chapter 3

Question 1

The large scale flow in the atmosphere is nearly

Answer 1

geostrophic

Question 2

the large scale flow in the atmosphere is nearly geostrophic

the ………………. and …………………. are …………………..

Answer 2

wind and mass fields are virtually in balance

Question 3

the large scale flow in the atmosphere is nearly geostrophic

the wind and mass fields are virtually in balance

In such an atmosphere, the isobars are

Answer 3

straight and parallel and the density is a function of pressure alone (barotropic)

Question 4

If geostrophy is assumed, there is

Answer 4

no vertical motion and there is no change in the spatial patterns of the height of isobaric surfaces.

Question 5

If geostrophy is assumed, there is no vertical motion and there is no change in the spatial patterns of the height of isobaric surfaces.

Hence, geostrophy cannot be used to

Answer 5

understand the development of weather systems

Question 6

Hence, geostrophy cannot be used to understand the development of weather systems, which requires

Answer 6

time changes in the spatial patterns of the height of isobaric surfaces

Question 7

………………………………………. can be used to understand the development of weather systems in ……………………………….

Answer 7

Quasi-geostrophic theory

a baroclinic atmosphere

Question 8

In a baroclinic atmosphere, the

Answer 8

surfaces of constant pressure and density intersect each other forming solenoids that leads to direct circulation and vertical motion.

Question 9

In a baroclinic atmosphere, the surfaces of constant pressure and density intersect each other forming solenoids that leads to direct circulation and vertical motion.

In such an atmosphere,

Answer 9

the spatial pattern of height field changes with time.

Question 10

Hence, the slight deviation of geostrophy (quasi-geostrophic) is of great importance to

Answer 10

understanding of atmospheric flow and weather systems

Question 11

The Quasi-Geostrophic (QG) Momentum Equations

For this analysis, it is convenient to use the

Answer 11

isobaric coordinate system

Question 12

For this analysis, it is convenient to use the isobaric coordinate system because

Answer 12

• meteorological measurements are generally referred to constant pressure surfaces and
• the dynamical equations are somewhat simpler in isobaric coordinates than in height coordinates.

Question 13

The scalar and vector horizontal momentum equations in (x,y,z) coordinate system can be written as:

Answer 13

Question 14

The scalar and vector horizontal momentum equations in (x,y,z) coordinate system can be written as:

where

Answer 14

Question 15

Equation (1) can be transferred to

Answer 15

x,y,p coordinates

Question 16

Equation (1) can be transferred to (x,y,p) coordinate system as follows:

Answer 16

Question 17

LHS of Eq.(2) can be expanded as follows:

Answer 17

Question 18

The QG Momentum Equations

Consider the momentum equation in vector form (Eq.3)

Answer 18

Question 19

The QG Momentum Equations

after considering the momentum equation in vector form

now you should

Answer 19

Split the horizontal wind into geostrophic and ageostrophic components

Question 20

The QG Momentum Equations

after concidering the momentum equation in vector form

plitting the horizontal wind into geostrophic and ageostrophic components:

Answer 20

Question 21

The QG Momentum Equations

• Consider the momentum equation in vector form (Eq.3):
• Splitting the horizontal wind into geostrophic and ageostrophic components:

the next step is

Answer 21

Substituting (4) in the coriolis term in (3)

Question 22

The QG Momentum Equations

• Consider the momentum equation in vector form (Eq.3):
• Splitting the horizontal wind into geostrophic and ageostrophic components:

Substituting (4) in the coriolis term in (3):

Answer 22

Question 23

Midlatitude ß-plane approximation

Answer 23

To retain the dynamical effect of the variation of the Coriolis parameter with latitude, f can be approximated by expanding its latitudinal dependence in a Taylor series about a reference latitude O| o

Question 24

The QG Momentum Equations

• Consider the momentum equation in vector form (Eq.3):
• Splitting the horizontal wind into geostrophic and ageostrophic components:
• Substituting (4) in the coriolis term in (3):

The next step is

Answer 24

Now, we replace the Coriolis parameter by f= f₀ +ßy , so that the momentum equations (Eq.5) become:

Question 25

The QG Momentum Equations * Consider the momentum equation in vector form (Eq.3): * Splitting the horizontal wind into geostrophic and ageostrophic components: * Substituting (4) in the coriolis term in (3): * Now, we replace the Coriolis parameter by f = f₀ + ßy , so that the momentum equations (Eq.5) become: the next step is

Answer 25

Expanding the RHS of Eq.(6)

Question 26

The QG Momentum Equations * Consider the momentum equation in vector form (Eq.3): * Splitting the horizontal wind into geostrophic and ageostrophic components: * Substituting (4) in the coriolis term in (3): * Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become: * Expanding the RHS of Eq.(6) the next step is

Answer 26

The last term in (7) is very small, and can be ignored, so we now have:

Question 27

The QG Momentum Equations * Consider the momentum equation in vector form (Eq.3): * Splitting the horizontal wind into geostrophic and ageostrophic components: * Substituting (4) in the coriolis term in (3): * Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become: * Expanding the RHS of Eq.(6) * The last term in (7) is very small, and can be ignored, so we now have but the next step is

