On sequential multiscale inversion and data assimilation

Multiscale approaches are very popular for example for solving partial differential equations and in many applied fields dealing with phenomena which take place on different levels of detail. The broad idea of a multiscale approach is to decompose your problem into different scales or levels and to use these decompositions either for constructing appropriate approximations or to solve smaller problems on each of these levels, leading to increased stability or increased efficiency. The idea of sequential multiscale is to first solve the problem in a large-scale subspace and then successively move to finer scale spaces. Our goal is to analyse the sequential multiscale approach applied to an inversion or state estimation problem. We work in a generic setup given by a Hilbert space environment. We work out the analysis both for an unregularized and a regularized sequential multiscale inversion. In general the sequential multiscale approach is not equivalent to a full solution, but we show that under appropriate assumptions we obtain convergence of an iterative sequential multiscale version of the method. For the regularized case we develop a strategy to appropriately adapt the regularization when an iterative approach is taken. We demonstrate the validity of the iterative sequential multiscale approach by testing the method on an integral equation as it appears for atmospheric temperature retrieval from infrared satellite radiances

A localized adaptive particle filter within an operational NWP framework

Particle filters are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naïve application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimension of many practical assimilation problems (known as the curse of dimensionality). The goal of this work is to develop a localized adaptive particle filter (LAPF), which follows closely the idea of the classical MCMC or bootstrap-type particle filter, but overcomes the problems of collapse and divergence based on localization in the spirit of the local ensemble transform Kalman filter (LETKF) and adaptivity with an adaptive Gaussian resampling or rejuvenation scheme in ensemble space. The particle filter has been implemented in the data assimilation system for the global forecast model ICON at Deutscher Wetterdienst (DWD). We carry out simulations over a period of 1 month with a global horizontal resolution of 52 km and 90 layers. With four variables analyzed per grid point, this leads to 6.6 × 106 degrees of freedom. The LAPF can be run stably and shows a reasonable performance. We compare its scores to the operational setup of the ICON LETKF

Modelling fore- and hindlimb peak vertical force differences in trotting horses using upper body kinematic asymmetry variables

Differences in peak vertical ground reaction forces (dFzpeak) between contralateral forelimbs and hindlimbs are considered the gold standard for quantifying weight-bearing lameness. However, measuring kinematics for the same purpose is more common and practical. Vertical movement asymmetries (VMA) of the horse's upper body have previously been correlated to fore- and hindlimb lameness. But the combined response of head, withers and pelvis VMA to fore- and hindlimb dFzpeak has not yet been thoroughly investigated. Deriving the kinetic responses from kinematics would help the interpretation and understanding of quantified weight-bearing lameness. In this retrospective study, 103 horses with a wide range of fore- and hindlimb dFzpeak had been trotted on a force-measuring treadmill synchronized with an optical motion capture system. VMA of the head, withers and pelvis as well as dFzpeak were extracted. Multiple linear mixed models and linear regressions of kinematic variables were used to model the dFzpeak. It was hypothesised that all included VMA would have a significant influence on the dFzpeak outcome variables. The results showed a complex relationship between VMA and dFzpeak where both amplitude and timing of the VMA were of importance. On average, the contribution percentage of VMA to fore/hind dFzpeak were 66/34% for head, 76/24% for withers and 33/67% for pelvis. The linear regressions for the fore/hindlimb models achieved mean measurement root mean squared errors of 0.83%/0.82% dFzpeak. These results might help determine the clinical relevance of upper body VMA and distinguish between primary fore, hind, ipsilateral and diagonal weight-bearing lameness

The conservation status of the world’s reptiles

Effective and targeted conservation action requires detailed information about species, their distribution, systematics and ecology as well as the distribution of threat processes which affect them. Knowledge of reptilian diversity remains surprisingly disparate, and innovative means of gaining rapid insight into the status of reptiles are needed in order to highlight urgent conservation cases and inform environmental policy with appropriate biodiversity information in a timely manner. We present the first ever global analysis of extinction risk in reptiles, based on a random representative sample of 1500 species (16% of all currently known species). To our knowledge, our results provide the first analysis of the global conservation status and distribution patterns of reptiles and the threats affecting them, highlighting conservation priorities and knowledge gaps which need to be addressed urgently to ensure the continued survival of the world’s reptiles. Nearly one in five reptilian species are threatened with extinction, with another one in five species classed as Data Deficient. The proportion of threatened reptile species is highest in freshwater environments, tropical regions and on oceanic islands, while data deficiency was highest in tropical areas, such as Central Africa and Southeast Asia, and among fossorial reptiles. Our results emphasise the need for research attention to be focussed on tropical areas which are experiencing the most dramatic rates of habitat loss, on fossorial reptiles for which there is a chronic lack of data, and on certain taxa such as snakes for which extinction risk may currently be underestimated due to lack of population information. Conservation actions specifically need to mitigate the effects of human-induced habitat loss and harvesting, which are the predominant threats to reptiles