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54 changes: 54 additions & 0 deletions docs/JOSS/paper.bib
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Expand Up @@ -127,4 +127,58 @@ @InProceedings{Lafortune1997
doi = {10.1145/258734.258801},
}

@Article{ESA2022,
author = {ESA},
journal = {European Space Agency, Noordwijk, The Netherlands, ESA-EOPSM-HARM-RP-4129, 369pp},
title = {{Report for Mission Selection: Earth Explorer 10 Candidate Mission Harmony}},
year = {2022},
}

@Article{Torres2012,
author = {Torres, Ramon and Snoeij, Paul and Geudtner, Dirk and Bibby, David and Davidson, Malcolm and Attema, Evert and Potin, Pierre and Rommen, BjÖrn and Floury, Nicolas and Brown, Mike and Traver, Ignacio Navas and Deghaye, Patrick and Duesmann, Berthyl and Rosich, Betlem and Miranda, Nuno and Bruno, Claudio and L’Abbate, Michelangelo and Croci, Renato and Pietropaolo, Andrea and Huchler, Markus and Rostan, Friedhelm},
journal = {Remote Sensing of Environment},
title = {GMES Sentinel-1 mission},
year = {2012},
issn = {0034-4257},
month = may,
pages = {9--24},
volume = {120},
doi = {10.1016/j.rse.2011.05.028},
publisher = {Elsevier BV},
}

@InProceedings{Scipal2017,
author = {Scipal, K. and Davidson, M.},
booktitle = {2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)},
title = {The SAOCOM-CS mission: ESA’s first bistatic and tomographic L-band mission},
year = {2017},
month = jul,
publisher = {IEEE},
doi = {10.1109/igarss.2017.8126909},
}

@InProceedings{Rosen2021,
author = {Rosen, Paul A. and Kumar, Raj},
booktitle = {2021 IEEE Radar Conference (RadarConf21)},
title = {NASA-ISRO SAR (NISAR) Mission Status},
year = {2021},
month = may,
publisher = {IEEE},
doi = {10.1109/radarconf2147009.2021.9455211},
}

@Article{FigaSaldana2002,
author = {Figa-Saldaña, J. and Wilson, J J.W. and Attema, E. and Gelsthorpe, R. and Drinkwater, M R and Stoffelen, A.},
journal = {Canadian Journal of Remote Sensing},
title = {The advanced scatterometer (ASCAT) on the meteorological operational (MetOp) platform: A follow on for European wind scatterometers},
year = {2002},
issn = {1712-7971},
month = jan,
number = {3},
pages = {404--412},
volume = {28},
doi = {10.5589/m02-035},
publisher = {Informa UK Limited},
}

@Comment{jabref-meta: databaseType:bibtex;}
20 changes: 9 additions & 11 deletions docs/JOSS/paper.md
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Expand Up @@ -38,31 +38,28 @@ The package utilizes a minimal set of core dependencies, namely: `numpy` @Harris
# Statement of need


Radiative transfer theory is used in a variety of contexts to retrieve biophysical characteristics from radar signals.
Radiative transfer theory is used in a variety of contexts to retrieve biophysical characteristics from radar signals. The `rt1_model` package was developed to study soil-moisture retrievals from incidence-angle dependent backscatter measurements in the microwave-domain, provided for example by the ASCAT scatterometer onboard the METOP satellites @FigaSaldana2002 or synthetic aperture radar (SAR) instruments such as Sentinel-1 @Torres2012, or the upcoming NISAR @Rosen2021 mission.

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

The description of the scattering characteristics of a rough surface covered by vegatation remains challenging.
The bi-static nature of the distribution functions used in the parametrization of soil- and vegetation characteristics furthermore enables potential application to bi-static measurements as provided by GNSS systems or constellations such as SAOCOM @Scipal2017 or the upcoming Sentinel-1 companion mission Harmony @ESA2022.

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.

## Distribution functions

The package provides a set of distribution functions (Isotropic, Rayleigh, HenyeyGreenstein, ...) that can be used to describe basic volume- or surface scatternig behaviors. More complex scattering scenarios can then be modelled by utilizing parametric linear-combinations.

To support possibly anisotropic scattering characteristics, all functions are furthermore implemented with respect to a generalized scattering angle \autoref{eq:scatangle} @Lafortune:
To support possibly anisotropic scattering characteristics, all functions are furthermore implemented with respect to a generalized scattering angle @Lafortune1997:

$$\cos(\Theta_a) = a_0 \cos(\theta) \cos(\theta_s) + \sin(\theta)\sin(\theta_s) [ a_1 \cos(\phi)\cos(\phi_s) + a_2 \sin(\phi) \sin(\phi_s)] \label{scatangle}$$
$$\cos(\Theta_a) = a_0 \cos(\theta) \cos(\theta_s) + \sin(\theta)\sin(\theta_s) [ a_1 \cos(\phi)\cos(\phi_s) + a_2 \sin(\phi) \sin(\phi_s)]$$

where ($\theta, \phi$) denote the incident azimuth and polar angle and $(\theta_s, \phi_s)$ the corresponding exit angles and $(a_0, a_1, a_2)$ are the generalization parameters.

For example, a combination of a forward- and a backward oriented HenyeyGreenstein peak defined as:
For example, a surface scattering distribution function that consists of a peak in specular direction and a second peak in incidence direction can be defined as:

$$BRDF = w * HG(-t, a_0=-1) + (1-w) * HG(t, a_0=1) \quad \textrm{with} \quad w, t \in (0,1)$$

can be implemented via:
and implemented via:

```
from rt1_model import surface
Expand All @@ -75,8 +72,9 @@ SRF = surface.LinComb([("w", SRF_1), ("1-w", SRF_2)])

![Linear Combination of surface BRDFs. \label{fig_lin_comb_brdf}](lin_comb_brdf.png)

## Parameter Retrieval

## Optimization
The documentation provides a set of retrieval examples...

![Example of the analyzer-widget for a RT1 model result. \label{fig_retrieval_static}](retrieval_static.png)

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