ECE 583. xˆ, x ˆ. b ˆ. Lecture 11 Aerosol size distribution retrieval, Gaseous absorber retrieval. Atmospheric Remote Sensing Retrievals

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Rudolf Miles
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1 11-1 ECE 583 Lecture 11 Aerosol size distribution retrieval, Gaseous absorber retrieval The Remote Sensing Retrieval Problem Atmospheric Remote Sensing Retrievals Based on some sort of relation defined by a physical process: (a) extinction - turbidity, aerosol SAGE occultation,.. (b) emission - atmospheric sounding, precipitation,.. (c) scattering - passive, cloud aerosol, ozone,.. - active, radar & lidar Progress is toward designing systems that combine active with passive Forward Problem (real) y=f(x) + y y = measurement F = Nature s forward model x = parameter desired y = error in measurement (noise, calibration error Often the relation between the measurement y and the parameter of interest x is not entirely understood xˆ y=f(,b) + y + f Inverse Problem xˆ I( y, b) The Retrieval Problem (non unique) Forward Problem (applied) y = f( ) + y + f f xˆ, b ˆ xˆ, b ˆ = our depiction of the forward model = estimates of x,y f = F(x,b) - f ( ˆ, b ) + f / b(ˆ bb), = error in forward model x ˆ Radiative transfer model (most common) Radiation + physical model Radiation model + NWP (radiance assimilation) b = model parameters that facilitate evaluation of f f = error of model For the most challenging problems we encounter, the largest uncertainty lies in the nature of forward model errors.

2 11 Instantaneous optical depth 11 What now? Once the intercept is known, it is possible to compute the total optical depth as a function of time P Solving for total optical depth gives the following lnv lnv λ λi τ λ i = mi PThen obtain graphs below (where molecular optical depth has been removed) Assume that the intercepts for a sensor are known and can be used to determine an instantaneous optical depth PAlso ignore diffuse-light effects and assume intercept is corrected for earth-sun distance PInstantaneous optical is then lnv lnv λ λi τ λ i = mi PConcentrate now on the spectral aspect of the data Spectral optical depth 11-5 Spectral optical depth Recall earlier discussion that showed optical depth as a function of wavelength White Sands Missile Range September 1, 21 Measured Total Optical Depth Total Derived Optical Depth Molecular Optical Depth Aerosol Optical Depth Ozone Optical Depth Wavelength (microns) Log-log space illustrates how we might be able to use the spectral optical depths to retrieve atmospheric parameters White Sands Missile Range September 1, 21 Measured Total Optical Depth Total Derived Optical Depth Molecular Optical Depth Aerosol Optical Depth Ozone Optical Depth ln[wavelength (microns)]

3 11-6 Spectral optical depth 11-7 Measured optical depth Previous plots were mix of model and actual measurements with the total optical depth being measured values PBelow are model only PShow the Rayleigh, aerosol, ozone, and total optical depths Previous plot based on modeled spectral optical depths from measurements at Ivanpah Playa, Nevada on June 27, 23 PData shown here are the retrieved optical depths from this date using methods that will be described later PShow both linear and log/log version of plots PNote that only the total can be obtained PHow do we get the components? Aerosol Inversion 11-9 Aerosol inversion Will leave the strict mathematical description of how to do an inversion for later in the course PThe concept of an inversion is that a set of measurements can be inverted to obtain the parameters that drive measurements PGiven the aerosol parameters Size distribution Index of refraction as a function of wavelength Shape Vertical distribution Column amount POne can compute the spectral optical depth for aerosol scattering at any wavelength PThen, in theory, given the spectral optical depths at a variety of wavelengths POne can compute the aerosol parameters While simple in concept, the inversion of spectral optical depth is non-trivial in practice PFirst, the problem is underdetermined Just from a surface view, the optical depth depends on both the extinction coefficient and number density In addition, the extinction coefficient depends on many of the parameters given on the previous viewgraph Adding more measurements simply keeps adding additional unknowns PSecond, we need to make numerous assumptions just to make the problem soluble Spherical aerosols Mie scattering PFurther, the functions that are used to go back and forth between the measurements and the desired parameter are smooth PDon t forget that the noise in the measurements also play a role

