## Properties and Variables of the Atmosphere

In meteorology and thermodynamics, simplifying assumptions are made regarding the structure and behaviour of the gaseous molecules and the atmosphere is treated as an ideal gas. The main assumptions of an ideal gas concept are that the molecules do not occupy any finite space and hence have no volume and that there are no forces of attraction or repulsion between any two molecules. The properties of the air that find important applications in meteorology and thermodynamics under these assumptions are pressure, temperature, and volume or density.

As will be shown later in this chapter, in an ideal gas these variables are related to each other by an equation of state. The space-time distributions of these properties or variables, along with the distribution of water vapour to be introduced later, determine in large measure the stability and behaviour of the atmosphere. The following pages give an introduction to these variables and their climatological (1979-1996) mean distributions over the globe during January and July at the peak of winter and summer respectively in the northern hemisphere.

### 2.3.1 Pressure 2.3.1.1 Definition

Pressure (p) of the atmosphere at any level is defined as the weight of the overlying column of air per unit area of the surface at that level. It is found by integrating the weight of air in small segments of height 5z upward from that level to the top of the atmosphere which is assumed to be at infinity and may be expressed by the integral p(h)=y p g §z (2.3.1)

h where p(h) is the pressure at height h, p is the mean density of the air in the height interval 5z and g is the acceleration due to gravity (the variation of which with height is neglected here) and the top of the atmosphere is assumed to be at infinity. According to the above definition, pressure is maximum at the earth's surface and decreases with height as more and more air is left below. In 1643, an Italian scientist Torricelli was the first to measure atmospheric pressure at the earth's surface by balancing it against the weight of a column of mercury of height 76 cm in a vacuum tube. He used mercury mainly because of its high specific gravity, 13.6. If he had used water, the column would have been 13.6 times taller, i.e., about 10.3 m, which would have been very unmanageable. He called the instrument a barometer (weight-meter). Because of the convenient height and accuracy of the mercury barometer, it has been adopted as a standard pressure-measuring instrument throughout the world. A portable version of the barometer which can make continuous measurement of atmospheric pressure at any location has also been devised. This is called the 'aneroid' barometer, which means the barometer without fluid. It consists of a small partially-evacuated metallic box with a flat top which moves up or down with variations in atmospheric pressure. The movement actuates a pen arm which records pressure on a calibrated revolving drum called the barograph. Aneroid barometers are widely used in aviation and other areas of human activity where it may be inconvenient to carry a mercury barometer.

Several systems of units are in vogue for measurement of atmospheric pressure. In c.g.s system, pressure is measured in dynes per square centimetre. Thus, at mean sea level (msl), the atmospheric pressure at 0°C is (76.0 x 13.6 x 981.0), or 1013.9 x 106 dynes cm~2. The equivalence in other systems of units is

1 Atmosphere = 1.013 x 106 dynes cm~2 = 1013 millibars = 1.013 x 105 Pascals

### 2.3.1.2 Space-Time Variation of Pressure

The pressure of the atmosphere varies in time and space. At any particular location, especially over the tropics, there is a prominent diurnal and seasonal variation of pressure. Atmospheric pressure varies along the earth's surface as well as with height. The total variation, 5p, following the movement of a parcel of air over an infinitesimally small time interval, 5t, may be expressed, in the Cartesian coordinates^, y, z), by the relation:

5p = (dp/dt) 5t + {(dp/dx) 5x +(dp/dy) 5y} + dp/dz) 5z (2.3.2)

where the operator d/dt is used to denote partial derivative of p with respect to the independent variable t. In (2.3.2), on the right-hand side, the first term denotes the barometric tendency at a fixed location, while the terms within the second bracket represent the horizontal variations of pressure and the last term denotes the vertical variation of pressure in the atmosphere.

In the limit when 5t ^ 0, we may write (2.3.2) in the form dp/dt = dp/dt + u dp/dx + v dp/dy + w dp/dz where u,v,w are the components of the velocity vector V along the x,y,z co-ordinates respectively, d/dt denotes total derivative following motion and d/dt is the partial derivative at a fixed location.

