 # GEU 0047: Meteorology Lecture 6 Stability and Cloud Development.

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GEU 0047: Meteorology Lecture 6 Stability and Cloud Development

Equilibrium vs. Stability Equilibrium’s 2 States: –Stable –Unstable Perturbed from its initial state, an object can either tend to return to original point (A. stable) or deviate away (B. unstable)

Atmospheric Stability

Solid lines: environmental lapse rate Dashed lines: parcel’s lapse rate Γ d : a constant

Γ w : NOT a constant

Atmospheric Stability If perturbed vertically, a stable air parcel will tend to go back to its original altitude, whereas an unstable parcel will usually accelerate away vertically. If rising/sinking, the air parcel tends to cool down/warm up, due to the change in ambient pressure with altitude. Remember e -1 change for every 7.29 km (scale height H p ) P = P o e -z/H p

Are the following 2 statements same (or contradictory)? 1.rising air cools 2.warm air rises Hhh…? Let’s think about it for a while!

Rising and Sinking Air

Determining the temperature in a rising air parcel consider a rising parcel of air -->> As the parcel rises, it will adiabatically expand and cool (recall our discussion in chapter 5 about rising parcels of air) adiabatic - a process where the parcel temperature changes due to an expansion or compression, no heat is added or taken away from the parcel the parcel expands since the lower pressure outside allows the air molecules to push out on the parcel walls since it takes energy for the parcel molecules to "push out" on the parcel walls, they use up some of their internal energy in the process. therefore, the parcel also cools since temperature is proportional to molecular internal energy

Eureka! (Archimedes’ Law) In air, scale reads the weight T 1 = W. Immersed in water, the additional buoyant force reduces the objects weight because of buoyancy F b. Thereby, T 2 = W - F b F b =  f V f g = displaced fluid weight T1T1 W T2T2 W FbFb

Buoyancy Archimedes Law: The buoyancy force is equal to the weight of the volume of fluid displaced. Weight of the volume of fluid* displaced  f V o g Weight (m g) of the object  o V o g The net force on an object is its weight minus the buoyancy F n =  o V o g -  f V o g *The environmental air is treated as a fluid in which a parcel of air is immersed.

Buoyancy and Acceleration Acceleration = Force/mass F = Weight - F b =  o V o g -  f V o g Acceleration = F/ (  o V o ) = g(  o V o -  f V o )/m = g(  o -  f )/  o

Buoyancy and Acceleration In air, replacing densities with temperatures using the ideal gas law, P =  R T, yields an equation for the acceleration of the air parcel, given the temperature and pressure of the parcel (T o, P o ) and those of the environment (T f, P f ). Acceleration = g(P o - P f )/P o = g(  f -  o )/  f Therefore, A large temperature difference means instability. a ~  T

Determining stability involves asking what happens to an air parcel if there is a small perturbation (vertical motion).What is its equilibrium like, stable or unstable?

Adiabatic Process: Expansion and cooling (or compression and heating) without any thermal exchange with the environment Adiabatic process does NOT mean isothermal process (What the hell …? Is Q = mc  T wrong?) Black: isothermal Blue: adiabatic

Dry Adiabats  dry : Temperature change within an unsaturated air parcel. ~-9.8 o C/1000m

Moist Adiabats  wet : Temperature change within a saturated air parcel. ~ -6 o C/1000m

Lapse Rate: change in Temperature with Altitude  = -  T/  z Environmental Lapse Rate: Radiosondes yield information about the environmental lapse rate. It is what it is…on average  ~ 6.5 o C/1000m. This lapse rate is used to estimate the stability after comparing with either the dry adiabatic lapse rate (  dry ) or moist adiabatic lapse rate (  wet ) of our imagery air parcel.

Some things you need to know: The gas laws Apply p =  R T to an air parcel with a unit mass,  p α =  R T; α: specific volume (α =   )  p Δα + Δp α =  R ΔT If this air parcel is in hydrostatic balance,  g  z = p top – p bottom = -  p  Δp = - ρ g Δz Now, if this air parcel takes in some heat energy  q while performing some work  w and causes an amount of internal energy change  u,  q =  w +  u = p Δ α +  u (1 st law of thermodynamics)

The specific heats C v : Spceific heat at constant volume C v ≡  q /  T, C v ≡  u /  T when α is constant C p : Spceific heat at constant pressure C p ≡  q /  T when p is constant C p = C v + R

 q = p Δ α +  u = p Δ α + C v  T =  (p α) - α Δp + C v  T =  (RT) - α Δp + C v  T = R  T - α Δp + C v  T = (C v + R)  T - α Δp = C p  T - α Δp = C p  T + g Δz C p ≡  q /  T when p is const. p α = RT Δp = - ρ g Δz If dry adiabatic,  q = 0  dry = -  T/  z = g/C p Adiabatic process and lapse rate

Moist Adiabatic Lapse Rate Unlike  dry,  wet = -  T/  z is NOT a constant, but varies with temperature and moisture content !

