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States of equilibrium:
● stable equilibrium
● unstable equilibrium
● neutral equilibrium
A. Stable equilibrium
B. Unstable
Neutral equilibrium
A body in stable equilibrium when a force is applied onto it and let go will return
to its original position like in 1.
( ii ) A body in unstable equilibrium like 2, will move away from its original position
when pushed and will never return to this position unless a force is applied to do
( iii ) Neutral equilibrium like in 3: no further forces are enacted but the body remains
on the new position.
Concept of a parcel of air: air is put into an imaginary elastic wrap. The small volumeof
air is now referred to as a parcel of air.
Assumptions about the parcel of air are:
(i )
the parcel can expand and contract but does not break apart, i e. remains as a
single unit.
( ii ) the parcel is thermally insulated i.e. no heat is added to it from the surrounding
(ambient) air and no heat escapes from the parcel to the surrounding air.
( iii ) the space occupied by the molecules within the parcel defines the air density.
( iv ) average speed of the molecules defines the temperature.
( v ) colliding molecules against the walls of the parcel determine the pressure.
( vi ) at the surface the parcel of air has the same temperature as the surrounding air.
(vii) no compensating motions occur as the parcel moves.
Adiabatic processes: when a thermally insulated parcel of air rises it expands due to
decrease in pressure, and then cools and then it sinks due to increase in pressure,
and warms up. This is called an adiabatic process because the air parcel expands
and cools or compresses and warms with no exchanges of heat with its
Application of the parcel of air and the adiabatic process
1.Dry adiabatic lapse rate: As long as the parcel remains unsaturated (i.e. humidity less
than 100%) the parcel of air will maintain a cooling or warming constant rate.
This rate is called the dry adiabatic lapse rate which is ≈ 10 degrees Celsius
for every 1000m or ≈ 1 degree per 100m ≈ 5,5 degrees per 1000
2. Moist adiabatic lapse rate: as the air rises it cools at the D.A.L.R and its humidity
increases as it approaches its dew point temperature and at dew point RH
becomes 100%(saturation ). Further
from this due point results in
condensation and cloud formation and latent heat is released into the rising air.
Because of the latent heat added in the parcel of air, during condensation offsets
some cooling due to expansion, the air no longer cools at the D.A.L.R but a lesser
rate called the moist(saturated ) adiabatic lapse rate.
● Unlike the DALR, the SALR is not constant. It varies from places to place due to
moisture content and temperature of the air.
● On sinking the parcel of air becomes unsaturated and descends at the DALR .
● Although SALR is not a constant we normally use 6 degrees Celsius per 1000m or 3,3
degrees F per 1000m.
Determination of stability in the atmosphere
This is done by comparing the temperature of rising parcel of air to that of its
1. Stable: If the rising parcel of air is colder than the environment is stable as it will be
more dense and will tend to sink its original position. It resists upward motion.
(a) A temperature profile, obtained from balloon borne instruments- a radiosonde
is called a “sounding”.
(b) “Lapse rate” is the rate at which the air temperature changes with elevation.
(c) “Environmental lapse rate” is the actual rate at which the temperature on a
particular date changes with altitude usually obtained from the soundings.
Note : 1) Dry (Unsaturated) cools at DALR
2) Saturated(moist air cools/warms at SALR-MALR)
A. Stability for lifted dry air
● warm advection aloft (warm air aloft)
● cold advection at the surface or lower levels. These can be brought about by
radiational cooling at the surface at night
cold air advection
air moving over a cold surface
air subsidence
Inversions: These occur sometimes at the surface but most frequently observed
aloft and are often associated with large high pressure systems where there is large
scale sinking. Over an inversion temp increases with height hence warm air overlies
cold air. Diagram
Role of inversions:
● act as lid to vertical motion and are often the level where stratiform clouds form (sc,st)
● give foggy weather below
● trap pollutants below
● hazy weather below due to trapping of pollutants
● clear weather above the inversion
● turbulence for aircrafts
B.Neutral stability:
i) For a dry parcel of air neutral stability is realised when DALR = ELR. Therefore at
every level the air would have the same temp and density as that of the surrounding air.
ii) For moist air neutral stability occurs when SALR = ELR
C. Unstable Air:
For unstable dry air , at every level the rising air is warmer and lighter
than the air around it and continues to rise. ELR > DALR
For unstable moist air, at every level, the moist air will be
warmer and lighter than the air around it hence continues to
rise. ELR > SALR
D.Conditional Instability:
Here when the air is moist it is unstable but when dry id stable.
Stability status depends on whether the air is moist or dry. DALR > ELR >SALR
E. Absolute Stability:
Regardless of weather the air is moist or dry, it is still warmer and
lighter than the surrounding air, hence continues to rise.
ELR >DALR >SALR. This occurs over a very shallow layer near the
surface on a very hot day.
Causes of Instability:
The atmosphere becomes more unstable if the ELR steepens ie when the temp drops
rapidly with height.
