About

Ian Grooms is an Associate Professor in the Department of Applied Mathematics at the University of Colorado Boulder. He received his Bachelor of Science in Mathematics from the College of William & Mary in 2005 and completed his PhD in Applied Mathematics at CU-Boulder in 2011. Following his doctoral studies, he was a postdoctoral researcher at the Courant Institute of Mathematical Sciences at NYU from 2011 to 2015. He joined the faculty of Applied Mathematics at CU-Boulder in the fall of 2015 and has been tenured since 2022. His research interests encompass ocean model development, the development of new data assimilation methods, and the theory of geophysical fluid dynamics and turbulence. Grooms is a lifetime member of both the American Geophysical Union (AGU) and the Society for Industrial and Applied Mathematics (SIAM). He serves as a co-chair of the Community Earth System Model (CESM) Ocean Model Working Group, is a member of the CLIVAR Ocean Model Development Panel, and is an editor for the Journal of Advances in Modeling Earth Systems. In addition, he is involved in leadership roles within the AGU, serving as president-elect for the 2025-2026 term and as president for the 2027-2028 term of the Nonlinear Geophysics section.

Research topics

• Artificial Intelligence
• Physics
• Geology
• Computer Science
• Meteorology
• Atmospheric sciences
• Algorithm
• Mechanics
• Geophysics
• Climatology
• Computer vision

Selected publications

• Demographics of Mesoscale Eddies in an Eddy-Permitting Ocean Model and Reanalysis

  arXiv (Cornell University) · 2026-04-24

  preprintOpen access

  Ocean mesoscale eddies can be thought of as the "weather" of the ocean and strongly influence the ocean's physics, chemistry, and biology; they influence other components of the Earth system via air-sea and sea-ice interactions, and are crucial drivers of marine heat waves. Thus, proper modeling of eddies in both historical and future climates is crucial to accurately capturing the Earth system. Climate projections using global coupled models with eddying ocean components are only recently starting to be more widely used. Despite their critical role in understanding and forecasting climate characteristics, these so-called eddy-permitting models have not been explored to verify that resolved eddies are realistic, and thus any downstream scientific testing of hypotheses in biogeochemistry, ocean physics or other associated Earth systems impacted by eddies hinge on this critical assumption. This paper compares observed eddies with lifetimes longer than 6 weeks present in $1/4^\circ$ satellite altimetry data with observed eddies in $1/4^\circ$ reanalysis data and ocean model output. When compared to eddies observed in satellite altimetry data, eddies in reanalysis data and ocean model output are missing almost 30% of the number of eddy trajectories. In addition to missing eddy trajectories, the characteristics of eddies in reanalysis data and ocean model output differ from eddies observed in satellite altimetry data. At a high level, eddies in reanalysis data and ocean model output tend to live longer, are larger, and are weaker than eddies in observed altimetry data. This paper presents a variety of statistics describing these differences both spatially and in global aggregate.

  PublisherDOI

• Stochastic GM+E: An energetically-informed stochastic backscatter scheme for ocean models

  2026-03-14

  articleOpen access1st authorCorresponding

  Global ocean models at resolutions that do not resolve mesoscale eddies lack variability, not just on scales that they cannot represent because they are below the grid scale, but also on resolvable scales. This research develops a backscatter parameterizations that increases variability on the resolved scales of a non-eddying model. The parameterization acts on the model's momentum equations, and sets the rate of backscatter, viz. the rate at which energy is injected to the resolved scales, proportional to the rate at which the Gent-McWilliams (GM) parameterization removes energy from the resolved scales. This models the physical process whereby mesoscales convert large-scale potential energy to kinetic energy, and then transfer that kinetic energy towards larger scales. These parameterization is implemented in the MOM6 ocean model, and results are presented on its impact in simulations at nominal 2/3-degree resolution. Stochastic GM+E acts primarily in the Southern Ocean, the North Atlantic Current, and the Kuroshio Extension, where it impacts SST variability and southern-hemisphere sea ice extent.

