Remote Sensing Exam 1

What is remote sensing

• The process of detecting and monitoring the physical characteristics of an area measuring its reflected and emitted radiation at a distance

• Special cameras  collect remotely sensed images which helps researchers “sense” things about earth

• remote sensing is acquiring information from a distance

Brief history

• History of remote sensing begins with photography and later aerial photogrammetry and satellite imaging

  • Ex: reconnaissance during WWI and WWII

Satellite remote sensing

• Traced to the early days of the space age

  • Russia v USA

• In 1946, V2 rockets acquired from Germany after WWII were launched to high altitudes from New Mexico

  • These rockets contained automated still or movie cameras that took pics as the vehicle ascended

Rapid development of remote sensing in cold war

The Corona program

a series of American strategic reconnaissance satellites produced and operated by the Central Intelligence Agency (CIA) Directorate of Science & Technology, with substantial assistance from the U.S. Air Force. The CORONA satellites were used for photographic surveillance of the Soviet Union (USSR), China, and other areas beginning in June 1959 and ending in May 1972.

Electromagnetic spectrum

• Satellite instruments utilizes the full range of the spectrum to explore and understanding process occurring here on earth and on other planetary bodies

Remote sensors can  be active or passive

• Passive sensors respond  to external stimuli

  • They record natural energy that is reflected or emitted from the earth’s surface

  • The most common source of radiation detected by passive sensors is reflected sunlight

• In contrast, active sensors use internal stimuli

  to collect data about Earth. For example, a

  laser-beam remote sensing system projects a

  laser onto the surface of Earth and measures the

  time that it takes for the laser to reflect back to

  its sensor

Resolution

plays a role in how data from a sensor can be used. Resolution can vary depending on the satellite’s orbit and sensor design. There are four types of resolution to consider for any dataset: radiometric, spatial, spectral, and temporal

Data Processing, Interpretation, and Quantitative Analysis:

Remote sensing data acquired from instruments aboard satellites require processing before the data are usable by most researchers and applied science users

NDVI

proxy for vegetation photosynthetic greenness

EMR spectrum

• Gamma, x ray, ultraviolet, visible light, infrared, microwaves, radio waves

• Gamma has the highest frequency → radio waves has the lowest frequency

• Wavelength = distance between peaks

  • Gamma has shortest wavelength

Electromagnetic radiation

• used by remote sensing techniques that enable us to measure reflections and emissions from the object of interest

Passive RS

records reflected EMR

Active RS

emits EMR and records the signal that bounced back

For land RS radiation travels through the following paths

atmosphere → surface → atmosphere → sensor (optics, filters, etc)

How is energy transferred

• Energy transferred 3 ways: conduction, convection, radiation (radiation is used by RS)

• Energy transmitted as electromagnetic waves (eg from sun to earth) 

  • Light, sunlight, radiation, radiant energy are all EMR

Wave model of electromagnetic radiation

In 1860, model of EMR as electromagnetic wave travelling at the speed of light

Electromagnetic wave

• electric and magnetic fluctuating orthogonal fields, perpendicular to the direction of travel

• Wavelength (lambda) = distance between crests (or troughs) [m]

• Frequency (v, pronounced as new): number of crests that pass a point per unit time - one crest every second has a frequency of one hertz [Hz]

• The range of wavelengths are referred to as the electromagnetic spectrum

The relationship between these is given by (c is the speed of light [m/s]: 

• c = lambda(v)

• v = c/lamdba

• Lambda = c/v

lambda = wavelength, v = frequency

The longer the wavelength, the lower the frequency and vice versa

• Longer lambda, lower v

• Shorter lambda, higher v

• Because c is constant

Ex: the average of visible light wavelength is 0.5x10^-6m, what is the frequency

• v = c/lambda

• 3x10^8 /(0.5x10^-6) = 6x10^14

Particle model of EMR

• Until 1905, radiation was thought of as a smooth continuous wave

• However, einstein’s observations did not fit the wave model

  • Einstein: radiation behaves as if composed of many individual packets called photons (aka light quanta)

• Einstein described electromagnetic energy as a wave and as a discrete packets of energy (or photons/light quanta)

• In the early 1900s, Planck described interactions of energy and matter. Thus quantum mechanics (also quantum theory or quantum physics) was proposed

the particle or energy carrier is called a photon, and each photon carries energy [in joules]

• q = h(v) = h(c/lambda)

• Where h = 6.62607015 x 10^-34 JHz^-1 is Planck's constant and energy (q) is expressed as joules [J]

