Hydrology, applied

Rivers, aquifers and other wet things that can flood your house

Refugees from Brazil’s Grande Seca drought of 1878

TBD: Ground water hydrology, surface water hydrology, coastal water hydrology… UCSB Climate hazards data.


AFAICT the go-to applied reference for groundwater is Anderson, Woessner, and Hunt (2015). I have skimmed it and now I know just enough to be dangerous. Fortunately I have my esteemed colleagues in hydrology, Stephanie Clark, Sreekanth-Janardhanan and Tao Cui, and who explain the tricky bits to me.

Stephanie’s recommendations for tutorial introductions:




An important industry standard from the USGS. See MODFLOW.


OrchardLANL/DPFEHM.jl: DPFEHM: A Differentiable Subsurface Flow Simulator

DPFEHM is a Julia module that includes differentiable numerical models with a focus on fluid flow and transport in the Earth’s subsurface. Currently it supports the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation.

Does not seem to support CUDA well but is nifty. Use in e.g. Pachalieva et al. (2022).

Pronounced “dip-fahhhh-m”, why not?


We treat physical simulations as a chain of multiple differentiable operators, such as discrete Laplacian evaluation, a Poisson solver, and a single implicit time-stepping for nonlinear PDEs. They are like building blocks that can be assembled to make simulation tools for new physical models.

Those operators are differentiable and integrated within a computational graph so that the gradients can be computed automatically and efficiently via analyzing the dependency in the graph. Also, independent operators run in parallel, thanks to the graph-based parallelization mechanism of TensorFlow. With the gradients, we can perform gradient-based PDE-constrained optimization for inverse problems.

FwiFlow is built on ADCME, a powerful static-graph-based automatic differentiation library for scientific computing (with TensorFlow backend). FwiFlow implements the idea of Intrusive Automatic Differentiation.

Geostats Framework

GeoStat Framework:

This Framework was created within the PhD project of Sebastian Müller at the Computational Hydrosystems Department at the UFZ Leipzig.

AnaFlow Quickstart

AnaFlow provides several analytical and semi-analytical solutions for the groundwater-flow equation.


WellTestPy is a python-package for handling well based field campaigns. You can easily estimate parameters of aquifer-heterogeneity from pumping test data.


Swift – A shallow water based integrated flood tool for urban flood inundation and adaptation

Swift is a toolkit for the end-to-end processing, simulation and analysis of floods. Users can design custom workflows by building on Swift’s computational shallow water solver and incorporating various input, processing and visualisation components, each tailored for flood modelling. The Swift toolkit provides hydrodynamic and coupled hydraulic modelling capability with analysis tools for mitigation options. Swift can be used for both catchment and coastal flood modelling, including sea level rise, for present and future flooding. The capabilities of Swift have been used in a number of flood mitigation projects for cities across Australia.


A porous flow solver which solves diverse PDEs but especially porous flow ones. C++/Python


A solver for surface water equations, targeting approximately the same problems as Swift, although possibly with fewer GPU accelerations.


Try Pangeo Hydrology Dataset Catalog, which lists some hydrology-focussed spatial data. Locally I might try Groundwater Use by Geoscience Australia


