Integrated SST Data Products: Sounders for atmospheric chemistry (NASA Aura mission):

Transcription

1 Lecture 9. Applications of passive remote sensing using emission: Remote sensing of SS. Principles of sounding by emission and applications temperature and atmospheric gases.. Remote sensing of sea surface temperature SS.. Concept of weighting functions: weighting functions for nadir and limb soundings. 3. Sounding of the atmospheric temperature. Examples: NOAA sounders. 4. Sounding of atmospheric gases. Appendix: Concept of an inverse problem. Required reading: S: Patty: 8 Additional reading: Summary of SS satellite products NOAA Optimum nterpolation /4 Degree Daily Sea Surface emperature Analysis: Reynolds R. W. et al. 7: Daily High-Resolution-lended Analyses for Sea Surface emperature. J. of Climate. ntegrated SS Data Products: Sounders for atmospheric chemistry NASA Aura mission:

2 . Remote sensing of sea-surface temperature SS. he concept of SS retrievals from passive infrared remote sensing: measure R radiances in the atmospheric window and correct for contribution from clear sky by using multiple channels called a split-window technique Using Eq.[8.] we can write the R radiance at OA: d exp exp ; [9.] Let s re-write this equation using the transmission function exp and that ] [ ; atm sur [9.] where atm is an effective blackbody temperature which gives the atmospheric emission d atm exp ] [ [9.3] We want to eliminate the term with atm in Eq.[9.3]. Suppose we can measure R radiances and at two adjacent wavelengths and ] [ atm sur [9.4] ] [ atm sur [9.5] NOE: wo wavelengths need to be close to neglect the variation in atm as a function of Let s apply the aylor s expansion to at temperature = atm atm atm [9.6] Applying this expansion for both wavelengths we have

3 atm atm [9.7] atm atm [9.8] and thus eliminating - atm we have / atm [ ] [9.9] / atm Let s introduce brightness temperatures for these two channels b and b = b and = b and apply [9.9] to b and to sur and / atm [ b ] [9.] / b atm / atm [ sur ] [9.] / sur atm Let s substitute the above expressions for b and sur in Eq.[9.5] / atm [ b atm] [9.] / / { atm [ sur atm]} atm[ ] / where and are transmissions in the channels and. Eq.[9.] becomes b sur atm Using Eq.[9.4] we can eliminate [ ] [9.3] atm sur b [ ] [9.4] where ; and are transmissions in the channels and. 3

4 Performing lineariation of Eq.[9.4] sur [ ] [9.5] b b b Principles of a SS retrieval algorithm: SS is retrieved based on the linear differences in brightness temperatures at two R channels. wo channels are used to eliminate the term involving atm and solve for sur. NOE: Clouds cause a serious problem in SS retrievals => need a reliable algorithm to detect and eliminate the clouds called a cloud mask. NOE: One needs to distinguish the bulk sea surface temperature from skin sea surface temperature: ulk -5 m depth SS measurements: Ships uoys since the mid-97s: buoy SSs are much less nosy that ship SSs Data from buoys are included in SS retrieval algorithms Skin SS from infrared satellite sensors: SR Scanning Radiometer and VHRR Very High Resolution Radiometer both flown on NOAA polar orbiting satellites: since mid-97 AVHRR Advanced Very High Resolution Radiometer series: provide the longest data set of SS: since channels started on NOAA-6 and since channels started on NOAA- able. AVHRR CHANNELS AVHRR Wavelength Channel µm

5 AVHRR MCSS Multi-Channel SS algorithm: SS = a b4 + b4 - b5 +c [9.6] where a and c are constants. 4 4 and 5 are transmission function at AVHRR channels 4 and Reynolds Optimal nterpolation Algorithm: Reynolds R. W. et al. 7: Daily High-resolution lended Analyses. J. of Climate. Merges Advanced Very High Resolution Radiometer AVHRR infrared satellite SS data and data from Advanced Microwave Scanning Radiometer AMSR on the NASA Data products have a spatial grid resolution of.5 and a temporal resolution of day. 5

