FINAL EXAM Flashcards
What is Convection?
- Vertical displacement of air-masses under the effect of buoyancy.
- Air warmed @ the surface to the point that it becomes positively buoyant -> rises.
- Air is cooled @ mid-tropospheric levels to the point that it becomes negatively buoyant -> sinks
- Alternative term: vertical overturning.
Differ moist convection from dry convection.
Moist: most easily observed since it leads to cloud formation and typically to precipitation.
Dry: Characteristic to atmospheric boundary layer: thermals, thermal rolls, thermal plumes.
From buoyancy driven convection + background flow –> 3D circulation develops producing +/- complex convective phenomenon.
Write from less to more complex.
Fair weather cumulus - Shower producing cumulus - Cumulonimbus clouds - Squall lines - Supercell storms - ...
What is characteristic of he convective circulation?
The organisation of the elements (individual clouds/thunderstorms) in a way that the convective circulation maintains itself and is long-lived
Describe the scale of convective phenomena
Thermals/cumulus/thunderstorm : L<10km T<1hr
Squalls/Supercells: 101000km T: monthly-seasonal
What is the mean global and annual rate of decrease of temperature in the lower 10 km of the atmosphere? Its name?
It is the mean environmental lapse rate ~ -7.0 deg/km
What sets the value of the mean environmental lapse rate?
Atmospheric column is heated through: radiation/conduction/convection –> value is the result of the thermal equilibrium achieved.
By what is convection triggered?
If excessive heating through radiation/conduction create a lapse rate exceeding equilibrium lapse rate –> convecion is triggered to return the atmospheric column to equilibrium
What are the two processes in play when re-equilibrating atmospheric column
1- Exchange of air-masses in the vertical (warm from low to higher levels/cold from higher to lower)
2- Mixing: mixing with environmental air along the ascent/descent and once air-mass has attained final position
Describe the energy as convection occurs
As temperature profile is perturbed from equi value -> reservoir of available potential energy (APE) created in low tropospheric levels.
Convection releases this energy (APE) by converting it to kinetic energy (KE) : updrafts/downdrafts. Eventually the KE is dissipated into microscale motions
Where does convection happens?
1. Away from the tropics
- Following insolation cycle (thunderstorms, squall lines, tornadoes, warm season/daytime)
- Cold air moving over a heat source (over water near polar regions dur to continental air travelling over the warmer ocean)
- Air mass becoming buoyant as result of lifting (frontal: mid-latitude frontal rainband, orographic lifting)
Draw a sketch of convection happening due to the insolation cycle
destabilisation of equi lapse rate due to heating at the surface.
Insolation @ surface
Draw a sketch of the polar lows
Often a cold pool of air @ mid-levels contributing to destabilising equi lapse rate
Cooling of surface
Draw a sketch of convection as result of forced lifting
- forced lifting up to intersection point A
- advancing cold air behind cold front -> receding warm air ahead of cold front
How can we measure convection?
- Experimental Campaings
- Radar Imagery
- Satellite Imagery
About Radars:
- What do radars measure?
- What do the antennas send?
- What is their target?
The echoreflectivity is measured to estimate the type and distribution of precipitation in the cloud/its distance and height
They send out directional pulses of microwave radiation
They target rain/snow.graupel/hail particles (some can even detect cloud drops/ice) such that the pulse is reflected back to the antenna. Distance is a few kilometers
About Satellite imagery:
-Visible Imagery (VIS)?
Images are obtained by reflecting sunlight
- > high reflectance (white): dense cirrus from Cumulonimbus clusters, fresh snow, nimbostratus clouds
- > Low reflectance: much of the earth’s surface (dark grey or black)
About Satellite imagery:
- Infrared wavelengths?
- What do radiometers sense?
- Water Vapour Imagery?
