of MW is lower than that of the more to determine where water parcels originate, it compressible NSOW. The NSOW reaches the is assumed that motion and mixing is mostly bottom of the North Atlantic, while the MW along a quasi-isentropic surface and that mixing does not. (As both types of water plunge 42 3. PHYSICAL PROPERTIES OF SEAWATER

(a) Salinity cold parcel is denser than the warm one at higher 32 34 36 38 40 pressure (lower panel). The pair labeled 2 illus- 30 trates the MW (warm, salty) and NSOW (cold, fresh) pair with their properties at the sills where 22 24 they enter the North Atlantic. At the sea surface, 20 which neither parcel ever reaches, the Mediterra- 26 28 nean parcel would actually be denser than the Nordic Seas parcel. Near the ocean bottom, represented by 4000 dbar (Figure 3.5b), the colder 10 (1) 30 Nordic Seas parcel is markedly denser than the (2) Mediterranean parcel. Therefore, if both parcels Potential temperature dropped to the ocean bottom from their respective 0 dbar 0 sills, without any mixing, the Nordic Seas parcel (b) 30 would lie under the Mediterranean parcel. (In actuality, as already mentioned, there is a large 38 40 42 amount of entrainment mixing as these parcels 20 drop down into the North Atlantic.) 44 The surfaces that we use to map and trace 46 water parcels should approximate isentropic surfaces. Early choices, that were an improve- 10 (1) ment over constant depth surfaces, included (2) 48 sigma-t surfaces (Montgomery, 1938) and even Potential temperature potential temperature surfaces (Worthington 0 4000 dbar and Wright, 1970). A method, introduced by 32 34 36 38 40 Lynn and Reid (1968), that produces surfaces Salinity that are closer to isentropic uses isopycnals FIGURE 3.5 Potential density relative to (a) 0 dbar and with a reference pressure for the potential (b) 4000 dbar as a function of potential temperature (relative density that is within 500 m of the pressure of to 0 dbar) and salinity. Parcels labeled 1 have the same interest. Therefore when working in the top density at the sea surface. The parcels labeled 2 represents 500 m, a surface reference pressure is used. Mediterranean (saltier) and Nordic Seas (fresher) source When working at 500 to 1500 m, a reference waters at their sills. pressure of 1000 dbar is used, and so forth. Experience has shown this pressure discretiza- downward, they entrain or mix with the waters tion is sufﬁcient to remove most of the problems that they pass through. This also has an effect associated with the effect of pressure on density. on how deep they fall, so the difference in When isopycnals mapped in this fashion move compressibility is not the only cause for different into a different pressure range, they must be outcomes.) patched onto densities at the reference pressure Restating this more generally, changing the in the new range. Reid (1989, 1994, 1997, 2003) reference pressure for potential density alters followed this practice in his monographs on the density difference between two water parcels Paciﬁc, Atlantic, and Indian Ocean circulations. (Figure 3.5). For the pair labeled 1, the densities It is less complicated to use a continuously are the same at the sea surface (upper panel). varying surface rather than one patched from Because the cold parcel compresses more than different reference pressures, although in prac- the warm one with increasing pressure, the tice there is little difference between them. DENSITY OF SEAWATER 43

“Neutral surfaces,” introduced by Ivers (1975), that include vertical excursions of more than a student working with J.L. Reid, use a nearly several hundred meters. continuously varying reference pressure. If a parcel is followed along its path from one 3.5.5. Linearity and Nonlinearity observation station to the next, assuming the in the Equation of State path is known, then it is possible to track its pressure and adjust its reference pressure and density As described earlier, the equation of state at each station. McDougall (1987a) refined this (3.6) is somewhat nonlinear in temperature, neutral surface concept and introduced it widely. salinity, and pressure; that is, it includes prod- Jackett and McDougall (1997) created a computer ucts of salinity, temperature, and pressure. For program for computing their version of this practical purposes, in theoretical and simple numerical models, the equation of state is some- neutral density, based on a standard climatology (average temperature and salinity on a grid for times approximated as linear and its pressure the whole globe, derived from all available obser- dependence is ignored: vations; Section 6.6.2), marching away from rzr0 þ aðT T0ÞþbðS S0Þ; a single location in the middle of the Pacific. (3.9) The Jackett and McDougall neutral density is a ¼ vr=vTandb ¼ vr=vS denoted gN with numerical values that are similar to those of potential density (with units where r0,T0,, and S0 are arbitrary constant of kg/m3). Neutral density depends on latitude, values of r, T, and S; they are usually chosen longitude, and pressure, and is defined only for as the mean values for the region being ranges of temperature and salinity that occur in modeled. Here a is the thermal expansion coeffi- the open ocean. This differs from potential cient, which expresses the change in density density, which is defined for all values of temper- for a given change in temperature (and should ature and salinity through a well-defined equa- not be confused with specific volume, defined tion of state that has been determined in the with the same symbol in Section 3.5.3), and laboratory and is independent of location. b is the haline contraction coefficient, which is Neutral density cannot be contoured as a function the change in density for a given change in of potential temperature and salinity analo- salinity. The terms a and b are nonlinear func- gously to Figure 3.5 for density or potential tions of salinity, temperature, and pressure; density. their mean values are chosen for linear models. The advantage of neutral density for Full tables of values are given in UNESCO mapping quasi-isentropic surfaces is that it (1987). The value of ar (at the sea surface and at removes the need to continuously vary the refer- a salinity of 35 psu) ranges from 53 106 K1 at ence pressure along surfaces that have depth a temperature of 0C to 257 106 K1 at a variation (since this is already done in an temperature of 20C. The value of br (at the approximate manner within the provided soft- sea surface and at a salinity of 35 psu) ranges ware and database). Neutral density is a conve- from 785 106 psu1 (at a temperature of 0C) nient tool. Both potential and neutral density to 744 106 psu1 (at a temperature of 20C). surfaces are approximations to isentropic Nonlinearity in the equation of state leads to surfaces. Ideas and literature on how to best the curvature of the density contours in Figures approximate isentropic surfaces continue to be 3.1 and 3.5. Mixing between two water parcels developed; neutral density is currently the must occur along straight lines in the tempera- most popular and commonly used approxima- ture/salinity planes of Figures 3.1 and 3.5. tion for mapping isentropes over large distances Becauseoftheconcavecurvatureofthedensity 44 3. PHYSICAL PROPERTIES OF SEAWATER contours, when two parcels of the same density Because double diffusive effects are apparent in but different temperature and salinity are the ocean’s temperatureesalinity properties, the mixed together, the mixture has higher density difference in diffusivities scales up in some way than the original water parcels. Thus the to the eddy diffusivity. Diffusivity and mixing concavity of the density contours means that are discussed in Chapter 7, and double diffusion there is a contraction in volume as water in Section 7.4.3.2. parcels mix. This effect is called cabbeling (Witte, 1902). In practice, cabbeling may be of 3.5.6. Static Stability and Brunt-Vaïsa¨la¨ limited importance, having demonstrable Frequency importance only where water parcels of very different initial properties mix together. Exam- Static stability, denoted by E, is a formal ples of problems where cabbeling has been measure of the tendency of a water column to a factor are in the formation of dense water in overturn. It is related to the density stratifica- the Antarctic (Foster, 1972) and in the modification, with higher stability where the water tion of intermediate water in the North Pacific column is more stratified. A water column is (Talley & Yun, 2001). statically stable if a parcel of water that is There are two other important mixing effects moved adiabatically (with no heat or salt associated with the physical properties of exchange) up or down a short distance returns seawater: thermobaricity and double diffusion. to its original position. The vigor with which Thermobaricity (McDougall, 1987b) is best the parcel returns to its original position explained by the rotation with depth of depends on the density difference between potential density contours in the potential theparcelandthesurroundingwatercolumn temperatureesalinity plane (Section 3.5.4). As at the displaced position. Therefore the rate of in Figure 3.5, consider two water parcels of change of density of the water column with different potential temperature and salinity in depth determines a water column’s static which the warmer, saltier parcel is slightly stability. The actual density of the parcel denser than the colder, fresher one. (This is increases or decreases as it is moved down or a common occurrence in subpolar regions up because the pressure on it increases or such as the Arctic and the Antarctic.) If these decreases, respectively. This adiabatic change two water parcels are suddenly brought to in density must be accounted for in the defini- a greater pressure, it is possible for them to tion of static stability. reverse their relative stratification, with the The mathematical derivation of the static colder, fresher one compressing more than stability of a water column is presented in detail the warmer one, and therefore becoming the in Pond and Pickard (1983) and other texts. The denser of the two parcels. The parcels would full expression for E is complicated. For very now be vertically stable if the colder, fresher small vertical displacements, static stability one were beneath the warmer, saltier one. Ther- might be approximated as mobaricity is an important effect in the Arctic, Ez ðl=rÞðvr=vzÞ (3.10a) defining the relative vertical juxtaposition of the Canadian and Eurasian Basin Deep Waters where r is in situ density. The water column is (Section 12.2). stable, neutral, or unstable depending on Double diffusion results from a difference in whether E is positive, zero, or negative, respec- diffusivities for heat and salt, therefore, it is tively. Thus, if the density gradient is positive not a matter of linearity or nonlinearity. At the downwards, the water column is stable and molecular level, these diffusivities clearly differ. there is no tendency for vertical overturn. DENSITY OF SEAWATER 45