● cold air advection aloft
● surface becoming warmer (warmer advection at the surface. Warming of surface may
be due: i) daytime solar heating of the surface
ii) influx of warm air brought in by wind(warm air advection)
iii) air moving over a warm surface. Diagram here
Two other ways in which a layer of air can be made unstable are i) mixing and ii) lifting.
i) Mixing: Rising cooling air lowers the temp towards the top while sinking warming
air increases the temp at the bottom. See diagram below
(a) Lifting the whole layer: The layer X-Y is initially absolutely stable since
X-Y is less than SALR. This layer is lifted, then there is a rapid decrease of air
density aloft and this causes the air to stretch out vertically. Due to stretching the top
layer cools more than the bottom. This steepens the lapse rates and we remain with a
layer X-Y which is now conditionally unstable. The layer would become more stable
if lowered down .
(b) Lifting a layer that is saturated at the bottom and dry at the top:
The bottom is moist follows A-A(moist adiabatic) and the top is
dry follows B-B(dry adiabat). The resulting layer A-B is now
absolutely unstable. The potential instability brought about by the
lifting of a layer whose surface is humid and whose top is dry is
called “ convective Instability”. This situation normally results in
severe t/stoms and tornadoes. Diagram
F. Latent Instability: Diagram
The parcel is forced to rise to B, and this is done along the dry adiabat. At B the
parcel is now saturated and moves at saturation adiabat up to C when its temp is now
equal to that of the environment(LFC) thereafter it rises up to D freely as it is warmer
than the environment. This parcel was in “latent instability Equilibrium”. Two
conditions must apply for a parcel in latent instability and these are: i) availability of
mechanical lifting to overcome stabilising forces at the lower levels up to (Lfc) ,ii) A
sufficient amount of moisture is needed to enable the air to become saturated at B.
Two cases of latent instability are known namely: i) Real latent instability – A case
when the positive area is larger than the negative area: ii) Pseudo latent instability –
when the negative area exceeds the positive area
Air with absolute stability strongly resists upward motion and if forced to rise it will
spread out horizontal forming a thin layer of clouds such as ci, altocumulus, sc, Ns, st
Definition of dew point: the temperature attained by air when cooled to attain
saturation at constant pressure and moisture content with respect to a flat surface of
Definition of Condensation:
Definition of Frost point: When the dew point is determined with respect to a flat
surface of ice.
For a period of a day a parcel of air may be assumed adiabatic due to the following:
● Air is a poor conductor of heat.
● Mixing with the surrounding is very slow.
● Temperature changes due to radioactive processes are small as compared to
expansion and contraction.
Thermodynamic diagrams
Diagrams used to study energy transformation or thermodynamic processes in the
atmosphere are referred to as “aerological diagrams”.
Types of thermodynamic diagrams:
1. Skew T- lnp diagram
2. Emagram
3. Tephigram
4. Stuve` T Diagram
Many aerological diagrams use pressure to depict the pictorial manner, the distribution of
temperature and moisture at a locality. On the other hand logarithm of pressure has been
found to be closely related to altitude is and this conveniently used for pressure in
thermodynamic diagrams.
Desirable properties of a thermodynamic diagram:
● The area enclosed by the lines representing the cyclic process should be proportional to
energy change or the work done during the process.
● As many lines as possible representing the basic process should be straight.
● The angle between the isotherms and the dry adiabatic should be as large as possible.
● In the lower atmosphere, the dry adiabatic and the saturation adiabatic should make an
appreciable angle.
Tφ Tephigram :
O stands for entropy, here entropy lines are the dry adiabats( line of constant θ. θ
potential temp is related to specific entropy (S) by
ds = cp d(lnθ), hence lines of constant potential temperature (dry adiabats) on a T – ln θ
diagram corresponds to an isentropic process. Diagram below for the Chart and lines
The (Tφ )Tephigram
In order to asses the stability of the atmosphere the following lines are used:
Dry adiabats: these are lines which show temp changes during an ascent or
descent. Potential temp (θ) is constant along each dry adiabat. SE-NW are
straight lines hence DALR = constant. These lines are the moving paths for
unsaturated or dry air.
Saturated adiabats: show temp changes during ascent or descent for
saturated air. These are curved lines SE-NW. Gradient varies from place to
place hence SALR is not a constant.
Pressure isobars curved orientation E-West.
Saturated Humidity ratio lines or saturation mixing ratio lines(SMRL),
labelled in gram/kg. These lines indicate mass of water vapour in grams
mixed with one kilogram of dry air. These are dotted lines with a SW-NE
Isotherms: Temp lines with a SW-NE orientation
Uses of a Tφ Tephigram
●ELR (environmental lapse rate) can be determined if a sounding is plotted at various
levels of the T θ .
