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61 changes: 61 additions & 0 deletions paper.bib
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Expand Up @@ -55,4 +55,65 @@ @Article{Yadav2022
publisher = {Elsevier BV},
}

@Article{Harris2020,
author = {Harris, Charles R. and Millman, K. Jarrod and van der Walt, Stéfan J. and Gommers, Ralf and Virtanen, Pauli and Cournapeau, David and Wieser, Eric and Taylor, Julian and Berg, Sebastian and Smith, Nathaniel J. and Kern, Robert and Picus, Matti and Hoyer, Stephan and van Kerkwijk, Marten H. and Brett, Matthew and Haldane, Allan and del Río, Jaime Fernández and Wiebe, Mark and Peterson, Pearu and Gérard-Marchant, Pierre and Sheppard, Kevin and Reddy, Tyler and Weckesser, Warren and Abbasi, Hameer and Gohlke, Christoph and Oliphant, Travis E.},
journal = {Nature},
title = {Array programming with NumPy},
year = {2020},
issn = {1476-4687},
month = sep,
number = {7825},
pages = {357--362},
volume = {585},
doi = {10.1038/s41586-020-2649-2},
publisher = {Springer Science and Business Media LLC},
}

@Article{Virtanen2020,
author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and van der Walt, Stéfan J. and Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and Kern, Robert and Larson, Eric and Carey, C J and Polat, İlhan and Feng, Yu and Moore, Eric W. and VanderPlas, Jake and Laxalde, Denis and Perktold, Josef and Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and Harris, Charles R. and Archibald, Anne M. and Ribeiro, Antônio H. and Pedregosa, Fabian and van Mulbregt, Paul and Vijaykumar, Aditya and Bardelli, Alessandro Pietro and Rothberg, Alex and Hilboll, Andreas and Kloeckner, Andreas and Scopatz, Anthony and Lee, Antony and Rokem, Ariel and Woods, C. Nathan and Fulton, Chad and Masson, Charles and Häggström, Christian and Fitzgerald, Clark and Nicholson, David A. and Hagen, David R. and Pasechnik, Dmitrii V. and Olivetti, Emanuele and Martin, Eric and Wieser, Eric and Silva, Fabrice and Lenders, Felix and Wilhelm, Florian and Young, G. and Price, Gavin A. and Ingold, Gert-Ludwig and Allen, Gregory E. and Lee, Gregory R. and Audren, Hervé and Probst, Irvin and Dietrich, Jörg P. and Silterra, Jacob and Webber, James T and Slavič, Janko and Nothman, Joel and Buchner, Johannes and Kulick, Johannes and Schönberger, Johannes L. and de Miranda Cardoso, José Vinícius and Reimer, Joscha and Harrington, Joseph and Rodríguez, Juan Luis Cano and Nunez-Iglesias, Juan and Kuczynski, Justin and Tritz, Kevin and Thoma, Martin and Newville, Matthew and Kümmerer, Matthias and Bolingbroke, Maximilian and Tartre, Michael and Pak, Mikhail and Smith, Nathaniel J. and Nowaczyk, Nikolai and Shebanov, Nikolay and Pavlyk, Oleksandr and Brodtkorb, Per A. and Lee, Perry and McGibbon, Robert T. and Feldbauer, Roman and Lewis, Sam and Tygier, Sam and Sievert, Scott and Vigna, Sebastiano and Peterson, Stefan and More, Surhud and Pudlik, Tadeusz and Oshima, Takuya and Pingel, Thomas J. and Robitaille, Thomas P. and Spura, Thomas and Jones, Thouis R. and Cera, Tim and Leslie, Tim and Zito, Tiziano and Krauss, Tom and Upadhyay, Utkarsh and Halchenko, Yaroslav O. and Vázquez-Baeza, Yoshiki},
journal = {Nature Methods},
title = {SciPy 1.0: fundamental algorithms for scientific computing in Python},
year = {2020},
issn = {1548-7105},
month = feb,
number = {3},
pages = {261--272},
volume = {17},
doi = {10.1038/s41592-019-0686-2},
publisher = {Springer Science and Business Media LLC},
}

