April 2018, 12(2): 261-280. doi: 10.3934/ipi.2018011

Reconstruction of cloud geometry from high-resolution multi-angle images

1. 

Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637, USA

2. 

Department of Mathematical Sciences, Rensselear Polytechnic Institute, Troy, NY 12180, USA

3. 

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Received  November 2015 Revised  October 2016 Published  February 2018

We consider the reconstruction of the interface of compact, connected "clouds" from satellite or airborne light intensity measurements. In a two-dimensional setting, the cloud is modeled by an interface, locally represented as a graph, and an outgoing radiation intensity that is consistent with a diffusion model for light propagation in the cloud. Light scattering inside the cloud and the internal optical parameters of the cloud are not modeled explicitly. The main objective is to understand what can or cannot be reconstructed in such a setting from intensity measurements in a finite (on the order of 10) number of directions along the path of a satellite or an aircraft. Numerical simulations illustrate the theoretical predictions. Finally, we explore a kinematic extension of the algorithm for retrieving cloud motion (wind) along with its geometry.

Citation: Guillaume Bal, Jiaming Chen, Anthony B. Davis. Reconstruction of cloud geometry from high-resolution multi-angle images. Inverse Problems & Imaging, 2018, 12 (2) : 261-280. doi: 10.3934/ipi.2018011
References:
[1]

M. D. Alexandrov et al., Derivation of cumulus cloud dimensions and shape from the airborne measurements by the Research Scanning Polarimeter, Remote Sensing of the Environment, 177 (2016), 144-152.

[2]

G. Bal, Inverse transport theory and applications, Inverse Problems, 25 (2009), 053001, 48pp.

[3]

B. CairnsE. E. Russell and L. D. Travis, Research Scanning Polarimeter: Calibration and ground-based measurements, SPIE Proc., 3754 (1999), 186-197.

[4]

S. Chandrasekhar, Radiative Transfer, Dover Publications, New York, 1960.

[5]

C. Cornet and R. Davies, Use of MISR measurements to study the radiative transfer of an isolated convective cloud: Implications for cloud optical thickness retrieval, J. Geophys. Res.-Atmospheres, 113 (2008), D04202. doi: 10.1029/2007JD008921.

[6]

A. B. Davis, Cloud remote sensing with sideways looks: Theory and first results using Multispectral Thermal Imager (MTI) data, SPIE Proc., 4725 (2002), 397-405. doi: 10.1117/12.478772.

[7]

A. B. Davis and A. Marshak, Solar radiation transport in the cloudy atmosphere: A 3D perspective on observations and climate impacts, Reports on Progress in Physics, 73 (2010), 026801 (70pp). doi: 10.1088/0034-4885/73/2/026801.

[8]

D. J. Diner et al., Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview, IEEE Transactions in Geoscience and Remote Sensing, 36 (1998), 1072-1087.

[9]

_____, The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI): A new tool for aerosol and cloud remote sensing, Atmospheric Measurement Techniques, 6 (2013), 2007-2025.

[10]

H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.

[11]

Á. Horváth and R. Davies, Feasibility and error analysis of cloud motion wind extraction from near-simultaneous multiangle MISR measurements, Journal of Atmospheric and Oceanic Technology, 18 (2001), 591-608.

[12]

_____, Simultaneous retrieval of cloud motion and height from polar-orbiter multiangle measurements, Geophysical Research Letters, 28 (2001), 2915-2918.

[13]

A. Levis, Y. Y. Schechner, A. Aides and A. B. Davis, Airborne three-dimensional cloud tomography, in Proceedings of the IEEE International Conference on Computer Vision 2015 (ICCV2015), (2015), 3379-3387. doi: 10.1109/ICCV.2015.386.

[14]

A. Levis, Y. Y. Schechner and A. B. Davis, Multiple-scattering microphysics tomography, in Proceedings of the 30th IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR17), (2017), http://openaccess.thecvf.com/content_cvpr_2017/papers/Levis_Multiple-Scattering_Microphysics_Tomography_CVPR_2017_paper.pdf. doi: 10.1109/CVPR.2017.614.

