Articles | Volume 16, issue 13
https://doi.org/10.5194/gmd-16-3765-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-3765-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
06 Jul 2023
Development and technical paper |
| 06 Jul 2023
| 06 Jul 2023
GStatSim V1.0: a Python package for geostatistical interpolation and conditional simulation
Emma J. MacKie
CORRESPONDING AUTHOR
Department of Geological Sciences, University of Florida, Gainesville, FL 32611, USA
Michael Field
Department of Geological Sciences, University of Florida, Gainesville, FL 32611, USA
Lijing Wang
Department of Earth and Planetary Sciences, Stanford University, Stanford, CA 94305, USA
Earth and Environmental Sciences Area, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Department of Earth and Planetary Sciences, Stanford University, Stanford, CA 94305, USA
Nathan Schoedl
Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
Department of Statistics, University of Florida, Gainesville, FL 32611, USA
Matthew Hibbs
Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA
Allan Zhang
Department of Statistics, University of Florida, Gainesville, FL 32611, USA
Related authors
Robert G. Bingham, Julien A. Bodart, Marie G. P. Cavitte, Ailsa Chung, Rebecca J. Sanderson, Johannes C. R. Sutter, Olaf Eisen, Nanna B. Karlsson, Joseph A. MacGregor, Neil Ross, Duncan A. Young, David W. Ashmore, Andreas Born, Winnie Chu, Xiangbin Cui, Reinhard Drews, Steven Franke, Vikram Goel, John W. Goodge, A. Clara J. Henry, Antoine Hermant, Benjamin H. Hills, Nicholas Holschuh, Michelle R. Koutnik, Gwendolyn J.-M. C. Leysinger Vieli, Emma J. MacKie, Elisa Mantelli, Carlos Martín, Felix S. L. Ng, Falk M. Oraschewski, Felipe Napoleoni, Frédéric Parrenin, Sergey V. Popov, Therese Rieckh, Rebecca Schlegel, Dustin M. Schroeder, Martin J. Siegert, Xueyuan Tang, Thomas O. Teisberg, Kate Winter, Shuai Yan, Harry Davis, Christine F. Dow, Tyler J. Fudge, Tom A. Jordan, Bernd Kulessa, Kenichi Matsuoka, Clara J. Nyqvist, Maryam Rahnemoonfar, Matthew R. Siegfried, Shivangini Singh, Vjeran Višnjević, Rodrigo Zamora, and Alexandra Zuhr
The Cryosphere, 19, 4611–4655, https://doi.org/10.5194/tc-19-4611-2025, https://doi.org/10.5194/tc-19-4611-2025, 2025
Short summary
Short summary
The ice sheets covering Antarctica have built up over millenia through successive snowfall events which become buried and preserved as internal surfaces of equal age detectable with ice-penetrating radar. This paper describes an international initiative working together on these archival data to build a comprehensive 3-D picture of how old the ice is everywhere across Antarctica and how this is being used to reconstruct past and to predict future ice and climate behaviour.
Michael Joseph Field, Emma Johanne MacKie, Lijing Wang, Atsuhiro Muto, and Niya Shao
EGUsphere, https://doi.org/10.5194/egusphere-2025-2680, https://doi.org/10.5194/egusphere-2025-2680, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Ice shelves are thinning and losing mass in West Antarctica because of interaction with warm water. The topography of the bedrock beneath the ice shelves is difficult to measure but important for understanding how quickly the ice shelves will melt. This study uses gravity data to infer the bedrock topography beneath the ice shelves. We use statistical methods to create an ensemble of bathymetry models that sample the uncertainty of the assumptions in the problem.
Nanna B. Karlsson, Dustin M. Schroeder, Louise Sandberg Sørensen, Winnie Chu, Jørgen Dall, Natalia H. Andersen, Reese Dobson, Emma J. Mackie, Simon J. Köhn, Jillian E. Steinmetz, Angelo S. Tarzona, Thomas O. Teisberg, and Niels Skou
Earth Syst. Sci. Data, 16, 3333–3344, https://doi.org/10.5194/essd-16-3333-2024, https://doi.org/10.5194/essd-16-3333-2024, 2024
Short summary
Short summary
In the 1970s, more than 177 000 km of observations were acquired from airborne radar over the Greenland ice sheet. The radar data contain information on not only the thickness of the ice, but also the properties of the ice itself. This information was recorded on film rolls and subsequently stored. In this study, we document the digitization of these film rolls that shed new and unprecedented detailed light on the Greenland ice sheet 50 years ago.