@Article{Meurer2017,
author = {Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and Čertík, Ondřej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, AMiT and Ivanov, Sergiu and Moore, Jason K. and Singh, Sartaj and Rathnayake, Thilina and Vig, Sean and Granger, Brian E. and Muller, Richard P. and Bonazzi, Francesco and Gupta, Harsh and Vats, Shivam and Johansson, Fredrik and Pedregosa, Fabian and Curry, Matthew J. and Terrel, Andy R. and Roučka, Štěpán and Saboo, Ashutosh and Fernando, Isuru and Kulal, Sumith and Cimrman, Robert and Scopatz, Anthony},
journal = {PeerJ Computer Science},
title = {SymPy: symbolic computing in Python},
year = {2017},
issn = {2376-5992},
month = jan,
pages = {e103},
volume = {3},
doi = {10.7717/peerj-cs.103},
publisher = {PeerJ},
}

@Article{Hunter2007,
author = {Hunter, John D.},
journal = {Computing in Science & Engineering},
title = {Matplotlib: A 2D Graphics Environment},
year = {2007},
issn = {1521-9615},
number = {3},
pages = {90--95},
volume = {9},
doi = {10.1109/mcse.2007.55},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
}

@Manual{symengine,
title = {SymEngine: A fast symbolic manipulation library},
author = {SymEngine-Contributors},
year = {2024},
url = {https://github.com/symengine/symengine},
}

@Comment{jabref-meta: databaseType:bibtex;}
34 changes: 26 additions & 8 deletions paper.md
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Expand Up @@ -11,8 +11,13 @@ authors:
- name: Raphael Quast
orcid: 0000-0003-0419-4546
affiliation: TU Wien, Department of Geodesy and Geoinformation, Research Unit Remote Sensing
- name: Wolfgang Wagner
orcid: 0000-0001-7704-6857
affiliation: TU Wien, Department of Geodesy and Geoinformation, Research Unit Remote Sensing
- name: Bernhard Raml
affiliation: TU Wien, Department of Geodesy and Geoinformation, Research Unit Remote Sensing

date: 12 December 2023
date: 24 April 2024

bibliography: paper.bib

Expand All @@ -22,18 +27,31 @@ bibliography: paper.bib

The `rt1_model` package implements a generic solution to the radiative transfer equation applied to the problem of a rough surface covered by a tenuous distribution of particulate media as described in @Quast2016.

It provides a flexible, object-oriented interface to specify the scattering characteristics
of the ground surface and the covering layer via parametric distribution functions and evaluate the resulting backscattering-coefficient ($\sigma_0$) for monostatic or bistatic measurement geometries as illustrated in \ref{fig_model}.
It provides a flexible, object-oriented interface to specify the scattering characteristics of the ground surface and the covering layer via parametric distribution functions and to evaluate the resulting backscattering-coefficient ($\sigma_0$) for monostatic or bistatic measurement geometries as illustrated in Figure \ref{fig_model}.

The underlying calculations are implemented via symbolic expressions, allowing the user to create fully customized model parameterizations. To speed up parameter retrieval stragegies, analytic solutions for the Jacobian of arbitrary model parameters are provided.

The package utilizes a minimal set of core dependencies: `numpy` @Harris2020, `scipy` @Virtanen2020, `sympy` @Meurer2017 (with optional `symengine` @symengine support) and a set of visualizations created with `matplotlib` @Hunter2007.

![Illustration of the scattering contributions considered in the RT1 model (from @QuastEtAl23) \label{fig_model}](docs/_static/model.png)
![Illustration of the scattering contributions considered in the RT1 model (from @Quast2023) \label{fig_model}](model.png)

# Statement of need

Radiative transfer theory has been used in a variety of contexts to retrieve biophysical
characteristics from radar signals. For example, the RT1 modeling framework was used for soil-moisture retrieval from microwave c-band radar data (@Quast2019, @Quast2023) and adapted for rice-crop monitoring @Yadav2022 from bistatic scatterometer data.

# Acknowledgements
Radiative transfer theory is used in a variety of contexts to retrieve biophysical characteristics from radar signals.

The presented generic solution to the problem of a rough surface covered by a tenuous distribution of particulate media with respect to parametric distribution functions allows a intuitive yet flexible way to parametrize


The description of the scattering characteristics of a rough surface covered by vegatation remains challenging.


With the increasing availability of bistatic measurements (for example from GNSS), the need for bi-static parameterization stragegies

For example, the RT1 modeling framework was used for soil-moisture retrieval from microwave c-band radar data (@Quast2019, @Quast2023) and adapted for rice-crop monitoring @Yadav2022 with a ground based bistatic scatterometer.




We acknowledge contributions from ...

# References

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