Gravity tomography at NASA! GRACE


Anderson, Mary P., William W. Woessner, and R. J. Hunt. 2015. Applied Groundwater Modeling: Simulation of Flow and Advective Transport. Second edition. London ; San Diego, CA: Academic Press.
Bakker, M., V. Post, C. D. Langevin, J. D. Hughes, J. T. White, J. J. Starn, and M. N. Fienen. 2016. Scripting MODFLOW Model Development Using Python and FloPy.” Groundwater 54 (5): 733–39.
Barnett, Steve, Nikki Harrington, Peter Cook, and Craig T. Simmons. 2020. Groundwater in Australia: Occurrence and Management Issues.” In Sustainable Groundwater Management: A Comparative Analysis of French and Australian Policies and Implications to Other Countries, edited by Jean-Daniel Rinaudo, Cameron Holley, Steve Barnett, and Marielle Montginoul, 109–27. Global Issues in Water Policy. Cham: Springer International Publishing.
Bruno, Pier Paolo G., and Aldo Vesnaver. 2021. Groundwater characterization in arid regions using seismic and gravity attributes: Al Jaww Plain, UAE.” Frontiers in Earth Science 8.
Cai, Yuzhi, and Dominic E. Reeve. 2013. Extreme Value Prediction via a Quantile Function Model.” Coastal Engineering 77 (July): 91–98.
Cranmer, Miles, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho. 2020. Lagrangian Neural Networks.” arXiv:2003.04630 [Physics, Stat], July.
Cui, Tao, Luk Peeters, Dan Pagendam, Trevor Pickett, Huidong Jin, Russell S. Crosbie, Matthias Raiber, David W. Rassam, and Mat Gilfedder. 2018. Emulator-Enabled Approximate Bayesian Computation (ABC) and Uncertainty Analysis for Computationally Expensive Groundwater Models.” Journal of Hydrology 564 (September): 191–207.
Gladish, Daniel W., Daniel E. Pagendam, Luk J. M. Peeters, Petra M. Kuhnert, and Jai Vaze. 2018. Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models.” Journal of Agricultural, Biological and Environmental Statistics 23 (1): 39–62.
Godfried, Isaac, Kriti Mahajan, Maggie Wang, Kevin Li, and Pranjalya Tiwari. 2020. FlowDB a Large Scale Precipitation, River, and Flash Flood Dataset.” arXiv:2012.11154 [Cs], December.
Guo, Hongwei, Xiaoying Zhuang, Pengwan Chen, Naif Alajlan, and Timon Rabczuk. 2022. Stochastic Deep Collocation Method Based on Neural Architecture Search and Transfer Learning for Heterogeneous Porous Media.” Engineering with Computers 38 (6): 5173–98.
He, QiZhi, David Barajas-Solano, Guzel Tartakovsky, and Alexandre M. Tartakovsky. 2020. Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport.” Advances in Water Resources 141 (July): 103610.
Hoffimann, Júlio, Maciel Zortea, Breno de Carvalho, and Bianca Zadrozny. 2021. Geostatistical Learning: Challenges and Opportunities.” Frontiers in Applied Mathematics and Statistics 7.
Kimura, Nobuaki, Ikuo Yoshinaga, Kenji Sekijima, Issaku Azechi, and Daichi Baba. 2020. Convolutional Neural Network Coupled with a Transfer-Learning Approach for Time-Series Flood Predictions.” Water 12 (1): 96.
Lee, Herbert K. H., Dave M. Higdon, Zhuoxin Bi, Marco A. R. Ferreira, and Mike West. 2002. Markov Random Field Models for High-Dimensional Parameters in Simulations of Fluid Flow in Porous Media.” Technometrics 44 (3): 230–41.
Leong, Ching. 2018. The Role of Narratives in Sociohydrological Models of Flood Behaviors.” Water Resources Research 54 (4): 3100–3121.
Li, Dongzhuo, Kailai Xu, Jerry M. Harris, and Eric Darve. 2020. Coupled Time-Lapse Full Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation.” arXiv.
Lutter, Michael, Christian Ritter, and Jan Peters. 2019. Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning.” arXiv:1907.04490 [Cs, Eess, Stat], July.