4 11-1 Aerosol inversion Aerosol inversion Plot shows the aerosol information that can be used in the inversion PScattering efficiency and the scattering efficiency times the particle area (K) for a given wavelength PDifferent wavelengths would shift the curves PSmooth shape and overlap limits the ease with which the inversion can be done PWould prefer to see something similar to the other sketch Radius (micrometers) With the advent of computers there are several options to inverting spectral optical depths to obtain aerosols PAssume various models and mathematically invert the results Junge distributions Multi-modal distributions This can be mathematically straightforward in some cases PLook-up table approaches Assume you know all possible combinations of inputs Theoretically compute the optical depths corresponding to your range of inputs -This is the forward problem Store results in a database Find the best match between the measurements and the look-up table entries PHopefully, it is obvious by now that there are more than one set of solutions to a given set of measurements PApproach described here is a straightforward mathematical calculation using the Junge distribution Junge distribution, redux Junge parameter Recall that the Junge distribution was introduced as one way to describe the number of aerosols at a given particle size PBased on the Junge parameter n(r)=n r - where is the Junge parameter with typical values between 2 and 4 PBased on measurements of particles in the stratosphere (1-5 km) PAlso referred to as a Power Law Distribution PMajor advantage is it simulates distributions with a single parameter POne key result of this is that Using the Junge distribution Assuming Mie scattering It can be shown that scattering is proportional to 1/ Write the Angstrom turbidity coefficient, = Optical depth is then ν 2 γ τ λ τ λ τ λ τ λ τ λ γ λ particulate ( ) = particulate ( ) = particulate ( ) and ln( particulate ( )) = ln( particulate ( )) Thus, given measurements of the aerosol optical depth at two wavelengths allows for the retrieval of a Junge parameter PProblem is that we cannot measure the aerosol optical depth The calibrated solar radiometer allows for a retrieval of total optical depth τ ( λ) = τ ( λ) + τ ( λ) + τ ( λ) total molecule particulate absorption Note, strictly speaking we cannot measure the total optical depth either; we are measuring a voltage (or current) related to the transmitted solar irradiance PStep 1 - locate a wavelength for which there is no absorption τ ( λ) = τ ( λ) + τ ( λ) total molecule particulate PStep 2 - solve for aerosol optical depth τ ( λ) = τ ( λ) τ ( λ) particulate total molecule PStep 3 - figure out the molecular optical depth

5 11-14 Molecular Scattering Model Molecular Optical Depth Will assume molecular scattering can be approximated by Rayleigh scattering PRayleigh approximation is valid for scattering by particles that are much smaller than the wavelength of light that is interacting with it r/<.1 In this case, simple theoretical modeling of the scattering with an oscillating dipole Strictly valid only for spherical particles PImportant results of this are Scattering is completely polarized at 9 and 27 degrees Scattering is inversely proportional to 4 Scattering is conservative, that is, no absorption - =1. Scattering is proportional to the number of scatterers PNumber of scatterers is proportional to the pressure τ Rayleigh ( P) = τrayleigh( P) P P Wavelength dependence of optical depth with wavelength goes as the inverse of wavelength to the fourth power PThen 4 λ τrayleigh ( λ) = τrayleigh ( λ) PSlope of line below in log-log space is E-5 1E Wavelength Molecular Optical Depth Molecular optical depth Molecular optical depth at a wavelength and pressure allows computation of values for any other wavelength & pressure P Rayleigh =.885 at P=923.4 mb and =55 nm Computed based on theoretical equations derived from the oscillating dipole approximation 8π ( M 1) ( 6+ 3α ) 16 τ Rayleigh = ρ 3. λ N 6 7α M = + + λ λ Where N is the molecular number density of is the column number density of is the depolarization factor of.279 PThen the molecular optical depth at mb (sea level) and a wavelength of 11 nm is. τrayleigh( P = , λ = 11) = τrayleigh( P = 9234., λ = 55) = PShould also include a temperature correction(especially at high altitude π ( n 1) Nc ( 6+ 3Pn ) P T τ molecular = λ N P P ( 6 7 ) T s n Measurement of the atmospheric pressure (and temperature) is sufficient to characterize the molecular optical depth at all wavelengths Ozone Absorption Total Total-Rayleigh H2 Absorption

6 11-18 Aerosol optical depth Spectral optical depth Removing the bands with absorption leads to the conclusion that a straight line fit of the spectral optical depth due to particulates in log-log space is reasonable P This linear fit approximation is Angstrom s turbidity law PAssumes that the aerosols follow a Junge size distribution Ignored due to probable instrument calibration uncertainty The slope of the straight-line fit is related to the Angstrom coefficient and the Junge parameter Technically, only need two wavelengths Graph below shows spectral optical depth for a single measurement in time (ignore dashed lines) Straight-line fit is computed for first three points and last four ignoring the water vapor band Issues with the fit Non-Junge distribution Calibration of the radiometer (Up-down error in plot) Spectral calibration (left-right) Temperature effects in the detector package (calibration) Intercept effect on Junge parameter 111 Impact of intercept on Junge parameter Improper calibration of the solar radometer leads to errors in determination of the spectral optical depth PGraphs below show the results of processing solar radiometer using two sets of intercepts PChanges the slope of the straight-line fit

