Generalyzed variance-covariance propagation law formulae and application to explicit least-squares adjustments

Standard formulae overlook the contribution of a number of terms in the derivation of variance-covariance matrices for parameters in nonlinear least squares adjustment. In a large class of nonlinear mathematical models, these terms can contribute to an important error in the estimation of parameter variances. Improved formulae are derived. A numerical example is given and the use of our improved formula in the case of least-squares adjustment in the explicit case (L=F(X)) is fully documented.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Quaternary drainage network reorganization in the Colombian Eastern Cordillera plateau

Dramatic drainage reorganization from initial longitudinal to transversal domains has occurred in the Eastern Cordillera of Colombia. We perform a regional analysis of drainage basin geometry and transformed river profiles based on the integral form of the slope-area scaling, to investigate the dynamic state of drainage networks and to predict the degree of drainage reorganization in this region. We propose a new model of drainage rearrangement for the Eastern Cordillera, based on the analyses of knickpoint distribution, normalized river profiles, landforms characteristic of river capture, erosion rates and palaeodrainage data. We establish that the oldest longitudinal basin captured by the Magdalena River network was the Suárez Basin at ≈409 ka, inferring the timing of abandonment of a river terrace using in situ produced cosmogenic beryllium-10 (¹⁰Be) depth profiles and providing a first estimation of incision rate of 0.07 mm/yr. We integrate published geochronologic data and interpret the last capture of the Sabana de Bogotá, providing a minimum age of the basin opening to the Magdalena drainage at ≈38 ka. Our results suggest that the Magdalena basin Increased its drainage area by integrating the closed basins from the western flank of the Eastern Cordillera. Our study also suggests that the Magdalena basin is an aggressor compared to the basins located in the eastern flank of the orogen and provides a framework for examining drainage reorganization within the Eastern Cordillera and in similar orogenic settings. The results improve our understanding of headward integration of closed basins across orogenic plateaux. © 2020 John Wiley & Sons, Ltd.     

A Compilation of Silicon and Thirty One Trace Elements Measured in the Natural River Water Reference Material SLRS-4 (NRC-CNRC)

The natural river water certified reference material SLRS-4 (NRC-CNRC, National Research Council-Conseil National de Recherches Canada) has been routinely analysed for major and trace elements by six French laboratories. Most measurements were made using inductively coupled plasma-mass spectrometry. For silicon and thirty one trace elements (rare earth elements, Ag, B, Br, Cs, Ga, Ge, Li, P, Pd, Rb, Se, Th, Ti, Tl, W, Y and Zr), no certified values are assigned by NRC-CNRC. We propose some compilation values and related uncertainties according to the results obtained by the different laboratories.     

A thick reflection nebula illuminated by a power law

We present the results of modelling the energy distribution of a power law reflected by a dusty cloud. We explore in a fully consistent manner the case in which the reflecting nebula is of considerable optical depth. We apply the model to the observations of the detached emission line cloud at 8 kpc from the nucleus of Pks 2152-69 for whichcontinuum flux measurements exist up to the far UV. Our results for the thick case qualitatively agree with the results of Fosburyet al. (1991) (who studied the optically thin case) in that we also need a population of grain sizes dominated by small grains (smaller on average than in models of the standard extinction curve) in order to reproduce the energy distribution of the detached continuum source. We model the high excitation emission line spectrum of the cloud using the code MAPPINGS. Photoionization calculations in which the ionized gas contains the reflecting dust can easily reproduce the high electronic temperature as well as theapparent case B Ly/H ratio observed in the detached cloud, confirming that dust is a workable hypothesis for explaining the Ly emission and the blue extended light detected around many high redhift radio galaxies.     

Thin Threads of Solar Filaments

High-resolution images obtained in H with the new Swedish Solar Telescope at La Palma, Spain, have been used for studies of fine-scale threads in solar filaments. The widths of the thin threads are 0.3 arcsec. The fact that the width of the thinnest threads is comparable to the diffraction limit of the telescope of about 0.14 arcsec, at the wavelength of H, suggests that even thinner threads may exist. Assuming that the threads represent thin magnetic strings, we conclude that only a small fraction of these are filled with observable absorbing plasma, at a given time. The absorbing plasma is continuously flowing along the thread structures at velocities 15± 10 kms^–1, which suggests that the flows must be field-aligned. In one case where a bundle of thin threads appears to be rooted in the nearby photosphere, we find that the individual threads connects with intergranular, dark lanes in the photosphere. We do not find signs of typical network fields at the roots of the fine threads, as normally evidenced by bright points in associated G-band images. It is suggested that filament threads are rooted in relatively weak magnetic fields.     

Radar observations of asteroid 1999 JM8

Abstract— We report results of delay‐Doppler observations of 1999 JM8 with the Goldstone 8560 MHz (3.5 cm) and Arecibo 2380 MHz (13 cm) radars over 18 days in July‐August 1999. The images place thousands of pixels on the asteroid and achieve range resolutions as fine as 15 m/pixel. The images reveal an asymmetric, irregularly shaped object with a typical overall dimension within 20% of 7 km. If we assume that 1999 JM8's effective diameter is 7 km, then the absolute magnitude, 15.15, and the average Goldstone radar cross section, 2.49 km², correspond to optical and radar albedos of 0.02 and 0.06, establishing that 1999 JM8 is a dark object at optical and radar wavelengths. The asteroid is in a non‐principal axis spin state that, although not yet well determined, has a dominant periodicity of ?7 days. However, images obtained between July 31 and August 9 show apparent regular rotation of features from day to day, suggesting that the rotation state is not far from principal axis rotation. 1999 JM8 has regions of pronounced topographic relief, prominent facets several kilometers in extent, numerous crater‐like features between ?100 m and 1.5 km in diameter, and features whose structural nature is peculiar. Arecibo images provide the strongest evidence to date for a circular polarization ratio feature on any asteroid. Combined optical and radar observations from April 1990 to December 2000 permit computation of planetary close approach times to within ± 10 days over the interval from 293 to at least 2907, one of the longest spans for any potentially hazardous asteroid. Integration of the orbit into the past and future shows close approaches to Earth, Mars, Ceres, and Vesta, but the probability of the object impacting Earth is zero for at least the next nine centuries.