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Course Syllabus can be found at: http://www.wx4sno.com/portfolio/BSU/Fall_2011/

This lecture will be posted AFTER class at:http://www.wx4sno.com/portfolio/BSU/Fall_2011/Lectures/

Lesson 11Solar Angle

Hess, McKnight’s Physical Geography, 10 ed. 17-20 pp.

Sun DeclinationRecall from last week, the vertical rays

(direct rays) are those from the sun that strike the Earth at a 90° angle.

The location of these vertical rays changes throughout the year◦ Located at the Tropic of Cancer during the

summer solstice◦ Located at the equator during the

equinoxes.The latitude at any given time of the

year where the sun’s vertical rays strike the Earth is known as the sun declination.

Sun Declination, cont.The sun’s declination can be

plotted on a graph, known as an analemma (next slide)◦The sun’s declination is plotted along

the vertical axis◦The days of the year are along the

analemma itselfSee page 52 of your lab manual

for an example

Solar AltitudeSolar altitude is the elevation of the

sun in the sky at noon local time◦ i.e. the angle of the noon sun above the

horizonCan be calculated mathematically:

where SA is the solar altitude and AD is the arc distanceArc distance (AD) is actually the

difference between the latitude your at and the declination of the sun at that time of year.

Let’s look at an example…

Solar Altitude ExampleSuppose it’s noon and we’re outside

on campus during a snowstorm on January 12th. The clouds and snow showers are blocking the sun from being visible. Even though we can’t see the sun, what is the solar altitude (sun’s elevation above the horizon)?

Solar Altitude Example, cont.The latitude of Muncie is 40° 11’ 36” N.Looking at our analemma, we find that on

January 12th, the sun’s declination is 21.5° S.

The arc distance (AD) can be found by subtracting the sun’s declination from our latitude: ° = AD◦ The reason there is a negative in front of the

21.5° is because the sun’s declination was “S” and in the southern hemisphere.

Solar Altitude Example, cont.Now that we know AD, plug into the

equation we were given:

Therefore, if we could see the sun through the clouds and snow, it would only be 28.5° above the horizon.◦ For additional examples, see page 51 and 53 in your lab

manual.

Tangent Rays and Daylight/DarknessIf we know the latitude of declination

for the sun (where it’s direct rays strike the Earth; from the analemma), then we can easily find the latitude of the tangent rays (those rays that skim past the earth).

Simply use this equation:

Where TR is the latitude of the tangent rays and Dec is the sun’s declination

Tangent Rays and Daylight/Darkness, cont.From our previous example, we found

that the declination of the sun on January 12th is 21.5° S. So, plugging that in:

So, we know that those latitudes above 68.5 N and 68.5 S receive either 24 hours of sunlight or 24 hours of darkness…but which is which?

Tangent Rays and Daylight/Darkness, cont.For the Northern Hemisphere,

remember this: ◦ If it (the day) is between March 20 and

September 22, then those areas north of the latitude of the tangent rays are experiencing 24 hours of daylight.

◦ If the day is between September 23 and March 21, then those areas north of the latitude of the tangent rays are experiencing 24 hours of darkness.

Lesson 12Insolation

Hess, McKnight’s Physical Geography, 10 ed. pp. 70, 80-84, and Fig. 4.17 on p. 78

InsolationFrom lesson 11 we now know that the

sun’s direct rays strike the earth at different locations throughout the year.

These differences give us our seasons and influence the amount of average daily insolation (incoming solar radiation)◦ Average daily insolation is the rate or

intensity of the sun’s radiation that strikes the surface over a 24-hour period Measured in watts per square meter (W· m-2) The average insolation hitting the Earth’s upper

atmosphere is ~ 1372 W· m-2. This is known as the solar constant

Insolation, cont.However, the amount of insolation

hitting the surface of the Earth varies widely due to three factors:1. The angle of incidence2. Day length3. Atmospheric obstructions

We will discuss each of these next…

Angle of IncidenceAngle of incidence: the angle at which the

Sun’s rays strike the surface of the Earth (solar altitude)◦ This can be directly related to the intensity of

radiation that reaches the surface.Areas that have a high angle of

incidence have a given amount of radiation concentrated on a small area◦ Therefore, radiation is higher in intensity

While areas with a low angle of incidence have that same amount of radiation concentrated on a larger area◦ Lower intensity radiation

Angle of Incidence, cont.

Angle of Incidence, cont.

Length of DayWe all know that the length of daylight

influences how much solar radiation is received (e.g. longer days generally mean warmer days)

Even if it is cloudy, longer days generally mean a significant increase in solar radiation received

Take a look at Fig. 3 and Fig. 4 on pages 58 and 59. These provide the hours of daylight and daily insolation, respectively, for location at the equator, 45° N and 90 N°.

Atmospheric ObstructionThe amount of atmosphere that

radiation has to travel through affects the total amount received.◦ e.g. If the angle of incidence is low, then

solar radiation has to travel through more atmosphere, thereby reducing the amount received when it finally reaches the surface

Water droplets (clouds) and other atmospheric particulates also affect the amount received.

The percentage of solar radiation reaching Earth’s surface through the atmosphere is listed in Fig. 5