Examination Questions & Model Answers (Academic year 2012 ...

UCL DEPARTMENT OF GEOGRAPHY

Examination Questions & Model Answers

(Academic year 2012-2013)

PLEASE PREPARE YOUR QUESTIONS AND ANSWERS BY USING THE FOLLOWING GUIDELINES; 1. Use Times New Roman 12 2. Enter the Module Code and Title 3. Please do not switch between text/fonts 4. Ensure all technical terms are correct 5. Each question must have the marks it’s worth shown 6. Show marks as e.g. [50 marks] not 50% or 50% of marks 7. Each question should be out of 100 marks 8. Run spell checker 9. If you are setting more than one question then please submit ONE file only 10. Please indicate the 2nd Marker 11. Please indicate if there any special instructions for e.g. if a question is compulsory Module Code:

GEOGG141

Module Title:

Principles and Practice of Remote Sensing

Contributor:

M. Disney 2nd Marker

P. Lewis

Special Instructions Question No:

1

EITHER

i) Using log-log scales, draw a figure representing the Planck blackbody energy distribution for two objects, at ~6000K and ~300K respectively. Describe THREE key properties the Planck energy distribution giving their relevance to remote sensing in each case. (60)

ii) What is the theoretical emissive power of the sun (in Wm-2), with a surface temperature is 5770K? How does the actual power differ from this in practice and why? (10)

iii) Show that around 36% of the total power of a blackbody at 5770K lies in the visible PAR (photosynthetically active radiation) region i.e. λ = 400-700 nm (0.4 to 0.7 µm). (30)

You may assume σ, the Stefan-Boltzmann constant = 5.7×10-8 Wm-2K-4. Values of the integral of the Planck energy distribution from 0 to λ as a function of λT, F0èλ, for blackbodies at various temperatures T are as follows:

UCL DEPARTMENT OF GEOGRAPHY λT (µmK ×103) F0èλ(λT) 2 0.067 3 0.273 4 0.481 5 0.634 6 0.738 8 0.856 10 0.914 12 0.945 14 0.963 16 0.974 18 0.981

OR

i) Derive an expression relating the orbital period T, of a satellite in a stable orbit, to its altitude above the Earth’s surface, h. Your answer should show all working for any derivations required and you should define all terms. (50)

ii) Use this expression to determine the altitude of a near-polar orbiting platform with an orbital period T = 100 minutes. (20)

iii) If the platform carries an imager with a swath of 2300km, what is the repeat time of the instrument at the equator, in days? (10)

iv) The altitude of a low-earth orbit sensor is typically not stable over time – why not? How is this issue dealt with in practice? (20)

You may assume ME, the Earth’s mass, to be 5.983x1024kg; the universal gravitational constant G to be 6.67x10-11 Nm2kg2; and the radius of the Earth to be 6.38x106m. Model Answer: EITHER:

i) 15 marks for this part, 45 for the three points – 15 for each. Figure must look like this for red and pink lines:


Figure must be labelled correctly and the key shape must be right (same for both lines); peak must be at about 0.5 um for Sun (6000k) and about 10um for Earth (300K), with total going from 0.1 to over 100 for Sun, and 3 to < 100 for Earth. Three points from Planck are: allows us to predict shape so we known energy between any two wavelengths so we know signal for EO measurement; integral gives us total energy output of a BB which is Stefan-Boltzman Law – good answer gives the Planck equation and SB (M = σT4); differential gives us the wavelength at which emittance is a maximum, λmax which is Wien’s displacement law i.e. λmax = k/T where k = µ2897mK. In log-log space λmax increases inversely with reducing T in linear fashion as in diagram.

ii) M =σT4 = 5.7x10-8 × 57704 = 63.2MWm-2. Actual power is lower than this, because sun is not a perfect blackbody i.e. emissivity < 1, so would be given by something like ε × 5.7x10-8 × 57704.

iii) Need total energy from 0.4-0.7um, so do for 0 to 0.7 and then 0 to 0.4 and subtract first. For 0-0.4, λT is 0.4 × 5770 = 2.308 µmK ×103 so interpolate between 2 and 3 i.e. (2.308-2) / (3-2) × (0.273-0.067) + 0.067 = 0.130. For 0.7, λT is 0.7 × 5770 = 4.039 µmK ×103 so interpolate between 4 & 5 (or just take 4, but….) i.e. (4.039-4) / (5-4) × (0.634-0.481) + 0.0.481 = 0.487. So final answer is difference i.e. 0.487 – 0.130 = 0.36 = 36%.

