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Introduction to quantitative Remote

SensingCoco Rulinda (CGIS-NUR) for PGD 2009

Advanced Remote Sensing – PGD 2009June 1 2009

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Qualitative vs. quantitative RS

Subject 1Date 1

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The Remote Sensing process

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• Time zones– UTC Universal Time, GMT Greenwich Mean Time.

Time zones are usually expressed as UTC+n, where n indicates the displacement from UTC

• Average Solar Energy arriving at the Earth– Solar constant 1367 Wm-2

– The solar constant is defined as the solar energy received by the Earth at the average distance to the sun r0, which is also defined as one Astronomical Unit (AU)

– 1 AU = 1.496x108 Km

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Earth-Sun distance corrections

• Because the orbit of the Earth around the sun is not a circle but an ellipse, the distance Earth-Sun varies throughout the year.

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Earth – Sun Distance (d) - LUT

• Distance Sun to Earth = ± 149 mln Km = 1 AU (Astronomical unit)J= Julian day Julian day: January 1st=001Sin is in radian January 2nd=002

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Solar declination δ

• The plane of revolution of the Earth around the Sun is called the ecliptic plane. The Earth itself rotates around the polar axis, which is inclined at approximately 23.5° from the normal to the ecliptic plane– The Earth’s rotation around its axis causes day and night

and diurnal changes energy arriving at the surface– The fact that the polar axis is tilted with respect to the

ecliptic plane causes the seasons, and when it is summer on the North Pole it is winter in the south pole and vice-versa

δ = 23.45 sin [360/365 (dn+284)]

Equation in degrees to describe the position of the sun through the solar declination

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Equation of time

• Because the Earth rotates around its axis and at the same time moves in an elliptical orbit around the sun, where the velocity of the Earth changes as a function of its distance to the Sun, there are slight irregularities (maximum 16 minutes) in the calculation of the Sun’s position and the determination of local time. Corrections can be made through the so-called equation of time (Et in radians)

Et = 0.000075 + 0.001868 cos (da) – 0.032077 sin (da) – 0.014615 cos (2da) – 0.04089 sin (2da)

There are several conventions to relate local longitude Lc to local solar time LAT (Local Apparent Time)

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A. Longitude is positive to the west and negative to the east

• Introduced by the USA, because it is far to the west and it is easier to count with positive numbers.

Lcor = 4 (Lstand-Lc)

Where Lstand is the longitude of the standard meridian. When Lstand

and Lc are expressed in degrees, then Lcor is in minute (because of the factor 4). Lc is the longitude at the position of the observer.

LAT = LST + Lcor /60 + Et /60

Where LST is the Local Standard Time (e.g. Central African Time = UTC+2). Note that the Local Standard Time is the time attached to the longitude of the standard meridian Lstand.

Note that LAT is the local solar time, not to be confused with the time on your watch (that is mostly like LST). Note the conversion faction 60 (to change from minutes to hours)

LAT and LST are in hours

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B. Longitude is negative to the West and Positive to the east

• It is the most common definition (with positive longitude to the east).

LAT = LST - Lcor /60 + Et /60

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C. Making use of UTC (Universal Time) and longitudes positive to the

east

• When the Universal Time or (GMT) is given, the LAT can be calculated as follows:

LAT = UTC + 4* Lc / 60 + Et / 60

With both LAT and UTC in hours (decimal). This equation is very useful in practice because satellite overpass times are usually given in UTC. Then you only need the Longitude Lc at the point of interest to determine the LAT

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Hour angle, day length and solar zenith angle

• The hour angle follows straightforward from the LAT as

ω = 15(LAT - 12) π/180The LAT must be given in hours, and ω is given in

radians.The solar zenith angle θ is then determined from:

cos θ = sin(φ)sin(δ)+cos(φ)cos(δ)cos(ω)

• where φ is the latitude of the observer, and δ the solar declination.

• Note that all values have to be entered in radians

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Definition of sun’s zenith, altitude and azimuth angles

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• At the hour of sunset θ =90° and then the sunset hour angle ωs is given as

cos(ωs) = − tan(φ)tan(δ )

• It also follows that the day length (number of daylight hours) is given by

N=2/15 cos-1 (tan(φ)tan(δ))

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Satellite Geometry

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Orbital characteristics

• Inclination• Mean distance to Earth (this determines its

speed)• Eccentricity

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