Layers of the Atmosphere:
The atmosphere of the earth may be categorized in terms of:
(i) Temperature
(ii) Ionization
(iii) Magnetic field, and
(iv) Radio wave propagation.
In terms of temperature, atmosphere may be categorized in four distinct layers, that is:
(i) The troposphere
(ii) The stratosphere
(iii) The mesosphere, and
(iv) The thermosphere.
In terms of magnetic field the atmosphere may be categorized into two layers, that is:
(i) The dynamosphere, and
(ii) The magnetosphere.
In terms of radio wave propagation, terrestrial atmosphere may be classified categorized into two:
(i) troposphere, and
(ii) ionosphere.
Ionosphere is dispersive medium in which propagation is frequency dependents. Troposphere is a non-dispersive medium specifically largely neutral.
Governing Equations:
Equation of State:
Charles' law defines that volume of fixed mass of gas is directly proportional to temperature, given that pressure remains constant. Therefore, at constant-pressure, all gases expand by the constant amount (equal to 1/273 of volume at 0oC) for every 1oC rise in temperature. This is called as Charles' constant-pressure law. Conversely, if volume is remaining constant, all gases experience increase in pressure (equal to 1/273 of their pressure at 0oC) for every 1oC rise in temperature. This is called as Charles' constant-volume law. Therefore, Charles' law defines that ratio of volume to temperature of fixed mass of gas is constant i.e. constant, V/T = constant if the pressure remains constant.
Boyles' law defines that volume of fixed mass gas is inversely proportional to pressure, if the temperature remains constant. Therefore, at constant temperature product of pressure and volume remains constant. This signifies that
pV = constant
In light of the laws, equation of state for ideal gas may be devises as follows:
pV = nkT'
Here p is pressure V is volume, n is number of molecules, T' is absolute temperature and k is Boltzmann constant. Equation of state reduces to pV = nT or p = (n/V)T
By defining number density N as number of molecules per unit volume:
N = n/V
Therefore, Equations may be written as:
p = NT,
Here N is number density.
Equation of Hydrostatic Equilibrium:
Equation of hydrostatic equilibrium expresses balance between gravitational force at any point and pressure gradient at that point. Therefore, hydrostatic equation may be defined as
dp/dz = -Ρg
Here p is pressure, Ρ is mass density, g is acceleration because of gravity and z is height. Equation signifies that change in pressure dp may be defined as
dp = -Ρgdz
Equations imply that
dp/P = -Ρgdz/NT or dp/p = -dz/H
Here scale height H is provided by
H = NT/Ρg
Scale height H may be expressed in terms of mean molecular mass m at any given height. The total mass M of molecules is provided by M = ΡV,
nm = ΡV
As
M = nm
Equation signifies that mean molecular mass m is provided by
m = Ρ(V/n)
Equation shows that mean molecular mass m is provided by
m = Ρ/N
Equation may now be rewritten as
H = (N/Ρ)(T/g) or H = (1/m)(T/g)
Thus, scale height H may be written as,
H = T/mg,
Here m is mean molecular mass at given height.
By integrating Equation from some reference height z = z0 (at pressure p = p0 to arbitrary height z (at a pressure p), you get following:
P0∫PdP/P = - z0∫zdz/H
ln p - lnp0 =- z0∫zdz/H
ln(p/p0) = - z0∫zdz/H
Thus p = p0exp(-z0∫zdz/H)
Equation illustrates how pressure p differs with height z. It illustrates that pressure decreases exponentially with height. Clearly, a large scale height is related with low-pressure regions of atmosphere. Equation may also be utilized to find distribution of number density with height. You will recall that
p = NT
So that , at some reference point where P = P0 and T = T0 number density N0 is provided by expression
P0 = N0T0
But equation illustrates that pressure p is ptovided by
P = P0exp(-z0∫zdz/H) Or N = (N0T0/T)exp(-z0∫zdz/H)
Equation shows that number density N diminishes exponentially with height also. It signifies that a large scale height is related with light gas. In the isothermal atmosphere temperature stays constant and scale height becomes constant as well. In consequence, equation reduces to
P = p0exp[-(z-z0)/H]
Hre p0 is pressure at some reference height z0. Also, in isothermal atmosphere, temperature remains constant so that T = T0 In this case, equation reduces to
N = N0exp[-(z-z0)/H]
Here N is number density at some reference height z0.
Snell's Law:
Snell's law defines that ratio of sine of angle of incidence to the sine of angle of refraction is a constant. That constant is a measure of refractive index. When the radio signal passes through atmosphere, its direction changes because of refraction. Consider neutral atmosphere which is horizontally stratified into m layers. If ionospheric refraction is neglected then total change in direction of radio signal passing through the atmosphere can be created by repeatedly applying Snell's law to every layer of atmosphere. In this case, Snell's law is provided by
n1sinψ1 = sinψm
Water Vapor:
Troposphere has both water vapor and dry air. Amount of water vapor differs with time and location. On the other hand, composition of dry air doesn't differ considerably with height. To understand water vapor one needs to have good knowledge of some vapor-related quantities like:
(i) Mixing ratio
(ii) Partial pressure of vapor, and
(iii) Relative humidity.