●Normands’ Rule: Diagram
The dry bulb temp(T) through the dry adiabat,the wet bulb temperature(Tw) through
the saturated adiabat and the dew point temp(Td) through the humidity mixing ratio
line all meet at a point called the “Normarnd’s point”. This is where condensation
occurs and hence referred to a the lifting condensation level(Lcf).
●Use of the Tephigram to evaluate unreported quantities:
Mixing Ratio (r) : Read off the dew point value given by the saturation
mixing ratio line passing through the point.
Saturation Mixing ratio(Rs): Read off the value of the saturation mixing
ration passing through the temperature point.
Relative Humidity (U)(RH): Read off r and Rs as indicated above then use
the formula RH = r/Rs * 100.
Potential temperature (O): This is the temp which the parcel of air would
have if brought dry adiabatically to a pressure of 1000hpa. Select the point on
the temperature curve then move along the dry adiabat until 1000 hpa. The
temp at this point is the potential temperature O.
Lifting condensation level (Lfc): This is the level to which dry air is raised
dry adiabatically to become saturated. See Normand’s theorem for its
Virtual temperature (Tv): This the temp of dry air having the same density
as the sample of moist air, provided the pressure is the same. Tv = T + r/6.
Icing levels
Cloud tops and bases
Depth of Clouds
Type of precipitation expected
These are solid or liquid particles suspended in the atmosphere. Effective radius ranges
from 0.005µ and 20µ. Aerosols are divided into three categories:
(a) Aitken nuclei:
< 0.1µ. These are usually too small to provide an important source of cloud condensation
(b) Large nuclei:
0.1 to 1µ. These are usually comprised of ammonia sulphates which are hydroscopic.
They are important for cloud formation.
(c) Giant nuclei:
> 1µ. These are composed of sodium chloride from the oceans after entering into the
atmosphere as air bubbles that break down. These are few but are the first to act as
condensation nuclei.
NB. Although there are processes continuously producing aerosols, their concentration
has been found to be constant. This is due to:
● Precipitation removing aerosols from the atmosphere.
● Gravitational forces: large particles raised by strong winds quickly settle down under
gravitational force.
Condensation nuclei
It is possible to conduct experiments where relative humidity can reach 500% without
condensation occurring. Condensation does not take place until the water vapour has a
suitable surface on which to condense. This is called the condensation nucleus.
(a) Heterogeneous nucleation: if condensation nucleus is other than water surface and
comprises of such surfaces as ions, small foreign particles and large foreign
substances. This is very important in cloud formation. Under atmospheric conditions.
(b) Homogeneous nucleation: when there is condensation of water vapour into a liquid
water surface. This is rare in the atmosphere and can form with up to 500%
NB. Condensation first occurs on giant nuclei( hydroscopic such as sea salt), then on
large nuclei( from industrial areas) which are more numerous than giant ones and account
for most of the development of droplets found in clouds.
Water can be cooled to below nominal freezing point and still remain liquid. This is super
cooling and the water is in a super cooled state. A cloud droplet or liquid will freeze
spontaneously when temperature falls below –40 degrees Celsius. Supercooling may
occur between 0 and –40 degrees. For freezing to occur to super cooled water, an ice
nucleus or freezing nucleus needs to be available for temperatures above –40 degrees.
Define “deposition”: vapour to solid ice, the freezing nuclei is now the ice which is now
the ice forming nuclei. (Talk about
A) Precipitation from clouds
1) Condensation forms tiny water droplets, which are subjected to forces of gravity and
buoyancy. At first the droplets accelerates downwards but as friction increases with
droplet speed, the forces eventually balance and acceleration is stopped but then the
droplet will fall at a constant speed relative to the air. This is known as the terminal
velocity. The larger the droplet, the greater the terminal velocity. Cloud droplets of
radii 10µ and 20µ have terminal velocities of about 1 and 5m/s respectively in still
air. In none precipitating clouds, updrafts will keep the droplets buoyant.
2) From the discussion it will take several hours for a droplet to reach the ground from a
height of 1 kilometre. In general, clouds need a radius of at least 100µ in order to read
the ground.
3) The condensation process is far too slow to account for the ground to the required
size in a reasonable time. So other process are needed to explain the formation of the
raindrop size in a short time.
B) Coalescence Theory
Development of droplet to raindrop size is mainly due to coalescence resulting from
droplet collision. The small and large droplets due to different terminal velocities. The
droplets collide and coalesce, thereby growing in size. (Talk about raindrop
C)Bergeron - Findeson Process in Mixed Cloud
Mixed cloud consists of ice crystals in predominantly super cooled water droplets.
Basis of the process: saturation vapour pressure over super cooled water is greater than
that over ice at the same temperature.
Explain the process: page 152 Retallact
Aggregation: is when individual ice crystals collide forming snow flakes.