• Since h is constant, the higher frequency (v), the more energy the photon has

• The shorter the wavelength, the more energy the photon has

Why do UV and not radio waves cause sunburn

• UV has shorter wavelengths and higher frequency and higher energy per quantum 

• The energy of UV per quanta is 10^-17/10^-27 = 10^10 = 100 billion times the energy as radio wave per quanta

Electromagnetic radiation energy

• Five elements to describe EMR

  • Total energy (joules)

  • Time (per second)

  • Area (per m2)

  • Direction (per Sr)

  • Frequency (per hz)

The total energy (Q) in a beam or ray is a function of the number (ni) and spectral makeup of the photons (vi) as follows

Q = sum of qi = sum of nihv

More convenient to think of a beam or bundle of rays not in terms of the total energy but rather in terms of

the rate at which the energy is passing or propagating

This rate of flow of energy is called the radiant flux, or power

and is defined as the first derivative of the radiant energy with respect to time (f) ie

Radiant flux

the energy received by a surface (no area info) per unit time

Often we are interested in the rate at which the radiant flux is delivered to a finite surface area (eg the responsive surface of a detector, such as the satellite sensor

This concept is given the term irradiance (E) and is defined as

Irradiance

the energy received by a surface per unit time per unit area

a concept called radiant emittance (M) or existence. It has the same unit as irradiance

Existence is the energy emitted by a surface per unit time per unit area

To describe the position of an object with respect to the earth (eg the location of a satellite/sun in the sky), we often use the spherical coordinate system

• Radial distance = r

• Polar angle = (theta)

  • Angle between z axis and point of interest

• Azimuthal angle = Angle between projection of point of interest to x axis

steradian

• the element of solid angle

  • The element of solid angle is defined as the conic angle encompassing the area element dA on the surface of a sphere of radius r and theta and phi are generic orientation angles

radiant intensity (I)

The term used to describe directional or dispersive information about the flux. Radiant intensity describes the flux per unit solid angle emitted from a point source in a particular direction

While the intensity (I) provides directional information

• it does not provide any spatial information

Radiance def

the energy received by a surface per unit time per unit projected area per unit solid angle

Spectral irradiance

• the irradiance of a surface per unit frequency (Wm^-2 Hz^-1)

Spectral intensity

• the intensity of a surface per unit frequency (WSr^-1Hz^-1)

Spectral radiance

the radiance of a surface per unit frequency

Electromagnetic radiation energy for sensors

• Satellite sensors detect radiant flux at specific wavelengths, leaving the projected source area from a particular direction and angle [Wm^-2Sr^-1Hz^-1]

Angle

• ratio of subtended arc length on circle to radius

  • Theta = l/r = length of arc/radius

  • Circle has 2pi radians

Solid angle

• ratio of subtended area on sphere to radius square

  • Omega = A/r^2

  • Sphere has 4pi radians

Source of Electromagnetic energy in the solar system

• Nuclear fusion on sun surface → a continuous spectrum of EMR emitted (all wavelengths ie visible light, gamma, etc)

• Some intercepted by earth when it interacts with the atmosphere and the surface

• Earth reflects energy back into space or absorbs it to reemit at longer wavelengths

Blackbody radiators

A blackbody is an idealised surface or cavity that has the property that all incident electromagnetic flux is perfectly absorbed and then reradiated (ie the reflectivity is zero and absorptivity is one)

Spectral exitance is a function of both temperature and wavelength

• By holding temperature fixed at selected values, a family of blackbody curves can be generated as shown relating spectral irradiance to wavelength

• These curves show

  • How the exitance increases with temperature

  • And peak values shifts to shorter wavelengths as the temperature increases

Stefan boltzmann law

By integrating the planck equation over all wavelengths, it yields the stefan-boltzmann equation

Stefan-boltzmann equation

total amount of energy emitted by a blackbody varies with the fourth power of temperature

How much solar energy reaches the top of the atmosphere of Earth?

Wien’s displacement law

Another fundamental natural law can be derived from the planck equation by taking the first derivative with respect to wavelength and setting it equal to zero

Note: in calc, this always means to get the max or min value of the function of interest. In the planck equation case, it is the max

Solar radiation spectrum

• Sun produces 42% of its energy in the visible region 0.4-0.7 m(blue to red light)

• The rest of energy is in wavelengths shorter than blue (<0.4m) and longer than red (>0.7m)

• Remote sensors can be made sensitive to energy in the nonvisible regions of the spectrum (and often are!)

