Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Resolution and discrimination - two sides of the same coin

The notions of resolution and discrimination of probability forecasts are revisited. It is argued that the common concept underlying both resolution and discrimination is the dependence (in the sense of probability theory) of forecasts and observations. More specifically, a forecast has no resolution if and only if it has no discrimination if and only if forecast and observation are stochastically independent. A statistical tests for independence is thus also a test for no resolution and, at the same time, for no discrimination. The resolution term in the decomposition of the logarithmic scoring rule, and the area under the Receiver Operating Characteristic will be investigated in this light.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Single-particle tracking uncovers dynamics of glutamate-induced retrograde transport of NF-κB p65 in living neurons

Retrograde transport of NF-κB from the synapse to the nucleus in neurons is mediated by the dynein/dynactin motor complex and can be triggered by synaptic activation. The calibre of axons is highly variable ranging down to 100 nm, aggravating the investigation of transport processes in neurites of living neurons using conventional light microscopy. In this study we quantified for the first time the transport of the NF-κB subunit p65 using high-density single-particle tracking in combination with photoactivatable fluorescent proteins in living mouse hippocampal neurons. We detected an increase of the mean diffusion coefficient (Dmean) in neurites from 0.12 ± 0.05 µm2/s to 0.61 ± 0.03 µm2/s after stimulation with glutamate. We further observed that the relative amount of retrogradely transported p65 molecules is increased after stimulation. Glutamate treatment resulted in an increase of the mean retrograde velocity from 10.9 ± 1.9 to 15 ± 4.9 µm/s, whereas a velocity increase from 9 ± 1.3 to 14 ± 3 µm/s was observed for anterogradely transported p65. This study demonstrates for the first time that glutamate stimulation leads to an increased mobility of single NF-κB p65 molecules in neurites of living hippocampal neurons.

Coupling an aerosol box model with one-dimensional flow: a tool for understanding observations of new particle formation events

Field observations of new particle formation and the subsequent particle growth are typically only possible at a fixed measurement location, and hence do not follow the temporal evolution of an air parcel in a Lagrangian sense. Standard analysis for determining formation and growth rates requires that the time-dependent formation rate and growth rate of the particles are spatially invariant; air parcel advection means that the observed temporal evolution of the particle size distribution at a fixed measurement location may not represent the true evolution if there are spatial variations in the formation and growth rates. Here we present a zero-dimensional aerosol box model coupled with one-dimensional atmospheric flow to describe the impact of advection on the evolution of simulated new particle formation events. Wind speed, particle formation rates and growth rates are input parameters that can vary as a function of time and location, using wind speed to connect location to time. The output simulates measurements at a fixed location; formation and growth rates of the particle mode can then be calculated from the simulated observations at a stationary point for different scenarios and be compared with the ‘true’ input parameters. Hence, we can investigate how spatial variations in the formation and growth rates of new particles would appear in observations of particle number size distributions at a fixed measurement site. We show that the particle size distribution and growth rate at a fixed location is dependent on the formation and growth parameters upwind, even if local conditions do not vary. We also show that different input parameters used may result in very similar simulated measurements. Erroneous interpretation of observations in terms of particle formation and growth rates, and the time span and areal extent of new particle formation, is possible if the spatial effects are not accounted for.