MSc Remote Sensing Principles 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 Recap 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? Temporal 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 Temporal Useful link: Dr. Hassan J. Eghbali

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 What determines temporal sampling? Dr. Hassan J. Eghbali

Orbital characteristics –orbital mechanics developed by Johannes Kepler ( ), German mathematician –Explained observations of Danish nobleman Tyco Brahe ( ) –Kepler favoured elliptical orbits (from Copernicus’ solar-centric system) Properties of ellipse? Orbits and swaths Dr. Hassan J. Eghbali

Flattened circle –2 foci and 2 axes: major and minor –Distance r 1 +r 2 = constant = 2a (major axis) –“Flatness” of ellipse defined by eccentricity, e =  1-b 2 /a 2 = c/a –i.e. e is position of the focus as a fraction of the semimajor axis, a Ellipse From Increasing eccentricity e circle = 0 As e  1, c  a and ellipse becomes flatter r1r1 r2r2 f1f1 f2f2 C 2a 2c 2b major axis minor axis Dr. Hassan J. Eghbali

Kepler’s Laws –deduced from Brahe’s data after his death –see nice Java applet and.ac.uk/~history/Java/Ellipse.html Kepler’s 1st law: –Orbits of planets are elliptical, with sun at one focus Kepler’s laws From: Dr. Hassan J. Eghbali

Kepler’s 2nd law –line joining planet to sun sweeps out equal areas in equal times Kepler’s laws From: Dr. Hassan J. Eghbali

Kepler’s 3rd law –“ratio of the squares of the revolutionary periods for two planets (P 1, P 2 ) is equal to the ratio of the cubes of their semimajor axes (R 1, R 2 )” –P 1 2 /P 2 2 = R 1 3 /R 2 3 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, 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 Kepler’s laws Dr. Hassan J. Eghbali

Orbital period for a given instrument and height? –Gravitational force F g = GM E m s /R sE 2 G is universal gravitational constant (6.67x Nm 2 kg 2 ); M E is Earth mass (5.983x10 24 kg); m s is satellite mass (?) and R sE is distance from Earth centre to satellite i.e. 6.38x h where h is satellite altitude –Centripetal (not centrifugal!) force F c = m s v s 2 /R sE where v s is linear speed of satellite (=  s R sE where  is the satellite angular velocity, rad s -1 ) –for stable (constant radius) orbit F c = F g –  GM E m s /R sE 2 = m s v s 2 /R sE = m s  s 2 R sE 2 /R sE –so  s 2 = GM E /R sE 3 Orbits: examples Dr. Hassan J. Eghbali

Orbital period T of satellite (in s) = 2  /  –(remember 2  = one full rotation, 360°, in radians) –and R sE = R E + h where R E = 6.38x10 6 m –So now T = 2  [(R E +h) 3 /GM E ] 1/2 Example: polar orbiter period, if h = 705x10 3 m –T = 2  [(6.38x x10 3 ) 3 / (6.67x *5.983x10 24 )] 1/2 –T = s = 98.8mins Example: altitude for geostationary orbit? T = ?? –Rearranging: h = [(GM E /4  2 )T 2 ] 1/3 - R E –So h = [(6.67x *5.983x10 24 /4  2 )(24*60*60) 2 ] 1/ x10 6 –h = 42.2x x10 6 = 35.8km Orbits: examples Dr. Hassan J. Eghbali

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 Orbits: aside r  l 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) and Orbital pros and cons Dr. Hassan J. Eghbali

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) Geostationary From METEOSAT 0° WGOES-W 135° WGOES-E 75° WGMS 140° EIODC 63° E Dr. Hassan J. Eghbali

METEOSAT - whole earth disk every 15 mins Geostationary From 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 –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 Geostationary orbits From Dr. Hassan J. Eghbali

Advantages –full polar orbit inclined 90 to equator typically few degrees off so poles not covered orbital period typically mins –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 days Polar & near polar orbits From Dr. Hassan J. Eghbali

(near) Polar orbits: NASA Terra From Dr. Hassan J. Eghbali

Near-polar orbits: Landsat From & –inclination 98.2 , T = 98.8mins – – 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: (near) Polar orbits From 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) Types of near-polar orbit 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 Near-ish: Equatorial orbit From Dr. Hassan J. Eghbali

TLEs (two line elements) – e.g. PROBA U 01049B 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 – – Orbital location? Dr. Hassan J. Eghbali

Swath describes ground area imaged by instrument during overpass Instrument swath one sample two samples three samples satellite ground swath direction of travel Dr. Hassan J. Eghbali

MODIS on-board Terra From Dr. Hassan J. Eghbali

Terra instrument swaths compared From 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 Broad swath Dr. Hassan J. Eghbali

MODIS: building global picture From Note across-track “whiskbroom” type scanning mechanism swath width of 2330km ( m resolution) Hence, 1-2 day repeat cycle Dr. Hassan J. Eghbali

AVHRR: global coverage From km swath, 1.1km pixels at nadir, but > 5km at edge of swath Repeats 1-2 times per day Dr. Hassan J. Eghbali

POLDER (RIP!) From 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, 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 Narrow swath Dr. Hassan J. Eghbali

Landsat: local view From 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 & QuickBird: very local view! QuickBird: 16.5km swath at nadir, 61cm! panchromatic, 2.44m multispectral IKONOS: 11km swath at nadir, 1m panchromatic, 4m multispectral 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 Variable repeat patterns From 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? –Information in angular signal! –More samples of viewing/illum. hemisphere gives more info. So.....angular resolution Dr. Hassan J. Eghbali

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 Solar principal plane Cross solar principal plane view zenith relative azimuth (view - solar) Dr. Hassan J. Eghbali

Angular sampling: broad swath 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) BUT 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... So, angular resolution 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 Radiometric resolution 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) Radiometric resolution Dr. Hassan J. Eghbali

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 2 8 (256) different DNs (0-255) Radiometric resolution 1 to 6 bits (left to right) –black/white (2 1 ) up to 64 graylevels (2 6 ) (DN values) –human eye cannot distinguish more than DN levels in grayscale i.e. ‘radiometric resolution’ of human eye 4-5 bits From Dr. Hassan J. Eghbali

Landsat: MSS 7bits, TM 8bits AVHRR: 10-bit (2 10 = 1024 DN levels) –TIR channel scaled (calibrated) so that DN 0 = -273°C and DN 1023 ~50°C MODIS: 12-bit (2 12 = 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 Radiometric resolution: examples Dr. Hassan J. Eghbali

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 Summary: angular, temporal resolution Dr. Hassan J. Eghbali

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 Summary: radiometric resolution Dr. Hassan J. Eghbali