OR

i) In stable orbit the gravitational force Fg = GMEms/RsE2 = centripetal force Fg = msvs2/RsE where G is universal gravitational constant (6.67x10-11 Nm2kg2); ME is Earth mass (5.983x1024kg); ms is satellite mass (unknown) and RsE is distance from Earth centre to satellite i.e. 6.38x106 + h where h is satellite altitude; vs is linear speed of satellite (=ωsRsE where ω is the satellite angular velocity, rad s-1 = 2π/T for orbital period T). So for stable orbit GME/(RsE+h)3 = (2π/T)2.

ii) Rearrange so h = [T2GME/4π2]1/3 - RsE, where T = 100x60 = 6x103 s, so h = 759.41km. iii) Repeat time is time taken to return to the same sub-satellite point on the Earth’s surface. Total

circumf of Earth = 2π*6.38x106 and we cover 2300km per orbit, so require 2π*6.38x106/2300x103 = 17.43 orbits, and at 100 mins per orbit this is 1742.9 mins = 1.21 days, or 1 day 5 hours.

iv) Altitude varies for two reasons – first, wobble up and down due to varying gravitational field strength of Earth due to variations in density; second, due to gradual degradation of orbit due to drag of atmosphere. In the first instance, we can monitor this (and even exploit it to estimate geoid); in the second we can either boost sensor periodically (requiring fuel) or we accept and allow orbit to decay before letting it fall back to Earth, or alternatively give it a large boost on decommissioning to an


effectively non-decaying orbit (beyond 1000km say). Good answer would mention atmospheric drag varies with solar activity.

UCL DEPARTMENT OF GEOGRAPHY Module Code:

GEOGG141

Module Title:


Contributor:


P. Lewis


2

Question i) Define the following terms and briefly detail their relevance to remote sensing: Spatial resolution (10) Radiance, L (10) SAR (10) Atmospheric window (10) Whiskbroom scanner (10) ii) Describe the key features of the bidirectional reflectance distribution function (BRDF) of a vegetated surface, using figures where appropriate (50) Model Answer: i) Spatial resolution: a measure of smallest angular or linear separation between two objects that can be resolved by sensor i.e. can be expressed either in distance (size of object) or in an angular sense. Relevance as defines spatial limitations of a sensor. Radiance – flux per unit projected area per unit solid angle leaving a source or reference surface L = d2P/dAprojd Ω, where dAproj = dAcosθ and θ is the angle between the outward surface normal of the area element dA and the direction of observation, Ω. Relevance is this is usually the measured at-surface signal we obtain via remote sensing. SAR – synthetic aperture radar. Method of synthesising a larger aperture by using motion of platform, and using pulses sent out, which are recombined with phase information maintained. Useful as can measure height of surface very accurately eg for topography & ice sheet dynamics. Key way of overcoming limitation of RADAR remote sensing (size of antennae). Atmospheric window – part of the EM spectrum where the Earth’s atmosphere is transparent to radiation. Good answer would give examples of windows in the visible & SWIR, & microwave (RADAR). Best answer would indicate that opacity of atmosphere between windows is due to absorption by gases eg O2, O3, CO2 and water vapour. For surface remote sensing we have to look in the atmospheric windows as only region where signal can escape to be measured. Whiskbroom scanner - moving mirror either rotates fully, or oscillates across the track i.e. perpendicular to direction of instrument travel. Examples are: Landsat MSS, TM. One way to design an opto-mechanical scanning system to allow instrument IFOV to be scanned across the surface to build up spatial coverage.

