QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/qj.156
Case-study of a principal-component-based radiative transfer forward model and retrieval algorithm using EAQUATE data† Xu Liu,a * Daniel K. Zhou,a Allen Larar,a William L. Smithb and Stephen A. Mangoc a
c
NASA Langley Research Center, Hampton,Virginia, USA b Hampton University, Virginia, USA NPOESS Integrated Program Office, Silver Spring, Maryland, USA
ABSTRACT: The objective of the paper is to apply a novel radiative transfer model and a physical retrieval algorithm to hyperspectral data taken during the European Aqua Atmospheric Thermodynamics Experiment (EAQUATE) campaign. A principal-component-based radiative transfer model (PCRTM) is used to calculate projection coefficients of the radiance spectrum onto a set of predefined empirical orthogonal functions (EOFs) and associated derivatives with respect to the state vector. Instead of fitting channel radiances, the physical retrieval algorithm iteratively fits the principal component (PC) scores or the EOF projection coefficients of the observed radiance spectrum using the PCRTM as its forward model. Since the EOFs are orthonormal to each other, only a few PC scores are needed to capture the information content of the radiance spectrum, therefore reducing the computational time needed for running both the forward model and the inversion. This paper demonstrates the application of such a physical algorithm for retrieving atmospheric temperature, moisture and ozone profiles, and surface properties such as surface skin temperature and surface emissivity. The results have been compared with those obtained with a NAST-I channel-based physical retrieval algorithm and with those obtained from collocated radiosonde and LIDAR measurements. Copyright 2007 Royal Meteorological Society KEY WORDS
remote sensing; inversion algorithm; physical retrievals; atmospheric profiles
Received 3 November 2006; Revised 14 May 2007; Accepted 6 June 2007
1.
Introduction
Hyperspectral sensors such as the Atmospheric InfraRed Sounder (AIRS), the Tropospheric Emission Spectrometer (TES), and the Infrared Atmospheric Sounding Interferometer (IASI) are capable of providing a large amount of information about the atmospheric thermodynamic properties, chemical composition, cloud properties, and surface properties (Prunet et al., 1998; Chahine et al., 2001; Beer et al., 2002; Beer, 2006). There is a lot of effort devoted to the development of fast radiative transfer models (RTMs) for simulating radiances observed by these hyperspectral instruments (McMillin et al., 1995, 1997; Armbruster and Fischer, 1996; Tjemkes and Schmetz, 1997; Matricardi and Saunders, 1999; Edwards and Francis, 2000; Saunders et al., 1999; Liu et al., 2003; Matricardi, 2003; Moncet et al., 2004; Strow et al., 2003, 2006; Clough et al., 2006). These models are much faster than line-by-line (LBL) RTMs, but it is still challenging to incorporate thousands of channel radiances into * Correspondence to: Xu Liu, NASA Langley Research Center, Hampton, VA 23681, USA. E-mail:
[email protected] † The contributions of Xu Liu, Daniel K. Zhou, Allen Larar and Stephen A. Mango were prepared as part of their official duties as United States Federal Government employees. Copyright 2007 Royal Meteorological Society
data assimilation systems or variational retrieval systems due to computational limitations. The AIRS, which was launched on 4 May 2002 aboard the NASA Earth Observing System (EOS) Aqua satellite, is a grating instrument with 2378 spectral channels. It measures thermal emission from the Earth’s atmosphere and the Earth’s surface (Aumann et al., 2003; Goldberg et al., 2003; Pagano et al., 2003). Data from Le Marshall et al. (2005a, 2005b, 2006) have shown positive impact on weather forecasts by assimilating only about 251 channels of AIRS. Currently, the AIRS level 2 physical retrieval algorithm uses only a few hundred channels for inverting atmospheric and surface properties (Chahine et al., 2001; Susskind et al., 2003, 2006). The TES instrument is a thermal emission Fourier Transform Spectrometer (FTS) with spectral resolutions of 0.1 cm−1 for down-looking mode and 0.025 cm−1 for limb observation mode (Beer et al., 2001, 2002). It was launched on 15 July 2004 on the NASA EOS-Aura spacecraft. It has been providing valuable information with regards to atmospheric ozone profiles (Beer, 2006; Kulawik et al., 2006). With such high spectral resolutions, the TES level 2 data processing uses sub-spectral bands to reduce computational time. The IASI was launched on 19 October 2006 aboard METOPA. It is a cross-track FTS with 8461 channels (Schluessel et al., 2005). With more than 8000 available channels,
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it will be an even bigger challenge to use all of them (Prunet et al., 1998; Rabier et al., 2002). Currently only a few hundred channels are planned to be used by the 1D variational retrieval algorithm and by data assimilation systems. Since some spectral channels are correlated with each other and a lot of them may carry redundant information, often only a few hundred channels are used for inversion to provide atmospheric and surface properties (Prunet et al., 1998; Rabier et al., 2002; Rodgers, 2002; Crevoisier et al., 2003). Some of the channel selections are done based on information content analysis and some of them are done manually (Fourri´e and Th´epaut, 2002, 2003). Due to computational limitations, usually only a few atmospheric conditions are included in the channel selection process. The selected channel set may be optimal for one set of atmosphere conditions, but not for another set. Fourri´e and Th´epaut have evaluated the two AIRS channel-selection schemes for application to numerical weather prediction and concluded that the robustness and quality of the selected channels depend on the training set and selection methods. In principle, using all nominal channels in a retrieval or data assimilation system will improve retrieval performances because the signal correlation among channels will help to minimize the impact of random noise on the inversion process. Aoki (2004, 2005) described a method of compressing high-resolution infrared spectra into a few hypothetical channels using empirical orthogonal functions (EOFs) derived from weighting functions. The method offers large compression ratio while preserving almost all the information content of the original channel spectra. Since the hypothetical channels are derived from a linearized form of the radiative transfer equation, the retrieval system has to store a large amount of information at numerous linearization points. This includes atmospheric state, the associated radiance spectrum, the weighting function eigenvectors, and the matrix relating radiance spectra to hypothetical channels. In this paper, we describe the application of a novel principalcomponent-based RTM (PCRTM) to the inversion of hyperspectral data. The forward model treats the whole spectrum together, therefore removing many redundant calculations that are needed for channel-based RTMs (Liu et al., 2005, 2006). The main idea of this forward model is to perform radiative transfer calculations in a compressed and orthogonal EOF space which has very compact information content. We then use this forward model as the core component for a physical retrieval algorithm. The retrieval algorithm performs inversion directly for atmospheric thermodynamic property and surface property in the EOF space. The Jacobian needed for the inversion is provided in EOF space directly by the PCRTM. There is no need to perform EOF transformations at each iteration step, therefore saving time for the inversion process. We have applied this novel retrieval algorithm to hyperspectral data taken by National Polar-orbiting Operational Environmental Satellites System (NPOESS) Airborne Sounder Testbed – Interferometer (NAST-I). Copyright 2007 Royal Meteorological Society
These data were taken during the European Aqua Thermodynamic Experiment (EAQUATE) field campaign in September 2004. The retrieval results will be compared to collocated lidar and radiosonde measurements, and with a channel-based physical retrieval algorithm which uses a subset of channels.