For larger vertical displacements, a much vertical scale, on the order of meters, they require better approximation uses local potential continuous profilers for detection. Unstable density, sn: conditions with vertical extents greater than tens of meters are uncommon below the surface layer. E ¼ðl=rÞðvsn=vzÞ (3.10b) The buoyancy (Brunt-Vaïsa¨la¨) frequency associ- Here the potential density anomaly sn is ated with internal gravity waves (Chapter 8) is computed relative to the pressure at the center an intrinsic frequency associated with static of the interval used to compute the vertical stability. If a water parcel is displaced upward gradient. This local pressure reference approxi- in a statically stable water column, it will sink mately removes the adiabatic pressure effect. and overshoot the original position. The denser Many computer subroutines for seawater prop- water beneath its original position will force it erties use this standard definition. An equiva- back up into lighter water, and it will continue lent expression for stability is oscillating. The frequency of the oscillation 2 depends on the static stability: the more strati- E ¼ðl=rÞðvr=vzÞðg=C Þ (3.10c) fied the water column, the higher the static where r is in situ density, g ¼ acceleration due stability and the higher the buoyancy frequency. to gravity, and C ¼ in situ sound speed. The The Brunt-Vaïsa¨la¨ frequency, N, is an intrinsic addition of the term g/C2 allows for the frequency of internal waves: compressibility of seawater. (Sound waves are N2 ¼ gEzg½ðl= Þð = zÞ (3.11) compression waves; Section 3.7.) r vsn v A typical density profile from top to bottom The frequency in cycles/sec (hertz) is of the ocean has a surface mixed layer with f ¼ N/2p and the period is s ¼ 2p/N. In the low stratification, an upper ocean layer with upper ocean, where E typically ranges from an intermediate amount of stratification, an 1000 108 to 100 108 m1, periods are intermediate layer of high stratification (pycno- s ¼ 10 to 33 min (Figure 3.6). For the deep ocean, cline), and a deep layer of low stratification E ¼ 1 108 m1 and s z 6h. (Section 4.2). The water in the pycnocline is The final quantity that we define based on very stable; it takes much more energy to vertical density stratification is the “stretching” displace a particle of water up or down part of the potential vorticity (Section 7.6). Poten- than in a region of lesser stability. Therefore tial vorticity is a dynamical property of a fluid turbulence, which causes most of the mixing analogous to angular momentum. Potential between different water bodies, is less able to vorticity has three parts: rotation due to Earth’s penetrate through the stable pycnocline than rotation (planetary vorticity), rotation due to through less stable layers. Consequently, the relative motions in the fluid (relative vorticity, pycnocline is a barrier to the vertical transport for instance, in an eddy), and a stretching of water and water properties. The stability of component proportional to the vertical change these layers is measured by E. In the upper in density, which is analogous to layer thickness 1000 m in the open ocean, values of E range 8 1 8 1 (Eq. 7.41). In regions where currents are weak, from 1000 10 m to 100 10 m ,with relative vorticity is small and the potential larger values in the pycnocline. Below 1000 m, vorticity can be approximated as E decreases; in abyssal trenches E may be as 8 1 low as 1 10 m . Qz ðf=rÞðvr=vzÞ (3.12a) Static instabilities may be found near the inter- faces between different waters in the process of This is sometimes called “isopycnic potential mixing. Because these instabilities occur at a small vorticity.” The vertical density derivative is 46 3. PHYSICAL PROPERTIES OF SEAWATER

Period (minutes) FIGURE 3.6 (a) Potential 30 15 10 density and (b) Brunt-Vaïsa¨la¨ 0 0 frequency (cycles/h) and period (minutes) for a profile in the western North Pacific.

1000 1000

2000 2000

3000 3000 Pressure (dbar)

4000 4000

5000 North Pacific 5000 24.258°N, 147.697°W

24 26 28 0246 Potential density Brunt−Väisälä Frequency (cycles per hour) calculated from locally referenced potential On further cooling the surface water becomes density, so it can be expressed in terms of lighter and the overturning stops. The water Brunt-Va¨isa¨la¨ frequency: column freezes from the surface down, with