Alternatively, we may write (2.3.2) in the vector form, dp/dt = dp/dt +(VH.VHp)+w dp/dz (2.3.3)

where VH denotes the horizontal velocity vector and VH the horizontal Del operator. The horizontal variation of pressure at the earth's surface is important because it is primarily the horizontal pressure gradient that forces the air to move from a region of high pressure to that of low pressure with an acceleration given by the vector relation,

Pressure gradient force = -Vp/p where p is mean air density. However, as will be shown in Chap. 11, this movement is considerably modified by the deflecting force of the earth's rotation and the retarding force of friction. In general, atmospheric pressure falls off with height. The fall of pressure with height causes an upward force, which, it can be shown (see Chap. 12), is approximately balanced by the downward force of gravity.

The balance relation (2.3.4) is usually called the hydrostatic approximation.

### 2.3.1.3 Vertical Variation of Pressure

The pressure at any height in the atmosphere can be computed with the aid of (2.3.4) and the equation of state (see 2.4.12 which relates pressure, density and temperature), as shown below:

Let p be pressure and T temperature at a height z above the earth's surface. Then, using the equation of state, p = pRT, we get

5p = -pg 5z = -(p/RT) g 5z or, §p/p = -(g/RT) §z (2.3.5)

Equation (2.3.5) can be integrated if the variation of T with height is known. If T is taken as constant and equal to the value T0 at the earth's surface, the integration yields p(z) = po exp(-gz/RTo) = po exp(-z/H) (2.3.6)

where H = RT0/g is called the scale height and p0 is the pressure at the earth's surface. For a value of T0 = 273K, H = 8.0km approximately.

However, it is known from measurements that the temperature in the lower atmosphere normally decreases with height. If it is assumed that T = T0 - Pz, where T0 is the temperature at the surface of the earth and P denotes a constant lapse rate of temperature with height, (2.3.5) may be written in the form

On integration, (2.3.7) gives ln p(z) = ln p0 + (g/pR) [ln {(T0 - pz)/T}] (2.3.8)

Equation (2.3.8) may be used to compute pressure at any height, provided the lapse rate of temperature in the intervening layer is specified.

2.3.1.4 Reduction of Surface Pressure to Mean Sea Level (msl)

The uneven topography of the earth's surface poses a problem for determination of msl pressure at high-level stations, if needed. The msl pressure at a high-level location is usually obtained by reducing the observed surface pressure to msl with the aid of the hydrostatic approximation (2.3.4). But the main problem here lies in finding the density distribution in the imaginary air column between the station level and the msl at the location. A mean value of density is usually assumed, based on the values of pressure and temperature at the station and the nearest msl or low-level station. The procedure applied may often lead to large errors at high mountain stations.

2.3.1.5 Msl Pressure Distribution Over the Globe

Fig. 2.1 shows the climatological msl pressure distributions over the globe during (a) January and (b) July.

Some noteworthy features of the pressure distribution are as follows:

In January (a), msl pressures in the northern hemisphere are generally high over the continents, with the highest pressure exceeding 1035 hPa located over central Asia, while they are generally low over neighboring oceans. Two intense low pressure areas appear over the northern oceans, one over the Icelandic area and the other over the Aleutian area. In the southern hemisphere, the distribution appears to be reverse, with relatively low pressures appearing over the continents of Africa(south of the equator), Australia and South America and relatively high pressures over the southern oceans.

In July (b), the pressure fields are more or less reverse of those in January. In the northern hemisphere, pressures are generally low over the continents with 'heat lows' appearing over most of the continents, while they are generally high over neighboring oceans. In the southern hemisphere, high pressures appear over the continents with relatively low pressures over adjoining oceans.

2.3.2 Temperature

### 2.3.2.1 Definition and Measurement

Temperature gives a measure of heat in a body. When a body is heated or cooled, its temperature changes. However, given the same quantity of heat, the rise in temperature is not quite the same for all bodies. It depends on a property of the body called

(p) Jan Mean Sea-level Pressure (hPa) Reanl dim (79-96)

Cfc) July Mean Sea-level Pressure (hPa) Reanl Clim (79-96)

Fig. 2.1 Climatological (1976-1996) mean sea level (msl) pressure (hPa) over the globe during (a) January and (b) July (Courtesy: NCEP/NCAR Reanalysis)

its heat capacity which is given by the product of its mass and a quantity called specific heat. Specific heat of a body is defined as the quantity of heat required to raise the temperature of unit mass of the body through 10C. Thus, specific heat is related to a given quantity of heat by the relation:

Heat added (or subtracted) = mass x specific heat x rise (or fall) in temperature

The unit of heat is a calorie which is the quantity of heat required to raise the temperature of 1g of water through 1 °C, usually from 15 to 16°C. Heat is measured by calorimeters.

