Chapter 2- Application of Theories

Question 1

Horizontal divergence can be expressed as:

Answer 1

Question 2

to compute horizontal divergence at (x0, y0) evaluate the derivative using the

Answer 2

central finite differences:

Question 3

Example-1: Calculate the horizontal divergence for the data given in Figure. Given:
∆x=∆y=50km

Answer 3

Question 4

Example-1: Calculate the horizontal divergence for the data given in Figure. Given:
∆x=∆y=50km

Example-2: Repeat the above calculations with small changes (errors) in winds.

Answer 4

Question 5

Divergence estimates using kinematic method areDivergence estimates using kinematic method are

Answer 5

very sensitive to small errors

Question 6

Vorticity is a

Answer 6

microscopic measure of rotation at any point in a fluid

Question 7

Vorticity is a microscopic measure of rotation at any point in a fluid. It may be considered to be

Answer 7

the local rotation of a fluid

Question 8

Vorticity is a microscopic measure of rotation at any point in a fluid. It may be considered to be the local rotation of a fluid. Vorticity is a

Answer 8

vector field, which is defined as the curl of velocity

w=-/x V

Question 9

where v =

Answer 9

(iu+ jv+ kw) is a 3d velocity field

Question 10

-/x V =

Answer 10

Question 11

w=

Answer 11

Question 12

Because horizontal winds are usually larger than

Answer 12

Question 13

Relative vorticity has units of

Answer 13

of s^-1 and vorticity is defined as positive in the counterclockwise direction

Question 14

The Earth is rotating about its axis at rate

Answer 14

Ω (s^-1).

Question 15

Since winds are defined

Answer 15

relative to the Earth’s surface, we express rotation about the Earth’s axis, in terms of those same coordinates, as:

Question 16

The vertical component of Earth vorticity is called the

Answer 16

coriolis parameter, f

Question 17

Absolute vorticity is

Answer 17

the vector combination of relative vorticity (ζ) and Earth vorticity (f):

ζ_a = ζ +f

Question 18

absolute vorticity of a fluid parcel is equal to

Answer 18

the sum of the (vertical) rotation of the fluid parcel relative to the earth (relative vorticity) and the vertical component of the rotation of the earth at that position.

Question 19

The gradient of a variable is

Answer 19

just the change in that variable as a function of distance

Question 20

The gradient of a variable is just the change in that variable as a function of distance. For instance,

Answer 20

the temperature gradient is just the temperature change divided by the distance over which it is changing: /_\T//_\ distance

Question 21

The gradient is a

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vector and has a direction as well as magnitude.

Question 22

Mathematically, the gradient vector is defined by

Answer 22

Question 23

for example

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Question 24

The gradient of a scalar is

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a vector whose direction is always normal to the isolines (contours) and pointing in the direction of increase

Question 25

We can define the normal vector, which is just the

Answer 25

unit vector in the direction of the increasing temperature. We will call this normal vector n

Question 26

The magnitude and direction of a 2D gradient vector for T can be determined by:

Answer 26

Question 27

............................................ then the gradient is zero

Answer 27

If the scalar is uniform in space

Question 28

Advection

Answer 28

The transport of an atmospheric property (e.g., temperature, humidity), which is variable in space, by wind is called ‘advection’.

Question 29

The transport of an atmospheric property (e.g., temperature, humidity), which is variable in space, by wind is called ‘advection’.  This transport process plays a very important part in

Answer 29

local changes of temperature and moisture, among other atmospheric properties

Question 30

Mathematically, advection is expressed as:

Answer 30

Question 31

Theoretically advection can be viewed as

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three dimensional

Question 32

Theoretically advection can be viewed as three dimensional. In operational meteorology the term advection is typically limited to

Answer 32

transport by the horizontal flow while vertical transport is called convection

Question 33

In Cartesian coordinates, horizontal advection is given by

Answer 33

Question 34

Example: The wind is from 330° at 25 m/s. The isotherms are oriented north-south as shown in the picture below, and are 100 km apart.

Answer 34

Question 35

For a thin layer, the geostrophic temperature advection is given by:

Answer 35

Question 36

Troughs

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Troughs which are the regions of low pressure are produced by large volumes of cool or cold air while large volumes of warm or hot air produce ridges, which are the regions of high pressure.

