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

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### 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: http://www.earth.nasa.gov/science/index.html

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: http://www.earth.nasa.gov/science/index.html

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

- 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

r2

2b

minor axis

f2

f1

C

- ecircle = 0
- As e 1, c a and ellipse becomes flatter

Increasing eccentricity

2c

2a

major axis

Ellipse

- 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

From http://mathworld.wolfram.com/Ellipse.html

Dr. Hassan J. Eghbali

- Kepler’s Laws
- deduced from Brahe’s data after his death
- see nice Java applet http://www-groups.dcs.st-and.ac.uk/~history/Java/Ellipse.html
- Kepler’s 1st law:
- Orbits of planets are elliptical, with sun at one focus

From:http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Dr. Hassan J. Eghbali

- Kepler’s 2nd law
- line joining planet to sun sweeps out equal areas in equal times

From:http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Dr. Hassan J. Eghbali

- 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

- 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

- 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 /42)T2 ]1/3 - RE
- So h = [(6.67x10-11*5.983x1024/42)(24*60*60)2 ]1/3 - 6.38x106
- h = 42.2x106 - 6.38x106 = 35.8km

Dr. Hassan J. Eghbali

r

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 = 2r = 2
- So, 360° = 2 radians

Dr. Hassan J. Eghbali

- 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)
- http://www.noaa.gov/ and http://www.goes.noaa.gov/

Dr. Hassan J. Eghbali

GOES-W 135° W

METEOSAT 0° W

IODC 63° E

GMS 140° E

Geostationary

- 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)

From http://www.sat.dundee.ac.uk/pdusfaq.html

Dr. Hassan J. Eghbali

- METEOSAT - whole earth disk every 15 mins

From http://www.goes.noaa.gov/f_meteo.html

Dr. Hassan J. Eghbali

- 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
- http://www.meteo.pt/landsaf/eumetsat_sat_char.html
- 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

From http://www.esa.int/SPECIALS/MSG/index.html

Dr. Hassan J. Eghbali

- 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

From http://collections.ic.gc.ca/satellites/english/anatomy/orbit/

Dr. Hassan J. Eghbali

(near) Polar orbits: NASA Terra

From http://visibleearth.nasa.gov/cgi-bin/viewrecord?134

Dr. Hassan J. Eghbali

- inclination 98.2, T = 98.8mins
- http://www.cscrs.itu.edu.tr/page.en.php?id=51
- http://landsat.gsfc.nasa.gov/project/Comparison.html

From http://www.iitap.iastate.edu/gccourse/satellite/satellite_lecture_new.html & http://eosims.cr.usgs.gov:5725/DATASET_DOCS/landsat7_dataset.html

Dr. Hassan J. Eghbali

- 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: http://lectureonline.cl.msu.edu/~mmp/kap7/orbiter/orbit.htm

From http://collections.ic.gc.ca/satellites/english/anatomy/orbit/

Dr. Hassan J. Eghbali

- 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

- 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

From http://trmm.gsfc.nasa.gov/

Dr. Hassan J. Eghbali

- TLEs (two line elements)
- http://www.satobs.org/element.html 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
- http://www.vectorsite.net/ttgps.html
- http://www.edu-observatory.org/gps/tracking.html

Dr. Hassan J. Eghbali

satellite ground swath

one sample

two samples

three samples

Instrument swath

- Swath describes ground area imaged by instrument during overpass

Dr. Hassan J. Eghbali

Terra instrument swaths compared

From http://visibleearth.nasa.gov/Sensors/Terra/

Dr. Hassan J. Eghbali

- MODIS, POLDER, AVHRR etc.
- 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

From http://visibleearth.nasa.gov/Sensors/Terra/

Dr. Hassan J. Eghbali

- 2400km swath, 1.1km pixels at nadir, but > 5km at edge of swath
- Repeats 1-2 times per day

From http://edc.usgs.gov/guides/avhrr.html

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.

From http://www-loa.univ-lille1.fr/~riedi/BROWSES/200304/16/index.html

Dr. Hassan J. Eghbali

- 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

- 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°)

From http://visibleearth.nasa.gov/Sensors/Terra/

Dr. Hassan J. Eghbali

QuickBird: 16.5km swath at nadir, 61cm! panchromatic, 2.44m multispectral

- http://www.digitalglobe.com

- IKONOS: 11km swath at nadir, 1m panchromatic, 4m multispectral
- http://www.spaceimaging.com/

IKONOS & QuickBird: very local view!

Dr. Hassan J. Eghbali

- 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

From http://earth.esa.int/rootcollection/eeo/ERS1.1.7.html

Dr. Hassan J. Eghbali

- 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?
- http://stress.swan.ac.uk/~mbarnsle/pdf/barnsley_et_al_1997.pdf
- Information in angular signal!
- More samples of viewing/illum. hemisphere gives more info.

Dr. Hassan J. Eghbali

relative azimuth (view - solar)

view zenith

Cross solar principal plane

Solar principal plane

Angular sampling: broad swath

- MODIS and SPOT-VGT: polar plots
- http://www.soton.ac.uk/~epfs/methods/polarplot.shtml
- Reasonable sampling BUT mostly across principal plane (less angular info.)
- Is this “good” sampling of BRDF

Dr. Hassan J. Eghbali

- 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

- 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

- 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?

- MODIS AND MISR: better sampling than either individually
- Combine observations to sample BRDF more effectively

Dr. Hassan J. Eghbali

- 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

- 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

- 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

- 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)

From http://ceos.cnes.fr:8100/cdrom/ceos1/irsd/pages/dre4.htm

Dr. Hassan J. Eghbali

Radiometric resolution: examples

- 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

- 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

- 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

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