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Grooms, Ian G

Associate Professor

Positions

• Associate Professor, Applied Mathematics

Research Areas

• Applied Mathematics
• Physical Oceanography

Research

research overview

• My research interests encompass subgrid-scale parameterization for global ocean models, the development of new data assimilation methods, and the theory of geophysical fluid dynamics and turbulence.

keywords

• applied mathematics, geophysical fluid dynamics, data assimilation

Publications

selected publications

• conference proceeding

  • Turbulence Model Development Using Markov Chain Monte Carlo Approximate Bayesian Computation 2019
  • Parameter Estimation using Wavelength Modulation Spectroscopy Temperature Measurements and Approximate Bayesian Computation.  EM3A.5-EM3A.5. 2018
  • A Parameter Estimation for a Pulsating Turbulent Buoyant Jet Using Approximate Bayesian Computation 2017
  • Parameter Estimation for a Turbulent Buoyant Jet with Rotating Cylinder Using Approximate Bayesian Computation 2017
  • Parameter Estimation for a Turbulent Buoyant Jet using Approximate Bayesian Computation 2017
  Parameter Estimation for a Turbulent Buoyant Jet Using Approximate Bayesian Computation 2016
  ... more

• journal article

  • Cross-Attractor Transforms: Improving Forecasts by Learning Optimal Maps Between Dynamical Systems and Imperfect Models.  Geophysical Research Letters. 2025
  • Asymptotic approximations for convection onset with Ekman pumping at low wavenumbers.  Journal of Fluid Mechanics. 2025
    
  • The Averaged Hydrostatic Boussinesq Ocean Equations in Generalized Vertical Coordinates.  Journal of Advances in Modeling Earth Systems. 2024
    
  • Parameterized Ekman boundary layers on the tilted f-plane.  Journal of Fluid Mechanics. 2024
  • A Quantile-Conserving Ensemble Filter Based on Kernel-Density Estimation.  Remote Sensing. 2024
  CONTINUOUS AND DISCRETE BAROCLINIC MODES IN CONTINUOUSLY VARYING STRATIFICATION.  SIAM Journal on Applied Mathematics. 2502-2521. 2024
  Backscatter in energetically-constrained Leith parameterizations.  Ocean Modelling. 2023
  
  Comparing Two Parameterizations for the Restratification Effect of Mesoscale Eddies in an Isopycnal Ocean Model.  Journal of Advances in Modeling Earth Systems. 2023
  Impact of Stochastic Ocean Density Corrections on Air-Sea Flux Variability.  Geophysical Research Letters. 2023
  
  Analog ensemble data assimilation in a quasigeostrophic coupled model.  Quarterly Journal of the Royal Meteorological Society. 1018-1037. 2023
  
  Two Methods for Data Assimilation of Wind Direction.  Tellus Series A: Dynamic Meteorology and Oceanography. 145-158. 2023
  Diagnosing Scale-Dependent Energy Cycles in a High-Resolution Isopycnal Ocean Model.  Journal of Physical Oceanography. 157-176. 2023
  
  Limits on the Rate of Conversion of Potential to Kinetic Energy in Quasigeostrophic Turbulence.  Fluids. 2022
  
  A comparison of nonlinear extensions to the ensemble Kalman filter Gaussian anamorphosis and two-step ensemble filters.  Computational Geosciences: modeling, simulation and data analysis. 633-650. 2022
  
  Parameterizing the Impact of Unresolved Temperature Variability on the Large-Scale Density Field: 2. Modeling.  Journal of Advances in Modeling Earth Systems. 2022
  
  GCM-Filters: A Python Package for Diffusion-based Spatial Filtering of Gridded Data.  Journal of Open Source Software. 3947-3947. 2022
  
  Machine learning techniques to construct patched analog ensembles for data assimilation.  Journal of Computational Physics. 2021
  
  Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system.  Nonlinear Processes in Geophysics. 565-583. 2021
  