Radiometers sense the intensity of the heat emission of the earth/ atmosphere components @ IR wavelengths
- > produce infrared images from which we can determine cloud top heights
- low intensity (white) : colder (higher cloud tops)
- high intensity (grey): warmer (lower cloud tops)
Detect water vapour in the infrared spectrum. @upper-mid levels of troposphere where winds are ruled by large-scale air masses
Describe what forms the ITCZ
What is the ITCZ a tracer of?
ITCZ: InterTropical Convergence Zone
-Trade winds from NH and SH come together @ equator, picking up moisture along their paths
- Convergence + Intense solar heating (sun’s zenith point)
- > buoyant, H2O loaded air masses
- > vertical upward lifting of air masses
- > vigorous convective activity manifesting as clusters of thunderstorms along the ITCZ belt
Tracer of Hadley circulation
Sketch the convecting development of ITCZ
South-North cross-section
- sensible heating @ surface along Southward trajectory
- radiative cooling in upper troposphere (anvil top)
- strong ascent in convective dev @ equatorial zone
- gentle sinking motion to the north of convecting zone (descending branch of Hadley cell)
What are Monsoons?
What is the most extensive Monsoon?
They are seasonally driven large-scale circulation.
Winter: from land-> ocean
Summer: from ocean-> land
The summer Asian monsoon: dominates the East Asian Sector, starts in June ends in September
Describe the circulation of monsoons
- air heated more rapidly over land
- air masses become buoyant and rises
- air mass of cool humid air is drawn from neighbooring ocean to the land
- humid air heated over land
- becomes buoyant
- rises
- its moisture condenses
- gives deep convection and heavy rains
What is the hyposometric equation
derive
Give the step by step circulation of monsoon
- By hyposometric eq delta Z land > delta Z ocean
- pressure surface pn is pushed higher up over land than ocean
- @ constant altitude P land>Pocean
- PGF towards ocean @ upper levels
- Air mass accumulation @ mid-upper levels
- Divergent flow @ mid-upper levels
- Low pressure center over Asia
- PGF towards land in response to the surface thermal low
- Convergence @ low level. This flow advects water vapour from the maritime to the continental boundary layer
- Humid air-masses become rapidly heater over continent -> lapse rate over land larger than equi -> favourable conditions for convective development
- Latent heat release on a massive scale over Asia
Sketch the Tropical cyclone structure
Outflow: @ mid and upper levels, from center outwards
Subsidence: gentle @ large radius
Ascent: Intense @ convective towers near the low pressure center
Inflow: @ low levels (ABL), inwards
What is the first theory of the formation of tropical cyclones?
(thermally driven)
Similar to thermally driven monsoonal circulation.
Convective heating by the cluster of thunderstorms over the warm ocean ->PGF in upper levels -> divergence in upper levels above heating source
Outflow-> generates low pressure center driving convergent flow in boundary layer towards convective cluster.
What is the second theory of the formation of tropical cylcones?
(Air-Sea Interaction)
Emphasis on the latent heat transfer from the ocean to the atmosphere
- depends on wind speed (controlling the evaporation rate)
- needs a small initial disturbance (wave) to provide necessary winds for strong evaporation.
- feedback:
- > strong winds increases rate of evaporation
- > increases the intensity of convection
- > increases the strength of converging winds
Necessity of Tsfc > 26 C
Derive the vorticity equation (only w.r.t. horizontal divergence)
Tells that divergence generates vorticity
Direction of vorticity/circulation
- > convergence
- > divergence
- > positive vorticity (ccw)
- >negative vorticity (cw)
Derive the time evolution of vorticity
t=tn -> vorticity» coriolis parameter
Vorticity grows exponentially with time
Derive how we can estimate the pressure tendency @ surface
From continuity equation in pressure coordinates.
The rate @ which pressure is falling in the tropical cyclone center is a function of the divergence in the atm column above.
-> The latter is a funciton of the amount of heating generated by the convection
The sinking and negative buoyancy in tropical cyclone is a result of what?
It is due to radiative cooling and the long timescale.
