An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

Simultaneous coupling of phototaxis and electrotaxis in Volvox algae

In nature, living creatures are affected by several stimuli simultaneously. The response of living creatures to stimuli is called taxis. In order to reveal the principles of taxis behavior in response to complex stimuli, we simultaneously applied photostimulation and electric stimulation perpendicularly to a Volvox algae solution. The probability distribution of the swimming direction showed that a large population of swimming cells moved in a direction that was the result of the composition of phototaxis and electrotaxis. More surprisingly, we uncovered the coupling of signs of taxis, i.e., coupling of phototaxis and electrotaxis induced positive electrotaxis, which did not emerge in the single stimulation experiments. We qualitatively explained the coupling of taxis based on the polarization of the swimming cells induced by the simultaneous photo- and electric stimulation.

Statistical-dynamical downscaling for wind energy potentials: evaluation and applications to decadal hindcasts and climate change projections

A statistical–dynamical downscaling (SDD) approach for the regionalization of wind energy output (Eout) over Europe with special focus on Germany is proposed. SDD uses an extended circulation weather type (CWT) analysis on global daily mean sea level pressure fields with the central point being located over Germany. Seventy-seven weather classes based on the associated CWT and the intensity of the geostrophic flow are identified. Representatives of these classes are dynamically downscaled with the regional climate model COSMO-CLM. By using weather class frequencies of different data sets, the simulated representatives are recombined to probability density functions (PDFs) of near-surface wind speed and finally to Eout of a sample wind turbine for present and future climate. This is performed for reanalysis, decadal hindcasts and long-term future projections. For evaluation purposes, results of SDD are compared to wind observations and to simulated Eout of purely dynamical downscaling (DD) methods. For the present climate, SDD is able to simulate realistic PDFs of 10-m wind speed for most stations in Germany. The resulting spatial Eout patterns are similar to DD-simulated Eout. In terms of decadal hindcasts, results of SDD are similar to DD-simulated Eout over Germany, Poland, Czech Republic, and Benelux, for which high correlations between annual Eout time series of SDD and DD are detected for selected hindcasts. Lower correlation is found for other European countries. It is demonstrated that SDD can be used to downscale the full ensemble of the Earth System Model of the Max Planck Institute (MPI-ESM) decadal prediction system. Long-term climate change projections in Special Report on Emission Scenarios of ECHAM5/MPI-OM as obtained by SDD agree well to the results of other studies using DD methods, with increasing Eout over northern Europe and a negative trend over southern Europe. Despite some biases, it is concluded that SDD is an adequate tool to assess regional wind energy changes in large model ensembles.

Computer simulations of the structure of colloidal ferrofluids

The structure of a ferrofluid under the influence of an external magnetic field is expected to become anisotropic due to the alignment of the dipoles into the direction of the external field, and subsequently to the formation of particle chains due to the attractive head to tail orientations of the ferrofluid particles. Knowledge about the structure of a colloidal ferrofluid can be inferred from scattering data via the measurement of structure factors. We have used molecular-dynamics simulations to investigate the structure of both monodispersed and polydispersed ferrofluids. The results for the isotropic structure factor for monodispersed samples are similar to previous data by Camp and Patey that were obtained using an alternative Monte Carlo simulation technique, but in a different parameter region. Here we look in addition at bidispersed samples and compute the anisotropic structure factor by projecting the q vector onto the XY and XZ planes separately, when the magnetic field was applied along the z axis. We observe that the XY- plane structure factor as well as the pair distribution functions are quite different from those obtained for the XZ plane. Further, the two- dimensional structure factor patterns are investigated for both monodispersed and bidispersed samples under different conditions. In addition, we look at the scaling exponents of structure factors. Our results should be of value to interpret scattering data on ferrofluids obtained under the influence of an external field.

