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Remote sensing and Hydrology. Remote sensing: Measuring environmental variables without any direct contact with a target Measuring strength of electromagnetic radiation Extraction of valuable information from the remote sensing data uses mathematically and statistically based algorithms.

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Remote sensing:

  • Measuring environmental variables without any direct contact with a target
  • Measuring strength of electromagnetic radiation
  • Extraction of valuable information from the remote sensing data uses mathematically and statistically based algorithms.
  • Understand EM radiative transfer
  • Understand sensor characteristics
  • resolution, orbit, etc.

Electromagnetic energy:

EM wave travel through vacuum at speed of light (c = 3 x 108 m/s). There are two field – electric field and magnetic field – intersect at right angle. Both vectors are perpendicular to the direction of wave (wave model)


Wavelength and frequency:


Where c = speed of light

(3.0 x 108 m/s)

λ = wavelength

Longer wavelength has higher frequency


Electromagnetic spectrum:

The Sun, earth or any objects emit a continuous spectrum of energy from gamma rays to radio waves.

Satellite sensors measure EM radiation from visible through microwave range


Strength of energy emitted depends on physical body temperature (-> blackbody radiation curve).

  • Stefan-Boltzmann law
  • -> Determine total energy, f(T)
  • Wein’s displacement law
  • -> Determine dominant λ

Measure of EM radiation

Radiant flux (Φλ) : energy per unit time, unit = [W]

Radiant flux density (Φλ/A) : unit = [W/m2]

Irradiance: incident radiant flux upon a unit area

Exitance: radiant flux leaving from a unit area

Radiance (Lλ) : Irradiance from a certain direction (θ), unit = [W/m2/sr]


Radiation budget equation

the total amount of incident radiant flux in specific wavelengths incident (Φi) must be sum of radiant flux reflected from the surface (Φreflected), the amount of radiant flux absorbed by the surface (Φabsorbed), and the amount of radiant flux transmitted through the surface (Φtransmitted):






Hemispherical Reflectance, Absorptance, and Transmittance

Divide both side of radiation budget equation by incident radiance

Absorptance (emissivity)

Absorptance = emissivity (Kirchhoffs law)



Reflectance is often used for remote sensing analysis

All depend on wavelength and materials



Redirection of EM radiation by hitting small particles

(typically in the atmosphere)

Three types of scattering:

Function of particle size (gas molecule, water vapor) relative to wavelength

For atmosphere

Rayleigh scattering

Particle size is smaller than wavelength

Scattering amount proportional to λ-4

Mie scattering

Particle size roughly equal to wavelength

Scattering amount proportional to λ-1

Nonselective scattering

Particle size is ~10 times larger than λ

Scattering amount not function of λ


Remote sensing sensor

Active vs. Passive

  • Active
  • EM Energy is emitted by a sensor toward target
  • Measure energy reflected by a target
  • e.g. radar
  • Passive
  • Measure EM energy emitted by earth or sun
  • e.g. satellite sensors



Some terminology

Instantaneous field of view (IFOV):

The solid angle over which a measurement is made at any instance. Given the sensor altitude and IFOV, spatial resolutions (linear distance) is determined

Swath width

Width of the strip that can be scanned by the sensor.


Point on the earth just underneath the sensor


B= pixel size

C= altitude


satellite orbit
Satellite orbit

Polar orbit vs. Equatorial orbit

A polar orbit is 90 degree angle of inclination to the equator (passing north and south poles), whereas an equatorial orbit is zero degree angle of inclination to equator.

Sun-synchronous (polar orbit)

A special case of polar orbit. Platform pass the same location at the (roughly) same local time.

Geostationary orbit (equatorial orbit)

A special case of equatorial orbit. Satellite rotate at the same speed of earth rotation. A satellite appears to be still at the sky all the time. A satellite altitude is very high (35850 km)

More info ->

polar orbit satellite
Polar orbit satellite

One rotation

Rotations per day

Advantage is daily global coverageThere are ascending path and descending path


Top view

Side view

Need several satellites to cover the entire earth

sensor resolution
Sensor resolution

Spatial – the size of field of view (pixel size)

Spectral – range of EM spectrum each band of sensor detects

Temporal – frequency of measurements at a certain location

Radiometric – sensitivity of a sensor to difference in EM energy strength

(recording resolution of sensor)

Radiometric: a sensor records EM energy as brightness value (integer)

Conversion from binary to decimal for 2-bit

00 = 0x21 +0x20 = 0

01 = 0x21 +1x20 = 1

10 = 1x21 +0x20 = 2

11 = 1x21 +1x20 = 3










sensor resolution19
Sensor resolution





remote sensing sensor visible thermal
Remote sensing – sensor (visible-thermal)

Landsat TM (Thematic Mapper )

Platform = Landsat 4, 5 (sun-synchronous orbit)

Swath width = 185 km

16 day repeat cycle

More info ->

remote sensing sensor visible thermal21
Remote sensing - sensor (visible-thermal)

Landsat ETM+ (Enhanced Thematic Mapper )