What can tropical cyclone be compared to in their steady state?
Can be compared to a carnot cycle heat engine.
- heat is gained @ low levels (Ts about 300 K)
- heat transferred upwards to the top and lost by radiative cooling (Ttop about 200 K)
vs Carnot:
Cyclic process where the fluid undergoes a series of change in which the volume changes and does external work —> returns to its initial conditions
What is Avogadro’s hypothesis
A given number of molecules of a gas occupies the same volume as the same number of molecules of another gas under the same T-p conditions
- > Mass * R is constant
- > Rd = 287J/degkg
Why is the mass of moist air hard to estimate?
Why are we interested in it?
Because of the changeable nature of moist content
- > allows calculation of Rw and density of moist air
- > density is essential for assessing whether the moist air-mass is sufficiently buoyant for convective development
Derive moist air density in terms of Rd, t, e, p and epsilon
p ~ p_d
conclusion: density moist< density dry under same p, T condition
Define the virtual temperature and derive it.
density moist = p/RdTv
Tv is the temperature that the parcel would have to acquire for its density to be the same if all moisture were removed (so the temperature has to rise) under constant pressure
What does the radiosonde measures?
How is does it infer water content?
How does it get the saturation vapour pressure?
How does it transmit RH?
It measures T and e
e/p = w/(w+epsi)
e_s is estimated as a function of temperature -> can infer w_s
from w and w_s RH is estimated and transmitted to the ground station
dq = du + dw
-Express dw in terms of volume expansion under the effect of a pressure force F
dw = F dx = pSdx = pdV
dw = pda for a unit mass alpha = m^3/kg
p𝑑𝛼 = work done by unit mass when specific volume increases @ external pressure p
Why is 𝐶𝑝 > 𝐶𝑣?
𝐶𝑝: amount of heat released/absorbed by unit mass to raise temperature by 1 degree @ constant p
Pressure kept constant: volume allowed to expand as heat is added –> certain amount of the heat is given to do work against environment necessary for increasing the volume
𝐶𝑣: heat capacity @ constant volume
(Thermodynamics)
What is the first law
What is the first form of first law
What is second form of first law
dq = (cv+R)dT - 𝛼dp
dq = cvdT + pda
dq = cpdT - 𝛼dp
What is enthalpy?
Under constant pressure what is the change of a system’s enthalpy?
sum of internal energy and product of the pressure and volume
dh = dq + 𝛼dp = cpdT
(dq)p = dh
Heat given to a thermodynamic system @ constant p is all consumed in the system’s enthalpy
Write dq in terms of the geopotential
𝛼dp = -gdz = 𝑑𝜑
dq = CpdT + 𝑑𝜑
dq = dh + 𝑑𝜑
dq = d(h+ 𝜑) = d(CpT + 𝜑)
How is the static energy defined?
And how is its changed defined?
S = h + 𝜑: sum of enthalpy and geopotential of an airmass
dS = du + pd𝛼 + 𝑑𝜑 : change in static energy is the change in its internal energy (du) + change in work done (pd𝛼) @ constant p + change in gravitational potential energy (𝑑𝜑)
What implies conservation of static energy?
Conservation of S is valid for air-masses that
a) do not exchange heat with environment
b) move in hydrostatic balance atmosphere (𝛼dp = -gdz = 𝑑𝜑 )
c) no change in phase
Derive from the conservation of static energy to lapse rate
-dT/dz = g/cp = Γ𝑑
Write the equation and define the potential temperature.
- associated with unsaturated/dry adiabatic motion
A parcel’s potential temperature is the temperature that an unsaturated parcel would have if it were move adiabatically from present pressure to reference pressure in hydrostatic atm.
𝜃 =𝑇 (𝑝0/𝑝)^(𝑅𝑑/𝐶𝑝)
What does the conservation of potential temperature tells us?
Gives relation between T and p.