Specific heat varies little with volume or pressure in the case of a liquid or solid but its variations in the case of a gas can be quite considerable, as will be shown later in Chap. 3.

Temperatures are measured by thermometers. There are different kinds of thermometers in use with different scales of measurements. Most thermometers are calibrated against some fixed points of temperature, usually the freezing point of water as the lower fixed point and the boiling point of water as the upper fixed point. Several scales of measurement are in use. In the Celsius or Centigrade (C) scale, the lower fixed point is marked as 0°C and the upper 100°C and the interval is divided into 100°. In the Fahrenheit (F) scale, the lower fixed point is marked 32°F, while the upper 212 °F and the interval is divided into 180°. Thus, 1 °C corresponds to 1.80 °F. There is also the Reamur scale in which the interval between the fixed points is divided into 80°. Temperature of the air measured by any of these thermometers is called the dry-bulb temperature.

However, the scale of temperature that is widely used in meteorology is called the Absolute or Kelvin scale of temperature, which is related to the centigrade scale by the expression, T = 273. 16 +1, where t is in degrees Centigrade and T in degrees Absolute or Kelvin. The absolute temperature is usually denoted by the capital letter T or K. From now on in this book we shall express temperature either in degrees of Centigrade (t), or Absolute (T or K), unless otherwise mentioned.

### 2.3.2.2 Temperature Distribution in the Atmosphere

Like barometric pressure, temperature of the air varies in time and space. The total change, 8T, in the temperature of a parcel of air over time 5t following motion in space may be expressed as

8T/8t = (dT/dt)+u (dT/dx)+v(dT/dy)+w (dT/dz) (2.3.9)

where u,v,w are the components of the velocity vector V along the co-ordinate axes x,y,z respectively. As in (2.3.3), (2.3.9) may be written in vector form dT/dt = dT/dt + Vh.VhT + w dT/dz (2.3.10)

The first term on the right-hand side of (2.3.10) gives the temporal variation of temperature at a fixed point, while the others are the so-called advective terms. We are all familiar with the diurnal and seasonal variations of temperature at the place where we live. Inter-annual and secular fluctuations also occur. The second term denotes the horizontal variation of temperature along the earth's surface, for example, between continents and oceans or between the equator and the poles. The last term denotes the variation of temperature with height. Since the maximum temperature occurs at the earth's surface, there is a gradient in the vertical direction with temperature normally decreasing both upward in the atmosphere and downward below the surface. The upward gradient often leads to static instability and upward transfer of heat by convection currents, while the downward gradient makes the subsurface layer thermally stable. In the latter case, heat can travel in the sub-surface layer mainly by conduction, though in the ocean other processes such as wind-driven turbulence, etc., may be at work to transport heat downward.

2.3.2.3 Temperature Distribution at the Earth's Surface

Like barometric pressure, there are several problems in getting a reliable set of air temperature values at the earth's surface and at different heights aloft, despite recent advances in measurement techniques. So far as the ocean surface temperatures are concerned, we have now a fairly reliable set of mean sea level temperatures over the global oceans. But the same cannot be said about the temperatures over the land where observations are complicated by orography and it is not easy to reduce the surface observations to mean sea level, if that were desired. If needed, the surface values are usually reduced to mean sea level by assuming a standard lapse rate of temperature for the height of a station but the procedure can lead to serious error for high-level stations. For this reason, Fig. 2.2 which shows the climatological surface temperature distribution over the globe during (a) January and (b) July gives the temperatures over land at 2m above the land surface, regardless of the altitude of the land station (Courtesy: NCEP/NCAR Reanalysis Project). Salient features of Fig. 2.2(a, b) are as follows:

In January (Fig. 2.2a), with maximum solar heating in the southern hemisphere, the temperatures in the northern hemisphere are generally lower than those in the same latitudes in the southern hemisphere and the land surface (as indicated by the 2m-level temperatures) is much colder than the adjoining oceans. In the southern hemisphere, however, the continents are much warmer than the oceans.