7 112 Absorption optical depth 113 Ozone retrieval Would still like to be able to retrieve column amounts of absorbing gases PRecall that τ ( λ) = τ ( λ) + τ ( λ) + τ ( λ) total molecule particulate absorption PThen the absorption optical depth can be found using τ ( λ) = τ ( λ) τ ( λ) τ ( λ) absorption total molecule particulate Total optical depth is obtained from the measurements Molecular optical depth obtained from assumption of Rayleigh scattering Aerosol optical depth is determined from the retrieval of the Junge parameter and the value at a reference wavelength PColumn amount of the absorber is found by knowing the relationship between absorber amount and optical depth Relationship between column amount and optical depth is determined by the spectral absorption coefficient Pa is the spectral absorption coefficient in units of 1/cm τ λo = 3 a η λ is the columnar ozone amount Units are height for a unit cross section (cm 2 ) PRecall the earlier plot for extinction coefficient Ozone retrieval 115 Measured versus modeled There can be multiple bands affected by ozone retrieval and the question becomes which is correct? PRare that all three bands give the same column amount Each has its own intercept uncertainty Junge parameter may be incorrect (or not valid) Errors in absorption coefficient PCan average all three PUse the maximum absorption band for primary retrieval and check with other bands Iterate between the ozone absorption and the Junge parameter Best compromise between the two Use the modeled ozone amount, the Junge parameter, and molecular to compare the measured values with the modeled PAgreement is quite good PShow the measured total and the predicted optical depths

8 117 Water vapor retrieval 116 Measured versus modeled Water vapor presents several different problems in our attempts to retrieve it through solar radiometery PStrong absorber Violates the assumption of linear relationship between airmass and transmittance Standard Langley plot will give errors P Temporal variability Water vapor can change dramatically during the day Also causes errors in the Langley approach P Spectral variability Water vapor absorption varies strongly with wavelength Causes problems with our band-averaged approach for Beer s Law Conversion from optical depth to column amount is difficult Using the retrieved Junge parameter, predicted Rayleigh, and column ozone can give a predicted total optical depth.8 PResults shown below.6 PDifferences caused by error.4 sources described previously Wavelength Wavelength 118 Water vapor spectral variability 119 Water vapor temporal variability Spectral variability due to water vapor absorption will be the key to the retieval of the column amount One of the reasons there is such interest in the water vapor amount is that it varies with time and space P Leads to daily weather effects PStrong impact on our climate PGraph here shows the variation in water vapor derived from solar radiometer compared to radiosonde results Radiosonde values increased by about 1-15% from morning to evening Solar radiometer data showed a midday increase of 4% from early morning missed by radiosondes

9 11 Langley plot effects 111 Langley plot effects The non-linear absorption effect causes the data to give an incorrect intercept and optical depth PData here are for four bands in the NIR PThe 94 band is affected by water 6 vapor PNote the linearity of the non-absorption 5.5 bands Partially due to the logarithmic scale Mostly due to this 5 being a good Langley day 76 nm 87 nm 94 nm 13 nm PCurvature in water 4.5 band gives an incorrect intercept Airmass One solution would be to limit the airmass range of the linear regressions to obtain better fits PQuestion is: Which intercept is correct? PIncorrect intercept gives an incorrect value for optical depth PIncorrect optical depth gives incorrect columnar amount nm Airmass nm Airmass 112 Modified Langley analysis 113 Aerosol correction Develop an approach that gives a more accurate assessment of the solar radiometer intercept PThe problem is that the absorption by water vapor is not linear with distance Certain lines in the band will saturate in absorption Further increase in water vapor amount (due to angle) will not give an increase in absorption The use of airmass is not suitable PDevelop a modified Langley analysis Rely on square root of airmass This is based theoretically on Goody s band model for absorption Correct measurements for aerosol scattering Correct measurements for molecular scattering Do linear regression of logarithm of corrected voltage against m 1/2 Aerosol scattering is determined in the same fashion as shown previously PAssume Junge size distribution PCan be based on all bands, two bands, or one band

10 114 Modified Langley example 115 Optical depth to water vapor The modified Langley approach allows for an accurated determination of the intercept PPossible to retrieve a water vapor optical depth P Difficulty is still the conversion between column amount and optical depth PData shown here are based on balloon results versus a measured optical depth Empirical line fit is shown Comparisons done on days for which solar radiometer showed little variation Radiosonde data also had to show little variation PRemarkable agreement when considering the physical differences in the approaches 116 Optical depth to water vapor A more elegant approach is to model the relationship between the optical depth and water vapor PResults here are based on a model developed at the UofA in the mid 198s POther approaches have since been developed PTwo results come from this. The first is that there is a conversion between optical depth and column amount The second is that the Langley approach results will depend upon the amount of water vapor in the atmosphere Note that the fit here between.5 and 1.5 in (mu) 1/2 does not go through zero Modified Langley Approach for IR Aerosol Photometer V rather than V is used in the Langley analysis Tg(,m) is the Lowtran calculated non exponential relation for the observation based on a separate non-photometer measurement of columnar water vapor.

11 117 Example results 118 Example results Results shown here compare various methods for aerosol correction and conversion to column amount Comparison between solar radiometer and microwave data PWill see in upcoming lectures how the microwave data work PAlso shown are balloon results PNote that the temporal structure in the data is most likely real

Course outline, objectives, workload, projects, expectations

Course outline, objectives, workload, projects, expectations Introductions Remote Sensing Overview Elements of a remote sensing observing system 1. platform (satellite, surface, etc) 2. experimental design