Description of the Earth’s Atmosphere

Abstract

The atmosphere’s dynamics have a direct effect on weather conditions and consequently on the climate and human existence. Emissions of air pollutants affect the public health, the ecosystem and result in climatic changes. The first chapter examines in depth the meteorology and the dynamics of the atmosphere. It examines the atmospheric structure, the chemical composition of the atmosphere and the change of meteorological parameters with height. There is also an examination of the Sun’s radiation effect on the Earth’s surface, on the atmosphere and finally the greenhouse effect.

Appendixes

1.1.1 Appendix 1: The Hydrostatic Equation

Figure 1.23 presents a vertical column of air of mass M (with height z₂₋z₁) in hydrostatic equilibrium. Since the air pressure is the same at all directions at specific height, the pressure which is applied vertically at the upper level of the column is equal to p₂ and in the lower level of the column is equal to p₁. The pressure difference is equal to ${p_1} - {p_2}$ and is in equilibrium from the gravitational force μ g:

Fig. 1.23

The forces which are applied to a vertical column of air in hydrostatic equilibrium

$$ {p_1} - {p_2} = Mg. $$

If we suppose that the surface of the air column is a unit surface, the volume of the column is equal to (${z_2} - {z_1}$). The mass of the column equals $M = \rho \,\left( {{z_2} - {z_1}} \right)$ and therefore:

$$ {p_1} - {p_2} = \rho g\,\left( {{z_2} - {z_1}} \right). $$

Having a column of very small width it can written that

$$ \frac{{{p_2} - {p_1}}}{{{z_2} - {z_1}}} \cong \frac{{\partial p}}{{\partial z}}. $$

From the above equations it can be concluded that

$$ \frac{{\partial p}}{{\partial z}} = - g\,\rho. $$

This is the expression of the hydrostatic equation. The minus sign expresses the fact that the pressure is decreasing with an increase of height.

Problems

1.1If the two horizontal constituents of the air velocity are u = − 5 m/s and v = +5 m/s, calculate the value of the total horizontal velocity and its direction.

1.2The vertical column of sulphur dioxide inside the plume which originated from the mountain Pinatubo (integrated from the Earth’s surface to the top of the stratosphere) was 3 × 10¹⁶ molecules/cm². The sulphur dioxide is transformed into sulphate aerosols. It is supposed that the whole quantity of sulphur dioxide is transformed. The aerosols have a mean diameter of 0.1 μm and are composed from sulphuric acid (75% per weight) and water (25% per weight). Calculate the surface area of aerosols integrated per unit surface area (μm² cm⁻²). For the units conversion it is supposed that the aerosol concentration exists in a homogeneous layer with a height of 5 km.

1.3The air temperature above the poles is T_π = 5°C and above the equator is T_Ι = 25°C. Examine if the tropopause above the equator is colder than above the poles. The vertical temperature lapse rate is the same in both areas and equal to 6.5°C/km. The tropopause height above the poles is equal to z_π = 8 km and above the equator equal to z_ι = 18 km.

1.4A typical concentration of hydroxyl radicals [OH] is close to 10⁶ molecules cm⁻³. What is the volume ratio, which corresponds to the above concentration, at sea level and temperature 298 Κ.

1.5Calculate the characteristic height (H) and the pressure value at height z = 200 m, when the air is dry and the pressure at height 100 m is equal to p_d = 990 mb and the mean temperature between the heights z = 100 m and z = 200 m is equal to T = 284 Κ.

1.6 Calculate the solar constant (the solar energy received on the Earth’s atmosphere surface perpendicular to the Sun’s rays). The Sun’s radius is R_sun = 6.96 × 10⁵ km, the temperature at the Sun’s surface is equal to T_sun = 5,780 K and the distance Earth – Sun equals 1.495 × 10⁸ km.

1.7What is the quantity (volume) of water vapour that must condense on the surface of an aluminum tin that holds a soda in order to heat the soda from 1°C to 16°C.? The density of water and soda are equal to ρ = 1,025 kg m⁻³, the thermal capacity of water and soda are 4,200 J Kg⁻¹, the volume of the can is 354 ml and the latent heat of water is equal to 2.5 10⁶ J kg⁻¹.

1.8Calculate the characteristic height (H(z)) for the pressure drop versus height in the atmosphere at height z = 200 m from the Earth’s surface. The air is dry and the pressure at height z = 100 m is p = 990 mb, and the average temperature between 100 and 200 m height is T = 284 K.

1.9Calculate the characteristic height (H(z)) for the pressure drop versus height in the atmosphere and the pressure at height z = 10 km from the Earth’s surface. At this height the pressure is equal to p = 250 mb and the temperature equal to T = 218 K (base of the troposphere). What is the atmospheric pressure at height z = 10.5 km ?

1.10(a) Calculate the arithmetic concentration of air molecules in the atmosphere at sea level pressure and temperature T = 288 Κ. The gas constant is equal to 0.083145 m³ mb mole⁻¹ K⁻¹. (b) What is the arithmetic concentration at atmospheric pressure 1 mb? Discuss the results.

1.11(a) Calculate the wave length that corresponds to the maximum of emitted radiation from the Earth’s and Sun’s surfaces. The effective temperature at the Sun’s surface is T = 5,785 K and the average surface temperature of Earth equal to T = 288 Κ. (b) Increasing by a factor of two the temperature of a black body, what will be the result to its radiation emission?