Accretion: when ice crystals collided and coalescence with super cooled water
1) Characteristics of electric charges:
Electric charges are of two types: positive and negative
Unlike charges attract and like charges repel
Atoms contain protons (positively charged), and electrons (negatively charged)
Neutral atoms have an equal number of electrons and protons
A positively charged body has a deficit of electrons and a negatively charged has
a deficit of protons
From one atom to another
An electrically charged body is capable of exerting an electric force on other
charged bodies in the neighbourhood. This field is known as an electric field
If A and B are points in an electric field such that a positive charge moves from
point A to point B, then A is said to be at a higher potential therefore an electric
current will flow from A to B via a conductor
Flow of positive charges from a point of high potential is known as conventional
current. Where as that of electrons from a point of low potential is called an
electric current
Current electricity deals with electrical charges in motion and static electricity
2) Electrical field of the atmosphere
In fine weather the atmosphere carries a net positive charge and the ground is
taken as zero
Rate of change of potential with height is called the potential gradient
In fine weather the potential difference is approximately 150 volts/m. This
increases to about 2000 volts/m in haze, fog or cloud
Light rain or drizzles may either increase or lower potential gradient as compared
to that of fair weather
Showers and heavy rain modify the electric field reaching large values in
thunderstorms such that a spark discharge or lightning occurs.
Evidence of atmospheric electricity
Saint Elmo’s fire: Static discharges may take place when ever the potential
gradient is large and can occur as radio noise, and on some occasions on the Saint
Elmo’s fire when a more or less continuos and luminous electric discharge is
produced around some parts of the aircraft.
Lightning: This is the greatest visible manifestation of atmospheric electricity.
Lightning is a large scale example of an electric spark and this may take place
between:(i) Cloud and the ground, (ii) Between two clouds, (iii) between two
parts of the same cloud, (iv) between a cloud and the surrounding air.
When the path of the discharge is visible as an irregular highly luminous spark,
referred to as “forked lightning”. When the discharge is obscured by clouds and
precipitation and is shown as diffuse glow, then it is called “sheet lightning”.
Thunder: During the lightning flash the atmosphere is suddenly and intensely
heated resulting in violent expansion which in turn produces sound waves heard
as thunder. Thunder and lightning occur at the same time but due to the fact that
light travels faster than sound, there is a delay between the two effects depending
on distance.
Critical Potential Gradients
Not all electric potential gradients end up with a spark or discharge. There are critical
values of electric potential gradient that depend on (i) conductivity of the air, (ii) the
distance between the two points.
● Dry air is a poor conductor and needs as much as 3x106 volts per metre in order to
break its insulating power for a discharge to occur.
● In the presence of water droplets, the conductivity of air is increased and hence in
clouds, lightning may occur with a potential gradient of 1x106 volts per metre.
Generation of Electrical charges in clouds(Diagram for a CB)
Generally, the cloud is said to have a positive polarity. Many theories have been proposed
to explain the separation of positive and negative charges in various parts of the cloud,
and these include:
● Movement of water drops or ice particles in an already existing electric field
● The freezing of water droplets
● The breaking or coalescence of water droplets
● Friction between ice crystals
● Evaporation and melting of ice particles
● Deposition of water vapour or ice crystals
None of the above processes has been able to successfully explain all the facts about
charge separation in a cloud, it is possible that several charge processes operate
Characteristics of the lightning flash
Discharges may take place between (i) cloud and earth, (ii) two parts of the same
cloud, (iii)between two different clouds, and (iv) between clouds and the
surrounding air.
Observations indicate that the flash consists of successive shocks. These follow
the channel made by the first stroke.
The leader stroke is sometimes continuos, builds downwards from the cloud to the
ground, but is not luminous. On other occasions a more rapid intermittent “leader
stroke”, occurs moving in steps and branching on the way to the ground. This
stroke is slightly luminous.
The leader stroke is followed by a “return stroke” from the ground to the cloud,
which is continuous and intensely luminous.
After about 0.1 seconds, a “dart leader” may return along the same path followed
by the “return stroke”. The dart and return strokes may be repeated several times.
Effects of Lightning Discharge
Intense heating to the ground and air as the current passes through.
Local fusing of roots (liquification) and soil
Water boiling instantly
Explosive expansion of boiling water may cause splitting of trees or shattering of
Atmospheric or spheric results in rapid fluctuation of electric current in lightning
resulting in generation of radiation which is detectable on radio receivers. This
process in known as atmospheric or spheric => this phenomenon may be used to
detect thunderstorms with lighting 2000km or more away.
Pedology is the study of soils, their origins, characteristics and utilisation.
A) Soil: There are two concepts –pedological( origin and classification), and
epaphological( properties of soil as they relate to production of food and fibre).
B) Soil forming factors:
 Parent material: can be igneous, metamorphic, or sedimentary. Nature of soil and
supply of minerals and fertility depend on the parent rock. Quartz soil may not be
rich in clay and be sandy.
Climate: affects weathering processes through temperature and rainfall, wind.
