State estimation using the particle filter with mode tracking

A particle filter is a data assimilation scheme that employs a fully nonlinear, non-Gaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N. 2008. IEEE Trans Signal Process 56:4583–97] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The aim of this paper is to test this hypothesis using the three dimensional stochastic Lorenz equations with direct observations. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to mode track depends on the number of particles used and the accuracy and frequency of the observations.

Muses

The Muses are goddesses and teachers of divine wisdom evoked in dance, music, and poetry. Late sources suggest that they invented the alphabet (Diod. Sic. 7.74.1) and the arts and sciences (Anth. Lat. 1.1.88; 1.2.664).

Ballet-Granite

Live Performance, Szuper Gallery + Curtain Razors Dur: 50 mins NTSC HD 2011 Direction/Conception - Susanne Clausen, Pavlo Kerestey, Michele Sereda Performance Installation - Susanne Clausen, Pavlo Kerestey Performers - Jason Cawood, Susanne Clausen, Blair Fornwald, Morgan Garneau, John Hampton, Pavlo Kerestey, Michele Sereda Cave Video - Susanne Clausen and Pavlo Kerestey Sound scape - Szuper Gallery Voice - Michele Sereda Ballet Band - Billy Hughes, Trent Mailander and Otis Young Music - Dance of the Spirits - Danilo Villalta Technical Direction - Kenneth Young Stage Management - Paul Crepeau Sound Support - Jeff Morton Structural Design Consultant - James Phillips and Caragana Production Design Inc Set Assistants - Rebbeca Donison and Shelby Lowe Headress - Alla Sidorenko Costume consultation - Dean Renwick Documentation, Still - Carey Shaw, Szuper Gallery Documentation, Moving - Gabriel Yahyahkeekoot Administration + PR - Carey Shaw and the Mackenzie Art Gallery Poster Design - Rio Saxon Design Produced by Curtain Razors and Szuper Gallery in collaboration with the Mackenzie Art Gallery with the support of the Canada Council for the Arts, the Saskatchewan Arts Board and the City of Regina Arts Advisory Committee.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.

The music instinct: the evolutionary basis of musicality

Why does music pervade our lives and those of all known human beings living today and in the recent past? Why do we feel compelled to engage in musical activity, or at least simply enjoy listening to music even if we choose not to actively participate? I argue that this is because musicality—communication using variations in pitch, rhythm, dynamics and timbre, by a combination of the voice, body (as in dance), and material culture—was essential to the lives of our pre-linguistic hominin ancestors. As a consequence we have inherited a desire to engage with music, even if this has no adaptive benefit for us today as a species whose communication system is dominated by spoken language. In this article I provide a summary of the arguments to support this view.

Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling

Satellite-based Synthetic Aperture Radar (SAR) has proved useful for obtaining information on flood extent, which, when intersected with a Digital Elevation Model (DEM) of the floodplain, provides water level observations that can be assimilated into a hydrodynamic model to decrease forecast uncertainty. With an increasing number of operational satellites with SAR capability, information on the relationship between satellite first visit and revisit times and forecast performance is required to optimise the operational scheduling of satellite imagery. By using an Ensemble Transform Kalman Filter (ETKF) and a synthetic analysis with the 2D hydrodynamic model LISFLOOD-FP based on a real flooding case affecting an urban area (summer 2007,Tewkesbury, Southwest UK), we evaluate the sensitivity of the forecast performance to visit parameters. We emulate a generic hydrologic-hydrodynamic modelling cascade by imposing a bias and spatiotemporal correlations to the inflow error ensemble into the hydrodynamic domain. First, in agreement with previous research, estimation and correction for this bias leads to a clear improvement in keeping the forecast on track. Second, imagery obtained early in the flood is shown to have a large influence on forecast statistics. Revisit interval is most influential for early observations. The results are promising for the future of remote sensing-based water level observations for real-time flood forecasting in complex scenarios.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties.

