Sam Stechmann

Professor, Dept of Mathematics
Affiliated Faculty, Dept of Atmospheric & Oceanic Sciences
Affiliated Faculty, Center for Climatic Research

Applied and Computational Mathematics
University of Wisconsin–Madison

contact   research   publications   cv   software   teaching

My research is in applied and computational math and atmospheric science:
  • Scientific machine learning, data science, stochastic processes, multiscale models, PDEs, numerical methods
  • Radiative transfer, tropical weather and climate, clouds and convection, Madden-Julian Oscillation

Seminar on Mathematics and Atmospheric Physics: see the seminar website

Full publication list: see publications

Select research highlights:

Scientific machine learning, element-by-element
  • Substantial speed-up via machine learning, in comparison to traditional numerical PDE methods
  • Operator learning within each element of finite element-type methods (e.g., discontinuous Galerkin)
  • Retains desirable features of finite element-type methods (e.g., applicability to complex domain geometry, etc.)
  • Du S, Stechmann S N, 2023: Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer. Submitted. [ arxiv ]
Inverse problems: adaptive-mesh inversion
  • Goal-oriented version of hp-adaptivity for reducing memory requirements
  • Recovers scattering coefficient even in some cases where other methods fail
  • Du S, Stechmann S N, 2023: Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion. Inverse Problems 39, 115002. (27 pages) [ pdf , journal ]
3D radiative transfer: fast, low-memory numerical methods
  • 3D radiative transfer is infeasible in most weather and climate simulations
  • Susbtantial memory reduction is demonstrated here
  • Toward an ambitious goal: to have cost of 3D radiative transfer that is comparable to one time step of fluid dynamics solver
  • Du S, Stechmann S N, 2023: Fast, low-memory numerical methods for radiative transfer via hp-adaptive mesh refinement. J. Comput. Phys. 480, 112021. (21 pages) [ pdf , journal ]
Conservation law for potential vorticity, with clouds
  • Extends the century-old conservation laws of Ertel's potential vorticity (PV) and Kelvin's circulation theorem to include salinity or clouds
  • Kooloth P, Smith L M, Stechmann S N, 2022: Conservation laws for potential vorticity in a salty ocean or cloudy atmosphere. Geophys. Res. Lett. 49, e2022GL100009. (8 pages) [ pdf , supporting information , journal ]
Energy of a cloudy atmosphere
  • Marsico D H, Smith L M, Stechmann S N, 2019: Energy decompositions for moist Boussinesq and anelastic equations with phase changes. J. Atmos. Sci. 76, 3569-3587. [ pdf , supplementary materials , journal ]
Expanding grid (x-grid) for efficient cloud simulations
  • Vertical mesh refinement for deep and shallow convection together
  • Marsico D H, Stechmann S N, 2020: Expanding grids for efficient cloud dynamics simulations across scales. Math. Clim. Weather Forecast. 6, 38-49. [ pdf , journal ]
Balanced and unbalanced moisture
  • Wetzel A N, Smith L M, Stechmann S N, Martin J E, Zhang Y, 2020: Potential vorticity and balanced and unbalanced moisture. J. Atmos. Sci. 77, 1913-1931. [ pdf , journal ]
Extreme precipitation events and climate change
  • Neelin J D, Sahany S, Stechmann S N, Bernstein D N, 2017: Global warming precipitation accumulation increases above the current-climate cutoff scale. Proc. Natl. Acad. Sci. 114, 1258-1263. [ pdf , supporting information , journal ]
Quasi-geostrophic equations with precipitation and phase changes

  • Smith L M, Stechmann S N, 2017: Precipitating quasigeostrophic equations and potential vorticity inversion with phase changes. J. Atmos. Sci. 74, 3285-3303. [ pdf , journal ]

Stochastic PDEs for tropical rainfall and waves
  • Stechmann S N, Hottovy S, 2017: Unified spectrum of tropical rainfall and waves in a simple stochastic model. Geophys. Res. Lett. 44, 10,713-10,724. [ pdf , supporting information , journal ]
Stochastic PDEs for water vapor, clouds, and rainfall

  • Hottovy S, Stechmann S N, 2015: A spatiotemporal stochastic model for tropical precipitation and water vapor dynamics. J. Atmos. Sci. 72, 4721-4738. [ pdf , journal ]

  • Stechmann S N, Hottovy S, 2016: Cloud regimes as phase transitions. Geophys. Res. Lett. 43, 6579-6587. [ pdf , supporting information , journal ]

Walker circulation and a singular limit
  • Stechmann S N, Ogrosky H R, 2014: The Walker circulation, diabatic heating, and outgoing longwave radiation. Geophys. Res. Lett. 41, 9097-9105. [ pdf, auxiliary material, journal ]

2013 Cover Article 		Climate science in the tropics: waves, vortices, and PDEs
  • Khouider B, Majda A J, Stechmann S N, 2013: Climate science in the tropics: waves, vortices, and PDEs. Nonlinearity 26, R1-R68. Invited review. [ pdf , journal ]
The Madden-Julian Oscillation (MJO): a nonlinear oscillator model

  • Thual S, Majda A J, Stechmann S N, 2014: A stochastic skeleton model for the MJO. J. Atmos. Sci. 71, 697-715. [ pdf , journal ]

  • Majda A J, Stechmann S N, 2011: Multiscale theories for the MJO. Intraseasonal Variability in the Atmosphere-Ocean Climate System, 2nd edition. Lau W K M, Waliser D E, editors. [ pdf, book ]

  • Majda A J, Stechmann S N, 2011: Nonlinear dynamics and regional variations in the MJO skeleton. J. Atmos. Sci., 68, 3053-3071. [ pdf , journal ]

  • Majda A J, Stechmann S N, 2009: The skeleton of tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. 106, 8417-8422. [ pdf, journal ]

Stochastic models for tropical precipitation and extreme events

  • Stechmann S N, Neelin J D, 2014: First-passage-time prototypes for precipitation statistics. J. Atmos. Sci. 71, 3269-3291. [ pdf , journal ]

  • Stechmann S N, Neelin J D, 2011: A stochastic model for the transition to strong convection. J. Atmos. Sci., 68, 2955-2970. [ pdf , journal ]

Multiscale models for cumulus cloud dynamics

  • Stechmann S N, 2014: Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation. J. Comput. Phys. 271, 99-117. [ pdf , journal ]

  • Stechmann S N, Stevens B, 2010: Multiscale models for cumulus cloud dynamics. J. Atmos. Sci., 67, 3269-3285. [ pdf, journal ]

Minimal models for precipitating turbulent convection
  • Hernandez-Duenas G, Majda A J, Smith L M, Stechmann S N, 2013: Minimal models for precipitating turbulent convection. J. Fluid Mech. 717, 576-611. [ pdf , journal ]