MeteorologyLab ESCI 241
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This 13 page Class Notes was uploaded by Cordie Miller on Thursday October 15, 2015. The Class Notes belongs to ESCI 241 at Millersville University of Pennsylvania taught by Alex DeCaria in Fall. Since its upload, it has received 59 views. For similar materials see /class/223517/esci-241-millersville-university-of-pennsylvania in Earth Sciences at Millersville University of Pennsylvania.
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Date Created: 10/15/15
ESCI 2A1 7 Meteoroloy Lesson 7 7 stahiIity Dr DeCana References and Reading MT Chapter 7 RELATION 0F CLOUD FORMATION TO UPWARD MOTION c As an air parcel is Iirted for whatever reason it cooIs due to adiahatic expansion o wiII occur and a cloud wiII form 0 Most clouds in the atmosphere form as a resuIt of upward verticaI motion 0 Upward motion caused by four main Iirting mechanisms 0 Convective Iirting o Orographic Iiiting a Convergence o ErontaI Iirting VERTICAL BALANCE OF EORCEs o 39 39 39 pmu see diagram we have 2 MinaAimg max ml Pui PAm 1 51 A F 52 L PIA mg 0 Recognizing that m pA 51 we have a lpzazpzg z 0 61 39 O From the first fundamental theorem of calculus we have pz z pz dl zgt0 6Z dz so that Newton s second law for the vertical forces on an air parcel becomes BUOYANCY O Letting properties of the air parcel itself be denoted with a prime and those of the surrounding air having no prime then Newton s second law for the air parcel is dz 77 g 1 0 If the surrounding atmosphere is in hydrostatic balance then from the hydrostatic equation we know that dp dz 0 g Using this in equation 1 gives a 7 7 g 2 0 Equation 2 shows that the buoyancy force depends on the difference in density between the air parcel and its surroundings 0 If the parcel is denser than the environment the acceleration will be downward If it is lighter than the environment the acceleration will be upward Equation 2 can also be written in terms of temperature Substituting for density from the ideal gas law and assuming the pressure of the air parcel is the same as the pressure of the environment p p we can write the acceleration in terms of temperature dz g 3 0 This shows us that warm air rises and cold air sinks BUOYANCY AND ARCHIMEDES PRINCIPLE O Buoyancy can be expressed in a somewhat different form by multiplying equation 2 by p V where Vis the volume of the parcel to get p39Va pVg p39Vg This equation is of the form ma Z Fz and shows that the air parcel accelerates in response to two forces 0 The downward force p Vg is just the weight of the air parcel 0 The upward force pVg is the weight of air that the parcel has displaced The fact that there is an upward force that is due to the weight of the displaced uid is known as Archimedes Principle 0 This is the reason why ships and balloons can oat 0 The upward force from Archimedes Law is really nothing other than the difference in the pressure force underneath vs above the object DRY ADIABATIC LAPSE RATE 0 An unsaturated air parcel that rises will cool at a rate given by LT 2 dz 0p 0 This formula says that if you lift an air parcel adiabatically its temperature will decrease which makes physical sense because the parcel will be expanding 0 We therefore can define a dry adiabatic lapse rate as Fd E i Dry Adiabatic Lapse Rate dz adiabatic Cp 0 For dry air c1 1007 Jkg lK l so that Pa 98 Ckm STABILITY IN A DRY ATMOSPHERE 0 Stability refers to whether an air parcel one moved vertically will continue to accelerate in the direction that it was pushed unstable or return in the direction from which it came stable 0 We ve already established that to determine the acceleration on the air parcel we need to compare its temperature with that of its surroundings 0 Imagine an air parcel that is in equilibrium with the environment so that T T To There will be no acceleration of the air parcel so the air parcel will remain at rest 0 If the air parcel is initially at the origin and is displaced a distance 1 T will change according to the adiabatic lapse rate so that T z To Hz 0 At altitude z the environmental temperature is Tz To 71 where 7is the environmental lapse rate 0 The acceleration at altitude z is from equation 3 F dz 7 d gz To7z 0 Whether the parcel has an upward downward or no acceleration depends on how the environmental lapse rate compares with the dryadiabatic lapse rate 0 If D lt 7 then the parcel will continue to accelerate upward after it was displaced upward and therefore the atmosphere is unstable 0 D 74 then the parcel will remain where it is after it was displaced upward and therefore the atmosphere is neutral 0 U gt 74 then the parcel will accelerate downward after it was displaced upward and therefore the atmosphere is stable POTENTIAL TEMPERATURE AND STABILITY 0 Potential temperature is defined