McInerney, David, Mark Thyer, Dmitri Kavetski, Bree Bennett, Julien Lerat, Matthew Gibbs, and George Kuczera. 2018. A Simplified Approach to Produce Probabilistic Hydrological Model Predictions.” Environmental Modelling & Software 109 (November): 306–14.
Newell, Barry, and Robert Wasson. 2002. “Social System Vs Solar System: Why Policy Makers Need History.” In. Grenoble.
Pachalieva, Aleksandra, Daniel O’Malley, Dylan Robert Harp, and Hari Viswanathan. 2022. Physics-Informed Machine Learning with Differentiable Programming for Heterogeneous Underground Reservoir Pressure Management.” arXiv.
Pagendam, Dan, Sreekanth Janardhanan, Joel Dabrowski, and Dan MacKinlay. 2023. A Log-Additive Neural Model for Spatio-Temporal Prediction of Groundwater Levels.” Spatial Statistics 55 (June): 100740.
Pirinen, Aleksis, Olof Mogren, and Mårten Västerdal. 2023. Fully Convolutional Networks for Dense Water Flow Intensity Prediction in Swedish Catchment Areas.” arXiv.
Qian, Elizabeth, Boris Kramer, Benjamin Peherstorfer, and Karen Willcox. 2020. Lift & Learn: Physics-Informed Machine Learning for Large-Scale Nonlinear Dynamical Systems.” Physica D: Nonlinear Phenomena 406 (May): 132401.
Raissi, Maziar, Alireza Yazdani, and George Em Karniadakis. 2020. Hidden Fluid Mechanics: Learning Velocity and Pressure Fields from Flow Visualizations.” Science 367 (6481): 1026–30.
Santos-Fernandez, Edgar, Jay M. Ver Hoef, Erin E. Peterson, James McGree, Daniel Isaak, and Kerrie Mengersen. 2021. Bayesian Spatio-Temporal Models for Stream Networks,” March.
Shen, Chaopeng, Xingyuan Chen, and Eric Laloy. 2021. Editorial: Broadening the Use of Machine Learning in Hydrology.” Frontiers in Water 3.
Siade, Adam J., Tao Cui, Robert N. Karelse, and Clive Hampton. 2020. Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory.” Water Resources Research 56 (3).
Siade, Adam J., Mario Putti, and William W. G. Yeh. 2010. Snapshot selection for groundwater model reduction using proper orthogonal decomposition.” Water Resources Research 46 (8): W08539.
Sun, Alexander Y., Bridget R. Scanlon, Zizhan Zhang, David Walling, Soumendra N. Bhanja, Abhijit Mukherjee, and Zhi Zhong. 2019. Combining Physically Based Modeling and Deep Learning for Fusing GRACE Satellite Data: Can We Learn From Mismatch? Water Resources Research 55 (2): 1179–95.
Tait, Daniel J., and Theodoros Damoulas. 2020. Variational Autoencoding of PDE Inverse Problems.” arXiv:2006.15641 [Cs, Stat], June.
Tartakovsky, Alexandre M., Carlos Ortiz Marrero, Paris Perdikaris, Guzel D. Tartakovsky, and David Barajas-Solano. 2018. Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks,” August.
Tonkin, Matthew, and John Doherty. 2009. Calibration-Constrained Monte Carlo Analysis of Highly Parameterized Models Using Subspace Techniques.” Water Resources Research 45 (12).
White, Jeremy T. 2018. A Model-Independent Iterative Ensemble Smoother for Efficient History-Matching and Uncertainty Quantification in Very High Dimensions.” Environmental Modelling & Software 109 (November): 191–201.
White, Jeremy T., Michael N. Fienen, and John E. Doherty. 2016a. pyEMU: A Python Framework for Environmental Model Uncertainty Analysis Version .01.” U.S. Geological Survey.
———. 2016b. A Python Framework for Environmental Model Uncertainty Analysis.” Environmental Modelling & Software 85 (November): 217–28.
Xu, Kailai, Dongzhuo Li, Eric Darve, and Jerry M. Harris. 2019. Learning Hidden Dynamics Using Intelligent Automatic Differentiation.” arXiv.
Yu, Xiayang, Tao Cui, J. Sreekanth, Stephane Mangeon, Rebecca Doble, Pei Xin, David Rassam, and Mat Gilfedder. 2020. Deep Learning Emulators for Groundwater Contaminant Transport Modelling.” Journal of Hydrology, August, 125351.

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