Climate affects vegetation, which in turn affects soil formation. Climate in
conjunction with parent material is of cardinal importance in soil formation.
Vegetation: this is the main source of organic matter in soil. Other functions of
vegetation are reduction in run off, reduction of soil erosion, increase in soil water
content (by providing cover), and improving soil structure and aeration.
Topography/ Relief: There is rapid run-off in steep slopes, slope affects climate
due to rain shadows, for example Queteniqua mountains in the Cape.
Organisms and animals; (a) human beings threat – soil erosion
(b) micro-organisms like bacteria and fungi assist in decomposition. Worms and
termites aerate the soil. Human beings fertilise, plough, irrigate and accelerate soil
Time; soils take a long time to form. 400 years under extreme conditions for
10mm, and 1000 years for 1m. It takes 3000 years to 13000 years to produce a
soil depth sufficient or mature for farming.
Soil definition
(a) Botkin and Heller (1995: 210). Soil may be defined as earth material modified over
time by physical, chemical, and biological processes such that, in addition to
supporting rooted plant life, they are altered from the original parent material into a
series of horizons parallel to the surface.
(b) Miller (1992): Soil is a complex mixture of eroded rock, mineral nutrients, decaying
organic matter, water, air and billions of living organisms, most of them microscopic
(c) Brandy soil definition; pedalogist – soil is a natural body (entity), biochemically
weathered and synthesised product of nature.
Edaphologist; soil is a natural habitat for plants
(d) Monk house; soil is the thin layer on the earth comprising minerals and particles
formed by break down of rocks, decayed organic material, living organisms, in the
water and in the atmosphere
The Soil Profile
Diagram of soil horizons:
A Horizon:
B Horizon:
C Horizon:
D Horizon:
Page 241 Waugh
The soil profile;
(a) Horizon – biological activity and humus content are at a maximum. There is leaching
and movement of soluble material downwards (eluviation).
(b) Horizon – zone of illuviation where clays from (a) are deposited. (a) and (b) are true
(c) Horizon – consists of recently weathered regolith.
(d) Horizon – is bed rock(rock that is intact)
There are 2 types of soil, namely
(i) mineral (inorganic soils)
(ii) organic soils
N.B. Most soils have on average organic matter ranging form 1 – 10%, but in swamp
places, marshes, organic matter can be as high as 80 – 95%.
Organic soils are soils with an organic content of over 20%
Mineral soils are those with organic matter less than or equal to 20% of their
composition, i.e. they are mostly composed of mineral matter.
In this program mineral soils will be studied as they are the most prevalent.
Physical properties of soil
Soil is composed of water (20-30%) mineral (45%) and organic matter (5%) and air.
Diagram of volume composition of soils
Two very important physical properties of soils are texture and structure
(a) Soil texture; refers to sizes of mineral particles. It refers to the relative proportions of
various sizes in a given soil.
(b) Soil structure; this is the arrangement of soil particles or soil aggregates
Soil structure and texture used together, help to determine the nutrient the nutrientsupplying ability of soils, water and air supplying capacities of soils to plant life
Soil texture
Study the texture of mineral particles of the soil. Soils are separated into groups
according to sizes called separates by the analytical process called the particle size
Using particle size analysis, the following classes come up:
coarse sand
fine sand
Physical nature of soil separates
a) Coarse fragments; these are fragments with greatest diameter 2-75mm. They give
rise to gravel or pebbles, and 75-250mm give rise to cobbles or flags, and those more
than 250mm are called stones
b) Sand; i) cannot be moulded as can clay, ii) water holding capacity is low because of
large spaces in between grains, iii) air and water passage is rapid, iv) hence they
facilitate good aeration and drainage but are very prone to drought
Soil textural classes
There are 3 classes:
sand; 15% or less clay
clay; 30-40% clay namely clay, sandy clay, silty clay
loam; a mixture of sand, loam and clay. Names of loam include silt loam, silt
clay loam, sandy clay loam, and clay loam
A soil continuum;
 mineral matter
 texture
 structure
 moisture
 air content
 organic matter (humus)
 organisms
 nutrients
 acidity (pH)
 temperature
Soil texture measurements
Coarse sand (diameter between 2-0.2mm)
Fine sand (0.2-0.02mm)
Silt (0.02-0.002mm)
Clay (less than 0.002mm)
N.B. How does soil texture affect farming activities
Water in the soil is given by:
W = α [R – (E + T + D)]
Where W = water content
α = constant
R = rainfall or precipitation
E = evaporation
D = drainage
Thermodynamics of the Atmosphere
1. Thermodynamics are a branch of physics which deal with:
(a) Heat as a form of energy
(b) Processes that involve heat changes and the conservation of energy
(c) Thermodynamics of both dry and moist air
(d) A change of state leads to the release or absorption of latent heat (eg. Vapour
to water and water to vapour)
2. Variables of state:
(a) To describe a sample of air we need to know its mass, volume, pressure,
temperature and composition
(b) In any physical processes the mass and composition are assumed to be
(c) The only variables are volume, pressure and air( variables of state)
(d) For this purpose dry air is treated as a perfect gas. Its equation of state can be
written as:
P = ρd Rd T
where ρ = density
Rd = specific gas constant = 287.04 Jkg-1K-1
The gas laws:
In meteorology, reference is made to initial and final equilibrium states of atmospheric
gases which have been subjected to specific energy processes or transformations.
