# Applications of Adjoint Based Assimilation

## Document Type

Presentation Abstract

## Presentation Date

11-2-2015

## Abstract

A numerical model is a tool for reasoning about situations where direct observations or experiments are impossible or very expensive to conduct. For example, it would be interesting to know the impact of warmer oceans on climate, but expensive to heat and cool them. In this approach to doing science, the credibility of the numerical models can be called into question because they fail to reproduce even the most obvious features of observations. This is in spite of their fidelity to the physics of the situation. To address such criticism, many models now assimilate large observational data sets to achieve an initial state that is consistent with observation. The assimilation problem is formulated as an optimization problem where the mismatch between observation and model result, or objective function, is minimized. Optimization is done in the typical way, by determining gradients or search directions of the objective function with respect to unknown parameters. At this point, a difficulty arises: the number of parameters is very large, and determining the gradients in a naive way is computationally prohibitive. Specifically, a derivative of each degree of freedom must be computed with respect to each unknown parameter. Nowadays, the number of degrees of freedom is in the millions and the number of parameters in the hundreds of thousands. The adjoint equation is the solution to this problem. The solution to a single linear system which is the size of the number of degrees of freedom provides search directions. In this talk I will discuss a numerical model for ice sheet modeling and the solution to adjoint equations to drive data assimilation. I will show several examples where adjoint based assimilation has been useful, and outline our next task, which will be to explore time dependent problems. A critical component of data collection, low cost, low power custom data loggers, will also be discussed.

## Recommended Citation

Johnson, Jesse, "Applications of Adjoint Based Assimilation" (2015). *Colloquia of the Department of Mathematical Sciences*. 486.

https://scholarworks.umt.edu/mathcolloquia/486

## Additional Details

Monday, November 2, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109