[15]

S. M. Lovejoy, The area-parameter relation for rain and clouds, Science, 216 (1982), 185-187.

[16]

B. B. Mandelbrot, Fractals: Form, Chance and Dimension, W. H. Freeman & Co., San Diego(CA), 1977.

[17]

R. Marchand and T. Ackerman, Evaluation of radiometric measurements from the NASA Multiangle Imaging SpectroRadiometer (MISR): Two-and three-dimensional radiative transfer modeling of an inhomogeneous stratocumulus cloud deck, J. Geophys. Res. - Atmospheres, 109 (2004), D18208.

[18]

A. Marshak and A. B. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Springer, New York, 2005. doi: 10.1007/3-540-28519-9.

[19]

W. G. K. MartinB. Cairns and G. Bal, Adjoint methods for adjusting three-dimensional atmosphere and surface properties to multi-angle polarimetric measurements, J. Quant. Spectroscopy Radiative Transfer, 144 (2014), 68-85. doi: 10.1016/j.jqsrt.2014.03.030.

[20]

W. G. K. Martin and O. P. Hasekamp, A demonstration of adjoint methods for multi-dimensional remote sensing of the atmosphere and surface, J. Quant. Spectroscopy Radiative Transfer, 204 (2018), 215-231. doi: 10.1016/j.jqsrt.2017.09.031.

[21]

C. MoroneyR. Davies and J. -P. Muller, Operational retrieval of cloud-top heights using MISR data, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 1532-1540. doi: 10.1109/TGRS.2002.801150.

[22]

J. -P. Muller et al., MISR stereoscopic image matchers: Techniques and results, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 1547-1559.

[23]

T. Nakajima and M. D. King, Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part 1: Theory, Journal of the Atmospheric Sciences, 47 (1990), 1878-1893. doi: 10.1175/1520-0469(1990)047<1878:DOTOTA>2.0.CO;2.

[24]

S. Platnick et al., The MODIS cloud products: Algorithms and examples from Terra, IEEE Transactions on Geoscience and Remote Sensing, 41 (2003), 459-473.

[25]

G. Seiz and R. Davies, Reconstruction of cloud geometry from multi-view satellite images, Remote Sensing of the Environment, 100 (2006), 143-149. doi: 10.1016/j.rse.2005.09.016.

[26]

P. G. Weber, Multispectral Thermal Imager mission overview, SPIE Proc., 3753 (1999), 340-346.

show all references

References:
[1]

M. D. Alexandrov et al., Derivation of cumulus cloud dimensions and shape from the airborne measurements by the Research Scanning Polarimeter, Remote Sensing of the Environment, 177 (2016), 144-152.

[2]

G. Bal, Inverse transport theory and applications, Inverse Problems, 25 (2009), 053001, 48pp.

[3]

B. CairnsE. E. Russell and L. D. Travis, Research Scanning Polarimeter: Calibration and ground-based measurements, SPIE Proc., 3754 (1999), 186-197.

[4]

S. Chandrasekhar, Radiative Transfer, Dover Publications, New York, 1960.

[5]

C. Cornet and R. Davies, Use of MISR measurements to study the radiative transfer of an isolated convective cloud: Implications for cloud optical thickness retrieval, J. Geophys. Res.-Atmospheres, 113 (2008), D04202. doi: 10.1029/2007JD008921.

[6]

A. B. Davis, Cloud remote sensing with sideways looks: Theory and first results using Multispectral Thermal Imager (MTI) data, SPIE Proc., 4725 (2002), 397-405. doi: 10.1117/12.478772.

[7]

A. B. Davis and A. Marshak, Solar radiation transport in the cloudy atmosphere: A 3D perspective on observations and climate impacts, Reports on Progress in Physics, 73 (2010), 026801 (70pp). doi: 10.1088/0034-4885/73/2/026801.

[8]

D. J. Diner et al., Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview, IEEE Transactions in Geoscience and Remote Sensing, 36 (1998), 1072-1087.

[9]

_____, The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI): A new tool for aerosol and cloud remote sensing, Atmospheric Measurement Techniques, 6 (2013), 2007-2025.

[10]

H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.

[11]

Á. Horváth and R. Davies, Feasibility and error analysis of cloud motion wind extraction from near-simultaneous multiangle MISR measurements, Journal of Atmospheric and Oceanic Technology, 18 (2001), 591-608.

[12]

_____, Simultaneous retrieval of cloud motion and height from polar-orbiter multiangle measurements, Geophysical Research Letters, 28 (2001), 2915-2918.