Emissivity

• In practice, there is no perfect blackbody

• To describe this phenomenon we introduce the concept of emissivity, defined as the ratio of the spectral exitance M_lambda(T)from an object at tempeeratire T to the spectral exitance from a blackbody at the same temperature

The emissivity describes

• how well an object radiates energy compared to the perfect blackbody radiator and is a unitless value with a range from 0 to 1

selective radiators

Objects whose emissivity is approximately constant with wavelength are referred to as gray bodies, while objects with spectrally varying emissivities

Objects that approximate gray body radiators over all or part of the spectrum are often

approximated by a black body that would produce equivalent irradiance

EMR in the atmosphere

• Unlike vacuum, the atmosphere may affect the radiation’s speed, wavelength, intensity, spectral distribution, and/or direction

• This happens by scattering or absorption in the atmosphere

  • Note that scattering can be divided into two casesL transmission and reflection

• Important for understanding surface and radiation interactions

Transmissivity

the ability of the material to allow the flux to propagate through it, denoted as transmittance 𝝉

reflectivity

• the ability of the material to turn incident flux back into the hemisphere above the material, denoted as reflectance r

absorptivity

the ability of the material to remove electromagnetic flux

from the system by converting incident flux to another form of energy, denoted as

absorptance, 𝜶

Due to energy conservation Transmissivity, reflectivity, and absorptivity must follow

𝝉 + 𝒓+ 𝜶 =1

Kirchoff's law states that

the emissivity must be numerically equal to the absorptance for surfaces in thermodynamic equilibrium

𝜺 = 𝜶

Scattering

unpredictable direction, function of lambda and size of atmospheric matter

Rayleigh scattering

• Gas molecule

• Small

• The result of EM wave interacting with very small particles or molecules. It occurs when the particles are much smaller than the wavelength of the incident flux

Mie scattering

• Smoke, dust

• Medium

• When the wavelength of the energy is approx equal to the size of the particles. Aerosols, small dust particles, fossil fuel combustion products, and suspended sea salts are some of the major atmospheric constituents in this size range

Nonselective scattering

• Water vapor

• Large

applies when the particles are very large compared to the wavelength of the incident energy. Large dust particles, water droplets, and ice crystals are sources of nonselective scattering

Rayleigh's law of scattering

• amount of scattering inverse to 1/lambda^4

  • The shorter the wavelength, the more EMR is scattered

  • Wavelength will not be changed by rayleigh scattering

Why is the sky blue

• Blue is the shortest wavelength in the visible band And is efficiently scattered during the day

Why is sunset red

When the sun angle is low, sunlight passes through more atmosphere during sunset/rise before reaching us - much violet and blue light is scattered away – and mostly the red light remains and reaches our eyes

more than 99% of the blue light received by satellite sensors are scattered light

Bad impact for remote sensing, atmosphere correction aims at removing the rayleigh scatter in images

Reflection

• There are various types of reflecting surfaces

  • Specular reflection: radiation is reflected off smooth surface

    • Water bodies, snow/ice, man made roofs

  • Diffused reflection; radiation reflected off rough surface and reflected in many directions

    • Forest canopy

The perfect reflection

• Lambert defined a perfectly diffuse surface called Lambertian surface

• Reflected radiation from a lambertian surface is a constant for any incidence angle, that is the radiance from a lambertian surface is the same in all directions

Characteristics of lambertian surfaces - the magic pi

• For a lambertian surface the radiance and exitance (or irradiance) are related by a factor of pi. This relationship is derived by rigorous mathematical derivations

  • L = E/pi

• For example if we assume a blackbody is lambertian radiator, the planck equation can be expressed in terms of spectral radiance as

Why clouds and fog banks appear white

• Non selective scattering: a mixture of all colors of light in approximately equal quantities produces white

Reflectance spectra

Reflectance spectra of three common surface materials (vegetation, soil, and water) measured by a hyperspectral sensor in comparison with the broad multispectral bands of landsat-7

Reflectance spectra application

• Range of -1 to 1

• Closer to 1 means more vegetation/green-ness

BRF, BRDF:

Incident energy is a beam in one direction, and reflected energy is also in one direction

HDRF

• incidence comes from all different angles (coming from the hemisphere, hemispherical), the reflected energy is one direction

DHR

incidence is one direction, reflection is in all directions

BHR

incidence is all directions, reflected is all directions

Recall Electromagnetic Radiation Energy

Bidirectional reflectance distribution function (BRDF)

The surface bidirectional reflectance distribution function (BRDF) describes the scattering of a parallel beam of incident light from one direction in the hemisphere to another direction in the hemisphere

Bidirectional reflectance factor

The BRF is defined as the ratio of the reflected flux from the surface area in a particular direction to the reflected flux from an ideal surface (ie nonabsorbing and nontransmitting lambertian surface) of the same area and under the same conditions of geometry and single directional illuminations is the reflected flux

• In MODIS and VIIRS reflectance data, you will always see BRF

• Surface BRF is interchangeable with surface reflection. It requires "atmospheric correction” to obtain surface BRF