as the temperature an air parcel would have if it were moved dryadiabatically to a reference pressure p0 1000 mb Rdcp o E P O In an adiabatic process potential temperature is conserved O The vertical acceleration on an air parcel can be written in terms of potential temperature a g 4 0 Imagine an air parcel that is in equilibrium with the environment so that 19 0 6b There will be no acceleration of the air parcel so the air parcel will remain at rest 0 If the air parcel is initially at the origin and is displaced a distance 1 0 will remain constant since this is an adiabatic process 0 At altitude z the environmental potential temperature is d 0 01 00 Z 39 d z 0 The acceleration at altitude z is from equation 4 d Qdz dz gz 0z 0 Thus whether the parcel has an upward downward or no acceleration depends on how the environmental potential temperature changes with height E gt 0 stable dz 0 neutral dz E lt 0 unstable dz STABILITY IN A MOIST ATMOSPHERE O The presence of water vapor changes our stability determination somewhat 0 Unless the air parcel is saturated we can treat it as though it is completely dry for stability purposes 0 Once an air parcel is saturated any further cooling will result in the release of latent heat due to condensation 0 The latent heat released will result in the temperature of the air parcel cooling at lesser rate as it rises than it would if it were dry O The lapse rate at which a saturated air parcel cools if lifted is called the saturatedadiabatic lapse rate and is a complicated function of temperature r5 LV RdT L2 8 1 r5 2 c p R dT 1 O The saturatedadiabatic lapse rate is always less than the dry adiabatic lapse rate 0 In very humid conditions near the ground F5 is around 4 Ckm 0 At very cold temperatures F5 approaches Pd because the air is so dry that there is little latent heat release 0 To assess the stability of a moist atmosphere we must compare the environmental lapse rate with both the dry and saturatedadiabatic lapse rates 0 D lt 7 and 1 lt 7 absolutely unstable 0 D gt 7 and 139 lt 7 conditionally unstable 0 D gt 7 and 1 gt 7 absolutely stable EXERCISES 1 A dry air parcel has a temperature of 20 C The environmental lapse rate is 5 Ckm The air parcel is forced to rise over a mountain that is 3 km high a What is the temperature of the air parcel at the top of the mountain b What is the temperature of the environment at the top of the mountain c What is the buoyant acceleration of the air parcel d Is the atmosphere stable or unstable P A moist air parcel has a temperature of 20 C and is forced to rise over the same mountain as in problem 1 If it reaches saturation while it is ascending will it be warmer or colder than the dry air parcel when it reaches the top of the mountain 3 The dry and moist air parcels from problems 1 and 2 now are forced to descend the other side of the mountain They both descend dry adiabatically Will their temperatures be the same once they reach the bottom If not which one will be warmer 4 For the following data find the potential temperature at the two altitudes Is the atmosphere stable or unstable Altitude m Pressure mb Temp C 0 K 1480 850 7 5700 500 15 5 Show that What assumptions did you have to make Are they reasonable ESCI 241 Meteorology Lesson 2 Thermodynamics ENERGY Energy is the capacity to do work Two main categories of energy 0 Potential energy stored energy I Example In a gravitational field PE mgh 0 Kinetic energy energy of motion KE 12m2 Other types of energy 0 Thermal energy total of the kinetic energy of all the molecules in a substance 0 Internal energy U the sum of thermal energy and any potential energy due to the forces between the molecules of a substance I Note that for an ideal gas since there are no intermolecular forces there is no potential energy between molecules Therefore for an ideal gas internal energy and thermal energy are identical Energy is conserved 0 Energy can be converted from one form to another but it cannot be created nor destroyed this is the 1st Law of Thermodynamics TEMPERATURE Temperature is related to the average kinetic energy of the molecules of a substance T olt KE Hot objects have faster moving molecules Cold objects have slower moving molecules Heat is energy that is in the process of being transferred from one object to another due to temperature differences TEMPERATURE SCALES 0 Temperature scales are rather arbitrary Meteorologists use three different scales 0 Fahrenheit F 0 0 F chosen as lowest temperature that a mixture of ice water and ammonia salt ammonium chloride can reach in equilibrium 0 32 F is the freezing point of pure water 0 96 F was originally chosen as the blood temperature of a healthy person now 986 F on the modern Fahrenheit scale 0 Fahrenheit s choices of his xed points seems arbitrary and his exact reasoning hasn t been