2 the deeper water remaining unfrozen. Q ¼ðf=gÞN (3.12b) However, at salinities greater than 24.7 psu, maximum density is achieved at the freezing 3.5.7. Freezing Point of Seawater point. Therefore more of the water column must be cooled before freezing can begin, so The salt in seawater depresses the freezing freezing is delayed compared with the fresh- point below 0C (Figure 3.1). An algorithm for water case. calculating the freezing point of seawater is given by Millero (1978). Depression of the freezing point is why a mixture of salt water 3.6. TRACERS and ice is used to make ice cream; as the ice melts, it cools the water (and ice cream) below Dissolved matter in seawater can help in 0C. At low salinities, below the salinity of tracing specific water masses and pathways of most seawater, cooling water reaches its flow. Some of these properties can be used for maximum density before freezing and sinks dating seawater (determine the length of time while still fluid. The water column then over- since the water was last at the sea surface; turns and mixes until the whole water column Section 4.7). Most of these constituents occur in reaches the temperature of maximum density. such small concentrations that their variations TRACERS 47 do not significantly affect density variations or ocean mixed layer waters at close to 100% satu- the relationship between chlorinity, salinity, ration. Below the surface layer, oxygen content and conductivity. (See Section 3.5 for comments drops rapidly. This is not a function of the on this.) These additional properties of seawater temperature of the water, which generally is can be: conservative or non-conservative; lower at depth, since cold water can hold more natural or anthropogenic (man-made); stable dissolved oxygen than warm water. (For or radioactive; transient or non-transient. The example, for a salinity of 35: at 30C, 100% text by Broecker and Peng (1982) describes the oxygen saturation occurs at 190 mmol/kg; at sources and chemistry of many tracers in detail. 10C it is 275 mmol/kg; and at 0C it is 350 For a tracer to be conservative there are no mmol/kg.) The drop in oxygen content and satu- significant processes other than mixing by ration with depth is due to respiration within which the tracer is changed below the surface. the water column, mainly by bacteria feeding Even salinity, potential temperature, and hence on organic matter (mostly dead plankton and density, can be used as conservative tracers fecal pellets) sinking from the photic zone. Since since they have extremely weak sources within there is no source of oxygen below the mixed the ocean. This near absence of in situ sources layer and photic zone, oxygen decreases with and sinks means that the spreading of water increasing age of the subsurface water parcels. masses in the ocean can be approximately traced Oxygen is also used by nitrifying bacteria, from their origin at the sea surface by their char- which convert the nitrogen in ammonium acteristic temperature/salinity values. Near the (NH4) to nitrate (NO3). surface, evaporation, precipitation, runoff, and The rate at which oxygen is consumed is ice processes change salinity, and many surface called the oxygen utilization rate. This rate heat-transfer processes change the temperature depends on local biological productivity so it (Section 5.4). Absolute salinity can be changed is not uniform in space. Therefore the decrease only very slightly within the ocean due to in oxygen from a saturated surface value is not changes in dissolved nutrients and carbon a perfect indication of age of the water parcel, (end of Section 3.4). Temperature can be raised especially in the biologically active upper ocean very slightly by geothermal heating at the ocean and continental shelves. However, below the bottom. Even though water coming out of thermocline, the utilization rate is more uniform bottom vents at some mid-ocean ridges can be and changes in oxygen following a water parcel extremely hot (up to 400C), the total amount correspond relatively well to age. of water streaming out of the vents is tiny, and Nutrients are another set of natural, non- the high temperature quickly mixes away, conservative, commonly observed properties. leaving a miniscule large-scale temperature These include dissolved silica, phosphate, and increase. the nitrogen compounds (ammonium, nitrite, Non-conservative properties are changed by and nitrate). Nutrients are essential to ocean chemical reactions or biological processes life so they are consumed in the ocean’s surface within the water column. Dissolved oxygen is layer where life is abundant; consequently, an example. Oxygen enters the ocean from the concentrations there are low. Nutrient content atmosphere at the sea surface. It is also increases with depth and age, as almost a mirror produced through photosynthesis by phyto- image of the oxygen decrease. Silica is used by plankton in the sunlit upper ocean (photic some organisms to form protective shells. Silica zone or euphotic zone) and consumed by respi- re-enters the water column when the hard parts ration by zooplankton, bacteria, and other crea- of these organisms dissolve as they fall to the tures. Equilibration with the atmosphere keeps ocean floor. Some of this material reaches the 48 3. PHYSICAL PROPERTIES OF SEAWATER seafloor and accumulates, creating a silica source the ocean through gas exchange. “Bomb” radio- on the ocean bottom as well. Some silica also carbon is an anthropogenic tracer that entered enters the water column through venting at the upper ocean as a result of atomic bomb tests mid-ocean ridges. The other nutrients (nitrate, between 1945 and 1963 (Key, 2001). In the ocean, nitrite, ammonium, and phosphate) re-enter 14C and 12C are incorporated by phytoplankton the water column as biological (bacterial) in nearly the same ratio as they appear in the activity decays the soft parts of the falling atmosphere. After the organic material dies detritus. Ammonium and phosphate are imme- and leaves the photic zone, the 14C decays radio- diate products of the decay. Nitrifying bacteria, actively, with a half-life of 5730 years. The ratio of which are present through the water column, 14Cto12C decreases. Since values are reported as then convert ammonium to nitrite and finally anomalies, as the difference from the atmo- nitrate; this process also, in addition to respira- spheric ratio, the reported oceanic quantities tion, consumes oxygen. Because oxygen is are generally negative (Section 4.7 and consumed and nutrients are produced, the ratios Figure 4.24). The more negative the anomaly, of nitrate to oxygen and of phosphate to oxygen the older the water. Positive anomalies are nearly constant throughout the oceans. These throughout the upper ocean originated from proportions are known as “Redfield ratios,” after the anthropogenic bomb release of 14C. Redfield (1934) who demonstrated the near- The natural, conservative isotope 3He origi- constancy of these proportions. Nutrients are nates in Earth’s mantle and is outgassed at vents discussed further in Section 4.6. in the ocean floor. It is usually reported in terms Other non-conservative properties related to of its ratio to the much more abundant 4He the ocean’s carbon system, including dissolved compared with this ratio in the atmosphere. It inorganic carbon, dissolved organic carbon, is an excellent tracer of mid-depth circulation, alkalinity, and pH, have been widely measured since its sources tend to be the tops of mid-ocean over the past several decades. These have both ridges, which occur at about 2000 m. The natural and anthropogenic sources and are anthropogenic component of 3He is described useful tracers of water masses. in the last paragraph of this Section. Isotopes that occur in trace quantities are also Another conservative isotope that is often useful. Two have been widely measured: 14C measured in seawater is the stable (heavy) and 3He. 14C is radioactive and non-conservative. isotope of oxygen, 18O. Measurements are again 3He is conservative. Both have predominantly reported relative to the most common isotope natural sources but both also have anthropogenic 16O. Rainwater is depleted in this heavy isotope sources in the upper ocean. Isotope concentra- of oxygen (compared with seawater) because it tions are usually measured and reported in terms is easier for the lighter, more common isotope of ratios to the more abundant isotopes. For 14C, of oxygen, 16O, to evaporate from the sea and the reported unit is based on the ratio of 14Cto land. A second step of reduction of 18O in atmo- 12C. For 3He, the reported unit is based on the spheric water vapor relative to seawater occurs ratio of 3He to 4He. Moreover, the values are often when rain first forms, mostly at warmer atmo- reported in terms of the normalized difference spheric temperatures, since the heavier isotope between this ratio and a standard value, usually falls out preferentially. Thus rainwater is taken to be the average atmospheric value (see depleted in 18O relative to seawater, and rain Broecker & Peng, 1982). formed at lower temperatures is more depleted Most of the 14C in the ocean is natural. It is than at higher temperatures. For physical ocean- created continuously in the atmosphere by ographers, 18O content can be a useful indicator cosmic ray bombardment of nitrogen, and enters in a high latitude region of whether the source of SOUND IN THE SEA 49 freshwater at the sea surface is rain/runoff/ of wave energy, either electromagnetic (light) or glacial melt (lower 18O content), or melted sea mechanical (sound). In the atmosphere, light in ice (higher content). In paleoclimate records, it the visible part of the spectrum is attenuated reflects the temperature of the precipitation less than sound; we can see much farther (higher 18O in warmer rain); ice formed during away than we can hear. In the sea the reverse the (cold) glacial periods is more depleted in is true. In clear ocean water, sunlight may be 18O than ice formed in the warm interglacials detectable (with instruments) down to 1000 m, and hence 18O content is an indicator of relative but the range at which humans can see details global temperature. of objects is rarely more than 50 m, and usually Transient tracers are chemicals that have been less. On the other hand, sound waves can be introduced by human activity; hence they are detected over vast distances and are a much anthropogenic. They are gradually invading better vehicle for undersea information than the ocean, marking the progress of water from light. the surface to depth. They can be either stable The ratio of the speed of sound in air to that or radioactive. They can be either conservative in water is small (about 1:4.5), so only a small or non-conservative. Commonly measured amount of sound energy starting in one medium transient tracers include chlorofluorocarbons, can penetrate into the other. This contrasts with tritium, and much of the upper ocean 3He and the relatively efficient passage of light energy 14C. Chlorofluorocarbons (CFCs) were intro- through the air/water interface (speed ratio duced as refrigerants and for industrial use. only about 1.33:1). This is why a person They are extremely stable (conservative) in standing on the shore can see into the water seawater. Their usage peaked in 1994, when but cannot hear any noises in the sea. Likewise, recognition of their role in expanding the ozone divers cannot converse underwater because hole in the atmosphere finally led to interna- their sounds are generated in the air in the tional conventions to phase out their use. throat and little of the sound energy is trans- Because different types of CFCs were used mitted into the water. Sound sources used in over the years, the ratio of different types in the sea generate sound energy in solid bodies a water parcel can yield approximate dates for (transducers), for example, electromagnetically, when the water was at the sea surface. Tritium in which the speed of sound is similar to that is a radioactive isotope of hydrogen that has in water. Thus the two are acoustically also been measured globally; it was released “matched” and the transducer energy is trans- into the atmosphere through atomic bomb mitted efficiently into the sea. testing in the 1960s and then entered the ocean, Sound is a wave. All waves are characterized primarily in the Northern Hemisphere. Tritium by amplitude, frequency, and wavelength 3 decays to He with a half-life of 12.4 years, which (Section 8.2). Sound speed (C), frequency (n), is comparable to the circulation time of the and wavelength (l) are connected by the wave 3 upper ocean gyres. When He is measured along equation C ¼ nl. The speed does not depend with tritium, the time since the water was at the on frequency, so the wavelength depends on sea surface can be estimated (Jenkins, 1998). sound speed and frequency. The frequencies of sounds range from 1 Hz or less (1 Hz ¼ 1 vibra- tion per second) to thousands of kilohertz 3.7. SOUND IN THE SEA (1 kHz ¼ 1000 cycles/sec). The wavelengths of sounds in the sea cover a vast range, from about In the atmosphere, we receive much of our 1500 m for n ¼ 1 Hz to 7 cm for n ¼ 200 kHz. information about the material world by means Most underwater sound instruments use 50 3. PHYSICAL PROPERTIES OF SEAWATER a more restricted range from 10 to 100 kHz, for is similar to Del Grosso (1974), to illustrate which the wavelengths are 14 to 1.4 cm. features of the relationship: There are many sources of sound in the sea. A hydrophone listening to the ambient sound C ¼ 1448:96 þ 4:59T 0:053T2 (3.14) in the sea will record a wide range of frequen- þ 1:34ðS 35Þþ0:016p cies and types of sounds, from low rumbles to high-frequency hisses. Some sources of under- in which T, S, and p are temperature, salinity, sea sounds are microseisms (10 e 100 Hz); ships and depth, and the constants have the correct (50 e 1500 Hz); the action of wind, waves, and units to yield C in m/s. The sound speed is rain at the surface (1 e 20 kHz); cavitation of 1449 m/s at T ¼ 0C, S ¼ 35, and p ¼ 0. The air bubbles and animal noises (10 e 400 Hz); sound speed increases by 4.5 m/s for DT ¼þ and fish and crustaceans (1 e 10 kHz). Noises 1 K, by 1.3 m/s for DS ¼þ1, and by 16 m/s associated with sea ice range from 1 e 10 kHz. for Dp ¼ 1000 dbar. Sound is a compressional wave; water mole- Sound speed is higher where the medium is cules move closer together and farther apart as less compressible. Seawater is less compressible the wave passes. Therefore sound speed when it is warm, as noted in the previous poten- depends on the medium’s compressibility. tial density discussion and apparent from the The more compressible a medium is for a given simplified equation (3.14). Seawater is also less density, the slower the wave since more compressible at high pressure, where the fluid activity is required to move the molecules. is effectively more rigid because the molecules The speed of sound waves in the sea, C, is are pushed together. Salinity variations have given by a negligible effect in most locations. In the upper layers, where temperature is high, sound C ¼ð Þ1=2 where ¼ 1ð = pÞ br b r vr v q;S: speed is high, and decreases downward with (3.13) decreasing temperature (Figure 3.7). However, pressure increases with depth, so that at mid- b is the adiabatic compressibility of seawater depth, the decrease in sound speed due to (with potential temperature and salinity cooler water is overcome by an increase in constant), r is the density, p is the pressure, q sound speed due to higher pressure. In most is the potential temperature, and S is the areas of the ocean, the warm water at the surface salinity. Since b and r depend (nonlinearly) and the high pressure at the bottom produce on temperature and pressure, and to a lesser maximum sound speeds at the surface and extent, salinity, so does the speed of sound bottom and a minimum in between. The waves. There are various formulae for the sound-speed minimum is referred to as the dependence of Eq. (3.13) on T, S, and p; all SOund Fixing And Ranging (SOFAR) channel. derived from experimental measurements. In Figure 3.6, the sound-speed minimum is at The two most accepted are those of Del Grosso about 700 m depth. In regions where tempera- (1974) and of Chen and Millero (1977); Del ture is low near the sea surface, for instance at Grosso’s equation is apparently more accurate, high latitudes, there is no surface maximum in based on results from acoustic tomography and sound speed, and the sound channel is found inverted echo sounder experiments (e.g., at the sea surface. Meinen & Watts, 1997). Both are long and Sound propagation can be represented in nonlinear polynomials, as is the equation of terms of rays that trace the path of the sound state. We present a simpler formula, which (Figure 3.8). In the SOFAR channel, at about itself is simplified from Mackenzie (1981) and 1100 m in Figure 3.8, sound waves directed at SOUND IN THE SEA 51

