Presentation on theme: "Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements - Tobias Otto."— Presentation transcript:
1Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements - Tobias Otto
2Content the active remote sensing equation derivation of the radar equationderivation of the lidar equationhow to apply the active remote sensing equation forcalibrationsystem performance analysis
3The 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 aboutthe system (relevant system parameters),the propagation path, andthe targets that are remotely sensedis 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
4The Active Remote Sensing Equation rangeactive remote systemtargetmean received poweractive remote sensingsystem constantrange dependentmeasurement geometrytargetcharacteristics(backward-scattering)transmission term(attenuation)
5Content active remote sensing equation derivation of the radar equationderivation of the lidar equationhow to apply the active remote sensing equation forcalibrationsystem performance analysis
6Radar Equation for a Point Target transmitterreceiverantennaerange RtargetPtGtσPrGrbackscattered power densityat receiving antennaisotropicantennaPt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)power density incidenton the targeteffective area / aperture ofthe receiving antenna
7Radar Equation for a Point Target transmitterreceiverantennaerange RtargetPtGtσPrGrtarget characteristicsradar constantPt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)free-spacepropagation
8From 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 targetto 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):
9range resolution volume Radar Resolutionθantenna beam-widthrange Rrange resolution volume(range-bin)c .. speed of lightB .. 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
10Range Resolution of a pulsed Active Remote Sensing Instrument
11Range Resolution of a pulsed Active Remote Sensing Instrument e.g. pulse duration 1 µs300 mf0
12Range Resolution of a pulsed Active Remote Sensing Instrument each sample consists of the sum of the backscattered signals of a volume with the length c·τ/2target 1responsetarget 2responsefor a pulsed active remote sensing instrument, the optimum sampling rate of the backscattered signal is 2/τ (Hz)target 3responseNow we samplethe backscattered signal.
13Radar Equation for Volume Targets 2rRθ/2tan(α) ≈ α (rad) for small αvolume reduction factor due toGaussian antenna beam pattern
14Isotropic Scattering Cross Section σ PbackscatteredSincident.. backscattered power (W).. incident power density (Wm-2)Depends on:frequency and polarisation of the electromagnetic wavescattering geometry / angleelectromagnetic properties of the scatterertarget shape hydrometeors can be approximated as spheres
15Isotropic Scattering Cross Section σ Monostatic isotropic scattering cross section of a conducting (metallic) sphere:a.. radius of the sphere.. wavelengthRayleigh region: a << normalised radar cross sectionResonance / Mie region:electrical sizeOptical region: a >> Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley.
16Radar Cross Section σhydrometeors are small compared to the wavelengths used in weather radar observations: weather radar wavelength 10cm max. 6mm raindrop diameterRayleigh 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
17Radar Equation for Weather Radar radar constantradar reflectivity factor z, solely a property of the observed precipitation
18Radar Reflectivity Factor z spans over a large range; to compress it into a smaller range of numbers, engineers prefer a logarithmic scale1 m3one raindropD = 1mmequivalent to1mm6m-3 = 0 dBZraindrop diameter#/m3Zwater volumeper cubic meter1 mm409636 dBZmm34 mm133.5 mm3Knowing the reflectivity alone does not help too much.It is also important to know the drop size distribution.
19Raindrop-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. 1m3.Often, the raindrop-size distribution is assumed to be exponential:concentration (m-3mm-1) slope parameter (mm-1)Marshall and Palmer (1948):N0 = 8000 m-3mm-1Λ = 4.1·R-0.21with the rainfall rate R (mm/h)
20Reflectivity – Rainfall Rate Relations reflectivity (mm6m-3)liquid water content (mm3m-3)raindrop volumerainfall rate (mm h-1)terminal fall velocitythe reflectivity measured by weather radars can be related to the liquid water content as well as to the rainfall rate:power-law relationshipthe 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
21Summary of the assumptions in the radar equation In the derivation of the radar equation for weather radars, the followingassumptions are implied:the hydrometeors are homogeneously distributed within the range-binthe hydrometeors are dielectric spheres made up of the same material with diameters small compared to the radar wavelengthmultiple scattering among the hydrometeors is negligibleincoherent scattering (hydrometeors exhibit random motion)the main-lobe of the radar antenna beam pattern can be approximated by a Gaussian functionfar-field of the radar antenna, using linear polarisationso far, we neglected the transmission term (attenuation)
22Content active remote sensing equation derivation of the radar equationderivation of the lidar equationhow to apply the active remote sensing equation forcalibrationsystem performance analysis