  PublisherDOI

• Mesoscale Eddy Verification in an Eddy-Permitting Ocean Models and Reanalysis Data

  2026-03-14

  articleOpen accessCorresponding

  Ocean mesoscale eddies are ubiquitous features of the open ocean and strongly influence the ocean’s physics, chemistry, and biology. Mesoscale eddies play a critical role in the climate system and regulating the exchange of heat and carbon with the atmosphere. They also play a significant role in the redistribution of heat, salt, carbon, and nutrients around the ocean. Thus, proper modeling of eddies in both historical and future climates is crucial to accurately capturing the Earth system. Climate projections using global coupled models with eddy ocean components have recently started to become more widely used. Despite their critical role in understanding and forecasting climate characteristics, these so-called eddy-permitting models have not been rigorously explored to verify that resolved eddies are realistic, and thus any downstream scientific testing of hypotheses in biogeochemistry, ocean physics or other associated Earth systems impacted by eddies hinge on this critical assumption. This presentation compares the characteristics and behavior of observed eddies in ¼ degree satellite altimetry data with eddies detected in ¼ degree reanalysis data and ocean model output. When compared to eddies observed in satellite altimetry data, eddies in reanalysis data and ocean model output are missing almost 30% of the number of eddy trajectories. Further, many characteristics of eddies in reanalysis data and ocean model output differ from eddies observed in altimetry data. At a high level, eddies in reanalysis data and ocean model output generally live longer, are larger, and are weaker than observed eddies in satellite altimetry data. These comparisons are made both locally and in the global aggregate to assess the differences in both the global distribution of eddy characteristics as well as differences in the regional eddy behavior.

  PublisherDOI

• Balancing Backscatter and Diffusion in a 1/4° Forced Global Ocean Model

  Journal of Advances in Modeling Earth Systems · 2026-03-01

  articleOpen accessSenior author

  Abstract Mesoscale ocean eddies in 1/4 global ocean models lie near the grid scale and are overdamped by viscosity, leading to reduced eddy kinetic energy, weak sea surface height variability, and mean‐state biases. Backscatter has been proposed to remedy this problem by re‐injecting dissipated energy, but its diabatic consequences are poorly characterized. We first show that using backscatter alone in a 1/4 forced CESM2‐MOM6 ocean–sea ice model produces unrealistically large southward heat transport. To address this problem, we define a non‐dimensional ratio (deformation radius over grid spacing) and adopt a nearly step‐like resolution function with a threshold of . Isopycnal height and tracer diffusion act where and backscatter acts where . We compare two backscatter schemes that differ mainly in where they apply backscatter. One applies backscatter broadly in the Southern Ocean, whereas the other confines it near western boundary currents. Both schemes energize the model by 20%–25%. When backscatter is applied in the Southern Ocean, it energizes and barotropizes the flow but also increases southward heat transport, warms surface temperatures, shifts deep winter mixed layers poleward, and reduces Antarctic sea ice. In contrast, limiting backscatter to western boundary currents strongly enhances eddy kinetic energy there while keeping Southern Ocean heat transport, sea surface temperatures, mixed‐layer depth, and sea ice much closer to the reference run. These results show strong sensitivity to backscatter placement and, in this configuration, favor confining it to western boundary currents.

  PublisherDOI

• Demographics of Mesoscale Eddies in an Eddy-Permitting Ocean Model and Reanalysis

