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physics
physical principles remote sensing
Questions and Answers of
Physical Principles Remote Sensing
The Planck formula can be inverted to obtain the brightness temperature from the spectral radiance as follows: Show that, for observations at a wavelength of 10.7 ?m, K1 and K2 have values of 851 W
Show that the amplitude of fully developed speckle has a Rayleigh distribution. Assume that the signal is composed of a very large number of components, each of which has the same amplitude but a
If the atmospheric microwave absorption coefficient γ varies with height z as γ = Ï Î²exp (-βz), Ï being the optical thickness of
The NASA Team algorithm for calculating sea-ice concentration from SSM/I data defines the polarisation ratio PR asand thegradient ratioGR aswhere, in both of these expressions,TfP represents the
ASAR operates at a frequencyof 5.3GHz. Its satellite platformis 775kmabove the Earth’s surface and has a speed relative to the surface of 6.73 kms-1. The swath width is 100 kmand the incidence
Identify the nature of the spatial filters whose kernels are given below:(i) (ii)
(i) Estimate appropriate values, corresponding to those in Table 11.1, for printed paper as a data storage medium. (ii) Estimate the potential data storage requirements from a 5-year spaceborne
Use the data of Table 7.1 to show that the effective area of a rectangular or circular paraboloidal antenna is roughly equal to its geometrical area.Table 7.1 HPBW (degrees) D (dB) Antenna type
A laser profiler is operated at a wavelength of 1μm from an altitude of 10000 m, and views at 45° to the nadir. Estimate the range corrections needed to account for the dry atmosphere and the water
An airborne scanning laser profiler transmits pulses at a frequency f0. Its field of view is scanned in a direction perpendicular to the aircrafts velocity through an angle
Explain how it is possible for the horizontal resolution of a radar altimeter to exceed the limit set by diffraction at the antenna, provided that the pulse duration tpis short enough, and derive the
A radar altimeter emits a pulse whose variation of power with time is Gaussian with a length of 3.00 ns between 1/e points. The pulse is reflected from a surface whose height distribution is Gaussian
Prove Equation (8.16).Equation 8.16 dP, P,(t+2(h – H)/c)f(h)dh dt 0-
For microwave radiation propagating vertically through the Earths atmosphere, the delay to a pulse as a result of the dry component of the atmosphere, expressed as an equivalent distance,
A chirp signal, in which the angular frequency rises uniformly from Ï0ÎÏ/2 to Ï0+ ÎÏ/2 over a time T, can be written as
A radar transmits a power of 4 kW at a wavelength of 5 cm and over a range of 800 km. If the radar can detect a received signal of 10 - 16 W, calculate the required gain of the antenna, and hence
A very simplified model of the radar back scattering coefficient of a sea surface is σ0 = A + Bcos 2ψ where ψ is the angle between the wind direction and the radar look azimuth, and A and B are as
A SAR operates at a wavelength of 6 cm and is used for interferometric SAR observations. In position M, the radar has (x, y) coordinates (-400000, +800000) m, while in position S its coordinates are
Prove Equations (10.2) to (10.5).Equation 10.2Equation 10.3Equation 10.4Equation 10.5 Av = 2GM RE R GM Av
Consider a satellite in orbit about a spherically symmetric planet. If the orbit is circular, the sub-satellite point travels uniformly along its circular track. If the orbit is not circular,
A satellite is in a circular sun-synchronous orbit with an inclination of 98.2°. It makes exactly 233 orbits of the Earth in exactly 16 days, and crosses the equator southbound at 0930h local time.
The nodal period of a satellite in a circular orbit of radius a and inclination i about the Earth is given by
The satellite Jason is in a circular orbit with a semimajor axis of 7714 km and an inclination of 66°.(i) Show that this orbit is suitable for altimetry.(ii) Comment on the suitability of the orbit
How many uniformly spaced geostationary satellites would be needed to ensure that all points on the Earth’s surface with latitudes less than 66.5° can be seen at an elevation angle of at least
A single band of an image has a histogram with a Gaussian distribution of standard deviations. Show that the theoretical limit to which the data can be compressed using Huffman coding is
(i) Show that if A, S and E are, respectively, isotropic smoothing (averaging), sharpening (high-boost) and edge-detection (high-pass) filters described in the spatial domain, and I is the identity
The relationship between spectral radiance Lλand brightness temperature T in a thermal infrared band of a satellite sensor can be expressed asFor band 6 of the Landsat-7 ETM +
A passive microwave radiometer operating at 37 GHz has an effective area of 0.3 m2, and can detect a change of 0.9 K in its antenna temperature. It is operated from an altitude of 800 km to observe a
At 10 GHz and a certain incidence angle, the apparent brightness temperatures of sea water, first-year ice and multi-year ice are 80 K, 252 K and 200 K respectively. At 37 GHz these figures become
A phased array is designed to operate at a wavelength of 6 cm. The antenna elements are spaced at intervals of 4 cm. (i) Show that if the beam is steered more than 30° away from the normal (θ
Verify the solution given in the text for the two-stream scattering model.
