Signal Processing for Remote Sensing - Chapter 11

11 Neural Network Retrievals of Atmospheric Temperature and Moisture Profiles from High-Resolution Infrared and Microwave Sounding Data William J. Blackwell CONTENTS 11.1 Introduction..................................................................................................................... 204 11.2 A Brief Overview of Spaceborne Atmospheric Remote Sensing............................ 205 11.2.1 Geophysical Parameter Retrieval................................................................... 207 11.2.2 The Motivation for Computationally Efficient Algorithms....................... 208 11.3 Principal Components Analysis of Hyperspectral Sounding Data........................ 208 11.3.1 The PC Transform............................................................................................. 209 11.3.2 The NAPC Transform...................................................................................... 209 11.3.3 The Projected PC Transform........................................................................... 209 11.3.4 Evaluation of Compression Performance Using Two Different Metrics ...................................................................................... 210 11.3.4.1 PC Filtering ....................................................................................... 210 11.3.4.2 PC Regression................................................................................... 211 11.3.5 NAPC of Clear and Cloudy Radiance Data................................................. 212 11.3.6 NAPC of Infrared Cloud Perturbations........................................................ 212 11.3.7 PPC of Clear and Cloudy Radiance Data..................................................... 214 11.4 Neural Network Retrieval of Temperature and Moisture Profiles........................ 216 11.4.1 An Introduction to Multi-Layer Neural Networks..................................... 216 11.4.2 The PPC–NN Algorithm.................................................................................. 217 11.4.2.1 Network Topology........................................................................... 218 11.4.2.2 Network Training............................................................................. 218 11.4.3 Error Analyses for Simulated Clear and Cloudy Atmospheres ............... 218 11.4.4 Validation of the PPC–NN Algorithm with AIRS=AMSU Observations of Partially Cloudy Scenes over Land and Ocean .............. 220 11.4.4.1 Cloud Clearing of AIRS Radiances............................................... 220 11.4.4.2 The AIRS=AMSU=ECMWF Data Set.............................................. 221 11.4.4.3 AIRS=AMSU Channel Selection..................................................... 221 11.4.4.4 PPC–NN Retrieval Enhancements for Variable Sensor Scan Angle and Surface Pressure.................................................. 223 11.4.4.5 Retrieval Performance..................................................................... 223 11.4.4.6 Retrieval Sensitivity to Cloud Amount........................................ 223 11.4.5 Discussion and Future Work.......................................................................... 224 ß 2007 by Taylor & Francis Group, LLC. 11.5 Summary.......................................................................................................................... 225 Acknowledgments..................................................................................................................... 228 References ................................................................................................................................... 228 11.1 Introduction Modern atmospheric sounders measure radiance with unprecedented resolution and accuracy in spatial, spectral, and temporal dimensions. For example, the Atmospheric Infrared Sounder (AIRS), operational on the NASA EOS Aqua satellite since 2002, pro-vides a spatial resolution of 15 km, a spectral resolution of n=Dn 1200 (with 2,378 channels from 650 to 2675 cmÿ1), and a radiometric accuracy on the order of+0.2 K. Typical polar-orbiting atmospheric sounders measure approximately 90% of the Earth’s atmosphere (in the horizontal dimension) approximately every 12 h. This wealth of data presents two major challenges in the development of retrieval algorithms, which estimate the geophysical state of the atmosphere