3.The di erence between insolation and net infrared radiation is the net heat flux across the top of the atmosphere.

Net Meridional Heat Transport To calculate the meridional heat transport in the atmosphere and the ocean, we first average the net heat flux through the top of the atmosphere in a zonal band. Because the meridional derivative of the transport is the zonal-mean flux, we calculate the transport from the meridional integral of the zonal-mean flux. The integral must be balanced by the heat transported by the atmosphere and the ocean across each latitude band.

Calculations by Trenberth and Caron (2001) show that the total, annualmean, meridional heat transport by the ocean and atmosphere peaks at 6 PW toward each pole at 35◦ latitude.

Oceanic Heat Transport The meridional heat transport in the ocean can be calculated three ways:

1.Surface Flux Method calculates the heat flux through the sea surface from measurements of wind, insolation, air, and sea temperature, and cloudiness. The fluxes are integrated to obtain the zonal average of the heat flux (figure 5.7). Finally, we calculate the transport from the meridional integral of the zonal-mean flux just as we did at the top of the atmosphere.

2.Direct Method calculates the heat transport from values of current velocity and temperature measured from top to bottom along a zonal section spanning an ocean basin. The flux is the product of northward velocity and heat content derived from the temperature measurement.

3.Residual Method first calculates the atmospheric heat transport from atmospheric measurements or the output of numerical weather models. This is the direct method applied to the atmosphere. The atmospheric transport is subtracted from the total meridional transport calculated from the top-of-the-atmosphere heat flux to obtain the oceanic contribution as a residual (figure 5.11).

Various calculations of oceanic heat transports, such as those shown in figure 5.11, tend to be in agreement, and the error bars shown in the figure are realistic. The total meridional transport of heat by the ocean is small compared with the total meridional heat transport by the atmosphere except in the tropics. At 35◦, where the total meridional heat transport is greatest, the ocean carries only 22% of the heat in the northern hemisphere, and 8% in the southern (Trenberth and Caron, 2001).

5.8Variations in Solar Constant

We have assumed so far that the solar constant, the output of light and heat from the sun, is steady. Recent evidence based on variability of sunspots and faculae (bright spots) shows that the output varied by ±0.2% over centuries (Lean, Beer, and Bradley, 1995), and that this variability is correlated with changes in global mean temperature of earth’s surface of ±0.4◦C. (figure 5.12). In addition, White and Cayan (1998) found a small 12 yr, 22 yr, and longerperiod variations of sea-surface temperature measured by bathythermographs

Figure 5.11 Northward heat transport for 1988 in each ocean and the total transport summed over all ocean calculated by the residual method using atmospheric heat transport from ecmwf and top of the atmosphere heat fluxes from the Earth Radiation Budget Experiment satellite. After Houghton et al. (1996: 212), which used data from Trenberth and Solomon (1994). 1 PW = 1 petawatt = 1015 W.

Figure 5.12 Changes in solar constant (total solar irradiance) and global mean temperature of earth’s surface over the past 400 years. Except for a period of enhanced volcanic activity in the early 19th century, surface temperature is well correlated with solar variability. After Lean, personal communication.

and ship-board thermometers over the past century. The observed response of earth to solar variability is about that calculated from numerical models of the coupled ocean-atmosphere climate system. Many other changes in climate and weather have been attributed to solar variability. The correlations are somewhat controversial, and much more information can be found in Hoyt and Schatten’s (1997) book on the subject.

5.9Important Concepts

1.Sunlight is absorbed primarily in the tropical ocean. The amount of sunlight changes with season, latitude, time of day, and cloud cover.

2.Most of the heat absorbed by the ocean in the tropics is released as water vapor which heats the atmosphere when water is condenses as rain. Most of the rain falls in the tropical convergence zones, lesser amounts fall in mid-latitudes near the polar front.

3.Heat released by rain and absorbed infrared radiation from the ocean are the primary drivers for the atmospheric circulation.

4.The net heat flux from the ocean is largest in mid-latitudes and o shore of Japan and New England.

5.Heat fluxes can be measured directly using fast response instruments on low-flying aircraft, but this is not useful for measuring heat fluxes over large oceanic regions.

6.Heat fluxes through large regions of the sea surface can be calculated from bulk formula. Seasonal, regional, and global maps of fluxes are available based on ship and satellite observations.

7.The most widely used data sets for studying heat fluxes are the International Comprehensive Ocean-Atmosphere Data Set and the reanalysis of meteorological data by numerical weather prediction models.

