Sampling error distribution for the ensemble Kalman filter update step

In recent years, data assimilation techniques have been applied to an increasingly wider specter of problems. Monte Carlo variants of the Kalman filter, in particular, the ensemble Kalman filter (EnKF), have gained significant popularity. EnKF is used for a wide variety of applications, among them for updating reservoir simulation models. EnKF is a Monte Carlo method, and its reliability depends on the actual size of the sample. In applications, a moderately sized sample (40–100 members) is used for computational convenience. Problems due to the resulting Monte Carlo effects require a more thorough analysis of the EnKF. Earlier we presented a method for the assessment of the error emerging at the EnKF update step (Kovalenko et al., SIAM J Matrix Anal Appl, in press). A particular energy norm of the EnKF error after a single update step was studied. The energy norm used to assess the error is hard to interpret. In this paper, we derive the distribution of the Euclidean norm of the sampling error under the same assumptions as before, namely normality of the forecast distribution and negligibility of the observation error. The distribution depends on the ensemble size, the number and spatial arrangement of the observations, and the prior covariance. The distribution is used to study the error propagation in a single update step on several synthetic examples. The examples illustrate the changes in reliability of the EnKF, when the parameters governing the error distribution vary.     

The data zoo in Astro-WISE

In this paper we describe the way the Astro-WISE information system (or simply Astro-WISE) supports the data from a wide range of instruments and combines multiple surveys and their catalogues. Astro-WISE allows ingesting of data from any optical instrument, survey or catalogue, processing of this data to create new catalogues and bringing in data from different surveys into a single catalogue, keeping all dependencies back to the original data. Full data lineage is kept on each step of compiling a new catalogue with an ability to add a new data source recursively. With these features, Astro-WISE allows not only combining and retrieving data from multiple surveys, but performing scientific data reduction and data mining down to the rawest data in the data processing chain within a single environment.     

Astro-WISE interfaces

From a simple text interface to a graphical user interfaces—Astro-WISE provides the user with a wide range of possibilities to interact with the information system according to the user’s tasks and use cases. We describe a general approach to the interfacing of a scientific information system. We use this approach to create a number of services, which allows the user to browse the data stored in the system, to process the data and to exchange the newly created images and catalogs with the users within the system and wider astronomical community. Reusability of interfaces and services is another important feature of our approach. It reduces the time and resources spent to interface other information systems created from Astro-WISE.     

Hydrofluoric Acid‐Free Digestion of Geological Samples for the Quantification of Rare Earth Elements by Inductively Coupled Plasma‐Optical Emission Spectrometry

Rare earth elements (REEs) are very important to technological development as well as to geochemical and environmental studies. In this work, hydrofluoric acid (HF) was replaced by condensed phosphoric acid (CPA) in the digestion of geological samples, and the quantification of REEs was performed by inductively coupled plasma‐optical emission spectrometry (ICP‐OES). Six international reference materials (RMs), named DC86318, CGL 111, CGL 124, CGL 126, OKA‐2 and COQ‐1 and three Brazilian ore samples, named Araxá, Catalão and Pitinga were analysed. Only zircon and xenotime, which are potential REE‐bearing minerals, were not completely dissolved. Nevertheless, no REE associated with zircon was detected. The investigated digestion method presented many advantages: It was relatively fast (3 h), avoided fluoride precipitation, it was less hazardous because handling diluted H₃PO₄ is safer than HF, NH₄F or NH₄HF₂ aqueous solutions, it preserved the quartz fittings of the measurement equipment and the final solution contained lower levels of total dissolved solids than those produced by the fusion method.     

Using a One-and-a-Half Order Closure Model of the Atmospheric Boundary Layer for Surface Flux Footprint Estimation

A knowledge of the distribution of the contribution of upwind sources to measurements of vertical scalar flux densities is important for the correct interpretation of eddy covariance data. Several approaches have been developed to estimate this so-called footprint function. Here a new approach based on the ensemble-averaged Navier—Stokes equations is presented. Comparisons of numerical results using this approach with results from other studies under a range of environmental conditions show that the model predictions are robust. Moreover, the approach outlined here has the advantage of a potential wide applicability, due to an ability to take into account the heterogeneous nature of underlying surfaces. For example, the model showed that any variations in surface drag, such as must occur in real life heterogeneous canopies, can exert a marked influence of the shape and extent of flux footprints. Indeed, it seems likely that under such circumstances, estimates of surface fluxes will be weighted towards areas of highest foliage density (and therefore quite likely higher photosynthetic rates) close to the measurement sensor. Three-dimensional footprints during the day and night were also determined for a mixed coniferous forest in european Russia. A marked asymmetry of the footprint in the crosswind direction was observed, this being especially pronounced for non-uniform plant distributions involving vegetation types with different morphological and physiological properties. The model also found that, other things being equal, the footprint peak for forest soil respiration is typically over twice the distance from the above canopy measurement sensor compared to that for canopy photosynthesis. This result has important consequences for the interpretation of annual ecosystem carbon balances by the eddy covariance method.     

Shallow virtual source redatuming by multi‐dimensional deconvolution

Recently, new on‐shore acquisition designs have been presented with multi‐component sensors deployed in the shallow sub‐surface (20 m–60 m). Virtual source redatuming has been proposed for these data to compensate for surface statics and to enhance survey repeatability. In this paper, we investigate the feasibility of replacing the correlation‐based formalism that undergirds virtual source redatuming with multi‐dimensional deconvolution, offering various advantages such as the elimination of free‐surface multiples and the potential to improve virtual source repeatability. To allow for data‐driven calibration of the sensors and to improve robustness in cases with poor sensor spacing in the shallow sub‐surface (resulting in a relatively high wavenumber content), we propose a new workflow for this configuration. We assume a dense source sampling and target signals that arrive at near‐vertical propagation angles. First, the data are preconditioned by applying synthetic‐aperture‐source filters in the common receiver domain. Virtual source redatuming is carried out for the multi‐component recordings individually, followed by an intermediate deconvolution step. After this specific pre‐processing, we show that the downgoing and upgoing constituents of the wavefields can be separated without knowledge of the medium parameters, the source wavelet, or sensor characteristics. As a final step, free‐surface multiples can be eliminated by multi‐dimensional deconvolution of the upgoing fields with the downgoing fields.