2.
Description of the PCRTM forward model
The theoretical basis of the PCRTM has been described by Liu et al. (2005, 2006). Unlike traditional rapid RTMs, which either predict channel radiances or transmittances, the PCRTM predicts the PC scores of the radiance spectrum, which contains information for all the channels. The relationship between the PC scores and the predictors (monochromatic radiances) is derived from the properties of eigenvectors and instrument line shape (ILS) functions. Each PC score, Yi , is calculated via a dot product of the corresponding eigenvector, Ui , and the channel spectrum, Rchan : Yi = Ui · Rchan . (1) The channel radiance is calculated via a convolution of the ILS function with monochromatic radiances, Rkmono , within the frequency span of the ILS, φ: N
Richan =
φk Rkmono
k=1 N
(2) φk
k=1
The PC score is linearly related to a set of monochromatic radiances (Equation (3)) because both eigenvectors and ILS functions in Equations (1) and (2) do not vary from one spectrum to another. Yi =
N
ak Rkmono .
(3)
k=1
Since the model treats the entire spectrum as a whole, the redundant radiative transfer calculations are avoided. On average, the PCRTM needs a much smaller number of predictors to predict each channel radiance than conventional channel-based RTMs, therefore making it computationally very fast. The PC score vector has a much smaller dimension than the original channel radiances. This reduction in dimensionality can be a factor of 10 to 80 for hyperspectral sensors. For example, the NAST-I instrument has 8632 channels and about 100 PC scores are enough to represent the radiance spectrum accurately to within the instrument noise level. It should be mentioned that the new retrieval algorithm developed in this study performs inversion in the EOF domain directly; radiance spectra are not needed for each iteration step, therefore minimizing the time needed for the inversion process. If for some reason a channel spectrum is needed, it can be obtained simply by linearly Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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combining the pre-stored eigenvectors with the PC scores as weights (Equation (4)). Channel spectra are only used to check spectral residuals for quality-control purposes in our algorithm. Rchan =
NPC
Yi Ui + ε,
(4)
i=1
where NPC is the number of significant PCs, and ε is a vector containing forward model errors. Usually, the values of ε are smaller than 0.04 K relative to the LBL RTM used in the training process. In summary, PCRTM is much faster than the channelbased RTM since it predicts PC scores (or ‘super channel’ magnitudes) directly instead of channel radiance or transmittance individually. The parametrization of PCRTM is physical and can be trained to any desired accuracy relative to (LBL) codes (Liu et al., 2006; Saunders et al., 2006). The radiance variation as a function of temperature, H2 O, O3 , CH4 , N2 O, CO, surface emissivity and observation geometry is captured via monochromatic radiative transfer calculations. The redundant spectral information is captured via EOF representation. In the PCRTM, the radiative transfer calculations are done monochromatically only at a small number of monochromatic frequencies and multiple scattering calculations can be performed efficiently. 3. Description of a physical retrieval algorithm based on PCRTM In the PCRTM retrieval algorithm, information from all channels is transformed into PC scores and the retrieval process can take advantage of maximum information content and retain the best signal-to-noise ratio of the observed spectrum. This way, there is no need to select a subset of channels for the sake of computational speed limitation. Instead of mapping the Jacobian from channel space to EOF space, the PCRTM provides this quantity directly, which saves unnecessary multiplications of large matrices. As mentioned before, the PC scores contain all the information with regard to atmospheric temperature vertical profile, moisture and trace gas vertical profiles, cloud properties, surface skin temperature, and surface emissivities. They can be regarded as super channels. There are many advantages of performing retrievals using PC scores as super channels in an inversion algorithm. First, by projecting a measured spectrum onto a set of PC eigenvectors, the random component of the instrument noises in the spectrum is reduced, which in turn makes the retrieval system more stable and accurate (Huang and Antonelli, 2001). Secondly, the dimensionality of PC scores is much smaller than the original spectrum due to the nature of the eigenvector transformation. This size difference will result in less computation in the inversion process. Since the error covariance matrix associated with measurement is a much smaller matrix, it is affordable to include correlated error terms in the inversions. Copyright 2007 Royal Meteorological Society
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Some examples of the correlated error terms are forward model errors and correlated errors introduced by apodizing an interferogram for an FTS system (McMillin et al., 1997; Barnet et al., 2000). Thirdly, by using PC scores, which are associated with spectral components larger than instrument noise, we are essentially using all the spectral channels in the inversion process, eliminating the need to select a subset of channels due to computational consideration. It is well known that the inversion of radiance to obtain atmospheric and surface parameters is an ill-posed problem, since the radiative transfer equation relating the observed radiance to the state vector is an inhomogeneous Fredholm integral equation of the first kind, which is often extremely ill-conditioned. The radiative transfer equation can be eventually reduced to yi =
Nx
Ki,j xj ,
(5)
j =1
or, in matrix form, Y = K · X,
(6)
where the vector Y represents either channel radiances or PC scores, and y and i are the individual element and the index number for Y. For example, i can be a channel frequency index for a radiance spectrum or can be simply an index number for PC scores. X is the state vector which is generally a function of atmospheric pressure (except surface properties). x and Nx are the individual element and the total number of elements for the state vector, respectively. K is the Jacobian, which is a function that smoothes the state vector. This smooth function makes it difficult to observe fine structures in the state vector since there are many solutions with slightly different fine structures that produce almost the same y. This complexity, in turn, causes the inversion of the state vector to be extremely sensitive to the instrument noise. There are different ways to regularize the solution. For example, Tikhonov regularization (Twomey, 1963) and maximum likelihood (Rodgers, 1976, 1990) are two commonly used methods. For atmospheric temperature and moisture profile retrievals, the maximum likelihood is well suited since there are large amount of historic climatological data on these quantities. We can build meaningful a priori information and the associated statistics. The iterative maximum likelihood solution is −1 −1 T −1 xn+1 − xa = (KT S−1 y K + Sa ) K Sy
× [(yn − ym ) + K(xn − xa )],
(7)
