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MSc Remote Sensing 2006-7 Principles of Remote Sensing 5: resolution II angular/temporal. Dr. Hassan J. Eghbali. Recap. Previously introduced spatial and spectral resolution narrow v broad band tradeoffs.... signal to noise ratio This week temporal and angular resolution

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Msc remote sensing 2006 7 principles of remote sensing 5 resolution ii angular temporal

MSc Remote Sensing 2006-7Principles of Remote Sensing 5: resolution II angular/temporal

Dr. Hassan J. Eghbali


  • Previously introduced

    • spatial and spectral resolution

    • narrow v broad band tradeoffs....

    • signal to noise ratio

  • This week

    • temporal and angular resolution

    • orbits and sensor swath

    • radiometric resolution

Dr. Hassan J. Eghbali


  • Single or multiple observations

  • How far apart are observations in time?

    • One-off, several or many?

  • Depends (as usual) on application

    • Is it dynamic?

    • If so, over what timescale?

Useful link:

Dr. Hassan J. Eghbali


  • Examples

    • Vegetation stress monitoring, weather, rainfall

      • hours to days

    • Terrestrial carbon, ocean surface temperature

      • days to months to years

    • Glacier dynamics, ice sheet mass balance, erosion/tectonic processes

      • Months to decades

Useful link:

Dr. Hassan J. Eghbali

What determines temporal sampling?

  • Sensor orbit

    • geostationary orbit - over same spot

      • BUT distance means entire hemisphere is viewed e.g. METEOSAT

    • polar orbit can use Earth rotation to view entire surface

  • Sensor swath

    • Wide swath allows more rapid revisit

      • typical of moderate res. instruments for regional/global applications

    • Narrow swath == longer revisit times

      • typical of higher resolution for regional to local applications

Dr. Hassan J. Eghbali

Orbits and swaths

  • Orbital characteristics

    • orbital mechanics developed by Johannes Kepler (1571-1630), German mathematician

    • Explained observations of Danish nobleman Tyco Brahe (1546-1601)

    • Kepler favoured elliptical orbits (from Copernicus’ solar-centric system)

  • Properties of ellipse?

Dr. Hassan J. Eghbali




minor axis




  • ecircle = 0

  • As e 1, c a and ellipse becomes flatter

Increasing eccentricity



major axis


  • Flattened circle

    • 2 foci and 2 axes: major and minor

    • Distance r1+r2 = constant = 2a (major axis)

    • “Flatness” of ellipse defined by eccentricity, e = 1-b2/a2 = c/a

    • i.e. e is position of the focus as a fraction of the semimajor axis, a


Dr. Hassan J. Eghbali

Kepler’s laws

  • Kepler’s Laws

    • deduced from Brahe’s data after his death

    • see nice Java applet

  • Kepler’s 1st law:

    • Orbits of planets are elliptical, with sun at one focus


Dr. Hassan J. Eghbali

Kepler’s laws

  • Kepler’s 2nd law

    • line joining planet to sun sweeps out equal areas in equal times


Dr. Hassan J. Eghbali

Kepler’s laws

  • Kepler’s 3rd law

    • “ratio of the squares of the revolutionary periods for two planets (P1, P2) is equal to the ratio of the cubes of their semimajor axes (R1, R2)”

    • P12/P22 = R13/R23

      • i.e. orbital period increases dramatically with R

  • Convenient unit of distance is average separation of Earth from Sun = 1 astronomical unit (A.U.)

    • 1A.U. = 149,597,870.691 km

    • in Keplerian form, P(years)2 R(A.U.)3

    • or P(years)  R(A.U.)3/2

    • or R(A.U.)  P(years)2/3

Dr. Hassan J. Eghbali

Orbits: examples

  • Orbital period for a given instrument and height?

    • Gravitational force Fg = GMEms/RsE2

      • G is universal gravitational constant (6.67x10-11 Nm2kg2); ME is Earth mass (5.983x1024kg); ms is satellite mass (?) and RsE is distance from Earth centre to satellite i.e. 6.38x106 + h where h is satellite altitude

    • Centripetal (not centrifugal!) force Fc = msvs2/RsE

      • where vs is linear speed of satellite (=sRsE where  is the satellite angular velocity, rad s-1)

    • for stable (constant radius) orbit Fc = Fg

    • GMEms/RsE2 = msvs2/RsE = ms s2RsE2 /RsE

    • so s2 = GME /RsE3

Dr. Hassan J. Eghbali

Orbits: examples

  • Orbital period T of satellite (in s) = 2/

    • (remember 2 = one full rotation, 360°, in radians)

    • and RsE = RE + h where RE = 6.38x106 m

    • So now T = 2[(RE+h)3/GME]1/2

  • Example: polar orbiter period, if h = 705x103m

    • T = 2[(6.38x106 +705x103)3 / (6.67x10-11*5.983x1024)]1/2

    • T = 5930.6s = 98.8mins

  • Example: altitude for geostationary orbit? T = ??

