Quantifying precision and accuracy of measurements of dissolved inorganic carbon stable isotopic composition using continuous-flow isotope-ratio mass spectrometry.

RATIONALE: We describe an analytical procedure that allows sample collection and measurement of carbon isotopic composition (δ(13)C(V-PDB) value) and dissolved inorganic carbon concentration, [DIC], in aqueous samples without further manipulation post field collection. By comparing outputs from two different mass spectrometers, we quantify with the statistical rigour uncertainty associated with the estimation of an unknown measurement. This is rarely undertaken, but it is needed to understand the significance of field data and to interpret quality assurance exercises. METHODS: Immediate acidification of field samples during collection in evacuated, pre-acidified vials removed the need for toxic chemicals to inhibit continued bacterial activity that might compromise isotopic and concentration measurements. Aqueous standards mimicked the sample matrix and avoided headspace fractionation corrections. Samples were analysed using continuous-flow isotope-ratio mass spectrometry, but for low DIC concentration the mass spectrometer response could be non-linear. This had to be corrected for. RESULTS: Mass spectrometer non-linearity exists. Rather than estimating precision as the repeat analysis of an internal standard, we have adopted inverse linear calibrations to quantify the precision and 95% confidence intervals (CI) of the δ(13)C(DIC) values. The response for [DIC] estimation was always linear. For 0.05-0.5 mM DIC internal standards, however, changes in mass spectrometer linearity resulted in estimations of the precision in the δ(13)C(VPDB) value of an unknown ranging from ± 0.44‰ to ± 1.33‰ (mean values) and a mean 95% CI half-width of ±1.1-3.1‰. CONCLUSIONS: Mass spectrometer non-linearity should be considered in estimating uncertainty in measurement. Similarly, statistically robust estimates of precision and accuracy should also be adopted. Such estimations do not inhibit research advances: our consideration of small-scale spatial variability at two points on a small order river system demonstrates field data ranges larger than the precision and uncertainties. However, without such statistical quantification, exercises such as inter-lab calibrations are less meaningful.

Flexible regression models over river networks.

Many statistical models are available for spatial data but the vast majority of these assume that spatial separation can be measured by Euclidean distance. Data which are collected over river networks constitute a notable and commonly occurring exception, where distance must be measured along complex paths and, in addition, account must be taken of the relative flows of water into and out of confluences. Suitable models for this type of data have been constructed based on covariance functions. The aim of the paper is to place the focus on underlying spatial trends by adopting a regression formulation and using methods which allow smooth but flexible patterns. Specifically, kernel methods and penalized splines are investigated, with the latter proving more suitable from both computational and modelling perspectives. In addition to their use in a purely spatial setting, penalized splines also offer a convenient route to the construction of spatiotemporal models, where data are available over time as well as over space. Models which include main effects and spatiotemporal interactions, as well as seasonal terms and interactions, are constructed for data on nitrate pollution in the River Tweed. The results give valuable insight into the changes in water quality in both space and time.