Mixing Ratio:
Mixture of dry air and water vapor is known as moist air. Mixing ratio provides a measure of amount of moisture in air. Mixing ratio w is stated as ratio of mass of water vapor to mass of dry air. Therefore,
w = mv/md = (mv/V)(V/md) = (mv/V)÷(md/V) = Ρv/Ρd
Here Ρ is density of water vapor and Ρd is density of dry air.
Equation of state holds for fixed mass of gas. It also holds for mixture of gases. Now, equation of state
pV = RT can be written in terms of specific volume and specific gas constant for ith gas as follows:
pV = miRiT
Here Ri is specific gas constant and mi is mean molecular mass of ith gas. Of course, specific gas constant Ri = R/mi, where R is universal gas constant. Equation can also be re-written in terms of specific volume as follows:
pV = miRiT or p = (mi/V)RiT
Or p = ΡiRiT Here Ρi is density of ith gas stated by Ρi = mi/V. Therefore, pressure p may be written as
p = ΡiRiT
The specific volume vi is mass per unit volume i.e. vi = V/mi = 1/Ρi
If this new version of th equation of state is applied to water vapor, you get
e = ΡvRvT
Here e is partial pressure of water vapor. If same version of equation of state is applied to dry air, you get
Pd = p-e = ΡdRdT
Where p is total pressure of moist air and d R is specific gas constant of dry air. Mixing ratio may thus be stated in light of equations:
Ρv = e/RvT
Ρd = P-e/RdT
But, the mixing ratio
w = Ρv/Ρd or w = e/RvT ÷ p-e/RdT
w = e/RvT x RdT/p-e
w = eRd/(Rv(p-e)) Or w = ε(e/p-e)
Where ε is ratio of specific gas constant for dry air to specific gas constant for vapor (i.e. ε = Rd/Rv)
Saturation Region:
Partial Pressure of Saturated Air:
In closed system, equilibrium will be recognized when number of water molecules passing from liquid phase to vapor phase is equal to number of water molecules passing from vapor to liquid phase. Any vapor which meets requirement is known as saturated vapor. Mixture of vapor and air under equilibrium conditions is known as a saturated air. When saturated air comes in contact with the unsaturated air, diffusion starts to happen. Molecules of water move from areas of higher concentration of water vapor to areas of lower concentration of water vapor. Partial pressure of the saturated water vapor depends on temperature. Warm air can have large amounts of water vapor. When warm air is cooled, surplus of the water vapor (over and above saturation value) at the new temperature condenses to form water. Condensation procedure leads to energy release. Energy released per unit mass is equal to latent heat of vaporization. Two more latent heats exist: latent heat of fusion and latent heat of sublimation. Latent heat of fusion is energy needed to change unit mass of ice to liquid water at same temperature. Latent heat of sublimation is sum of latent heat of fusion and latent heat of vaporization. By extension of Equation saturation mixing ratio wsat may be expressed as
wsat =ε(esat/p-esat)
If total pressure p is considerably higher than saturated partial pressure e of water vapor then saturation mixing ratio becomes wsat ≈ ε(e/p)
Relative humidity rh is ratio of mixing ratio to saturation mixing ratio. Therefore, if p is large compared with both e and esat relative humidity rh is provided by:
rh = ε(e/P)÷ε(esat/P)
=ε(e/P)x(Pεesat)
e/esat
Therefore
rh = w/wsat≈e/esat
It is frequently essential to define relative humidity in percentage. In this situation two expressions for relative humidity become:
rh = 100w/wsat% ≈ 100e%/esat
Here rh is relative humidity and p is large compared with both e and esat.
Propagation Delay:
Condition of troposphere has the deep effect on radio wave propagation. Radio signal suffers delay by neutral atmosphere. Total delay relies on refractivity along the path of radio signal. Refractivity itself relies on primary parameters such as temperature and pressure.
Fermat's principle is basic physical law governing radio wave propagation. Fermat's principle illustrates that light and other electromagnetic waves will follow path between two points that involves least travel time. The optical (or electromagnetic) distance S between source and receiver as:
S = ∫cdt where c is speed of light and t is time. The electromagnetic path s as:
S = ∫vdt
Here v is propagation speed given by v = ds/dt
Refractive index n of medium is ratio of the speed of light in free space to speed of light in medium i.e.
n = c/v or v = c/n
Where c is speed of light in vacuum and v is speed of light in medium. Excess path length D caused by troposphere is provided by:
D = [∫n(s)ds - ∫ds] + [∫sds - ∫ldl]
Excess path length D is also known as delay. It is estimated in slant direction caused by troposphere.