where the subscripts n and a represent iteration number and a priori, respectively. Ym is the PC scores of the measured radiance spectrum, which were generated via EOF transformations. Yn is the forward-model-calculated PC scores using the state vector obtained from the nth iteration. Sy and Sa are error covariance matrices Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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associated with y (instrument noise and forward model errors, etc.) and background state vector xa , respectively. We can start the iteration with an x0 equal either to the climatology background xa or to a first guess which comes from a regression retrieval. It should be mentioned that due to discretization of Equation (1) and the nature of the smoothing function K, having too many vertical levels for x will result in unstable solutions. For example, radiosondes do not produce good moisture measurements above a certain altitude (i.e. 300–100 mb) and the a priori covariance matrix elements for levels above that altitude are highly correlated due to simple extrapolations used to obtain upper-atmospheric moisture profiles. This correlation will lead to an ill-conditioned Sa matrix if all vertical pressure levels are used in the inversion process, which in turn will produce bad retrievals if this ill condition is not removed. Therefore, most of the inversion algorithms have different vertical scales from the radiative transfer forward model. One can use broad functions such as trapozoidal function used by AIRS level 2 retrieval algorithm to represent the vertical profiles or use an EOF transformation of the vertical profiles (Smith, 1968). We choose to use an EOF transformation in our retrieval algorithm to represent vertical profiles and to stabilize the solution. It also reduces the dimensionality of the state vector and Jacobian, which further improves retrieval computational speed. Another important issue for an inversion algorithm is how to deal with nonlinearity. The radiative transfer equation is a double integral equation with one integral in the vertical pressure domain and the other integral in the frequency domain which is related to ILS. When the first guess is very close to the final solution, the iterative form shown in Equation (7) may be adequate, but when the solution is further away from the final solution, the nonlinearity has to be taken into account explicitly. Our experience shows that for the hyperspectral remotesensing problem, even if the first guess is from regression, we have to deal with the nonlinearity problem. Our current inversion algorithm is based on a nonlinear Levenberg–Marquardt method (Marquardt, 1963; Press et al., 1992) with climatology covariance and a priori information as constraints: −1 −1 T −1 xn+1 − xa = (KT S−1 y K + λD + Sa ) K Sy
× [(yn − ym ) + K(xn − xa )],
(8)
where D is a diagonal matrix whose elements are determined by the diagonal elements of the KT S−1 y K matrix. λ is varied according to the value of the cost function at each iteration. The cost function is defined as −1 C = (yn − ym )S−1 y (yn − ym ) + (xn − xa )Sa (xn − xa ). (9) The new physical inversion algorithm has been successfully applied to the NAST-I instrument, which is a Fourier Transform infrared spectrometer with a spectral resolution of 0.25 cm−1 and a continuous spectral coverage from 645 to 2700 cm−1 (Cousins and Smith, 1997;
Copyright 2007 Royal Meteorological Society
Smith et al., 1999, 2005). It would be very computationally intensive (or impractical) to include all 8632 NASTI channels in a conventional physical inversion algorithm. On the other hand, the PCRTM retrieval approach uses PC scores generated from all NAST-I channels and performs physical retrieval very rapidly. Table I shows the frequency range and dimensionalities of the original channel number and number of PC scores for each NAST-I spectral band. The number of PC scores is determined by projecting a group of representative NAST-I spectra onto PCRTM eigenvectors and then regenerating the NAST-I spectra using various numbers of PC scores. Results show that beyond the PC score numbers shown in Table I, the regenerated spectra do not change significantly and the changes are below the NAST-I instrument noise levels. As mentioned above, the retrieval algorithm also compresses the state vector into profile-based PCs. It serves to reduce the dimensionality of the state vector and stabilize the solution. Table II shows the original pressure grid or frequency grid for various components of the state vector and the dimensions after the EOF compression. Since surface emissivity curves are broad spectral features, there is no need to retrieve them at each channel frequency. Following the approach used by our regression algorithm (Zhou et al., 2002), we compress the surface emissivity into PC scores as well. The surface emissivity EOFs were generated from an ensemble of surface emissivities calculated using the Musuda ocean emissivity model (Musuda, 1988; Wu and Smith, 1997) and selected from the Salisbury emissivity library (Salisbury and D’Aria, 1992). The atmospheric temperature and moisture profile EOFs were generated from regional radiosondes. To illustrate the computational savings of the new retrieval approach, Table III lists the dimensions and the Table I. Comparison of matrix dimensions for various retrieval approaches. NAST-I spectral band Band 1 Band 2 Band 3
Frequency range (cm−1 )
No. of channels
No. of PC scores
645–1300 1290–2000 1984–2700
2718 2946 2968
40 30 30
Table II. Comparison of state vector dimensions before and after EOF compression. State vector
Atmospheric temperature profile Atmospheric moisture profile Atmospheric ozone profile Surface skin temperature Surface emissivity
Pressure or frequency grid
Number of EOFs used
101 101 100 1 8631
19 10 6 1 5
Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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Table III. Comparison of matrix dimensions for various retrieval approaches. Vector or matrix names/dimensions
Channel-based approach (all channels)
Channel-based approach (697 channels)
PCRTM-based retrieval approach
8632 41 8632 × 41 8632 × 8632 41 × 41 ∼2 sec
697 41 697 × 41 697 × 697 41 × 41 ∼0.16 sec
100 41 100 × 41 100 × 100 41 × 41 ∼0.04 sec
Y X K Sy Sx Time for calculating K and Y
speed of channel-based and PCRTM-based retrievals. We assume that the channel-based retrieval uses either all or a subset of NAST-I channels. If all the NAST-I channels are used for the retrieval, the forward calculations of Y and K are about a factor of 50 slower than the channelbased approach. It also takes more time to perform KT S−1 y K matrix calculation when both K and Sy have large dimensions. Currently, the NAST-I channel-based physical retrieval algorithm uses 697 channels and it produces good retrieval results compared with collocated validation data (Zhou et al., 2007). It is about a factor of 4 times slower than the PCRTM approach. Figure 1 shows a flow diagram of the PCRTM retrieval algorithm. The algorithm starts by reading in forward model parameter files, the climatology background and associated covariance matrix, and the sensor information such as instrument noise, etc. Before entering an iteration loop, the observed radiance spectra are converted to PC scores via EOF projections. The inversion process only deals with a quantity in the EOF domain. The retrieved state vector is converted into a normal pressure grid or frequency grid via EOF transformations to obtain atmospheric profiles or surface emissivities. If radiance spectra are desired, an EOF transformation of the PCRTM calculated PC scores would be performed. 4. Validate retrieval algorithm using EAQUATE data Cuomo et al. (2005) and Taylor et al. (2007) have summarized the EAQUATE campaign and the instruments involved. This study will concentrate on the flight data taken during 9–10 September 2004. There were more than 18 000 spectra collected during this flight. As the aircraft flew forward, the NAST-I instrument performed cross-track scans producing spectra in 13 fields of view (one at nadir and six at each side of the aircraft). The cross-track scan angles varied from −43° degree to +43° . The flight pattern of the PROTEUS aircraft is shown in Figure 2. Most of the observations were made over land with a small portion of the flight over the sea. The measurements were made during night-time under clear-sky conditions most of the time. The footprint size at the nadir is about 2 km for this flight. The aircraft made several overpasses above a ground validation site, (Potenza, Italy, 40.646 ° N, 15.808 ° E, elevation 770 m above sea level). A Raman lidar system (equipped with a Nd : YAG Copyright 2007 Royal Meteorological Society
Figure 1. Flow diagram of the PCRTM retrieval algorithm.