    • Rearranging: h = [(GME /42)T2 ]1/3 - RE

    • So h = [(6.67x10-11*5.983x1024/42)(24*60*60)2 ]1/3 - 6.38x106

    • h = 42.2x106 - 6.38x106 = 35.8km

Dr. Hassan J. Eghbali



Orbits: aside

  • Convenience of using radians

    • By definition, angle subtended by an arc  (in radians) = length of arc/radius of circle i.e.  = l/r

    • i.e. length of an arc l = r

    • So if we have unit circle (r=1), l = circumference = 2r = 2

    • So, 360° = 2 radians

Dr. Hassan J. Eghbali

Orbital pros and cons

  • Geostationary?

    • Circular orbit in the equatorial plane, altitude ~36,000km

    • Orbital period?

  • Advantages

    • See whole Earth disk at once due to large distance

    • See same spot on the surface all the time i.e. high temporal coverage

    • Big advantage for weather monitoring satellites - knowing atmos. dynamics critical to short-term forecasting and numerical weather prediction (NWP)

      • GOES (Geostationary Orbiting Environmental Satellites), operated by NOAA (US National Oceanic and Atmospheric Administration)

      • and

Dr. Hassan J. Eghbali

GOES-E 75° W

GOES-W 135° W


IODC 63° E

GMS 140° E


  • Meteorological satellites - combination of GOES-E, GOES-W, METEOSAT (Eumetsat), GMS (NASDA), IODC (old Meteosat 5)

    • GOES 1st gen. (GOES-1 - ‘75  GOES-7 ‘95); 2nd gen. (GOES-8++ ‘94)


Dr. Hassan J. Eghbali


  • METEOSAT - whole earth disk every 15 mins


Dr. Hassan J. Eghbali

Geostationary orbits

  • Disadvantages

    • typically low spatial resolution due to high altitude

    • e.g. METEOSAT 2nd Generation (MSG) 1x1km visible, 3x3km IR (used to be 3x3 and 6x6 respectively)

      • MSG has SEVIRI and GERB instruments


    • Cannot see poles very well (orbit over equator)

      • spatial resolution at 60-70° N several times lower

      • not much good beyond 60-70°

    • NB Geosynchronous orbit same period as Earth, but not equatorial


Dr. Hassan J. Eghbali

Polar & near polar orbits

  • Advantages

    • full polar orbit inclined 90 to equator

      • typically few degrees off so poles not covered

      • orbital period typically 90 - 105mins

    • near circular orbit between 300km (low Earth orbit) and 1000km

    • typically higher spatial resolution than geostationary

    • rotation of Earth under satellite gives (potential) total coverage

      • ground track repeat typically 14-16 days


Dr. Hassan J. Eghbali

(near) Polar orbits: NASA Terra


Dr. Hassan J. Eghbali

Near-polar orbits: Landsat

  • inclination 98.2, T = 98.8mins



From &

Dr. Hassan J. Eghbali

(near) Polar orbits

  • Disadvantages

    • need to launch to precise altitude and orbital inclination

    • orbital decay

      • at LEOs (Low Earth Orbits) < 1000km, drag from atmosphere

      • causes orbit to become more eccentric

      • Drag increases with increasing solar activity (sun spots) - during solar maximum (~11yr cycle) drag height increased by 100km!

    • Build your own orbit:


Dr. Hassan J. Eghbali

Types of near-polar orbit

  • Sun-synchronous

    • Passes over same point on surface at approx. same local solar time each day (e.g. Landsat)

    • Characterised by equatorial crossing time (Landsat ~ 10am)

    • Gives standard time for observation

    • AND gives approx. same sun angle at each observation

      • good for consistent illumination of observations over time series (i.e. Observed change less likely to be due to illumination variations)

      • BAD if you need variation of illumination (angular reflectance behaviour)

  • Special case is dawn-to-dusk

    • e.g. Radarsat 98.6° inclination

    • trails the Earth’s shadow (day/night border)

    • allows solar panels to be kept in sunlight all the time)

Dr. Hassan J. Eghbali

Near-ish: Equatorial orbit

  • Inclination much lower

    • orbits close to equatorial

    • useful for making observations solely over tropical regions

  • Example

    • TRMM - Tropical Rainfall Measuring Mission

    • Orbital inclination 35.5°, periapsis (near point: 366km), apoapsis (far point: 3881km)

    • crosses equator several times daily

    • Flyby of Hurrican Frances (24/8/04)

    • iso-surface


Dr. Hassan J. Eghbali

Orbital location?

