The Hydrologic Cycle

Now we turn from the flows of energy about the Earth to deal with the resulting movements of water. These include the process of evaporation discussed in Chapter 4, resulting in water vapour in the atmosphere. Water vapour is an important greenhouse gas (Section 2.7) and a key component of the hydrologic cycle symbolised in Figure 6.1.

The hydrologic cycle consists of the circulation of water from land and ocean to atmosphere, then condensation, normally into cloud, followed by precipitation back either to the oceans, or to the land, where the water either evaporates or flows back to sea and evaporates there. The continual movement between the parts in Figure 6.2 is like the cycles of carbon dioxide illustrated in Figure 1.3. Such a pattern of related processes is called a system. Within this system, the atmosphere holds very little of the world's water, and the time any molecule spends as atmospheric humidity is only a few days, on average (Note 6.A).

The world contains huge amounts of each kind of water, together constituting the hydrosphere. The mass of vapour in the air is about thirteen million million tonnes (i.e. 13x1012 tonnes, or 13 teratonnes), which could provide a rainfall of 25 mm over the entire Earth. Lakes, rivers and underground water together make up a thousand times this amount. The Antarctic and Arctic icecaps hold nearly three times as much again and the oceans a further thirty times as much (i.e. 1.4x1018 tonnes). Such quantities imply an important role in atmospheric processes.

Three Ways Make Cents
Figure 6.1 Symbolic pattern of flows of water in the hydrologic cycle.
Water Cycle With Storages And Flows
Figure 6.2 Quantities involved in the hydrologic cycle. A box represents a storage, whose capacity is expressed in petatonnes (i.e. 1015 tonnes). The italicised numbers represent annual flows in teratonnes (i.e. 1012 tonnes). Slightly different numbers are given by various authors.

On the way from atmosphere to ocean, some of the water spends appreciable time in the cryosphere, the regions of snow and ice on high mountains and at the Poles. Ninety per cent of the ice now is in Antarctica; there was twice as much there during the Ice Ages of the 'Pleistocene epoch' ending 10,000 years ago (Chapter 15).

A consequence of a greater rainfall and smaller evaporation in the northern hemisphere, compared with the southern (see Preface), is that, on average, winds must carry moisture northwards across the equator, and oceans flow southwards across it, to maintain the continuity of the hydrologic cycle.

6.2 DESCRIBING THE AIR'S HUMIDITY

The quantity of water in a given amount of air can be stated in several ways (Note 6.B). The most common are as follows:

Vapour Pressure (hPa)

This index of atmospheric water is indirect, in terms of the consequent vapour pressure e (in hectopascal units) discussed in Section 4.2. It is proportional to the water-vapour content of the air. The variation of the saturation (i.e. maximum) vapour pressure with temperature was given in Table 4.1, and is illustrated in Figure 6.3, using the right-hand vertical scale. However, the vapour pressure of air in the real world is normally less than the saturation value; air's condition is generally represented by a point to the right of the curve in Figure 6.3, like G. Bodies of air with the characteristics shown by A, B, C, D and F in Figure 6.3 are saturated (or moist), while air indicated by E (to the left of the curve) is super-saturated.

When the air's temperature increases from 0°C to 5°C, the extra water vapour that can be held is shown by the distance between the horizontal lines through D and C for instance, equivalent to about 2.5 g/m3 in this case. The

-

l/i ■

-

//

-

/

// F //

^jC i

i i

5 10 15 20 temperature: °C

25 30

30jjt

5 10 15 20 temperature: °C

25 30

Figure 6.3 The water-vapour content and vapour pressure of saturated air at various temperatures, from Table 4.1. (The values of absolute humidity shown on the left vertical axis apply only at sea-level.)

rapid increase of saturation water-vapour pressure with temperature is known as the Clausius Clapeyron effect. A consequence is that a much larger additional amount BA (i.e. 7 g/ m3) can be accommodated in heating from 25°C to 30°C. These amounts condense back out of the air as cloud or dew when saturated air is cooled back to the lower temperature. Comparison of what can be held at different temperatures explains why rainfalls are much heavier in warm climates (Chapter 10).