In July (Fig. 2.2b), with the maximum solar heating in the northern hemisphere, the temperature field is reversed not only between the hemispheres but also between continents and oceans. This means that in the northern hemisphere, temperatures over the continents are in general higher than those over the neighboring oceans, whereas in the southern hemisphere, continents are much cooler than the neighboring oceans.

In general, the temperature maxima over both continents and oceans follow the seasonal movement of the sun, though with a certain time lag which may vary from about a month over land to about two months over oceans. This difference is largely due to much lower thermal inertia (heat capacity) of land surface than that of ocean.

### 2.3.2.4 Vertical Temperature Distribution

Observations show that the vertical variations of pressure and temperature in the atmosphere follow entirely different pattern. This is evident from Fig. 2.3 which

Jan Sea Surface Temp (C) and 2m Temp CLiM Reani (79-96)

Jan Sea Surface Temp (C) and 2m Temp CLiM Reani (79-96)

0 60E 120E tflO 120W 60W 0

60E 120E 180 120W 6ÖW 0

Fig. 2.2 Climatological (1979-1996) mean temperature (°C) at surface over the globe: (a) January, (b) July. Temperature over land is at height 2 m above land surface (Courtesy: NCEP/NCAR Reanalysis)

60E 120E 180 120W 6ÖW 0

Fig. 2.2 Climatological (1979-1996) mean temperature (°C) at surface over the globe: (a) January, (b) July. Temperature over land is at height 2 m above land surface (Courtesy: NCEP/NCAR Reanalysis)

shows the vertical distribution of mean air temperature in the 1962 U.S. standard atmosphere. It shows that while pressure decreases almost exponentially with height, the temperature varies differently in different atmospheric layers.

The four principal layers of the atmosphere defined by Fig. 2.3 are: the troposphere, the stratosphere, the mesosphere and the thermosphere. The troposphere is

TEMPERATURE i°K)

Fig. 2.3 Vertical distribution of temperature in the U.S. standard atmosphere

TEMPERATURE i°K)

Fig. 2.3 Vertical distribution of temperature in the U.S. standard atmosphere the lowest layer which extends to a height varying between about 9 km and 16 km depending upon the season and latitude. In this layer, the temperature drops from a value of about 15 °C at the earth's surface steadily with height at the rate of about 6.5°C per km till a minimum value of about -55°C to -60 °C is reached at a level called the tropopause. The temperature distribution in the troposphere is maintained by convective and turbulent transfer of heat due to absorption of solar radiation at the surface to the atmosphere.

Above the troposphere lies the stratosphere where the temperature increases gradually with height to reach a maximum of about 0 °C at a height of about 50 km. The increase of temperature in this layer is due to the presence of ozone which absorbs ultra-violet radiation from the sun and acts as a source of heat for the atmosphere. Since ozone controls the thermal structure of this layer, it is also sometimes called the ozonosphere. The top of the stratosphere is called the stratopause. Above the stratopause, the temperature drops again to reach a minimum of about -100°C at about 80 km. The level of this minimum temperature is called the mesopause. The mesopause marks the level from where the temperature starts rising again, this time almost monotonously to large values at a great height of the atmosphere. This uppermost layer is called the thermosphere. The importance of this layer lies in the fact that it intercepts the highly-charged solar rays from space and the high-energy ultra-violet radiation from the sun which are both harmful to life at the earth's surface. The atoms and molecules of gases such as oxygen and nitrogen present in this layer absorb the high-energy short-wave radiation from the sun and get ionized. The ionized layer by reflecting radio waves helps in global telecommunication. For this reason, this layer is also sometimes called the ionosphere.

The temperature of the thermosphere varies greatly with solar activity, with a value of about 2000 K at the time of 'active sun' and 500 K at the time of 'quiet sun' at 500 km altitude (Banks and Kockarts (1973). Because of the large variation in the thermal structure of the thermosphere with active and quiet sun, this part of the thermosphere is often called the heterosphere. Above the heterosphere lies the exosphere.