UCL DEPARTMENT OF GEOGRAPHY ii) Need to define the BRDF first as ratio of incremental radiance, dLe, leaving surface through an infinitesimal solid angle in direction Ω(θv, φv), to incremental irradiance, dEi, from illumination direction Ω’(θi, φi) [sr-1]. In practice this is defined over finite area and λ as well i.e. units are [sr-1um-1]. Good answer would give the equation. Then need to explain that BRDF varies with view and sun angle and vegetation structure. General principle is an upward bowl-shape for dense homogeneous veg, volume scattering as a fn of path length through the canopy. Good answer would show this behaviour on angular plot and explain the origin. For shadow-dominated (sparse, clumped) canopies BRDF more like a downward bowl-shape. In this case we might expect hot-spot i.e. peak of reflectance where sun angle and view angle coincide due to minimised shadowing – again, angular plot and the explanation for good answer. Best answer would give some examples of applications, and sensors from which BRDF derived (MODIS being the obvious case).


GEOGG141

Module Title:


Contributor:


P. Lewis


3

EITHER i) Briefly outline the operating principles of discrete return AND full-waveform lidar systems, using

figures were appropriate. (20) ii) Sketch the full-waveform lidar returns that might result from the surfaces and lidar configurations

shown below. You can assume that: in a) and b) the crown height is much larger than footprint diameter (eg 30m trees, < 1m footprint) and the footprint strikes the canopy at or near the apex of the tree crown; in c) the footprint is approximately the same diameter as the width of the scene shown. You should assume that the vertical bin size of all lidar returns is << than the canopy height. Briefly explain in each case the key features of the returns. (45)

a) Small-footprint (<1m).

b) Small-footprint (<1m).

c) Large footprint (eg 30m).

iii) Outline how lidar systems are being used to improve our understanding of forested ecosystems.

(35) OR:

i) The RADAR equation can be stated in terms of received power, 𝑃! at a RADAR antenna as:

𝑃! =𝑃!𝐺!𝜆!𝜎4𝜋 !𝑅!

Define the various terms in the equation and outline the various physical principles that determine the form of the equation. (40)

ii) Describe the principles of RADAR interferometry, using figures wherever possible. Your answer

should discuss issues that might affect the success of interferometric measurements. (60)

UCL DEPARTMENT OF GEOGRAPHY Model Answer: LIDAR question

i) Discrete return is simply time-of-flight of known laser pulse i.e. distance to first return is ct/2 where c is speed of light and t is total time of flight (out and back). Full waveform, pulse is digitised to we get returns from multiple distances depending on target type and vertical resolution of pulse digitisation (bin size). Good answer would show figs of these and mention pros/cons.

ii) Anything along the lines of: a) Small-footprint (<1m).

b) Small-footprint (<1m).

c) Large footprint (eg 30m).

Key points are: a) pick up shape of canopy and hard ground return; b) slower increase in return due to canopy shape and ‘smeared’ ground return due to understory; c) ‘smear’ of ground return particularly (but also canopy) due to the topography i.e. getting returns from the ground on the RHS when still getting canopy returns from LHS of footprint covering whole scene. 15 marks for each case.

iii) Measurement of height and/or structure are the key here. For the first, can be related to biomass via allometric equations allowing most direct estimate of standing biomass from EO. Lack of global coverage so only ICESAT from space, but increasing amounts of airborne surveys. Still suffers problems where very dense & few gaps BUT is direct. A good answer would cover most of this and give some examples of where it has been applied (eg the Saatchi et al. map of global tropics biomass; forest inventory and mapping – very big application). Best answer would mention both the height AND structure information. This is used for eg habitat mapping AND changes eg for deforestation, degradation and even changes in soil height (peat depth). Need some key examples for either/both cases and ideally something on limitations.

