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Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 1 Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR.

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Presentation on theme: "Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 1 Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR."— Presentation transcript:

1 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 1 Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements - Tobias Otto

2 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 2 Content the active remote sensing equation derivation of the radar equation derivation of the lidar equation how to apply the active remote sensing equation for calibration system performance analysis

3 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 3 The Active Remote Sensing Equation is an analytical expression for the power received by an active remote sensing system, i.e. RADAR, LIDAR or SODAR (RAdio / LIght / SOnic Detection and Ranging) merges all the knowledge about the system (relevant system parameters), the propagation path, and the targets that are remotely sensed is frequently applied for active remote sensing instrument: design and performance analysis, calibration, conversion of the received power into a meaningful measurement, i.e. an observable that ideally solely depends on the targets itself

4 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 4 The Active Remote Sensing Equation active remote system target active remote sensing system constant range dependent measurement geometry target characteristics (backward-scattering) transmission term (attenuation) range mean received power

5 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 5 Content active remote sensing equation derivation of the radar equation derivation of the lidar equation how to apply the active remote sensing equation for calibration system performance analysis

6 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 6 Radar Equation for a Point Target PtPt PrPr GtGt GrGr transmitter receiver antennaerange R target σ P t.. transmitted power (W) G t.. antenna gain on transmit R.. range (m) σ.. radar cross section (m 2 ) G r.. antenna gain on receive P r.. received power (W) backscattered power density at receiving antenna isotropic antenna power density incident on the target effective area / aperture of the receiving antenna

7 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 7 Radar Equation for a Point Target PtPt PrPr GtGt GrGr transmitter receiver antennaerange R target σ P t.. transmitted power (W) G t.. antenna gain on transmit R.. range (m) σ.. radar cross section (m 2 ) G r.. antenna gain on receive P r.. received power (W) radar constant target characteristics free-space propagation

8 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 8 From Point to Volume Targets -the radar equation for a point target needs to be customised and expanded to fit the needs of each radar application (e.g. moving target indication, synthetic aperture radar, and also meterological radar) -active remote sensing instruments have a limited spatial resolution, they do not observe single targets (raindrops, ice crystals etc.), instead they always measure a volume filled with a lot of targets volume target (distributed target) instead of a point target -to account for this, the radar cross section is replaced with the sum of the radar cross sections of all scatterers in the resolution volume V (range-bin):

9 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 9 Radar Resolution range R range resolution volume (range-bin) c..speed of light B..bandwidth of the transmitted signal ( the bandwith of a rectangular pulse is the inverse its duration B=1/ τ ) Δr is typically between 3m - 300m, and the antenna beam-width is between 0.5° - 2° for weather radars θ antenna beam-width

10 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 10 Range Resolution of a pulsed Active Remote Sensing Instrument

11 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 11 Range Resolution of a pulsed Active Remote Sensing Instrument e.g. pulse duration 1 µs 300 m f0f0

12 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 12 Range Resolution of a pulsed Active Remote Sensing Instrument target 1 response target 2 response target 3 response Now we sample the backscattered signal. each sample consists of the sum of the backscattered signals of a volume with the length c·τ/2 for a pulsed active remote sensing instrument, the optimum sampling rate of the backscattered signal is 2/τ (Hz)

13 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 13 Radar Equation for Volume Targets R θ/2 r tan(α) α (rad) for small α 2 volume reduction factor due to Gaussian antenna beam pattern

14 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 14 Isotropic Scattering Cross Section σ P backscattered S incident.. backscattered power (W).. incident power density (Wm -2 ) Depends on: -frequency and polarisation of the electromagnetic wave -scattering geometry / angle -electromagnetic properties of the scatterer -target shape hydrometeors can be approximated as spheres

15 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 15 Isotropic Scattering Cross Section σ Monostatic isotropic scattering cross section of a conducting (metallic) sphere: a.. radius of the sphere.. wavelength Rayleigh region: a << Resonance / Mie region: Optical region: a >> Figure: D. Pozar, Microwave Engineering, 2 nd edition, Wiley. normalised radar cross section electrical size

16 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 16 Radar Cross Section σ hydrometeors are small compared to the wavelengths used in weather radar observations: weather radar wavelength 10cm max. 6mm raindrop diameter Rayleigh scattering approximation can be applied; radar cross section for dielectric spheres: D |K| 2..hydrometeor diameter.. radar wavelength.. dielectric factor depending on the material of the scatterer

17 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 17 Radar Equation for Weather Radar radar constantradar reflectivity factor z, solely a property of the observed precipitation

18 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 18 Radar Reflectivity Factor z spans over a large range; to compress it into a smaller range of numbers, engineers prefer a logarithmic scale 1 m 3 one raindrop D = 1mm equivalent to 1mm 6 m -3 = 0 dBZ raindrop diameter#/m 3 Zwater volume per cubic meter 1 mm dBZ mm 3 4 mm136 dBZ33.5 mm 3 Knowing the reflectivity alone does not help too much. It is also important to know the drop size distribution.