FIGURE 3.7 For station Papa in the Pacific Ocean at 39N, 146W, August, 1959: (a) temperature (C) and salinity (psu) profiles, (b) corrections to sound speed due to salinity, temperature, and pressure, (c) resultant in situ sound-speed profile showing sound-speed minimum (SOFAR channel). moderate angles above the horizontal are where the temperature decreases substantially refracted downward, across the depth of the as depth increases. At high latitudes where the sound-speed minimum, and then refracted temperatures near the surface may be constant upward; they continue to oscillate about the or even decrease toward the surface, the sound sound-speed minimum depth. (Rays that travel speed can have a surface minimum (Figure 3.8a). steeply up or down from the source will not be The much shallower sound channel, called channeled but may travel to the surface or a surface duct, may even be in the surface layer. bottom and be reflected there.) Low frequency In this case, downward directed sound rays sound waves (hundreds of hertz) can travel from a shallow source are refracted upward considerable distances (thousands of kilome- while upward rays from the subsurface source ters) along the SOFAR channel. This permits are reflected downward from the surface and detection of submarines at long ranges and has then refracted upward again. In this situation, been used for locating lifeboats at sea. Using detection of deep submarines from a surface the SOFAR channel to track drifting subsurface ship using sonar equipment mounted in the floats to determine deep currents is described hull may not be possible and deep-towed sonar in Chapter S6, Section S6.5.2 of the supple- equipment may be needed. In shallow water mental materials located on the textbook (e.g., bottom depth <200 m), reflection can occur Web site. both from the surface and from the bottom. The deep SOFAR channel of Figure 3.8b is A pulse transmitted from a source near the characteristic of middle and low latitudes, SOFAR channel axis does not appear to 52 3. PHYSICAL PROPERTIES OF SEAWATER

FIGURE 3.8 Sound ray diagrams: (a) from a shallow source for a sound-speed proﬁle initially increasing with depth in upper mixed layer to a shallow minimum and then decreasing, and (b) from a sound source near the speed minimum in the sound channel for a typical open ocean sound-speed proﬁle.