laser with second and third harmonic generators) was located at Potenza measuring atmospheric temperature and moisture profiles (Di Girolamo et al., 2004). We will concentrate on the pass around 0035 UTC since a special radiosonde was launched above Potenza at that time. We will compare our retrieval results with both the lidar measurement and the radiosonde measurement. We will also compare with results obtained using the standard NAST-I regression and physical retrievals (Zhou et al., 2002, 2005, 2007). We will study the dependency of the retrieval on the first guess. Before the retrieval starts, we project the measured NAST-I spectra onto pre-stored radiance PC components to obtain the PC scores or super channels. We then start the physical inversion by running the PCRTM forward model using a climatological first guess, which was generated using 1661 historic radiosonde ascents collected from 27.7 ° N to 79.4 ° N latitudes. The output of Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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Figure 2. Proteus flight track and NAST-I footprint on the Earth’s surface at the nadir. This figure is available in colour online at www.interscience.wiley.com/qj
the PCRTM-generated PC scores are fitted to the super channels generated from the measurement. The state vector in EOF space is adjusted according to Equation (8). The updated state vector is then transformed into physical atmospheric parameters such as temperature and moisture profiles before being used to calculate updated radiance PC scores using the PCRTM forward model. The iterative retrieval continues until either the change in the cost function is less than 5% or a maximum iteration number is reached. Currently, the maximum iteration number is set to be 6. Usually, the iteration will converge at the third or the fourth iteration. It should be emphasized that the cost function is calculated using PC scores and the associated PC score error covariance matrix (Equation (9)). To check the quality of the fits and to facilitate the physical interpretation of the retrievals, we transformed the fitted radiance PC scores into channel spectra. We then statistically compare the fitted spectra with both the original radiance spectra and the radiance PC noisefiltered radiance spectra. Figure 3 shows the statistics of the radiance differences. The root mean square (RMS) errors are calculated using 1437 NAST-I fields of view at nadir. The algorithm is capable of fitting the NASTI radiances to the instrument noise level. Figure 3(a) shows two spectra, one from the mean of the observed NAST-I spectra (blue) and the other from the mean of the PCRTM calculated spectra (red). Since the NASTI instrument is a high-spectral-resolution spectrometer, some of the spectral lines (such as some water and CO2 lines) have very large optical depth at line centres or band centres. These lines only sense radiation emitted near the aircraft altitude, which is very cold. The NASTI radiances in the 2280–2390 cm−1 spectral region are very small and sometimes have negative values. They are not plotted in the figure since a negative radiance cannot be converted to a brightness temperature. The blue curve in Figure 3(b) shows the RMS difference between Copyright 2007 Royal Meteorological Society
the observed and retrieval-calculated NAST-I radiances. The red curve is the NAST-I instrument noise equivalent difference temperature, N ET . It is converted from the noise equivalent difference radiance, N ER, using the NAST-I brightness temperature spectrum shown in Figure 3(a). Since the centre of the short-wave CO2 spectral region and some water spectral lines have very low brightness temperatures, the N ET in those spectral regions are large. It is obvious that the signal-to-noise ratio in these spectral regions are not as good as those that sense warmer parts of the atmosphere or the Earth’s surface, which illustrates why it is so important to use all the channels to beat down the random noise. The PCRTM approach does exactly that. By projecting the observed radiances onto the PC eigenvectors, the random noise gets reduced. The effect is demonstrated in Figure 3(c). The blue curve shows the RMS differences of the PCRTM calculated radiances and PC noise-filtered NAST-I radiances. The RMS errors are much smaller than those shown in Figure 3(b). There are different ways to validate the fast radiative transfer forward model used in the retrieval (in this case, the PCRTM). One way is to compare the PCRTMgenerated radiance with those generated by LBLRTM. The RMS error between PCRTM and LBLRTM is usually less than 0.1 K depending on how many predictors are used in the forward model (Liu et al., 2005, 2006). But this approach does not account for the errors due to inaccurate knowledge of the spectral line parameters. Another approach is to compute calculated NAST-I spectra using collocated radiosondes or lidar measurements. However, for the Potentza site, we do not have an independent measurement of the land surface emissivity spectrum in the NAST-I spectral region. Over the ocean the surface emissivities are better known, but we do not have a good collocated radiosonde. A third approach is to retrieve atmospheric and surface parameters from the NAST-I Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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Figure 3. (a) shows the mean of 1437 observed NAST-I spectra (blue) and the mean of the PCRTM calculated spectra (red). (b) shows the RMS difference between the observed and calculated NAST-I radiances (blue). The red curve is the NAST-I instrument noise calculated using the mean brightness temperature spectrum shown in (a). (c) shows the RMS difference between the EOF noise filter radiances and the PCRTM calculated radiances (blue), with the instrument N ET (red) shown again as a reference.
spectra using the PCRTM retrieval algorithm, and then compare the retrieved temperature and moisture profiles with collocated radiosondes and lidar measurements. We have studied all three approaches in this paper. For the first approach, we used the lidar-measured temperature and moisture profiles as inputs to both the LBLRTM and the PCRTMs. The trace gas vertical profiles are fixed to the standard US atmosphere. The surface emissivity is assumed to be 0.98 at all NAST-I channel frequencies. For the second approach, we picked a NAST-I-observed spectrum measured over Potenza and compare it with the ones calculated using the RTMs mentioned above. Figure 4(a) shows the observed NAST-I spectrum (blue) and the calculated NAST-I spectrum using the PCRTM (red). The LBLRTM calculated spectrum is not shown since it agrees with PCRTM very well. The blue curve in Figure 4(b) shows the difference between the observed NAST-I spectrum and the PCRTM calculated spectrum. The red curve is the difference between the PCRTM and LBLRTM calculated spectra. They are generally less than 0.1 K as mentioned before. This indicates that the PCRTM is capable of modelling the NAST-I spectrum very well relative to the LBLRTM calculations. The PCRTM forward model errors relative to LBLRTM are negligible compared with other sources of error such as the knowledge of molecular spectroscopic parameters, the true atmospheric state, and the true surface parameters. The differences near 1050 cm−1 , 1300 cm−1 , 2150 cm−1 (blue curve, Figure 4(b)) are due to the incorrect amount of trace gas amount for O3 , N2 O, CH4 and CO in the Copyright 2007 Royal Meteorological Society
radiative transfer forward model. The difference for surface channels is due to the assumption of constant emissivities in the radiative transfer forward calculation. The differences for the upper atmospheric water channels near 1400–1800 cm−1 are due lack of sensitivity of the lidar measurement for the high-altitude water vapour. If we use a radiosonde moisture profile as our input to the PCRTM forward model, the difference in this region will be even bigger. On the other hand, the lidar temperature profile and the radiosonde temperature profile agree very well all the way up to the aircraft altitude. The differences in the spectral region from 650 cm−1 to 750 cm−1 are most likely due to the inaccurate CO2 line parameters in the radiative transfer modelling. Figure 5 shows a cross-section of the retrieved atmospheric temperature and humidity for the whole flight track. The vertical white lines in the plots are retrievals discarded due to the turn of the aircraft. The blanks between 0 and 2 km are due to the fact that we only plot profiles above the surface elevations. There are apparent changes in temperature profiles in the altitude range from 4 to 10 km and near the Earth’s surfaces (Figure 5(a)). The moisture profiles show a moist layer in the altitude range from 7 to 10 km and a dry layer around 6 km. If we carefully match the flight time with the physical locations of the NAST-I footprints on the ground, we see clearly the repeated atmospheric features when the aircraft flew to the same location (see Figure 2). For example, the water vapour between 3 and 5 km varied along the flight track. These variations are mostly symmetrical around Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
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Figure 4. (a) shows an observed NAST-I spectrum near Potenza (blue) and a PCRTM-calculated spectrum using a lidar measurement (red). In (b), the blue curve is the difference between the two spectra shown in (a), and the red curve is the difference between the LBLRTM- and PCRTM-calculated spectra.