Variables of state
A system is a specific sample of matter. Equilibrium state of a system can
completely be specified by the following finite properties namely, pressure,
temperature and volume. These properties are known as variables of state or
thermodynamic variables.
A small system can be described thermodynamically by its volume (ΔV), and
mass (Δm), pressure (P), temperature (T) and composition. I f the system passes
through physical properties without mass or composition change then three
variables will be left. These are volume, pressure and temperature. These are the
basic variables of state and their values completely describe the state of a given
Volume is expressed as the specific volume (α) which is volume per unit mass.
α = ΔV/ Δm therefore α = 1 / ρ
the reciprocal of density = Δm / ΔV = ρ
Boyle’s Law;
By Robert Boyle 1660,
P α 1 / V,
meaning PV = k1 where
k1 is a constant for a given
mass of gas at a given
Boyle’s law states that the pressure of a given mass of gas kept at a constant
temperature is inversely proportional to its volume. This is mostly useful or true at
low temperatures.
Charles’s Law;
V α T, meaning that V = k2 T,
where k2 is the constant for a given mass
Of gas kept at constant pressure and T is
Expressed in Kelvins
That is, the volume of a given mass of gas at constant pressure is directly
proportional to its temperature in Kelvins.
Note that 1 Kelvin = 273.15 + c
where c is degrees Celsius
Combinations of Charles’ and Boyle’s law gives us:
PV = kT
This is the equation of state.
A convenient way of expressing the mass of a substance is through the mole or
molecular weight.
H2 = 2kgmol-1; H = 1kgmol-1; O2 = 32kgmol-1; O = 16kgmol-1
It has been established that each mole of a gas contains the same number of
molecules which is equal to 6.02 x 1023 and this is called Avogadro’s number.
Molar volume;
This is the volume occupied by a mole of gas and this varies with pressure and
PV = kT is referred to as the ideal gas law.
If T is constant, we get:
PV = k
 Boyle’s Law
If P is constant, we get Charles’s law:
V = kT
Given the following information, use the equation of state to calculate the
universal gas constant denoted by R*.
Molar volume = 22.414m3 per mole
Pressure standard atmosphere = 1013.25mb = 101325 Newton m-2 (temp=273.15
PV = R*T, meaning that R* = PV/T = (101325x22.414)/273.15 = 8314
Equation of state of an ideal gas:
PV = R*T. Truly speaking, no gas behaves ideally, but real gases behave so when
pressures are extremely low.
In meteorology, unit mass of the gas is 1kg and volume is specific volume α.
α = V/m
P(v/m) = R*T
R = R*/M = specific gas constant
PV = R*T becomes:
Pα = RT, where R = specific gas constant is now known as the ideal gas
Dalton’s Law of partial pressures:
For a mixture of gases:
P = Σ =P1 + P2 + P3 + …Pk = total pressure
Pn = pressure of the net components. The total pressure exerted by a mixture of
gas is equal to the sum of the partial pressures which would be exerted if it, alone,
occupied the whole entire volume at the temperature of the mixture.
Phases Of Water
1. Solid phase ( ice )
2. Liquid phase ( water )
3. Vapour stage ( water vapour )
The Clausius Claperon equation
This equation shows the differential relationships between saturation vapour pressure (es),
and the temperature which is below the critical temperature (Te ). Diagram of The
Clausius Claperon equation below
TC = evaporation curve
TA = sublimation curve
TB = melting curve
NB. From the graphs, saturation vapour over super cooled water is greater than that over
ice, meaning that the slope of the curve TA is greater than that of the curve TC.
Diagram of the cyclic processes in water phases:
Sublimation: Conversion of a solid to a vapour without an intervening liquid phase.
Latent heat of fusion: heat is used
Latent heat of vaporisation: heat is used
Sublimation heat is released or used
Freezing heat is released
Condensation heat is released
If a few ice crystals are formed in a cloud of super cooled water, then the vapour pressure
will be greater than the saturation vapour pressure over water, but less over ice. Excess of
water vapour over super cooled water than over ice.
TC = evaporation curve
TA = sublimation curve
TB = melting curve
NB. From the graphs, saturation vapour over super cooled water is greater than that over
ice, meaning that the slope of the curve TA is greater than that of the curve TC.
Hence condensation forms on the ice crystals, depleting the supply of water vapour in the
cloud. The super cooled droplets then evaporate in order to restore vapour in the cloud.