distant receivers as a sharp pulse but as in the refracted ray paths compensates for a drawn-out signal rising slowly to a peak fol- the greater distance they travel, so the direct lowed by a sharp cutoff. The peak before the ray arrives last. cutoff is the arrival of the sound energy along Sound is used widely to locate and observe the sound channel axis (direct signal), while solid objects in the water. Echo sounders are the earlier arrivals are from sound that trav- used to measure bottom depths to the ocean’s eled along the refracted ray routes. It might maximum depth of more than 11,000 m. SONAR appear in Figure 3.8b that the refracted rays (SOund Navigation And Ranging) can deter- have to travel a greater distance than the mine the direction and distance to a submarine direct ray and would thus be delayed, but at ranges of hundreds of meters and to schools this is an illusion. Figure 3.8b is drawn with of fish at somewhat lesser ranges. Sidescan gross vertical exaggeration to enable the rays sonars determine the structure of the ocean to be shown clearly, but the differences in bottom and can be used to locate shipwrecks. distances traveled by refracted rays and the Acoustically tracked Swallow floats (see direct rays are very small; the greater speed Chapter S6, Section S6.5.2 of the supplemental SOUND IN THE SEA 53 material on the textbook Web site) provided toward the sea surface at dusk to feed and some of the first direct observations of deep back down at dawn. This layer was first identi- currents. Current speeds (or the speed of fied because of the scattering produced by the a ship relative to the water) are often measured plankton and (gas-filled) fish bladders. using the reflection of sound waves from small Sound is used to determine the speed of particles moving with the water, applying the ocean currents and of ships, using a technique principle of Doppler shift. Because temperature called acoustic Doppler profiling (see Chapter and density affect the sound velocity, sound can S6, Section S6.5.5.1 of the supplemental material be used to infer ocean water characteristics and located on the textbook Web site). Sound is their variations. Sound is used to measure transmitted from a source and reflects off the surface processes such as precipitation, a measure- particles (mainly plankton) in the water and ment that is otherwise nearly impossible to returns back to a receiver. If the source is moving determine. relative to the particles, then the received sound In echo sounding, short pulses of sound wave has a different frequency from the trans- energy are directed vertically downward where mitted wave, a phenomenon called Doppler they reflect off of the bottom and return to the shifting. Doppler shift is familiar to anyone ship. (Echo sounders are also used to detect who has listened to the sound of a siren when shoals of fish, whose air bladders are good reflec- an emergency vehicle first approaches (Doppler tors of sound energy. Modern “fish finders” are shifting the sound to a higher frequency and, simply low-cost echo sounders designed to therefore, a higher pitch) and then retreats respond to the fish beneath the vessel.) The away (Doppler shifting the sound to a lower acoustic travel time, t, yields the depth D ¼ frequency and lower pitch). Acoustic Doppler Cot/2, where Co is the mean sound speed speed logs are common on ships and give a rela- between the surface and the bottom. Trans- tively accurate measure of the speed of the ship ducers in ordinary echo sounders are not much through the water. If the ship’s speed is tracked larger than the wavelength of the sound, so the very precisely using, for instance, GPS naviga- angular width of the sound beam is large. Wide tion, then the ship speed can be subtracted beams cannot distinguish the details of bottom from the speed of the ship relative to the water topography. For special sounding applications, to yield the speed of the water relative to the much larger sound sources that form a narrower GPS navigation, providing a measure of current beam are used. It is also possible to improve the speeds. Acoustic Doppler current profilers are resolution by using higher frequencies (up to 100 also moored in the ocean to provide long-term kHz or even 200 kHz), but the absorption of records of current speeds. sound energy by seawater increases roughly as Sound can be used to map the ocean’s the square of the frequency, so higher frequency temperature structure and its changes, through echo sounders cannot penetrate as deeply. a technique called acoustic tomography (see Inhomogeneities distort an initial sharp Chapter S6, Section S6.6.1 of the supplemental sound pulse so that the signal received at material located on the textbook Web site). Since a hydrophone is likely to have an irregular tail sound speed depends on temperature, temp- of later arrival sounds. This is referred to as erature changes along a ray path result in travel reverberation. One source of reverberation is the time changes. With extremely accurate clocks, “deep scattering layer,” which is biological in these changes can be detected. If multiple ray nature. This layer is characterized by diel paths crisscross a region, the travel time changes (day/night) vertical migrations of several can be combined using sophisticated data anal- hundreds of meters; the organisms migrate ysis techniques to map temperature changes in 54 3. PHYSICAL PROPERTIES OF SEAWATER the region. This technique has been especially Absorption (attenuation) of the sun’s energy useful in studying the three-dimensional struc- in the upper layer depends on the materials ture of deep convection in regions and seasons within the water; therefore these materials affect that are virtually impossible to study from how heating is distributed in the surface layer research ships. Similar techniques have been and affects mixed layer processes. General applied to very long distance monitoring of circulation models that are run with observed basin-average ocean temperature, which is forcing sometimes use information about light possible because of the lack of attenuation of attenuation, affecting mixed layer formation sound waves over extremely long distances and, consequently, sea surface temperature in (Munk & Wunsch, 1982). However, large-scale the model. monitoring of ocean temperature changes Section 3.8.1 describes the optical properties using sound has been eclipsed by the global of seawater and Section 3.8.2 describes the temperatureesalinity profiling float array, Argo, quantity that is observed as ocean color. Exam- which provides local as well as basin-average ples of observations are shown in Chapter 4. information. Much more information about ocean acoustics 3.8.1. Optical Properties can be found in textbooks such as Urick (1983). The sun irradiates the earth with a peak in the visible spectrum (wavelengths from about 400 3.8. LIGHT AND THE SEA to 700 nm, from violet to red, where 1 nm ¼ 109 m). Sunlight behaves differently in water This is a very brief introduction to a complex and air. The ocean absorbs light in much shorter subject. Full treatments are available in various distances than the atmosphere. When this short- sources; some suggestions are Mobley (1995) wave energy penetrates the sea, some of it is and Robinson (2004). scattered, but much is absorbed, almost all Sunlight with a range of wavelengths enters within the top 100 m. The energy is attenuated the sea after passing through the atmosphere. approximately exponentially. This is the photic Within the upper layer of the ocean, up to 100 (euphotic) zone, where photosynthesis occurs. m depth or more, the visible light interacts This penetration of solar energy into the ocean’s with the water molecules and the substances upper layer is also important in the ocean’s heat that are dissolved or suspended in the water. budget (Chapter 5). The light provides energy for photosynthesis A schematic overview of the ocean’s optical and also heats the upper layer. Processes of back- processes is shown in Figure 3.9, after Mobley scattering, absorption, and re-emission result in (1995), who provides much greater detail and the visible light (ocean color) that emerges back precise expressions for each of the quantities from the ocean surface into the atmosphere. in the diagram. Each of the quantities can be This emerging radiation is then measured with observed, with greater or lesser difficulty. At instruments above the sea surface, including the top of the diagram, the external environ- satellites. For satellite observations, the atmo- mental quantities that determine the amount sphere again affects the signal from the sea. of radiation entering the ocean are the sun’s Observations of ocean color by satellites can radiance distribution, which depends on its then be related to the processes within the ocean position and on sky conditions; the sea state, that affect the emerging light, including an abun- since this determines how much radiation is dance of phytoplankton, particulate organic reflected without entering the sea; and the ocean carbon, suspended sediment, and so forth. bottom, if it is shallow enough to intercept the LIGHT AND THE SEA 55

FIGURE 3.9 Schematic Environment of optical processes in Incident radiance (sun seawater. Adapted and position and sky conditions) simpliﬁed from Mobley Sea State (1995), with added indi- Bottom condition cators of seawater heating and photosynthesis, as Reflectance well as satellite observa- (ocean color) tion of ocean color. Apparent optical Radiometric quantities Inherent optical properties of the ocean properties of seawater Downwelling and upwelling Reflectance irradiance Absorption Downwelling and upwelling Photosynthetically available Scattering irradiance attenuation radiation (PAR) PAR attenuation

Upper layer heating Photosynthesis light. The inherent optical properties of the observation point; therefore it is the integral of seawater determine how it absorbs and scatters radiance over all solid angles, and has units of radiation, as a function of wavelength; this W/m2 for total irradiance, or W/(m2 nm) for depends on the matter that is dissolved, sus- spectral irradiance (which is a function of wave- pended, or active (in the case of phytoplankton). length). Next, upwelling irradiance is defined as The environmental conditions and inherent the irradiance from all solid angles below the optical properties work together through a radi- observation point; downwelling irradiance ative transfer equation to set the radiometric would come from all angles above that point. quantities of the medium. Here it is useful to Reflectance is the ratio of upwelling irradiance provide some definitions of the radiometric to downwelling irradiance, defined at a point; quantities listed in the middle box of Figure 3.9. reflectance defined this way has no units. It is First, we note that light from a source, which not the same as actual reflected light from the could be at any point in a medium in which light sea surface. Rather, reflectance is the light is diffused or scattered, illuminates a complete emerging from the ocean. For remote sensing, sphere around the source. Therefore the solid in which the radiation from the ocean’s surface angle, measured in “steradians” (sr), is a useful is being measured from a specified location, measure, similar to area. Next, the flux of energy rather than from all directions, reflectance can from the light is measured in Watts (J/sec). The be defined alternatively as the ratio of upwelling radiance is the flux of energy per unit area and radiance to downwelling irradiance; in this case, per unit steradian; it is measured in units of reflectance has units of (sr1). W/(sr m2). If the radiance is measured as a func- Finally, the amount of radiation available for tion of wavelength of the light (i.e., spectral photosynthesis (photosynthetically available radiance), then its units are W/(sr m2 nm) if radiation; PAR) is measured in photons s1 m2. wavelength is measured in nanometers. Returning to Figure 3.9, the rightmost bottom The irradiance is the total amount of radiance box lists the apparent optical properties of the that reaches a given point (i.e., where your seawater. These include the rate at which light optical measurement is made), so it is the sum is attenuated within the water column, and of radiance coming in from all directions to the how much light returns back out through the 56 3. PHYSICAL PROPERTIES OF SEAWATER sea surface (indicated as reflectance). The irradi- because of the extra attenuation due to sus- ance and PAR are attenuated with increasing pended particulate matter and dissolved mate- depth as the radiation is absorbed, scattered, rials. The largest attenuation coefficient listed and used for photosynthesis by phytoplankton. in the table, K ¼ 2m1, represents very turbid Attenuation is often approximately exponential. water with many suspended particles. If attenuation were exactly exponential, of the In seawater, the attenuation coefficient K Kz form I(z) ¼ Io e , where Io is the radiation also varies considerably with wavelength. intensity at the sea surface, I the intensity at Figure 3.10b shows the relative amounts of a depth z meters below the surface, and K the energy penetrating clear ocean water to 1, 10, vertical attenuation coefficient of the water, and 50 m as a function of wavelength (solid then the apparent optical properties would be curves). Light with blue wavelengths penetrates expressed in terms of the e-folding depth, K. deepest; penetration by yellow and red is much The actual attenuation is not exponential, so less. That is, blue light, with wavelength of the attenuation coefficient, K, is proportional about 450 nm, has the least attenuation in clear to the depth derivative of the radiation intensity ocean water. At shorter and longer wavelengths (and would be equal to the e-folding depth if the (in the ultraviolet and red), the attenuation is dependence were exponential). much greater. The increased attenuation in the The effects of depth and constant attenuation ultraviolet is not important to the ocean’s heat coefficient on light intensity are illustrated in budget, because the amount of energy reaching Table 3.3, from Jerlov (1976). The coefficient K sea level at such short wavelengths is small. depends mainly on factors affecting absorption Much more solar energy is contained in and of light in the water and to a lesser extent on beyond the red end of the spectrum. Virtually scattering. The last two columns of Table 3.3 all of the energy at wavelengths shorter than indicate the range of penetrations found in the visible is absorbed in the top meter of water, actual seawater. while the energy at long wavelengths (1500 nm The smallest attenuation coefficient in Table or greater) is absorbed in the top few 3.3 (K ¼ 0.02 m1) represents the clearest ocean centimeters. water and deepest penetration of light energy. All wavelengths are attenuated more in Energy penetrates coastal waters less readily turbid water than in clear water. In clear ocean