Alice C. Frémand, Peter Fretwell, Julien A. Bodart, Hamish D. Pritchard, Alan Aitken, Jonathan L. Bamber, Robin Bell, Cesidio Bianchi, Robert G. Bingham, Donald D. Blankenship, Gino Casassa, Ginny Catania, Knut Christianson, Howard Conway, Hugh F. J. Corr, Xiangbin Cui, Detlef Damaske, Volkmar Damm, Reinhard Drews, Graeme Eagles, Olaf Eisen, Hannes Eisermann, Fausto Ferraccioli, Elena Field, René Forsberg, Steven Franke, Shuji Fujita, Yonggyu Gim, Vikram Goel, Siva Prasad Gogineni, Jamin Greenbaum, Benjamin Hills, Richard C. A. Hindmarsh, Andrew O. Hoffman, Per Holmlund, Nicholas Holschuh, John W. Holt, Annika N. Horlings, Angelika Humbert, Robert W. Jacobel, Daniela Jansen, Adrian Jenkins, Wilfried Jokat, Tom Jordan, Edward King, Jack Kohler, William Krabill, Mette Kusk Gillespie, Kirsty Langley, Joohan Lee, German Leitchenkov, Carlton Leuschen, Bruce Luyendyk, Joseph MacGregor, Emma MacKie, Kenichi Matsuoka, Mathieu Morlighem, Jérémie Mouginot, Frank O. Nitsche, Yoshifumi Nogi, Ole A. Nost, John Paden, Frank Pattyn, Sergey V. Popov, Eric Rignot, David M. Rippin, Andrés Rivera, Jason Roberts, Neil Ross, Anotonia Ruppel, Dustin M. Schroeder, Martin J. Siegert, Andrew M. Smith, Daniel Steinhage, Michael Studinger, Bo Sun, Ignazio Tabacco, Kirsty Tinto, Stefano Urbini, David Vaughan, Brian C. Welch, Douglas S. Wilson, Duncan A. Young, and Achille Zirizzotti
Earth Syst. Sci. Data, 15, 2695–2710, https://doi.org/10.5194/essd-15-2695-2023, https://doi.org/10.5194/essd-15-2695-2023, 2023
Short summary
Short summary
This paper presents the release of over 60 years of ice thickness, bed elevation, and surface elevation data acquired over Antarctica by the international community. These data are a crucial component of the Antarctic Bedmap initiative which aims to produce a new map and datasets of Antarctic ice thickness and bed topography for the international glaciology and geophysical community.
Marion A. McKenzie, Lauren E. Miller, Jacob S. Slawson, Emma J. MacKie, and Shujie Wang
The Cryosphere, 17, 2477–2486, https://doi.org/10.5194/tc-17-2477-2023, https://doi.org/10.5194/tc-17-2477-2023, 2023
Short summary
Short summary
Topographic highs (“bumps”) across glaciated landscapes have the potential to affect glacial ice. Bumps in the deglaciated Puget Lowland are assessed for streamlined glacial features to provide insight on ice–bed interactions. We identify a general threshold in which bumps significantly disrupt ice flow and sedimentary processes in this location. However, not all bumps have the same degree of impact. The system assessed here has relevance to parts of the Greenland Ice Sheet and Thwaites Glacier.
Zhen Yin, Chen Zuo, Emma J. MacKie, and Jef Caers
Geosci. Model Dev., 15, 1477–1497, https://doi.org/10.5194/gmd-15-1477-2022, https://doi.org/10.5194/gmd-15-1477-2022, 2022
Short summary
Short summary
We provide a multiple-point geostatistics approach to probabilistically learn from training images to fill large-scale irregular geophysical data gaps. With a repository of global topographic training images, our approach models high-resolution basal topography and quantifies the geospatial uncertainty. It generated high-resolution topographic realizations to investigate the impact of basal topographic uncertainty on critical subglacial hydrological flow patterns associated with ice velocity.
