**K**

**E**

**Y**

**N**

**O**

**T**

**E**

**S**

**P**

**E**

**A**

**K**

**E**

**R**

**Combining Observations with Models: Penalized Likelihood
and Related Methods in Numerical Weather Prediction**

**Grace Wahba**

University of
Wisconsin, Madison

**ABSTRACT**

We will look at variational data assimilation as practiced by atmospheric scientists, with the eyes of a statistician. Recent operational numerical weather prediction models operate on what might be considered a very grand penalized likelihood point of view: A variational problem is set up and solved to obtain the evolving state of the atmosphere, given heterogeneous observations in time and space, a numerical model embodying the nonlinear equations of motion of the atmosphere, and various physical constraints and prior physical and historical information. The idea is to obtain a sequence of state vectors which are "close" to the observations, close to a trajectory satisfying the equations of motion, and simultaneously respects the other information available. The state vector may be as big as 10

^{7}, and the observation vector 10^{5}or 10^{6}, leading to some interesting implementation questions. Interesting nonstandard statistical issues abound.

BIOGRAPHYGrace Wahba is the John Bascom Professor of Statistics and Professor of Biostatistics at the University of Wisconsin, Madison. She is a Fellow of the Institute of Mathematical Statistics, The American Statistical Association, and the American Association for the Advancement of Science, and was recently elected to the American Academy of Arts and Sciences. She received the first Emanuel and Carol Parzen Prize for Statistical Innovation, the COPSS Elizabeth Scott Award, and the International Meetings on Statistical Climatology Achievement Award. Her research involves multivariate function estimation and model building with heterogeneous sources of information with applications in numerical weather prediction, climate, biostatistical model building and risk factor estimation, and supervised machine learning. She is most proud of her many and talented former students.