8.The atmosphere transports most of the heat needed to warm latitudes higher than 35◦. The oceanic meridional transport is comparable to the atmospheric meridional transport only in the tropics.

9.Solar output is not constant, and the observed small variations in output of heat and light from the sun seem to produce the changes in global temperature observed over the past 400 years.

more accurate definition. The Joint Panel recommended in 1966 (Wooster, Lee, and Dietrich, 1969) that salinity and chlorinity be related using:

This is the same as (6.1) for S = 35.

Salinity Based on Conductivity At the same time (6.2) was adopted, oceanographers had began using conductivity meters to measure salinity. The meters were very precise and relatively easy to use compared with the chemical techniques used to measure chlorinity. As a result, the Joint Panel also recommended that salinity be related to conductivity of sea water using:

where C(S, 15, 0) is the conductivity of the sea-water sample at 15◦C and atmospheric pressure, having a salinity S derived from (6.4), and C(35, 15, 0) is the conductivity of standard “Copenhagen” sea water. Millero (1996) points out that (6.3) is not a new definition of salinity, it merely gives chlorinity as a function of conductivity of seawater relative to standard seawater.

Practical Salinity Scale of 1978 By the early 1970s, accurate conductivity meters could be deployed from ships to measure conductivity at depth. The need to re-evaluate the salinity scale led the Joint Panel to recommend in 1981 (jpots, 1981; Lewis, 1980) that salinity be defined using only conductivity, breaking the link with chlorinity. All water samples with the same conductivity ratio have the same salinity even though the their chlorinity may di er.

The Practical Salinity Scale of 1978 is now the o cial definition:

where C(S, 15, 0) is the conductivity of the sea-water sample at a temperature of 14.996◦C on the International Temperature Scale of 1990 (its-90, see §6.2) and standard atmospheric pressure of 101 325 Pa. C(KCl, 15, 0) is the conductivity of the standard potassium chloride (KCl) solution at a temperature of 15◦C and standard atmospheric pressure. The standard KCl solution contains a mass of 32.435 6 grams of KCl in a mass of 1.000 000 kg of solution. Millero (1996: 72) and Lewis (1980) gives equations for calculating salinity at other pressures and temperatures.

Comments The various definitions of salinity work well because the ratios of the various ions in sea water are nearly independent of salinity and location in

the ocean (table 6.1). Only very fresh waters, such as are found in estuaries, have significantly di erent ratios. The result is based on Dittmar’s (1884) chemical analysis of 77 samples of sea water collected by the Challenger Expedition and further studies by Carritt and Carpenter (1959).

The importance of this result cannot be over emphasized, as upon it depends the validity of the chlorinity: salinity: density relationships and, hence, the accuracy of all conclusions based on the distribution of density where the latter is determined by chemical or indirect physical methods such as electrical conductivity. . .—Sverdrup, Johnson, Fleming (1942).

The relationship between conductivity and salinity has an accuracy of around

±0.003 in salinity. The very small error is caused by variations in constituents such as SiO2 which cause small changes in density but no change in conductivity.

Table 6.1 Major Constituents of Sea Water

Reference Seawater and Salinity The Practical Salinity Scale of 1978 introduced several small problems. It led to confusion about units and to the use of “practical salinity units” that are not part of the definition of Practical Salinity. In addition, absolute salinity di ers from salinity by about 0.5%. And, the composition of seawater di ers slightly from place to place in the ocean, leading to small errors in measuring salinity.

To avoid these and other problems, Millero et al (2008) defined a new measure of salinity, the Reference Salinity, that accurately represents the Absolute Salinity of an artificial seawater solution. It is based on a Reference Composition of seawater that is much more accurate than the values in Table 6.1 above. The Reference Composition of the artificial seawater is defined by a list of solutes and their mole fractions given in Table 4 of their paper. From this, they defined artificial Reference Seawater to be seawater having a Reference Composition solute dissolved in pure water as the solvent, and adjusted to its thermodynamic equilibrium state. Finally, the Reference Salinity of Reference Seawater was defined to be exactly 35.16504 g kg−1.

With these definitions, plus many details described in their paper, Millero et al (2008) show Reference Salinity is related to Practical Salinity by:

The equation is exact at S = 35. Reference Salinity is approximately 0.47% larger than Practical Salinity. Reference Salinity SR is intended to be used as an SI-based extension of Practical Salinity.