Solar radiation ECE 583. Solar radiation. Value for E - Solar radiation

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1 7-2 Solar radiation ECE 583 Lecture 7a Solar spectrum, atmospheric transmittance spectrum, absolute radiometry, radiometry field-of-view The sun is the primary source of energy that drives the earth s weather and climate PPeak of solar radiant exitance is at approximately 5 m PDistance from the earth to sun varies from.983 to.67 AU AU is an astronomical unit and is the ratio of the actual distance to the mean distance Using /R 2 gives a difference of 7% in the irradiance between minimum and maximum distance PIrradiance (not spectral irradiance) at the top of the earth s atmosphere for normal incidence is 367 W/m 2 at AU Book reference: James Hansen, Storms of my Grandchildren, Value for E - Solar radiation 7-4 Solar radiation Solar constant has been studied since the early 9s Solar constant is not as well understood at the spectral level PSamuel Langley s work for the Smithsonian Institute used groundbased measurements from mountain tops PNext improvement was balloon-borne instruments P 96s and later used rocketsondes and space-based instruments PCurrently agreed upon value for solar constant is 367 W/m 2 (based on the work of Frohlich) PSolar variability at very short wavelengths PCalibration uncertainty at longer wavelengths PKnowledge in the VNIR is better than the SWIR MODTRAN-based WRC-Based Wavelength (micrometer) nm averages 5-nm averages -nm averages Wavelength (micrometer)

2 7-5 Solar irradiance at the earth 7-6 Where do irradiance values come from? When taking into account the earth-sun distance it can be shown that solar energy dominates in VNIR/SWIR and emitted terrestrial dominates in the TIR Sun emits more energy than the earth at ALL wavelengths Geometry effects reduce the irradiance on the earth such that at longer wavelengths the terrestrial emission dominates Call the VNIR/SWIR the solar reflective MWIR is more difficult to work with since both solar and terrestrial must be considered.e+2.e+9.e+6.e+3.e+ Solar exitance (58 K) Solar irradiance Terrestrial exitance (3 K).E-3. The solar spectral irradiance has been determined via measurements from absolute radiometers PThese systems are well characterized so that for a given output the input irraidiance can be be determined PTechnology is not that new Radiation thermocouple by Nobile and the calorimetric pyrheliometer by Pouillet in the 83s Langley s bolometer design in the 88s Abbot improved on the pyrheliometer in early 9s More recently there has been a shift in the designs to cavity approaches PSamuel Langley s work for the Smithsonian Institute used ground-based measurements from mountain tops PNext improvement was balloon-borne instruments P96s and later used rocketsondes and space-based instruments PCurrently agreed upon value for solar constant is 367 W/m 2 (based on the work of Frohlich) PSpectral quantities are still being debated 7-7 Absolute radiometry Combine the detectors and spectral selection to build an absolute radiometer PIgnore atmospheric conditions for now PAbsolute radiometry is typically accomplished through electrically calibrated radiometers (ECRs) Radiant power on thermal detector Compare to the electrical power required to obtain the same signal 7-8 Absolute measurements of solar irradiance ACRIM III Cutaway Radiant Power Thermal Converter Thermal transducer Signal Processing View Limiting Electrical Power

3 7-9 Absolute measurements 7- Absolute measurements ACRIM (shown on previous viewgraph) and TIM rely on similar designs and approaches P Cavity radiometers PACRIM is older design PTIM is the more recent version used on SORCE Baffles TIM Cutaway Cavity View-Limiting 7- Average values by instrument 7-2 Bias correction Bias has been corrected using overlapping data sets PFortunately, there has been overlap PQuestion is which sensor is correct?

4 7-3 Causes for differences 7-4 One cause for difference As expected, there are many causes for the biases that are larger than the uncertainties P Underestimated uncertainties PKnowledge of the apertures is not sufficiently accurate Cannot account for.3% TSI differences Does not explain inter-cavity variations within single instrument PDifferences in the substitution portion of the sensors PScattering in the optical elements POptical diffraction effect of.2% in ACRIM and is not corrected PUncertainties in the dark measurements Can be large corrections that depend on FOV and vary with temperature Darks are not measured regularly on several instruments PHeating of the apertures TIM instrument has precision aperture further from the cavity reducing stray light and diffraction effects Sunlight View-Limiting Sunlight View-Limiting Sunlight View-Limiting Sunlight View-Limiting Additional light allowed into instrument can scatter into cavity Majority of light is blocked before entering instrument Failure to correct for light diffracted into cavity erroneously increases signal Failure to correct for light diffracted out of cavity erroneously decreases signal 7-5 Attenuation of solar irradiance 7-6 Best absolute measurements are obtained above the earth s atmosphere PCurve here shows atmospheric effects on solar irradiance P Scattering dominates at short wavelengths P Absorption dominates at long wavelengths Exo-atmospheric value With molecular scattering With absorption Now remove the solar irradiance from the previous curve and examine the transmittance specifically PWill get at definition of transmittance later, but concept is well known PGraph shown derived from MODTRAN3 for US Standard Atmosphere, 2.54 cm column water vapor, default ozone, and 6-degree zenith angle PNo scattering.3.9.2

5 Same curve as previous one except scattering by molecules has been included At longer wavelengths, absorption plays a stronger role with some spectral regions having complete absorption

