Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Elevated organic carbon pulses persist in estuarine environment after major storm events

Estuaries regulate transport of dissolved organic carbon (DOC) from land to ocean. Export of terrestrial DOC from coastal watersheds is exacerbated by increasing major rainfall and storm events and human activities, leading to pulses of DOC that are shunted through rivers downstream to estuaries. Despite an upward trend of extreme events, the fate of the pulsed terrestrial DOC in estuaries remains unclear. We analyzed the effects of seven major tropical cyclones (TC) from 1999 to 2017 on the quantity and fate of DOC in the Neuse River Estuary (NC, USA). Significant TC-induced increases in DOC were observed throughout the estuary; the increase lasting from around 50 d at head-of-tide to over 6 months in lower estuary. Our results suggest that pulsed terrestrial DOC associated with TCs temporarily overwhelms the estuarine filter's abiotic and biotic degradation capacity under such high flow events, enhancing the shunt of terrestrial carbon to the coastal ocean

Predicting Sources of Dissolved Organic Nitrogen to an Estuary from an Agro-Urban Coastal Watershed

Dissolved organic nitrogen (DON) is the nitrogen (N)-containing component of dissolved organic matter (DOM) and in aquatic ecosystems is part of the biologically reactive nitrogen pool that can degrade water quality in N-sensitive waters. Unlike inorganic N (nitrate and ammonium) DON is comprised of many different molecules of variable reactivity. Few methods exist to track the sources of DON in watersheds. In this study, DOM excitation-emission matrix (EEM) fluorescence of eight discrete DON sources was measured and modeled with parallel factor analysis (PARAFAC) and the resulting model ("FluorMod") was fit to 516 EEMs measured in surface waters from the main stem of the Neuse River and its tributaries, located in eastern North Carolina. PARAFAC components were positively correlated to DON concentration. Principle components analysis (PCA) was used to confirm separation of the eight sources and model validation was achieved by measurement of source samples not included in the model development with an error of 70% of DON was attributed to natural sources, nonpoint sources, such as soil and poultry litter leachates and street runoff, accounted for the remaining 30%. This result was consistent with changes in land use from urbanized Raleigh metropolitan area to the largely agricultural Southeastern coastal plain. Overall, the predicted fraction of nonpoint DON sources was consistent with previous reports of increased organic N inputs in this river basin, which are suspected of impacting the water quality of its estuary

Use of Geospatial, Hydrologic, and Geochemical Modeling to Determine the Influence of Wetland-Derived Organic Matter in Coastal Waters in Response to Extreme Weather Events

Flooding from extreme weather events (EWE), such as hurricanes, exports large amounts of dissolved organic matter (DOM) to both estuaries and coastal waters globally. Hydrologic connectivity of wetlands to adjacent river channels during flood events can potentially have a major control on the DOM exported to coastal waters after EWEs. In this study, a geographic information system based flood model was used to: (1) determine the volume of flooded wetlands in a river corridor following Hurricane Matthew in 2016; (2) compute the resulting volume fluxes of DOM to the Neuse River Estuary-Pamlico Sound (NRE-PS), in eastern North Carolina and (3) use the flood model to quantify the wetland contribution to DOM export. The flood model-derived contributions were validated with a Bayesian Monte Carlo mixing model combining measurements of DOM quality: specific UV Absorbance at 254 nm (SUVA254), spectral slope ratio (SR), and stable isotope ratios of dissolved organic carbon (δ13C-DOC). Results indicated that (1) hydrologic connectivity of the freshwater riparian wetlands caused the wetlands to become the primary source of organic matter (OM) that was exported into the NRE-PS after Matthew and (2) this source lingered in these coastal waters in the months after the storm. Thus, in consideration of the pulse-shunt concept, EWE such as Hurricane Matthew cause pulses of DOM from wetlands, which were the primary source of the OM shunted from the terrestrial environment to the estuary and sound. Wetlands constituted ca. 48% of the annual loading of DOC into the NRE and 16% of DOC loading into the PS over a period of 30 days after Hurricane Matthew. Results were consistent with prior studies in this system, and other coastal ecosystems, that attributed a high reactivity of DOM as the underlying reason for large CO2 releases following EWE. Adapting the pulse-shunt concept to estuaries requires the addition of a “processing” step to account for the DOM to CO2 dynamics, thus a new pulse-shunt process is proposed to incorporate coastal waters. Our results suggest that with increasing frequency and intensity of EWE, strengthening of the lateral transfer of DOM from land to ocean will occur and has the potential to greatly impact coastal carbon cycling