  Diffusion-Based Smoothers for Spatial Filtering of Gridded Geophysical Data.  Journal of Advances in Modeling Earth Systems. 2021
  
  The fidelity of exponential and IMEX integrators for wave turbulence: Introduction of anew near-minimax integrating factor scheme.  Journal of Computational Physics. 2021
  
  The fidelity of exponential and IMEX integrators for wave turbulence: Introduction of a new near-minimax integrating factor scheme (vol 434, 109992, 2021).  Journal of Computational Physics. 2021
  A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity.  PLoS One. 2021
  Multivariate localization functions for strongly coupled data; assimilation in the bivariate Lorenz ’96 system 2021
  
  Flow parameter estimation using laser absorption spectroscopy and approximate Bayesian computation.  Experiments in Fluids: experimental methods and their applications to fluid flow. 2021
  
  Analog ensemble data assimilation and a method for constructing analogs with variational autoencoders.  Quarterly Journal of the Royal Meteorological Society. 139-149. 2021
  
  On the control of subantarctic stratification by the ocean circulation.  Climate Dynamics. 299-327. 2021
  Parameterizing the Impact of Unresolved Temperature Variability on the Large-Scale Density Field: Part 1. Theory..  Journal of Advances in Modeling Earth Systems. 2020
  
  Vertical Structure of Ocean Mesoscale Eddies with Implications for Parameterizations of Tracer Transport.  Journal of Advances in Modeling Earth Systems. 2020
  
  On energy exchanges between eddies and the mean flow in quasigeostrophic turbulence.  Journal of Fluid Mechanics. 2020
  
  Rigorous bounds on the heat transport of rotating convection with Ekman pumping.  Journal of Mathematical Physics. 2020
  
  A FAST TUNABLE BLURRING ALGORITHM FOR SCATTERED DATA.  SIAM Journal on Scientific Computing. A2281-A2299. 2020
  
  An eddifying Stommel model: fast eddy effects in a two-box ocean.  Geophysical and Astrophysical Fluid Dynamics. 505-526. 2019
  
  Energy-conserving Galerkin approximations for quasigeostrophic dynamics.  Journal of Computational Physics. 23-40. 2019
  
  Exact instantaneous optimals in the non-geostrophic Eady problem and the detrimental effects of discretization.  Theoretical and Computational Fluid Dynamics. 125-139. 2019
  
  Diagnosing, modeling, and testing a multiplicative stochastic Gent-McWilliams parameterization.  Ocean Modelling. 1-10. 2019
  
  Multiscale Models in Geophysical Fluid Dynamics.  Earth and Space Science. 668-675. 2018
  Parameter estimation for complex thermal-fluid flows using approximate Bayesian computation.  Physical Review Fluids. 2018
  Comparing Eddy-Permitting Ocean Model Parameterizations via Lagrangian Particle Statistics in a Quasigeostrophic Setting.  Journal of Geophysical Research: Oceans. 5637-5651. 2018
  Improving Particle Filter Performance by Smoothing Observations.  Monthly Weather Review. 2433-2446. 2018
  
  Some effects of horizontal discretization on linear baroclinic and symmetric instabilities.  Ocean Modelling. 106-116. 2018
  
  Assimilation of ocean sea-surface height observations of mesoscale eddies.  Chaos: an interdisciplinary journal of nonlinear science. 2017
  
  Simulations of eddy kinetic energy transport in barotropic turbulence.  Physical Review Fluids. 2017
  
  A note on 'Toward a stochastic parameterization of ocean mesoscale eddies'.  Ocean Modelling. 30-33. 2017
  
  The Effects of Mesoscale Ocean-Atmosphere Coupling on the Quasigeostrophic Double Gyre.  Fluids. 2016
  A Gaussian-product stochastic Gent-McWilliams parameterization.  Ocean Modelling. 27-43. 2016
  
  Investigations of non-hydrostatic, stably stratified and rapidly rotating flows.  Journal of Fluid Mechanics. 430-458. 2016
  
