讲解EARTH-SUN留学生、辅导C/C++编程 UNIVERSITYGEOG 1200

SAINT MARY’S UNIVERSITYGEOG 1200

DEPARTMENT OF GEOGRAPHY

Module 1:  EARTH-SUN RADIATION SYSTEM AND SEASONS

Objectives

The objectives of this lab are:

1.To describe differences in seasonal variations at different latitudes on Earth.

2.To explain differences in seasonal variations.

Section 1:  Key Terms

The following key terms are relevant to this lab.

Equator

North Pole

South Pole

Arctic Circle

Antarctic Circle

Tropic of Cancer

Tropic of Capricorn

Subsolar point

Solar declination

Summer Solstice

(June 21)

Winter Solstice (Dec. 21)

Spring (or Vernal) Equinox (March 21)

Autumnal Equinox

(Sept. 22)

Axial tilt

Circle of illumination

Revolution

Rotation

Note:  Dates for solstices and equinoxes are for the Northern Hemisphere.  For the Southern Hemisphere the seasonal labels are reversed.

Before moving ahead, ensure your understanding of these terms. Most found in Chapter of your textbook.

Figure 1 shows the names and positions of the seven important lines of latitude on Earth:

Figure 1

Section 2:  Describing Seasonal Variations on Earth

For this section the amount of insolation (incoming solar radiation), as measured at the top of the atmosphere (TOA), will be used to represent the prime control of seasonal variations on Earth.  Differences in seasonal variations at different latitudes on Earth will be described by plotting graphs of insolation over time, with the values to plot to be obtained by reading directly off Figure 2 (next page).

Figure 2(from Christopherson and Byrne, 2009, Figure 2.10)

Values for the North Pole

(W m-2):

J:   0

F:   0

M:   0

A:240

M:450

J:530

J:480

A:290

S: 40

O:   0

N:   0

D:   0

1.At each of the latitudes a) – h) below, use Figure 2 above to obtain values of daily insolation (units: Watts per square meter, or W m-2) for each month of the year.  Read off the values at the middle of each month’s column, and estimate intermediate values between the lines.  For example, the value for January at 40°N would be ~180 W m-2. (If you read off the value for January at 40°N, do you get this answer?  Try it now and make sure.)

Plot the values on the graphs provided (on a separate sheet) and connect the points with smoothed lines.

To help you get started, values for the North Pole are given (above right) and the points have been plotted on the corresponding graph.  Go through the North Pole values to confirm you understand how to read values from the graph.  Note that the June value must be greater than 500 W m-2 but less than 550 because there is no 550 line shown, so an intermediate value of 530 W m-2 was estimated.

a)North Pole

b)South Pole

c)Arctic Circle

d)Antarctic Circle

e)45°N, Halifax’s latitude

f)Tropic of Cancer

g)Equator

h)Tropic of Capricorn

2.Recall that the amount of insolation is being used to represent seasonal variations on Earth, because in simple terms more insolation results in warmer temperatures.  Use the completed graphs from Question 1 to summarize seasonal variations by answering these questions:

a)Describe how seasonal extremes of insolation (the difference between maximum and minimum values) vary with latitude.

b)How do the patterns of seasonal variation at latitudes in the northern hemisphere (e.g., the Tropic of Cancer) compare with the patterns at the corresponding latitudes in the southern hemisphere (e.g., the Tropic of Capricorn)?

Section 3:  Explaining Seasonal Variations

The two key controls on the amount of insolation received at any latitude during the year are 1) the angle of incidence, which determines over how much surface area incoming beams of insolation are spread, and 2) daylength.

Subsolar Point and Solar Declination

Due to the geometry of the Earth-Sun system, at any time of the year the Sun appears to be directly overhead one point on Earth.  That point is called the subsolar point.  Beams of insolation arrive perpendicular to the surface only at the latitude of the subsolar point.  At all other latitudes, the beams of insolation arrive at an oblique angle.  During the year, the subsolar point migrates in a regular and predictable pattern to latitudes north and south of the Equator.  The latitude of the subsolar point at a given time is called the solar declination.  Solar declination (which has units of degrees) is shown with a dashed line on Figure 2.

[Note that for Questions 3 and 4, all of the answers are contained within the list a) – h) in Question 1.]

3.What is the highest latitude in the northern hemisphere to which the subsolar point migrates annually?  And the highest latitude in the southern hemisphere?

4.At the Spring (Vernal) Equinox (labeled on Figure 2), what is the latitude of the subsolar point?  And at the Autumnal Equinox, the Summer Solstice, and the Winter Solstice?

Intensity of Insolation

Because the Earth’s surface is curved, the intensity of insolation is not equal at all locations (recall Figure 2.9 in the textbook).  Only at the subsolar point is the intensity at its maximum.  At all other locations, the more obliquely the surface is oriented to the insolation, the lower the intensity of insolation.  Using some simple trigonometry (Equation 1), the intensity of insolation received at different places can be calculated.  The answer from Equation 1 will be a percentage of the intensity of insolation re-ceived on a flat surface that is perpendicular to the insolation.  Answers will be no smaller than 0 and no larger than 100.

Equation 1:X = sin(90 – L) x 100where:X = intensity of insolation (percent)

sin = the sine function

L = latitude (°), a positive value whether N or S

For Equation 1, first find the answer for (90 – L), then press the sin button, and then multiply that result x 100.

