November 3 IDR To do: What we have, what we’d like to do Modeling Mathematical/numerical approaches What we need inside the codes Tasks

What we promised to do Volcanic eruption column, plume advection and dispersion Where is the cloud likely to be # hours from now? Quantifiable likelihoods and confidence intervals/error metrics

Sources of uncertainty Volcanological: – Column height – Size distribution within column Translates into – Vent radius – Eruption rate/mass flux – Particle size distribution

Sources of uncertainty Meteorological: – Local windfield – Time evolution of windfield

Sources of uncertainty Modeling/numerical: – What is the effective equation of XXX code (numerical diffusion) – How does code account for local windfield variability? – How accurate is XXXcode in horizontal/vertical directions?

Column modeling Use a vent model (e.g. BENT) to replace column uncertainty with physical model and epistemicly uncertain parameters (radius, flux) Reasonable distributions of parameters to characterize vent and exflux

Windfield modeling Reconstructed windfields roughly known (known at a few points), but local uncertainty large. Predictive modeling must characterize all the uncertainty in weather prediction in a few parameters

Under the hood Inside XXXcode (WRF?) – Distributions for spatial fluctuations, temporal changes? – How to characterize the accuracy of the relatively sparse (compared to computational grid) windfield samples? – How is advection, diffusion computed?

Numerics Characterize all sources of uncertainty Remove uncertainty where possible, replace with physics (and physical model uncertainty) where possible Distributions for uncertain parameters Simulations for aleatoric uncertainty Reconstruct output distributions

Numerics Several approaches – Basic advection-diffusion equation, uncertain speed, boundary conditions. What is known? What is computed? – PCQ/gaussian sum marriage – Alternatives?

To do – short term Advection-diffusion solver, analysis, simulation WRF(?) details, pull source code apart Column-WRF(?) marriage and characterize all the uncertain inputs required

AGU plans ?