Robert G. Bingham, Julien A. Bodart, Marie G. P. Cavitte, Ailsa Chung, Rebecca J. Sanderson, Johannes C. R. Sutter, Olaf Eisen, Nanna B. Karlsson, Joseph A. MacGregor, Neil Ross, Duncan A. Young, David W. Ashmore, Andreas Born, Winnie Chu, Xiangbin Cui, Reinhard Drews, Steven Franke, Vikram Goel, John W. Goodge, A. Clara J. Henry, Antoine Hermant, Benjamin H. Hills, Nicholas Holschuh, Michelle R. Koutnik, Gwendolyn J.-M. C. Leysinger Vieli, Emma J. MacKie, Elisa Mantelli, Carlos Martín, Felix S. L. Ng, Falk M. Oraschewski, Felipe Napoleoni, Frédéric Parrenin, Sergey V. Popov, Therese Rieckh, Rebecca Schlegel, Dustin M. Schroeder, Martin J. Siegert, Xueyuan Tang, Thomas O. Teisberg, Kate Winter, Shuai Yan, Harry Davis, Christine F. Dow, Tyler J. Fudge, Tom A. Jordan, Bernd Kulessa, Kenichi Matsuoka, Clara J. Nyqvist, Maryam Rahnemoonfar, Matthew R. Siegfried, Shivangini Singh, Vjeran Višnjević, Rodrigo Zamora, and Alexandra Zuhr
The Cryosphere, 19, 4611–4655, https://doi.org/10.5194/tc-19-4611-2025, https://doi.org/10.5194/tc-19-4611-2025, 2025
Short summary
Short summary
The ice sheets covering Antarctica have built up over millenia through successive snowfall events which become buried and preserved as internal surfaces of equal age detectable with ice-penetrating radar. This paper describes an international initiative working together on these archival data to build a comprehensive 3-D picture of how old the ice is everywhere across Antarctica and how this is being used to reconstruct past and to predict future ice and climate behaviour.
Michael Joseph Field, Emma Johanne MacKie, Lijing Wang, Atsuhiro Muto, and Niya Shao
EGUsphere, https://doi.org/10.5194/egusphere-2025-2680, https://doi.org/10.5194/egusphere-2025-2680, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Ice shelves are thinning and losing mass in West Antarctica because of interaction with warm water. The topography of the bedrock beneath the ice shelves is difficult to measure but important for understanding how quickly the ice shelves will melt. This study uses gravity data to infer the bedrock topography beneath the ice shelves. We use statistical methods to create an ensemble of bathymetry models that sample the uncertainty of the assumptions in the problem.
Nanna B. Karlsson, Dustin M. Schroeder, Louise Sandberg Sørensen, Winnie Chu, Jørgen Dall, Natalia H. Andersen, Reese Dobson, Emma J. Mackie, Simon J. Köhn, Jillian E. Steinmetz, Angelo S. Tarzona, Thomas O. Teisberg, and Niels Skou
Earth Syst. Sci. Data, 16, 3333–3344, https://doi.org/10.5194/essd-16-3333-2024, https://doi.org/10.5194/essd-16-3333-2024, 2024
Short summary
Short summary
In the 1970s, more than 177 000 km of observations were acquired from airborne radar over the Greenland ice sheet. The radar data contain information on not only the thickness of the ice, but also the properties of the ice itself. This information was recorded on film rolls and subsequently stored. In this study, we document the digitization of these film rolls that shed new and unprecedented detailed light on the Greenland ice sheet 50 years ago.
