Appendix C: Screening results

<table><caption>**Table C1.** Remaining parameters after the screening step for each output variable. In the XXX_XXX_XXX syntax of parameter names, the first block is the type of element the parameter refers to (soil horizon, river, vegetation, pesticide, HU or VFS), and the second part is the parameter name, while the last part is the element index the parameter refers to (soil horizon or vegetation type).</caption><thead><tr><th>Water subsurface flow</th><th>Pesticide subsurface flow</th><th>Water surface runoff</th><th>Pesticide surface runoff</th></tr></thead><tbody><tr><td>soilhorizon_theras_2</td><td>soilhorizon_theras_12</td><td>soilhorizon_theras_11</td><td>soilhorizon_theras_11</td></tr><tr><td>soilhorizon_theras_4</td><td>soilhorizon_theras_15</td><td>soilhorizon_theras_15</td><td>soilhorizon_theras_12</td></tr><tr><td>soilhorizon_theras_6</td><td>soilhorizon_theras_2</td><td>soilhorizon_theras_2</td><td>soilhorizon_theras_13</td></tr><tr><td>soilhorizon_theras_7</td><td>soilhorizon_theras_4</td><td>soilhorizon_theras_4</td><td>soilhorizon_theras_15</td></tr><tr><td>soilhorizon_theras_8</td><td>soilhorizon_theras_6</td><td>soilhorizon_theras_6</td><td>soilhorizon_theras_2</td></tr><tr><td>soilhorizon_theras_10</td><td>soilhorizon_theras_7</td><td>soilhorizon_theras_7</td><td>soilhorizon_theras_4</td></tr><tr><td>soilhorizon_theras_3</td><td>soilhorizon_theras_8</td><td>soilhorizon_theras_8</td><td>soilhorizon_theras_6</td></tr><tr><td>soilhorizon_theras_4</td><td>soilhorizon_theras_10</td><td>soilhorizon_theras_10</td><td>soilhorizon_theras_7</td></tr><tr><td>soilhorizon_theras_8</td><td>soilhorizon_theras_2</td><td>soilhorizon_theras_15</td><td>soilhorizon_theras_8</td></tr><tr><td>soilhorizon_theras_10</td><td>soilhorizon_theras_4</td><td>soilhorizon_theras_2</td><td>soilhorizon_theras_10</td></tr><tr><td>soilhorizon_moc_13</td><td>soilhorizon_theras_8</td><td>soilhorizon_theras_4</td><td>soilhorizon_theras_15</td></tr><tr><td>soilhorizon_mn_3</td><td>soilhorizon_theras_10</td><td>soilhorizon_theras_8</td><td>soilhorizon_theras_2</td></tr><tr><td>soilhorizon_mn_4</td><td>soilhorizon_pore_6</td><td>soilhorizon_theras_10</td><td>soilhorizon_theras_4</td></tr><tr><td>soilhorizon_mn_6</td><td>soilhorizon_moc_12</td><td>soilhorizon_pore_9</td><td>soilhorizon_theras_8</td></tr><tr><td>soilhorizon_mn_8</td><td>soilhorizon_moc_15</td><td>soilhorizon_mn_11</td><td>soilhorizon_theras_10</td></tr><tr><td>soilhorizon_mn_10</td><td>soilhorizon_moc_2</td><td>soilhorizon_mn_2</td><td>soilhorizon_moc_6</td></tr><tr><td>soilhorizon_Kx_3</td><td>soilhorizon_moc_6</td><td>soilhorizon_mn_4</td><td>soilhorizon_moc_12</td></tr><tr><td>soilhorizon_Kx_4</td><td>soilhorizon_moc_9</td><td>soilhorizon_mn_6</td><td>soilhorizon_mn_11</td></tr><tr><td>soilhorizon_Kx_8</td><td>soilhorizon_mn_11</td><td>soilhorizon_mn_7</td><td>soilhorizon_mn_16</td></tr><tr><td>soilhorizon_Kx_10</td><td>soilhorizon_mn_16</td><td>soilhorizon_mn_8</td><td>soilhorizon_mn_2</td></tr><tr><td>soilhorizon_Ks_11</td><td>soilhorizon_mn_4</td><td>soilhorizon_mn_10</td><td>soilhorizon_mn_4</td></tr><tr><td>soilhorizon_Ks_13</td><td>soilhorizon_mn_6</td><td>soilhorizon_Kx_8</td><td>soilhorizon_mn_6</td></tr><tr><td>soilhorizon_Ks_14</td><td>soilhorizon_mn_8</td><td>soilhorizon_Kx_10</td><td>soilhorizon_mn_7</td></tr><tr><td>soilhorizon_Ks_15</td><td>soilhorizon_mn_10</td><td>soilhorizon_Ks_12</td><td>soilhorizon_mn_8</td></tr><tr><td>soilhorizon_Ks_16</td><td>soilhorizon_Kx_12</td><td>soilhorizon_Ks_13</td><td>soilhorizon_mn_10</td></tr><tr><td>soilhorizon_Ks_3</td><td>soilhorizon_Kx_9</td><td>soilhorizon_Ks_15</td><td>soilhorizon_Ks_15</td></tr><tr><td>soilhorizon_Ks_4</td><td>soilhorizon_Kx_10</td><td>soilhorizon_Ks_16</td><td>soilhorizon_Ks_2</td></tr><tr><td>soilhorizon_Ks_6</td><td>soilhorizon_Ks_12</td><td>soilhorizon_Ks_4</td><td>soilhorizon_Ks_4</td></tr><tr><td>soilhorizon_Ks_7</td><td>soilhorizon_Ks_14</td><td>soilhorizon_Ks_6</td><td>soilhorizon_Ks_8</td></tr><tr><td>soilhorizon_Ks_8</td><td>soilhorizon_Ks_15</td><td>soilhorizon_Ks_8</td><td>soilhorizon_Ks_9</td></tr><tr><td>soilhorizon_Ks_9</td><td>soilhorizon_Ks_16</td><td>soilhorizon_Ks_9</td><td>soilhorizon_hg_3</td></tr><tr><td>soilhorizon_Ks_10</td><td>soilhorizon_Ks_2</td><td>soilhorizon_Ks_10</td><td>soilhorizon_hg_4</td></tr><tr><td>soilhorizon_hg_16</td><td>soilhorizon_Ks_4</td><td>soilhorizon_hg_4</td><td>soilhorizon_hg_8</td></tr><tr><td>soilhorizon_hg_2</td><td>soilhorizon_Ks_6</td><td>soilhorizon_hg_6</td><td>soilhorizon_bd_6</td></tr><tr><td>soilhorizon_hg_4</td><td>soilhorizon_Ks_8</td><td>soilhorizon_hg_8</td><td>soilhorizon_bd_13</td></tr><tr><td>soilhorizon_hg_8</td><td>soilhorizon_Ks_9</td><td>soilhorizon_hg_10</td><td>soilhorizon_bd_12</td></tr><tr><td>soilhorizon_hg_9</td><td>soilhorizon_Ks_10</td><td>soilhorizon_bd_3</td><td>river_ks</td></tr><tr><td>soilhorizon_bd_2</td><td>soilhorizon_hg_4</td><td>river_ks</td><td>river_di</td></tr><tr><td>river_ks</td><td>soilhorizon_hg_6</td><td>river_di</td><td>plot_hpond</td></tr><tr><td>river_di</td><td>soilhorizon_hg_8</td><td>plot_hpond</td><td>pest_Koc_1</td></tr><tr><td>plot_hpond</td><td>soilhorizon_hg_10</td><td>vfz_hpond</td><td>pest_DT50_1</td></tr><tr><td>VFS_hpond</td><td>soilhorizon_bd_11</td><td>veget_LAlharv_1</td><td>HU_adsorpthick</td></tr><tr><td></td><td>soilhorizon_bd_12</td><td>veget_F10_1</td><td>veget_Zr_1</td></tr><tr><td></td><td>soilhorizon_bd_13</td><td></td><td>veget_manning_1</td></tr><tr><td></td><td>soilhorizon_bd_15</td><td></td><td>veget_F10_1</td></tr><tr><td></td><td>soilhorizon_bd_2</td><td></td><td></td></tr><tr><td></td><td>soilhorizon_bd_6</td><td></td><td></td></tr><tr><td></td><td>soilhorizon_bd_9</td><td></td><td></td></tr><tr><td></td><td>river_ks</td><td></td><td></td></tr><tr><td></td><td>river_di</td><td></td><td></td></tr><tr><td></td><td>plot_hpond</td><td></td><td></td></tr><tr><td></td><td>veget_Zr_1</td><td></td><td></td></tr><tr><td></td><td>pest_Koc_1</td><td></td><td></td></tr><tr><td></td><td>pest_DT50_1</td><td></td><td></td></tr></tbody></table>
**Code and data availability.** The PESHMELBA model is an open-source model coded in Python (Version 2.7.17) and Fortran 90 and embedded in the OpenPALM coupler (Version 4.3.0). The code for the OpenPALM coupler is available from http://www.cerfacs.fr/globc/PALM_WEB/user.html#download (Fouilloux and Piacentini, 1999) after registration. The exact version of PESHMELBA used to produce the simulations is archived on Zenodo (https://doi.org/10.15454/2HAU8R, Rouzies et al., 2022a) as are input data and scripts used to produce all the sensitivity indices presented in this paper (https://doi.org/10.15454/2YVY4O, Rouzies et al., 2022b). These scripts use the open-source MATLAB software for uncertainty quantification UQLab Version 2.0.0 (https://www.uqlab.com, Marelli and Sudret, 2014). The R package randomForestSRC is freely available for download at https://cran.r-project.org (R Core Team, 2017).

