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The atmosphere of the earth is a layer of gases surrounding the planet earth that is retained by Earth’s gravity. In the atmosphere, the presence of water vapour serves as greenhouse gas in the atmosphere being the gas that absorbs most solar radiation (Kiehl and Trenberth, 1997). Water vapour can lead to global warming as it is both a symptom and a cause of greenhouse effect.

Atmospheric stratification describes the structure of the atmosphere, dividing it into distinct layers, each with specific characteristics such as temperature or composition. The atmosphere has a mass of about 5 x 1018kg, three quarters of which is within 11km of the surface (NOAA, 1999). The atmosphere becomes thinner and thinner with increasing altitude, with no definite boundary between the atmospheric effects become noticeable during atmospheric reentry of spacecraft. The karman line, at 100km, also is often regarded as the boundary between atmosphere and outer space (Nikhil, 2013).

Air is the name given to atmosphere used in breathing and photosynthesis. Figure 1.1 shows that dry air contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases. Air contains a variable amount of water vapour, on average around 1%. While air content and atmospheric pressure vary at different layers, air suitable for survival of terrestrial animals is currently only known to be found in Earth’s troposphere and artificial atmospheres (Ahrens, 2006).

Figure 1.1: The composition of the earth atmosphere

Source: Bob, 2013


Figure 1.2:  Comparison of the 1962 US standard atmosphere graph of the geometric altitude against air density, pressure, speed of sound and temperature with approximate altitudes of various objects.

Source: NOAA, 1962

In general, air density and pressure decreases in the atmosphere as height increases. However, temperature has more complicated profile with altitude. Because the general pattern of this profile is constant and recognizable through the means such as balloon soundings, temperature provides a useful metric to distinguish between atmospheric layers. Figure 1.2 shows the different layers of the Earth’s atmosphere in relation with air density, pressure, temperature and speed of sound. In this way, Earth’s atmosphere can be divided into five main layers. They are as follows:

Troposphere: The lowest atmospheric layer, the troposphere, is the thinnest of the layers, but it contains about 80% of the mass of the atmosphere. This is the region where most of what we know as “weather” takes place. Almost all clouds and precipitation form in the troposphere; weather fronts, hurricanes, and thunderstorm are tropospheric phenomena. Figure 1.2 shows that temperature and speed sound increases from the troposphere to the tropopause layer in a horizontal axis, ascending vertically upward as the temperature and speed of sound increases to the other upper layer. Weather activity produces much upward and downloads motion, so the troposphere is region of mixing: the prefix “tropo” comes from the Greek word for “turning over.”

Stratosphere: Above the tropopause the stratosphere begins. The temperature usually stops decreasing; it becomes roughly constant at first and then begins to increase with height. The air in the stratosphere is very dry, generally having less than 0.05 percent of the maximum amount of water vapour found near the ground. Clouds are very rare here, except for occasional thunderstorm penetration in the lower part. The stratosphere ends at about 50 kilometers (31 miles) above the surface at the stratopause. Here the density of the air is only about one thousandth of that at sea level, but the temperature may be about 0°C and is sometimes near 20°C. Temperature increases in the stratosphere because of the presence of ozone. Ozone’s absorption of ultraviolet radiation leads to warmer air that can sometimes reach temperatures as high as those found at the ground. This temperature distribution—warmer air above colder air—dampens vertical motion and mixing. This produces a stratified distribution of material, hence the name of this layer. There is little mixing across the tropopause; thus material injected into the stratosphere from an explosive volcano, for instance, can remain there for several years.

Mesosphere: Of the remaining mass, about 99 percent is in the next layer, called the   mesosphere. The mesosphere, or middle atmosphere, begins above the stratopause. The amount of ozone here is very small, so the temperature ceases to increase and begins to drop as the air loses heat to space by radiation, mainly from carbon dioxide. The temperature drops to near -90°C at the top of this layer, the mesopause, at an altitude of about 85 to 90 kilometers. The mesosphere is where meteors heat up and become visible.

Thermosphere: Above the mesopause, in the thermosphere, the temperature begins to increase again because the gases there absorb the very short ultraviolet waves of the Sun’s radiation; that radiation does not penetrate any lower. The thermosphere, together with the upper reaches of the mesosphere, is the region of the ionosphere. Auroras form in the thermosphere above both Polar Regions when gases in this layer are excited by particles from the Sun. The top of this layer, the thermopause, is not well defined. It is estimated to be at between 500 and 1,000 kilometers and changes radically with the amount of sunlight falling on it. The temperature in this region is not well defined either, but values over 1,000°C are sometimes reported.

Exosphere: Beyond the thermosphere is a region called the exosphere. In this layer, the last of the atmospheric “spheres,” the air is so rarefied that gas molecules may not collide with each other, and a few escape Earth’s gravitational field altogether. In the exosphere the atmosphere gradually gives way to the radiation belts and magnetic fields of outer space (Dargan, 2009). 

The Sun: The sun is a sphere of intensely hot gaseous matter with a diameter of 1.39 x 109  m and is, on the average, 1.5 x 1011 m from the earth. As seen from the earth, the sun rotates on its axis about once every 4 weeks. However, it does not rotate as a solid body; the equator takes about 27 days and the polar region take about 30 days for each rotation.