  • TLEs (two line elements)

    • e.g.

      PROBA 1

      1 26958U 01049B 04225.33423432 .00000718 00000-0 77853-4 0 2275

      2 26958 97.8103 302.9333 0084512 102.5081 258.5604 14.88754129152399

  • DORIS, GPS, Galileo etc.

    • DORIS: Doppler Orbitography and Radiopositioning Integrated by Satellite

    • Tracking system providing range-rate measurements of signals from a dense network of ground-based beacons (~cm accuracy)

    • GPS: Global Positioning System



Dr. Hassan J. Eghbali

direction of travel

satellite ground swath

one sample

two samples

three samples

Instrument swath

  • Swath describes ground area imaged by instrument during overpass

Dr. Hassan J. Eghbali

MODIS on-board Terra


Dr. Hassan J. Eghbali

Terra instrument swaths compared


Dr. Hassan J. Eghbali

Broad swath


    • swaths typically several 1000s of km

    • lower spatial resolution

    • Wide area coverage

    • Large overlap obtains many more view and illumination angles (much better termporal & angular (BRDF) sampling)

    • Rapid repeat time

Dr. Hassan J. Eghbali

MODIS: building global picture

  • Note across-track “whiskbroom” type scanning mechanism

  • swath width of 2330km (250-1000m resolution)

  • Hence, 1-2 day repeat cycle


Dr. Hassan J. Eghbali

AVHRR: global coverage

  • 2400km swath, 1.1km pixels at nadir, but > 5km at edge of swath

  • Repeats 1-2 times per day


Dr. Hassan J. Eghbali


  • Polarisation and Directionality of Earth’s Reflectance

    • FOV ±43° along track, ±51° across track, 9 cameras, 2400km swath, 7x6km resn. at nadir

    • POLDER I 8 months, POLDER II 7 months....

Each set of points corresponds to given viewing zenith and azimuthal angles for near-simultaneous measurements over a region defined by lat 0°±0.5° and long of 0°±0.5° (Nov 1996)

Each day, region is sampled from different viewing directions so hemisphere is sampled heavily by compositing measurements over time

From Loeb et al. (2000) Top-of-Atmosphere Albedo Estimation from Angular Distribution Models Using Scene Identification from Satellite Cloud Property Retrievals, Journal of Climate, 1269-1285.


Dr. Hassan J. Eghbali

Narrow swath

  • Landsat TM/MSS/ETM+, IKONOS, QuickBird etc.

    • swaths typically few 10s to 100skm

    • higher spatial resolution

    • local to regional coverage NOT global

    • far less overlap (particularly at lower latitudes)

    • May have to wait weeks/months for revisit

Dr. Hassan J. Eghbali

Landsat: local view

  • 185km swath width, hence 16-day repeat cycle (and spatial res. 25m)

  • Contiguous swaths overlap (sidelap) by 7.3% at the equator

  • Much greater overlap at higher latitudes (80% at 84°)


Dr. Hassan J. Eghbali

  • IKONOS: 11km swath at nadir, 1m panchromatic, 4m multispectral


IKONOS & QuickBird: very local view!

Dr. Hassan J. Eghbali

Variable repeat patterns multispectral

  • ERS 1 & 2

    • ATSR instruments, RADAR altimeter, Imaging SAR (synthetic aperture RADAR) etc.

    • ERS 1: various mission phases: repeat times of 3 (ice), 35 and 168 (geodyssey) days

    • ERS 2: 35 days


Dr. Hassan J. Eghbali

So.....angular resolution multispectral

  • Wide swath instruments have large overlap

    • e.g. MODIS 2330km (55), so up to 4 views per day at different angles!

    • AVHRR, SPOT-VGT, POLDER I and II, etc.

    • Why do we want good angular sampling?

      • Remember BRDF?


    • Information in angular signal!

    • More samples of viewing/illum. hemisphere gives more info.

Dr. Hassan J. Eghbali

relative azimuth (view - solar) multispectral

view zenith

Cross solar principal plane

Solar principal plane

Angular sampling: broad swath

  • MODIS and SPOT-VGT: polar plots


  • Reasonable sampling BUT mostly across principal plane (less angular info.)