Riverine Discharge and Phytoplankton Biomass Control Dissolved and Particulate Organic Matter Dynamics over Spatial and Temporal Scales in the Neuse River Estuary, North Carolina

Estuaries function as important transporters, transformers, and producers of organic matter (OM). Along the freshwater to saltwater gradient, the composition of OM is influenced by physical and biogeochemical processes that change spatially and temporally, making it difficult to constrain OM in these ecosystems. In addition, many of the environmental parameters (temperature, precipitation, riverine discharge) controlling OM are expected to change due to climate change. To better understand the environmental drivers of OM quantity (concentration) and quality (absorbance, fluorescence), we assessed both dissolved OM (DOM) and particulate OM (POM) spatially, along the freshwater to saltwater gradient and temporally, for a full year. We found seasonal differences in salinity throughout the estuary due to elevated riverine discharge during the late fall to early spring, with corresponding changes to OM quantity and quality. Using redundancy analysis, we found DOM covaried with salinity (adjusted r2 = 0.35, 0.41 for surface and bottom), indicating terrestrial sources of DOM in riverine discharge were the dominant DOM sources throughout the estuary, while POM covaried with environmental indictors of terrestrial sources (turbidity, adjusted r2 = 0.16, 0.23 for surface and bottom) as well as phytoplankton biomass (chlorophyll-a, adjusted r2 = 0.25, 0.14 for surface and bottom). Responses in OM quantity and quality observed during the period of elevated discharge were similar to studies assessing OM quality following extreme storm events suggesting that regional changes in precipitation, as predicted by climate change, will be as important in changing the estuarine OM pool as episodic storm events in the future

Ecosystem Capacity for Microbial Biodegradation of Munitions Compounds and Phenanthrene in Three Coastal Waterways in North Carolina, United States

Munitions compounds (i.e., 2,4,6-trinitrotoluene (TNT), octahy-dro-1,3,5,7-tetranitro-1,3,5,7-tetrazocin (HMX), and hexadydro-1,3,5-trinitro-1,3,5-triazin (RDX), also called energetics) were originally believed to be recalcitrant to microbial biodegradation based on historical groundwater chemical attenuation data and laboratory culture work. More recently, it has been established that natural bacterial assemblages in coastal waters and sediment can rapidly metabolize these organic nitrogen sources and even incorporate their carbon and nitrogen into bacterial biomass. Here, we report on the capacity of natural microbial assemblages in three coastal North Carolina (United States) estuaries to metabolize energetics and phenanthrene (PHE), a proxy for terrestrial aromatic compounds. Microbial assemblages generally had the highest ecosystem capacity (mass of the compound mineralized per average estuarine residence time) for HMX (21-5463 kg) RDX (1.4-5821 kg) PHE (0.29-660 kg) TNT (0.25-451 kg). Increasing antecedent precipitation tended to decrease the ecosystem capacity to mineralize TNT in the Newport River Estuary, and PHE and TNT mineralization were often highest with increasing salinity. There was some evidence from the New River Estuary that increased N-demand (due to a phytoplankton bloom) is associated with increased energetic mineralization rates. Using this type of analysis to determine the ecosystem capacity to metabolize energetics can explain why these compounds are rarely detected in seawater and marine sediment, despite the known presence of unexploded ordnance or recent use in military training exercises. Overall, measuring the ecosystem capacity may help predict the effects of climate change (warming and altered precipitation patterns) and other perturbations on exotic compound fate and transport within ecosystems and provide critical information for managers and decision-makers to develop management strategies based on these changes

Lingering Carbon Cycle Effects of Hurricane Matthew in North Carolina's Coastal Waters