6 Microwave vs. R SS retrievals Factor affecting nfrared radiometry Microwave radiometry radiometry Magnitude of emitted radiation from the sea surface [+] large [-] small Sensitivity of brightness to SS [+] large [-] small is proportional to Emissivity [+] = about [-] = about.5 Clouds [-] Not transparent [+] Clouds largely transparent improvement at longer wavelengths Sea state e.g. [+] ndependent [-] varies with sea state roughness Atmospheric [-] Requires complex [+] Easily corrected with interference Spatial resolution Viewing direction on surface Absolute calibration Presently achievable sensitivity Presently achievable absolute accuracy correction [+] A narrow beam can be focused. Diffraction is not a problem in achieving high spatial resolution with a small instrument multichannel radiometer [+] Diffraction controls the beam at large wavelengths. Large antenna required for high spatial resolution [+] Surface radiance largely independent of viewing direction [-] varies with viewing direction [+] Readily achieved using heated [-] Absolute calibration on-board target target not readily achieved. degree K.5 degree K.6 degree K degree K 6

7 7. Concept of weighting functions: weighting functions for nadir and limb soundings. Recall Eq.[8.8] that gives the upward intensity in the plane-parallel atmosphere with emission neglecting scattering: d exp exp and that exp and exp d d where is the cosine of enith angle of observation. Eq.[8.8] can be re-written in terms of transmission function see Eq. 8.5 as d d d [9.9] Eq.[9.9] can be expressed in different vertical coordinates such as P or lnp. Let s denote an arbitrary vertical coordinate by ~ so Eq.[9.9] becomes d W ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ [9.] where the weighting function is defined in the general form as d d W ~ ~ ~ ~ ~ [9.] Physical meaning of the weighting function: Radiances emitted from a layer d ~ is determined by a blackbody emission ~ of the layer weighted by the factor d W ~ ~ ~

8 Let s re-write the solutions of the radiative transfer equation for upward and downward radiances in the altitude coordinate. Recall that the optical depth of a layer due to absorption by a gas in this layer is u u Let s express the optical depth in terms of a mass absorption coefficient of the absorbing gas and its density k du hus transmission between and along the path at is and k gasd [9.] exp k gasd [9.3] d k d gas exp k gas d [9.4] herefore for the upward intensity and downward intensities at the altitude we have d d [9.5] d and thus d d [9.6] d exp exp k gas d k gas d k gas d [9.7] k gasd k gasd exp [9.8] 8

9 NOE: Eq.[9.7] is fundamental to remote sensing of the atmosphere. t shows that the upwelling intensity in the R is a product of the Planck function spectral transmittance and weighting function. nformation on temperature is included in the Planck function while the density profile of relevant absorbing gases is involved in the weighting function. hus one can retrieve the profile of temperature if the profiles of relevant absorbing gases are known or vice versa. Weighting functions for near-nadir sounding: From Eq.[9.5] upwelling radiance detected by a satellite sensor at or where is d d [9.9] d W d W d d thus from Eq.[9.4] we have k gas W exp k gasd d [9.3] [9.3] decreases with altitude increases with altitude 9

10 Figure 9. Examples of weighting functions for nadir sounding for optically thick left pair and optically thin right pair media.

11 Weighting functions for limb sounding: he intensity measured by a satellite for limb viewing geometry is the integral of the emission along a line-of-sign h is the tangent altitude d s h s ds [9.3] ds s is the transmission function along the path of length s from the outer levels of the atmosphere at s. Figure 9. Viewing geometry of limb sounding. We can relate s and as R h s R [9.33] where R is the radius of the Earth. Using that R>>h we have s R h [9.34] hus Eq.[9.3] becomes h d ds d ds d [9.35] h

12 and where h W h d [9.36] W h for < h h d W h R / h for > h [9.37] ds enhancement of the tangent path relative to a vertical path Limb sounding has higher sensitivity to emission from trace gases CO NO N O ClO Advantages of limb sounding: Can measure emission from gases of low concentrations Surface emission does not effect limb sounding Good vertical distribution since it senses outgoing radiation from just a few kilometers above the tangent height => weighting functions have spikes see S:fig.7.8 Disadvantages of limb sounding: Can not be used below the troposphere Requires precise information of the viewing geometry