[13]

A. Levis, Y. Y. Schechner, A. Aides and A. B. Davis, Airborne three-dimensional cloud tomography, in Proceedings of the IEEE International Conference on Computer Vision 2015 (ICCV2015), (2015), 3379-3387. doi: 10.1109/ICCV.2015.386.

[14]

A. Levis, Y. Y. Schechner and A. B. Davis, Multiple-scattering microphysics tomography, in Proceedings of the 30th IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR17), (2017), http://openaccess.thecvf.com/content_cvpr_2017/papers/Levis_Multiple-Scattering_Microphysics_Tomography_CVPR_2017_paper.pdf. doi: 10.1109/CVPR.2017.614.

[15]

S. M. Lovejoy, The area-parameter relation for rain and clouds, Science, 216 (1982), 185-187.

[16]

B. B. Mandelbrot, Fractals: Form, Chance and Dimension, W. H. Freeman & Co., San Diego(CA), 1977.

[17]

R. Marchand and T. Ackerman, Evaluation of radiometric measurements from the NASA Multiangle Imaging SpectroRadiometer (MISR): Two-and three-dimensional radiative transfer modeling of an inhomogeneous stratocumulus cloud deck, J. Geophys. Res. - Atmospheres, 109 (2004), D18208.

[18]

A. Marshak and A. B. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Springer, New York, 2005. doi: 10.1007/3-540-28519-9.

[19]

W. G. K. MartinB. Cairns and G. Bal, Adjoint methods for adjusting three-dimensional atmosphere and surface properties to multi-angle polarimetric measurements, J. Quant. Spectroscopy Radiative Transfer, 144 (2014), 68-85. doi: 10.1016/j.jqsrt.2014.03.030.

[20]

W. G. K. Martin and O. P. Hasekamp, A demonstration of adjoint methods for multi-dimensional remote sensing of the atmosphere and surface, J. Quant. Spectroscopy Radiative Transfer, 204 (2018), 215-231. doi: 10.1016/j.jqsrt.2017.09.031.

[21]

C. MoroneyR. Davies and J. -P. Muller, Operational retrieval of cloud-top heights using MISR data, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 1532-1540. doi: 10.1109/TGRS.2002.801150.

[22]

J. -P. Muller et al., MISR stereoscopic image matchers: Techniques and results, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 1547-1559.

[23]

T. Nakajima and M. D. King, Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part 1: Theory, Journal of the Atmospheric Sciences, 47 (1990), 1878-1893. doi: 10.1175/1520-0469(1990)047<1878:DOTOTA>2.0.CO;2.

[24]

S. Platnick et al., The MODIS cloud products: Algorithms and examples from Terra, IEEE Transactions on Geoscience and Remote Sensing, 41 (2003), 459-473.

[25]

G. Seiz and R. Davies, Reconstruction of cloud geometry from multi-view satellite images, Remote Sensing of the Environment, 100 (2006), 143-149. doi: 10.1016/j.rse.2005.09.016.

[26]

P. G. Weber, Multispectral Thermal Imager mission overview, SPIE Proc., 3753 (1999), 340-346.

Figure 1.  Geometry of cloud interface
Figure 2.  Left: A cloud model. Right: Simulated radiances $u_j(X) : = u(X,Z,\theta_j)$ for that cloud using (7) with $j = 1,\dots,J = 5$ (specifically, $\theta \in \{90,90\pm26.1,90\pm45.6\}$ in degrees clockwise from the positive $x$ axis) for a uniform $\alpha$ and $\beta = \sin\phi$.
Figure 3.  True angular radiation function $\beta(\phi) = \sin\phi$ (in green), reconstructed function (in blue), and initial guess (in red).
[1]

Carlos E. Kenig, Mikko Salo, Gunther Uhlmann. Reconstructions from boundary measurements on admissible manifolds. Inverse Problems & Imaging, 2011, 5 (4) : 859-877. doi: 10.3934/ipi.2011.5.859

[2]

Guillaume Bal, Ian Langmore, François Monard. Inverse transport with isotropic sources and angularly averaged measurements. Inverse Problems & Imaging, 2008, 2 (1) : 23-42. doi: 10.3934/ipi.2008.2.23