The sin function can be found on most calculators, but the calculator must be in degrees mode―not radians mode―for Equation 1 to give correct results.  Check your calculator now to see if you get these correct answers:  sin(0) = 0, sin(45) = 0.71, and sin(90) = 1.

5.Complete Table 1.  This table corresponds to the Spring and Autumn Equinoxes, when the solar declination is 0°.

After completing the column for the northern latitudes, ask yourself if there is a shortcut for completing the column for the southern latitudes without doing any more calculations.  (There is!)

The purpose of completing Table 1 is to show how the intensity of insolation varies with latitude.

Table 1:  Proportions of Insolation at the Equinoxes

Latitude (°N)X = sin (90 – L)

x 100Latitude (°S)X = sin (90 – L)

x 100Latitude (°)X = sin (90 – L)

x 100

901566.5°N

75263023.5°N

6045         0°

456023.5°S

307566.5°S

1590

Note that the intensity of insolation is calculated here for the equinox dates when the solar declination is 0°.  At other times of the year, the latitude of maximum insolation intensity corresponds to the solar declination, and the intensity of insolation at other latitudes corresponds proportionally.

Circles of Illumination

At any one time, only (and exactly) one half of the Earth is illuminated by the Sun; that is, the circle of illumination.  This is why we have periods of day and night, as the Earth rotates on its axis daily through the circle of illumination.  Because of the axial tilt (23?° from vertical), the range of latitudes receiving solar illumination varies during Earth’s annual revolution around the Sun.

6.Figure 3 shows the Earth in two dimensions at the Summer Solstice, with the Northern Hemisphere tilted towards the Sun.  On the diagram, lightly shade the half of the Earth that does not receive insolation.  To determine the correct half, draw a straight line between the highest point on the circle perimeter (the highest point is below the vertical dashed line at the top of the circle, not at the North Pole, because the Earth is tilted) and the lowest point on the circle perimeter.  Then shade the side of Earth facing away from the insolation.  Label the unshaded portion of the diagram DAY, and the shaded portion NIGHT.

Figure 3

(Summer Solstice)

7.Repeat the circle of illumination exercise for the Autumn Equinox (Figure 4), Winter Solstice (Figure 5), and Spring Equinox (Figure 6).

Figure 4

(Autumnal Equinox)

Note that the Earth is still tilted on its axis of rotation at an angle of 23.5°.  However, to draw the diagrams for the equinoxes on a flat sheet of paper, the perspective (location from which Earth is being viewed) must be changed in comparison to the solstices.

Figure 5

(Winter Solstice)

Figure 6

(Spring Equinox)

8.As shown in Figure 2, there are some latitudes that do not receive any insolation during certain parts of the year.  In Figures 3-6, the range of latitudes that do receive insolation falls within the unshaded (DAY) part of the diagram.  Consult Figures 3-6 to fill in Table 2 by listing the most northerly and southerly latitudes that receive insolation at the solstices and equinoxes.  Give latitude values in degrees (°, including the hemisphere, N or S).

Table 2:  Range of Latitudes Receiving Insolation

DateMost Northerly LatitudeMost Southerly Latitude

Summer Solstice

Autumn Equinox

Winter Solstice

Spring Equinox

Daylength

In addition to the angular relationship between Earth surfaces and insolation, daylength is the other principal factor that controls seasonal variations.  Figures 3-6 can be used to estimate daylengths at different latitudes.

9.Estimate daylengths for the Summer Solstice by using Figure 3 and these steps:

a)Using a ruler with mm markings, measure the full length of each line listed in Table 3, in mm (except the North and South Poles which will be addressed in part e below).  Be precise with your measurements.  This length is A.

b)Measure the length of part of the line that lies within the circle of illumination (the part labeled DAY).  This length is B.

c)Calculate the proportion of the lengths of the two lines (shorter [B] divided by longer [A]), and express as a decimal value.  This result is C.  In equation form:  C = B/A.

d)Multiply C x 24 (hours).  The answer is the value D.

e)For the North and South Poles, which are actually points not lines, it is not possible to measure line length.  However, you can examine Figure 3 and the other answers in the table below to figure out what the daylengths are at the poles.

Table 3:  Daylengths at the Summer Solstice

A

Length of line

(mm)B

Length of line within circle of illumination

(mm)C

C = B / A

(no units)D

D = C x 24

(hours)

North Pole――――――――――――

Arctic Circle

Tropic of Cancer

Equator6331.50.512

Tropic of Capricorn

Antarctic Circle

South Pole――――――――――――

If you have done everything correctly, you should find that for the Equator, line B is half the length of line A and the final answer is 12 hours (A = 63 mm; B = 31.5 mm; C = B / A = 0.5; and D = 0.5 x 24 = 12 hours).

10.Repeat Question 9 for the Autumnal Equinox, using Figure 4 and Table 4.

Table 4:  Daylengths at the Autumnal Equinox

A

Length of line

(mm)B

Length of line within circle of illumination

(mm)C

C = B / A

(no units)D

D = C x 24

(hours)

North Pole――――――――――――

Arctic Circle

Tropic of Cancer

Equator6331.50.512

Tropic of Capricorn

Antarctic Circle

South Pole――――――――――――

Graphs for Question 1

Write the name of the line of latitude on

the blank line above each graph.

The order of the graphs a) - h) has been chosen to enable summary and comparison in Question 2.