13 3. Sounding of atmospheric temperature. Let s find the simplest solution of Eq.[9.A] see Appendix assuming that transmittance and hence weighting functions does not depend on temperature. hus Eq.[9.A] is linear in. A standard approach is to express as a linear function of N variables b j : N b L [9.38] where L j is a set of representation functions such as polynomials or sines and cosines. Eq.[9.A] becomes j N N b j L j W d Cijb i i j [9.39] j j where the square matrix C whose elements j j Cij L j W d can be easily calculated. hus for the N unknown b j there are N equations which can be solved. he solution of Eq.[9.39] is called an exact solution to the linear problem. i Problems: Eq.[9.39] is ill-conditioned i.e. any experimental error in the measurements can be greatly amplified and the solution can be physically meaningless though it satisfies Eq.[9.39]. Strategy: instead of an exact solution find the solution that lies within the experimental error of measurements => it gives us more freedom in a choice of a solution but a new problem is how to make this choice. hus the problem of retrieval can be re-stated as: Given the measured radiances the statistical experimental error the weighting functions and any other relative information what solutions for are physically meaningful? 3

14 A priori information is often used to provide other relative information. A priori information for the retrievals of temperature: Radiosonde data Forecast atmospheric dynamical models Example: GOES soundings are generated every hour using a numerical weather prediction model forecast as a 'first guess' NOAA sounders: HRS/ High Resolution nfrared Radiation Sounder : channels resolution 9 km nadir MSU Microwave sounding Unit: 4 channels resolution km nadir SSU Stratospheric Sounding Unit: 3 channels in the 5-m CO band resolution km nadir [HRS+MSU+SSU] is called OVS ROS N Operational Vertical Sounder NOE: MSU+ SSU were replaced by AMSU-A and AMSU- Advanced Microwave Sounding Units on NOAA K L M series. Retrieval methods for temperature sounding: Physical retrievals Statistical retrievals Hybrid retrievals Physical retrievals: use the forward modeling to do an iterative retrieval of the temperature profile Steps: Selection of a first-guess initial temperature profile. Calculation of the weighting functions. 3 Forward modeling of the radiance in each channel of a sensor. 4 f the calculated radiance agrees with the measured radiance within the noise level of the sensor the current profile gives the solution. 4

15 5 f convergence has not been achieved the current profile is adjusted and steps through 5 are repeated until a solution is found. Advantages: Relevant physical processes are taken into account at each step. No data is necessary Disadvantages: Computationally intensive Requires accurate predictions of the transmittance Statistical retrievals: Do not solve the radiative transfer i.e. no forward modeling. nstead a training data set a set of radiosonde soundings that are collocated in time and space with satellite soundings is used to establish a statistical relationship between the measured radiances and temperature profiles. hese relationships are then applied to other measurements of the radiances to retrieve the temperature. Advantages: Computationally easy and fast does not require to solve the radiative transfer equation. Disadvantages: A large training data set covering different region seasons land types etc. is required. Physical processes are hidden in the statistics. Hybrid retrievals: also called inverse matrix methods Use the weighing functions but do not solve the radiative transfer equation and available data but for a limited data set. 5

16 4. Sounding of atmospheric gases. Strategy: make satellite measurements at frequencies in absorption bands of atmospheric gases. he principles of the methods for gas retrievals are generally the same as for temperature retrievals but gas inversion is more difficult: he inverse problem is more nonlinear for constituents because they enter the radiative transfer equation through the mixing ratio profile in the exponent. t is not possible to separate the radiative transfer equation into the product of a simple constituent function and one which is constituent-independent. he second main problem is that in some cases the radiances are insensitive to changes in the mixing ratio. For instance for an isothermal atmosphere at temperature any mixing ratio profile will result in the same radiances i.e.. n practice we find this problem in the retrieval of low-level water vapor; because the temperature of the water vapor is close to that of the surface infrared radiances are relatively insensitive to changes in low-level water vapor. Examples of sounders and other sensors for remote sensing of gaseous species: GOME Global Oone Monitoring Experiment ESA-ERS retrievals of O3 NO HO ro SO HCHO OCLO SCAMACHY Scanning maging Absorption Spectrometer for Atmospheric Cartography ESA-ENVSA -present retrievals of O O3 NO NO NO HO ro SO HCHO HCO CO OCLO CO CH4 MOP Measurements Of Pollution n he roposphere NASA erra 999-present retrievals of CO and CH4 retrieval algorithm involves weighing function 6