The sun has an effective blackbody temperature of 5777 K.1 The temperature in the central interior regions is variously estimated at 8 x 106 to 40 x 106 K and the density is estimated to be about 100 times that of water. The sun is, in effect, a continuous fusion reactor with its constituent gases as the ‘‘containing vessel’’ retained by gravitational forces. Several fusion reactions have been suggested to supply the energy radiated by the sun. The one considered the most important is a process in which hydrogen (four protons) combines to form helium (one helium nucleus); the mass of the helium nucleus is less than that of the four protons, mass having been lost in the reaction and converted to energy.

The energy produced in the interior of the solar sphere at temperatures of many millions of degrees must be transferred out to the surface and then be radiated into space.

A succession of radiative and convective processes occur with successive emission, absorption, and re-radiation; the radiation in the sun’s core is in the x-ray and gamma-ray parts of the spectrum, with the wavelengths of the radiation increasing as the temperature drops at larger radial distances.

A schematic structure of the sun is shown in Figure 1.3. It is estimated that 90% of the energy is generated in the region of 0 to 0.23R (where R is the radius of the sun), which contains 40% of the mass of the sun. At a distance 0.7R from the center, the temperature has dropped to about 130,000 K and the density has dropped to 70 kg/m3; here convection processes begin to become important, and the zone from 0.7 to 1.0R is known as the convective zone. Within this zone the temperature drops to about 5000 K and the density to about 10-5 kg/m3.

The sun’s surface appears to be composed of granules (irregular convection cells), with dimensions from 1000 to 3000 km and with cell lifetime of a few minutes. Other features of the solar surface are small dark areas called pores, which are of the same order of magnitude as the convective cells, and larger dark areas called sunspots, which vary in size. The outer layer of the convective zone is called the photosphere. The edge of the photosphere is sharply defined, even though it is of low density (about 10-4 that of air at sea level). It is essentially opaque, as the gases of which it is composed are strongly ionized and able to absorb and emit a continuous spectrum of radiation. The photosphere is the source of most solar radiation.

Outside the photosphere is a more or less transparent solar atmosphere, observable during total solar eclipse or by instruments that occult the solar disk. Above the photosphere is a layer of cooler gases several hundred kilometers deep called the reversing layer. Outside of that is a layer referred to as the chromospheres, with a depth of about 10,000 km. This is a gaseous layer with temperatures somewhat higher than that of the photosphere but with lower density. Still further out is the corona, a region of very low density and of very high (106 K) temperature.

This simplified picture of the sun, its physical structure, and its temperature and density gradients will serve as a basis for appreciating that the sun does not, in fact, function as a blackbody radiator at a fixed temperature. Rather, the emitted solar radiation is the composite result of the several layers that emit and absorb radiation of various wavelengths.

Figure 1.3: The structure of the sun

Source: Iqbal, 1983

Solar constant: The rate of total solar energy at all wavelengths incident on a unit surface area exposed normally to rays of the sun at one astronomical unit.

Figure 1.3 shows schematically the geometry of the sun-earth relationships. The eccentricity of the earth’s orbit is such that the distance between the sun and the earth varies by 1.7%. At a distance of one astronomical unit, 1.495 x 1011 m, the mean earth-sun distance, the sun subtends an angle of 320. The radiation emitted by the sun and its spatial relationship to the earth result in a nearly fixed intensity of solar radiation outside of the earth’s atmosphere. The solar constant Gsc, is the energy from the sun per unit time received on a unit area of surface perpendicular to the direction of propagation of the radiation at mean earth-sun distance outside the atmosphere.

Figure 1.4: The Earth-Sun relationship

Source: Iqbal, 1983

Atmospheric Precipitable Water Vapour: Atmospheric precipitable water vapor is the amount of water in vapor form above an area on the surface of the earth. It is usually expressed in centimeters of condensed water. Precipitable water in the atmosphere possesses many features of interest to scientist:

(i)                 It absorbs solar radiation in absorption bands in the solar spectrum (the principal wavelengths are at approximately 0.72, 0.81, 0.94, 1.10, 1.38, and 1.87 m); and,

(ii)    It is taken up by atmospheric aerosols, increasing their size with increasing atmospheric relative humidity, with large increases in size at saturation and above, leading to cloud formation.

(iii)    It attenuates electromagnetic radiation in the atmosphere, a fact of significance to astronomy, radar, telecommunication and remote sensing.

(iv)              Water vapor, at whichever level it occurs, has a strong effect on the temperature of the atmosphere.

(v)                The vapor phase plays an important role in the hydrological cycle in addition to its effect on climate and weather systems.

Additionally, the vapor phase plays an important role in the hydrological cycle, and it affects the climate and weather systems (Garrison, 1992, Follette et al., 2008). Its presence attenuates electromagnetic radiation in the atmosphere, which is significant to astronomy, radar, telecommunications and remote sensing. Water vapor, at all levels, strongly affects the temperature of the atmosphere.