19 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 19 Raindrop-Size Distribution N(D) where N(D) is the raindrop-size distribution that tells us how many drops of each diameter D are contained in a unit volume, i.e. 1m 3. Often, the raindrop-size distribution is assumed to be exponential: concentration (m -3 mm -1 ) slope parameter (mm -1 ) Marshall and Palmer (1948): N 0 = 8000 m -3 mm -1 Λ= 4.1·R with the rainfall rate R (mm/h)

20 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 20 Reflectivity – Rainfall Rate Relations reflectivity (mm 6 m -3 ) liquid water content (mm 3 m -3 ) rainfall rate (mm h -1 ) the reflectivity measured by weather radars can be related to the liquid water content as well as to the rainfall rate: power-law relationship the coefficients a and b vary due to changes in the raindrop-size distribution or in the terminal fall velocity. Often used as a first approximation is a = 200 and b = 1.6 terminal fall velocity raindrop volume

21 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 21 Summary of the assumptions in the radar equation In the derivation of the radar equation for weather radars, the following assumptions are implied: the hydrometeors are homogeneously distributed within the range-bin the hydrometeors are dielectric spheres made up of the same material with diameters small compared to the radar wavelength multiple scattering among the hydrometeors is negligible incoherent scattering (hydrometeors exhibit random motion) the main-lobe of the radar antenna beam pattern can be approximated by a Gaussian function far-field of the radar antenna, using linear polarisation so far, we neglected the transmission term (attenuation)

22 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 22 Content active remote sensing equation derivation of the radar equation derivation of the lidar equation how to apply the active remote sensing equation for calibration system performance analysis

23 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 23 Lidar Equation for Volume Targets laser laser beam receiver field of view telescope area receiver P r.. received power (W) P t.. transmitted power (W) A L.. laser beam cross section (m 2 ) c.. speed of light (ms -1 ) τ.. temporal pulse length (s) R.. range (m) σ.. isotropic scattering cross section (m 2 ) A.. area of the primary receiver optics (m 2 ) backscattered power density at the telescope power density incident on the target telescope aperture

24 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 24 Lidar Equation for Volume Targets laser laser beam receiver field of view telescope area receiver P r.. received power (W) P t.. transmitted power (W) A L.. laser beam cross section (m 2 ) c.. speed of light (ms -1 ) τ.. temporal pulse length (s) R.. range (m) σ.. isotropic scattering cross section (m 2 ) A.. area of the primary receiver optics (m 2 ) η.. receiver efficiency (how many of the incoming photons are detected) O(R).. receiver-field-of-view overlap function T(R).. transmission term (attenuation)

25 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 25 Lidar Equation for Volume Targets laser laser beam receiver field of view telescope area receiver

26 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 26 Lidar Equation for Volume Targets laser laser beam receiver field of view telescope area receiver with the backscatter coefficient β (m -1 sr -1 ): number concentration differential scattering cross section (m 2 sr -1 ) π indicating scattering in the backward direction

27 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 27 Lidar Equation for Volume Targets backscatter coefficient transmission term (attenuation) lidar system constant range dependent measurement geometry Both the backscatter coefficient and the transmission term (attenuation) contain significant contributions from molecular scattering (gases like oxygen, nitrogen) Rayleigh scattering and particle scattering (liquid and solid air pollution particles such as sulfates, mineral dust, sea-salt, pollen but also larger hydrometeors as rain, ice, hail and graupel) resonance or optical scattering Difficult to differentiate with power measurements only.

28 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 28 Summary: Radar and Lidar Equation active remote system target C active remote sensing system constant M(R) range dependent measurement geometry B(R) target characteristics T(R) transmission term (attenuation) monostatic, i.e. co-located transmitter and receiver Radar equation for volume targets Lidar equation for volume targets

29 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 29 Summary: Radar and Lidar Equation Radar: Radar observations of the atmosphere mainly contain contributions from hydrometeors which are Rayleigh scatterers at radar frequencies. This allows the definition of the reflectivity z, a parameter that is only dependent on the hydrometeor microphysics and independent on the radar wavelength, i.e. the reflectivity within the same radar resolution volume measured by different radars should be equal Lidar: Both the backscatter coefficient β and the transmission term T contain significant contributions from molecular scattering (gases like oxygen, nitrogen) Rayleigh scattering and particle scattering (liquid and solid air pollution particles such as sulfates, mineral dust, sea-salt, pollen but also larger hydrometeors as rain, ice, hail and graupel) resonance or optical scattering Lidar measurements of the atmosphere comprise contributions from all three scattering regimes Rayleigh, resonance and optical scattering it requires more than a simple power measurement to separate them. For this reason, lidar measurements are also strongly dependent on the lidar frequency and can not be easily compared to each other.

