Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

Abstract. Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.

[1]  John L. Gustafson,et al.  Reevaluating Amdahl's law , 1988, CACM.

[2]  Diandong Ren,et al.  A Revised Force–Restore Model for Land Surface Modeling , 2004 .

[3]  Andrzej Mazur,et al.  COLOBOC - MOSAIC parameterization in COSMO model v. 4.8 , 2011 .

[4]  J. D. Tarpley,et al.  Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model , 2003 .

[5]  Arash Massoudieh,et al.  Transient age distributions in subsurface hydrologic systems , 2016 .

[6]  Jim E. Jones,et al.  Approved for Public Release; Further Dissemination Unlimited Newton-krylov-multigrid Solvers for Large-scale, Highly Heterogeneous, Variably Saturated Flow Problems , 2022 .

[7]  R D Falgout,et al.  Enabling computational technologies for subsurface simulations , 1999 .

[8]  Fotini Katopodes Chow,et al.  Coupling groundwater and land surface processes: Idealized simulations to identify effects of terrain and subsurface heterogeneity on land surface energy fluxes , 2010 .

[9]  R. Maxwell,et al.  A high-resolution simulation of groundwater and surface water over most of the continental US with the integrated hydrologic model ParFlow v3 , 2015 .

[10]  R. Maxwell,et al.  A comparison of two physics-based numerical models for simulating surface water–groundwater interactions , 2010 .

[11]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[12]  Reed M. Maxwell,et al.  Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model , 2009 .

[13]  M. Celia,et al.  A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation , 1990 .

[14]  Reed M. Maxwell,et al.  Human impacts on terrestrial hydrology: climate change versus pumping and irrigation , 2012 .

[15]  Terri S. Hogue,et al.  Impact of lateral flow and spatial scaling on the simulation of semi‐arid urban land surfaces in an integrated hydrologic and land surface model , 2016 .

[16]  T. Stanelle,et al.  The comprehensive model system COSMO-ART – Radiative impact of aerosol on the state of the atmosphere on the regional scale , 2009 .

[17]  A. Allievi,et al.  Application of Bubnov-Galerkin formulation to orthogonal grid generation , 1992 .

[18]  C. Steefel,et al.  A new kinetic approach to modeling water-rock interaction: The role of nucleation, precursors, and Ostwald ripening , 1990 .

[19]  Jeremy S. Pal,et al.  Land surface coupling in regional climate simulations of the West African monsoon , 2009 .

[20]  Young-Jin Park,et al.  Simulating complex flow and transport dynamics in an integrated surface-subsurface modeling framework , 2008 .

[21]  Carl I. Steefel,et al.  Scale dependence of mineral dissolution rates within single pores and fractures , 2008 .

[22]  Mauro Sulis,et al.  A Scale-Consistent Terrestrial Systems Modeling Platform Based on COSMO, CLM, and ParFlow , 2014 .

[23]  Homer F. Walker,et al.  Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[24]  Luís Eça 2D Orthogonal Grid Generation with Boundary Point Distribution Control , 1996 .

[25]  Gianluca Iaccarino,et al.  An approach to local refinement of structured grids , 2002 .

[26]  Jeremy S. Pal,et al.  The coupling of the Common Land Model (CLM0) to a regional climate model (RegCM) , 2005 .

[27]  Reed M. Maxwell,et al.  Evaluating the relationship between topography and groundwater using outputs from a continental‐scale integrated hydrology model , 2015 .

[28]  M. Baldauf,et al.  Operational Convective-Scale Numerical Weather Prediction with the COSMO Model: Description and Sensitivities , 2011 .

[29]  E. Sudicky,et al.  The integrated hydrologic model intercomparison project, IH‐MIP2: A second set of benchmark results to diagnose integrated hydrology and feedbacks , 2017 .

[30]  Stefan Kollet Technical note: Inference in hydrology from entropy balance considerations , 2016 .

[31]  M. Mccabe,et al.  Assessing the impact of model spin‐up on surface water‐groundwater interactions using an integrated hydrologic model , 2012 .

[32]  Reed M. Maxwell,et al.  Hydrologic and land–energy feedbacks of agricultural water management practices , 2011 .

[33]  David A. Benson,et al.  A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms , 2017 .

[34]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[35]  Peter Bayer,et al.  The Influence of Rain Sensible Heat and Subsurface Energy Transport on the Energy Balance at the Land Surface , 2009 .

[36]  E. Sudicky,et al.  Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media , 1996 .