as a function of space and time from upwelling spectral radiances measured by the sensor. The first challenge concerns the robustness of the retrieval operator and involves maximal use of the geophysical content of the radiance data with minimal interference from instrument and atmospheric noise. The second is to implement a robust algorithm within a given computational budget. Estimation tech-niques based on neural networks (NNs) are becoming more common in high-resolution atmospheric remote sensing largely because their simplicity, flexibility, and ability to accurately represent complex multi-dimensional statistical relationships allow both of these challenges to be overcome. In this chapter, we consider the retrieval of atmospheric temperature and moisture profiles (quantity as a function of altitude) from radiance measurements at microwave and thermal infrared wavelengths. A projected principal components (PPC) transform is used to reduce the dimensionality of and optimally extract geophysical information from the spectral radiance data, and a multi-layer feedforward NN is subsequently used to estimate the desired geophysical profiles. This algorithm is henceforth referred to as the ‘‘PPC–NN’’ algorithm. The PPC–NN algorithm offers the numerical stability and effi-ciency of statistical methods without sacrificing the accuracy of physical, model-based methods. The chapter is organized as follows. First, the physics of spaceborne atmospheric remote sensing is reviewed. The application of principal components transforms to hyperspectral sounding data is then presented and a new approach is introduced, where the sensor radiances are projected into a subspace that reduces spectral redun-dancy and maximizes the resulting correlation to a given parameter. This method is very similar to the concept of canonical correlations introduced by Hotelling over 70 years ago [1], but its application in the hyperspectral sounding context is new. Second, the use of multi-layer feedforward NNs for geophysical parameter retrieval from hyperspectral measurements (first proposed in 1993 [2]) is reviewed, and an overview of the network parameters used in this work is given. The combination of the PPC radiance compression operator with an NN is then discussed, and per-formance analyses comparing the PPC–NN algorithm to traditional retrieval methods are presented. ß 2007 by Taylor & Francis Group, LLC. 11.2 A Brief Overview of Spaceborne Atmospheric Remote Sensing The typical measurement scenario for spaceborne atmospheric remote sensing is shown in Figure 11.1. A sensor measures upwelling spectral radiance (intensity as a function of frequency) at various incidence angles. The sensor data is usually cali-brated to remove measurement artifacts such as gain drift, nonlinearities, and noise. The spectral radiances measured by the sensor are related to geophysical quantities, such as the vertical temperature profile of the atmosphere, and therefore must be converted into a geophysical quantity of interest through the use of an appropriate retrieval algorithm. The radiative transfer equation describing the radiation intensity observed at altitude L, viewing angle u, and frequency n can be formulated by including reflected atmospheric and cosmic contributions and the radiance emitted by the surface as follows [3,4]: ðL ðL Rn(L) ¼ kn(z)Jn[T(z)]exp ÿ secukn(z0)dz0 secudz 0 z L z þ rneÿt*secu kn(z)Jn[T(z)]exp ÿ secukn(z0)dz0 secudz 0 0 þ rneÿ2t*secuJn(Tc) þ «neÿt*secuJn(Ts) (11:1) Detector output 2 1.5 1 0.5 0 −0.5 −1 −1.5 −21 0 1 Time Spectral radiance 300 290 280 270 260 250 240 230 220 210 200 500 1000 1500 2000 2500 3000 Wavelength Temperature profile 105 104 103 1 180 200 220 240 260 280 300 Temperature Calibraton Retrieval algorithm FIGURE 11.1 Typical measurement scenario for spaceborne atmospheric remote sensing. Electromagnetic radiation that reaches the sensor is emitted by the sun, cosmic background, atmosphere, surface, and clouds. This radiation can also be reflected or scattered by the surface, atmosphere, or clouds. The spectral radiances measured by the sensor are related to geophysical quantities, such as the vertical temperature profile of the atmosphere, and therefore must be converted into a geophysical quantity of interest through the use of an appropriate retrieval algorithm. ß 2007 by Taylor & Francis Group, LLC. wh ere«n is the surfac e em issirvitiys, the sur face re