Saturation Vapor Pressure (SVP) e s =  o exp{L/R v (1/T o -1/T)} Known as Clausius-Clapeyron relation discovered when two engineers were working on the thermodynamics of water vapor to produce a more efficient steam engine.  o = 611 Pascals R v = 461 J/K/kg ( e α = R v T ) T o = 273 o K (i.e., 0 o C) L = { L v = 2.50 x 10 6 J/kg} = { L d = 2.83 x 10 6 J/kg}

Mixing Ratio r = mass of water vapor / mass of dry air =  v /  d How does the T d change in rising and sinking air? For an air parcel at T and P, what is its water vapor content? T P

Moist adiabatic process  q = C p  T + g Δz  q = -L v  r s, for a saturated air parcel (r s : saturation mixing ratio) -L v  r s = C p  T + g Δz  wet = -  T/ Δz = L v /C p *  r s /Δz + g/C p = L v /C p *  r s /Δz +  dry = L v /C p *  r s /ΔT *ΔT/ ΔZ +  dry = - L v /C p  r s /ΔT  wet +  dry (1 + L v /C p  r s /ΔT)  wet =  dry Because  r s /ΔT is always positive,  wet <  dry

Air Parcel Adiabatic Plot Air parcel representation (pressure, temperature, mixing ratio) = Temperature = Humidity X

Dry Adiabatic Process Both air parcel points (temperature, humidity) move together to the new pressure. Temperature along the dry adiabat, Humidity along an isohume or constant moisture content, because no moisture leaves the parcel.

Moist Adiabatic Process At some level, the adiabats and isohumes converge. T and T d then cool along the moist (saturated) adiabat. The difference between the actual mixing ratio in a cloud and the original mixing ratio is the distance between X and O on the plot. It is equal to the amount of condensation produced.

Lifting Condensation Level (LCL) When unsaturated air is lifted, it cools at the dry adiabatic rate. If lifted high enough, the temperature will drop below the dew point. Drier air must be lifted higher than moist air to encounter LCL. The height at which saturation just occurs is called the saturation level or the lifting condensation level (LCL). This height (in meters) can be estimated for cumulus-type clouds and is approximated by Z LCL = 125/(T - T d ), where T d is the dew point temperature derived from the vapor pressure equation encountered before: e =  o exp{L v /R v (1/T o -1/T d )}

Absolute Stability (Dry) The parcel of air is cooler and heavier than the surrounding air around it at all levels.  dry When perturbed it will tend to return to its original position.

Absolute Stability (Wet) The atmosphere is always stable when the environmental lapse rate is less than the moist adiabatic rate.  wet

Stratus clouds (cirrostratus, altostratus, nimbostratus) form in stable air.

A Stable Atmosphere Stability favors a small environmental lapse rate. Ways to make the lapse rate small…. –Warm the air aloft (Inversions) warm advection (warm front) slowly sinking air (high pressure) –Cool the air near the ground (Fogs) calm night radiative cooling cold advection (cold front) air moving over a cold surface Dashed: before Solid: after

Fig. 6-5, p. 143 When the surface air is saturated in a stable atmos., a persistent fog (or haze) may form.

Subsidence (sinking air) Descending of a layer of air causes it to warm and shrink via adiabatic compression. A temperature inversion can develop (warm air over cool).

Fig. 1, p. 144 Subsidence inversion

Absolutely Unstable (Dry) The atmosphere is always unstable when the environmental lapse rate is greater than the dry adiabatic rate.  dry >  wet

Absolutely Unstable (Wet) The parcel of air is warmer and lighter than the surrounding air around it at all levels. When perturbed it will tend to accelerate away from its original position.

Cumulus-type clouds

Stability Conditions An atmosphere with an environmental lapse rate  will be... Always Stable if  Dry  Wet Always Unstable if  Dry  Wet What About Between?

Conditional Stability (Dry) In this example the dry air is cooler and heavier than the air around it at all levels. It is stable. The environmental lapse rate is less than the dry adiabatic lapse rate. But,  Dry    Wet

Conditionally Unstable (Wet) A saturated parcel is warmer than the surrounding air at all levels. It is unstable. With an environmental lapse rate between the dry and moist adiabatic rates, stability depends upon whether the air is saturated or not.