Effect of uncertainty in surface mass balance--elevation feedback on projections of the future sea level contribution of the Greenland ice sheet

We apply a new parameterisation of the Greenland ice sheet (GrIS) feedback between surface mass balance (SMB: the sum of surface accumulation and surface ablation) and surface elevation in the MAR regional climate model (Edwards et al., 2014) to projections of future climate change using five ice sheet models (ISMs). The MAR (Modèle Atmosphérique Régional: Fettweis, 2007) climate projections are for 2000–2199, forced by the ECHAM5 and HadCM3 global climate models (GCMs) under the SRES A1B emissions scenario. The additional sea level contribution due to the SMB– elevation feedback averaged over five ISM projections for ECHAM5 and three for HadCM3 is 4.3% (best estimate; 95% credibility interval 1.8–6.9 %) at 2100, and 9.6% (best estimate; 95% credibility interval 3.6–16.0 %) at 2200. In all results the elevation feedback is significantly positive, amplifying the GrIS sea level contribution relative to the MAR projections in which the ice sheet topography is fixed: the lower bounds of our 95% credibility intervals (CIs) for sea level contributions are larger than the “no feedback” case for all ISMs and GCMs. Our method is novel in sea level projections because we propagate three types of modelling uncertainty – GCM and ISM structural uncertainties, and elevation feedback parameterisation uncertainty – along the causal chain, from SRES scenario to sea level, within a coherent experimental design and statistical framework. The relative contributions to uncertainty depend on the timescale of interest. At 2100, the GCM uncertainty is largest, but by 2200 both the ISM and parameterisation uncertainties are larger. We also perform a perturbed parameter ensemble with one ISM to estimate the shape of the projected sea level probability distribution; our results indicate that the probability density is slightly skewed towards higher sea level contributions.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Reconnection at the high-latitude magnetopause during northward interplanetary magnetic field conditions

The Polar spacecraft had a prolonged encounter with the high-latitude dayside magnetopause on May 29, 1996. This encounter with the magnetopause occurred when the interplanetary magnetic field was directed northward. From the three-dimensional electron and ion distribution functions measured by the Hydra instrument, it has been possible to identify nearly all of the distinct boundary layer regions associated with high-latitude reconnection. The regions that have been identified are (1) the cusp; (2) the magnetopause current layer; (3) magnetosheath field lines that have interconnected in only the Northern Hemisphere; (4) magnetosheath field lines that have interconnected in only the Southern Hemisphere; (5) magnetosheath field lines that have interconnected in both the Northern and Southern Hemispheres; (6) magnetosheath that is disconnected from the terrestrial magnetic field; and (7) high-latitude plasma sheet field lines that are participating in magnetosheath reconnection. Reconnection over this time period was occurring at high latitudes over a broad local-time extent, interconnecting the magnetosheath and lobe and/or plasma sheet field lines in both the Northern and Southern Hemispheres. Newly closed boundary layer field lines were observed as reconnection occur-red first at high latitudes in one hemisphere and then later in the other. These observations establish the location of magnetopause reconnection during these northward interplanetary magnetic field conditions as being at high latitudes, poleward of the cusp, and further reinforce the general interpretation of electron and ion phase space density signatures as indicators of magnetic reconnection and boundary layer formation.

Energy and pitch-angle dispersions of LLBL/cusp ions seen at middle altitudes: predictions by the open magnetosphere model

Numerical simulations are presented of the ion distribution functions seen by middle-altitude spacecraft in the low-latitude boundary layer (LLBL) and cusp regions when reconnection is, or has recently been, taking place at the equatorial magnetopause. From the evolution of the distribution function with time elapsed since the field line was opened, both the observed energy/observation-time and pitch-angle/energy dispersions are well reproduced. Distribution functions showing a mixture of magnetosheath and magnetospheric ions, often thought to be a signature of the LLBL, are found on newly opened field lines as a natural consequence of the magnetopause effects on the ions and their flight times. In addition, it is shown that the extent of the source region of the magnetosheath ions that are detected by a satellite is a function of the sensitivity of the ion instrument . If the instrument one-count level is high (and/or solar-wind densities are low), the cusp ion precipitation detected comes from a localised region of the mid-latitude magnetopause (around the magnetic cusp), even though the reconnection takes place at the equatorial magnetopause. However, if the instrument sensitivity is high enough, then ions injected from a large segment of the dayside magnetosphere (in the relevant hemisphere) will be detected in the cusp. Ion precipitation classed as LLBL is shown to arise from the low-latitude magnetopause, irrespective of the instrument sensitivity. Adoption of threshold flux definitions has the same effect as instrument sensitivity in artificially restricting the apparent source region.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 1. Theory