  ArXiv.org · 2026-04-24

  articleOpen access

  Ocean mesoscale eddies can be thought of as the "weather" of the ocean and strongly influence the ocean's physics, chemistry, and biology; they influence other components of the Earth system via air-sea and sea-ice interactions, and are crucial drivers of marine heat waves. Thus, proper modeling of eddies in both historical and future climates is crucial to accurately capturing the Earth system. Climate projections using global coupled models with eddying ocean components are only recently starting to be more widely used. Despite their critical role in understanding and forecasting climate characteristics, these so-called eddy-permitting models have not been explored to verify that resolved eddies are realistic, and thus any downstream scientific testing of hypotheses in biogeochemistry, ocean physics or other associated Earth systems impacted by eddies hinge on this critical assumption. This paper compares observed eddies with lifetimes longer than 6 weeks present in $1/4^\circ$ satellite altimetry data with observed eddies in $1/4^\circ$ reanalysis data and ocean model output. When compared to eddies observed in satellite altimetry data, eddies in reanalysis data and ocean model output are missing almost 30% of the number of eddy trajectories. In addition to missing eddy trajectories, the characteristics of eddies in reanalysis data and ocean model output differ from eddies observed in satellite altimetry data. At a high level, eddies in reanalysis data and ocean model output tend to live longer, are larger, and are weaker than eddies in observed altimetry data. This paper presents a variety of statistics describing these differences both spatially and in global aggregate.

  PublisherOA PDF

• Asymptotic approximations for convection onset with Ekman pumping at low wavenumbers

  arXiv (Cornell University) · 2025-01-02

  preprintOpen access

  Ekman pumping is a phenomenon induced by no-slip boundary conditions in rotating fluids. In the context of Rayleigh-Bénard convection, Ekman pumping causes a significant change in the linear stability of the system compared to when it is not present (that is, stress-free). Motivated by numerical solutions to the marginal stability problem of the incompressible Navier-Stokes (iNSE) system, we seek analytical asymptotic solutions which describe the departure of the no-slip solution from the stress-free. The substitution of normal modes into a reduced asymptotic model yields a linear system for which we explore analytical solutions for various scalings of wavenumber. We find very good agreement between the analytical asymptotic solutions and the numerical solutions to the iNSE linear stability problem with no-slip boundary conditions.

  PublisherOA PDFDOI

• Balancing Backscatter and Diffusion in a $1/4^\circ$ Forced Global Ocean Model

  2025-09-04 · 1 citations

  articleOpen accessSenior author

  Mesoscale ocean eddies in \nicefrac{1}{4}$^\circ$ global ocean models lie near the grid scale and so are overdamped by viscous closures, resulting in excessive damping of eddy kinetic energy, underestimation of sea surface height variability, and biases such as the North Atlantic sea surface temperature dipole. Backscatter, which is implemented here through a negative Laplacian viscosity, remedies these problems by re-injecting a portion of the dissipated energy. We compare two backscatter formulations in CESM2-MOM6: a prognostic eddy-energy backscatter closure and the instantaneous Leith+E closure. Either scheme, used alone, consistently produces excessive southward heat transport and triggers recurring Weddell Sea polynyas. Guided by idealized models, we introduce a resolution function mask that applies isopycnal height and tracer diffusion where the ratio of deformation radius to grid spacing is below one-half and applies backscatter elsewhere. This hybrid approach arrests polynya formation and increases kinetic energy by 20–25\%. The hybrid prognostic eddy-energy backscatter scheme energizes and barotropizes the Southern Ocean at the cost of increasing heat transport and reducing sea ice. In contrast, the hybrid Leith+E scheme mainly intensifies western boundary currents with small impacts on the Southern Ocean. Our results emphasize the sensitivity of backscatter to where it is applied and the need to understand and quantify the diabatic effects of backscatter in global ocean models.

  PublisherOA PDFDOI

• Ekman-driven buoyancy flux in quasi-geostrophic flow

  Journal of Fluid Mechanics · 2025-10-09

  articleSenior author

  In this investigation, the effect of Ekman pumping on a quasi-geostrophic (QG) system is explored via the vertical buoyancy flux. The vertical buoyancy flux is the quantity in QG flows that is responsible for the adiabatic transfer between kinetic energy (KE) and available potential energy (APE), as well as the slow-time evolution of the mean buoyancy. Ekman pumping (or suction) is a phenomenon that arises through conservation of mass at no-slip boundaries of rotating fluid systems. Three-dimensional QG numerical simulations are run with and without Ekman pumping at the bottom boundary, as well as with and without a realistic stratification profile. Through theory and numerical experiment, it is shown that Ekman pumping drives a conversion of energy from APE to KE at small scales, and from KE to APE at large scales, even in the absence of a mean isopycnal slope. It is also shown that Ekman pumping affects the mean buoyancy by slightly weakening the stratification near the bottom boundary.