RADAR question

i) Terms are: 𝑃!= transmitter power (W); G is gain (a good answer would mention this assumes transmitting and receiving antennae same i.e. bi-static G2); 𝜆 =wavelength (m); 𝜎 =radar scattering cross section; R = range (m). Form arises via considering power output by transmitted, spreading outward per unit solid angle (area of a sphere, in both out and return directions hence 4𝜋 !𝑅!. The


scattering cross section arises out of considering the projected area of the target in both the incident and scattered directions as well as the scattering properties of the surface (i.e. gain of target) in both directions.

ii) Must discuss the concepts of phase difference to resolve distances, baselines, coherence information and phase unwrapping to produce coherence images and then interferograms. Discuss issues of how phase unwrapping works (co-registration, complex multiplication). Good answer would include options such as single pass, repeat pass, and mention missions (eg SRTM, ERS1, 2 etc). Reasons for problems basically come down to decoherence: difference between pairs/passes – atmospheric water vapour, surface changes eg moisture, roughness changes. A very good answer would include at least one applications eg DEM generation; small topographic variations i.e. deformation, subsidence, volcanoes; ice sheet dynamics.


GEOGG141

Module Title:


Contributor:


P. Lewis


4

Question EITHER:

i) Outline THREE types of scattering that occur in the Earth’s atmosphere, giving any possible wavelength and directional dependencies of each scattering type. (30)

ii) Describe ONE method of accounting for the effects of atmospheric scattering on remote sensing data. You should discuss the pros and cons of the method you discuss. (50)

iii) Briefly outline TWO other pre-processing stages that are typically applied to remotely sensed data to convert from raw DN values to quantitative measurements. (20)

OR: You are asked to provide an outline proposal for a new satellite remote sensing system (platform or platforms) that would dramatically improve our ability to quantify deforestation and degradation at 500m scale, focusing only on the tropics. Budget is not initially an issue. Your proposal should carefully consider the mission requirements, and carefully describe the resulting trade-offs that may be required in sensor type(s), wavelength(s), spatial resolution and orbit. (100) Model Answer:

i) 10 marks for each. Rayleigh scattering: (particles << λ) due to dust, soot or some gaseous components (N2, O2). Very strongly inversely wavelength dependent (1/λ4). Some directional dependence, function of scatter number density and distance. Mie scattering: (particles approx. same size as λ), e.g. dust, pollen, water vapour. Strongly directional (backscattering), affects longer λ than Rayleigh, BUT weak dependence on λ, mostly in the lower portions of the atmosphere where larger particles more abundant, dominates when cloud conditions are overcast i.e. large amount of water vapour (mist, cloud, fog) results in almost totally diffuse illumination. Non-selective: (particles >> λ) e.g. water droplets and larger dust particles; all λ affected about equally (hence name), results in fog, mist, clouds etc. appearing white = equal scattering of red, green and blue λs.

ii) Either empirical method such as empirical line correction which requires identifying v dark (eg clear deep water, dense veg) and bright stable targets, dust/desert then assuming L = gain * DN + offset, where offset is atmospheric path radiance. Requires a priori knowledge of ground, and assumes Lambertian surface (no angular effects), large homogeneous areas (ignores adjacency effects) and stability i.e. stays same over time. Also is per-band i.e. assumes same scattering


across whole image. So, ok for narrow swath instruments (eg IKONOS, Landsat) but not for wider swath airborne or moderate res. satellite. Another method would be using full radiative transfer model of the atmosphere such as MODTRAN or 6S. Big advantage is it does the job properly accounting for gaseous absorption, aerosols etc. and can be done per pixel. Down side is slow(er) and requires, ideally, info. on atmospheric properties (aerosol optical depth, ozone and water concentrations, types of aerosol etc). The 6S model is used for operational MODIS products. A third method would be to use multi-angle data as per MISR to actually include the atmosphere in any retrieval process as you get multiple path length estimates and so can solve fo the atmospheric radiance.

iii) 10 marks for each. Could be any two of: radiometric calibration - account for sensor response and non-linearities; radiometric correction – account for striping, dropped lines etc.; geometric correction – accounting for sensor and surface movement by camera modelling and resampling. Good answers would provide a little bit of detail on each method chosen. OR Scope for many types of system. Not limited to current systems and in fact should move beyond this. MUST consider the constraints – tropical, annual sampling (so a few observations a year would suffice) and 1km resolution covering whole tropics so needs to be quite large-scale. ‘Topical’ should immediately suggest optical may be limited so either need several platforms, or even better, a RADAR instrument eg a P-band RADAR that is sensitive to high biomass. The degradation issue means we need to get change, and not just loss, so perhaps an optical + RADAR system . Budget not an issue so could include a lidar as well for the structure degradation e.g. giving spots of 20-50m footprint, waveform data over narrow swaths. To get coverage could have 2 (or more) of them perhaps? And dual wavelength even better (for a very good answer). Wavelengths would need to be, optical 400-2500 for veg properties. A good answer would highlight what’s currently available and so make clear why the proposed system would be better.