A method for estimating both the Alfvén speed and the field-aligned flow of the magnetosheath at the magnetopause reconnection site is presented. The method employs low-altitude cusp ion observations and requires the identification of a feature in the cusp ion spectra near the low-energy cutoff which will often be present for a low-latitude dayside reconnection site. The appearance of these features in data of limited temporal, energy, and pitch angle resolution is illustrated by using model calculations of cusp ion distribution functions. These are based on the theory of ion acceleration at the dayside magnetopause and allow for the effects on the spectrum of flight times of ions precipitating down newly opened field lines. In addition, the variation of the reconnection rate can be evaluated, and comparison with ground-based observations of the corresponding sequence of transient events allows the field-aligned distance from the ionosphere to the reconnection site to be estimated.

EISCAT observations of ion composition and temperature anisotropy in the high-latitude F-region

The papers by Winser et al. [(1990) J. atmos. terr. Phys.52, 501] and Häggström and Collis [(1990) J. atmos. terr. Phys.52, 519] used plasma flows and ion temperatures, as measured by the EISCAT tristatic incoherent scatter radar, to investigate changes in the ion composition of the ionospheric F-layer at high latitudes, in response to increases in the speed of plasma convection. These studies reported that the ion composition rapidly changed from mainly O+ to almost completely (>90%) molecular ions, following rapid increases in ion drift speed by >1 km s−1. These changes appeared inconsisent with theoretical considerations of the ion chemistry, which could not account for the large fractions of molecular ions inferred from the obsevations. In this paper, we discuss two causes of this discrepancy. First, we reevaluate the theoretical calculations for chemical equilibrium and show that, if we correct the derived temperatures for the effect of the molecular ions, and if we employ more realistic dependences of the reaction rates on the ion temperature, the composition changes derived for the faster convection speeds can be explained. For the Winser et al. observations with the radar beam at an aspect angle of ϕ = 54.7° to the geomagnetic field, we now compute a change to 89% molecular ions in < 2 min, in response to the 3 km s−1 drift. This is broadly consistent with the observations. But for the two cases considered by Häggström and Collis, looking along the field line (ϕ = 0°), we compute the proportion of molecular ions to be only 4 and 16% for the observed plasma drifts of 1.2 and 1.6 km s−1, respectively. These computed proportions are much smaller than those derived experimentally (70 and 90%). We attribute the differences to the effects of non-Maxwellian, anisotropic ion velocity distribution functions. We also discuss the effect of ion composition changes on the various radar observations that report anisotropies of ion temperature.

Observations of nonthermal plasmas at different aspect angles

Data are presented from the EISCAT (European Incoherent Scatter (Facility)) CP-3-E experiment which show large increases in the auroral zone convection velocities (>2 km s−1) over a wide range of latitudes. These are larger than the estimated neutral thermal speed and allow a study of the plasma in a nonthermal state over a range of observing angles. Spectra are presented which show a well-defined central peak, consistent with an ion velocity distribution function which significantly departs from a Maxwellian form. As the aspect angle decreases, the central peak becomes less obvious. Simulated spectra, derived using theoretical expressions for the O+ ion velocity distribution function based on the generalized relaxation collision model, are compared with the observations and show good first-order, qualitative agreement. It is shown that ion temperatures derived from the observations, with the assumption of a Maxwellian distribution function, are an overestimate of the true ion temperature at large aspect angles and an underestimate at low aspect angles. The theoretical distribution functions have been included in the “standard” incoherent scatter radar analysis procedure, and attempts have been made to derive realistic ionospheric parameters from nonthermal plasma observations. If the expressions for the distribution function are extended to include mixed ion composition, a significant improvement is found in fitting some of the observed spectra, and estimates of the ion composition can be made. The non-Maxwellian analysis of the data revealed that the spectral shape distortion parameter, D*, was significantly higher in this case for molecular ions than for atomic ions in a thin height slab roughly 40 km thick. This would seem unlikely if the main molecular ions present were NO+. We therefore suggest that N2+ formed a significant proportion of the molecular ions present during these observations.