TABLE 3.3 Amount of Light Penetrating to Speciﬁed Depths in Seawater as a Percentage of that Entering Through the Surface

L Vertical Attenuation Coefﬁcient K (m 1) Clearest Ocean Water Turbid Coastal Water Depth (m) K ¼ 0.02 K ¼ 0.2 K ¼ 2 0 100% 100% 100% 100% 100% 198 82 14 45 18 2 96 67 2 39 8

10 82 14 0 22 0 50 37 0 0 5 0 100 14 0 0 0.5 0

Jerlov, 1976. LIGHT AND THE SEA 57

FIGURE 3.10 (a) Attenuation

coefﬁcient kl, as a function of wavelength l (mm) for clearest ocean water (solid line) and turbid coastal water (dashed line). (b) Relative energy reaching 1, 10, and 50 m depth for clearest ocean water and reaching 1 and 10 m for turbid coastal waters.

water, there is enough light at 50 to 100 m to Red or yellow objects appear darker in color permit a diver to work, but in turbid coastal or even black as they are viewed at increasing waters almost all of the energy may have been depths because the light at the red end of the absorbed by a depth of 10 m. K is larger for spectrum has been absorbed in the upper turbid water than clear (Figure 3.10a), and the layers and little is left to be reflected by the least attenuation is in the yellow part of the objects. Blue or green objects retain their colors spectrum. In turbid water, less energy pene- to greater depths. trates to 1 m and 10 m, and the maximum pene- The presence of plankton in seawater also tration is shifted to the yellow (Figure 3.10b). changes the penetration depth of solar radia- (The energy reaching 50 m in this turbid tion, and hence the depth at which the sun’s water is too small to show on the scale of this heat is absorbed. This changes the way the graph.) surface mixed layer develops, which can in In clear ocean water, the superior penetra- turn impact the plankton, leading to a feedback. tion of blue and green light is evident both There are significant and permanent geograph- visually when diving and also in color photo- ical variations in this vertical distribution of graphs taken underwater by natural light. absorption, since some regions of the world 58 3. PHYSICAL PROPERTIES OF SEAWATER ocean have much higher biological productivity inorganic materials carried into the ocean by than others. rivers can impart their own color to the water. In some fjords, the low-salinity surface layer 3.8.2. Ocean Color may be milky white from the finely divided “rock flour” produced by abrasion in the To the eye, the color of the sea ranges from glaciers and carried down by the melt water. deep blue to green to greenish yellow (Jerlov, The sediment can be kept in suspension by 1976). Broadly speaking, deep or indigo blue turbulence in the upper layer for a time, but color is characteristic of tropical and equatorial when it sinks into the saline water, it flocculates seas, particularly where there is little biological (forms lumps) and sinks more rapidly. When production. At higher latitudes, the color diving in such a region the diver may be able changes through green-blue to green in polar to see only a fraction of a meter in the upper regions. Coastal waters are generally greenish. layer but be able to see several meters in the Two factors contribute to the blue color of saline water below. open ocean waters at low latitudes. Because The color of seawater and depth of penetra- water molecules scatter the short-wave (blue) tion of light were traditionally judged using light much more than the long-wave (red) light, a white Secchi disk (see Chapter S6, Section the color seen is selectively blue. In addition, S6.8 of the supplemental materials located on because the red and yellow components of the textbook Web site) lowered from the ship. sunlight are rapidly absorbed in the upper few This method has been superseded by a suite of meters, the only light remaining to be scattered instruments that measure light penetration at by the bulk of the water is blue. Looking at the different wavelengths, transparency of the sea from above, sky light reflected from the water at various wavelengths, and fluorescence. surface is added to the blue light scattered Most important, color observations are now from the body of the water. If the sky is blue, made continuously and globally by color the sea will still appear deep blue, but if there sensors on satellites. are clouds, the white light reflected from the Ocean color is a well-defined quantity, related sea surface dilutes the blue scattered light to reflectance (Figure 3.9 and definition in from the water and the sea appears less Section 3.8.1). Reflectance, or ocean color, can intensely blue. be measured directly above the ocean’s surface. If there are phytoplankton in the water, their Observations of ocean color since the 1980s chlorophyll absorbs blue light and also red light, have been made from satellites, and must be which shifts the water color to green. (This is corrected for changes as the light passes also why plants are green.) The organic prod- upward through the atmosphere. Ocean color ucts from plants may also add yellow dyes to observations are then converted, through the water; these will absorb blue and shift the complex algorithms, to physically useful quan- apparent color toward the green. These shifts tities such as the amount of chlorophyll in color generally occur in the more productive present, or the amount of particulate organic high-latitude and coastal waters. In some carbon, or the amount of “yellow substance” coastal regions, rivers carry dissolved organic (gelbstoff) that is created by decaying vegeta- substances that emphasize the yellowish green tion. With global satellite coverage, these quan- color. The red color that occurs sporadically in tities can be observed nearly continuously and some coastal areas, the so-called red tide, is in all regions. caused by blooms of reddish brown phyto- Robinson (2004) provided a complete treat- plankton. Mud, silt, and other finely divided ment of the optical pathways involved in ocean LIGHT AND THE SEA 59 color remote sensing, starting with consider- contribution is from the atmospheric pathway ation of the total radiance observed by the satel- Lp. The water-leaving and reflected radiances lite sensor. Many pathways contribute to the are much smaller. Because of the weak signal observed radiance. These can be grouped into strength for the ocean pathways (water-leaving an atmospheric path radiance (Lp), a “water- radiance), ocean color remote sensing requires leaving radiance” from just below the sea very precise atmospheric correction of the surface (Lw), and a radiance due to all surface visible light sensed by the satellite. Complex reflections (Lr) within the instantaneous field radiative transfer models are invoked to carry of view of the satellite sensor. The radiance Ls out this correction and often the accuracy of received at the satellite sensor is the chlorophyll estimates depends critically on this atmospheric correction. After correction, Ls ¼ Lp þ TLw þ TLr (3.15) the resultant radiances are analyzed for various components related to biological activity, partic- T is the transmittance, which gives the ularly chlorophyll. proportion of radiance that reaches the sensor The biggest effect of chlorophyll on the spec- without being scattered out of the field of view. trum of reflectance (normalized water-leaving The water-leaving radiance provides the radiance) is to reduce the energy at the blue information about ocean color, so it is the end of the spectrum compared with the spec- desired observed quantity. It is closely related trum for clear water. This is demonstrated in to the reflectance; the ratio of water-leaving Figure 3.11 (H. Gordon, personal communica- radiance just above the sea surface to downwel- tion, 2009). Here the spectrum of radiance is ling irradiance incident on the sea surface is the shown with and without correction for the “remote sensing reflectance,” or “normalized atmosphere. When the atmosphere is not water-leaving radiance.” The three net radiance removed, there is virtually no difference terms depend on the wavelength and on the between the spectra for low and high chloro- turbidity of the seawater. The largest phyll waters. When the atmospheric signal is

