Comment on acp-2021-973

This study examines the sensitivity of the posterior mean to change in the prior assumptions. Three plausible choices of prior which include informative, relative-non informative and non-informative priors are considered. The paper considers information level for a prior to cause a notable change in the Bayesian posterior point estimate. The study develops a framework for evaluating a bound for a robust posterior point estimate. The Ellipsoid Bound theorem is employed to derive the Ellipsoid Bound for an independent normal gamma prior distribution. The proposed modification ellipsoid bound for the large prior was establised by varrying different variance co-variance sizes for the independent normal gamma prior. This bound represents the range for the posterior mean when is insensitive and when it’s sensitive in both location and spread. The result shows that; for a large prior parameter value (greater than the OLS estimate) with a positive definite prior variance covariance matrix, and prior parameter values interval which contains the OLS estimate then, the posterior estimate will be less than both the OLS and the prior estimates. Similarly, if the lower bound of the prior parameter values range is greater than the OLS estimate then: The posterior estimate will be greater than the OLS estimate but smaller than the prior estimate. Furthermore, it is observed that no matter the degrees of confidence in the prior values, data information is powerful enough to modify it.

[1] We estimate monthly continental-scale CO emissions for 2006 by optimally fitting prior emissions used by the GEOS-Chem chemistry transport model to retrieved profile measurements of CO from the Measurement Of Pollution In The Troposphere (MOPITT) satellite instrument. We focus on the range of emission estimates obtained by using different versions of the MOPITT profile data, and by better describing enhanced vertical mixing of emissions from wildfires. We find that annual posterior CO emissions estimates for 2006 range from 1003 to 1180 Tg CO, within the range of prior estimates (1243 ± 617 Tg CO). We generally find larger differences in posterior CO emissions from using different versions of the MOPITT data than from improving the description of wildfires, with the exception of fires over Indonesia. Posterior emissions over regions with wildfires have a large seasonal cycle, as expected, which can be substantially different from prior emission estimates. We find GFEDv2 prior emissions underestimate the duration of the biomass burning season for North Africa by as much as 1 month. We also find posterior emissions over Indonesia are a factor of 2 higher than prior emissions (83 ± 42 Tg CO) in 2006 due to widespread fires during July–December. Posterior emissions over Canada during 2006 are a factor of 2–3 higher than prior emissions (9 ± 4.6 Tg CO). We also find a seasonal cycle of CO emissions over North America and Europe, in agreement with previous studies, which is not described by prior emissions.

Abstract. Numerical atmospheric dispersion models (ADMs) are used for predicting the health and environmental consequences of nuclear accidents in order to anticipate countermeasures necessary to protect the populations. However, these simulations suffer from significant uncertainties, arising in particular from input data: weather conditions and source term. Meteorological ensembles are already used operationally to characterize uncertainties in weather predictions. Combined with dispersion models, these ensembles produce different scenarios of radionuclide dispersion, called “members”, representative of the variety of possible forecasts. In this study, the fine-scale operational weather ensemble AROME-EPS (Applications of Research to Operations at Mesoscale-Ensemble Prediction System) from Météo-France is coupled with the Gaussian puff model pX developed by the IRSN (French Institute for Radiation Protection and Nuclear Safety). The source term data are provided at 10 min resolution by the Orano La Hague reprocessing plant (RP) that regularly discharges 85Kr during the spent nuclear fuel reprocessing process. In addition, a continuous measurement campaign of 85Kr air concentration was recently conducted by the Laboratory of Radioecology in Cherbourg (LRC) of the IRSN, within 20 km of the RP in the North-Cotentin peninsula, and is used for model evaluation. This paper presents a probabilistic approach to study the meteorological uncertainties in dispersion simulations at local and medium distances (2–20 km). First, the quality of AROME-EPS forecasts is confirmed by comparison with observations from both Météo-France and the IRSN. Then, the probabilistic performance of the atmospheric dispersion simulations was evaluated by comparison to the 85Kr measurements carried out during a period of 2 months, using two probabilistic scores: relative operating characteristic (ROC) curves and Peirce skill score (PSS). The sensitivity of dispersion results to the method used for the calculation of atmospheric stability and associated Gaussian dispersion standard deviations is also discussed. A desirable feature for a model used in emergency response is the ability to correctly predict exceedance of a given value (for instance, a dose guide level). When using an ensemble of simulations, the “decision threshold” is the number of members predicting an event above which this event should be considered probable. In the case of the 16-member dispersion ensemble used here, the optimal decision threshold was found to be 3 members, above which the ensemble better predicts the observed peaks than the deterministic simulation. These results highlight the added value of ensemble forecasts compared to a single deterministic one and their potential interest in the decision process during crisis situations.