• BRF is used as the inputs of many satellite products, eg land cover type, NDVI, leaf area index etc

Hemispherical directional reflectance factor (HDRF)

Similar in definition to BRF expect that illuminations is allowed from the entire upper hemisphere

Directional hemispherical reflectance (DHR)

Refers to the special case of illumination from a collimated beam. It is the ratio of the flux for light reflected by a surface area into a hemisphere to the illumination flux when the target is illuminated with a parallel beam of light only from the direction theta sub i

Black sky albedo

• The DHR is sometimes referred to as the black sky albedo (BSA)

• It is the albedo that would be expected for collimated beam irradiance only, with no diffuse radiation - thus the black sky designation

• In a satellite product what does it mean for black sky albedo

Bi hemispherical reflectance or albedo

The albedo or bi-hemispherical reflectance (BHR) is the ratio of the flux ΦC of light reflected from surface area dS into a hemisphere to theincident flux ΦD, when the area is illuminated by an arbitrary radiation field, 𝐿D, hemispherical in angular extent.

White sky albedo

Since 𝐴_BHR generally depends on the incident illumination 𝐿D, this quantity is not just a function of the intrinsic scattering properties of the surface. However, for the special case when 𝑳𝒊 is isotropic, 𝐴_BHR then becomes a function of the surface scattering properties only. This case is sometimes called “the white sky albedo” (WSA).

These adjectives “black” and “white” are not related to the color of the sky, but rather theangular distribution of light intensity. In the field, the closest approximation to this casehappens under a deep cloud deck that may generate (recall the non-selective scattering),at its base, an almost isotropic diffuse downward radiation field.

Does white sky albedo reflect the real world case

yes

The BRDF effect

Refers to that reflectance from a surface depends upon the direction of the incident radiation (and its characteristics), the surface radiative properties, and the direction from which the surface is being viewed

BRF, HDRF, DHR, and BHR are

unitless

Atmospheric absorption

Radiation is absorbed by the atmosphere and could be reradiated at other wavelengths

Absorption band

Wavelength interval where radiation is absorbed

Absorption

Bad for remote sensing because no/less energy is available to be sensed

Atmospheric window

The EMR region with limited or almost no absorption by the atmosphere are known as the atmospheric window

Why do the thermal bands have coarser resolution(s)

Low frequency and long wavelength means less energy per quanta. Need broader bands and larger area per footprint to gain sufficient energy for the sensors to detect

Astronomical unit

• The astronomical unit (AU) is a unit of length, roughly the distance from the earth to the sun and approximately equal to 150 million kilometers or 8.3 light minutes

• The actual distance from earth to the sun varies by about 3% as earth orbits the sun, from a max (aphelion) to a min (perihelion) and back again once each year

The astronomical unit was originally conceived as the average of Earth’s aphelion and perihelion; however, since 2012 it has been defined as exactly 1.495978707 x 10^11 m

Astronomical almanac

The earth’s orbit is an ellipse around the sun with the sun at one of the foci. Thus sun earth distance varies throughout the year (about 3%)

The Astronomical Almanac is an almanac published by the United States Naval Observatory (USNO) and His Majesty's Nautical Almanac Office (HMNAO). It provides tables of the daily earth-sun distance (“true geocentric distance”) in au.

Julian date

• The julian date (JD) of any instant is the Julian day number plus the fraction of a day since the preceding noon in universal time (UT)

• Julian dates are expressed as julian day number with a decimal fraction added

• The Julian date records the interval of time in mean solar days and fractions of a day since 12:00 UT Jan 1, 4713 B.C.

E.g, Noon UT on Aug 30, 2023, has Julian date 2460187.0

Day of year

• DOY counts the day number since january 1 of the year of interest

• Many remote sensing data’s naming system use DOY as one of their key information

Geographic coordinate system (GCS) and longitude and latitude

• The GCS is a spherical or geodetic coordinate system for measuring and communicating positions directly on earth as latitude and longitude

• Latitude, or angular distance away from the equator, is marked by parallels. By convention, north latitude is considered positive, and south is negative

• Longitude is marked by meridians. It indicates angular distance away from a reference meridian at Greenwich, England now called prime/ephemeris meridian. By convention, east is positive and west are negative

Subsolar point

• The location on the globe of the single point at which the sun is directly overhead

• The solar longitude, which is the longitude of the subsolar point, varies with the time of day due to the earth’s rotation in a day

• The latitude of the subsolar point, which is also referred to as the sun’s declination, varies with the seasons from about 23.44 S to 23.44 N

An equinox occurs when the declination is 0º that day (~ March 21 and ~September 22).