flectiTvitiys, the surfac e tempe ra-ture, kn(z) is the atmosphe ric absorp tion coeft*ficiisentt,he atmospher ic zenith opac ity, Tc is the cos mic ba ckground tempe rature+0(2.0.71376 K), andJ (T) is the radi ance intensi ty em itted by a black body at temTp, erwahtuicrhe is given by the Planck equat ion: Jn(T) ¼ hn3 ehn=kT ÿ 1Wmÿ2 sterÿ1 Hzÿ1 (11:2) The first term in Equa tion 11.1 can be recast in terms of a transmiTttance func tion Rn(L) ¼ ðL Jn[T(z)]dTn(z)dz (11:3) 0 The derivative of the transmittance function with respect to altitude is often called the temperature weighting function Wn(z)dTn(z) (11:4) and gives the relative contribution of the radiance emanating from each altitude. The temperature weighting functions for the Advanced Microwave Sounding Unit (AMSU) are shown in Figure 11.2. AMSU-A weighting functions 60 50 Channel 40 14 13 30 12 11 20 10 9 8 10 7 6 AMSU-B weighting functions 10−2 183 ± 1 GHz 10−1 183 ± 3 GHz 100 183 ± 7 GHz 00 FIGURE 11.2 5 3 4 0.2 0.4 0.6 dT/d(In P) 150 GHz 89 GHz 0 0.1 0.2 0.3 0.4 dT/d(In (water vapor burden)) AMSU-A temperature profile (left) and AMSU-B water vapor profile (right) weighting functions ß 2007 by Taylor & Francis Group, LLC. 11.2.1 Geophysical Parameter Retrieval The objective of the geophysical parameter retrieval algorithm is to estimate the state of the atmosphere (represented by parameter matrix X, say), given observations of spectral radiance (represented by radiance matrix R, say). There are generally two approaches to this problem, as shown in Figure 11.3. The first approach, referred to here as the vari-ational approach, uses a forward model (for example, the transmittance and radiative transfer models previously discussed) to calculate the sensor radiance that would be measured given a specific atmospheric state. Note that the inverse model typically does not exist, as there are generally an infinite number of atmospheric states that could give rise to a particular radiance measurement. In the variational approach, a ‘‘guess’’ of the atmospheric state is made (this is usually obtained through a forecast model or historical statistics), and this guess is propagated through the forward models thereby producing an estimate of the at-sensor radiance. The measured radiance is compared with this estimated radiance, and the state vector is adjusted so as to reduce the difference between the measured and estimated radiance vectors. Details on this methodology are discussed at length by Rodgers [5], and the interested reader is referred there for a more thorough treatment of the methodology and implementation of variational retrieval methods. The second approach, referred to here as the statistical, or regression-based, approach, does not use the forward model explicitly to derive the estimate of the atmospheric state vector. Instead, an ensemble of radiance–state vector pairs is assembled, and a statistical charac-terization (p(X), p(R), and p(X,R)) is sought. In practice, it is difficult to obtain these probability density functions (PDFs) directly from the data, and alternative methods are often used. Two of these methods are linear least-squares estimation (LLSE), or linear regression, and nonlinear least-squares estimation (NLLSE). NNs are a special class of NLLSEs, and will be discussed later. • A forward model relates the geophysical state of the atmosphere to the radiances measured by the sensor. Variational approach: X º [T (r,t), W (r,t), O (r,t),…] surface reflectivity, solar illumination, etc. observing system (bandwidth, resolution, etc.) Observation noise A “guess” of the atmospheric state is adjusted iteratively until modeled radiance “matches” observed radiance. g = ||R – Robs|| + h(X ) “Regularization” term Statistical (regression-based) approach: An ensemble of radiance −state vector pairs is assembled, and a statistical relationship between the two is dervied empirically. X = g(Robs), where g(·) is argmin ||Xens – g(Rens)|| g(·) Examples of g(·) include LLSE and neural network FIGURE 11.3 Variational and statistical approaches to geophysical parameter retrieval. In the variational approach, a forward model is used to predict at-sensor radiances based on atmospheric state. In the statistical approach, an empirical relationship between at-sensor radiances and atmospheric state is derived using an ensemble of radiance–state vectors. ß 2007 by Taylor & Francis Group, LLC. ... - tailieumienphi.vn