Question 37

The winds on upper level charts blow

Answer 37

parallel to the contour lines generally from west to east

Question 38

The winds on upper level charts blow parallel to the contour lines generally from west to east.  This is a little difference from

Answer 38

surface winds which blow across the isobars toward low pressure

Question 39

Temperature drops as you move from

Answer 39

west to east and from south to north

Question 40

For example, the highest point on the 850 mb surface (.............. m or so) is found above

Answer 40

1800 the hot air near the SW corner

Question 41

For example, the highest point on the 850 mb surface (1800 m or so) is found above the hot air near the SW corner. The lowest point

Answer 41

(a little less than 1000 m) is found in the coldest air near the NE corner of the picture.

Question 42

The above distribution of height contours can be explained by noting that:

Answer 42

(1) pressure decreases with increasing altitude, and (2) pressure decreases more rapidly in cold high-density air than it does in warm low-density air.

Question 43

The counterclockwise winds spinning around the LOW move

Answer 43

warm air northward and cold air southward

Question 44

The counterclockwise winds spinning around the LOW move warm air northward and cold air southward.  Warm air is found

Answer 44

west of the HIGH and to the east of the LOW. This is where the two ridges on the upper level chart are also found.

Question 45

Warm air is found west of the HIGH and to the east of the LOW. This is where the two ridges on the upper level chart are also found.  Similarly, cold air is found

Answer 45

below an upper level trough.

Question 46

The yellow Ox marked on the upper level chart directly above the surface L is

Answer 46

a good location for a surface LOW to form, develop, and strengthen (strengthening means the pressure in the surface low will get even lower; this is also called "deepening").

Question 47

The reason for this is that the yellow Ox is a location where there is often

Answer 47

upper level divergence

Question 48

Similarly, the pink Ox is where we often find

Answer 48

upper level convergence

Question 49

Similarly, the pink Ox is where we often find upper level convergence. this causes

Answer 49

the pressure in the center of the surface high to get even higher.

Question 50

The area around a jet streak can be divided into four quadrant relative to the

Answer 50

Question 51

it can be shown dynamically that for ............................................ are areas of divergence

Answer 51

straight flow in the upper troposphere, the left front and right rear quadrants (C and D)

Question 52

are areas of divergence while ................................... are areas of convergence

Answer 52

right front and left rear quadrants (D and A)

Question 53

Areas of divergence in the upper troposphere are typically associated with

Answer 53

upward synoptic scale vertical motion

Question 54

area of upper level convergence are typically associated with

Answer 54

downward synoptic scale vertical motion

Question 55

Where upper level convergence occurs air

Answer 55

sinks to promote high pressure at the surface.

Question 56

Where upper-level divergence occurs air

Answer 56

is pulled up from the surface to help create low pressure near the ground.

Question 57

Wave cyclones dissolve when

Answer 57

they no longer have the upper level divergence to maintain them

Question 58

The combination of rising and sinking air creates

Answer 58

direct and indirect circulations in the rear (AB) and front (CD) regions across the jet stream, respectively

Question 59

Because cyclones need ..................... to maintain themselves

Answer 59

divergence in the upper troposphere

Question 60

Because cyclones need divergence in the upper troposphere to maintain themselves, the divergence/convergence regions around the jet streak have

Answer 60

direct affect on the surface lows and highs

Question 61

The vorticity pattern associated with a (straight flowing) jet streak show

Answer 61

a strong positive relative vorticity maximum to the left of the jet maximum (plus) and a weaker negative relative vorticity minimum to the right ( minus).

Question 62

The location of the vorticity maximum and minimum indicate that there should be

Answer 62

positive vorticity advection (PVA) in the left exit and right entrance regions.

Question 63

Quasi-geostrophic theory indicated the PVA is favorable for

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cyclone development.

Question 64

Hence, the typical location of a intensifying surface low center is in

Answer 64

the left exit region

Question 65

while ............................... are common in the right entrance region.

Answer 65

newly formed frontal waves

Question 66

A jet streak moves

Answer 66

within the trough-ridge pattern at the same time it influences the amplification or de-amplification of the trough-ridge pattern.

Question 67

Below is an example of a jet streak de-amplifying (weakening) a trough

Answer 67

A strong jet streak on the right side of a trough will cause that trough to de-amplify (lift)

Question 68

amplifying (image)

Answer 68

If a strong jet streak is on the left side of a trough, the trough will amplify (dig)