Alice C. Frémand, Peter Fretwell, Julien A. Bodart, Hamish D. Pritchard, Alan Aitken, Jonathan L. Bamber, Robin Bell, Cesidio Bianchi, Robert G. Bingham, Donald D. Blankenship, Gino Casassa, Ginny Catania, Knut Christianson, Howard Conway, Hugh F. J. Corr, Xiangbin Cui, Detlef Damaske, Volkmar Damm, Reinhard Drews, Graeme Eagles, Olaf Eisen, Hannes Eisermann, Fausto Ferraccioli, Elena Field, René Forsberg, Steven Franke, Shuji Fujita, Yonggyu Gim, Vikram Goel, Siva Prasad Gogineni, Jamin Greenbaum, Benjamin Hills, Richard C. A. Hindmarsh, Andrew O. Hoffman, Per Holmlund, Nicholas Holschuh, John W. Holt, Annika N. Horlings, Angelika Humbert, Robert W. Jacobel, Daniela Jansen, Adrian Jenkins, Wilfried Jokat, Tom Jordan, Edward King, Jack Kohler, William Krabill, Mette Kusk Gillespie, Kirsty Langley, Joohan Lee, German Leitchenkov, Carlton Leuschen, Bruce Luyendyk, Joseph MacGregor, Emma MacKie, Kenichi Matsuoka, Mathieu Morlighem, Jérémie Mouginot, Frank O. Nitsche, Yoshifumi Nogi, Ole A. Nost, John Paden, Frank Pattyn, Sergey V. Popov, Eric Rignot, David M. Rippin, Andrés Rivera, Jason Roberts, Neil Ross, Anotonia Ruppel, Dustin M. Schroeder, Martin J. Siegert, Andrew M. Smith, Daniel Steinhage, Michael Studinger, Bo Sun, Ignazio Tabacco, Kirsty Tinto, Stefano Urbini, David Vaughan, Brian C. Welch, Douglas S. Wilson, Duncan A. Young, and Achille Zirizzotti
Earth Syst. Sci. Data, 15, 2695–2710, https://doi.org/10.5194/essd-15-2695-2023, https://doi.org/10.5194/essd-15-2695-2023, 2023
Short summary
Short summary
This paper presents the release of over 60 years of ice thickness, bed elevation, and surface elevation data acquired over Antarctica by the international community. These data are a crucial component of the Antarctic Bedmap initiative which aims to produce a new map and datasets of Antarctic ice thickness and bed topography for the international glaciology and geophysical community.
Marion A. McKenzie, Lauren E. Miller, Jacob S. Slawson, Emma J. MacKie, and Shujie Wang
The Cryosphere, 17, 2477–2486, https://doi.org/10.5194/tc-17-2477-2023, https://doi.org/10.5194/tc-17-2477-2023, 2023
Short summary
Short summary
Topographic highs (“bumps”) across glaciated landscapes have the potential to affect glacial ice. Bumps in the deglaciated Puget Lowland are assessed for streamlined glacial features to provide insight on ice–bed interactions. We identify a general threshold in which bumps significantly disrupt ice flow and sedimentary processes in this location. However, not all bumps have the same degree of impact. The system assessed here has relevance to parts of the Greenland Ice Sheet and Thwaites Glacier.
Zhen Yin, Chen Zuo, Emma J. MacKie, and Jef Caers
Geosci. Model Dev., 15, 1477–1497, https://doi.org/10.5194/gmd-15-1477-2022, https://doi.org/10.5194/gmd-15-1477-2022, 2022
Short summary
Short summary
We provide a multiple-point geostatistics approach to probabilistically learn from training images to fill large-scale irregular geophysical data gaps. With a repository of global topographic training images, our approach models high-resolution basal topography and quantifies the geospatial uncertainty. It generated high-resolution topographic realizations to investigate the impact of basal topographic uncertainty on critical subglacial hydrological flow patterns associated with ice velocity.