Another measure of atmospheric water is the dewpoint temperature, already mentioned in Section 4.7 and Note 5.C. The term is often shortened to dewpoint. It is a point on a temperature scale, not a point in space, being the temperature to which the air must be cooled for the moisture present to represent saturation. Alternatively, it is the temperature of a can of drink from the refrigerator when the dew just disappears from the surface. In other words, it is the temperature of water with a vapour pressure equal to that of the ambient atmosphere. Air cooled below the dewpoint deposits dew on available surfaces, or else forms cloud droplets (Note 6.B).

An analogy is with water in a sponge, whose capacity represents the maximum amount of moisture that can be held as vapour, at the temperature around. So a full sponge represents saturated air. The more common situation of unsaturated air is like the sponge when only part full. Then cooling of the air resembles squeezing the sponge smaller, since cool air can hold less vapour (Section 4.2). Eventually the sponge's capacity is reduced to the volume of the water within it, i.e. the sponge is small enough to be full. This corresponds to the dewpoint. Further squeezing of the sponge makes excess water leak out, representing dew or cloud (Section 4.7).

Advantages of the dewpoint as a way of describing air's water content include the obvious physical meaning, the ease of measurement (just cool the air until dew forms, and then note the temperature), simple units (i.e. degrees Celsius) and direct comparability with the current air temperature to ascertain nearness to saturation. Another point in favour is that it can be compared with the measured daily-minimum temperature to check them both: it is unlikely that the minimum can be much below the dewpoint, since condensation occurs below dewpoint, releasing heat which prevents further cooling.

A disadvantage is that the dewpoint changes when the air rises to levels of lower pressure, even when no condensation takes place (Note 6.B).

The counterpart of dewpoint is the frostpoint when temperatures are below freezing. It is the temperature at which ice has the same vapour pressure as that of water vapour in the air. At that temperature, the rate of water molecules escaping from ice matches the rate of those from the air impacting on the ice surface, i.e. their vapour pressures are equal. The rate is less than in evaporation from supercooled water at the same temperature, i.e. from water that remains unfrozen despite being colder than 0°C—as can occur in clouds (Chapters 8 and 9). The reason for the lower rate of escape from ice (i.e. its lower vapour pressure) is that water molecules are bound more strongly within the solid than within the liquid. In fact, the extra binding force is why the solid is more rigid and why latent heat is needed for melting (Section 4.1). It follows that the frostpoint is higher than the dewpoint; ice has to be warmer than water to match the air's vapour pressure. For instance, an atmosphere with a vapour pressure of 5 hPa is in balance with water at -2.7°C and ice at -2.4°C. Similarly, the vapour pressure of water at -10°C is 2.86 hPa, whilst that of ice at the same temperature is only 2.60 hPa. These small differences are important in the 'Bergeron process' within clouds which contain both supercooled droplets and ice crystals together (Chapter 9).

Relative Humidity (%)

A measure of atmospheric moisture more widely known than either vapour pressure or dewpoint is relative humidity, or simply RH. This is the ratio of the air's vapour pressure (e) to the saturated vapour pressure at the air's temperature e, expressed as a percentage, i.e. RH equals 100 e/es %. In other words, it is the ratio of the water actually present in the air to the maximum amount that could be present at the air's temperature.

It is a feature of RH that it determines the absorption of moisture by natural fibres, such as hair or timber. Conversely, the absorption of moisture (causing a string to twist, for example)

gives a direct indication of the relative humidity, so it is easy to measure. On the other hand, it is a poor index of the amount of moisture in the atmosphere, because RH depends on the temperature as well as on the moisture. If the temperature varies, so does the RH, even though the air's moisture (shown by the dewpoint, say) hardly alters (Figure 6.4).

The connection between RH and natural fibres is sometimes important. An RH above 85 per cent causes deterioration of stored cotton lint, promotes diseases on the leaves of crops (e.g. potato blight) and makes ironwork rust. Such high RH values occur for about 2,300 hours annually in Sydney, but only 1,700 in Adelaide, for instance.