Can estimate a parcel’s new T @ new p giving the new density and compare it with the environment profile -> assess if it is more buoyant as it rises
Gives a way to assess the stability of an air-mass w.r.t. air above/below
Derive the Moist Static Energy
Under what conditions is Se conserved?
dq = Hr + Sh + LHR
LHR = -Ldw
dq = d(CpT + 𝜑)
-> d(CpT + 𝜑 + w) = Hr + Sh
with Se = CpT + 𝜑 + w = CpT + gz + w
Se: sum of (enthalpy) + (potential energy) + latent energy)
Conserved if Hr + Sh = 0 (not subject to radiative heating/cooling or heating/cooling due to conduction)
How is Se conserved?
What does dSe means and to what process is it related?
Balancing dw, dz and dT :continuously redistributed between the 3 terms
no exchange of energy with environment in hydrostatic atmosphere
-> moist/saturated adiabatic displacement
From first law of thermodynamic as for dry adiabatic ascent.
𝑑𝑞 = 𝑐𝑝𝑑𝑇−𝛼𝑑. Get 𝜃𝑒 equation
see the derivation
Sketch a T-z graph to differ static stability from static instability
Static Stability: Γ𝑒𝑛𝑣 < Γ𝑑
Static Instability: Γ𝑒𝑛𝑣 >Γ𝑑
What is the typical stability of the atmosphere?
Typically statically stable (Γ𝑒𝑛𝑣 < Γ𝑑) and conditionally unstable (Γ𝑒𝑛𝑣 >Γ𝑠).
Stable to an adiabatically ascending dry parcel but unstable to ascending parcel.
Dry parcel is negatively buoyant and moist parcel positively buoyant
What needs to happen for the LCL to be above the capping inversion?
The area of CIN is annihilated. This happens when the heating @ Earth’s surface is sufficient to generate strong thermals that erode the capping inversion
What other process can happen to “conquer” CIN region?
lifting from frontal or orography
What do we mean when we say that instability is released?
When the CAPE in the conditionally unstable area of the sounding above LFC is accessed by the rising parcel and free convection happens
Draw a sketch to infer potential instability.
What are the criterion of Potential instability?
- dTa’b’/dz > Γ𝑆
ie. 𝑑𝜃𝑒/dz < 0 (typically, 𝑑𝜃𝑒/dz is positive in the atmosphere)
- > above is the criteria to detect potential instability
Write down the governing equations of a lifted parcel
- Hydrostatic balance
- upward force: acceleration
- rewrite in terms of vertical displacement of parcel
- d^2zpc/dt^2 = g 𝑔𝜃′/𝜃_0
- …
- get N^2
dp/dz = −𝜌𝑒𝑛𝑣 𝑔
𝜌𝑝𝑐 𝑑𝑤/𝑑𝑡 +𝑑𝑝/𝑑𝑧 =−𝜌𝑝𝑐𝑔
𝜌𝑝𝑐 𝑑^2𝑧𝑝𝑐/𝑑𝑡^2 = (𝜌𝑒𝑛𝑣 −𝜌𝑝𝑐 )𝑔
…
-Brunt-Vaisala frequency
Take ln on 𝜃 formula and then take the derivative on both sides. Derive 1/𝜃 d𝜃/dz
1/𝜃 d𝜃/dz = 1/T(Γ𝑑 −Γ𝑒𝑛𝑣)
What is needed and what happens when N^2 > 0
Γ𝑒𝑛𝑣 < Γ𝑑 –> N^2 is positive: statically stable atmosphere-> Parcel accelerates towards altitude of origin and executes a set of stable vertical oscillations around equilibrium position
d^2zpc/dt^2 and zpc of opposite sign
What is needed and what happens when N^2<0
Γ𝑒𝑛𝑣 > Γ𝑑: statically unstable atmosphere-> unstable parcel->accelerates away from origin
d^2zpc/dt^2 and zpc of same sign
What is the solution for N^2>0?