  • Is this “good” sampling of BRDF

Dr. Hassan J. Eghbali

Angular sampling: broad swath multispectral

  • POLDER I !

  • Broad swath (2200km) AND large 2D CCD array gave huge number of samples

    • 43 IFOV along-track and 51 IFOV across-track

Dr. Hassan J. Eghbali

BUT....... multispectral

  • Is wide swath angular sampling REALLY multi-angular?

    • Different samples on different days e.g. MODIS BRDF product is composite over 16 days

    • minimise impact of clouds, maximise number of samples

  • “True” multi-angular viewing requires samples at same time

    • need to use several looks e.g. ATSR, MISR (& POLDER)

Dr. Hassan J. Eghbali

Angular sampling: narrow swath multispectral

  • ATSR-2 and MISR polar plots

  • Better sampling in principal plane (more angular info.)

  • MISR has 9 cameras

Dr. Hassan J. Eghbali

Angular sampling: combinations? multispectral

  • MODIS AND MISR: better sampling than either individually

  • Combine observations to sample BRDF more effectively

Dr. Hassan J. Eghbali

So, angular resolution multispectral

  • Function of swath and IFOV

    • e.g. MODIS at nadir ~1km pixel

    • remember l = r  so angle (in rads)  = r/l where r this time is 705km and l ~ 1km so angular res ~ 1.42x10-6 rads at nadir

    • at edge of swath ~5km pixel so angular res ~ 7x10-6 rads

  • Sampling more important/meaningful than resolution in angular sense...

Dr. Hassan J. Eghbali

Radiometric resolution multispectral

  • Had spatial, spectral, temporal, angular.....

  • Precision with which an instrument records EMR

    • i.e. Sensitivity of detector to amount of incoming radiation

    • More sensitivity == higher radiometric resolution

      • determines smallest slice of EM spectrum we can assign DN to

    • BUT higher radiometric resolution means more data

      • As is the case for spatial, temporal, angular etc.

  • Typically, radiometric resolution refers to digital detectors

    • i.e. Number of bits per pixel used to encode signal

Dr. Hassan J. Eghbali

Radiometric resolution multispectral

  • Analogue

    • continuous measurement levels

    • film cameras

    • radiometric sensitivity of film emulsion

  • Digital

    • discrete measurement levels

    • solid state detectors (e.g. semiconductor CCDs)

Dr. Hassan J. Eghbali

  • 1 to 6 bits (left to right) multispectral

    • black/white (21) up to 64 graylevels (26) (DN values)

    • human eye cannot distinguish more than 20-30 DN levels in grayscale i.e. ‘radiometric resolution’ of human eye 4-5 bits

Radiometric resolution

  • Bits per pixel

    • 1 bit (0,1); 2bits (0, 1, 2, 3); 3 bits (0, 1, 2, 3, 4, 5, 6, 7) etc.

    • 8 bits in a byte so 1 byte can record 28 (256) different DNs (0-255)


Dr. Hassan J. Eghbali

Radiometric resolution: examples multispectral

  • Landsat: MSS 7bits, TM 8bits

  • AVHRR: 10-bit (210 = 1024 DN levels)

    • TIR channel scaled (calibrated) so that DN 0 = -273°C and DN 1023 ~50°C

  • MODIS: 12-bit (212 = 4096 DN levels)

  • BUT precision is NOT accuracy

    • can be very precise AND very inaccurate

    • so more bits doesn’t mean more accuracy

  • Radiometric accuracy designed with application and data size in mind

    • more bits == more data to store/transmit/process

Dr. Hassan J. Eghbali

Summary: angular, temporal resolution multispectral

  • Coverage (hence angular &/or temporal sampling) due to combination of orbit and swath

    • Mostly swath - many orbits nearly same

      • MODIS and Landsat have identical orbital characteristics: inclination 98.2°, h=705km, T = 99mins BUT swaths of 2400km and 185km hence repeat of 1-2 days and 16 days respectively

    • Most EO satellites typically near-polar orbits with repeat tracks every 16 or so days

    • BUT wide swath instrument can view same spot much more frequently than narrow

  • Tradeoffs again, as a function of objectives

Dr. Hassan J. Eghbali

Summary: radiometric resolution multispectral

  • Number of bits per pixel

    • more bits, more precision (not accuracy)

    • but more data to store, transmit, process

    • most EO data typically 8-12 bits (in raw form)

  • Tradeoffs again, as a function of objectives

Dr. Hassan J. Eghbali