  PublisherDOI

• Data Assimilation With An Integral-Form Ensemble Square-Root Filter

  arXiv (Cornell University) · 2025-03-01

  preprintOpen accessSenior author

  Geoscientific applications of ensemble Kalman filters face several computational challenges arising from the high dimensionality of the forecast covariance matrix, particularly when this matrix incorporates localization. For square-root filters, updating the perturbations of the ensemble members from their mean is an especially challenging step, one which generally requires approximations that introduce a trade-off between accuracy and computational cost. This paper describes an ensemble square-root filter which achieves a favorable trade-off between these factors by discretizing an integral representation of the Kalman filter update equations, and in doing so, avoids a direct evaluation of the matrix square-root in the perturbation update stage. This algorithm, which we call InFo-ESRF ("Integral-Form Ensemble Square-Root Filter"), is parallelizable and uses a preconditioned Krylov method to update perturbations to a high degree of accuracy. Through numerical experiments with both a Gaussian forecast model and a multi-layer Lorenz-type system, we demonstrate that InFo-ESRF is competitive or superior to several existing localized square-root filters in terms of accuracy and cost.

  PublisherDOI

• Two‐step ensemble data assimilation on the simplex: Application to sea‐ice concentration

  Quarterly Journal of the Royal Meteorological Society · 2025-11-27

  articleSenior author

  Abstract Ensemble‐based data assimilation is widely used in atmospheric and oceanic sciences to improve modeled state estimates by incorporating observations. Ensemble Kalman filters are a class of data‐assimilation methods that assume the joint distribution in observation‐state space is Gaussian. Two‐step ensemble data assimilation is an alternative framework that relaxes Gaussianity assumptions. It works by first making a scalar update in observation space and then updating the state‐space variables accordingly. This article develops a non‐Gaussian parametric approach to the second step, the state‐space update, that is designed specifically for variables constrained to the simplex. The method assumes the joint observation‐state space prior is a mixed Dirichlet and constructs an analysis ensemble using transport methods. Results from the assimilation of sea‐ice concentration into a single‐column sea‐ice model (Icepack) show that, for ensemble sizes and , the new method outperforms existing approaches.

  PublisherDOI

Recent grants

• Improving Particle Filter Performance in Spatially-Extended Problems Using Generalized Random Field Likelihoods

  NSF · $220k · 2018–2021

• A Stochastic Approach to Representing Unresolved Mesoscales in Ocean Circulation Models

  NSF · $578k · 2017–2022

• Methods for Nonlinear, Non-Gaussian, and Data-Driven Ensemble Data Assimilation in Large-Scale Applications

  NSF · $150k · 2022–2025

• Collaborative Research: Ocean Transport and Eddy Energy

  NSF · $708k · 2019–2025

Frequent coauthors

• Niraj Agarwal

  Cooperative Institute for Research in Environmental Sciences

  40 shared

• Andrew J. Majda

  Courant Institute of Mathematical Sciences

  38 shared

• Scott Bachman

  36 shared

• Malte F. Jansen

  University of Chicago

  34 shared

• Nora Loose

  Princeton University

  31 shared

• Frank O. Bryan

  NSF National Center for Atmospheric Research

  26 shared

• Keith Julien

  University of Colorado Boulder

  21 shared

• Philip Pegion

  20 shared

Labs

• Ian Grooms's LabPI

  Not provided

Education

• B.S., Mathematics

  College of William & Mary

  2005

• Ph.D., Applied Mathematics

  CU-Boulder

  2011

Awards & honors

• Lifetime member of AGU
• Lifetime member of SIAM
• Co-chair of the Community Earth System Model (CESM) Ocean Mo…
• Member of the CLIVAR Ocean Model Development Panel
• Editor for the Journal of Advances in Modeling Earth Systems