Figure 5. Cross-sections of (a) the retrieved atmospheric temperature profiles (K) and (b) atmospheric humidity mixing ratio (g kg−1 ) on a logarithmic scale.
the vertical white lines where the aircraft made turns. As seen from Figure 2, after the aircraft made turns, it mostly flew along the same track but in different directions. This Copyright 2007 Royal Meteorological Society
means that the retrieved humidity profiles are consistent whenever the aircraft are making measurements at the same locations. Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
CASE-STUDY OF A RADIATIVE TRANSFER FORWARD MODEL AND RETRIEVAL ALGORITHM
To quantify the quality of the retrieval, we selected a flight segment when the Proteus aircraft overpassed the Potenza validation ground site around 0035 UTC because a special radiosonde was launched during that period. We also compare our retrieval results with those obtained using the existing NAST-I EOF regression and channel-based physical retrieval algorithm. The NASTI EOF regression retrieval algorithm (Zhou et al., 2002, 2005) projects 4424 channels of NAST-I spectra onto a set of radiance eigenvectors generated using an ensemble of radiosondes and an Optimal Spectral Sampling RTM (Moncet et al., 2001; Liu et al., 2003). It retrieves atmospheric temperature, moisture and ozone profiles, cloud parameters, surface skin temperature, and surface emissivities. The NAST-I channel-based physical retrieval algorithm uses 697 NAST-I channels and uses the results from the EOF regression as a first guess (Zhou et al., 2007). An iterative minimum information method is used to further improve atmospheric thermodynamic properties and surface skin temperature. The surface emissivities are fixed to the values retrieved by the regression algorithm. Figure 6(a) shows a comparison of the PCRTM retrieved temperature profile with those from the NAST-I regression retrieval, channel-based physical retrieval, the radiosonde, and the lidar measurements. The radiosonde and the lidar-measured temperature profiles agree with each other very well. In general, the temperature profiles retrieved from all three NAST-I retrieval algorithms
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have similar error patterns relative to radiosonde or lidar (Figure 6(b)). From 9 to 14 km, all three NASTI retrieval methods agree with each other to within 0.2 K. In the altitude range from 6 to 9 km, the differences between the PCRTM retrieval and the channelbased physical retrieval get larger (∼1.6 K). The channelbased retrievals have better agreement with radiosonde and lidar. From 0.7 km to 6 km, the PCRTM retrieval seems to have better agreement with radiosonde and lidar (less than 1 K). The difference near the surface could be due to the difference in emissivity retrievals in the different algorithms. The PCRTM algorithm retrieves surface emissivities simultaneously with atmospheric profiles while the NAST-I channel-based physical retrieval fixed the emissivity to that retrieved from the regression algorithm. For the atmospheric water vapour vertical profiles (Figure 6(c,d)), again all three NAST-I retrievals have similar error patterns relative to radiosonde and lidar. The radiosonde moisture measurement seems to have a cold bias from 8 km to 12 km compared with the lidar and the NAST-I retrievals. This bias has been confirmed by simulating both the AIRS and the NAST-I radiances measured over Potenza using the temperature and moisture profiles from this radiosonde and comparing them with the observed radiances (Allen et al., 2005). For altitude above 12 km, the lidar measurement has relatively large errors due to small signal-to-noise ratios. Therefore, our comparisons mainly concentrate in the
Figure 6. (a) NAST-I retrieved temperature profiles compared with sonde and lidar measurements, and (b) differences from lidar. (c, d) are as (a, b), but for humidity mixing ratio profiles. Copyright 2007 Royal Meteorological Society
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altitude range from 0.7 to 12 km. Although it is not apparent in Figure 6(c), the PCRTM retrieval algorithm seems to have a better agreement with the lidar measurement in the altitude range from 8 to 11 km. This is more apparent when we convert the humidity mixing ratio (g kg−1 ) into relative humidity (Figure 7). This improved agreement may be due to the fact that the PCRTM uses all moisture channels, while the channel-based physical retrieval uses a subset of channels. As discussed before, the strong H2 O lines have low brightness temperature (or low radiance) and therefore have worse signal-to-noise ratio. Using more H2 O channels will help to reduce the impact of random noises on the retrieval. Figure 7 also shows that the physically based retrievals provide better moisture retrieval when compared to the regression retrieval. It is apparent from Figures 6 and 7 that the NAST-I retrievals are not capturing the fine vertical structures of the water vapour vertical profiles near the surface. Since the temperature and moisture profiles were compressed into EOF space, we performed a study to evaluate the impact of EOF representation errors on the retrieval. We projected the Potenza special radiosonde temperature and moisture profiles onto temperature and moisture eigenvectors generated using the historical radiosonde database mentioned before, and then regenerated the sonde profiles using various numbers of eigenvectors. The result is presented in Figure 8. When 19 temperature EOFs were
Figure 7. Comparison of NAST-I retrieved relative humidity profiles with those of radiosonde and lidar measurements.
used to represent the sonde profile, the EOF representation errors (red curve, Figure 8(b)) seem to be small at altitudes except in the range from 1.5 to 5 km where there are two fine vertical structures. When 25 EOFs were used to represent the sonde temperature profile, the errors (blue curves) get much smaller. Our retrieval uses 19 temperature EOFs to compress temperature profiles. This number was empirically determined by looking at the RMS errors of the regenerated profiles (less than 0.6 K for
Figure 8. (a) Temperature profile from radiosonde and regenerated using indicated EOFs. (b) Differences of two EOF regenerations from radiosonde data. (c, d) are as (a, b), but for mixing ratio. Copyright 2007 Royal Meteorological Society
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vertical structure greater than 1.0 km). For the retrievals over Potenza, it is clear that the PCRTM retrieval errors above 5 km are definitely not due to the EOF transformation of the temperature profiles because 19 EOFs can represent the vertical structure in that altitude range very well. On the other hand, the errors in the altitude range from 1.5 to 5 km (the cyan curve in Figure 6(a)) seem to follow the same pattern as the red curve in Figure 8(b). One would think that the retrieval algorithm should use more temperature EOFs when retrieving temperature profiles. However, studies show that increasing the number of temperature EOFs from 19 to 25 does not change temperature retrieval errors. This indicates that other factors such as random noise and systematic errors are preventing us from retrieving the fine structure of the temperature profile. Nevertheless, we may want to increase the number of EOFs for temperature retrievals in the future if the climatology profiles used to generate the EOFs have large variations. For the water vapour profile, using 9 EOFs does not capture the fine structures in the altitude range from 1 to 6 km. All the NASTI retrieved humidity profiles have similar error patterns to the red curve Figure 8(d). Increasing the EOF numbers to 30 produces a good representation of the water vapour vertical structures (blue curves in Figure 8(c,d)), but the PCRTM retrieval still cannot resolve those features. Again the limiting factor is not the EOF representation using only 10 water vapour EOFs in the PCRTM retrieval algorithm. The fact that our channelbased retrieval algorithms do not use EOF representations of the vertical profiles and the retrieved errors are similar to the PCRTM retrieval algorithm supports our conclusion above. In all of our NAST-I retrieval algorithms, no bias corrections were made to the NAST-I spectra to account
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for forward model errors and instrument systematic errors. Currently, the PCRTM treats the NAST-I noise as uncorrelated noise only. We plan to go back to NAST-I level 1 data and characterize the NAST-I correlated noise source and include them correctly in the error covariance. Since bias tuning was not performed in our retrievals, errors due to radiative transfer calculations such as CO2 line-mixing parametrizations and water vapour continua characterizations are likely to impact on our retrieval accuracies. The PCRTM fast forward model was trained with v8.3 of the LBLRTM, while the OSS fast forward model was trained with v6.01 of the LBLRTM. In v8.3, the chi line-shape factor and the continuum for CO2 optical depth calculations have been modified in the 500 cm−1 to 900 cm−1 regions, resulting in an overall increase in CO2 absorption (Clough et al., 2006). In version 6.01 of the LBLRTM, the CKD 2.4.1 water continuum model was used while the version 8.3 uses the MT CKD 1.0 continuum model. Clough et al. have made changes to both CO2 line-coupling parametrizations and continuum model (MT CKD v1.3). We plan to train the PCRTM fast forward model using the most recent version of LBLRTM to study the impact of spectroscopy on the retrievals. Since we do not have ground truth for land surface emissivity, we picked a case to study the ocean emissivity retrievals. Figure 9 shows an example of the retrieved ocean surface emissivity and a laboratory-measured emissivity from the Johns Hopkins University emissivity library database. Since the emissivity is a function of sea surface wind speed, its magnitude and shape are expected to change. Overall, the agreement is good. The retrieval does not have sensitivity for the spectral region where the NAST-I channels doe not sense the surface (e.g. 1350–1900 cm−1 ).