Cited articles
Broomhead, D. S. and Lowe, D.: Radial basis functions, multi-variable functional interpolation and adaptive networks, Tech. rep., Royal Signals and Radar Establishment Malvern, United Kingdom, 1988. a
Carle, S. F.: T-PROGS: Transition probability geostatistical software, Version 2.1, Department of Land, Air and Water Resources, University of California, Davis, 1999. a
Chiles, J.-P. and Delfiner, P.: Geostatistics: modeling spatial uncertainty, Vol. 497, John Wiley & Sons, https://doi.org/10.1007/s11004-012-9429-y, 2009. a
Chu, W., Hilger, A. M., Culberg, R., Schroeder, D. M., Jordan, T. M., Seroussi, H., Young, D. A., Blankenship, D. D., and Vaughan, D. G.: Multisystem synthesis of radar sounding observations of the Amundsen Sea sector from the 2004–2005 field season, J. Geophys. Res.-Earth, 126, e2021JF006296, https://doi.org/10.1029/2021JF006296, 2021. a
Cockett, R., Kang, S., Heagy, L. J., Pidlisecky, A., and Oldenburg, D. W.: SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications, Comput. Geosci., 85, 142–154, 2015. a
Cooper, M. A., Jordan, T. M., Schroeder, D. M., Siegert, M. J., Williams, C. N., and Bamber, J. L.: Subglacial roughness of the Greenland Ice Sheet: relationship with contemporary ice velocity and geology, The Cryosphere, 13, 3093–3115, https://doi.org/10.5194/tc-13-3093-2019, 2019. a
Costa, A. C. and Soares, A.: Homogenization of climate data: review and new perspectives using geostatistics, Math. Geosci., 41, 291–305, 2009. a
CReSIS: CReSIS Radar Depth Sounder, Digital Media, http://data.cresis.ku.edu/ (last access: 1 August 2022), 2022. a
Cressie, N. and Hawkins, D. M.: Robust estimation of the variogram: I, J. Int. Ass. Math. Geol., 12, 115–125, 1980. a
Daly, C., Quental, S., and Novak, D.: A faster, more accurate Gaussian simulation, in: Proceedings of the Geocanada Conference, Calgary, AB, Canada, 10–14, https://www.searchanddiscovery.com/pdfz/abstracts/pdf/2014/90172cspg/abstracts/ndx_daly.pdf.html (last access: 28 June 2023), 2010. a
Dimitrakopoulos, R. and Luo, X.: Generalized sequential Gaussian simulation on group size ν and screen-effect approximations for large field simulations, Math. Geol., 36, 567–591, 2004. a
Emery, X. and Maleki, M.: Geostatistics in the presence of geological boundaries: Application to mineral resources modeling, Ore Geol. Rev., 114, 103124, https://doi.org/10.1016/j.oregeorev.2019.103124, 2019. a
Franke, R.: Scattered data interpolation: tests of some methods, Math. Comput., 38, 181–200, 1982. a
GMS: GMS 10.6 Editions & Pricing, https://www.aquaveo.com/software/gms-pricing (last access: 1 August 2022), 2021. a
Goovaerts, P.: Ordinary cokriging revisited, Math. Geol., 30, 21–42, 1998. a
Goovaerts, P.: Geostatistics in soil science: state-of-the-art and perspectives, Geoderma, 89, 1–45, 1999. a
Gwinner, K., Scholten, F., Spiegel, M., Schmidt, R., Giese, B., Oberst, J., Heipke, C., Jaumann, R., and Neukum, G.: Derivation and validation of high-resolution digital terrain models from Mars Express HRSC data, Photogramm. Eng. Rem. S., 75, 1127–1142, 2009. a
Haas, A. and Dubrule, O.: Geostatistical inversion-a sequential method of stochastic reservoir modelling constrained by seismic data, First break, 12, https://doi.org/10.3997/1365-2397.1994034, 1994. a
Harris, C. R., Millman, K. J., Van Der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., del Río, J. F., Wiebe, M., Peterson, P., Gérard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., and Oliphant, T. E.: Array programming with NumPy, Nature, 585, 357–362, 2020. a
Journel, A. G. and Huijbregts, C. J.: Mining geostatistics, Academic Press, 600 pp., ISBN-10: 0123910501, 1976. a
Journel, A. G. and Rossi, M.: When do we need a trend model in kriging?, Math. Geol., 21, 715–739, 1989. a
Kelkar, M. and Perez, G.: Applied geostatistics for reservoir characterization, Society of Petroleum Engineers, 274 pp., ISBN-10: 1555630952, 2002. a
Kitanidis, P. K.: Introduction to geostatistics: applications in hydrogeology, Cambridge University Press, 272 pp., ISBN: 9780521587471, 1997. a
