An algebraic interpretation of the multivariate qq-Krawtchouk polynomials

The multivariate quantum $q$-Krawtchouk polynomials are shown to arise as matrix elements of "$q$-rotations" acting on the state vectors of many $q$-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations and recurrence relations. The extension to an arbitrary number of variables is presentedComment: 22 pages; minor correction

Coastal aquifers: Scientific advances in the face of global environmental challenges

This article has been published in final form at http://dx.doi.org/10.1016/j.jhydrol.2017.04.046 © 2017 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (25 May 2017) in accordance with the publisher’s copyright polic

Common Data Fusion Framework : An open-source Common Data Fusion Framework for space robotics

Multisensor data fusion plays a vital role in providing autonomous systems with environmental information crucial for reliable functioning. In this article, we summarize the modular structure of the newly developed and released Common Data Fusion Framework and explain how it is used. Sensor data are registered and fused within the Common Data Fusion Framework to produce comprehensive 3D environment representations and pose estimations. The proposed software components to model this process in a reusable manner are presented through a complete overview of the framework, then the provided data fusion algorithms are listed, and through the case of 3D reconstruction from 2D images, the Common Data Fusion Framework approach is exemplified. The Common Data Fusion Framework has been deployed and tested in various scenarios that include robots performing operations of planetary rover exploration and tracking of orbiting satellites

The Impact of Soil Tension on Isotope Fractionation, Transport, and Interpretations of the Root Water Uptake Origin

The new isotope module in HYDRUS-1D can be used to infer the origin of root water uptake (RWU), a suitable dynamic indicator for agriculture and forest water management. However, evidence shows that the equilibrium fractionation between liquid water and water vapor within the soil is affected not only by soil temperature but also by soil tension. How soil tension affects isotope transport modeling and interpretations of the RWU origin is still unknown. In this study, we evaluated three fractionation scenarios on model performance for a field data set from Langeoog Island: (a) no fractionation (Non_Frac), (b) the soil temperature control on equilibrium fractionation as described by the standard Craig-Gordon equation (CG_Frac), and (c) CG_Frac plus the soil tension control on equilibrium fractionation (CGT_Frac). The model simulations showed that CGT_Frac led to more depleted isotopic compositions of surface soil water than CG_Frac. The vertical origin of RWU was estimated using the water balance (WB) calculations and the Bayesian mixing model (SIAR). While the former directly used water flow outputs, the latter used as input simulated isotopic compositions (using different fractionation scenarios) of RWU and soil water. Both methods provided similar variation trends with time and depth in different soil layers' contributions to RWU. The contributions of all soil layers interpreted by the CGT_Frac scenario were always between Non_Frac and CG_Frac. The temporal origin of RWU was deduced from particle tracking (PT, releasing one hypothetical particle for individual precipitation event and tracking its movement based on the water balance between particles) and a virtual tracer experiment (VTE, assigning a known isotope composition to individual precipitation event and tracking its movement based on the cumulative isotope flux). Both methods revealed similar variation trends with time in drainage and root zone (RZ) travel times. The interpreted drainage and RZ travel times were generally ranked as Non_ Frac > CGT_Frac > CG_Frac. Overall, the factors considered in the standard CG equation dominated isotope fractionation, transport, and interpretations of the RWU origin. Isotope transport-based methods (SIAR, VTE) were more computationally demanding than water flow-based methods (WB, PT)

On the Propagation of Reaction Fronts in a Sandy Aquifer Over 20+ Years: Lessons From a Test Site in Northwestern Germany

Despite reduction measures, nitrate and aluminum concentrations remain high in aquifers in northwestern Europe. To evaluate the effectiveness of groundwater protection policies, the long-term fate of these contaminants in groundwater needs to be understood. The groundwater catchment of the Haren water works, NW Germany, was characterized hydrogeochemically in the late 1990s, which provides an opportunity to study the solute fronts over a two-decade period and conduct a post-audit of the predicted front movement. Results indicate that, despite a significant reduction of the atmospheric acid loads, the acidification of soil and groundwater at the forest site persists. Removal of sorbed aluminum is required to induce a noticeable improvement, which will take at least several decades. The unexpected appearance of nitrate at the site, caused by a land use change in 1998, highlights the need for long-term monitoring. Core data at the agricultural site show that the denitrification front has moved very little between 1998 and 2017, in accordance with previous forecasts. Denitrification by-products, mainly sulfate and nitrogen, have migrated from the upper into the lower aquifer. A reactive transport model demonstrated how the link between the regional groundwater flow, pyrite oxidation, and the temporal variability of the nitrate concentration in recharge water, as reconstructed from age tracers, result in the observed vertical distribution of sulfate and nitrogen. This study demonstrates how long-term monitoring, aided by model-based data interpretation, can be used to successfully study and predict the fate of contaminants in groundwater. © 2021. The Authors

Error in hydraulic head and gradient time-series measurements: a quantitative appraisal

&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Abstract.&amp;lt;/strong&amp;gt; Hydraulic head and gradient measurements underpin practically all investigations in hydro(geo)logy. There is sufficient information in the literature to suggest that head measurement errors may be so large that flow directions can not be inferred reliably, and that their magnitude can have as great an effect on the uncertainty of flow rates as the hydraulic conductivity. Yet, educational text books contain limited content regarding measurement techniques and studies rarely report on measurement errors. The objective of our study is to review currently-accepted standard operating procedures in hydrological research and to determine the smallest head gradients that can be resolved. To this aim, we first systematically investigate the systematic and random measurements errors involved in collecting time series information on hydraulic head at a given location: (1) geospatial position, (2) point of head, (3) depth to water, and (4) water level time series. Then, by propagating the random errors, we find that with current standard practice, horizontal head gradients&amp;amp;#8201;&amp;lt;&amp;amp;#8201;10&amp;lt;sup&amp;gt;&amp;amp;#8722;4&amp;lt;/sup&amp;gt; are resolvable at distances&amp;amp;#8201;&amp;amp;#10886;&amp;amp;#8201;170&amp;amp;#8201;m. Further, it takes extraordinary effort to measure hydraulic head gradients&amp;amp;#8201;&amp;lt;&amp;amp;#8201;10&amp;lt;sup&amp;gt;&amp;amp;#8722;3&amp;lt;/sup&amp;gt; over distances&amp;amp;#8201;&amp;lt;&amp;amp;#8201;10&amp;amp;#8201;m. In reality, accuracy will be worse than our theoretical estimates because of the many possible systematic errors. Regional flow on a scale of kilometres or more can be inferred with current best-practice methods, but processes such as vertical flow within an aquifer cannot be determined until more accurate and precise measurement methods are developed. Finally, we offer a concise set of recommendations for water level, hydraulic head and gradient time series measurements. We anticipate that our work contributes to progressing the quality of head time series data in the hydro(geo)logical sciences, and provides a starting point for the development of universal measurement protocols for water level data collection.&amp;lt;/p&amp;gt; </jats:p

Future-proofing hydrogeology by revising groundwater monitoring practice

Groundwater is an important global resource and its sustainable use faces major challenges. New methods and advances in computational science could lead to much improved understanding of groundwater processes and subsurface properties. A closer look at current groundwater monitoring practice reveals the need for updates with a special focus on the benefits of high-frequency and high-resolution datasets. To future-proof hydrogeology, this paper raises awareness about the necessity for improvement, provides initial recommendations and advocates for the development of universal guide-lines