No abstract

[1] We apply an energy balance model to the snow cover for snowpack accumulation and ablation at a continuous permafrost site on Spitsbergen for the snow-covered periods from fall 1998 to winter 2000. The model includes net radiative, turbulent, ground, snow, and rain heat flux. The balance yields two distinct types of snow ablation: winter and spring ablation. Energy transferred by sensible heat and rain input reduces the snow cover during the winter, creating internal ice lenses and basal ice. The snowpack ablates during spring in two stages in both years. During the first stage, surface melt and subsequent internal freezing compact and reduce the snow cover, but no runoff is produced. This phase lasts more than twice as long as the second stage. During the second stage, which takes 14 days in both years, melt rates from the snowpack are represented well using the energy balance model. Ground heat fluxes are comparable during spring in both years, but the long persistence of the snow cover in 2000 delays the thawing of the ground. Due to the duration of the snow cover during spring snow melt of both years, the total energy supplied to the ground is significant, between 30 and 50% of the total energy supplied by net radiation.

Abstract. Most permafrost is located in the Arctic, where frozen organic carbon makes it an important component of the global climate system. Despite the fact that the Arctic climate changes more rapidly than the rest of the globe, observational data density in the region is low. Permafrost thaw and carbon release to the atmosphere are a positive feedback mechanism that can exacerbate global warming. This positive feedback functions via changing land–atmosphere energy and mass exchanges. There is thus a great need to understand links between the energy balance, which can vary rapidly over hourly to annual timescales, and permafrost, which changes slowly over long time periods. This understanding thus mandates long-term observational data sets. Such a data set is available from the Bayelva site at Ny-Ålesund, Svalbard, where meteorology, energy balance components and subsurface observations have been made for the last 20 years. Additional data include a high-resolution digital elevation model (DEM) that can be used together with the snow physical information for snowpack modeling and a panchromatic image. This paper presents the data set produced so far, explains instrumentation, calibration, processing and data quality control, as well as the sources for various resulting data sets. The resulting data set is unique in the Arctic and serves as a baseline for future studies. The mean permafrost temperature is −2.8 °C, with a zero-amplitude depth at 5.5 m (2009–2017). Since the data provide observations of temporally variable parameters that mitigate energy fluxes between permafrost and atmosphere, such as snow depth and soil moisture content, they are suitable for use in integrating, calibrating and testing permafrost as a component in earth system models.The presented data are available in the Supplement for this paper (time series) and through the PANGAEA and Zenodo data portals: time series (https://doi.org/10.1594/PANGAEA.880120, https://zenodo.org/record/1139714) and HRSC-AX data products (https://doi.org/10.1594/PANGAEA.884730, https://zenodo.org/record/1145373).

[1] Random walk particle tracking (RWPT) is a well established and efficient alternative to grid-based Eulerian approaches when simulating the advection-dispersion transport problem in highly heterogeneous porous media. However, RWPT methods suffer from a lack of accuracy when the dispersion tensor or the water content is spatially discontinuous. We present improvements to the concept of a partially reflecting barrier used to account for these discontinuities: (1) the nonlinear time splitting with ffiffiffiffiffi ffiÁt 2 p that corrects for the systematic overestimation of the second dispersion displacement across an element interface when linear time splitting is used; (2) the one-sided reflection coefficient that correctly represents the effect of discontinuous dispersion coefficients and water content but eliminates redundant reflections of the two-sided reflection coefficient and limits the error for discrete Át ; and (3) the transformation of the dispersive displacement across the element interface for complex multidimensional transport problems. The proposed improvements are verified numerically by comparison with an analytical solution and a reference RWPT method. The results indicate an increased efficiency and accuracy of the new RWPT algorithm. Because the new algorithm efficiently simulates both advectionand dispersion-dominated transport conditions, it enhances the applicability of RWPT to scenarios in which both conditions occur, as, for example, in the highly transient unsaturated zone. The algorithm is easily implemented and it is shown that the computational benefit increases with increasing variability of the hydraulic parameter field.Citation: Bechtold, M., J. Vanderborght, O. Ippisch, and H. Vereecken (2011), Efficient random walk particle tracking algorithm for advective-dispersive transport in media with discontinuous dispersion coefficients and water contents, Water Resour. Res.,

