land-surface\, a re characterised by high dimensions\, nonlinearity \, and complex relations between system variables.

While Gaussian-based approximations such as Ensemble Kalman Filters and Smoothers and global v ariational

methods have been used quite extens ively in this field\, numerous problems ask for me thods that can handle

strong nonlinearities. I n this talk I will discuss recent progress using p article filters.

Three main areas of acti ve research in particle filtering can be distingui shed\, exploring localisation\,

exploring pro posal densities\, and exploring (optimal) transpor tation (and mergers of these ideas are on the

horizon). In localisation the idea is to split the high-dimensional problem in several smaller probl ems

that then need to be stitched together in a smart way. The first approximate applications o f this methodology

have just made it to weathe r prediction\, showing the exponentially fast deve lopments here. However\,

the &lsquo\;stitching &rsquo\; problem remains outstanding. The proposal density methodology discussed next might be

f ruitful to incorporate here.

In the propo sal density approach one tries to evolve states in state space such that they obtain very similar we ights

in the particle filter. Challenges are\, of course\, the huge dimensions\, but these also provide opportunities via

the existence of typ ical sets\, which lead to preferred parts of state space for the particles. Recent attempts to explo it

typical sets will be discussed.

Fi nally\, we will discuss recent progress in (optima l) transportation. The idea here is that a set of prior particles

has to be transformed to a set of posterior particles. This is an old problem in optimal transportation. However\,

the optimal ity condition poses unnecessary constraints\, and by relaxing the optimality constraint we are able to

formulate new efficient methods. Specifica lly\, by iteratively minimising the relative entro py between the probability

density of the pri or particles and the posterior a sequence of trans formations emerges for each particle that seems

to be tractable even for very high dimensional s paces. A new idea is to explore localisation to ob tain a more

accurate description of the target posterior\, but without the stitching issues ment ioned above.

So far\, model reduction tec hniques\, emulation\, and machine learning techniq ues have been unsuccessful for

these high-dime nsional state estimation problems\, but I&rsquo\;m keen to further understand the possibilities and limitations. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR