Chapter 5:: Humidity and Moisture
Introduction
There are several variable used to characterize atmospheric water vapor. Different techniques for quantifying water vapor provide direct measurements of certain variables. Before discussing these techniques, it is useful to review the basic quantities used to quantify moisture and to show the interrelationship amount these variable.
Water vapor
Water vapor pressure is the partial pressure exerted by water vapor molecules in an atmospheric volume. To illustrate vapor pressure, the concept of equilibrium vapor pressure considers a closed container shown to the left. This picture illustrates a liquid water surface that is included in a container with a vacuum in the column above the water surface. As water vapor molecules evaporate from the surface the vapor pressure will increase. As this pressure increases, there will be condensation of water vapor molecules at the surface. The condensation rate will increase as the vapor pressure increases. At the point where the evaporation rate is equal to the condensation rate, we define the vapor pressure as the equilibrium or saturation vapor pressure. If now, the temperature of the system is increased, the evaporation rate will increase and the vapor pressure will increase again until a new equilibrium pressure will be obtained. Thus, as temperature increases the saturation vapor pressure increases. If one were to plot this relationship, shown would look like what is shown in the figure below.
SVP Curve
Thus saturation vapor pressure es is a function of temperature, such that es(T). The vapor pressure e of an air parcel is the measure of the moisture content, while the saturation vapor pressure is a function of temperature. The ideal gas law provides the relationship between e, and water vapor density ρv as
(4.1)
where Rv is the specific gas constant for water vapor (461 J K-1 kg-1). The relationship between saturation vapor pressure es and temperature is given by the Clausius-Clapeyron equation as
(4.2)
where is the latent heat of vaporization or enthalpy of vaporization. It decreases slowly with temperature and has a value of 2.5*106J kg-1 at 0oC and a value of 2.25*106J kg-1 at 100oC. At 0oC es = 6.108mb and at 100oC es=1013.25mb. For small intervals of temperature around some reference temperature and es value, the Clausius-Clapeyron equation can be integrated assuming a constant value of . This gives us
(4.3)
where in this expression temperature is in Kelvin and quantities subscripted with a o are reference values. An empirical expression for es as a function of temperature that is valid for temperatures from -60oC to 40oC is given by Bolton (1980) as
(4.4)
where T in this expression is in oC, this expression can also be inverted to give
(4.5)
Other Humidity Variables
Dewpoint, Td, is the temperature to which air would have to be cooled isobarically to reach saturation. This process can be seen that
(4.6)
Similarly, this can be inverted to give an expression for TD as a function of vapor pressure e as
(4.7)
Relative humidity, RH, is the ration of the vapor pressure e to the saturation vapor pressure es(T), such that
(4.8)
Where e is from the web bulb temperature and es is from the regular temperature.
Mixing ratio, r, is the ratio of the mass of the vapor mv to the mass of the dry air md in a parcel such that
(4.9)
Specific humidity, q, is the ratio of the mass of the vapor to the total mass (mv + md) or
(4.10)
Using the definition for w and q it can be show that
(4.11)
Mixing ratio and specific humidity are conserved in the adiabatic descent for unsaturated air parcels. By the definition r and q are non-dimensional, although it is common to represent these in dimensional form as g/kg by multiplying the non-dimensional quantities by a factor of 1000. For example r = 10-2 = 10 g/kg. Saturation mixing ratio rs and specific humidity qs can be also defined as the values a parcel would have if it were saturated. Thus it follows that
(4.12)
From these definitions it follows that the RH is
(4.13)
This expression for RH is in common use by the meteorology community.
Enthalpy
In the absence of an external field, the enthalpy may be defined as
(4.14)
where U is the internal energy (in joules), p is the pressure of the system, (in pascals), and V is the volume, (in cubic meters). The enthalpy is an arbitrary concept but the enthalpy change ΔH is more useful because it is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings. The change of enthalpy can be represented by
(4.15)
The first law of thermodynamics can be written as
(4.16)
where δQ represents the infinitesimal amount of energy attributed or added to the system, and δW represents the infinitesimal amount of energy acted out by the system on the surroundings. Combing (4.15) and (4.16) and representing δW as pδV, we have…/.
?
(4.16)
For isobaric process, δp=0. (4.16) can be represented as
(4.17)
where specific heat at constant pressure.
Wet bulb temperature
Wet bulb temperature, Tw, is the coldest temperature that air can be cooled to by evaporation. An expression for Tw as a function of other humidity parameters can be derived using conservation of enthalpy in an isobaric, adiabatic process involving either evaporation or condensation of water mass. This conservation can be written as
(4.18)
where the subscript i indicates an initial value, the subscript f indicates a final value, and cp is the specific heat of moist air, which can be approximated in most applications as the value for dry air (1005 J kg-1 K-1). If liquid water is evaporated in a parcel, the parcel will cool as the water vapor mixing ratio increases. A good rule of thumb obtained from the equation (4.18) is that if 1gram of liquid water is evaporated or condensed isobarically in 1 kg of air, the air will cool (warm) by 1oC as the mixing ratio increases (decreases) by 1 g/kg. For the determination of moisture using wet bulb temperature, the environmental temperature and mixing ratio (i.e., dry bulb) are designated as the ambient T and r, and the final wet bulb temperature is Tw while the final mixing ratio is rs(Tw). Thus equation (3.18) becomes
(4.19)
Since , equation (4.19) can be written as
(4.20)
where the quantity in the brackets has a value of 0.065mb K-1 at sea level and it is called the psychometric constant (although it is not really a constant since p can vary). Further, since and , it follows that and that .
Humidity variables at T<0oC
For temperature below freezing point, the equilibrium (or saturation) vapor pressure can be defined in two ways. One is for super-cooled water where the saturation vapor pressure is that given by the values discussed earlier for liquid water. The other is the saturation vapor pressure with respect to ice esi.
To physically understand the difference between es and esi, consider a container with a layer of water in the bottom as shown previously. If the water is super cooled and remains in liquid form at some temperature below freezing, the vapor pressure is that with respect to a pure water surface and in equilibrium the evaporation from the water surface will balance the condensation on the surface. Consider what happens to that equilibrium, however, if the liquid water is replaced with ice at the same temperature. Because of the increase molecular forces in the ice relative to those in the liquid, the evaporation rate will decrease, and the condensation rate will now exceed the evaporation rate and the vapor pressure will continue to decrease until the condensation rate decreases and again comes to equilibrium with the evaporation rate. Thus esi will be less than es.
The saturation vapor pressure with respect to ice can be quantified using the Clausius-Claperyon equation (4.2) where is replaced with the enthalpy (latent heat) of sublimation where
at 0oC,
Since it follow from (4.2) that
Values for esi can be calculate from equation (4.3) where replaces. At temperatures < 0oC, we can also define the relative humidity with respect to ice as
(4.21)
Thus it is possible to have condition that are unsaturated with respect to water but saturated with respect to ice since RHiRH. This result has important consequences for cloud physics at temperatures below freezing point.
Frost point temperature, TF, can be defined as the temperature a parcel of air can be cooled isobarically to form frost. If the dew-point is greater than 0oC, the frost point cannot be defined. But at temperature where the dewpoint is <0oC, the frost point will be higher than the dewpoint. Thus, the general frost is not formed by dew freezing, since as air cooled below freezing the frost point will be reached before the dew point.
Humidity Measurements
Physical principles: condensation
The above illustrates the measurement of humidity via a condensation principle. The thermoelectric cooler will cool the mirror to the point that dew will form, so that when a light source shines on the mirror, the optical detector would not pick it up. Then we may use a thermometer to measure the dew point. This process can be repeated until they get a precise measurement. The advantage is that it is capable of high accuracy; the disadvantage though is its slow repose, because of the cooling of the mirror takes time.
Sling psychrometer
It consists of two thermometers mounted in such a way that they can be ventilated by slinging. The bulb of one of the thermometers is covered by a muslin cloth that is wetted with distilled water. The two thermometers are then ventilated by slinging. The temperature of the wet bulb will lower as water from the wick is evaporated. The lower the humidity, the greater the difference between the wet and dry bulb temperatures. The lowest that can be reached by evaporative cooling is the wet bulb temperature. The vapor pressure at sea level is related to the we and dry bulb temperature as
(4.22)
where Tw is the wet bulb temperature, T is the dry bulb temperature, and es is the saturation vapor pressure that can be obtained from the graph above.
For accurate measurement of humidity by the wet-dry method; it is important to protect the thermometers from radiant heat and ensure a sufficiently high speed of airflow over the wet bulb. One of the most precise types of wet-dry bulb psychrometer was invented in the late 19th century by Adolph Richard Aßmann (1845-1918). In this device, each thermometer is suspended within a vertical tube of polished metal, and that tube is in turn suspended within a second metal tube of slightly larger diameter; these double tubes serve to isolate the thermometers from radiant heating. Air is drawn through the tubes with a fan that is driven by a clockwork mechanism to ensure a consistent speed (some modern versions use an electric fan with electronic speed control).
One difficulty for accurate humidity measurement is under the condition when the air temperature is below freezing. In this case, we can use a thermostatically-controlled electric heater to raise the temperature of outside air to above freezing. In this arrangement, a fan draws outside air past (1) a thermometer to measure the ambient dry-bulb temperature, (2) a heating device, (3) a second thermometer to measure the dry-bulb temperature of the heated air, then finally (4) a wet-bulb thermometer. Humidity can be determined using three temperature measurements. According to the WMO Guide, "The principle of the heated psychrometer is that the water vapour content of an air mass does not change when it is heated. However, since the humidity of the ambient air is calculated indirectly from three temperature measurements, in such a device accurate thermometer calibration is even more important than for a two-bulb configuration.
Humidity measurement is among the more difficult problems in basic meteorology. Hygrometers need regular recalibration.
Other hygrometers
Hygrometers can be made based on other mechanisms of using sensitivity of various physical processes with water vapor as a function of relative humidity. Like electric resistance, surface resistively, mechanical characteristics.
Hair tension hygrometer: In a simple mechanical type of hygrometer the sensing element is usually an organic material which expands and contracts with changes in the moisture in the surrounding air. The material used most is human hair, which elongates as relative humidity increases. It consists of a bundle of hair that is held under a slight tension by a spring, and a magnifying linkage that actuates a pointer.
Electronic hygrometers: Modern instruments use electronic means of recording the information. The two most common electronic sensors are capacitive or resistive sensors. Capacitive sensor: Capacitance is the ability of a body to hold an electrical charge, or a measure of the amount of electric charge stored (or separated) for a given electric potential. A common form of charge storage device is a parallel-plate capacitor. The capacitive sensors sense water vapor by measuring the change in capacitance caused by the amount of water vapor present. Resistive sensor: It normally uses a thin film that changes conductivity according to absorbed water. The common one is polymer membrane.
Extinction of light: At certain wavelengths the absorption and scattering of light can be a strong function of water vapor density. The Lyman alpha hydrometer:
They have fast repose and are precise, but not very accurate, because of temperature and pressure sensitivity, plus salts may get in the way. Some times it is used in combination with slower but more accurate sensors.
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