Platform = Landsat 7 (sun-synchronous orbit)

Swath width = 185 km

16 day repeat cycle

More info ->

remote sensing sensor visible thermal22
Remote sensing - sensor (visible-thermal)

AVHRR (Advanced Very High Resolution Radiometer)

Platform = NOAA Polar orbiting Environment satellite

Swath width = 2400 km

Long history since 1979

Daily global coverage (morning and afternoon acquisition)

More info ->

remote sensing sensor visible thermal23
Remote sensing - sensor (visible-thermal)

MODIS (Moderate resolution Imaging Spectroradiometer)

There are 36 bands (0.4 - 14.385 μm) visible to thermal

Platform = EOS Terra and Aqua (Sun-synchronous orbit)

Terra (morning equator-crossing) and Aqua (morning equator-crossing)

Swath width = 2330 km

More info ->

remote sensing sensor passive microwave
Remote sensing – sensor (passive microwave)
  • Can measure precipitation, soil moisture, snowpack volume (SWE, depth), Sea Surface temperature (SST)
  • Not affected by cloud (visible sensor is affected by cloud)
  • Coarse spatial resolution
  • Polarization
  • Electric field component (or magnetic field) of EMenergy can vibrate in any directions perpendicular to the direction of travel. This vibration direction can also evolve with time



Fixed vibration plane

Rotating Vibration plane

Viewed along the travel direction


Brightness temperature (Tb)

Tb value is usually given for passive mircowave data.

Terrestrial matters are not perfect blackbody (graybody).

Total energy emitted by graybody = blackbody radiation (given by plank law)times emissivity (0<ε<1)

Tb is given using emissivity (Tb = ε*T where T: actual physical temperature [K])

Emissivity is function of polarization, frequency, and materials


Rayleigh-Jeans approximation

Plank’s law

Rayleigh-Jeans approximation -> exp(x) ~ 1+x for longer λ

Radiation of graybody is given by

remote sensing sensor passive microwave27
Remote sensing – sensor (passive microwave)

SSM/I (Special Sensor Microwave Imager)

Platform = Defense Meteorological Satellite Program (DMSP)

sun-synchronous orbit

Swath width = 1394 km

Daily global coverage (morning and afternoon acquisition)

More info ->

remote sensing sensor passive microwave28
Remote sensing – sensor (passive microwave)

AMSR (Advanced Microwave Scanning Radiometer)

Platform = EOS (Earth Observing System) Aqua

Swath width = 1445 km

Daily global coverage (morning and afternoon acquisition)

More info ->

application for snow measurement
Application for snow measurement

Use visible – infrared sensors, passive microwave sensor, depending on what needs to be measured

  • Snow cover area (SCA)
    • Pixel level (Snow / no snow per pixel)
    • Subpixel level (percentage of SCA over pixel)
  • Physical properties of snowpack
    • Albedo
    • Grain size
    • Depth (SWE)

Only estimate of depth (SWE) requires passive microwave data

sca algorithm normalized difference snow index
SCA algorithm (Normalized difference snow index)

To discriminate between Snow and cloud


For Landsat TM

Use reflectance

Snow if NDSI >0.4

No snow, otherwise


TM band2

MODIS band4

TM band5

MODIS band6

Snow if NDSI > 0.4 &

Reflectance (band 2) > 11%

No snow, otherwise

sca algorithm subpixel level sca mapping
SCA algorithm (subpixel level SCA mapping)

Linear spectral mixture analysis

Reflectance measured at each band is a linear combination of reflectance from individual surface (endmembers) such as snow, rock, or vege

Rλ: reflectance measured at band of wavelength λ

Rλ,i: reflectance of endmember, i, for band of wavelength λ

Fi : the fraction of endmember, i, over the pixel

M: the number of endmenber

ελ: residual error at wavelength λ

Find F for each endmember with numerical scheme that minimizes the sum of error

Use multispectral sensors (MODIS, AVHRR, Landsat TM) or hyperspectral sensors (better because of more bands)


Subpixel level SCA mapping

Binary SCA mapping

Source: Dozier, J., and T. H. Painter, Multispectral and hyperspectral remote sensing of alpine snow properties, Annual Review of Earth and Planetary Sciences, 32, 465-494

swe or snow depth algorithm
SWE (or snow depth) algorithm
  • Require passive microwave data because EM radiation from shorter wavelength (visible – infrared sensors) cannot penetrate full depth of snowpack, but microwave does.
  • Tb measured over the snow cover is “cold” compared to bare ground because snow grains scatters microwave radiation (Mie scattering)
  • Algorithm to extract SWE from Tb data set is under development
text for remote sensing and useful online
Text for remote sensing and useful online
  • John R. Jensen, Remote Sensing of the Environment:
  • NASA remote sensing tutorial:
  • Natural resources Canada, Earth Sciences Sectors:

Article for remote sensing for hydrology

Engman, T, E. Recent advances in remote sensing in hydrology,

Reviews of Geophysics, VOL. 33, NO. S1, 967-976, 1995.

- general overview of remote sensing application to hydrology, no math, a little old