GEOGG141

Module Title:


Contributor:


P. Lewis


5

Question

i) Describe THREE key physical properties that affect vegetation reflectance across the 400-2500nm wavelength range. You should use figures wherever possible. (30)

ii) The scalar radiative transfer equation in vegetation can be expressed as 𝜇𝜕𝐼 𝑧,𝛀𝜕𝑧

= −𝜅!𝐼 𝑧,𝛀 + 𝐽! 𝑧,𝛀

Define the various terms in this expression, in particular the two expressions on the right hand side. (30)

iii) Describe TWO things that we need to consider in order to solve this equation for a vegetation canopy. (40)

Model Answer:

i) Good answer MUST include fig. Split into: visible (400-700nm) - chlor. pigments, low reflectance across, higher in the green, all < 10%; NIR (700-1100nm) much higher, due to leaf internal structure (air/cell size/spacing); SWIR (1100-2500) gradually declining with potentially strong abs features at 1400 and 2100 due to water. Could show individual pigments including chlor absorption as for the prospect model.

ii) On LHS, 𝜇 is cosine of the incoming direction vector, 𝛀 with the local normal; 𝐼 𝑧,𝛀 is the incoming specific intensity (or radiance) and so !" !,𝛀

!" expresses rate of change with depth, z in

the canopy. The first term on RHS is the extinction term i.e. negative as is reduction of specific 𝐼 𝑧,𝛀 with depth z in the canopy, modified by volume extinction coefficient 𝜅! which encapsulates how much material intercepted along the path and how absorbing it is. Second term on RHS is the source term i.e. scattered (trans, refl) radiation upward and downward. Really good answer would define it i.e. 𝐽! 𝑧,𝛀 = 𝑃 𝑧,𝛀′ → 𝛀!! 𝐼 𝛀!,𝛀 𝑑𝛀′ where P is vol. scatt. phase fn. and this expresses probability of photon at depth z being scattered from illum direction 𝛀 to view direction 𝛀′.

iii) Any two of: i) description of canopy architecture i.e. depth, leaf area density – simplest case Beer’s Law plane parallel medium (1D), attenuation, but a good answer would suggest limitations of this and then issue of finite leaf size and orientation, and how these might be overcome; ii) description of leaf scattering – simplest Lambertian case, or more complex couple leaf-canopy RT model; iii) description of soil scattering – again, v. simple Lambertian case, or more complex rough soil models (eg Ciernewski, Hapke etc).


GEOGG141

Module Title:


Contributor:

Paul Groves 2nd Marker

Marek Ziebart


6

Question i) Using figures wherever possible, describe how stand-alone GNSS user equipment determines its position in real time. You should make clear the requirements for each component of the system. [40 marks] ii) Explain the effects of the ionosphere on GNSS range measurements, including their possible variation, and give TWO ways in which they can be mitigated in practice. [40 marks] iii) Give three different examples of differential carrier-phase positioning [20] Model Answer: i) A complete answer should include all the following – partial marks for some:

• Should state that the satellites transmit known ranging codes or pseudo-random-noise (PRN) codes to the user.

• Satellites also transmit ephemeris data, from which their positions and velocities may be determined and satellite clock corrections

• Receivers measure the time of arrival of the signals from the satellites. • Receivers determine pseudo-ranges by differencing the measured time of arrival with the time of

transmission obtained from the signal modulation, and then multiplying by the speed of light. Pseudo-range is range perturbed by timing offsets

• A good answer should state that the 3D position and receiver clock offset is determined by solving

simultaneous equations of the form ( ) ( ) clockusersatT

usersat δρρ +−−= rrrr , where ρ is the measured pseudo-range, rsat is the known satellite position, ruser is the user position to be determined and dρclock is the receiver clock offset to be determined. The clock offset is needed because receiver clocks are not synchronised. Alternatively, positioning may be explained in terms of the intersection of the surfaces of spheres (or hyperspheres).

