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Synoptic Meteorology-II > Chapter 1: Analysis of Mid-lat syn systems using balance equations > Flashcards

Chapter 1: Analysis of Mid-lat syn systems using balance equations Flashcards

1
Q

the two derived scalar quantities of the horizontal wind

A

Stream function

velocity potential

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2
Q

stream function is represented by

A
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3
Q

velocity potential is represented by

A
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4
Q

The horizontal wind is then represented by these scalars as:

A
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5
Q

the term means

A
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6
Q

the term means

A
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7
Q

psi represents

A

Stream function

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8
Q

chi represents

A

velocity potential

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9
Q

the following equation is the

A

The horizontal wind

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10
Q

the rotational (non-divergent) part of horizontal wind is represented by the term

A
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11
Q

the divergent (irrational) part of horizontal wind is represented by the term

A
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12
Q

Stream function, velocity potential are the

A

two derived scalar quantities of the horizontal wind

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13
Q

The scalar equations for u and v can then be written in form of (stream function) and (velocity potential)as

A
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14
Q

If one of the scalars (stream function) or (velocity potential) is set equal to zero, then the wind that remains can be one of the following

A
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15
Q

Non-divergent or Rotational wind:

in non-divergent:

A
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16
Q

Non-divergent or Rotational wind:

in scalar notation:

A
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17
Q

irrotational or divergent wind:

the irrotational wind:

A
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18
Q

irrotational or divergent wind:

in scalar notation:

A
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19
Q

the following stands for

A

vorticity

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20
Q

vorticity in terms of stream function

For horizontal motion that is rotational (non-divergent), the velocity components are given by

A
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21
Q

Vorticity (ع ) in terms of streamfunction

substituting u and v for ع

A
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22
Q

the velocity field and the vorticity can both be represented in terms of

A

the variation of the single scalar field, (psi)

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23
Q

…………………………… and ……………………… can both be represented in terms of the variation of the single scalar field, (psi)

A

the velocity field

the vorticity

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24
Q

Obtain an expression for divergence of an irrotational wind

A
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25
Q

The barotropic vorticity is written as

A
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26
Q

the barotropic vorticity states that

A

the absolute vorticity is conserved following the hor. motion.

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27
Q

The barotropic vorticity equation can be written as

A

prognostic eqn. for vorticity

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28
Q

The barotropic vorticity equation can be written as a prognostic eqn. for vorticity in the form:

A
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29
Q

the following term represents

A

local tendency of relative vorticity

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30
Q

the following term represents

A

advection of absolute vorticity

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31
Q

prognostic equation for vorticity’s condition

A
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32
Q

prognostic equation for vorticity can be solved

A

numerically

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33
Q

prognostic equation for vorticity can be solved numerically to

A

predict the evolution of the streamfunction

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34
Q

prognostic equation for vorticity can be solved numerically to predict the evolution of the stream function, and hence

A

of the vorticity and wind fields.

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35
Q

The QG vorticity equation in pressure coordinates can be written as

A
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36
Q

the following equation is a

A

prognostic equation for the geostrophic relative vorticity.

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37
Q

The QG vorticity equation in pressure coordinates states that

A

the local change of geostrophic relative vorticity is a function of three terms

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38
Q

The QG vorticity equation in pressure coordinates states that the local change of geostrophic relative vorticity is a function of three terms

A
  • A) the geostrophic horizontal advection of geostrophic relative vorticity,
  • (B) the geostrophic meridional advection of planetary vorticity, and
  • (C) the vertical stretching of planetary vorticity .
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39
Q

terms A and B in the QG vorticity equation related to

A

horizontal advection of geostrophic relative vorticity and meridional advection of planetary vorticity.

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40
Q

A

A
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41
Q

B

A
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42
Q

C

A
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43
Q

D

A
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44
Q

E

A
45
Q

F

A
46
Q

G

A
47
Q

H

A
48
Q

I

A
49
Q

the following is shown by the …………………………….

A

500 hPa geopotential field

50
Q

_East of the trough (Region-II):_
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the ……………. of the ………………..

A

base of the trough

51
Q

East of the trough (Region-II):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the base of the trough where the ………… is ………………………….

A

vorticity is cyclonic عg​ >0

52
Q

East of the trough (Region-II):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the base of the trough where the vorticity is cyclonic to region of

A

anti cyclonic vorticity (عg​ < 0)

53
Q

East of the trough (Region-II):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the base of the rough where the vorticity is cycloncic to region of anticyclonic vorticity.
this implies ………………………………………

thus

A

an increase in geostrophic relative vorticity (PVA).