23Lidar Equation for Volume Targets laserlaser beamreceiverreceiver fieldof viewtelescopeareaPr .. received power (W)Pt .. transmitted power (W)AL .. laser beam cross section (m2)c .. speed of light (ms-1)τ .. temporal pulse length (s)R .. range (m)σ .. isotropic scattering cross section (m2)A .. area of the primary receiver optics (m2)backscattered power densityat the telescopepower density incidenton the targettelescope aperture
24Lidar Equation for Volume Targets laserlaser beamreceiverreceiver fieldof viewtelescopeareaPr .. received power (W)Pt .. transmitted power (W)AL .. laser beam cross section (m2)c .. speed of light (ms-1)τ .. temporal pulse length (s)R .. range (m)σ .. isotropic scattering cross section (m2)A .. area of the primary receiver optics (m2)η .. receiver efficiency (how many of theincoming photons are detected)O(R) .. receiver-field-of-view overlap functionT(R) .. transmission term (attenuation)
25Lidar Equation for Volume Targets laserlaser beamreceiverreceiver fieldof viewtelescopearea
26Lidar Equation for Volume Targets laserlaser beamreceiverreceiver fieldof viewtelescopeareadifferential scatteringcross section (m2sr-1)number concentrationwith the backscatter coefficient β (m-1sr-1):π indicating scatteringin the backward direction
27Lidar Equation for Volume Targets range dependentmeasurement geometrylidar system constantbackscattercoefficienttransmission term(attenuation)Both the backscatter coefficient and the transmission term (attenuation) contain significant contributions frommolecular scattering (gases like oxygen, nitrogen) Rayleigh scatteringandparticle 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 scatteringDifficult to differentiate with power measurements only.
28Summary: Radar and Lidar Equation targetmonostatic, i.e. co-locatedtransmitter and receiveractive remote systemC active remote sensing system constantM(R) range dependent measurement geometryB(R) target characteristicsT(R) transmission term (attenuation)Radar equation for volume targetsLidar equation for volume targets
29Summary: Radar and Lidar Equation 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 isonly 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 equalLidar:Both the backscatter coefficient β and the transmission term T contain significant contributions frommolecular scattering (gases like oxygen, nitrogen) Rayleigh scatteringandparticle 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 scatteringLidar 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.
30Measurement example from Cabauw, Netherlands UV-LidarTransportable Atmospheric RadarUncalibrated attenuated backscatterCalibrated reflectivity not corrected for propagation effects.C active remote sensing system constantM(R) range dependent measurement geometryB(R) target characteristicsT(R) transmission termWhich terms of the active remote sensing equation contribute the figures of lidar backscatter and radar reflectivity shown above?data available at
31Content active remote sensing equation derivation of the radar equationderivation of the lidar equationhow to apply the active remote sensing equation forcalibrationsystem performance analysis
32Calibration of Active Remote Sensing Measurements C active remote sensing system constantM(R) range dependent measurement geometryB(R) target characteristicsT(R) transmission term (attenuation)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 constant ∙ can be determined analytically using the system specifications, however for an accurate calibration, extensive measurements of the system are needed ∙ because it can vary e.g. due to aging of hardware components, hardware changes it needs to be constantly monitored
33Content active remote sensing equation derivation of the radar equationderivation of the lidar equationhow to apply the active remote sensing equation forcalibrationsystem performance analysis
34signal-to-noise ratio Radar performanceWhat 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 (Pmds).radar receiversignal-to-noise ratioPMDSkTBr.. minimum detectable signal.. Boltzmann constant.. noise temperature.. receiver bandwidthradar receiver noise expressed in terms of thermal noise using the Rayleigh-Jeans approximationwhich is valid at microwaves (not for lidar!)
35Radar performanceResult of radar performance calculation of an arbitrary weather radar:How could we increase the sensitivity? reduce the range resolution (B ) increase transmit power (Pt ) reduce the noise floor of the system (Pmds ) reduce the radar wavelength (λ )If we use a small wavelength (e.g. cloud radar at 35 GHz), we are able to detect veryweak 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 zmin but also a zmax given by the dynamic range of the receiver (a cloud radar receiver can be saturated by heavy precipitation)
36IDRA 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 (zmin) of the radar.data available at
37SummaryThe 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 shifteda Raman lidar needs a high average laser power and has additional receiver chanels for the Raman backscatter spectrum of gases such as N2 or H2O
38Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements - Tobias Ottoweb references R. E. Rinehart, “Radar for Meteorologists”, Rinehart Publications, 5th edition, 2010.R. J. Doviak and D. S. Zrnić, “Doppler Radar and Weather Observations”, Academic Press, 2nd edition, 1993.V. N. Bringi and V. Chandrasekar, “Polarimetric Doppler Weather Radar: Principles and Applications”, Cambridge University Press, 1st edition, 2001.C. Weitkamp, “Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere”, Springer, 2005.