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ATMOSPHERIC STABILITY States of equilibrium: ● stable equilibrium ● unstable equilibrium ● neutral equilibrium A. Stable equilibrium B. Unstable C. equilibrium Neutral equilibrium (i) 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 so. ( 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 surroundings. 1 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 surroundings. 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 i) radiational cooling at the surface at night ii) cold air advection iii) air moving over a cold surface iv) air subsidence 2 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: i) 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 ii) 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 3 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 iv) Lifting: (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 4 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. 5 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 CLOUD DEVELOPMENT: 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 water. 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 6 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: i) Dry adiabats: these are lines which show temp changes during an ascent or ii) iii) iv) 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 orientation. 7 v) 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: i) Mixing Ratio (r) : Read off the dew point value given by the saturation mixing ratio line passing through the point. ii) Saturation Mixing ratio(Rs): Read off the value of the saturation mixing ration passing through the temperature point. iii) Relative Humidity (U)(RH): Read off r and Rs as indicated above then use the formula RH = r/Rs * 100. iv) 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. v) 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 determination vi) 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. vii) Inversions: 8 viii) Icing levels ix) Cloud tops and bases x) Depth of Clouds xi) Type of precipitation expected CLOUDS, PRECIPITATION, AND LIGHTNING Aerosols 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 nuclei. (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% saturation. 9 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. SUPER COOLING OF DROPLETS 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 multiplication). 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 10 (i) (ii) Aggregation: is when individual ice crystals collide forming snow flakes. Accretion: when ice crystals collided and coalescence with super cooled water droplets. ATMOSPHERIC ELECTRICITY 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 11 ● 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 (a) (b) (c) 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) 12 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 simultaneously. 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 roots Humans Infrastructure 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. 13 PEDOLOGY 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. 14 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 erosion 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 decomposers. (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: 15 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 soils (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%. (a) Organic soils are soils with an organic content of over 20% (b) 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 16 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 analysis. Using particle size analysis, the following classes come up: i) coarse sand ii) fine sand iii) silt iv) clay 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: i) sand; 15% or less clay ii) clay; 30-40% clay namely clay, sandy clay, silty clay iii) 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 a) b) c) d) Coarse sand (diameter between 2-0.2mm) Fine sand (0.2-0.02mm) Silt (0.02-0.002mm) Clay (less than 0.002mm) 17 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 18 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 constant (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. A.1. 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 system. Volume is expressed as the specific volume (α) which is volume per unit mass. α = ΔV/ Δm therefore α = 1 / ρ 19 the reciprocal of density = Δm / ΔV = ρ A.2. 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 temperature 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. A.3. 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 A.4. 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. A.5. Molar volume; This is the volume occupied by a mole of gas and this varies with pressure and temperature. 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 20 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 kelvins). PV = R*T, meaning that R* = PV/T = (101325x22.414)/273.15 = 8314 J/mol/Kelvin A.6 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 constant A.7 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 21 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. 1) 2) 3) 4) 5) 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 1. More SVP (H) excess Ice particle Vapour to solid 22 Less SVP (L) deficit sublimation 2. Vapour pressure reduced super cooled droplet evaporates to restore balance(H) Vapour to solid L sublimation 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 i) It is always expressed with respect to a plane surface ii) ew = saturation vapour pressure with respect to a plane water surface iii) ei = saturation vapour pressure with respect to a plane ice surface iv) 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. i.e. 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 r=ε e/p-e (d) Saturation mixing ratio (rs): value of the mixing ratio if the air is saturated. 23 Two types of saturation mixing ratios: i) rw = saturation mixing ratio with respect to water ii) 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 % or 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 24 4.) 5.) 6.) 7.) 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. 25 CLOUD FORMATION Clouds form due to condensation, which is a result of cooling. Cooling is brought about by: 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: i) mechanical turbulence (frictional turbulence) ii) Convection (thermal turbulence) iii) Oragraphic ascent iv) 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. Cloud undulations occur from condensation on the crest and evaporation on the trough. The clouds formed are stratocumulus. Other types of turbulence clouds are: i) Altocumulus ii) Strata fractus (St fra) iii) 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 26 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 castellinus (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: i) divergence in the upper atmosphere ii) fronts iii) depressions iv) troughs 27 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 ·cirrostratus · 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 NB. (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. 28 (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 burst (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 cumulonimbus(CB). Relative sizes of raindrops, cloud droplet and condensation nuclei: Diagram 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 29