In order to assess the role of submarine groundwater discharge (SGD) and its impact on the carbonate system on the northern South China Sea (NSCS) shelf, we measured seawater concentrations of four radium isotopes ^{223,224,226,228}Ra along with carbonate system parameters in June–July, 2008. Complementary groundwater sampling was conducted in coastal areas in December 2008 and October 2010 to constrain the groundwater end-members. The distribution of Ra isotopes in the NSCS was largely controlled by the Pearl River plume and coastal upwelling. Long-lived Ra isotopes (²²⁸Ra and ²²⁶Ra) were enriched in the river plume but low in the offshore surface water and subsurface water/upwelling zone. In contrast, short-lived Ra isotopes (²²⁴Ra and ²²³Ra) were elevated in the subsurface water/upwelling zone as well as in the river plume but depleted in the offshore surface water. In order to quantify SGD, we adopted two independent mathematical approaches. Using a three end-member mixing model with total alkalinity (TAlk) and Ra isotopes, we derived a SGD flux into the NSCS shelf of 2.3–3.7 × 10⁸ m³ day⁻¹. Our second approach involved a simple mass balance of ²²⁸Ra and ²²⁶Ra and resulted in a first order but consistent SGD flux estimate of 2.2–3.7 × 10⁸ m³ day⁻¹. These fluxes were equivalent to 12–21 % of the Pearl River discharge, but the source of the SGD was mostly recirculated seawater. Despite the relatively small SGD volume flow compared to the river, the associated material fluxes were substantial given their elevated concentrations of dissolved inorganic solutes. In this case, dissolved inorganic carbon (DIC) flux through SGD was 153–347 × 10⁹ mol yr⁻¹, or ~23–53 % of the riverine DIC export flux. Our estimates of the groundwater-derived phosphate flux ranged 3–68 × 10⁷ mol yr⁻¹, which may be responsible for new production on the shelf up to 0.3–6.3 mmol C m⁻² d⁻¹. This rate of new production would at most consume 11 % of the DIC contribution delivered by SGD. Hence, SGD may play an important role in the carbon balance over the NSCS shelf

In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grü nwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Abstract. Organic matter in surface sediments from the upper reach of the Pearl River Estuary and Lingdingyang Bay, as well as the adjacent northern South China Sea shelf was characterized using a variety of techniques, including elemental (C and N) ratio, bulk stable organic carbon isotopic composition (δ 13 C), and carbohydrate composition analyses. Total organic carbon (TOC) content was 1.21 ± 0.45% in the upper reach, down to 1.00±0.22% in Lingdingyang Bay and to 0.80 ± 0.10% on the inner shelf and 0.58 ± 0.06% on the outer shelf. δ 13 C values ranged from −25.1‰ to −21.3‰ in Lingdingyang Bay and the South China Sea shelf, with a trend of enrichment seawards. The spatial trend in C/N ratios mirrored that of δ 13 C, with a substantial decrease in C/N ratio offshore. Total carbohydrate yields ranged from 22.1 to 26.7 mg (100 mg OC) −1 , and typically followed TOC concentrations in the estuarine and shelf sediments. Total neutral sugars, as detected by the nine major monosaccharides (lyxose, rhamnose, ribose, arabinose, fucose, xylose, galactose, mannose, and glucose), were between 4.0 and 18.6 mg (100 mg OC) −1 in the same sediments, suggesting that significant amounts of carbohydrates were not neutral aldoses. Using a two end-member mixing model based on δ 13 C values and C/N ratios, we estimated that the terrestrial organic carbon contribution to the surface sediment TOC was ca. 78±11% for Lingdingyang Bay, 34±4% for the inner shelf, and 5.5 ± 1% for the outer shelf. The molecular composition of the carbohydrate in the surface sediments also suggested that the inner estuary was rich in terrestrially derived carbohydrates but that their contribution decreased offshore. A relatively high abundance of deoxyhexoses in the estuary and Correspondence to: M. Dai (mdai@xmu.edu.cn) shelf indicated a considerable bacterial source of these carbohydrates, implying that sediment organic matter had undergone extensive degradation and/or transformation during transport. Sediment budget based on calculated regional accumulation rates showed that only ∼50% of the influxes of terrestrial organic carbon were accumulated in the estuary. This relatively low accumulation efficiency of terrestrial organic matter as compared to the total suspended solids (accumulation efficiency ∼73%) suggested significant degradation of the terrestrial organic carbon within the estuarine system after its discharge from the river. This study demonstrated that the combination of the bulk organic matter properties together with the isotopic composition and molecular-level carbohydrate compositions can be an efficient way to track down the source and fate of organic matter in highly dynamic estuarine and coastal systems. The predominance of terrestrially originated organic matter in the sediment and its generally low accumulation efficiency within the estuary is not surprising, and yet it may have important implications in light of the heavy anthropogenic discharges into the Pearl River Estuary during the past thirty years.

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

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