[3]

Gérard Gagneux, Olivier Millet. A geological delayed response model for stratigraphic reconstructions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 457-474. doi: 10.3934/dcdss.2016007

[4]

Jutta Bikowski, Jennifer L. Mueller. 2D EIT reconstructions using Calderon's method. Inverse Problems & Imaging, 2008, 2 (1) : 43-61. doi: 10.3934/ipi.2008.2.43

[5]

Nuutti Hyvönen, Lassi Päivärinta, Janne P. Tamminen. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. Inverse Problems & Imaging, 2018, 12 (2) : 373-400. doi: 10.3934/ipi.2018017

[6]

Corinna Burkard, Roland Potthast. A time-domain probe method for three-dimensional rough surface reconstructions. Inverse Problems & Imaging, 2009, 3 (2) : 259-274. doi: 10.3934/ipi.2009.3.259

[7]

Melody Alsaker, Jennifer L. Mueller. Use of an optimized spatial prior in D-bar reconstructions of EIT tank data. Inverse Problems & Imaging, 2018, 12 (4) : 883-901. doi: 10.3934/ipi.2018037

[8]

Hiroshi Isozaki. Inverse boundary value problems in the horosphere - A link between hyperbolic geometry and electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (1) : 107-134. doi: 10.3934/ipi.2007.1.107

[9]

Klas Modin. Geometry of matrix decompositions seen through optimal transport and information geometry. Journal of Geometric Mechanics, 2017, 9 (3) : 335-390. doi: 10.3934/jgm.2017014

[10]

Robert J. McCann. A glimpse into the differential topology and geometry of optimal transport. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1605-1621. doi: 10.3934/dcds.2014.34.1605

[11]

Guillaume Bal, Alexandre Jollivet. Stability estimates in stationary inverse transport. Inverse Problems & Imaging, 2008, 2 (4) : 427-454. doi: 10.3934/ipi.2008.2.427

[12]

Brittan Farmer, Cassandra Hall, Selim Esedoḡlu. Source identification from line integral measurements and simple atmospheric models. Inverse Problems & Imaging, 2013, 7 (2) : 471-490. doi: 10.3934/ipi.2013.7.471

[13]

Giovanni Alessandrini, Elio Cabib. Determining the anisotropic traction state in a membrane by boundary measurements. Inverse Problems & Imaging, 2007, 1 (3) : 437-442. doi: 10.3934/ipi.2007.1.437

[14]

Mourad Sini, Nguyen Trung Thành. Inverse acoustic obstacle scattering problems using multifrequency measurements. Inverse Problems & Imaging, 2012, 6 (4) : 749-773. doi: 10.3934/ipi.2012.6.749

[15]

Guillaume Bal, Alexandre Jollivet. Generalized stability estimates in inverse transport theory. Inverse Problems & Imaging, 2018, 12 (1) : 59-90. doi: 10.3934/ipi.2018003

[16]

Kim Knudsen, Mikko Salo. Determining nonsmooth first order terms from partial boundary measurements. Inverse Problems & Imaging, 2007, 1 (2) : 349-369. doi: 10.3934/ipi.2007.1.349

[17]

Carlos J. S. Alves, Nuno F. M. Martins, Nilson C. Roberty. Full identification of acoustic sources with multiple frequencies and boundary measurements. Inverse Problems & Imaging, 2009, 3 (2) : 275-294. doi: 10.3934/ipi.2009.3.275

[18]

Antonino Morassi, Edi Rosset, Sergio Vessella. Unique determination of a cavity in an elastic plate by two boundary measurements. Inverse Problems & Imaging, 2007, 1 (3) : 481-506. doi: 10.3934/ipi.2007.1.481

[19]

Elena Beretta, Elisa Francini, Sergio Vessella. Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements. Inverse Problems & Imaging, 2014, 8 (3) : 611-644. doi: 10.3934/ipi.2014.8.611

[20]

Mikko Orispää, Markku Lehtinen. Fortran linear inverse problem solver. Inverse Problems & Imaging, 2010, 4 (3) : 485-503. doi: 10.3934/ipi.2010.4.485

2017 Impact Factor: 1.465

Metrics

  • PDF downloads (56)
  • HTML views (199)
  • Cited by (0)

Other articles
by authors

[Back to Top]