A probabilistic assessment of calcium carbonate export and dissolution in the modern ocean

The marine cycle of calcium carbonate (CaCO3) is an important element of the carbon cycle and co-governs the distribution of carbon and alkalinity within the ocean. However, CaCO3 export fluxes and mechanisms governing CaCO3 dissolution are highly uncertain. We present an observationally constrained, probabilistic assessment of the global and regional CaCO3 budgets. Parameters governing pelagic CaCO3 export fluxes and dissolution rates are sampled using a Monte Carlo scheme to construct a 1000-member ensemble with the Bern3D ocean model. Ensemble results are constrained by comparing simulated and observation-based fields of excess dissolved calcium carbonate (TA*). The minerals calcite and aragonite are modelled explicitly and ocean–sediment fluxes are considered. For local dissolution rates, either a strong or a weak dependency on CaCO3 saturation is assumed. In addition, there is the option to have saturation-independent dissolution above the saturation horizon. The median (and 68 % confidence interval) of the constrained model ensemble for global biogenic CaCO3 export is 0.90 (0.72–1.05) Gt C yr−1, that is within the lower half of previously published estimates (0.4–1.8 Gt C yr−1). The spatial pattern of CaCO3 export is broadly consistent with earlier assessments. Export is large in the Southern Ocean, the tropical Indo–Pacific, the northern Pacific and relatively small in the Atlantic. The constrained results are robust across a range of diapycnal mixing coefficients and, thus, ocean circulation strengths. Modelled ocean circulation and transport timescales for the different set-ups were further evaluated with CFC11 and radiocarbon observations. Parameters and mechanisms governing dissolution are hardly constrained by either the TA* data or the current compilation of CaCO3 flux measurements such that model realisations with and without saturation-dependent dissolution achieve skill. We suggest applying saturation-independent dissolution rates in Earth system models to minimise computational costs.

Predicting the onset of psychosis in patients at clinical high risk: practical guide to probabilistic prognostic reasoning

Prediction of psychosis in patients at clinical high risk (CHR) has become a mainstream focus of clinical and research interest worldwide. When using CHR instruments for clinical purposes, the predicted outcome is but only a probability; and, consequently, any therapeutic action following the assessment is based on probabilistic prognostic reasoning. Yet, probabilistic reasoning makes considerable demands on the clinicians. We provide here a scholarly practical guide summarising the key concepts to support clinicians with probabilistic prognostic reasoning in the CHR state. We review risk or cumulative incidence of psychosis in, person-time rate of psychosis, Kaplan-Meier estimates of psychosis risk, measures of prognostic accuracy, sensitivity and specificity in receiver operator characteristic curves, positive and negative predictive values, Bayes’ theorem, likelihood ratios, potentials and limits of real-life applications of prognostic probabilistic reasoning in the CHR state. Understanding basic measures used for prognostic probabilistic reasoning is a prerequisite for successfully implementing the early detection and prevention of psychosis in clinical practice. Future refinement of these measures for CHR patients may actually influence risk management, especially as regards initiating or withholding treatment.

Intervals for the assessment of measurement agreement: Similarities, differences, and consequences of incorrect interpretations

Several intervals have been proposed to quantify the agreement of two methods intended to measure the same quantity in the situation where only one measurement per method and subject is available. The limits of agreement are probably the most well-known among these intervals, which are all based on the differences between the two measurement methods. The different meanings of the intervals are not always properly recognized in applications. However, at least for small-to-moderate sample sizes, the differences will be substantial. This is illustrated both using the width of the intervals and on probabilistic scales related to the definitions of the intervals. In particular, for small-to-moderate sample sizes, it is shown that limits of agreement and prediction intervals should not be used to make statements about the distribution of the differences between the two measurement methods or about a plausible range for all future differences. Care should therefore be taken to ensure the correct choice of the interval for the intended interpretation.