54
Q

East of the trough (region -II)
meridional Adv of planetary vorticity

the meridional flow is from ……………….. ( )

A

south to north

vg > 0

55
Q

East of the trough (region -II)
meridional Adv of planetary vorticity

the meridional flow is from south to north (vg>0)
…………………….. is ………………. ( )

A
56
Q

East of the trough (region -II)
meridional Adv of planetary vorticity

The meridional flow is from south to north (vg > 0).
􏰎 = 􏰃􏰊⁄􏰃􏰔 is positive (> 0).

thus

A
57
Q

West of the trough (Region-I):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the ……………. of the ………………..

A

Apex of the ridge

58
Q

West of the trough (Region-I):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the apex of the ridge where …………….. is ………………

A

the vorticity is anticyclonic (عg < 0)

59
Q

West of the trough (Region-I):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the apex of the ridge where the vorticity is anticyclonic (عg < 0) to region of …………………….. ( )

A

cyclonic vorticity (عg >0)

60
Q

West of the trough (Region-I):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the apex of the ridge where the vorticity is anticyclonic (عg < 0) to region of cyclonic vorticity (عg >0)
this implies ………………. in ………………………….. ( )

A

a decrease

geostrophic relative vorticity (NVA)

61
Q

West of the trough (Region-I):
Hor. Adv. Geostrophic Rel. Vorticity:

Large-scale flow is directed from the apex of the ridge where the vorticity is anticyclonic (عg < 0) to region of cyclonic vorticity (عg >0)
this implies a decrease in geostrophic relative vorticity (NVA)
Thus

A
62
Q

West of the trough (Region-I):
Meridional Adv. of planetary vorticity

The meridional flow is from ……………… to ………………… ( )

A

north to south (vg < 0)

63
Q

West of the trough (Region-I):
Meridional Adv. of planetary vorticity

b= ……………………… is …………………. ( )

thus

A
64
Q

Thus, the two advection terms are of …………………….sign in both the regions.

A

opposite

65
Q

Which of the two advection terms dominates the other?

For shortwave troughs, or those of

A

zonal (east-west) extent less than approximately 3,000 km

66
Q

Which of the two advection terms dominates the other?

For shortwave troughs, or those of zonal (east-west) extent less than approximately 3,000 km, ……………………………..dominates over ………………………………

A

the geostrophic horizontal advection of geostrophic relative vorticity

the geostrophic meridional advection of planetary vorticity.

67
Q

Which of the two advection terms dominates the other?

For shortwave troughs, or those of zonal (east-west) extent less than approximately 3,000 km, the geostrophic horizontal advection of geostrophic relative vorticity dominates over the geostrophic meridional advection of planetary vorticity. Thus, these features generally move ……………… with the ………………………..

A

eastward

westerly large-scale flow

68
Q

Which of the two advection terms dominates the other?

For longwave troughs, or those of

A

onal extent greater than approximately 10,000 km

69
Q

Which of the two advection terms dominates the other?

For longwave troughs, or those of zonal extent greater than approximately 10,000 km, …………………………………………dominates over …………………………………

A

the geostrophic meridional advection of planetary vorticity

the geostrophic horizontal advection of geostrophic relative vorticity.

70
Q

Which of the two advection terms dominates the other?

For longwave troughs, or those of zonal extent greater than approximately 10,000 km, the geostrophic meridional advection of planetary vorticity dominates over the geostrophic horizontal advection of geostrophic relative vorticity. Thus, to ………………………..

A

first approximation

71
Q

Which of the two advection terms dominates the other?

For longwave troughs, or those of zonal extent greater than approximately 10,000 km, the geostrophic meridional advection of planetary vorticity dominates over the geostrophic horizontal advection of geostrophic relative vorticity. Thus, to first approximation, these features move ……….. or …………………. against the ………………………

A

westward, or retrogress, against the westerly large-scale flow.

72
Q

Troughs of ……………………………extent (between …………………..) tend to move……………………….

A

intermediate zonal

3,000-10,000 km

eastward

73
Q

Troughs of intermediate zonal extent (between 3,000-10,000 km) tend to move eastward, but at a rate of speed ……………………………… than that of the …………………………………

A

slower to much slower

westerly large-scale flow.

74
Q

When there is rising motion:

A
75
Q

When there is rising motion:

A
76
Q

When there is rising motion:

A
77
Q

When there is rising motion:

A
78
Q

When there is rising motion:

A
79
Q

rising motion gives rise

A

to an increase in geostrophic relative vorticity

80
Q

By analogy, sinking motion implies a

A

decrease in geostrophic relative vorticity.