Representativity error for temperature and humidity using the Met Office high-resolution model

The observation-error covariance matrix used in data assimilation contains contributions from instrument errors, representativity errors and errors introduced by the approximated observation operator. Forward model errors arise when the observation operator does not correctly model the observations or when observations can resolve spatial scales that the model cannot. Previous work to estimate the observation-error covariance matrix for particular observing instruments has shown that it contains signifcant correlations. In particular, correlations for humidity data are more significant than those for temperature. However it is not known what proportion of these correlations can be attributed to the representativity errors. In this article we apply an existing method for calculating representativity error, previously applied to an idealised system, to NWP data. We calculate horizontal errors of representativity for temperature and humidity using data from the Met Office high-resolution UK variable resolution model. Our results show that errors of representativity are correlated and more significant for specific humidity than temperature. We also find that representativity error varies with height. This suggests that the assimilation scheme may be improved if these errors are explicitly included in a data assimilation scheme. This article is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.

Effort and affect: engaging with film performance

In order to consider our emotional and physical involvement with film this chapter explores the rapport between camera and performer and how this impacts on the construction of engagement, drawing on critical approaches across the disciplines of film, dance and philosophy to describe our spatial, emotional and sensuous relationship to characters and bodies on-screen. Concern with the relationship between what is happening on screen and the shaping of our engagement is developed through attention to the effort of a particular performance, using close analysis to make sense of the affect invited by qualities of movement and how they are presented in moment from Rosemary’s Baby (Polanski, 1968).

RMetS special interest group meeting: high resolution data assimilation

Data assimilation (DA) systems are evolving to meet the demands of convection-permitting models in the field of weather forecasting. On 19 April 2013 a special interest group meeting of the Royal Meteorological Society brought together UK researchers looking at different aspects of the data assimilation problem at high resolution, from theory to applications, and researchers creating our future high resolution observational networks. The meeting was chaired by Dr Sarah Dance of the University of Reading and Dr Cristina Charlton-Perez from the MetOffice@Reading. The purpose of the meeting was to help define the current state of high resolution data assimilation in the UK. The workshop assembled three main types of scientists: observational network specialists, operational numerical weather prediction researchers and those developing the fundamental mathematical theory behind data assimilation and the underlying models. These three working areas are intrinsically linked; therefore, a holistic view must be taken when discussing the potential to make advances in high resolution data assimilation.

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

Evidence of a topographic signal in surface soil moisture derived from ENVISAT ASAR wide swath data

The susceptibility of a catchment to flooding is affected by its soil moisture prior to an extreme rainfall event. While soil moisture is routinely observed by satellite instruments, results from previous work on the assimilation of remotely sensed soil moisture into hydrologic models have been mixed. This may have been due in part to the low spatial resolution of the observations used. In this study, the remote sensing aspects of a project attempting to improve flow predictions from a distributed hydrologic model by assimilating soil moisture measurements are described. Advanced Synthetic Aperture Radar (ASAR) Wide Swath data were used to measure soil moisture as, unlike low resolution microwave data, they have sufficient resolution to allow soil moisture variations due to local topography to be detected, which may help to take into account the spatial heterogeneity of hydrological processes. Surface soil moisture content (SSMC) was measured over the catchments of the Severn and Avon rivers in the South West UK. To reduce the influence of vegetation, measurements were made only over homogeneous pixels of improved grassland determined from a land cover map. Radar backscatter was corrected for terrain variations and normalized to a common incidence angle. SSMC was calculated using change detection. To search for evidence of a topographic signal, the mean SSMC from improved grassland pixels on low slopes near rivers was compared to that on higher slopes. When the mean SSMC on low slopes was 30–90%, the higher slopes were slightly drier than the low slopes. The effect was reversed for lower SSMC values. It was also more pronounced during a drying event. These findings contribute to the scant information in the literature on the use of high resolution SAR soil moisture measurement to improve hydrologic models.