Explosive volcanic eruptions can produce large masses of tephra that are transported over long distances, with potential impacts on the ground and to aircraft. Volcanic Ash Advisory Centers (VAACs) provide advice to aviation following an eruption, using atmospheric dispersion models, initialized with eruption source parameters (ESPs) and driven by forecast meteorological data. In this paper, we develop a framework for producing probabilistic forecasts incorporating uncertainty in these inputs. Meteorological uncertainty is typically provided as an ensemble of numerical weather prediction (NWP) data and ESPs include eruption plume height and mass eruption rate (MER); these are linked by atmospheric processes, and their relationship can be modeled by Bayesian regression to quantify their uncertainties. These uncertainties can be propagated through the model to compute probabilistic quantities of ash concentration. The linearity of the advection‐diffusion‐sedimentation (ADS) equation solved by dispersion models allows us to run a single simulation for each of the NWP ensemble members, and then rescale the results to any combination of MER (or height) and emission profile. This gives a computational speed‐up compared to conventional approaches of computing every combination of ESPs and NWP. We demonstrate our method in the operational setting of the London VAAC, using the UK Met Office's NAME dispersion model, although it can be applied to any eruption scenario using any dispersion model that solves the ADS equation. The major source of uncertainty for this case study arises from the MER (due to limited variation in NWP data), although both sources of uncertainty are significant.

Nitrous Oxide (N₂O) is a long-lived and highly potent greenhouse gas, recognized as the third most significant contributor to radiative forcing, with a substantial proportion of its emissions originating from a large area source, agricultural soils, due to the application of mineral fertilizer and livestock manure. As part of the Horizon Europe project EYE-CLIMA, we performed atmospheric inversions to improve the estimates of N2O fluxes across Europe at two spatial resolution scales. The first inversion, spanning the period from 2005 to 2023, was performed at a resolution of 0.5° × 0.5°. The second inversion, covering the period from 2018 to 2023, was carried out at a higher resolution of 0.2° × 0.2°. The method integrates the Community Inversion Framework (CIF) with the Lagrangian particle dispersion model, FLEXPART v11 (CIF-FLEXPART), to estimate N2O emissions using ground-based measurements of atmospheric N2O concentrations. Comprehensive prior N2O flux estimates were generated by incorporating monthly data from key source categories, including agriculture, other anthropogenic activities such as combustion, industry or waste treatment, biomass burning, natural soils, and ocean fluxes. For consistency, observed atmospheric concentrations of N2O were sourced from a newly harmonized dataset for Europe, compiled collaboratively by EYE-CLIMA and the Horizon Europe projects AVENGERS and PARIS.Following the inversion, the modelled concentrations showed improved agreement with observations, capturing the seasonal cycle and increasing trend from 2005 onward. Statistical analyses revealed high correlations between modelled and observed concentrations at most stations. The N2O emissions from the inversion differ from the prior estimates in intensity and spatial distribution with increased emissions in regions of specifically high agricultural activity and reductions in other areas. Monthly flux variations exhibited a consistent seasonal cycle, with peak emissions occurring in early summer (May–June) and lower emissions during winter months. Across all years, total posterior emissions were lower than the prior estimates. While the phase of the seasonal cycle remained consistent from year to year, interannual variability in the amplitude was observed.

Ensemble-type numerical uncertainty information from single model integrations

This paper aims to study the state estimation problem under the stochastic event-triggered (SET) schedule. A posterior-based SET mechanism is proposed, which determines whether to transmit data by the effect of the measurement on the posterior estimate. Since this SET mechanism considers the whole posterior probability density function, it has better information screening capability and utilization than the existing SET mechanisms that only consider the first-order moment information of measurement and prior estimate. Then, based on the proposed SET mechanism, the corresponding exact minimum mean square error estimator is derived by Bayes rule. Moreover, the prediction error covariance of the estimator is proved to be bounded under moderate conditions. Meanwhile, the upper and lower bounds on the average communication rate are also analyzed. Finally, two different systems are employed to show the effectiveness and advantages of the proposed methods.

