Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.

Pumping Rate and Size of Demosponges—Towards an Understanding Using Modeling

Filter-feeding sponges pump large amounts of water and contribute significantly to grazing impact, matter transport and nutrient cycling in many marine benthic communities. For ecological studies it is therefore of interest to be able to estimate the pumping rate of different species from their volume size or osculum cross-sectional area by means of experimentally determined allometric correlations. To help understand allometric data correlations and observed large variations of volume-specific pumping rate among species we developed a model that determines the pumping rate as a function of the size (volume) of a tubular-type demosponge described by 4 geometric length scales. The model relies on a choanocyte-pump model and standard pressure loss relations for flow through the aquiferous system, and density and pumping rate per choanocyte is assumed to be constant. By selecting different possibilities for increase of the length scales, which may also simulate different growth forms, we demonstrate that the model can imitate the experimental allometric correlations. It is concluded that the observed dependence of pumping rate on size is primarily governed by the hydraulics of pump performance and pressure losses of the aquiferous system rather than, e.g., decreasing density of choanocytes with increasing sponge size.

Coarse and Fine Particulate Organic Matter Transport by a Fourth-Order Mountain Stream to Lake Bourget (France)

Transport of coarse particulate organic matter (CPOM) derived from forest litterfall has been hardly studied in rivers, unlike fine particulate organic matter (FPOM) or dissolved organic matter (DOM). Yet, many rivers are dammed or run into lakes, and there is growing evidence that CPOM accumulation in river delta participates substantially in ecological processes such as greenhouse gas emissions of lakes and reservoirs. We investigated the transport of CPOM and FPOM by the Leysse River (discharge from 0.2 to 106 m3 s−1) to Lake Bourget (France) in relation to aerial litter deposition, river network length, and discharge. Over a 19-month study period, the volume-weighted mean CPOM and FPOM concentrations were 1.3 and 7.7 g m−3, respectively. Most CPOM and FPOM transport occurred during major flood events, and there were power relationships between maximum discharge and particulate organic matter (POM) transport during these events. The annual export of CPOM (190 t AFDM) was 85% of the litter accumulation in autumn on permanent sections of the riverbed (224 t AFDM), which suggests that export is a major process compared to breakdown. Export of CPOM was 1.25 t yr−1 km−2 of the forested catchment area. This study highlights the need to account for long-range CPOM transport to describe the fate of litter inputs to streams and to quantify the organic matter input and processing in lakes and reservoirs.

Local Two-Dimensional Splitting Schemes for 3D Suspended Matter Transport Problem Parallel Solution

A 3D model of suspended matter transport in coastal marine systems is considered, which takes into account many factors, including the hydraulic size or the rate of particle deposition, the propagation of suspended matter, sedimentation, the intensity of distribution of suspended matter sources, etc. The difference operators of diffusion transport in the horizontal and vertical directions for this problem have significantly different characteristic spatiotemporal scales of processes, as well as spectra. With typical sampling, applied to shallow-water systems in the South of Russia (the Sea of Azov, the Tsimlyansk reservoir), the steps in horizontal directions are 200-1000 meters, the coefficients of turbulent exchange (turbulent diffusion) are (103-104) m2/sec; in the vertical direction - - - steps of 0.1 m-1 m, and the coefficients of microturbulent exchange in the vertical — (0.1-1) m2/sec. If we focus on the use of explicit locally twodimensional - - - locally one-dimensional splitting schemes, then the permissible values of the time step for a two-dimensional problem will be about 10-100 seconds, and for a one-dimensional problem in the vertical direction - - - 0.1 – 1 sec. This motivates us to construct an additive locally-two-dimensional-locallyonedimensional splitting scheme in geometric directions. The paper describes a parallel algorithm that uses both explicit and implicit schemes to approximate the two-dimensional diffusion-convection problem in horizontal directions and the one-dimensional diffusion-convection problem in the vertical direction. The two-dimensional implicit diffusion-convection problem in horizontal directions is numerically solved by the adaptive alternating-triangular method. The numerical implementation of the one-dimensional diffusion-convection problem in the vertical direction is carried out by a sequential run-through method for a series of independent one-dimensional three-point problems in the vertical direction on a given layer. To increase the efficiency of parallel calculations, the decomposition of the calculated spatial grid and all grid data in one or two spatial directions - in horizontal directions-is also performed. The obtained algorithms are compared taking into account the permissible values of time steps and the actual time spent on performing calculations and exchanging information on each time layer.