In 2016, Hurricane Matthew accounted for 25% of the annual riverine C loading to the Neuse River Estuary-Pamlico Sound, in eastern North Carolina. Unlike inland watersheds, dissolved organic carbon (DOC) was the dominant component of C flux from this coastal watershed and stable carbon isotope and chromophoric dissolved organic matter evidence indicated the estuary and sound were dominated by wetland-derived terrigenous organic matter sources for several months following the storm. Persistence of wetland-derived DOC enabled its degradation to carbon dioxide (CO2), which was supported by sea-to-air CO2 fluxes measured in the sound weeks after the storm. Under future increasingly extreme weather events such as Hurricane Matthew, and most recently Hurricane Florence (September 2018), degradation of terrestrial DOC in floodwaters could increase flux of CO2 from estuaries and coastal waters to the atmosphere

A landscape perspective of Holocene organic carbon cycling in coastal SW Greenland lake-catchments

Arctic organic carbon (OC) stores are substantial and have accumulated over millennia as a function of changes in climate and terrestrial vegetation. Arctic lakes are also important components of the regional C-cycle as they are sites of OC production and CO2 emissions but also store large amounts of OC in their sediments. This sediment OC pool is a mixture derived from terrestrial and aquatic sources, and sediment cores can therefore provide a long-term record of the changing interactions between lakes and their catchments in terms of nutrient and C transfer. Sediment carbon isotope composition (δ13C), C/N ratio and organic C accumulation rates (C AR) of 14C-dated cores covering the last ∼10,000 years from six lakes close to Sisimiut (SW Greenland) are used to determine the extent to which OC dynamics reflect climate relative to lake or catchment characteristics. Sediment δ13C ranges from −19 to −32‰ across all lakes, while C/N ratios are 20 (mean = 12), values that indicate a high proportion of the organic matter is from autochthonous production but with a variable terrestrial component. Temporal trends in δ13C are variable among lakes, with neighbouring lakes showing contrasting profiles, indicative of site-specific OC processing. The response of an individual lake reflects its morphometry (which influences benthic primary production), the catchment:lake ratio, and catchment relief, lakes with steeper catchments sequester more carbon. The multi-site, landscape approach used here highlights the complex response of individual lakes to climate and catchment disturbance, but broad generalisations are possible. Regional Neoglacial cooling (from ∼5000 cal yr BP) influenced the lateral transfer of terrestrial OC to lakes, with three lakes showing clear increases in OC accumulation rate. The lakes likely switched from being autotrophic (i.e. net ecosystem production > ecosystem respiration) in the early Holocene to being heterotrophic after 5000 cal yr BP as terrestrial OC transfer increased

Optical proxies for terrestrial dissolved organic matter in estuaries and coastal waters

Dissolved organic matter (DOM) absorbance and fluorescence were used as optical proxies to track terrestrial DOM fluxes through estuaries and coastal waters by comparing models developed for several coastal ecosystems. Key to using these optical properties is validating and calibrating them with chemical measurements, such as lignin-derived phenols-a proxy to quantify terrestrial DOM. Utilizing parallel factor analysis (PARAFAC), and comparing models statistically using the OpenFluor database (http://www.openfluor.org) we have found common, ubiquitous fluorescing components which correlate most strongly with lignin phenol concentrations in several estuarine and coastal environments. Optical proxies for lignin were computed for the following regions: Mackenzie River Estuary, Atchafalaya River Estuary (ARE), Charleston Harbor, Chesapeake Bay, and Neuse River Estuary (NRE) (all in North America). The slope of linear regression models relating CDOM absorption at 350 nm (a350) to DOC and to lignin, varied 5-10-fold among systems. Where seasonal observations were available from a region, there were distinct seasonal differences in equation parameters for these optical proxies. The variability appeared to be due primarily to river flow into these estuaries and secondarily to biogeochemical cycling of DOM within them. Despite the variability, overall models using single linear regression were developed that related dissolved organic carbon (DOC) concentration to CDOM (DOC = 40 ± 2 × a350 + 138 ± 16; R2 = 0.77; N = 130) and lignin (Σ8) to CDOM (Σ8 = 2.03 ± 0.07 × a350 - 0.47 ± 0.59; R2 = 0.87; N = 130). This wide variability suggested that local or regional optical models should be developed for predicting terrestrial DOM flux into coastal oceans and taken into account when upscaling to remote sensing observations and calibrations