17 NASA satellite mission for atmospheric chemistry: EOS Aura: launched July Aura includes HRDLS MLS ES and OM instruments. HRDLS High Resolution Dynamics Limb Sounder an infrared limb-scanning radiometer designed to sound the upper troposphere stratosphere and mesosphere to determine temperature; the concentrations of O3 HO CH4 NO NO HNO3 NO5 ClONO CFCl CFCl3 and aerosols; and the locations of polar stratospheric clouds and cloud tops. HRDLS performs limb scans in the vertical at multiple aimuth angles measuring infrared emissions in channels ranging from 6. m to 7.76 m. MLS Microwave Limb Sounder measures lower stratospheric temperature and concentrations of H O O 3 ClO ro HCl OH HO HNO 3 HCN and N O. MLS observes in spectral bands centered near the following frequencies: 8 GH primarily for temperature and pressure; 9 GH primarily for H O HNO 3 and continuity with UARS MLS measurements; 4 GH primarily for O 3 and CO; 64 GH primarily for N O HCl ClO HOCl ro HO and SO ; and.5 H primarily for OH. OM Oone Monitoring nstrument continues the OMS record for total oone also will measure NO SO ro OClO and aerosol characteristics. 7

18 ES ropospheric Emission Spectrometer a high-resolution infrared-imaging Fourier transform spectrometer with spectral coverage of 3. to 5.4 µm at a spectral resolution of.5 cm -. ES provides simultaneous measurements of NO y CO O 3 and H O. Figure 9.3 he atmospheric parameters measured by HRDLS MLS OM and ES. he altitude range where these parameters are measured are shown as the vertical scale. n several cases the measurements overlap which provides independent perspectives and cross calibration of the measurements. 8

19 ============================================================= APPENDX. Concept of an inverse problem. Advanced reading: C. D. Rodgers nverse methods for atmospheric sounding: heory and practice Eq.[9. 9 ] which gives the solution of the radiative transfer equation with emission for the outgoing intensity at the top of the atmosphere where ; W d d W is the weighting function. d Forward problem is to calculate outgoing radiances for given temperature and gas concentration profiles. nverse problem in remote sounding is to determine what temperature and gas concentration profiles could have produced a set of radiances observed at closely spaced wavenumbers. Let s assume that is negligible small. he for nadir sounding we have W d [9.A] i i i where i i = N is the wavenumbers i.e. centers of the finite spectral bands of a spectrometer. We can ignore the frequency dependence of the Planck function if i are closely spaced. Eq.[9.A] becomes W d [9.A] i i Consider that measurements are done in the CO absorbing band so the weighting function are known and is unknown. hus we want to solve Eq.[9.A] to find and hence. 9

20 Eq.[9.A] is a so-called Fredholm integral equation of the first kind which has long been known for many associated difficulties. he general form of the Fredholm integral equation because the limits of the integral are fixed not variable of the first kind because fx appears only in the integral is where fx is unknown in our case b g y f x K y x dx [9.A3] Ky x is called the kernel or kernel function in our case gy is known in our case i a W i Problems in solving the inverse problem i.e. problems in solving Eq.[9.A] he inverse problem is ill-posed i.e. underconstrained because there are only a finite number of measurements and the unknown is a continuous function. his inverse problem is ill-conditioned i.e. any experimental error in the measurements of radiances can be greatly amplified so that the solution becomes meaningless