Figure 9. PCRTM-retrieved sea surface emissivity (blue) and the measured one from the JHU emissivity library (red). Copyright 2007 Royal Meteorological Society
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Figure 10(a) shows the surface skin temperature retrieved using the PCRTM retrieval algorithm with a climatology first guess. Figure 10(b) shows the difference of the retrieved surface skin temperatures retrieved using a climatology first guess and those retrieved using a regression first guess. Figure 10(c) shows the digital elevations for the ground footprints covered by the NAST-I observations. Figure 10(d) shows a histogram of the surface skin temperature differences due to the first guesses. All NAST-I observations taken during the September 9 to 10 flight were included in the plots. It can be seen from Figure 10 that the surface skin temperatures over the sea surfaces are much higher than those of the land surfaces. The sea surface temperature over the Adriatic Sea is lower than that over the Tyrrhenian Sea. There are a few cold areas over the Tyrrhenian Sea along the NAST-I flight path, which could be due to cloud coverage. Over the land, there are more variations in the retrieved surface skin temperatures, which are due to mountain terrain variations. To emphasize the terrain variation, the upper limit of the digital elevation in the plot is set to be 1.0 km. It is clear that the surface skin temperatures are anti-correlated with the digital elevations of the surfaces, with temperature over mountain tops lower than those close to sea level. This anti-correlation is to be expected for measurements taking during the night when the solar radiation is not present. The histogram (Figure 10(d)) shows that the retrieved surface skin temperature is not very sensitive to the first
guess. To confirm the robustness of the retrieval system, we have plotted the temperature and moisture profiles retrieved from the regression first guess. The results are almost identical to those shown in Figure 6. This seems to indicate that the retrieval algorithm is capable of providing consistent solutions regardless of the starting point – a desirable feature to have. 5.
Conclusions
In conclusion, a new type of fast radiative transfer model (PCRTM) and retrieval algorithm has been developed. Instead of modelling and inverting traditional channel spectra, the new approach models the eigenvector transformed super channels (or PC scores) directly. For a given state vector, the PCRTM provides PC scores and associated Jacobian. The PCRTM can also produce channel radiances for the purpose of quality control and for the physical interpretation of the data. By performing retrieval in EOF space, the algorithm is essentially using all the available channels, but with much smaller dimensions and greater speed. The inversion approach is based on a maximum likelihood approach and uses the Levengerg–Marguardt algorithm for dealing with nonlinearity of the radiative transfer equation. The algorithm is very stable and is capable of producing consistent retrievals with different initial guesses. The algorithm has been applied to more than 18 000 NAST-I spectra taken on 9 and 10 September 2004 in
Figure 10. (a) PCRTM-retrieved surface skin temperature, (b) difference of the retrieved surface temperature between different first guesses, (c) surface digital elevations, and (d) histogram of the skin temperature differences. Copyright 2007 Royal Meteorological Society
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Italy. The retrieval algorithm is capable of fitting NAST-I radiances to within instrument noise level over most frequency ranges. Using the atmospheric profiles measurement by the lidar instrument over Potenza, the PCRTM forward model calculated NAST-I radiance spectrum agrees very well with that calculated using the LBLRTM, indicating very good accuracy of the fast RTM. A case-study over the Potenza validation site shows that the PCRTM-retrieved temperature profile compared well with those obtained from the NAST-I EOF regression algorithm and the NAST-I channel-based physical retrieval algorithm. All the NAST-I retrieved temperatures agree with radiosonde and LIDAR measurements reasonably well and are expected to improve when we include bias tuning in the future. The PCRTM-retrieved moisture profile agrees with the channel-based physical retrieval very well, except in the altitude range from 10 to 12.5 km where the PCRTM retrieval method seems to be better. This result may be attributed to the use of all channels in the PCRTM retrieval algorithm. Both NASTI physical retrieval algorithms produce better moisture retrievals compared with the regression retrievals. We will look into more cases and study the impact of the systematic errors on the retrievals. The PCRTM forward model will be updated using improved LBLRTMs. Acknowledgements The authors would like to acknowledge the contributions from the NASA Langley Research Center and the Instituto di Meteodologie per l’Analisi Ambientale. We are grateful to Paolo Di Girolamo from the Universit`a degli Studi della Basilicata for providing the LIDAR retrievals. This work is supported by funds from NASA Headquarters, the NPOESS Integrated Program Office (IPO), and NASA Largley Research Center. The authors acknowledge support from NASA Headquarters Earth Science Division Associate Director for Research, Dr. Jack A. Kaye, and IPO Algorithm Division Chief, Dr. Karen St. Germain. We are thankful to AER Inc. for providing the LBLRTM and OSS fast radiative