The cross-section of a glass prism is an equilateral triangle. The refractive index of the glass is 1.601 at a free-space wavelength of 0.4 μm and 1.569 at 0.7 μm. Show that if white light is
Sunlight is incident on a rough surface at an angle of 450 to the normal. Calculate the brightness temperature of the surface at wavelengths of 4 μm and 10 μm, assuming that the surface is a
Derive Equations (6.12) and (6.13).Equation 6.12Equation 6.13 F = Fo cos(ot – zVoCp/2K) exp(-zVoCp/2K) Fo |T = cos(ot — zVоСр/2K — п/4) еxp(-?VоСp/2K).
A two-look TIR radiometer views the same point on the Earths surface at nadir and at 60 degrees from nadir. The brightness temperature of the detected radiation is T1and T2respectively.
The output of the band 6 sensor of the Landsat-7 ETM + instrument, as represented by an integer pixel value in an image, is the nearest integer to 16.03(L + 3.2) + 1, where L is the at-satellite
A surface shows daily temperature fluctuations with amplitude 23 K, lagging 2.3 hours behind the fluctuations in incoming solar radiation. Use the model of thermal inertia developed in this chapter
Assume that the atmospheric absorption coefficient γ varies with height h asand use the simple model of limb-sounding geometry derived in Section 6.7.4 to show that the reduction in
Show that Doppler broadening will dominate over pressure broadening of a spectral line for a gas at temperature T and pressure p provided that the wavelength of the spectral line is less than kT/pσ,
The attenuation coefficient of a typical tropospheric aerosol is 0.1 km-1 at sea level, and the total optical thickness of the aerosol for a vertical path through the atmosphere is 0.2. By assuming
Estimate the illuminance at the Earths surface due to solar illumination when the Sun is 450above the horizon. Use Equation (5.1), but approximate the function V(λ) shown in
A vertical aerial photograph reveals a tall building. The foot of one corner of the building has (x, y) coordinates (30.5, 62.0) (both measured in mm from the lower left-hand corner of the negative),
Show that Equation (2.31) can be approximated by Equation (2.33) at sufficiently low frequencies. exp(x) ≈ 1 + x when |x| << 1.
Show that the real and imaginary parts of the refractive index of a non-magnetic material are given by
A commonly used approximation to the absorption length is
Sea water has an electrical conductivity σ of typically about 4 S m-1. The real part of its dielectric constant at radio frequencies of 100 MHz and below is 88.2. By assuming that the imaginary part
Randomly polarised radiation at a wavelength of 3 cm is incident on a plane water surface at an angle of 83o to the normal. Calculate the Stokes vector, and hence polarisation state, of the
Show that the diffuse albedo for specular reflection of perpendicularly polarised radiationand confirm that this expression has the correct limiting forms as the refractive index n tends to 1 and to
A rough surface has a BRDF proportional to cos(θ0)cos(θ1), where θ0 and θ1 are respectively the angles of the incident and scattered radiation measured from the surface normal. The BRDF has no
Consider scattering form a surface with r.m.s. height variation of λ/2, where λ is the wavelength. Show that the stationary phase model can describe this scattering provided that the incident angle
A typical pack of freshly fallen snow has a density of 100 kg m-3 and consists of ice crystals which can be modelled as spheres of radius 0.5 mm. Show that if the snow pack is sufficiently deep it
Prove Equation 3.29.vvg = c2,
According to the Minnaert model of surface scattering, the BRDF R is given bywhere A and a are constants; θ0 and θ1 are the angles between the incident and scattered rays,
If scattering is insignificant, show that the radiative transfer equation may be written asand if hf = kT this can be rewritten asBy comparing these two equations, show thatExplain its significance.
The absorption cross-section at 20 GHz of a water droplet with a radius of 48 μm is about 2 × 10-11 m2. Hence calculate the absorption coefficient of a cloud consisting of droplets of radius 48 μm
Assuming that the temperature T of the troposphere is given by the expression T = 288 - 0.0065z, where T is measured in kelvin and z is the altitude in meters, and that the pressure p in kPa is given
The meteorological visibility in fog is defined as the distance that gives an optical thickness of 4. If a typical fog has a mass density of 10-3 kg water per cubic metre and gives a visibility of
A typical 35-mm camera with a standard lens and normal outdoor film can be assumed to have the following parameters: focal length f = 50 mm; spatial resolution l = 40 lp/mm; film format w = 25 x 35
Use Equation (4.12) to show that, at low microwave frequencies, the absorption coefficient of a cloud of water droplets is given approximately by(i.e. independent of the droplet size), where ris the
Use the data of Table 4.3 to estimate the effective raindrop radius, number density and sedimentation rate for rain rates of 1 and 100 mm/hr, assuming that all the drops are spherical and have the
An aerial photographic system is used for stereophotography. The film negative is a square of sides, the focal length is f, the baseline is band the photographs (which are acquired with the camera
Show that the Fourier transform of the Gaussian functionis proportional toand interpret the result. - ю) f(1) = exp – 202 ioto o?o² exp 2
Calculate the ratio of the spectral radiances of black bodies at 300 K and 6000 K at (i) A wavelength of 0.1 μm, (ii) A wavelength of 1 μm, (iii) A frequency of 1000 GHz, (iv) A
When radiation having a Stokes vector S = [S0, S1, S2, S3] is incident on an antenna that receives only linearly x-polarised radiation, the detected power is proportional to S.P, where P = [1,1,0,0].
The electric field of an electromagnetic wave in free space is given byEx = 0Ey = Ecos(ωt - kx)Ez = 2Esin(ωt - kx)where E = 1 kVm-1. Find (i) the direction of propagation,(ii) the