FIGURE 3.11 Example of observations of water-leaving radiance observed by the Multi-angle Imaging SpectroRadiometer (MISR), with bands observed by satellite color sensors indicated. Solid curves: low chlorophyll water (0.01 mg/m3). Dotted curves: high chlorophyll water (10.0 mg/m3). The two lower curves have the atmospheric signal removed. (H. Gordon, personal communication, 2009.) 60 3. PHYSICAL PROPERTIES OF SEAWATER removed, the desired difference emerges. The and salinity structure in the upper layer by high chlorophyll spectrum is depressed at melting and freezing, and is a major hindrance the blue end of the spectrum and elevated at to navigation. Ice cover is an important part of the green and red. Earth’s climate feedbacks because of its high Ocean color observations from satellites can reflectivity, that is, its high albedo (Section also be used as a proxy for the attenuation prop- 5.4.3). The iceealbedo feedback, which affects erties of seawater, which can be used in mixed climate, is described in Section 5.4.5, and is espe- layer models that are set up to be run with cially important in the Arctic (Section 12.8). observed atmospheric forcing. Absorption of solar radiation in the ocean heats the upper 3.9.1. Freezing Process layer. The time and space distribution of absorption is directly related to the substances in the When water loses sufficient heat (by radia- water column, and this affects ocean color. In tion, conduction to the atmosphere, convection, practice, at present most mixed layer models or evaporation) it freezes to ice, in other words, in ocean general circulation models use a sum it changes to the solid state. Initial freezing of two exponentially decaying functions that occurs at the surface and then the ice thickens are proxies for attenuation of red light (quickly by freezing at its lower surface as heat is con- absorbed) and blue-green light (penetrating ducted away from the underlying water much deeper), with coefficients based on through the ice to the air. assumption of a particular Jerlov (1976) water The initial freezing process is different for type (Paulson & Simpson, 1977). However, fresh and low-salinity water than for more explicit incorporation of biological effects on saline water because the temperature at which attenuation (incorporation of ocean color obser- water reaches its maximum density varies vations and of bio-optical models along with with salinity. Table 3.4 gives the values of the mixed layer models) is being tested widely freezing point and temperature of maximum and is a likely direction for the future, since density for water of various salinities. (Note the effects on modeled mixed layer temperature that the values are for freezing, etc., at atmo- are clear (Wu, Tang, Sathyendranath, & Platt, spheric pressure. Increased pressure lowers 2007) and can in fact affect the temperature the freezing point, which decreases by about of the overlying atmosphere (Shell, Frouin, 0.08 K per 100 m increase in depth in the sea.) Nakamoto, & Somerville, 2003). To contrast the freezing process for freshwater and seawater, first imagine a freshwater lake where the temperature initially decreases 3.9. ICE IN THE SEA from about 10C at the surface to about 5C

Ice in the sea has two origins: the freezing of TABLE 3.4 Temperatures of the Freezing Point (tf) and seawater and the ice broken off from glaciers. of Maximum Density (trmax) for Fresh and The majority of ice comes from the first of these Salt Water sources and is referred to as ; the glaciers sea ice S 0 10 20 24.7 30 35 psu supply “pinnacle” icebergs in the Northern Hemisphere and flat "tabular" icebergs in the tf 0 0.5 1.08 1.33 1.63 1.91 C Southern Hemisphere. Sea ice alters the heat trmax þ3.98 þ1.83 0.32 1.33 d C and momentum transfers between the atmo- Note that the values for freezing and so forth are at atmospheric sphere and the ocean, is a thermal insulator, pressure. Increased pressure lowers the freezing point, which damps surface waves, changes the temperature decreases by about 0.08 K per 100 m increase in depth in the sea. ICE IN THE SEA 61 at about 30 m depth. As heat is lost through the first process is the formation of needle-like surface, the density of the water increases and crystals of pure ice, which impart an “oily” vertical convective mixing (overturn) occurs appearance to the sea surface (grease or frazil with the temperature of the surface water layer ice). The crystals increase in number and form gradually decreasing. This continues until the a slush, which then thickens and breaks up upper mixed layer cools to 3.98C and then into pancakes of approximately one meter further cooling of the surface water causes its across. With continued cooling, these pancakes density to decrease and it stays near the top. grow in thickness and lateral extent, eventually The result is a rapid loss of heat from a thin forming a continuous sheet of floe or sheet ice. surface layer, which soon freezes. For seawater Once ice has formed at the sea surface, when of salinity ¼ 35 psu of the same initial temper- the air is colder than the water below, freezing ature distribution, surface cooling first results continues at the lower surface of the ice and in a density increase and vertical mixing by the rate of increase of ice thickness depends on convention currents occurs through a gradually the rate of heat loss upward through the ice increasing depth, but it is not until the (and any snow cover). This loss is directly whole column reaches 1.91C that freezing proportional to the temperature difference commences. As a much greater volume of between top and bottom surfaces and inversely water has to be cooled through a greater proportional to the thickness of the ice and snow temperature range than in the freshwater cover. case, it takes longer for freezing to start in With very cold air, a sheet of sea ice of up to salt water than in freshwater. A simple calcula- 10 cm in thickness can form in 24 hours, the tion for a column of freshwater of 100 cm depth rate of growth then decreasing with increasing and 1 cm2 cross-section initially at 10C shows ice thickness. Snow on the top surface insulates that it takes a heat loss of l63 J to freeze the top it and reduces the heat loss markedly, depend- 1 cm layer, whereas for a similar column of ing on its degree of compaction. For instance, seawater of S ¼ 35 psu it takes a loss of 305 J 5 cm of new powder snow may have insulation to freeze the top 1 cm because the whole equivalent to 250e350 cm of ice, while 5 cm of column has to be cooled to 1.91C rather settled snow can be equivalent to only 60e100 than just the top 1 cm to 0C for the freshwater. cm of ice, and 5 cm of hard-packed snow can Note that as seawater of salinity <24.7 psu be equivalent to only 20e30 cm of ice. has a higher temperature of maximum density As an example of the annual cycle of the than its freezing point, it will behave in a manner development of an ice sheet at a location in the similar to freshwater, although with a lower Canadian Arctic, ice was observed to start to freezing point. For seawater of salinity >24.7 form in September, was about 0.5 m thick in psu, (in high latitudes) the salinity generally October, 1 m in December, 1.5 m in February, increases with depth, and the stability of the and reached its maximum thickness of 2 m in water column usually limits the depth of Maydafter which it started to melt. convection currents to 30e50 m. Therefore ice starts to form at the surface before the deep 3.9.2. Brine Rejection water reaches the freezing point. Generally, sea ice forms first in shallow water In the initial stage of ice-crystal formation, salt near the coast, particularly where the salinity is is rejected and increases the density of the neigh- reduced by river runoff and where currents are boring seawater, some of which then tends to minimal. When fully formed, this sea ice con- sink and some of which is trapped among the nected to the shore is known as “fast ice.” The ice crystals forming pockets called “brine cells.” 62 3. PHYSICAL PROPERTIES OF SEAWATER