Refractivity N:
Refractive index n is always small number (in the neighborhood of 1). It is frequently more suitable to work with parameter with large spread. For that reason, refractivity N is frequently utilized. In relation to refractive index n, refractivity N is stated by expression
N = (n-1)x106
Plainly, range of values of refractivity can be much more manageable than corresponding range of values of refractive index. For example, in ionosphere values of refractivity N ranges from zero to approx 300, while values of refractive index n stays clustered in neighborhood of unity. Neutral atmosphere has both dry air and water vapor. For this reason, refractivity N can be split in dry air component and water vapor component. Therefore, we may write
N = Nd + Nv
Here Nd refractivity of is dry air and Nv is refractivity of water vapor. This is a wise decision as dry air content stays almost constant in time while water vapor content differs widely in time and space.
For frequencies up to 20GHz, refractivity may be written, as function of temperature and partial pressure, in the given manner:
Nd = (k1(Pd/T)Zd-1) and Nv = (k2(e/T) + k3(e/T2))Zv -1
Here Zλ is compressibility factor of dry air, Zv is compressibility factor for water vapor and ki(i=1,2,3) are dimensional constants. Unit of k1 and k2 is Kelvin per millibar; (Kmbar-1). Unit of k3 is Kelvin squared per millibar (K2 mbar-1). For the ideal gas, compressibility factor is equal to 1. Any departure of Z from unity accounts for non-ideal behaviour of affected gas. Luckily, compressibility factor for both dry air and water vapor is roughly equal to 1, so that Zd ≈ Zv ≈ 1
Therefore, dry air and water vapor may be treated as ideal gases. In this situation, equations reduce to
Nd = k1(Pd/T) and Nv = k2(e/T) + k3(e/T2) respectively.
Above troposphere, there is practically no more water vapor. Therefore, at high altitudes contribution of wet refractivity to total refractivity becomes small. This is so due to wet refractivity drops much faster than dry refractivity as height increases.
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at info@tutorsglobe.com
Phylum Aschelminthes tutorial all along with the key concepts of Features of Aschelminthes, Classification of Aschelminthes, Feature of Ascaris Lumbricoides, Structural Adaptation of Ascan Lumbricoides
The Mammalian kidney tutorial all along with the key concepts of Structure of the Mammalian kidney, Functions of the Kidney and Diseases of the Kidney
The AICPA sets usually accepted professional and technical standards for CPAs in several areas. The AICPA held a control in this field until the 1970’s.
tutorsglobe.com natural selection assignment help-homework help by online modern concept of natural selection tutors
tutorsglobe.com blood group typing assignment help-homework help by online tissue transplantation tutors
Cleavage patterns in major groups of organisms tutorial all along with the key concepts of Blastula formationin sea urchin, Fate maps and the determination of sea urchin blastomeres, Axis specification, Cleavage in Early Amphibian Development, Cleavage in Fish Eggs, Cleavage in Mammal and Cleavage in Snail eggs
Theory and lecture notes of Rational Functions and Asymptotes all along with the key concepts of Vertical Asymptotes, Horizontal Asymptotes, Holes, Oblique Asymptotes. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Rational Functions and Asymptotes.
Theory and lecture notes of Simplified Database System all along with the key concepts of Simplified Database System, Illustration of Database with Conceptual Data Model, Example of a simple Database. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Simplified Database System.
Incompatibility mechanisms tutorial all along with the key concepts of Self-incompatibility in plants, Mechanisms of self-incompatibility, Gametophytic self-incompatibility, Heteromorphic self-incompatibility, Cryptic self-incompatibility, Self-compatibility
Damped Harmonic Motion tutorial all along with the key concepts of restoring force, damping force, instantaneous velocity of oscillator, Solutions of differential equation, Heavy Damping, Critical Damping, Logarithmic Decrement, Relaxation Time
tutorsglobe.com ureotelism assignment help-homework help by online excretion tutors
Selected Financial Reporting Standards , IAS 8 Accounting Policies, Changes in Accounting Estimates and Errors, IAS 10 Events after the Reporting Period
tutorsglobe.com inspiration assignment help-homework help by online respiration tutors
Macroscopic Property of Dielectrics tutorial all along with the key concepts of Simple Model of the Dielectric Material, Dielectric in an Electric Field, Non-Polar and Polar Molecules, Polarization Vector, Gauss' Law in a Dielectric, Dielectric Strength and Breakdown
tutorsglobe.com some early views of heredity assignment help-homework help by online heredity tutors
1952100
Questions Asked
3689
Tutors
1459984
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!