Numerical simulation of particle trajectory and atmospheric dispersion has been performed for an airborne accidental release from a nuclear power plant site. A Long‐range Particle transport and Dispersion Model (LPDM) based on a Lagrangian approach is developed and tested in this work. The Lagrangian transport/dispersion model is directly coupled with an atmospheric prediction model, RAMS (Regional Atmospheric Modeling System), to provide necessary meteorological fields in a three‐dimensional domain. An advantage of this direct coupling is that the meteorological data generated by RAMS can be used directly for trajectory calculations without storage, thus reducing the CPU time consumed in the data storage and retrieval. This effort was done to be able to use this directly coupled modelling system for real‐time predictions in case of an accidental release from a potential site.The simulated Lagrangian trajectories were compared with those obtained using observed hourly weather data obtained from an on‐site meteorological tower. The results indicated that this one‐way coupling between LPDM‐RAMS provided almost identical trajectories when compared with those obtained using LPDM alone driven by hourly observed wind data. The comparison demonstrated the reliability of the RAMS meteorological predictions for the site under consideration. The comparison also indicated that LPDM (run in a stand alone mode), with hourly‐observed wind data, could also be used for trajectory calculations over flat terrain.The model was developed on a parallel processing computer (SGI workstation, ORIGIN 2000 computer with eight processors) for use in real‐time forecast mode. The computational time was about one‐third of the simulation time, while using four processors. The model options need to be explored to reduce the computational time further and test its performance for real‐time atmospheric dispersion applications. Copyright © 2009 Royal Meteorological Society

3 experiments investigated the effects on posterior probability estimates of: (1) prior probabilities, amount of data, and diagnostic impact of the data; (2) payoffs; and (3) response modes. Ss usually behaved conservatively, i.e., the difference between their prior and posterior probability estimates was less than that prescribed by Bayes' theorem. Conservatism was unaffected by prior probabilities, remained constant as the amount of data increased, and decreased as the diagnostic value of each datum decreased. More learning occurred under payoff than under nonpayoff conditions and between-S variance was less under payoff conditions. Estimates were most nearly Bayesian under the (formally inappropriate) linear payoff, but considerable overestimation resulted; the log payoff condition yielded less conservatism than the quadratic payoff. Estimates were most nearly Bayesian when Ss estimated odds on a logarithmic scale.

Numerical models of atmospheric dispersion are used for predicting the health and environmental consequences of nuclear accidents, in order to anticipate the countermeasures necessary to protect the populations. However, the simulations of these models suffer from significant uncertainties, arising in particular from input data: weather conditions and source term. To characterize weather uncertainties, it is essential to combine a well-known source term data and meteorological ensembles to generate ensemble dispersion simulations which has the potential to produce different possible scenarios of radionuclides dispersion during emergency situations. In this study, the fine-scale operational weather ensemble AROME-EPS from Météo-France is coupled to the Gaussian puff model pX developed by French Institute for Radiation Protection and Nuclear Safety (IRSN). The source term data is provided by Orano La Hague reprocessing plant (RP) that regularly discharges 85Kr during the spent nuclear fuel reprocessing process. Then, to evaluate the dispersion results, a continuous measurement campaign of 85Kr air concentration was recently conducted by the Laboratory of Radioecology in Cherbourg (LRC) of IRSN, around RP in the North-Cotentin peninsula. This paper presents a probabilistic approach to study the meteorological uncertainties in dispersion simulations at local and medium distances (2–20 km). As first step, the quality of AROME-EPS forecasts is confirmed by comparison with observations from both Météo-France and IRSN. The following step is to assess the probabilistic performance of the dispersion ensemble simulation, as well as the sensitivity of dispersion results to the method used to calculate atmospheric stability fields and their associated dispersion Gaussian standard deviations. Two probabilistic scores are used: Relative Operating Characteristic (ROC) curves and Peirce Skill Score (PSS). The results show that the stability diagnostics of Pasquill provides better dispersion simulations. In addition, the ensemble dispersion performs better than deterministic one, and the optimum decision threshold (PSS maximum) is 3 members. These results highlight the added value of ensemble forecasts compared to a single deterministic one, and their potential interest in the decision process during crisis situations.

Numerical models of atmospheric dispersion are used for predicting the health and environmental consequences of nuclear accidents, in order to anticipate the countermeasures necessary to protect the populations. However, the simulations of these models suffer from significant uncertainties, arising in particular from input data: weather conditions and source term. To characterize weather uncertainties, it is essential to combine a well-known source term data and meteorological ensembles to generate ensemble dispersion simulations which has the potential to produce different possible scenarios of radionuclides dispersion during emergency situations. In this study, the fine-scale operational weather ensemble AROME-EPS from Météo-France is coupled to the Gaussian puff model pX developed by French Institute for Radiation Protection and Nuclear Safety (IRSN). The source term data is provided by Orano La Hague reprocessing plant (RP) that regularly discharges 85Kr during the spent nuclear fuel reprocessing process. Then, to evaluate the dispersion results, a continuous measurement campaign of 85Kr air concentration was recently conducted by the Laboratory of Radioecology in Cherbourg (LRC) of IRSN, around RP in the North-Cotentin peninsula. This paper presents a probabilistic approach to study the meteorological uncertainties in dispersion simulations at local and medium distances (2–20 km). As first step, the quality of AROME-EPS forecasts is confirmed by comparison with observations from both Météo-France and IRSN. The following step is to assess the probabilistic performance of the dispersion ensemble simulation, as well as the sensitivity of dispersion results to the method used to calculate atmospheric stability fields and their associated dispersion Gaussian standard deviations. Two probabilistic scores are used: Relative Operating Characteristic (ROC) curves and Peirce Skill Score (PSS). The results show that the stability diagnostics of Pasquill provides better dispersion simulations. In addition, the ensemble dispersion performs better than deterministic one, and the optimum decision threshold (PSS maximum) is 3 members. These results highlight the added value of ensemble forecasts compared to a single deterministic one, and their potential interest in the decision process during crisis situations.