Conditional Stability If air can be lifted to a level where it is saturated, instability would result.

Instability Causes Instability favors a large environmental lapse rate. Ways to increase the lapse rate …. –Cool the air aloft cold advection (jet stream) radiative cooling (emitting IR to space) –Warm the air near the ground influx of warm air (warm advection) daytime solar heating of the surface air moving over a warm surface Dashed: before Solid: after

Mixing Instability Mixing may occur via convection or turbulence.

Stratus Formation Mixing stable air close to saturation can cause stratus-type clouds. The upper layer cools and saturates while the lower layer warms and dries out, increasing the environmental lapse rate.

Stratocumulus

Rising Instability As a stable layer rises, the change in density spreads it out. If it remains unsaturated, the top cools faster than below.

Convective Instability An inversion layer with a saturated bottom and an unsaturated top. The top layer cools at  dry while the bottom layer cools at  wet (because of latent heat release.) This leads to absolute instability associated with severe storms (Ch.14).

Mechanisms responsible for cloud development Convective Uplift Orographic Uplift Convergence Uplift Frontal Uplift

Convective Uplift Vertical Motion via Convection: exchange of thermal energy by mass motion. Hot air rises because it is less dense. Lifting a parcel of air to a height where condensation occurs, releases the latent heat stored in the water vapor as clouds form.

Convective Cloud Heights Cumulus-type cloud height is approximated as Z LCL = 125/(T - T d ), where the constant 125 comes from the difference on average between  Dry ~ 10 o K/1000m and  DewPt ~ 2 o K/1000m. With knowledge of the air temperature and dew point, determining cumulus cloud base heights is simple. With observation of cloud base height and air temperature, the dew point (hence moisture content) is estimated.

Orographic Uplift Vertical Motion via Orographic Uplift: air that encounters steep topography is forced to rise.

Convergence Uplift Vertical Motion via Convergence: advection winds that encounter each other force rising motion away from the surface. Air rises because there is nowhere else to go.

Frontal Uplift Vertical Motion via Frontal Uplift: a cold air mass encounters warm air or a warm air mass encounters cooler air. Since colder air is more dense, it displaces the warm air upward in a cold front or a warm front along the air masses boundary.

Cumulus Convection A warm wet bottom and a cool dry top. Convection leads to large vertical development while the sinking air in between the clouds is clear.

Cumulus Conditions The stability of air above the condensation level greatly influences the vertical development of the clouds.

Cumulus Development Instability may reach to the top of the troposphere where cumulonimbus clouds “anvil” out in response to the stable inversion layer of the stratosphere.

Entrainment Entrainment: mixing of environmental air into a current, jet or convection (cloud). When mixing of cooler, dry air occurs into convectively unstable clouds, the clouds cool much more quickly. The rate of cooling can approach the dry adiabatic rate and the convective instability will cease. If the air is warm and moist, the instability grows along with the vertical development. Hence, our interest in water vapor (moisture) and infrared (cloud heights) images.

Mountain Rain Shadow Orographic lifting, adiabatic cooling, heating and loss of moisture content.

Potential Temperature (θ) Temperature an air parcel would have if moved dry adiabatically to near surface (p 0 = 1000mb). θ would remain constant if an air parcel is subjected to only dry adiabatic transformations.  q = C p  T – αΔp = 0 p α =  R T; => α =  R T/p C p R -1  T/T = Δp/p θ = T(p 0 /p) exp(R/C p ), is called Poisson’s equation by meteorologists The reversible adiabatic process is called isentropic process

Summary 1.A parcel of air in stable/unstable equilibrium will return/depart its original position. 2.A rising parcel of unsaturated air will cool at the dry adiabatic rate of (~ 10 o C/1000m); a descending unsaturated parcel warms at this rate. 3.A rising parcel of saturated air will cool at the moist adiabatic rate of (~ 6 o C/1000m); a descending saturated parcel warms at this rate. 4.The environmental lapse rate is the rate that the actual air temperature decreases with increasing altitude.  = -  T/  z

Summary (cont.) 5.Absolute Stability: Air at surface is cooler than air aloft (inversion), or the environmental lapse rate is greater than the dry adiabatic rate. 6.Instability can be initiated if surface air warms, air aloft cools, or vertical lifting occurs (convection, convergence, fronts, topography). 7.Conditional Instability: Environmental lapse rate is between the moist and dry adiabatic rates. Unsaturated air is lifted to a point where condensation occurs and becomes warmer than the surrounding air.