81
Q

divergence equation can be obtained as

A
82
Q

this equation is called

A

the balance equation

83
Q

the balance equation can be used to find

A
84
Q

the balance equation. It can be used to find 􏰂 if Φ is known, or Φ if 􏰂 is known.

 It is useful for example, if we wish to compute the

A

forcing functions in the height tendency and quasi-geostrophic w equations , in the absence of height (Φ) data

85
Q

It is useful for example, if we wish to compute the forcing functions in the height tendency and quasi-geostrophic 􏰗 equations , in the absence of height (Φ) data.

STEPS (step 1)

A
  1. The vorticity field can be computed from the wind field, if it is available.
86
Q

It is useful for example, if we wish to compute the forcing functions in the height tendency and quasi-geostrophic 􏰗 equations , in the absence of height (Φ) data.

STEPS (step 2)

A

The stream function 􏰂 can then be determined from vorticity using eq.7, given proper boundary conditions.

87
Q

It is useful for example, if we wish to compute the forcing functions in the height tendency and quasi-geostrophic 􏰗 equations , in the absence of height (Φ) data.

STEPS (step 3)

A

Then, the geopotential height field Φ can be computed from equation (11), again given proper boundary conditions.

88
Q

It is useful for example, if we wish to compute the forcing functions in the height tendency and quasi-geostrophic 􏰗 equations , in the absence of height (Φ) data.

STEP 4

A

Since, temperature is related to the vertical gradient of Φ (explained below) through the hydrostatic equation, we can compute temperature from wind field.

89
Q

The geopotential Φ at any point in the Earth’s atmosphere is defined as

A

he work that must be done against the Earth’s gravitational field to raise a mass of 1 kg from sea level to that point.

90
Q

The geopotential Φ at any point in the Earth’s atmosphere is defined as the work that must be done against the Earth’s gravitational field to raise a mass of 1 kg from sea level to that point.

 In other words, Φ is

A

the gravitational potential energy per unit mass.

91
Q

In other words, Φ is the gravitational potential energy per unit mass. The units of geopotential are

A

J kg−1 or m2 s−2

92
Q

The work (in joules) in raising

A

1 kg from z to z +dz is gdz

93
Q

The work (in joules) in rising 1 kg from z to z +dz is gdz. the geopotential Φ(z) at height z is thus given by

A
94
Q

The work (in joules) in rising 1 kg from z to z +dz is gdz. the geopotential Φ(z) at height z is thus given by

where the geopotential Φ 0 at sea level (z = 0) has been taken as

A

zero

95
Q

the thickness of the layer of air between two isobaric surfaces is proportional to the mean temperature of air in the layer.

A
96
Q

the equation states that

A

the thickness of the layer of air between two isobaric surfaces is proportional to the mean temperature of air in the layer.

97
Q

……………………………………… is conserved following the hor. motion.

A

the absolute vorticity

98
Q

……………………………………………. can be written as a prognostic eqn. for vorticity

A

The barotropic vorticity equation

99
Q

………………………………………….. can be solved numerically

A

prognostic equation for vorticity

100
Q

………………………………………………………………………………… predict the evolution of the stream function

A

prognostic equation for vorticity can be solved numerically to

101
Q

…………………………………………………………………… the local change of geostrophic relative vorticity is a function of three terms (A) the geostrophic horizontal advection of geostrophic relative vorticity, (B) the geostrophic meridional advection of planetary vorticity, and (C) the vertical stretching of planetary vorticity

A

the QG vorticity equation in pressure coordinates

102
Q

……………………………………………… related to horizontal advection of geostrophic relative vorticity and meridional advection of planetary vorticity

A

consider the terms-A and B

103
Q

east of the trough (region-II)

hor. Adv. Geostrophic Rel. Vorticity

A
104
Q

East of the trough (Region-II)

Meridional Adv. of Planetary Vorticity

A
105
Q

West of the trough (Region-I)

Hor. Adv. Geostrophic Rel. Vorticity

A
106
Q

West of the trough (Region-I)

Meridional Adv. of Planetary Vorticity

A
107
Q

the balance equation

A
108
Q

……………………………………………………………. the work that must be done against the Earth’s gravitational field to raise a mass of 1 kg from sea level to that point.

A

The geopotential Φ at any point in the Earth’s atmosphere

109
Q

J kg−1 or m2 s−2 are the units of

A

geopotential

Synoptic Meteorology-II (7 decks)

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