transfer code. We also the two anonymous reviewers for their helpful comments. References Aoki T. 2004. Channel compression of trace gas remote sounder by expanding the weighting function with empirical orthogonal functions, J. Meteorol. Soc. Japan 82: 1081–1093. Aoki T. 2005. Channel compression of high-resolution infrared spectra using a hypothetical channel system. J. Meteorol. Soc. Japan 83: 41–55. Armbruster W, Fischer J. 1996. Improved method of exponential sum fitting of transmissions to describe the absorption of atmospheric gases. Appl. Opt. 12: 1931–1941. Aumann HH, Chahine MT, Gautier C, Goldberg MD, Kalnay E, McMillin LM, Revercomb H, Rosenkranz PW, Smith WL, Staelin DH, Strow LL, Susskind J. 2003. AIRS/AMSU/HSB on Aqua Mission: Design, science objectives, data products, and processing system. IEEE Trans Geosci. Remote Sensing 41: 253–264. Barnet CD, Blaisdell JM, Susskind J. 2000. Practical methods for rapid and accurate computation of interferometric spectra for remote sensing applications. IEEE Trans. Geosci. Remote Sensing 38: 169–183. Copyright 2007 Royal Meteorological Society
255
Beer R, Bowman KW, Brown PD, Clough SA, Eldering A, Goldman A, Lampal M, Luo M, Murcray FJ, Osterman GB, Rinsland CP, Rodgers CD, Shephard M, Kulawik SS, Worden HM, Worden J. 2002. ‘TES Level 2 Algorithm theoretical basis document’, version 1.16. JPL D-16 474. Jet Propulsion Laboratory: Pasadena. Beer R. 2006. TES on the Aura Mission: Scientific objectives, measurements, and analysis overview. IEEE Trans. Geosci. Remote Sensing 44: 1102–1105. Beer R, Glavich TA, Rider DM. 2001. Tropospheric emission spectrometer for the Earth Observing System’s Aura satellite. Appl. Opt. 40: 2356–2367. Chahine MT, Aumann H, Goldberg M, McMillin L, Rosenkranz P, Staelin D, Strow L, Susskind J, Gunson M. 2001. AIRS Level 2 Algorithm theoretical basis document, version 2.2. JPL D-17006. Jet Propulsion Laboratory: Pasadena. Clough SA, Shephard MW, Worden J, Brown PD, Worden HM, Luo M, Rodgers CD, Rinsland CP, Goldman A, Brown L, Kulawik SS, Eldering A, Lampel MC, Osterman G, Beer R, Bowman K, Cady-Pereira KE, Mlawer EJ. 2006. Forward model and Jacobians for tropospheric emission spectrometer retrievals. IEEE Trans. Geosci. Remote Sensing 44: 1308–1323. Cousins D, Smith WL. 1997. National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Airborne Sounder Testbed-Interferometer (NAST-I). Proc. SPIE 3127: 323–331. Crevoisier C, Chedin A, Scott NA. 2003. AIRS channel selection for CO2 and other trace-gas retrievals. Q. J. R. Meteorol. Soc. 129: 2719–2740. Cuomo V, Amodeo A, Antonelli P, Boselli A, Bozzo A, Cornacchia C, D’Amico G, Di Bisceglie M, Esposito F, Di Girolamo P, Grieco G, Larar AM, Leone L, Madonna F, Maestri T, Marchese R, Masiello G, Meoli G, Mona L, Pandolfi M, Pappalardo G, Pavese G, Pisani G, Restieri R, Rizzi R, Romano F, Rossi E, Rossi F, Sabatino D, Serio C, Smith WL Jr, Spinelli N, Summa D, Todini G, Villacci D, Wang X, Zhou DK. 2005. The Italian phase of the EAQUATE measurement campaign. Proc. SPIE 5979: 396–409. Di Girolamo P, Marchese R, Whiteman DN, Demoz BB. 2004. Rotational Raman lidar measurements of atmospheric temperature in the UV. Geophys. Res. Lett. 31: L01106, doi:10.1029/2003GL018342. Edwards DP, Francis GL. 2000. Improvements to the correlatedk radiative transfer method: Application to satellite infrared sounding. J. Geophys. Res. 105(D14): 18135–18156. DOI: 10.1029/2000JD900131. Fourri´e N, Th´epaut J-N. 2002. ‘Validation of the NESDIS near-realtime AIRS channel selection’. Tech. Memo. 390. ECMWF: Reading, UK. Fourri´e N, Th´epaut J-N. 2003. Evaluation of the AIRS near-real-time channel selection for application to numerical weather prediction. Q. J. R. Meteorol. Soc. 129: 2425–2439. Goldberg MD, Qu Y, McMillin LM, Wolf W, Zhou L, Divakarla M. 2003. AIRS near real-time products and algorithms in support of operational numerical weather prediction. IEEE Trans. Geosci. Remote Sensing 41: 379–389. Huang H-L, Antonelli P. 2001. Application of principal component analysis to high-resolution infrared measurement compression and retrieval. J. Appl. Meteorol. 40: 265–388. Kulawik SS, Worden H, Osterman G, Luo M, Beer R, Kinnison DE, Bowman KW, Worden J, Eldering A, Lampel M, Steck T, Rodgers CD. 2006. TES atmospheric profile retrieval characterization: An orbit of simulated observations. IEEE Trans. Geosci. Remote Sensing 44: 1324–1333. Le Marshall J, Jung J, Derber J, Chahine M, Treadon R, Lord S, Goldberg M, Wolf W, Liu HC, Joiner J, Woollen J, Todling R, van Delst P, Tahara Y. 2006. Improving global analysis and forecasting with AIRS. Bull. Am. Meteorol. Soc. 87: 747–750. Le Marshall J, Jung J, Derber J, Treadon R, Lord S, Goldberg M, Wolf W, Liu HC, Joiner J, Woollen J, Todling R. 2005a. AIRS hyperspectral data improves southern hemisphere forecasts. Aust. Meteorol. Mag. 54: 57–60. Le Marshall J, Jung J, Derber J, Treadon R, Lord S, Goldberg M, Wolf W, Liu HC, Joiner J, Woollen J, Todling R. 2005b. Impact of Atmospheric InfraRed Sounder observations on weather forecasts. Eos – Trans. Am. Geophys. Union 86: 109. Liu X, Smith WL, Zhou DK, Larar A. 2005. A principal componentbased radiative transfer forward model (PCRTM) for hyperspectral instruments. Proc. SPIE Int. Soc. Opt. Eng. 5655: 96–105. Liu X, Moncet J-L, Zhou DK, Smith WL. 2003. A fast and accurate forward model for the NAST-I Instrument. Paper OMB2 in Optical Remote Sensing. OSA Technical Digest Series, Optical Society of America: Washington, DC. Q. J. R. Meteorol. Soc. 133: (S3) 243–256 (2007) DOI: 10.1002/qj