• At least four satellites must be tracked to provide sufficient measurements to determine the 3D position and receiver clock offset.


ii) Full answer covers: • The ionosphere propagation delay/error is due to refraction of the signal as it passes through the

ionosphere. The signal travels more slowly, resulting in a positive range error. • The ionosphere error varies with time of day; it is largest during the afternoon and smallest at night.

This is because solar radiation causes the ionisation of the ionosphere to increase; without it, recombination dominates, so the ionisation decreases. The greater the ionisation, the greater the refraction and hence the greater the delay.

• The ionosphere delay is greater at lower elevations because the signal passes through more ionosphere. It is approximately 3 times bigger at low elevation than at zenith. (A diagram would be good here)

• The ionosphere error is frequency-dependent. • It varies mostly (~99%) as f−2, where f is the frequency. • Using a dual frequency receiver, the ionosphere propagation error can be estimated from the

difference in pseudo-range measured on the two or more frequencies and then used to correct the pseudo-ranges.

For mitigation: • The ionosphere error is spatially correlated, varying slowly as the user location changes. • Differencing ranging measurements made by different receivers within a few hundred kilometres

cancels out most of the ionosphere delay. • Differential positioning uses a reference receiver at a known location, transmitting ranging

measurements or corrections to the “rover” receiver at an unknown location where they are subtracted. (Alternatively, data from both receivers may be stored and differenced in post processing.

iii) Three cases as follows:

• Positioning may be real-time, using a data-link, or post-processed, in which case measurements are stored for processing later.

• Positioning may be static, where the rover is stationary, combining data from many epochs, or kinematic, where the rover is moving, requiring a ‘new’ position every epoch.

• A single base-station may be used, usually owned by the operator of the rover or a network of reference stations may be used, with data supplied by a survey provider. (Virtual reference station and precise point positioning (PPP) are types of network approach).

ρ1

ρ3

ρ2

Single range position locus (sphere)

Three range position solution

Dual range position locus (circle of intersection)


GEOGG141

Module Title:


Contributor:

Jonathan Iliffe 2nd Marker

Marek Ziebart


7

Question i) Explain why a locally defined site grid will often be adopted for a construction project, rather than the officially recognised coordinate reference system for surveying and mapping in the country or region concerned. [25 marks] ii) Explain how you would set about incorporating GNSS data in a global datum such as WGS84 or ETRF89, with utilities and property data in a national coordinate system such as the Ordnance Survey National Grid, into a local site grid. Your answer should make clear what information and/or tools would be required. You should be careful to distinguish between cases where a local site grid has been established by a local survey and cases where it has a defined relationship with a known datum. [75 marks] Model Answer: i) This is basically a discussion of scale factor – expect to see a definition of this. Then explain that by covering a large area a national survey grid leads to distortions of up to around 0.1% for GB – or 1000 ppm. A site grid covers a smaller area, so there is no need for this distortion. A local one has scale factor unity, even over a couple of km. No need for corrections. ii) Could base the answer around the following diagram:


If the local grid is defined by physical monuments and ground survey observations of these, then it is essentially like the CRS10/Engineering datum in the diagram. In that case a satellite datum would act like datum B, and a transformation from GNSS would be carried out by an initial projection into a locally defined system (eg Transverse Mercator with a local central meridian) and then something like a 2D similarity transformation. In practice, done by occupying local points with GPS and then this type of transformation would be worked out “invisibly” to the user. Difficult to do this with national mapping data. If the local grid has a defined datum, there are several ways to do this. Most likely it would be on the same as the satellite datum, in which case it is simply a defined projection – no transformation is necessary, only a conversion. The OS data could be brought in from the OSGB36 datum via GridInquest – that would effectively be a direct step from CRS8 to CRS3, and then it just needs re-projecting. Alternatively the local grid could be something like a true scale one on OSGB36, in which case the above would just need changing around.

Examination Questions & Model Answers (Academic year 2012 ...

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