z(𝑡) =𝐴cos(sqrt(𝑁^2)𝑡+𝜑)
frequency = N T = 2pi/N
What is the solution for N^2<0?
zpc = A(exp(-Nt) + exp(Nt))/2
-> after few steps: zpc = A/2 exp(Nt)
Exponential increase with time of the parcel’s distance from its original position z_0
Structure of the atmospheric boundary layer
Approximate the height of each sublayer
Where is wind shear the weakest?
molecular boundary layer: 1cm
surface layer: 50-150m
mixedlayer:1.5km
inversion layer: above 1.5km
Further up from the surface to h = 50-100m
What are Thermal rolls/plumes?
What do they modulate?
Thermally generated eddies.
They are able to develop @ 50-100m because wind shear is weak.
They tend to be larger and more variable in size than mechanical eddies
They modulate the structure and frequency of the mechanical turbulence eddies ->the mechanical eddies as we approach top of surface layer become intermittent (erupt in short bursts separated by longer quiet periods)
Sketch graphs differing night the ABL @ Nighttime and daytime
- nighttime: inversion: stable layer + residual mixed layer shorter
- daytime: more turbulence (thermal plumes more present), conditionally unstable layer @ the surface…
What does the mixed layer properties involve?
- upwards/downwards transfer of the properties by the buoyant thermals
- entrainment by the thermals of warmer, drier, less turbulent air from the level of the capping inversion downwards into the mixed layer,
What can happen in the afternoon hours after the peak of downward solar radiative flux?
As temperature reaches its max value, the capping inversion tends to acquire uniform T,w,C values due to the mixing such that the CIN region can be annihilated and air lifted up to their LCL.
Rederive the diurnal variation of the capping height (sample exercice)
See Derivation.
What is the steering level?
The level @ which the background speed u(z) is equal to the speed of cloud motion c
What is the relative flow for an observer that moves with the cloud/storm?
u(z)-c
background wind speed - c
What is the difference between lot of shear vs no shear conditions?
In general, the more the shear, the more long-lived the convective development/no shear: convective development are shallow and short lived
No shear conditions: upright updraft/downdraft –>downdrafts kills the heating @ surface (=reason for updraft) –> circulation does not persist
Mid-Latitude Squall Lines
Development 1
Describe Pre-storm conditions
- @ low levels
- @ upper levels
- Region A (identify)
- Squall lines overtakes air mass in sector ahead of the storm
- Squall line acts as a slowly moving obstacle to the westerly winds. Winds overtake the storm air-mass
- weak, low level pre-storm inversion: prevents convection from breaking out in the pre-storm environment
Mid-Latitude Squall Lines
Development 2
1.
2.
3.
4.
- Warm moist air inwards from the pre-storm sector
- Warm moist air is lifted upwards. Uplift provided by the advancing col,d, downdraft air.
- In upper levels (sector B): updraft deflects towards the East due to PGF within the storm-> spreads ahead of storm->anvil cloud (evaporating ice crystals)
- Dry environmental air drawn into the squall from the west becomes moist as precipitation from the updraft falls into it-> becomes cold due to evaporation and dense –> begins to sink creating the downdraft
Mid Latitude Squall-lines
Conditions and outbreak of instability?
Originally: convectively unstable state (𝑑𝜃𝑒/dz < 0)
As the squall line forms and enters its maintenance cycle, air from high 𝜃𝑒 is continuously moved upwards/air of lower 𝜃𝑒 moved down –> convectively unstable state is neutralised d𝜃𝑒/dz = 0
Sketch a cross section of mid-latitude squall line radar imagery
-continuous formation of new cells created by the lifting or air over the “cold gust front”
Multicell storms
What is the background wind configuration?
Typically wind veering with height:
VL: direction of low level inflow
Vm: environmental mid-level flow, typically coincides with direction of movement of individual cells
C: direction of storm motrion
Multicell storms
What is the most favourable synoptic situation?
What is the development of cells?