  On Galerkin Approximations of the Surface Active Quasigeostrophic Equations.  Journal of Physical Oceanography. 125-139. 2016
  
  A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane.  Physics of Fluids. 2015
  
  Ensemble Filtering and Low-Resolution Model Error: Covariance Inflation, Stochastic Parameterization, and Model Numerics.  Monthly Weather Review. 3912-3924. 2015
  
  Asymptotic behavior of heat transport for a class of exact solutions in rotating Rayleigh-Benard convection.  Geophysical and Astrophysical Fluid Dynamics. 145-158. 2015
  
  A framework for variational data assimilation with superparameterization.  Nonlinear Processes in Geophysics. 601-611. 2015
  Bounds on heat transport in rapidly rotating Rayleigh-Benard convection.  Nonlinearity. 29-41. 2015
  
  NUMERICAL SCHEMES FOR STOCHASTIC BACKSCATTER IN THE INVERSE CASCADE OF QUASIGEOSTROPHIC TURBULENCE.  SIAM: Multiscale Modeling and Simulation. 1001-1021. 2015
  Stochastic superparameterization in a quasigeostrophic model of the Antarctic Circumpolar Current.  Ocean Modelling. 1-15. 2015
  Submesoscale baroclinic instability in the balance equations.  Journal of Fluid Mechanics. 256-272. 2015
  Ensemble Kalman filters for dynamical systems with unresolved turbulence.  Journal of Computational Physics. 435-452. 2014
  New perspectives on superparameterization for geophysical turbulence.  Journal of Computational Physics. 60-77. 2014
  Stochastic superparameterization in quasigeostrophic turbulence.  Journal of Computational Physics. 78-98. 2014
  
  STOCHASTIC SUPERPARAMETERIZATION IN A ONE- DIMENSIONAL MODEL FOR WAVE TURBULENCE.  Communications in Mathematical Sciences. 509-525. 2014
  Mesoscale Eddy Energy Locality in an Idealized Ocean Model.  Journal of Physical Oceanography. 1911-1923. 2013
  
  Efficient stochastic superparameterization for geophysical turbulence.  Proceedings of the National Academy of Sciences of USA. 4464-4469. 2013
  
  Multiscale models for synoptic-mesoscale interactions in the ocean.  Dynamics of Atmospheres and Oceans. 95-107. 2012
  Statistical and physical balances in low Rossby number Rayleigh-Benard convection.  Geophysical and Astrophysical Fluid Dynamics. 392-428. 2012
  Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation.  Journal of Computational Physics. 3630-3650. 2011
  On the interactions between planetary geostrophy and mesoscale eddies.  Dynamics of Atmospheres and Oceans. 109-136. 2011
  Model of Convective Taylor Columns in Rotating Rayleigh-Benard Convection.  Physical Review Letters. 2010
  MOLECULAR EMBEDDING VIA A SECOND ORDER DISSIMILARITY PARAMETERIZED APPROACH.  SIAM Journal on Scientific Computing. 2733-2756. 2009
  ... more