Responses of Root Characteristic Parameters and Plant Dry Matter Accumulation, Distribution and Transportation to Nitrogen Levels for Spring Maize in Northeast China

Improving nitrogen use efficiency is a significant scientific problem to be solved. Two maize hybrids JD27 (Jidan 27) and SD19 (Sidan 19) were selected to study the effects of nitrogen levels on root characteristic parameters and plant dry matter accumulation, distribution and transportation. We set five different nitrogen levels, which were nitrogen deficiency (000N), low nitrogen (075N), medium nitrogen (150N), high nitrogen (225N) and excessive nitrogen (300N). The results showed that the root length and root surface area of JD27 were significantly higher than those of SD19 under 075N. With the increase of nitrogen levels, the root difference among varieties gradually decreased. The root length, projection area, total surface area and total volume reached the maximum values at silking stage. The average root diameter kept stable or decreased slowly with the growth stage. The dry matter accumulation of JD27 was higher than that of SD19 at all growth stages. Increasing the amount of nitrogen fertilizer can promote the transport of dry matter to grain and improve dry matter transport efficiency after anthesis. Under the treatment of medium and high nitrogen fertilizer, maize was easy to obtain a higher yield, but excessive nitrogen fertilizer inhibited the increase of yield. This study provides theoretical and practical guidance for maize production techniques.

Parcels 2.2 - An increasingly versatile, open-source Lagrangian ocean simulation tool

<p>Lagrangian simulations contribute to the study and comprehension of particulate-matter transport, its dissolution and dispersion in the oceans. Parcels is an open-source, Python-based module for Lagrangian ocean simulations. It is a known tool in the oceanographic community that has been applied to a variety of case studies, such as the tracing of microplastics, the backtracking of ocean floor plankton, and the migration of fish. In this module, particles are advected over time according to a selected flow field, where those particles can represent particulate-matter, biota or other objects with physical, hydrodynamic or biogeochemical properties. In this contribution, we present the substantial extensions of Parcels with respect to usability, physics modelling aspects of particle advection, and computational aspects of versatile, scalable and efficient simulations.</p><p>Specifically, a suite of simple, concise notebook tutorials are tailored to novice user, covering step-by-step simulation setup instructions, whereas self-contained special-issue tutorials address advanced- and proficient user requirements. The considerable expansion of supported OGCM flow field input formats (e.g. MITgcm, POP and MOM5, among others) is a major interest in Parcels v2.2 for our steadily-growing user base.</p><p>The new version further integrates previously-published physics methods into practical lagrangian particle simulations. As such, we implement an analytical advection scheme in addition to existing Runge-Kutta advection schemes. Furthermore, two-dimensional advection-diffusion is upgraded with the Milstein stochastic integration scheme and improved documentation. Those capabilities enable a more consistent modelling of diffusion- and uncertainty-dominated fluid transport processes.</p><p>The case studies performed with previous versions indicate increased computational demands. Simulations are run over long decadal time scales as well as over day-periods with sub-second temporal increments, involving multiple basins and global scenarios, while also modelling increasingly complex particle processes. Overall, our developments respond to the big-data requirements of modern oceanographic studies, which include the aspects of (i) high record volume (i.e. large number of particles), (ii) high dimensionality in multi-variate records, (iii) high spatial resolution, (iv) high temporal resolution, (v) high scenario (i.e. case study) variability and (vi) the prevention of numerical error accumulation over long simulation time scales.</p><p>The novel features of Parcels v2.2 are illustrated on distinct case studies within our contribution, in order to connect the technical features to their impact on particulate-matter ocean transport studies.</p>