The faster the freezing, the more brine is trapped. the ice crystals) or less (if the brine has escaped Sea ice in bulk is therefore not pure water-ice but and gas bubbles are present.) Values from 924 to has a salinity of as much as 15 psu for new ice 857 kg/m3 were recorded on the Norwegian (and less for old ice because gravity causes the Maud Expedition (Malmgren, 1927). brine cells to migrate downward in time). With The amount of heat required to melt sea ice continued freezing, more ice freezes out within varies considerably with its salinity. For S ¼ 0 the brine cells leaving the brine more saline, in psu (freshwater ice) it requires 19.3 kJ/kg from a process called brine rejection.Someofthesalts 2 C and 21.4 kJ/kg from 20 C, while for sea may even crystallize out. ice of S ¼ 15 psu, it requires only 11.2 kJ/kg Because of brine rejection, the salinity of first- from 2C but 20.0 kJ/kg from 20C. The small year ice is generally 4e10 psu, for second-year difference of heat (2.1 kJ/kg) needed to raise the ice (ice that has remained frozen beyond the first temperature of freshwater ice from 20Cto year) salinity decreases to 1e3 psu, and for 2C is because no melting takes place; that is, multiyear ice salinity may be less than 1 psu. If it is a true measure of the specific heat of pure sea ice is lifted above sea level, as happens ice. However, for sea ice of S ¼ 15 psu, more when ice becomes thicker or rafting occurs, the heat (8.8 kJ/kg) is required to raise its tempera- brine gradually trickles down through it and ture through the same range, because some ice eventually leaves almost salt-free, clear old ice. near brine cells melts and thus requires latent Such ice may be melted and used for drinking heat of melting as well as heat to raise its temper- whereas melted new ice is not potable. Sea ice, ature. Note also that less heat is needed to melt therefore, is considered a material of variable new ice (S ¼ 15 psu) than old ice, which has composition and properties that depends very a lower salinity. much on its history. (For more detail see Doronin & Kheisin, 1975.) 3.9.4. Mechanical Properties of Sea Ice As a result of brine rejection, the salinity of the unfrozen waters beneath the forming sea Because of the spongy nature of first-year sea ice increases. When this occurs in shallow ice (crystals þ brine cells) it has much less regions, such as over continental shelves, the strength than freshwater ice. Also, as fast freezing increase in salinity can be marked and can result results in more brine cells, the strength of ice in formation of very dense waters. This is the formed this way is less than when freezing occurs dominant mechanism for formation of the slowly; in other words, sea ice formed in very deep and bottom waters in the Antarctic cold weather is initially weaker than ice formed (Chapter 13), and for formation of the densest in less cold weather. As the temperature of ice part of the North Pacific Intermediate Water decreases, its hardness and strength increase, in the Pacific (Chapter 10). Brine rejection is and ice becomes stronger with age as the brine a central process for modification of water cells migrate downward. When ice forms in masses in the Arctic as well (Chapter 12). calm water, the crystals tend to line up in a pattern and such ice tends to fracture along cleavage 3.9.3. Density and Thermodynamics planes more easily than ice formed in rough of Sea Ice water where the crystals are more randomly arranged and cleavage planes are not formed. The density of pure water at 0C is 999.9 The mechanical behavior of sea ice is kg/m3 and that of pure ice is 916.8 kg/m3. complex when temperature changes. As the ice However the density of sea ice may be greater temperature decreases below its freezing point, than this last figure (if brine is trapped among the ice expands initially, reaches a maximum ICE IN THE SEA 63 expansion, and then contracts. For instance, an ridges increase the wind stress). Typical ice ice floe of S ¼ 4 psu will expand by 1 m per speeds are 1 to 2% of the wind speed. 1 km length between 2 and 3C, reaches its (b) Frictional drag on the bottom of an ice sheet maximum expansion at 10C, and thereafter moving over still water tends to slow it contracts slightly. Ice of S ¼ 10 psu expands down, while water currents (ocean and 4 m per 1 km length from 2to3C, and tidal) exert a force on the bottom of the ice in reaches its maximum expansion at 18C. The the direction of the current. Because current expansion on cooling can cause an ice sheet to speeds generally decrease with increase in buckle and “pressure ridges” to form, while depth, the net force on deep ice and icebergs contraction on further cooling after maximum will be less than on thin ice, and pack ice will expansion results in cracks, sometimes wide, move past icebergs when there is significant in the ice sheet. wind stress. Pressure ridges can also develop as a result of (c) In the cases of (a) and (b), the effect of the wind stress on the surface driving ice sheets Coriolis force (Section 7.2.3) is to divert together. The ridges on top are accompanied the ice motion by 15e20 degrees to the by a thickening of the lower surface of the ice right of the wind or current stress in the by four to five times the height of the surface Northern Hemisphere (to the left in the ridges. Sea ice generally floats with about five- Southern Hemisphere). (It was the sixths of its thickness below the surface and observation of the relation between wind one-sixth above, so relatively small surface direction and ice movement by Nansen, ridges can be accompanied by deep ridges and communicated by him to Ekman, that underneath d depths of 25 to 50 m below the caused the latter to develop his well- sea surface have been recorded. Thickening of known theory of wind-driven currents.) an ice sheet may also result from rafting when It is convenient to note that as surface wind or tide forces one ice sheet on top of friction causes the surface wind to blow at another or when two sheets, in compression, about 15 degrees to the left of the surface crumble and pile up ice at their contact. Old isobars, the direction of the latter is ridges, including piled up snow, are referred approximately that in which the ice is to as hummocks. As they are less saline than likely to drift (Northern Hemisphere). newer pressure ridges, they are stronger and (d) If the ice sheet is not continuous, collisions more of an impediment to surface travels than between individual floes may occur with the younger ridges. a transfer of momentum (i.e., decrease of speed of the faster floe and increase of speed of the slower). Energy may go into 3.9.5. Types of Sea Ice and its Motion ice deformation and building up ridges at impact. This is referred to as internal Sea ice can be categorized as fast ice (attached ice resistance and increases with ice to the shore), pack ice (seasonal to multiyear ice concentration, that is, the proportion of area with few gaps), and cap ice (thick, mostly multi- covered by ice. The effect of upper surface year ice), as described in Section 12.7.1. Several roughness (R on a scale of 1 to 9) and ice forces determine the motion of sea ice if it is concentration (C on a scale of 1 to 9) on the not landfast: speed of the ice V (expressed as a percentage (a) Wind stress at the top surface (the of the wind speed) is given by: V ¼ R(1 magnitude depending on the wind speed 0.08C) (taken to only one decimal place), and the roughness of the ice surface as so that the speed of the ice increases with 64 3. PHYSICAL PROPERTIES OF SEAWATER

roughness but decreases with increased 2. Sensible heat polynyas result from relatively ice concentration. Note that for very close warm water upwelling to the surface pack ice, stresses of wind or current are and melting the ice there. Another term integrated over quite large areas and the often encountered is flaw polynya,which local motion may not relate well to the local means that the polynya occurs at the wind. boundary between fast ice and pack ice. Because most polynyas include a mixture 3.9.6. Polynyas and Leads of these forcings, nomenclature is tending toward being more specific about the Regions of nearly open water within the ice forcing (mechanicalewind; convectivee pack are often found where one might expect melting: Williams, Carmack, & Ingram, to find ice. These open water areas are critical 2007). for airesea heat exchange, since ice is a rela- Wind-forced polynyas are usually near coast- tively good insulator. Small breaks between ice lines or the edges of ice shelves or fast ice, where floes are called ; these are created by motion leads winds can be very strong, often forced by strong of the ice pack and have random locations. landesea temperature differences (katabatic Larger recurrent open water areas are called winds). The open water is often continually polynyas. There are two types of polynyas, freezing in these polynyas since they are kept depending on the mechanism maintaining open through mechanical forcing. These wind- the open water (Figure 3.12; see also Barber & forced polynyas act as ice factories, producing Massom, 2007): larger amounts of new ice than regions where 1. Latent heat polynyas are forced open by winds, the ice is thicker and airesea fluxes are mini- often along coasts or ice shelf edges. New ice mized by the ice cover. If these polynyas occur soon forms; latent heat from the forming sea over shallow continental shelves, the brine ice is discharged to the atmosphere at a rate rejected in the ongoing sea ice formation of as much as 200e500 W/m2. process, together with temperatures at the

(a) Wind-forced (latent heat) polynya (b)

Wind

Heat loss Melting (sensible heat) polynya, driven by mixing Polynya Sea ice Heat loss Cold, fresher Brine Polynya D Sea ice rejection ense s he Melting lf Tidal mixing w a Cold, fresher te r

Cold, Vertical Warm, saltier saltier excursion

FIGURE 3.12 Schematics of polynya formation: (a) latent heat polynya kept open by winds and (b) sensible heat polynya kept open by tidal mixing with warmer subsurface waters (after Hannah et al., 2009). ICE IN THE SEA 65 freezing point, can produce especially dense 2009), as is a recurrent polynya over Kashevarov shelf waters. This is one of the major mecha- Bank in the Okhotsk Sea (Figure 10.29). nisms for creating very dense waters in the global ocean (Section 7.11), particularly around 3.9.7. Ice Break-up the coastlines of Antarctica (Chapter 13) and the Arctic (Chapter 12), as well as the densest Ice break-up is caused by wave action, tidal (intermediate) water formed in the North Pacific currents, and melting. Melting of ice occurs in the Okhotsk Sea (Chapter 10). when it gains enough heat by absorption of Polynyas that are maintained by melting solar radiation and by conduction from the within the ice pack result from mixing of the air and from nearby seawater to raise its cold, fresh surface layer with underlying temperature above the melting point. The warmer, saltier water. These polynyas might absorption of radiation depends on the albedo also produce sea ice along their periphery of the surface (proportion of radiation since the airesea fluxes will be larger than reflected), which varies considerably; for through the ice cover, but the upward heat example, the albedo for seawater is from 0.05 flux from the underlying warmer water means to 0.10 (it is a very good absorber of radiation), that they produce new ice much less efficiently for snow-free sea ice it is from 0.3 to 0.4, while than wind-forced polynyas. The vertical mixing for fresh snow it is 0.8 to 0.9. Dark materials, can result from convection within the polynya, like dirt and dust, have a low albedo of 0.1 which can occur in deep water formation sites to 0.25 and absorb radiation well. Such mate- such as the Odden-Nordbukta in the Greenland rial on ice can form a center for the absorption Sea (Section 12.2.3). In shallow regions, the mix- of radiation and consequent melting of ice ing process can be greatly enhanced by tides around it, so puddles can form. These can moving the waters over undersea banks absorb heat because of the low albedo of (Figure 3.12b). A number of the well-known water and may even melt right through an polynyas in the Canadian Archipelago in ice sheet. When any open water forms, it the Arctic Ocean are tidally maintained absorbs heat and causes rapid melting of ice (Figure 12.23 from Hannah, Dupont, & Dunphy, floating in it.