Q vector Flashcards
What will QG Theory do for us?
–It reveals how …………………………………….. and ………………………………… constrain and simplify atmospheric motions, but in a realistic manner
hydrostatic balance and geostrophic balance
What will QG Theory do for us?
It provides a simple framework within which we can understand and diagnose the ……………………………………
evolution of three-dimensional synoptic-scale weather systems
What will QG Theory do for us?
It predicts the evolution of synoptic-scale systems by
diagnosing changes in the local geopotential height field from the observed distributions of vorticity advection and temperature advection.
What will QG Theory do for us?
It estimates synoptic-scale ………………………………………………………….
vertical motions from the observed distribution of vorticity and temperature advection.
What will QG Theory do for us?
It helps us to understand how the ………………………………………………….and the ………………………………………………………………….interact to create ………………………………..that result in realistic synoptic scale weather patterns
mass fields (via horizontal temperature advection)
momentum fields (via horizontal vorticity advection)
vertical circulations
What will QG Theory do for us?
It offers physical insight into the forcing of ………………………………………………. and ……………………………………………………….associated with mid-latitude cyclones
vertical motion and the cloud/precipitation patterns
Rotational momentum:
Rotation around an axis (less effort)
Momentum equations and linear momentum
momentum equations: du/dt, dv/dt. dw/dt
linear momentum: ΣF = dp/dt = m* d/dt = ma
From our mathematical derivation of QG theory, QG theory has the following assumptions
- Geostrophic balance (i.e. we neglect all local changes in the ageostrophic wind) >> No difference between geostrophic & wind (actual)
- Hydrostatic balance >> No vertical motion (parcel of air at rest)
- Horizontal advection by the geostrophic winds only (i.e. we neglect the advection of the ageostrophic momentum by the geostrophic wind and the vertical advection of momentum)
- No friction or orographic effects
- No diabatic heating / cooling
- No spatial or temporal changes in static stability >> consider midlatitude weather is stable
meaning of adiabatic
No change of heat between air parcel and surrounding air “when air parcel is rising it will cool due to expansion/increase of volume”
(Source of heat must exist)
QG Height Tendency Equation
The following equation represents
QG height tendency equation
Term A corresponds to
local horizontal advection of geostrophic vorticity
Term B correspond to
change in temperature advection with height
QG omega equation
The following equation represents
QG omega equation
Term A correspond to
change in vorticity advection with height
Term B correspond to
local maximum in temperature advection
If large changes in the vorticity advection with height are observed, then you should expect…………………………………….
large vertical motions
The stronger the temperature advection, the stronger the ……………………….
vertical motion
If WAA is observed at several consecutive pressure levels, expect a…………………………………………………motion
deep layer of rising
The QG omega equation is proportional to
vorticity advection & advection of maximum temperature (local)
vorticity advection & advection of maximum temperature (local) usually work
opposite to each other
if term A in the QG omega equation is +ve and term B is -ve the result is
rising air
you can find which is dominant cold advection or cyclonic by
Q vectors because they are working against each other
“rate of change of potential temperature in geostrophic balance”
If term A and B are working together
PVA and WAA are on top of each other
The Q-vector is defined as
the change of the potential temperature gradient vector of a parcel following the geostrophic motion.
Q-vector equation
the following equation is for
Q-vectors
What does each term in the Q-vector equation mean?
dg /dt : rate of change of potential temperature gradient in geostrophic motion
gradient of potential temperature
0: potential temperature
for the equation both terms on the LHS are the
both terms are the second derivative of omega
the first term is horizontally the second term is vertically (the divergence of Q)
in the equation w is
w is proportional to -2 grad Q
w depends on divergence and convergence of Q
when Q is positive and when its negative……
+ve > sinking air > divergence
-ve> rising air > convergence
when grad Q is positive
Divergence on the ground
the purpose of Q-vectors
to solve conflict between omega equation
Q vectors are useful for the following reason
Eliminates competition between terms in the QG 𝜔 equation
The weaknesses of Q-vectors are as follows
It contains all of the limiting assumptions of QG theory (i.e. neglect of diabatic heating/cooling, variations in static stability, etc.)
𝑄 is typically evaluated within ………………………..because this brackets the level of non-divergence ………………………..
400-700 mb
(~550 mb )
in the upper trough the gradient is from
high to low
in the upper ridge …..
warming in the upper air > stable air > ridge
A and B are areas of
A: cooling
B: Warming