Low level southerly flow with high moisture content & upper level westerly flow of dry air –>U.S. @ mid-western states
Generation of new cells as moist inflow is lifted up over the cold downdraft air.
As new cell develops in the South, older cells become cut-off from moist inflow -> updrafts of the older cells weaken –> dissipation
What is a gust front?
Interface between lower density and higher density fluid, it known as “density” or “gravity” currents
Sketch a gust front structure
- Beneath rotor: reverse circulation
- small eddies turbulence
- nose structure
- bigger eddy: rotor
What is the Rosby number?
What is the momemtum equation?
Ro = V/fL
- Large scale phenomena: L large -> Ro small -> Du/Dt may be omitted in momemtum equation
- Small scale phenomena: L small -> Ro large –> fv may be omittef
Du/Dt - fv = -1/𝜌 dp/dx
Classify Rosby numbers for cumulonimbus, supercell storm, tornadoes
- Ro = 30 (fv omitted)
- Ro = 3 (non omitted)
- Ro = 300 (fv omitted)
From x-momemtum equation, derive the speed progation of a squall line
U = sqrt(2(∆𝜌𝑔ℎ)/𝜌0)
deeper and denser air mass behind the gust front leads to faster propagation
What is the horizontal divergence from the continuity equation?
Rewrite how vorticity grows with time
dw/dz = -(du/dx + dv/dy)
The vertical velocity distribution in a storm generates/enhances the low level convergence of flow into the storm and the upper level divergence
exponential rate is dw/dz
Supercell gust fronts:
What are the two branches that form in a supercell liftetime?
Forward flank gust front
Rear flank gust front
Write the key steps from x and y momemtum equation to complete vorticity equation
See derivation
divergence term + tilting term + friction term
What is needed for positive vorticity 𝜼 along the gust front in y direction
A storm that grows in a sheared background flow: du/dz != 0 and has a cross-section like in the classical squall line
𝜼 = du/dz - dw/dx
How does a localised strong updraft look like?
How does it contribute in the vorticity equation?
Sketch the two branches beside the updraft relating to that
du/dz != 0, dw/dy != 0
tilting term contributes to generation of ζ vorticity.
ccw to the left, cw to the right
From gradient wind balance to cyclostrophic balance
What does it mean for the two vortices in a supercell storm?
- centrifugal force & large rosby
- V^2/R = 1/𝜌 dp/dn = cyclostrophic balance
In cyclostrophic balance, centrifugal force Ce is directef away from center of curvature and the PGF is directed towards the center to balance it
–> Low pressure center is always the center of curvature
–> can be in clockwise/ccw (no constraints
—> the two vortices develop into low pressure centers
Tornadoes
From z and x momemtum equations
what does dw/dt describes?
Derive to get baroclinic generation of vorticity η
The vertical acceleration occuring as hydrostatic balanced pertubed due to the buoyant parcel (𝜌′ =𝜌𝑝𝑐 −𝜌𝑒𝑛𝑣)
Take a cross-section across the supercell gust’s front
What leads to vorticity η?
𝜕𝜃/𝜕𝑥 > 0 –> 𝑑η/𝑑𝑡<0
The presence of temperature cross frontal gradients leads to generation of vorticity η along the gust front
-Development of a horizontal North-South oriented component of vorticity in association with the cross-gust-frontal temperature gradient
–> further tightening of the gradient 𝜕𝜃/𝜕𝑥 leads to intensification of η
Sketch the stages of η.
-see the sketch
–> subsequent generation of more tornadoes. A family of tornadoes is generated along the gust frontal surface.
As the rear flank downdraft intensifies –> cold low level outflow;
- wraps cyclonically around the existing center of rotation (tornado 1)
- further south along the gust front, pushes against the oncoming moist inflow
As a result progressively;
- T1 center becomes cut-off fromt the moist inflow
- gust front futher south is intensifying thus creating new center of vorticity T2. As vortex T2 intensifies, vortex T1 dissipates
