Results of an aqueous source term model for a radiological risk assessment of the Drigg LLW Site, U.K.

A radionuclide source term model has been developed which simulates the biogeochemical evolution of the Drigg low level waste (LLW) disposal site. The DRINK (DRIgg Near field Kinetic) model provides data regarding radionuclide concentrations in groundwater over a period of 100,000 years, which are used as input to assessment calculations for a groundwater pathway. The DRINK model also provides input to human intrusion and gaseous assessment calculations through simulation of the solid radionuclide inventory. These calculations are being used to support the Drigg post closure safety case. The DRINK model considers the coupled interaction of the effects of fluid flow, microbiology, corrosion, chemical reaction, sorption and radioactive decay. It represents the first direct use of a mechanistic reaction-transport model in risk assessment calculations.

Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

The DigiBog model of peatland development 1: rationale, conceptual model, and hydrological basis

Using a literature review, we argue that new models of peatland development are needed. Many existing models do not account for potentially important ecohydrological feedbacks, and/or ignore spatial structure and heterogeneity. Existing models, including those that simulate a near total loss of the northern peatland carbon store under a warming climate, may produce misleading results because they rely upon oversimplified representations of ecological and hydrological processes. In this, the first of a pair of papers, we present the conceptual framework for a model of peatland development, DigiBog, which considers peatlands as complex adaptive systems. DigiBog accounts for the interactions between the processes which govern litter production and peat decay, peat soil hydraulic properties, and peatland water-table behaviour, in a novel and genuinely ecohydrological manner. DigiBog consists of a number of interacting submodels, each representing a different aspect of peatland ecohydrology. Here we present in detail the mathematical and computational basis, as well as the implementation and testing, of the hydrological submodel. Remaining submodels are described and analysed in the accompanying paper. Tests of the hydrological submodel against analytical solutions for simple aquifers were highly successful: the greatest deviation between DigiBog and the analytical solutions was 2·83%. We also applied the hydrological submodel to irregularly shaped aquifers with heterogeneous hydraulic properties—situations for which no analytical solutions exist—and found the model's outputs to be plausible.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Decay to equilibrium for jump processes with heavy tails

The case is made for a more careful analysis of the large time asymptotic of infinite particle systems in the thermodynamic limit beyond zero density. The insufficiency of current analysis even in the model case of free particles is demonstrated. Recent advances based on more sophisticated analytical tools like functions of mean variation and Hardy spaces are sketched.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Aerosol microphysics simulations of the Mt.~Pinatubo eruption with the UM-UKCA composition-climate model

We use a stratosphere–troposphere composition–climate model with interactive sulfur chemistry and aerosol microphysics, to investigate the effect of the 1991 Mount Pinatubo eruption on stratospheric aerosol properties. Satellite measurements indicate that shortly after the eruption, between 14 and 23 Tg of SO2 (7 to 11.5 Tg of sulfur) was present in the tropical stratosphere. Best estimates of the peak global stratospheric aerosol burden are in the range 19 to 26 Tg, or 3.7 to 6.7 Tg of sulfur assuming a composition of between 59 and 77 % H2SO4. In light of this large uncertainty range, we performed two main simulations with 10 and 20 Tg of SO2 injected into the tropical lower stratosphere. Simulated stratospheric aerosol properties through the 1991 to 1995 period are compared against a range of available satellite and in situ measurements. Stratospheric aerosol optical depth (sAOD) and effective radius from both simulations show good qualitative agreement with the observations, with the timing of peak sAOD and decay timescale matching well with the observations in the tropics and mid-latitudes. However, injecting 20 Tg gives a factor of 2 too high stratospheric aerosol mass burden compared to the satellite data, with consequent strong high biases in simulated sAOD and surface area density, with the 10 Tg injection in much better agreement. Our model cannot explain the large fraction of the injected sulfur that the satellite-derived SO2 and aerosol burdens indicate was removed within the first few months after the eruption. We suggest that either there is an additional alternative loss pathway for the SO2 not included in our model (e.g. via accommodation into ash or ice in the volcanic cloud) or that a larger proportion of the injected sulfur was removed via cross-tropopause transport than in our simulations. We also critically evaluate the simulated evolution of the particle size distribution, comparing in detail to balloon-borne optical particle counter (OPC) measurements from Laramie, Wyoming, USA (41° N). Overall, the model captures remarkably well the complex variations in particle concentration profiles across the different OPC size channels. However, for the 19 to 27 km injection height-range used here, both runs have a modest high bias in the lowermost stratosphere for the finest particles (radii less than 250 nm), and the decay timescale is longer in the model for these particles, with a much later return to background conditions. Also, whereas the 10 Tg run compared best to the satellite measurements, a significant low bias is apparent in the coarser size channels in the volcanically perturbed lower stratosphere. Overall, our results suggest that, with appropriate calibration, aerosol microphysics models are capable of capturing the observed variation in particle size distribution in the stratosphere across both volcanically perturbed and quiescent conditions. Furthermore, additional sensitivity simulations suggest that predictions with the models are robust to uncertainties in sub-grid particle formation and nucleation rates in the stratosphere.