I am a PhD student in applied mathematics, under the supervision of Prof. Boualem Khouider. My work concerns tropical convection modeling, i.e. using fluid dynamics to predict the lifecycles of clouds near the equator. Tropical convection models are an important puzzle piece in mankind's quest to accurately forecast the weather and climate - not only for such tropical phenomena as monsoons and hurricanes, but indeed for weather and climate over the entire globe (consider the devastating impacts of atmosperic river-induced floods throughout Vancouver Island, for example).
A plain-language summary of my topic is provided in the following section. For the experts: I am developing a scale-aware mass-flux convection model which marries the stochastic multicloud model of Khouider and others, with a prognostic relaxation of the quasi-equilibrium assumption. Early work on this topic was published in JAMES in 2019 (see publications below).
My academic interests encompass mathematics, statistics, computer science (particularly machine learning and statistical learning theory), and atmospheric physics. There is a special place in my heart for fields of math whose proofs begin with such statements as "let ε>0," or "let U be open."
My extracurricular interests currently range from chess to kickboxing, poetry to salsa dancing.
Here is one of the salsa routines I have choreographed and performed; and
here is another.
Summary of research
I am developing a cloud model which handles so-called "grey-scale" resolutions. As an analogy, consider that one person laughing will sound qualitatively different from an entire crowd laughing. But what will three, or four, or even ten, people laughing sound like - will that sound bear more in common with the laughter of an individual, or of a group? What number of people demarcates this qualitative transition? How many grains of sand does it take to make a
pile of sand?
A similar story holds for cloud models. On the one hand, operating at very high resolutions, cloud-resolving models distinguish each individual cloud clearly like a single laugh. On the other hand, so-called "quasi-equilibrium mass-flux models" operate at very coarse resolutions and distinguish only ensembles of clouds operating in tandem like a crowd of people laughing. There is a "sour-spot" at intermediate resolutions where neither the high- nor low-resolution models correctly capture the cloudy behavior. The model I am developing seeks to address this issue.
Education
- PhD in Applied Mathematics at University of Victoria, 2021-Present,
- Honours in Mathematics and Computer Science with Statistics minor at University of Victoria, 2015-2021,
- Dean's List, Recipient of Governor General's Silver Medal (for highest graduating GPA among UVic students).
Publications
- E. Leclerc, G. MacGillivray and J. Warren, "Switching (m,n)-mixed graphs with respect to Abelian groups", Manuscript submitted to Theoretical Computer Science, 2021, arxiv link
- B. Khouider and E. Leclerc, "Toward a stochastic relaxation for the quasi-equilibrium theory of cumulus parameterization: Multicloud instability, multiple equilibria, and chaotic dynamics", Journal of Advances in Modeling Earth Systems, vol. 11, no. 8, pp. 2474-2502, 2019, paper
Posters
- AGU Fall Meeting 2023,
- Canadian Meteorological and Oceanographic Society (CMOS) 2023,
- CIRM 2575 Avancés mathématiques dans les flux géophysiques,
- AGU Fall Meeting 2021,
- PIMS Scientific Grand Challenges and New Perspectives in Applied Mathematics: Ocean,
Atmosphere and Climate Sciences,
- UVic JCURA Fair 2019,
- UVic Honours Fest 2019 (Top Presenter in Mathematics and Statistics).
Oral presentations
- "Interdisciplinary Collaborations in Mathematics", panelist, at UVic Graduate Seminar, 2024,
- "Toward a Stochastic Relaxation for the Quasi-Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria, and Chaotic Dynamics" at CMOS Conference, 2021,
- "A Whirlwind of Mathematics" at UVic Students in Undergraduate Mathematics Seminar, 2020 (slides; this was an informal, gentle introduction to fluid dynamics and vorticity for a general undergraduate audience),
- "Switching Homomorphisms on Mixed Graphs" at UVic Discrete Math Seminar, 2019,
- "Deriving the Navier-Stokes Equations" at UVic Students in Undergraduate Mathematics Seminars, 2019 (2-part talk),
- "A Stochastic Cloud Parametrization" at UVic Undergraduate Mathematics Conference, 2018,
- "Minkowski's Theorem" at CMS Math Camp, 2018 (this was an interactive talk on the geometry of numbers, for engaged high school students).
TA Appointments, abbreviated
- Math & Stats Assistance Centre tutor (6 semesters)
- Math & Stats Assistance Centre head tutor (1 semester)
- Marker: Math 211 (Matrix Algebra 1), Math 101 (Calculus II), Math 122 (Logic and Foundations), Math 492 (Waves in the Atmosphere and Ocean)
- Tutorial instructor: Math 100 (1 semester), Math 101 (3 semesters), Math 110 (2 semesters), Math 200 (4 semesters)
Conferences
- AGU Fall Meeting 2023,
- Canadian Meteorological and Oceanographic Society (CMOS) Congress, 2023
- MSRI 991 - Integral Equations, 2022
- CIRM 2575 Avancés mathématiques dans les flux géophysiques, 2022
- Canadian Meteorological and Oceanographic Society Conference 2021,
- AGU Fall Meeting 2021,
- Workshop on Spatial Organisation of Convection, Clouds and Precipitation, 2021,
- PIMS Scientific Grand Challenges and New Perspectives in Applied Mathematics: Ocean, Atmosphere and Climate Sciences, 2019,
- Canadian Undergraduate Math Conference, 2018,
- UVic Undergraduate Math Conference, 2017, 2018.