Krige, D. G.: A statistical approach to some basic mine valuation problems on the Witwatersrand, J. S. Afr. I. Min. Metall., 52, 119–139, 1951. a
Lark, R. M.: Towards soil geostatistics, Spat. Stat.-Neth., 1, 92–99, 2012. a
Law, R., Christoffersen, P., MacKie, E., Cook, S., Haseloff, M., and Gagliardini, O.: Complex motion of Greenland Ice Sheet outlet glaciers with basal temperate ice, Science Advances, 9, eabq5180, https://doi.org/10.1126/sciadv.abq5180, 2023. a
MacGregor, J. A., Fahnestock, M. A., Catania, G. A., Paden, J. D., Prasad Gogineni, S., Young, S. K., Rybarski, S. C., Mabrey, A. N., Wagman, B. M., and Morlighem, M.: Radiostratigraphy and age structure of the Greenland Ice Sheet, J. Geophys. Res.-Earth, 120, 212–241, 2015. a
MacKie, E., Schroeder, D., Caers, J., Siegfried, M., and Scheidt, C.: Antarctic topographic realizations and geostatistical modeling used to map subglacial lakes, J. Geophys. Res.-Earth, 125, e2019JF005420, https://doi.org/10.1029/2019JF005420, 2020. a
MacKie, E., Field, M., Wang, L., Yin, Z., Schoedl, N., and Hibbs, M.: GStatSim, Version 1.0, Zenodo [code], https://doi.org/10.5281/zenodo.7274640, 2022. a, b
Mälicke, M.: SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python, Geosci. Model Dev., 15, 2505–2532, https://doi.org/10.5194/gmd-15-2505-2022, 2022. a
Mariethoz, G.: A general parallelization strategy for random path based geostatistical simulation methods, Comput. Geosci., 36, 953–958, 2010. a
McKinney, W.: Data structures for statistical computing in python, in: Proceedings of the 9th Python in Science Conference, Austin, TX, 445, 51–56, 2010. a
Müller, S., Schüler, L., Zech, A., and Heße, F.:
GSTools v1.3: a toolbox for geostatistical modelling in Python, Geosci. Model Dev., 15, 3161–3182, https://doi.org/10.5194/gmd-15-3161-2022, 2022. a
Murphy, B. S.: PyKrige: development of a kriging toolkit for Python, in: AGU fall meeting abstracts, San Francisco, December 2014, H51K-0753, https://geostat-framework.readthedocs.io/en/latest/ (last access: 29 June 2023), 2014. a
Neven, A., Dall'Alba, V., Juda, P., Straubhaar, J., and Renard, P.: Ice volume and basal topography estimation using geostatistical methods and ground-penetrating radar measurements: application to the Tsanfleuron and Scex Rouge glaciers, Swiss Alps, The Cryosphere, 15, 5169–5186, https://doi.org/10.5194/tc-15-5169-2021, 2021. a
Ng, F. S., Ignéczi, Á., Sole, A. J., and Livingstone, S. J.: Response of surface topography to basal variability along glacial flowlines, J. Geophys. Res.-Earth, 123, 2319–2340, 2018. a
Nunes, R., Soares, A., Schwedersky, G., Dillon, L., Guerreiro, L., Caetano, H., Maciel, C., and Leon, F.: Geostatistical inversion of prestack seismic data, in: Ninth International Geostatistics Congress, Oslo, Norway, June, 2012, 1–8, http://geostats2012.nr.no/pdfs/1747134.pdf (last access: 29 June 2023), 2012. a, b
Nussbaumer, R., Mariethoz, G., Gravey, M., Gloaguen, E., and Holliger, K.: Accelerating sequential gaussian simulation with a constant path, Comput. Geosci., 112, 121–132, 2018. a
Oh, S.-H. and Kwon, B.-D.: Geostatistical approach to Bayesian inversion of geophysical data: Markov chain Monte Carlo method, Earth Planets Space, 53, 777–791, 2001. a
Parizek, B., Christianson, K., Anandakrishnan, S., Alley, R., Walker, R., Edwards, R., Wolfe, D., Bertini, G., Rinehart, S., Bindschadler, R., and Nowicki, S. M. J.: Dynamic (in) stability of Thwaites Glacier, West Antarctica, J. Geophys. Res.-Earth, 118, 638–655, 2013. a
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E.: Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res., 12, 2825–2830, 2011. a
Porter, C., Morin, P., Howat, I., Noh, M.-J., Bates, B., Peterman, K., Keesey, S., Schlenk, M., Gardiner, J., Tomko, K., Willis, M., Kelleher, C., Cloutier, M., Husby, E., Foga, S., Nakamura, H., Platson, M., Wethington Jr., M., Williamson, C., Bauer, G., Enos, J., Arnold, G., Kramer, W., Becker, P., Doshi, A., D'Souza, C., Cummens, P., Laurier, F., and Bojesen, M.: ArcticDEM, Version 3, Harvard Dataverse [data set], https://doi.org/10.7910/DVN/OHHUKH, 2018. a