6 Transmittance and path length Graph here shows the atmospheric transmittance through the atmosphere for three starting altitudes PVertical distribution of the absorbers plays a role in the transmittance PTransmittance is non linear with path length km Chappuis Bands O km Sea Level O 2 H 2 O 7-23 Transmittance and path length 7-24 Spectral variation Showing VNIR and SWIR spectral range further illustrates the non-linear aspect of transmittance Transmittance can vary strongly with wavelength PPlot here is based on MODTRAN output for vertical path and 2.54 cm of column water vapor PResolution is cm - wavenumber interval with a 2 cm - averaging Wavenumber (/cm)

7 7-25 Spectral resolution 7-26 Spectral resolution In this case, the spectral sampling and resolution have both been increased relative to previous graph P2 cm - sampling with 4 cm - resolution PResolution is determined by a moving triangle function with the given width Wavenumber (/cm) Sampling is every 4 cm - and an 8 cm - triangle function PMODTRAN s native calculations are done in wavenumber space due to the equal energy intervals with frequency as opposed to wavelength PStill strong variability with wavelength is present Wavenumber (/cm) 7-27 Spectral transmittance 7-28 Field of view Keeping a high spectral sampling interval but large averaging interval allows for detailed view of the overall absorption band PAll of these results are modeled ouptut PMODTRAN results are similar to LOWTRAN but not identical Wavenumber (/cm) Diagrams here illustrate the field of view of two simplistic radiometer designs PChief ray from the edge of the detector travels without deviation through the center of the pupil in the case of a collector with optical elements with power PThe FOV is determined through similar triangle geometry PThe case of a radiometer without collection optics gives an FOV determined by the tube length and aperture size Detector dimension, d Focal Length, f IFOV=d/f Chief ray

8 7-29 Field of View Should use the largest value reasonable for IFOV as opposed to most optimistic PFigures at right illustrate two methods for computing the IFOV of a system Simple tube radiometer (that is a tube IFOV with the detector at the end) Field of view is determined by the length of the tube, size of the aperture and technically the size of the detector PRely on the diagram above right This is okay since the detectors are small relative to the entrance aperture size Much easier calculation IFOV Would not be sufficient in the case of high-accuracy requirements such as absolute solar irradiance work Limiting Detector Detector 7-3 Tube radiometer design Simple radiometer consists of an aperture and detector separated by a given distance PAsk the following questions for the solar case (assume point source) Detector area increases? area increases? Either distance decreases? PWhat is the impact of a larger FOV? Solar source with area A s and output radiant flux of s Distance, S s of area A a FOV Distance, S d Detector with area A d 7-3 Tube radiometer design 7-32 Tube design To ensure that all rays strike the area of diameter D d limits R to be DA Dd tan if ( D D ) << l 2 2 2lR θ R D A D d = lr θ R max DA + D d = lr A d R The maximum angle for which any rays can still strike a part of the area of diameter D d is DA + Dd tan if ( D + D ) << l 2 2 2lR A d R Reduction of stray light and improved FOV is achieved through baffles inside the tube Receiver length, l R Full angle of FOV, R Detector with diameter D d of diameter D a

9 Lens-based radiometer What does a lens or mirror do for the radiometric system? PPlace the detector at the focal distance of the lens for simplicity Focal plane Can place the detector at other locations with similar results PFocal length and detector size define the resolution angles PLens size and focal length (equivalently, f/#) define the speed angles Speed angles Resolution angles Lens-based radiometer Produces an image of the source while giving a betterdefined field of view P Field of view of the simple aperture radiometer is not well defined for similar reasons as a pinhole can image the sun PChief ray defines the FOV of the basic radiometer PShould consider the transmittance of the lens and reflections from it PAddition of the lens makes the lens the limiting aperture and the detector size the field stop (assume no vignetting) Distance, S s Source with area A s and output radiant flux of s Lens with area A a Distance, S d Detector with area A d 7-35 Lens-base FOV Maximum acceptance angle,, defines the field of view half angle for which rays can focus on the detector Ptan = d/2f PThroughput (collection ability of the optical system) can be written as the product of A A det (A lens /f 2 ) A lens (A det /f 2 ) PFor solar radiometry the problem is more closely related to the schematic at right and there is no solid angle because the source is plane parallel 7-36 Tube radiometer Examine the case again of the small solar source as we did before with the tube radiometer PAsk the following questions? Detector area increases? area increases? Either distance decreases? PWhat is the impact of a larger aperture? Distance, S s Distance, S d

10 7-37 Two-lens receiver 7-38 Sensor FOV versus aperture Another commonly-used design in solar radiometry makes use of two lenses d PObjective lens is imaged on the θr tanθr = detector f o PField stop determines the field of + = S = fo + fe view S S fe PCommon to make the field lens ddet S f e the field stop as well = d S f f o Objective lens S S d fs Field stop f e fs Field lens o d det Detector For solar radiometry, the collection area plays a bigger role in radiant flux than FOV P The size of the collection optics if there our any elements with power Mirror Lens P Radiant flux through a simple tube radiometer defined by area of the detector P Assumes the FOV is larger than the angle subtended by the sun P Still want the FOV to be as small as possible Ensures light is only coming from the sun Star light when in space Scattered light from the atmosphere when at the ground P Ideally want the FOV of the sensor to match the angular size of the sun Practically not feasible Requires perfect pointing