Thus water turns from a super cooled state to ice crystals. Ice crystals grow at the
expense of super cooled droplets.
Super cooled droplet
More SVP (H)
Ice particle
Vapour to solid
Less SVP (L)
Vapour pressure
super cooled droplet
evaporates to restore
Vapour to solid
The process continues and the ice crystals will grow at the expense of super
cooled water droplets (Bergeron-Findeson Process).
Equation of state of water vapour
e cv = Rv T
e = vapour pressure, cv = specific volume of water vapour, T = temperature in K
The specific gas constant for water vapour is Rv = 461.51Jkg-1K-1.
Moisture variables
Moist air is a mixture of dry air and moist air.
(a) Vapour pressure: vapour pressure is that part of the atmospheric pressure which is
exerted by water vapour. The unit measurement is the millibar = 102 Nm-2.
(b) Saturation vapour pressure: pressure exerted by water vapour when the space
immediately above the surface is saturated at the prevailing temperature
It is always expressed with respect to a plane surface
ew = saturation vapour pressure with respect to a plane water surface
ei = saturation vapour pressure with respect to a plane ice surface
Saturation water vapour pressure increases with temperature
(c) Mixing ratio(r): This is the ratio of mass (mi) of water vapour present to the mass of
dry air in the sample.
r = mv / md, if V is the volume of the sample.
r = (mv / V) / (md / V) = ρv / ρd, ρv and ρd are densities of water
vapour and dry air (page 81 –83)
Rd / Rv = mv / md = ε ≈ 0.622
(d) Saturation mixing ratio (rs): value of the mixing ratio if the air is saturated.
Two types of saturation mixing ratios:
rw = saturation mixing ratio with respect to water
ri = saturation mixing ratio with respect to ice
rs = 0.622 es / (P – es)
(e) Relative Humidity (V): is the ratio of the actual mixing ratio of a sample of air at a
given pressure and temperature to the saturation mixing ratio of the air at that
pressure and temperature.
V = r / rs x 100 %
V = e / es x 100 %
V = RH is the amount of moisture in a sample of air compared to the maximum amount
the sample of air would hold when saturated at the same pressure and temperature
expressed as a percentage (shoko).
(f) Specific humidity (q): is the ratio of the mass (mv) of water vapour present to the
mass of moist air
q = mv / (mv + md)
md = mass od dry air, mv + md = mass of moist air
(g) Virtual temperature (Tv): is the temperature at which dry air at the same total
pressure would have the same density as the given sample.
Tv = T (1 + 0.61r)
Tv = T + 1/6 (103r)
T = 273
Definitions: Processes where pressure is kept constant are known as isobaric processes.
1.) Dew point temperature: when assumed that no water vapour is allowed to enter or
leave the parcel of air so mixing ratio (r) remains constant. If the parcel of air is cool
at constant pressure (isobarically), a temperature will be reached at which it becomes
saturated. This temperature is called dew point temperature (Td). Condensation occurs
when cooling occurs below the dew point.
2.) Wet bulb temperature (Tw): when cooling a parcel of air at constant pressure by
evaporation of liquid water into it until it is saturated. The temperature at which it
becomes saturated is called the wet bulb temperature. General r increases.
3.) Virual temperature:(Explanation) Diagram
Moist air 22
Dry air 22
Give 2 examples of air, one moist and the other dry, at the same temperature and
pressure. Using the equations of state, ρm = [1 / (1 + 0.61r)] ρd, where ρm and ρd are
the densities of moist and dry air respectively. Since ρd decreases with temperature at
constant pressure. Therefore to have the 2 densities equal, the temperature of the dry
air should be increased. This increased temperature arrived at in trying to match the
densities is called the virtual temperature.
Equivalent temperature: For most air if the water vapour in the sample condenses at
constant pressure, the latent heat released during condensation is used to warm the
sample. The temperature reached when all the water vapour in the sample has been
condensed is called the equivalent temperature (Te).
Potential temperature (θ):This is the temperature which a sample of air would have
if brought dry adiabatically to a pressure of 1000 hPa
Wet bulb potential temperature(θw): from the intersection of the Td through the
(HMRL) and the temperature (through the dry adiabat) called Normand’s point, move
down along the saturation adiabats until 1000hPa is reached. The temperature read at
this point is θw.
Equivalent temperature (Te): This is another isobaric process in moist air. When the
latent heat released during condensation of water vapour is used to warm the sample
of air. The temperature reached when all the water vapour in the sample has
condensed is called the equivalent temperature. It can be obtained on the TФ but it is
not of practical use.
Clouds form due to condensation, which is a result of cooling. Cooling is brought about
1) Radiation
2) Advection of cold
3) Convection
4) Adiabatic ascents
The most important cooling mechanism for cloud formation is adiabatic cooling as a
result of expansion of air during vertical motion.