Remy, N.: S-GeMS: the stanford geostatistical modeling software: a tool for new algorithms development, in: Geostatistics Banff 2004, edited by: Leuangthong, O. and Deutsch, C. V., Springer, 865–871, https://doi.org/10.1007/978-1-4020-3610-1_89, 2005. a
Remy, N., Boucher, A., and Wu, J.: Applied geostatistics with SGeMS: A user's guide, Cambridge University Press, https://doi.org/10.1017/CBO9781139150019, 2009. a
Sarra, S. A. and Kansa, E. J.: Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations, Advances in Computational Mechanics, 2, 220 pp., 2009. a
Seroussi, H., Nakayama, Y., Larour, E., Menemenlis, D., Morlighem, M., Rignot, E., and Khazendar, A.: Continued retreat of Thwaites Glacier, West Antarctica, controlled by bed topography and ocean circulation, Geophys. Res. Lett., 44, 6191–6199, 2017. a
Shamsipour, P., Marcotte, D., Chouteau, M., and Keating, P.: 3D stochastic inversion of gravity data using cokriging and cosimulation, Geophysics, 75, I1–I10, 2010. a
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics, Math. Geol., 34, 1–21, 2002. a
Torrence, C.: DC Polar Stereographic Projection lon/lat conversion: polar_convert, https://github.com/nsidc/polarstereo-lonlat-convert-py/ (last access: 1 March 2023), 2019. a
Van Rossum, G., Warsaw, B., and Coghlan, N.: PEP 8–style guide for python code, Python.org, 1565, https://peps.python.org/pep-0008/ (last access: 1 September 2022), 2001. a
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Jarrod Millman, K., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, I.,
Feng, Y., Moore, E. W., VanderPlas,J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Methods, 17, 261–272, 2020. a
Volkova, A. and Merkulov, V.: Iterative Approach of Gravity and Magnetic Inversion through Geostatistics, in: Petroleum Geostatistics 2019, vol. 2019, European Association of Geoscientists & Engineers, 1–5, https://doi.org/10.3997/2214-4609.201902257, 2019. a, b
Wernecke, A., Edwards, T. L., Holden, P. B., Edwards, N. R., and Cornford, S. L.: Quantifying the impact of bedrock topography uncertainty in Pine Island Glacier projections for this century, Geophys. Res. Lett., 49, e2021GL096589, https://doi.org/10.1029/2021GL096589, 2022. a
Wilkinson, M. D., Dumontier, M., Aalbersberg, I. J., et al.: The FAIR Guiding Principles for scientific data management and stewardship, Scientific Data, 3, 1–9, 2016. a
Xiong, X., Grunwald, S., Myers, D. B., Kim, J., Harris, W. G., and Bliznyuk, N.: Assessing uncertainty in soil organic carbon modeling across a highly heterogeneous landscape, Geoderma, 251, 105–116, 2015. a
Yin, Z., Zuo, C., MacKie, E. J., and Caers, J.: Mapping high-resolution basal topography of West Antarctica from radar data using non-stationary multiple-point geostatistics (MPS-BedMappingV1), Geosci. Model Dev., 15, 1477–1497, https://doi.org/10.5194/gmd-15-1477-2022, 2022. a
Youngman, B. D. and Stephenson, D. B.: A geostatistical extreme-value framework for fast simulation of natural hazard events, P. Roy. Soc. A-Math. Phy., 472, 20150855, https://doi.org/10.1098/rspa.2015.0855, 2016. a
Zuo, C., Yin, Z., Pan, Z., MacKie, E. J., and Caers, J.: A Tree-Based Direct Sampling Method for Stochastic Surface and Subsurface Hydrological Modeling, Water Resour. Res., 56, e2019WR026130, https://doi.org/10.1029/2019WR026130, 2020. a
Short summary
Earth scientists often have to fill in spatial gaps in measurements. This gap-filling or interpolation can be accomplished with geostatistical methods, where the statistical relationships between measurements are used to inform how these gaps should be filled. Despite the broad utility of these methods, there are few freely available geostatistical software applications. We present GStatSim, a Python package for performing different geostatistical interpolation methods.
Earth scientists often have to fill in spatial gaps in measurements. This gap-filling or...