256
X. LIU ET AL.
Liu X, Smith WL, Zhou DK, Larar A. 2006. Principal Componentbased Radiative Transfer Forward Model (PCRTM) for hyperspectral sensors, Part I: Theoretical concept. Appl. Opt. 45: 201–209. Marquardt D. 1963. An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11: 431–441. Masuda K, Takashima T, Takayama Y. 1988. Emissivity of pure and sea waters for the model sea surface in the infrared window regions. Remote Sensing Environ. 24: 319–329. Matricardi M. 2003. ‘RTIASI-4, a new version of the ECMWF fast radiative transfer model for infrared atmospheric sounding interferometer’. Tech. Memo. 425, ECMWF: Reading, UK. Matricardi M, Saunders RW. 1999. A fast radiative transfer model for simulation of IASI radiances. Appl. Opt. 38: 5679–5691. McMillin LM, Goldberg MD, Ding H, Susskind J, Barnet CD. 1997. A forward calculation for interferometers: method and validation. Appl. Opt. 37: 3059–3068. McMillin LM, Crone LJ, Kleespies TJ. 1995. Atmospheric transmittance of an absorbing gas. 5: Improvements to the OPTRAN approach. Appl. Opt. 34: 8396–8399. Moncet J-L, Liu X, Helene R, Snell H, Zaccheo S, Lynch R, Eluszkiewicz J, He Y, Uymin G, Lietzke C, Hegarty J, Boukabara S, Lipton A, Pickle J. 2001. ‘Algorithm Theoretical Basis Document (ATBD) for the Cross-track Infrared Sounder (CrIS) Environmental Data Records (EDR). v1.2.3’. AER Document Released to ITT and Integrated Program Office. http://npoesslib.ipo.noaa.gov/ IPOarchive/SCI/atbd/cris atbd 03 09 01.pdf. Moncet J-L, Uymin G, Snell HE. 2004. Atmospheric radiance modeling using the optimal spectral sampling (OSS) method. Proc. SPIE Int. Soc. Opt. Eng. 5425: 368–374. Musuda K, Takashima T, Takayama Y. 1988. Emissivity of pure and sea waters for the model sea surface in the infrared window regions. Remote Sensing Environ. 24: 313–29. Pagano TS, Aumann HH, Hagan DE, Overoye K. 2003. Prelaunch and in-flight radiometric calibration of the Atmospheric Infrared Sounder (AIRS). IEEE Trans. Geosci. Remote Sensing 41: 265–273. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. 1992. Numerical Recipes. (2nd edition). Cambridge University Press: Cambridge, UK. Prunet P, Th´epaut J-N, Cass´e V. 1998. The information content of clear-sky IASI radiances and their potential for numerical weather prediction. Q. J. R. Meteorol. Soc. 124: 211–241. Rabier F, Fourri´e N, Chafa¨ı D, Prunet P. 2002. Channel selection methods for Infrared Atmospheric Sounding Interferometer radiances. Q. J. R. Meteorol. Soc. 128: 1011–1027. Rodgers CD. 1976. Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation. Rev. Geophys. Space Phys. 14: 609–624. Rodgers CD. 1990. Characterization and error analysis of profiles retrieved from remote-sounding measurements. J. Geophys. Res. 95: 5587–5595. Rodgers CD. 2002. Inverse Methods for Atmospheric Sounding – Theory and Practice. World Scientific: Singapore. Salisbury JW, D’Aria DM. 1992. Emissivity of terrestrial material in the 8–14 µm atmospheric window. Remote Sens. Environ. 42: 83–106. Saunders R, Matricardi M, Brunel P. 1999. An improved fast radiative transfer model for assimilation of satellite radiance observations. Q. J. R. Meteorol. Soc. 125: 1407–1425. Saunders R, Rayer P, Brunel P, von Engeln A, Bormann N, Strow L, Hannon S, Heilliette S, Liu X, Miskolczi F, Han Y, Masiello G,
Copyright 2007 Royal Meteorological Society
Moncet J-L, Uymin G, Sherlock V, Turner DS. 2006. A comparison of radiative transfer models for simulating AIRS radiances. J. Geophys. Res. 112: D01S90, DOI: 10.1029/2006JD007088. Schluessel P, Hultberg TH, Phillips PL, August T, Calbet X. 2005. The operational IASI Level 2 processor. Adv. Space Res. 36: 982–988. Smith WL. 1968. An improved method for calculating tropospheric temperature and moisture from satellite radiometer measurements. Mon. Weather Rev. 96: 387–396. Smith WL, Larar AM, Zhou DK, Sisko CA, Li J, Huang B, Howell HB, Revercomb HE, Cousins D, Gazarik MJ, Mooney D. 1999. NAST-I: results from revolutionary aircraft sounding spectrometer. In SPIE Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, Larar AM. (ed.) SPIE 3756: 2–8. Smith WL, Zhou DK, Larar AM, Mango SA, Howell HB, Knuteson RO, Revercomb HE, Smith WL Jr. 2005. The NPOESS Airborne Sounding Testbed Interferometer – Remotely sensed surface and atmospheric conditions during CLAMS. J. Atmos. Sci. 62: 1117–1133. Strow LL, Hannon SE, De Souza-Machado S, Motteler HE, Tobin D. 2003. An overview of the AIRS radiative transfer model. IEEE Trans. Geosci. Remote Sensing 41: 303–313. Strow LL, Hannon SE, De-Souza Machado S, Motteler HE, Tobin DC. 2006. Validation of the Atmospheric InfraRed Sounder radiative transfer algorithm. J. Geophys. Res. 111: D09S06, DOI:10.1029/2005 JD006146. Susskind J, Barnet C, Blaisdell J, Iredell L, Keita F, Kouvaris L, Molnar G, Chahine M. 2006. Accuracy of geophysical parameters derived from Atmospheric Infrared Sounder/Advanced Microwave Sounding Unit as a function of fractional cloud cover. J. Geophys. Res. 111: D09S17, DOI:10.1029/2005JD006272. Susskind J, Barnet CD, Blaisdell JM. 2003. Retrieval of atmospheric and surface parameters from AIRS/AMSU/HSB data in presence of clouds. IEEE Trans. Geosci. Remote Sensing 41: 390–409. Taylor JP, Smith WL, Cuomo V, Larar AM, Zhou DK, Serio C, Maestri T, Rizzi R, Newman SM, Antonelli P, Mango SA, Di Girolamo P, Esposito F, Grieco G, Summa D, Restieri R, Masiello G, Romano F, Pappalardo G, Pavese G, Mona L, Amodeo A, Pisani G. 2007. EAQUATE – An international experiment for hyperspectral atmospheric sounding validation. Bull. Am. Meteorol. Soc. In press. Tjemkes SA, Schmetz J. 1997. Synthetic satellite radiances using the radiance sampling method, J. Geophys. Res. 102: 1807–1818. Twomey S. 1963. On the numerical solution of Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature. J. Assoc. Comput. Math. 10: 97–101. Wu XQ, Smith WL. 1997. Emissivity of rough sea surface for 8–13 microns: Modeling and verification. Appl. Opt. 36(12): 2609–2619. Zhou DK, Smith WL, Li J, Howell HB, Cantwell GW, Larar AM, Knuteson RO, Tobin DC, Revercomb HE, Mango SA. 2002. Thermodynamic product retrieval methodology for NAST-I and validation. Appl. Opt. 41: 6957–6967. Zhou DK, Smith WL, Cuomo V, Taylor JP, Barnet CD, Di Girolamo P, Pappaglardo G, Larar AM, Liu X, Newman SM, Lee C, Mango SA. 2007. Retrieval validation during the European AQUA Thermodynamic Experiment. Q. J. R. Meteorol. Soc. 133: 203–215. Zhou DK, Smith WL, Liu X, Larar AM, Huang H-LA, Li J, McGill MJ, Mango SA. 2005. Thermodynamic and cloud parameters retrieval using infrared spectral data. Geophys. Res. Lett. 32: L15805.
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