Due to the environmental impacts of water vapor, there is increasing interest in its measurement at the surface and in its total abundance in a vertical column through the atmosphere. The latter parameter is called the integrated or precipitable water vapor (PWV), and its measurement is the central subject of this research. PWV is the amount of liquid water that would be obtained if all the vapor in the atmosphere within the vertical column were compressed to the point of condensation (Dupont et al., 2008).

In contrast to the other greenhouse gases, the amount of PWV in the atmosphere can vary considerably with prevailing conditions, including time of day, wind direction, and temperature. This variability makes PWV an extremely difficult quantity to measure. Additionally, detailed data of the water content are an important input data for hydrological, energetic and radiation models (Smirnov and Moore, 2001; Zhai and Eskridge, 1997; Dai et al., 2002; Cohen et al., 2000; Bokoye et al., 2003).

Precipitable Water Vapour in the Troposphere: The troposphere contains 75 percent of the atmosphere's mass—on an average day the weight of the molecules in air is 1.03 kg/sq cm (14.7 lb/sq in)—and most of the atmosphere's water vapour. Water vapour varies by volume in the atmosphere from a trace, or 0% to about 4%. Therefore, on average, only about 2 to 3% of the molecules in the air are water vapour molecules. The amount of water vapour in the air is small in extremely arid areas and in location where the temperatures are very low (i.e. polar regions, very cold weather). The volume of water vapour is about 4% in very warm and humid tropical air. The amount of water vapour in the air cannot exceed 4% because temperature sets a limit to how much water vapour can be in the air. Even in tropical air, once the volume of water vapour in the atmosphere approaches 4% it will begin to condense out of the air.

The condensing of water vapour prevents the percentage of water vapour in the air from increasing. If temperatures were much warmer, there would be a potential to have more than 4% water vapour in the atmosphere (Claudette, 2014).

The concentration of water vapour in the atmosphere reflects the number of molecules of water compared with the total number of air molecules (mainly nitrogen and oxygen). Humidity is a measure of the amount of water vapour in the air. One way to represent humidity is the mixing ratio, defined as the mass of water vapour "mixed with" each unit mass of air. The mixing ratio is usually expressed as the number of grams of water vapour in each kilogram of air. In the atmosphere, the mixing ratio can vary from nearly zero (in deserts, Polar Regions and at high altitudes) to as much as 30 grams per kilogram (in warm, moist tropical regions). Other measurements of humidity include the relative humidity, which reflects the ratio of the actual pressure of water vapour in a sample of air to the pressure necessary to saturate that air at a given temperature and dew point temperature, the temperature to which the air must be cooled for water vapour to reach saturation.


Because of the variability of water vapour in space, the study of precipitable water vapour is important in knowing the amount of rainfall of a particular area. Precipitable water vapour (water vapour) changes with time of the day. There is no instrument that can measure precipitable water vapour directly in rue atmosphere because of its short live in the atmosphere that is why atmospheric scientist developed different models for the estimation of the atmosphere precipitable water vapour.

Different methods developed by atmospheric scientists to estimate the amount of atmospheric precipitable water vapour: Teten (1930) developed a relation between total precipitable water vapour and surface dew point in the equation (1.1)

     -           -           -           -           -           (1.1)

where  is the dew point temperature. Leckner (1972) model is an equation relating atmospheric precipitable water with surface absolute humidity.

Many researchers have used Tetens models, Smith model, Leckner model to estimate precipitable water vapour. Oladiran (2008) used Smith’s method to estimate precipitable water vapour for Jos, Balogun and Adedokun, Babatunde also use a different method to estimate the amount of precipitable water using low-level, mid-level and upper-level total tropospheric precipitable water vapour.

No work has been done on this particular topic for Kaduna North that is why this topic is considered using Leckner model because it relates temperature, relative humidity and vapour pressure.   


The following are the research questions;

(i)                 How much atmospheric precipitable water vapour in Kaduna north?

(ii)               What is the influence of precipitable water vapour in Kaduna north?


The aim of the study is to estimate the atmospheric precipitable water vapour in Kaduna metropolis Kaduna North using surface meteorological data.

The objectives of the study are:

(i)                 To estimate the amount of precipitable water vapour in Kaduna North.

(ii)               To investigate the influence of precipitable water vapour in Kaduna North.


The scope of the study is based on the estimation of the precipitable water vapour in Kaduna North using surface meteorological data. These surface data consist of vapour pressure, temperature and relative humidity.

The spatial scope of the study is Kaduna north, it is located between latitude  and   of the Equator and longitude   and   of the Greenwich meridian.

Kaduna North consists of a mixed population of about 364,575 people according to 2006 National population census which majorly is dominated by the Hausas. It comprises of seven (7) districts; Doka, Kawo, Hayin Banki, Malali, Kabala, Abakpa and Gabassawa.

The scope of the study is centered on the objectives which are the estimation of precipitable water vapour and the influence of precipitable water vapour in Kaduna North.

The data used were obtained from Nigerian Meteorological Agency (NIMET) and Kaduna State Water Board (KSWB) for the period of 9 years (from 2006-2014).

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