The cleft ion fountain: a two-dimensional kinetic model

The transport of ionospheric ions from a source in the polar cleft ionosphere through the polar magnetosphere is investigated using a two-dimensional, kinetic, trajectory-based code. The transport model includes the effects of gravitation, longitudinal magnetic gradient force, convection electric fields, and parallel electric fields. Individual ion trajectories as well as distribution functions and resulting bulk parameters of density, parallel average energy, and parallel flux for a presumed cleft ionosphere source distribution are presented for various conditions to illustrate parametrically the dependences on source energies, convection electric field strengths, ion masses, and parallel electric field strengths. The essential features of the model are consistent with the concept of a cleft-based ion fountain supplying ionospheric ions to the polar magnetosphere, and the resulting plasma distributions and parameters are in general agreement with recent low-energy ion measurements from the DE 1 satellite.

Superthermal ion signatures of auroral acceleration processes

The retarding ion mass spectrometer on the Dynamics Explorer 1 spacecraft has generated a unique data set which documents, among other things, the occurrence of non-Maxwellian superthermal features in the auroral topside ionosphere distribution functions. In this paper, we provide a representative sampling of the observed features and their spatial morphology as observed at altitudes in the range from a few thousand kilometers to a few earth radii. At lower altitudes, these features appear at auroral latitudes separating regions of polar cap and subauroral light ion polar wind. The most common signature is the appearance of an upgoing energetic tail having conical lobes representing significant ion heat and number flux in all species, including O+. Transverse ion heating below the observation point at several thousand kilometers is clearly associated with O+ outflows. In some events observed, transverse acceleration apparently involves nearly the entire thermal plasma, the distribution function becomes highly anisotropic with T⊥ > T∥, and may actually develop a minimum at zero velocity, i.e., become a torus having as its axis the local magnetic field direction. At higher altitudes, the localized dayside source region appears as a field aligned flow which is dispersed tailward across the polar cap according to parallel velocity by antisunward convective flow, so that upflowing low energy O+ ions appear well within the polar cap region. While this flow can appear beamlike in a given location, the energy dispersion observed implies a very broad energy distribution at the source, extending from a few tenths of an eV to in excess of 50 eV. On the nightside, upgoing ion beams are found to be latitudinally bounded by regions of ion conics whose half angles increase with increasing separation from the beam region, indicating low altitude transverse acceleration in immediate proximity to, and below, the parallel acceleration region. These observations reveal a clear distinction between classical polar wind ion outflow and O+ enhanced superthermal flows, and confirm the importance of low altitude transverse acceleration in ionospheric plasma transport, as suggested by previous observations.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Challenges in quantifying wind generation's contribution to securing peak demand

Wind generation's contribution to supporting peak electricity demand is one of the key questions in wind integration studies. Differently from conventional units, the available outputs of different wind farms cannot be approximated as being statistically independent, and hence near-zero wind output is possible across an entire power system. This paper will review the risk model structures currently used to assess wind's capacity value, along with discussion of the resulting data requirements. A central theme is the benefits from performing statistical estimation of the joint distribution for demand and available wind capacity, focusing attention on uncertainties due to limited histories of wind and demand data; examination of Great Britain data from the last 25 years shows that the data requirements are greater than generally thought. A discussion is therefore presented into how analysis of the types of weather system which have historically driven extreme electricity demands can help to deliver robust insights into wind's contribution to supporting demand, even in the face of such data limitations. The role of the form of the probability distribution for available conventional capacity in driving wind capacity credit results is also discussed.