30 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 30 Measurement example from Cabauw, Netherlands Uncalibrated attenuated backscatter UV-LidarTransportable Atmospheric Radar Calibrated reflectivity not corrected for propagation effects. Which terms of the active remote sensing equation contribute the figures of lidar backscatter and radar reflectivity shown above? C active remote sensing system constant M(R) range dependent measurement geometry B(R) target characteristics T(R) transmission term data available at

31 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 31 Content active remote sensing equation derivation of the radar equation derivation of the lidar equation how to apply the active remote sensing equation for calibration system performance analysis

32 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 32 Calibration of Active Remote Sensing Measurements AMS Glossary of Meteorology: The process whereby the magnitude of the output of a measuring instrument (e.g., the level of mercury in a thermometer or the detected backscatter power of a meteorological radar) is related to the magnitude of the input force (e.g., the temperature or radar reflectivity) actuating that instrument. For the calibration of a radar / lidar measurement (output: mean received power), we need to know - the range dependent measurement geometry (range normalisation, easy and accurate) -the active remote sensing system constantcan be determined analytically using the system specifications, however for an accurate calibration, extensive measurements of the system are neededbecause it can vary e.g. due to aging of hardware components, hardware changes it needs to be constantly monitored C active remote sensing system constant M(R) range dependent measurement geometry B(R) target characteristics T(R) transmission term (attenuation)

33 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 33 Content active remote sensing equation derivation of the radar equation derivation of the lidar equation how to apply the active remote sensing equation for calibration system performance analysis

34 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 34 Radar performance What is the minimum reflectivity detectable by a meteorological radar? Determined by the minimum received power that can be discerned from the noise floor, i.e. the minimum detectable signal (P mds ). P MDS k T B r.. minimum detectable signal.. Boltzmann constant.. noise temperature.. receiver bandwidth radar receiver signal-to-noise ratio radar receiver noise expressed in terms of thermal noise using the Rayleigh-Jeans approximation which is valid at microwaves (not for lidar!)

35 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 35 Radar performance Result of radar performance calculation of an arbitrary weather radar: How could we increase the sensitivity? reduce the range resolution (B ) increase transmit power (P t ) reduce the noise floor of the system (P mds ) reduce the radar wavelength (λ ) If we use a small wavelength (e.g. cloud radar at 35 GHz), we are able to detect very weak echoes (e.g. fog). Are those radars also suited for the observation of heavy rain? attenuation by rain increases with frequency radar has a limited dynamic range, i.e. there is a z min but also a z max given by the dynamic range of the receiver (a cloud radar receiver can be saturated by heavy precipitation)

36 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 36 IDRA reflectivity measurement of insects in summer Why are there only insects close to the radar, because the radar microwaves are keeping them warm and cosy? Of course not, insects are weak echoes. The radar can not detect them at far ranges because the echo is from a certain range on below the sensitivity (z min ) of the radar. data available at

37 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 37 Summary The active remote sensing equation is an expression for the mean received power only. But beside power (amplitude), electromagnetic waves are also characterised by their frequency, phase and polarisation. Those are the properties that are exploited to gather more independent measurements of the atmosphere in order to separate e.g. transmission from backward-scattering, or for lidar particle from molecular scattering. Advanced active remote sensing instruments: Doppler radar / lidar dual-polarisation radar / lidar multi-frequency radar / lidar Raman lidar, taking advantage of the inelastic / Raman scattering which leads to a change of the molecules quantum state (the energy level), such that the frequency of the scattered photon is shifted a Raman lidar needs a high average laser power and has additional receiver chanels for the Raman backscatter spectrum of gases such as N 2 or H 2 O

38 Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology 38 webhttp://atmos.weblog.tudelft.nl referencesR. E. Rinehart, Radar for Meteorologists, Rinehart Publications, 5 th edition, R. J. Doviak and D. S. Zrnić, Doppler Radar and Weather Observations, Academic Press, 2 nd edition, V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar: Principles and Applications, Cambridge University Press, 1 st edition, C. Weitkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer, Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements - Tobias Otto


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