**Author contributions.** All authors contributed to writing the text and to all stages of editing. PCE computation was performed by BS and ER, whereas HSIC and RF indices' computation was led by ER, with extensive support from CL and AV.

**Competing interests.** The contact author has declared that none of the authors has any competing interests.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Acknowledgements.** The authors kindly acknowledge Jérémy Verrier for his support on HIICS cluster usage, Stefano Marelli for his support on UQlab and PCE usage for GSA, Bertrand Ioss for his advice on the computation of RF feature importance measures, and Julien Pelamatti for his help on interpreting HSIC results.

**Review statement.** This paper was edited by Charles Onyutha and reviewed by Fanny Sarrazin, Heng Dai, Razi Sheikholeslami, and one anonymous referee.

## References

Alipour, A., Jafarzadegan, K., and Moradkhani, H.: Global sensitivity analysis in hydrodynamic modeling and flood inundation mapping, 152, 105398, https://doi.org/10.1016/j.envsoft.2022.105398, 2022.

Alletto, L., Pot, V., Giuliano, S., Costes, M., Perdrieux, F., and Justes, E.: Temporal variation in soil physical properties improves the water dynamics modeling in a conventionally-tilled soil, Geoderma, 243–244, 18–28, https://doi.org/10.1016/j.geoderma.2014.12.006, 2015.

Antoniadis, A., Lambert-Lacroix, S., and Poggi, J.-M.: Random forests for global sensitivity analysis: A selective review, Reliab. Eng. Syst. Safe., 206, 107312, https://doi.org/10.1016/j.ress.2020.107312, 2021.

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Aulia, A., Jeong, D., Mohd Saaid, I., Kania, D., Taleb Shuker, M., and El-Khatib, N. A.: A Random Forests-based sensitivity analysis framework for assisted history matching, J. Petrol. Sci. Eng., 181, 106237, https://doi.org/10.1016/j.petrol.2019.106237, 2019.

Balasubramanian, K., Sriperumbudur, B. K., and Lebanon, G.: Ultrahigh Dimensional Feature Screening via RKHS Embeddings, International Conference on Artificial Intelligence and Statistics, 2013.

Becker, W. E., Tarantola, S., and Deman, G.: Sensitivity analysis approaches to high-dimensional screening problems at low sample size, J. Stat. Comput. Sim., 88, 2089–2110, https://doi.org/10.1080/00949655.2018.1450876, 2018.

Bénard, C., Da Veiga, S., and Scornet, E.: Mean decrease accuracy for random forests: inconsistency, and a practical solution via the Sobol-MDA, Biometrika, 109, 881–900, https://doi.org/10.1093/biomet/asac017, 2022.

Blatman, G. and Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys., 230, 2345–2367, https://doi.org/10.1016/j.jcp.2010.12.021, 2011.

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**Code and data availability.** The PESHMELBA model is an open-source model coded in Python (Version 2.7.17) and Fortran 90 and embedded in the OpenPALM coupler (Version 4.3.0). The code for the OpenPALM coupler is available from http://www.cerfacs.fr/globc/PALM_WEB/user.html#download (Fouilloux and Piacentini, 1999) after registration. The exact version of PESHMELBA used to produce the simulations is archived on Zenodo (https://doi.org/10.15454/2HAU8R, Rouzies et al., 2022a) as are input data and scripts used to produce all the sensitivity indices presented in this paper (https://doi.org/10.15454/2YVY4O, Rouzies et al., 2022b). These scripts use the open-source MATLAB software for uncertainty quantification UQLab Version 2.0.0 (https://www.uqlab.com, Marelli and Sudret, 2014). The R package randomForestSRC is freely available for download at https://cran.r-project.org (R Core Team, 2017).

**Author contributions.** All authors contributed to writing the text and to all stages of editing. PCE computation was performed by BS and ER, whereas HSIC and RF indices' computation was led by ER, with extensive support from CL and AV.

**Competing interests.** The contact author has declared that none of the authors has any competing interests.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Acknowledgements.** The authors kindly acknowledge Jérémy Verrier for his support on HIICS cluster usage, Stefano Marelli for his support on UQlab and PCE usage for GSA, Bertrand Ioss for his advice on the computation of RF feature importance measures, and Julien Pelamatti for his help on interpreting HSIC results.

**Review statement.** This paper was edited by Charles Onyutha and reviewed by Fanny Sarrazin, Heng Dai, Razi Sheikholeslami, and one anonymous referee.