[37]  Paul G. Constantine,et al.  Exploring the Sensitivity of Photosynthesis and Stomatal Resistance Parameters in a Land Surface Model , 2017 .

[38]  Reed M. Maxwell,et al.  Development of a Coupled Land Surface and Groundwater Model , 2005 .

[39]  Wolfram Rühaak,et al.  On the impact of explicitly predicted runoff on the simulated atmospheric response to small-scale land-use changes—an integrated modeling approach , 2002 .

[40]  C. Steefel,et al.  A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution rea , 1994 .

[41]  Reed M. Maxwell,et al.  Evaluation of simple to complex parameterizations of bare ground evaporation , 2015 .

[42]  Jimy Dudhia,et al.  Development of a next-generation regional weather research and forecast model. , 2001 .

[43]  Cecelia DeLuca,et al.  Coupling technologies for Earth System Modelling , 2012 .

[44]  C. Paniconi,et al.  Surface‐subsurface flow modeling with path‐based runoff routing, boundary condition‐based coupling, and assimilation of multisource observation data , 2010 .

[45]  R. Dickinson,et al.  The Common Land Model , 2003 .

[46]  William L. Briggs,et al.  A multigrid tutorial, Second Edition , 2000 .

[47]  John E. McCray,et al.  Mountain pine beetle infestation impacts: modeling water and energy budgets at the hill‐slope scale , 2013 .

[48]  Reed M. Maxwell,et al.  Effects of root water uptake formulation on simulated water and energy budgets at local and basin scales , 2016, Environmental Earth Sciences.

[49]  H. J Haussling,et al.  A method for generation of orthogonal and nearly orthogonal boundary-fitted coordinate systems , 1981 .

[50]  Fotini Katopodes Chow,et al.  Isolating effects of terrain and soil moisture heterogeneity on the atmospheric boundary layer: Idealized simulations to diagnose land‐atmosphere feedbacks , 2015 .

[51]  Reed M. Maxwell,et al.  The impact of subsurface conceptualization on land energy fluxes , 2013 .

[52]  Wa’il Y. Abu-El-Sha’r,et al.  Application of the high performance computing techniques of parflow simulator to model groundwater flow at Azraq basin , 2007 .

[53]  Robert D. Falgout,et al.  Numerical simulation of groundwater flow on MPPs , 1994 .

[54]  Robert D. Falgout,et al.  Analysis of subsurface contaminant migration and remediation using high performance computing , 1998 .

[55]  William C. Skamarock,et al.  A time-split nonhydrostatic atmospheric model for weather research and forecasting applications , 2008, J. Comput. Phys..

[56]  Steven F. Carle,et al.  Analysis of groundwater migration from artificial recharge in a large urban aquifer: A simulation perspective , 1999 .

[57]  Luca Delle Monache,et al.  Development and verification of a new wind speed forecasting system using an ensemble Kalman filter data assimilation technique in a fully coupled hydrologic and atmospheric model , 2013 .

[58]  C. Woodward,et al.  Preconditioning Newton-Krylor Methods for Variably Saturated Flow , 2000 .

[59]  Annamaria Mazzia,et al.  Coupling water flow and solute transport into a physically-based surface–subsurface hydrological model , 2011 .

[60]  R. Maxwell,et al.  Demonstrating fractal scaling of baseflow residence time distributions using a fully‐coupled groundwater and land surface model , 2008 .

[61]  Paul G. Constantine,et al.  Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model , 2015, Comput. Geosci..

[62]  Markus Geimer,et al.  Implementation and scaling of the fully coupled Terrestrial Systems Modeling Platform (TerrSysMP v1.0) in a massively parallel supercomputing environment - a case study on JUQUEEN (IBM Blue Gene/Q) , 2014 .

[63]  Carol S. Woodward,et al.  Development of a Coupled Groundwater-Atmosphere Model , 2011 .

[64]  Carol S. Woodward,et al.  User Documentation for KINSOL v2.2.0 , 2004 .

[65]  S. Ashby,et al.  A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations , 1996 .

[66]  C. Duffy,et al.  A Second‐Order Accurate, Finite Volume–Based, Integrated Hydrologic Modeling (FIHM) Framework for Simulation of Surface and Subsurface Flow , 2009 .

[67]  Andreas Hense,et al.  Studying the influence of groundwater representations on land surface‐atmosphere feedbacks during the European heat wave in 2003 , 2016 .

[68]  Anthony M. Castronova,et al.  Integrated modeling within a Hydrologic Information System: An OpenMI based approach , 2013, Environ. Model. Softw..