Answer 27

By the definition of the geostrophic wind

Question 28

The QG Momentum Equations * Consider the momentum equation in vector form (Eq.3): * Splitting the horizontal wind into geostrophic and ageostrophic components: * Substituting (4) in the coriolis term in (3): * Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become: * Expanding the RHS of Eq.(6) * The last term in (7) is very small, and can be ignored, so we now have * By the definition of the geostrophic wind the next step is

Answer 28

Substituting (9) in (8), the first two terms on the right-hand side of (8) cancel, resulting in

Question 29

The approximate QG horizontal momentum equation thus has the form:

Answer 29

Question 30

The rate of change of momentum following the total motion is approximately equal to

Answer 30

the rate of change of the geostrophic momentum following the geostrophic wind

Question 31

The rate of change of momentum following the total motion is approximately equal to the rate of change of the geostrophic momentum following the geostrophic wind:

Answer 31

Question 32

................................................................................. is approximately equal to the rate of change of the geostrophic momentum following the geostrophic wind

Answer 32

The rate of change of momentum following the total motion

Question 33

As discussed earlier, though the atmosphere is close to being in geostrophic balance, the unbalanced component of the wind (the ageostrophic wind) is very important for

Answer 33

the dynamics of synoptic disturbances

Question 34

Now, we derive an equation for the ageostrophic wind. For this, consider the

Answer 34

simplified horizontal momentum equations

Question 35

Now, we derive an equation for the ageostrophic wind. For this, consider the simplified horizontal momentum equations:

Answer 35

Question 36

Thus, the ageostrophic wind, which is the

Answer 36

deviation of the real wind from the geostrophic wind,

Question 37

Thus, the ageostrophic wind, which is the deviation of the real wind from the geostrophic wind, is mathematically expressed as:

Answer 37

Question 38

The ageostrophic wind is a measure of the

Answer 38

horizontal acceleration

Question 39

As shown in figure, the ageostrophic wind points to the

Answer 39

left of the geostrophic acceleration (in NHS)

Question 40

the ageostrophic wind figure

Answer 40

Question 41

the bold line is representing

Answer 41

the height contour

Question 42

the thin line represents

Answer 42

isotachs

Question 43

the wind barbs represent

Answer 43

the geostrophic wind

Question 44

the figure represents

Answer 44

a typical jet streak

Question 45

ageostrophic wind is to the left of the geostrophic acceleration, the ageostrophic wind will be oriented as

Answer 45

Question 46

the ageostrophic wind is divergent in

Answer 46

the right entrance and left-exit regions of the jet streak

Question 47

the ageostrophic wind is convergent in

Answer 47

the other regions

Question 48

the ageostrophic wind is divergent in the right entrance and left-exit regions of the jet streak, and convergent in the other regions This leads to

Answer 48

upward motion in the right-entrance and left-exit regions and downward motion in the other two regions of the jet streak.

Question 49

The Isallobaric Wind – Vector Form step 1

Answer 49

Expanding the total derivative on the RHS of Eq.12:

Question 50

Thus the forcing of the ageostrophic wind can be divided conveniently into the two parts, the

Answer 50

isallobaric wind and the advective wind.

Question 51

the isallobaric wind is writen as

Answer 51

Question 52

The scalar components of the isallobaric wind can be obtained as:

Answer 52

Question 53

from the equation of isallobaric wind is determined by the

Answer 53

gradient of the isolines of do p/do t

Question 54

what are the isolines

Answer 54

These are the lines connecting the equal amounts of surface pressure change (isallobars)

Question 55

These are the lines connecting the equal amounts of surface pressure change (isallobars). In figure, we have:

Answer 55

Question 56

The direction of the isallobaric wind is

Answer 56

perpendicular to the isallobars

Question 57

The direction of the isallobaric wind is perpendicular to the isallobars, always pointing

Answer 57

towards the falling pressure

Question 58

The direction of the isallobaric wind is perpendicular to the isallobars, always pointing towards the falling pressure (i.e., pointing to

Answer 58

the minimum value where the strongest pressure decrease) in surface pressure is located.

Question 59

the second term on the RHS of is the

Answer 59

advective term

Question 60

The scalar components of the advective wind can be written as:

Answer 60

Question 61

The advective wind arises when

Answer 61

the geostrophic wind is not uniform, as in diffluent or confluent flow pattern.

Question 62

In diffluent flow pattern (fig), the geostrophic wind

Answer 62

decreases in positive x-direction

Question 63

In diffluent flow pattern (fig), the geostrophic wind decreases in positive x-direction due to

Answer 63

the larger spacing between the isobars indicating smaller pressure gradient.

Question 64

In the analogous case of a confluent flow the wind speed will

Answer 64

increase

Question 65

The divergence of the isallobaric wind is:

Answer 65

Question 66

Divergence of the isallobaric wind When heights are falling: the isallobaric wind is ..........................

Answer 66

convergent

Question 67

Divergence of the isallobaric wind When heights are rising: the isallobaric wind is ............................

Answer 67

divergent

Question 68

The divergence of the advective wind can be obtained as: where ع_g is the ................................ and V_g.\-/ع_g is the ..................................

Answer 68

where ع_g is the geostrophic vorticity and V_g.\-/ع_g is the vorticity advection

Question 69

When there is Positive Vorticity Advection (PVA): the advective wind is ..................

Answer 69

divergent

Question 70

When there is Negative Vorticity Advection (NVA): the advective wind is ..........................

Answer 70

convergent