## References

Alipour, A., Jafarzadegan, K., and Moradkhani, H.: Global sensitivity analysis in hydrodynamic modeling and flood inundation mapping, 152, 105398, https://doi.org/10.1016/j.envsoft.2022.105398, 2022.

Alletto, L., Pot, V., Giuliano, S., Costes, M., Perdrieux, F., and Justes, E.: Temporal variation in soil physical properties improves the water dynamics modeling in a conventionally-tilled soil, Geoderma, 243–244, 18–28, https://doi.org/10.1016/j.geoderma.2014.12.006, 2015.

Antoniadis, A., Lambert-Lacroix, S., and Poggi, J.-M.: Random forests for global sensitivity analysis: A selective review, Reliab. Eng. Syst. Safe., 206, 107312, https://doi.org/10.1016/j.ress.2020.107312, 2021.

Arcement, G. and Schneider, V.: Guide for selecting Manning's roughness coefficients for natural channels and flood plains, Tech. rep., U.S. G.P.O., 1989.

Archer, G. E. B., Saltelli, A., and Sobol, I. M.: Sensitivity measures, ANOVA-like Techniques and the use of bootstrap, J. Stat. Comput. Sim., 58, 99–120, https://doi.org/10.1080/00949659708811825, 1997.

Aulia, A., Jeong, D., Mohd Saaid, I., Kania, D., Taleb Shuker, M., and El-Khatib, N. A.: A Random Forests-based sensitivity analysis framework for assisted history matching, J. Petrol. Sci. Eng., 181, 106237, https://doi.org/10.1016/j.petrol.2019.106237, 2019.

Balasubramanian, K., Sriperumbudur, B. K., and Lebanon, G.: Ultrahigh Dimensional Feature Screening via RKHS Embeddings, International Conference on Artificial Intelligence and Statistics, 2013.

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Bénard, C., Da Veiga, S., and Scornet, E.: Mean decrease accuracy for random forests: inconsistency, and a practical solution via the Sobol-MDA, Biometrika, 109, 881–900, https://doi.org/10.1093/biomet/asac017, 2022.

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Buis, S., Piacentini, A., and Déclat, D.: PALM: a computational framework for assembling high-performance computing applications, Concurr. Comp.-Pract. E., 18, 231–245, https://doi.org/10.1002/cpe.914, 2006.

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Song, X., Zhang, J., Zhan, C., Xuan, Y., Ye, M., and Xu, C.: Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications, J. Hydrol., 523, 739–757, https://doi.org/10.1016/j.jhydrol.2015.02.013, 2015.

Sudret, B.: Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Safe., 93, 964–979, https://doi.org/10.1016/j.ress.2007.04.002, 2008.

Tang, Y., Reed, P., Wagener, T., and van Werkhoven, K.: Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation, Hydrol. Earth Syst. Sci., 11, 793–817, https://doi.org/10.5194/hess-11-793-2007, 2007.

Tarantola, S., Giglioli, N., Jesinghaus, J., and Saltelli, A.: Can global sensitivity analysis steer the implementation of models for environmental assessments and decision-making?, Stoch. Env. Res. Risk A., 16, 63–76, https://doi.org/10.1007/s00477-001-0085-x, 2002.

Tissot, J.-Y. and Prieur, C.: A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices, J. Stat. Comput. Sim., 85, 1358–1381, https://doi.org/10.1080/00949655.2014.971799, 2015.

Touzani, S. and Busby, D.: Screening Method Using the Derivative-based Global Sensitivity Indices with Application to Reservoir Simulator, Oil Gas Sci. Technol., 69, 619–632, https://doi.org/10.2516/ogst/2013195, 2014.

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van Griensven, A., Meixner, T., Grunwald, S., Bishop, T., Diluzio, M., and Srinivasan, R.: A global sensitivity analysis tool for the parameters of multi-variable catchment models, J. Hydrol., 324, 10–23, https://doi.org/10.1016/j.jhydrol.2005.09.008, 2006.

Varado, N., Braud, I., and Ross, P.: Development and assessment of an efficient vadose zone module solving the 1D Richards' equation and including root extraction by plants, J. Hydrol., 323, 258–275, https://doi.org/10.1016/j.jhydrol.2005.09.015, 2006.

Walter, M., Gao, B., and Parlange, J.-Y.: Modeling soil solute release into runoff with infiltration, J. Hydrol., 347, 430–437, https://doi.org/10.1016/j.jhydrol.2007.09.033, 2007.

Wang, S., Huang, G., Baetz, B., and Huang, W.: A polynomial chaos ensemble hydrologic prediction system for efficient parameter inference and robust uncertainty assessment, J. Hydrol., 530, 716–733, https://doi.org/10.1016/j.jhydrol.2015.10.021, 2015.

Yang, J.: Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis, Environ. Modell. Softw., 26, 444–457, https://doi.org/10.1016/j.envsoft.2010.10.007, 2011.
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