This paper develops a Bayes model for step-stress accelerated life testing. The failure times at each stress level are exponentially distributed, but strict adherence to a time-transformation function is not required. Rather, prior information is used to define indirectly a multivariate prior distribution for the failure rates at the various stress levels. Our prior distribution preserves the natural ordering of the failure rates in both the prior and posterior estimates. Methods are developed for Bayes point estimates as well as for making probability statements for use-stress life parameters. The approach is illustrated with an example.

Eruption source parameters (ESPs) are crucial for characterising volcanic eruptions and are essential inputs to numerical models used for hazard assessment. Key ESPs of explosive volcanic eruptions include plume height, mass eruption rate, eruption duration, and grain-size distribution. Some of these ESPs can be directly observed during an eruption, but others are difficult to measure in real-time, or indeed, accurately and precisely quantify afterwards. Estimates of ESPs for eruptions that cannot be observed, for example, due to the remote location of a volcano or poor weather conditions, are often defined using expert judgement and data from past eruptions, both from the volcano of interest and analogue volcanoes farther afield. Analysis of such information is time intensive and difficult, particularly during eruption response. These difficulties have resulted in the production of datasets to aid quick identification of ESPs prior to or during an eruption for use in operational response settings such as those at volcano observatories and Volcanic Ash Advisory Centres. These resources include the Mastin et al. (2009a) ESP dataset and the Catalogue of Icelandic Volcanoes and European Catalogue of Volcanoes aviation tables. Here, we review and compare these resources, which take different approaches to assigning ESPs. We identify future areas for development of these resources, highlighting the need for frequent updates as more knowledge of volcanic activity is gained and as modelling capabilities and requirements change.

A Lagrangian atmospheric dispersion model combining a three dimensional prognostic sea‐land breeze model has been developed and applied to the analysis of mesoscale atmospheric dispersion of radiological releases from the nuclear power plants in mountainous coastal regions. The hydrostatic primitive equations in the terrain‐following coordinate system were used in the sea‐land breeze model, and a Markov chain process and a kernel density estimator were used in the Lagrangian particle dispersion model. In this study, the mesoscale atmospheric circulation and particle dispersion simulations around the Wolsung nuclear power site located on the east coastline of Korea were carried out for two synoptic weather conditions on a clear day in summer by using the developed models. The simulated results showed that the atmospheric dispersions were affected by wind directions of sea breeze and land breeze according to synoptic weather conditions. And the simulated results have very good agreement with the observations.

ABSTRACTGround‐penetrating radar (GPR) data affected by waveguide dispersion are not straightforward to analyse. Therefore, waveguide dispersed common midpoint measurements are typically interpreted using so‐called dispersion curves, which describe the phase velocity as a function of frequency. These dispersion curves are typically evaluated with deterministic optimization algorithms that derive the dielectric properties of the subsurface as well as the location and depth of the respective layers. However, these methods do not provide estimates of the uncertainty of the inferred subsurface properties. Here, we applied a formal Bayesian inversion methodology using the recently developed DiffeRential Evolution Adaptive Metropolis algorithm. This Markov Chain Monte Carlo simulation method rapidly estimates the (non‐linear) parameter uncertainty and helps to treat the measurement error explicitly. We found that the frequency range used in the inversion has an important influence on the posterior parameter estimates, essentially because parameter sensitivity varies with measurement frequency. Moreover, we established that the measurement error associated with the dispersion curve is frequency dependent and that the estimated model parameters become severely biased if this frequency‐dependent nature of the measurement error is not properly accounted for. We estimated these frequency‐dependent measurement errors together with the model parameters using the algorithm. The posterior distribution of the model parameters derived in this way compared well with inversion results for a reduced frequency bandwidth which is an alternative, yet subjective method to reduce the bias introduced by this frequency‐dependent measurement error. Altogether, our inversion procedure provides an integrated and objective methodology for the analysis of dispersive GPR data and appropriately treats the measurement error and parameter uncertainty.