Teaching

courses taught

• APPM 1360 - Calculus 2 for Engineers
  Primary Instructor - Spring 2019 / Fall 2023
  Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Degree credit not granted for this course and MATH 2300.
• APPM 3310 - Matrix Methods and Applications
  Primary Instructor - Spring 2018 / Fall 2018 / Fall 2020 / Spring 2021 / Spring 2023 / Fall 2024
  Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Degree credit not granted for this course and MATH 2130 and MATH 2135.
• APPM 4380 - Modeling in Applied Mathematics
  Primary Instructor - Fall 2021
  An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 5380.
• APPM 4510 - Data Assimilation in High Dimensional Dynamical Systems
  Primary Instructor - Fall 2019 / Fall 2021 / Fall 2023
  Develops and analyzes approximate methods of solving the Bayesian inverse problem for high-dimensional dynamical systems. After briefly reviewing mathematical foundations in probability and statistics, the course covers the Kalman filter, particle filters, variational methods and ensemble Kalman filters. The emphasis is on mathematical formulation and analysis of methods. Same as APPM 5510, STAT 4250 and STAT 5250.
• APPM 4720 - Open Topics in Applied Mathematics
  Primary Instructor - Spring 2018
  Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 15 total credit hours. Same as APPM 5720.
APPM 5380 - Modeling in Applied Mathematics
Primary Instructor - Fall 2021
An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Department enforced prerequisites: APPM 2350 or MATH 2400 and APPM 2360. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 4380.
APPM 5480 - Methods of Applied Mathematics: Approximation Methods
Primary Instructor - Spring 2024
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods and applications to differential and integral equations. Department enforced prerequisite: APPM 5470.
APPM 5510 - Data Assimilation in High Dimensional Dynamical Systems
Primary Instructor - Fall 2019 / Fall 2021 / Fall 2023
Develops and analyzes approximate methods of solving the Bayesian inverse problem for high-dimensional dynamical systems. After briefly reviewing mathematical foundations in probability and statistics, the course covers the Kalman filter, particle filters, variational methods and ensemble Kalman filters. The emphasis is on mathematical formulation and analysis of methods. Same as APPM 4510, STAT 4250 and STAT 5250.
APPM 5600 - Numerical Analysis 1
Primary Instructor - Fall 2018
Solution of nonlinear algebraic equations, interpolation, integration, approximation, and numerical linear algebra. Department enforced prerequisite: APPM 3310 or MATH 2130 and experience with a scientific programming language.
APPM 5620 - Numerical Linear Algebra
Primary Instructor - Spring 2020 / Spring 2022
Develops and analyzes methods for the solution of square nonsingular linear systems, linear least squares problems, eigenvalue problems, and rank estimation. Direct and iterative methods are covered, as well as methods for dense and sparse problems. Requires solid background in linear algebra and proficiency with scientific computing.
APPM 5720 - Open Topics in Applied Mathematics
Primary Instructor - Spring 2018 / Fall 2019 / Fall 2020
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 6 total credit hours. Same as APPM 4720.
APPM 6950 - Master's Thesis
Primary Instructor - Spring 2020 / Fall 2020
May be repeated up to 6 total credit hours.
APPM 7400 - Topics in Applied Mathematics
Primary Instructor - Spring 2020 / Spring 2021 / Fall 2021 / Spring 2022
Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
APPM 8000 - Colloquium in Applied Mathematics
Primary Instructor - Spring 2023
Introduces graduate students to the major research foci of the Department of Applied Mathematics.
APPM 8700 - Mathematical Geosciences Seminar
Primary Instructor - Fall 2023 / Fall 2024
Research-level seminar that explores applications of mathematical and statistical modeling, analysis, and computation in the geosciences. Provides a vehicle for the development, presentation, and dissemination of new topics in the mathematical geosciences. Formerly offered as a special topics course.
MATH 5600 - Numerical Analysis 1
Primary Instructor - Fall 2018
Solution of nonlinear algebraic equations, interpolation, approximation theory and numerical integration. Department enforced prerequisites: MATH 2130 or MATH 2135 or APPM 3310 and experience with a scientific programming language. Instructor consent required for undergraduates.
... more

Background

education and training

• Ph.D., University of Colorado Boulder 2011
• B.S., College of William and Mary 2005

awards and honors

• Nonlinear Geophysics Section/Donald L. Turcotte Award, conferred by American Geophysical Union, 2011

International Activities

geographic focus

• Australia  Country
• Canada  Country
• France  Country
• United Kingdom  Country

Other Profiles

ORCID iD

• http://orcid.org/0000-0002-4678-7203

Google Scholar

• https://scholar.google.com/citations?hl=en&user=Fd7O5tgAAAAJ

Github

• https://github.com/iangrooms