The RH should be within 50-65 per cent (and the temperature range below 10 K) for the storage of documents; there is fungal damage at higher humidities and embrittlement of the paper at lower. Paintings are best stored at 45-55 per cent RH and 18-22°C. Sudden changes of humidity are particularly undesirable.

Saturation Deficit (hPa)

A better index of atmospheric moisture is the saturation deficit (D). This is the difference between the possible (i.e. the saturation vapour pressure es) and the actual vapour pressures (e-e), whereas the relative humidity is the ratio of the two. It differs from the term (es -e) in Dalton's equation (Note 4.E), where es refers to saturation at the temperature of the water surface. The saturation deficit D refers to conditions within the air alone, where es is the svp at the air's temperature. Fortunately, the two temperatures are often similar in the case of evaporation from an open water surface (Section 5.3). So the deficit can be related to evaporation in climates where it depends more on advection than on radiation (Notes 5.D and 6.B). Also, the deficit is related to crop growth (Note 6.C).

Hydrological Cycle Deficit

0 2 4 6 8 1012141618202224 hours

Figure 6.4 Variations during the day of the screen temperature, relative humidity (RH) and dewpoint, averaged over 17—22 September 1974 at Marsfield, Sydney. The large variation in RH is mostly due to the temperature cycle. The small variation in dewpoint is related to the local air flow, especially a sea-breeze in the afternoon.

Mixing Ratio r (g/kg)

This is the ratio of the mass of water vapour in a unit mass of air (excluding the vapour). Obviously, the ratio is very small, since air consists mostly of nitrogen and oxygen (Table 1.3). So the figure is multiplied by a thousand and expressed in units of grams of water per kilogram of dry air. For instance, air at sea-level at 10°C can hold up to 7.6 g/kg.

Unlike the dewpoint, the mixing ratio has the advantage of remaining unaltered when a parcel of air rises or falls in the atmosphere, so long as there is no evaporation or condensation. Such an unchanging characteristic is easier to consider than those which fluctuate, so the mixing ratio is the preferred measure of humidity in considering cloud (Chapter 8) and rain formation (Chapter 9).

6.3 MEASURING THE AIR'S HUMIDITY

The humidity may be measured by a psychrometer (Figure 6.5), which comprises two thermometers, one of which has a sleeve of wet fabric around the bulb, cooling the bulb by evaporation. This wet-bulb thermometer shows a reading Tw, lower than that of the dry-bulb thermometer which reads the ambient air temperature T. The difference [T-TJ is called the wet-bulb depression and is proportional to the rate of cooling of the wet bulb, due to the evaporation from its moist surface. Consideration of the energy balance of the wet bulb (Note 6.D) yields the equation of Henri Regnault (1810-78) for deriving the ambient vapour pressure e:

Absolute Humidity Method Regnault
Figure 65 A sling psychrometer. Grasping the handle, one swings the thermometers around by a rapid wrist action to ventilate the bulbs through the air. After a minute or two the motion is stopped and readings are taken immediately.

e=ew-0.67 (T-Tw) hPa where esw is the saturation vapour pressure (Table 4.1) at the wet-bulb temperature Tw, not the air temperature T.

The equation indicates the practical requirements for reliable measurements. The two thermometers must be matched (showing the same value when both are dry), the wick must be saturated with water at about room temperature, and both thermometers must be adequately ventilated, e.g. by swinging them around (Figure 6.5).

One may obtain the vapour pressure without using Regnault's equation, by inserting the psychrometer readings into a psychrometric chart (Figure 6.6). This illustrates that all the moisture variables T, Tw, e, RH, Td and r can be determined when any two are known.

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Responses

  • kristian
    Is the dew point temperature (Td) of unsaturated air lower or higher than Tw?
    9 years ago
  • Selassie
    Is a high saturation deficit an indication of low moisture content in the air?
    9 years ago

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