[69]  Brian D. Wood,et al.  The role of scaling laws in upscaling , 2009 .

[70]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[71]  Clemens Simmer,et al.  The Influence of Hydrologic Modeling on the Predicted Local Weather: Two-Way Coupling of a Mesoscale Weather Prediction Model and a Land Surface Hydrologic Model , 2002 .

[72]  Mauro Sulis,et al.  Evaluating the dual‐boundary forcing concept in subsurface–land surface interactions of the hydrological cycle , 2016 .

[73]  Reed M. Maxwell,et al.  Groundwater-fed irrigation impacts spatially distributed temporal scaling behavior of the natural system: a spatio-temporal framework for understanding water management impacts , 2014 .

[74]  A. Robock,et al.  Incorporating water table dynamics in climate modeling: 3. Simulated groundwater influence on coupled land‐atmosphere variability , 2008 .

[75]  Peter E. Thornton,et al.  Improvements to the Community Land Model and their impact on the hydrological cycle , 2008 .

[76]  S. Kollet,et al.  Spatio-temporal validation of long-term 3D hydrological simulations of a forested catchment using empirical orthogonal functions and wavelet coherence analysis , 2015 .

[77]  Ci Steefel,et al.  OS3D/GIMRT software for modeling multicomponent-multidimensional reactive transport , 2000 .

[78]  Clemens Simmer,et al.  Coupling Groundwater, Vegetation, and Atmospheric Processes: A Comparison of Two Integrated Models , 2017 .

[79]  Robert D. Falgout,et al.  hypre: A Library of High Performance Preconditioners , 2002, International Conference on Computational Science.

[80]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[81]  R. Maxwell,et al.  The groundwater land-surface atmosphere connection: Soil moisture effects on the atmospheric boundary layer in fully-coupled simulations , 2007 .

[82]  Jason E. Smerdon,et al.  Effects of bottom boundary placement on subsurface heat storage: Implications for climate model simulations , 2007 .

[83]  G. Amdhal,et al.  Validity of the single processor approach to achieving large scale computing capabilities , 1967, AFIPS '67 (Spring).

[84]  Carol S. Woodward,et al.  Improved numerical solvers for implicit coupling of subsurface and overland flow , 2014 .

[85]  Laura E. Condon,et al.  Implementation of a linear optimization water allocation algorithm into a fully integrated physical hydrology model , 2013 .

[86]  Reed M. Maxwell,et al.  Infiltration in Arid Environments: Spatial Patterns between Subsurface Heterogeneity and Water‐Energy Balances , 2010 .

[87]  Curtis D Mobley,et al.  On the numerical generation of boundary-fitted orthogonal curvilinear coordinate systems , 1980 .

[88]  M. Visbal,et al.  Generation of orthogonal and nearly orthogonal coordinates with gridcontrol near boundaries , 1982 .

[89]  Fotini Katopodes Chow,et al.  Effects of soil moisture heterogeneity on boundary layer flow with coupled groundwater, land-surface, and mesoscale atmospheric modeling , 2006 .

[90]  Rafael Muñoz-Carpena,et al.  Insights on geologic and vegetative controls over hydrologic behavior of a large complex basin – Global Sensitivity Analysis of an integrated parallel hydrologic model , 2014 .

[91]  Zong-Liang Yang,et al.  Impacts of vegetation and groundwater dynamics on warm season precipitation over the Central United States , 2009 .

[92]  Eric M LaBolle,et al.  Review of the Integrated Groundwater and Surface‐Water Model (IGSM) , 2003, Ground water.

[93]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[94]  E. Mouche,et al.  A generalized Richards equation for surface/subsurface flow modelling , 2009 .

[95]  Steven G. Smith,et al.  Modeling groundwater flow on MPPs , 1993, Proceedings of Scalable Parallel Libraries Conference.

[96]  Reed M. Maxwell,et al.  Quantifying changes in age distributions and the hydrologic balance of a high-mountain watershed from climate induced variations in recharge , 2015 .

[97]  Reed M. Maxwell,et al.  Streamline-based simulation of virus transport resulting from long term artificial recharge in a heterogeneous aquifer , 2003 .

[98]  Reed M. Maxwell,et al.  Examining regional groundwater–surface water dynamics using an integrated hydrologic model of the San Joaquin River basin , 2016 .

[99]  Clemens Simmer,et al.  Impacts of grid resolution on surface energy fluxes simulated with an integrated surface-groundwater flow model , 2015 .

[100]  R. Maxwell A terrain-following grid transform and preconditioner for parallel, large-scale, integrated hydrologic modeling , 2013 .