recorded 0 Celsius C 0 Zero point determined by freezing point of water 0 100 point corresponds to boiling point of water 0 Conversion from Celsius to Fahrenheit F g C 32 O A change of 1 C is equivalent to a change of 1K or 18 F 0 Kelvin K O Referred to as the absolute temperature scale 0 Zero point determined by the lowest theoretical temperature to which any matter can be cooled entropy not energy is zero at absolute zero I It is theoretically impossible to cool as substance to absolute zero in a finite number of steps and therefore a temperature of absolute zero is unattainable This is known as the principle of unattainability of absolute zero I The coldest temperature achieved so far as of 2009 is 3X10 9 K 0 Degree interval is same as in Celsius 0 Conversion from Kelvin to Celsius C K 27315 0 A change of IR is equivalent to a change of 1 C or 18 F 0 Note If you are interested in historical accounts of thermometers and the creation of the various temperature scales you can try the following two books A History of the Thermometer and its use in Meteorology by Middleton Johns Hopkins Press 1966 or Inventing Temperature Measurement and Scientific Progress by H Chang Oxford University Press 2004 FIRST LAW OF THERMODYNAMICS 0 Energy is conserved O The internal energy U of an air parcel can be changed by either heating the parcel Q the parcel or by doing work W d U dQ dW 0 Positive work implies work being done on the air parcel whereas negative work implies work being done by the air parcel 0 An expanding air parcel does work on its environment d W lt 0 Therefore an expanding air parcel will lose internal energy and cool 0 Conversely a shrinking air parcel has work done on it by the environment d W gt 0 Therefore a shrinking air parcel will gain internal energy and warm SENSIBLE HEAT AND HEAT CAPACITY O Sensible heat results in a change of temperature 0 The amount of heat required to raise the temperature of an object by 1 C is called the heat capacity C 0 Heat capacity depends on both the amount and type of the substance 0 Units of heat capacity are J K 1 O The heat capacity will depend on whether the pressure or volume changes during the heating 0 If pressure is held constant then the heat capacity is denoted as Cp 0 If volume is held constant then the heat capacity is denoted as Cv 0 Heat capacity per unit mass is called the specific heat cv Cv m cp C p m 0 Units of specific heat are J kg391 K O The specific heat at constant pressure is larger than the specific heat at constant volume 0 This is because at constant volume all the heat goes into raising the temperature but at constant pressure the gas can also expand and do work so some of the heat goes into doing work instead of raising the temperature PHASE CHANGES AND LATENT HEAT 0 The amount of heat required to change the phase of a unit mass of a substance is called the latent heat 0 The amount of latent heat depends on the substance and the process The pI OCESSES are Melting solid to liquid absorbs heat Freezing liquid to solid releases heat Evaporation liquid to vapor absorbs heat Condensation vapor to liquid releases heat Sublimation solid to vapor absorbs heat I Deposition vapor to solid releases heat 0 Latent heating is an important heat source and sink for the atmosphere HEAT TRANSFER 0 Heat can be moved or transported in one of three ways 0 Conduction Transfer of heat through physical contact 0 Convection Transfer of heat through movement of uid I In Meteorology the term convection is used solely for vertical transport by a uid Horizontal transport is referred to as advection 0 Radiation Transfer of heat through electromagnetic waves EXERCISES 1 The speci c heat of water at constant pressure is 1 ca g391 C 1 a What is the heat capacity at constant pressure of 2 kg of water b How much energy must be added to 2 kg of water to increase the temperature by 3 C 2 How much heat is released by the condensation of 3 kg of water vapor The latent heat of vaporization is 600 cal kg39l 3 A 3 kg block of aluminum has a heat capacity constant pressure of 2691 J K71 A 05 kg block of beryllium has a heat capacity constant pressure of 912 J K71 Which one has a higher speci c heat at constant pressure 4 A 15 kg parcel of dry air is at a temperature of 15 C and a pressure of 1013 mb E How many moles of air are in the parcel The molecular weight of air is 2896 gmol Fquot What is the volume of the parcel P If 50 KJ of heat are added to the parcel while its volume is held constant what is the new temperature of the parcel The speci c heat of air at constant volume is 717 J kgquot1 K71 Q If 50 KJ of heat are added to the parcel while its pressure is held constant what is the new temperature of the parcel The speci c heat of air at constant pressure is 1005 J kg 1 K71
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