Vertical motions resulting in cloud formation are:
mechanical turbulence (frictional turbulence)
Convection (thermal turbulence)
Oragraphic ascent
Slow widespread ascent
Gradual widespread upward motion of moist air leads to development of sheets or layers
of clouds covering large areas of the sky called stratiform clouds and vigorous vertical
produce cumuliform clouds separated by clear spaces.
(a) Mechanical turbulence mixing:
 When the air is sufficiently moist, turbulent motion will produce widespread
stratiform clouds on the upper part of the layer
 Turbulence tends to distribute the water vapour content evenly in the layer
 Condensation occurs at the mixing condensation level (MCL)
Clouds stratiform of various thickness are formed with frequent breaks in the
 Cloud undulations occur from condensation on the crest and evaporation on the
trough. The clouds formed are stratocumulus.
 Other types of turbulence clouds are:
Strata fractus (St fra)
Cumulus fractus (Cu fra)
Fractus means broken. These are clouds of bad weather occurring below rain
bearing clouds like nimbostratus, altostratus, and cumulonimbus.
(b) Convection:
 Occur when the air is heated, becomes less dense and rises resulting in
cumuliform clouds. Rising thermals reach the convective condensation level
where clouds have their bases. Clouds may develop into the following stages:
small, medium and large
(a) Cumulus fractus
(b) Cumulus humilus (Cu hum)
(c) Cumulus congestus (Cu con)
(d) Cumulonimbus calvus (CB calvus)
(e) Cumulonimbus capillalis (CB willanvill)
When there is an inversion there is the fair weather cumulus and the top of the cloud base
spreads to form stratocumulus.
Very stable moist conditions give heavy showers (from Cu) and thunderstorms and hail.
Clouds at any stage may become unstable – altocumulus castellinus and cumulus
(c) Oragraphic ascent:
When moist air is forced to rise over mountains or barriers, stratus, cumulus, CB,
altocumulus lenticular standing form as wave clouds on the windward wit clear
clouds on the leeward side.
(d) Slow widespread ascent:
 Results form large wind systems such as depression fronts. This is usually over
very large areas and ascent is very slow and may take several days. Causes of
widespread ascent can be:
divergence in the upper atmosphere
Cloud Classification
Ten main groups of clouds can be distinguished. Each group is called a genus(plural
genera). Each genus is further divided into species or varieties. The ten genera are:
· cirrus
· cirrocumulus
· altocumulus
· altostratus
· nimbostratus
· stratocumulus
· stratus
· cumulus
· cumulonimbus
Cloud heights range from sea level to the top of the tpropopause and since the tropopause
altitude varies in space and time, cloud tops are generally higher in the tropics followed
by middle and higher latitude.
The parts of the atmosphere in which clouds form is divided into parts called ètages,
namely: high ètage, middle ètages and low ètage. The ètages overlap and their limits
vary with latitude.
The ètages are as follows:
1) High ètage
Cirrus, cirrocumulus, cirrocumulus (high level clouds) (CB)
2) Medium ètage
Altocumulus, altostratus, cumulonimbus(CB)
3) Low ètage
Stratus, stratocumulus, cumulonimbus(CB), low level clouds
(a) Altostratus is usually in the medium ètage but often extends to high ètage
(b) Nimbostratus is mostly found in the medium ètage, but often extends into the
other ètages.
(c) Cumulus and cumulonimbus usually have their bases in the low ètages, but
can have tops in the medium and high ètages.
Types of precipitation
(a) Rain: falling drops of liquid water with a diameter of at least 0.5mm. Rain mostly
falls from nimbostratus, altocumulus, altostratus, and thick stratocumulus. When
small raindrops evaporate before reaching the ground, the result is virga. This shows
as an evaporating breaks of precipitation.
(b) Drizzle: fine uniform drops with a diameter of less than 0.5mm. Drizzle is from
stratus clouds
(c) Shower: falls from cumulus, large cumulus, and can be heavy thus is called cloud
(d) Thunderstorm: this is precipitation that can occur with lightning and thunder (CB)
(e) Snow: most of the precipitation reaching the ground begins as snow. When the
freezing level is sufficiently low, then the snow can reach the ground before melting
(f) Ice:
(g) Frost:
(h) Acid rain:
(i) Hail: from the thunderstorm it is small or relatively large frozen ice pellets from the
Relative sizes of raindrops, cloud droplet and condensation nuclei:
Collision and coalescence process
In warm clouds with tops warmer than -15°C. Some cloud droplets are larger than ashes
and larger drops fall at faster speeds and hence collide with small droplets and merge and
the droplet may be blown up by an updraft and on descending the process is repeated
until the updrafts can no longer keep the droplets suspended in the air, then it falls as a
raindrop. Important factors are:
1.) The cloud’s liquid water content
2.) Range of droplet sizes
3.) Cloud thickness
4.) Strength of updrafts in the cloud
5.) Electrical charge of droplets and the electric field in the cloud. Enhanced
coalescence is observed when colliding droplets have opposite electrical charges