SUMMARY A discontinuous Galerkin method for the solution of the immiscible and incompressible two‐phase flow problem based on the nonsymmetric interior penalty method is presented. Therefore, the incompressible Navier–Stokes equation is solved for a domain decomposed into two subdomains with different values of viscosity and density as well as a singular surface tension force. On the basis of a piecewise linear approximation of the interface, meshes for both phases are cut out of a structured mesh. The discontinuous finite elements are defined on the resulting Cartesian cut‐cell mesh and may therefore approximate the discontinuities of the pressure and the velocity derivatives across the interface with high accuracy. As the mesh resolves the interface, regularization of the density and viscosity jumps across the interface is not required. This preserves the local conservation property of the velocity field even in the vicinity of the interface and constitutes a significant advantage compared with standard methods that require regularization of these discontinuities and cannot represent the jumps and kinks in pressure and velocity. A powerful subtessellation algorithm is incorporated to allow the usage of standard time integrators (such as Crank–Nicholson) on the time‐dependent mesh. The presented discretization is applicable to both the two‐dimensional and three‐dimensional cases. The performance of our approach is demonstrated by application to a two‐dimensional benchmark problem, allowing for a thorough comparison with other numerical methods. Copyright © 2012 John Wiley & Sons, Ltd.

Abstract.A classical transport experiment was performed in a field plot of 2.5 m 2 using the dye tracer brilliant blue. The measured tracer distribution demonstrates the dominant role of the heterogeneous soil structure for solute transport. As with many other published experiments, this evidences the need of considering the macroscopic structure of soil to predict flow and transport.We combine three different approaches to represent the relevant structure of the specific situation of our experiment: i) direct measurement, ii) statistical description of heterogeneities and iii) a conceptual model of structure formation.

No abstract

A pplication of Richards' equation at large scales is complicated by heterogeneity and nonlinearity, which prohibit upscaling from smaller to larger scales through simple averaging, as shown by Hopmans et al. (2002) and Beven (2001). Th e heterogeneity of the soil material can be taken into account in distributed modeling of water dynamics at larger scales using methods like pedotransfer functions (Wagner et al., 2001) or geostatistical tools (Yeh and Zhang, 1996). However, because of computational limitations, an increase of the model area is typically accompanied by a coarsening of the spatial discretization used in the numerical solution of Richards' equation. Downer and Ogden (2003) showed that this may actually lead to problems with the convergence of the solver and that the spatial discretization must be in the range of 1 cm or less in the case of infi ltration fronts close to the surface due to numerical stability issues. Similar results were found by van Dam and Feddes (2000). Ross (1990) showed that the spatial discretization is especially critical in sandy material and proposed a dynamic discretization scheme at the front, which increased the effi ciency considerably.Th e aim of this note is to recall that an upper limit of the spatial discretization for solving Richards' equation exists. Th is is not relevant for stationary fl ow fi elds, but it is especially true for infi ltration and drainage processes, which are considered here. If the spatial discretization is above a critical limit, this infl uences not only the convergence of the solver, which may be improved by more elaborate numerical techniques, but also the accuracy of the solution. We provide a simple estimation of the critical limit of spatial discretization for infi ltration or drainage processes into homogeneous soil at a given initial water potential, ψ m . In this case, the critical limit depends on the shape of the hydraulic functions and the steepness of the local gradient of total water potential. TheoryIf the water retention characteristic θ(ψ m ), relating water content θ and matric potential ψ m , and the hydraulic conductivity function K(θ) are known, water fl ow can be calculated from Richards' equation. Th e soil hydraulic functions are usually given by a set of parameters for one of the common parametrizations, such as the van Genuchten model (van Genuchten, 1980) or the Brooks-Corey model (Brooks and Corey, 1966). Since analytical solutions of Richards' equation are scarce and limited to very special cases, the partial diff erential equation is usually solved numerically based on discretizations in space and time. While the time step is often adapted automatically, an adaptive discretiza-Water dynamics in soil at spatial scales larger than the representative elementary volume (REV) of the porous structure are typically described by Richards' equation, which relates the fl ux law of Buckingham-Darcy to the mass balance of soil water. It is based on the soil water retention characteristics and the hydraulic conductivity functio...