[101]  Reed M. Maxwell,et al.  Influences of subsurface heterogeneity and vegetation cover on soil moisture, surface temperature and evapotranspiration at hillslope scales , 2011 .

[102]  Carl I. Steefel,et al.  ParCrunchFlow: an efficient, parallel reactive transport simulation tool for physically and chemically heterogeneous saturated subsurface environments , 2015, Computational Geosciences.

[103]  Reed M. Maxwell,et al.  Propagating Subsurface Uncertainty to the Atmosphere Using Fully Coupled Stochastic Simulations , 2011 .

[104]  L. A. Richards Capillary conduction of liquids through porous mediums , 1931 .

[105]  Jan Vanderborght,et al.  Monitoring and Modeling the Terrestrial System from Pores to Catchments: The Transregional Collaborative Research Center on Patterns in the Soil–Vegetation–Atmosphere System , 2015 .

[106]  Olaf Kolditz,et al.  Surface‐subsurface model intercomparison: A first set of benchmark results to diagnose integrated hydrology and feedbacks , 2014 .

[107]  Stefan Kollet,et al.  Influence of soil heterogeneity on evapotranspiration under shallow water table conditions: transient, stochastic simulations , 2009 .

[108]  G. Meehl,et al.  OVERVIEW OF THE COUPLED MODEL INTERCOMPARISON PROJECT , 2005 .

[109]  S. Seneviratne,et al.  COSMO-CLM2: a new version of the COSMO-CLM model coupled to the Community Land Model , 2011 .

[110]  P. Huyakorn,et al.  A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow , 2004 .

[111]  A. Atchley,et al.  Human health risk assessment of CO2 leakage into overlying aquifers using a stochastic, geochemical reactive transport approach. , 2013, Environmental science & technology.

[112]  Christopher J. Duffy,et al.  Evaluation of the Parameter Sensitivities of a Coupled Land Surface Hydrologic Model at a Critical Zone Observatory , 2014 .

[113]  R. Maxwell,et al.  Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model , 2006 .

[114]  Amanda S. Hering,et al.  Quantitative assessment of groundwater controls across major US river basins using a multi-model regression algorithm , 2015 .

[115]  Yousef Saad,et al.  Hybrid Krylov Methods for Nonlinear Systems of Equations , 1990, SIAM J. Sci. Comput..

[116]  S. Stisen,et al.  Inter-comparison of three distributed hydrological models with respect to seasonal variability of soil moisture patterns at a small forested catchment , 2016 .

[117]  S. Hubbard,et al.  Effects of physical and geochemical heterogeneities on mineral transformation and biomass accumulation during biostimulation experiments at Rifle, Colorado. , 2010, Journal of contaminant hydrology.

[118]  Reed M. Maxwell,et al.  Spin‐up behavior and effects of initial conditions for an integrated hydrologic model , 2015 .

[119]  Benjamin Fersch,et al.  Fully coupled atmospheric‐hydrological modeling at regional and long‐term scales: Development, application, and analysis of WRF‐HMS , 2016 .

[120]  Keith Beven,et al.  Robert E. Horton's perceptual model of infiltration processes , 2004 .

[121]  R. Maxwell,et al.  Capturing the influence of groundwater dynamics on land surface processes using an integrated, distributed watershed model , 2008 .

[122]  S. Valcke,et al.  The OASIS3 coupler: a European climate modelling community software , 2012 .

[123]  Carsten Burstedde,et al.  Enhancing speed and scalability of the ParFlow simulation code , 2017, Computational Geosciences.

[124]  Matthew F. McCabe,et al.  Impacts of model initialization on an integrated surface water–groundwater model , 2015 .

[125]  Jan Vanderborght,et al.  Proof of concept of regional scale hydrologic simulations at hydrologic resolution utilizing massively parallel computer resources , 2010 .

[126]  D. E. Prudic,et al.  GSFLOW - Coupled Ground-Water and Surface-Water Flow Model Based on the Integration of the Precipitation-Runoff Modeling System (PRMS) and the Modular Ground-Water Flow Model (MODFLOW-2005) , 2008 .

[127]  Chaopeng Shen,et al.  A process-based, distributed hydrologic model based on a large-scale method for surface–subsurface coupling , 2010 .

[128]  Carl I. Steefel,et al.  A Reactive-Transport Model for Weathering Rind Formation on Basalt , 2011 .

[129]  Andrew J. Miller,et al.  Untangling the effects of urban development on subsurface storage in Baltimore , 2015 .