scholarly journals Objectified quantification of uncertainties in Bayesian atmospheric inversions

2015 ◽  
Vol 8 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
J.-L. Bonne ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Spatial Scales ◽  
Surface Fluxes ◽  
Large Set ◽  
Error Statistics ◽  
Observation Operator ◽  
Probability Of Occurrence ◽  
Error Distributions ◽  
The Impact ◽  
Atmospheric Inversions

Abstract. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

scholarly journals Objectified quantification of uncertainties in Bayesian atmospheric inversions

2014 ◽  
Vol 7 (4) ◽  
pp. 4777-4827 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
J.-L. Bonne ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Spatial Scales ◽  
Surface Fluxes ◽  
Error Statistics ◽  
Observation Operator ◽  
Aggregation Pattern ◽  
Error Distributions ◽  
The Impact ◽  
Meso Scale ◽  
Atmospheric Inversions

Abstract. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. At the meso-scale, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results and enhance the classical Bayesian inversion framework through a marginalization on all the plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is complicated and not explicitly describable. We then carry out a Monte-Carlo sampling relying on an approximation of the probability of occurence of the error distributions. This approximation is deduced from the well-tested algorithm of the Maximum of Likelihood. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly includes the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of emission aggregation pattern and sampling protocol in order to reduce the computation costs of the method. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the meso-scale with real observation sites in Eurasia. Observing System Simulation Experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted gas. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionnaly, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission regions reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyze. These scales proved to be consistent with the chosen aggregation patterns.

scholarly journals Towards better error statistics for atmospheric inversions of methane surface fluxes

2013 ◽  
Vol 13 (14) ◽  
pp. 7115-7132 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
S. Conil ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Transport Model ◽  
Vertical Mixing ◽  
Real Data ◽  
Surface Fluxes ◽  
Error Statistics ◽  
The North ◽  
Error Covariance ◽  
Methane Fluxes ◽  
General Statistical

Abstract. We adapt general statistical methods to estimate the optimal error covariance matrices in a regional inversion system inferring methane surface emissions from atmospheric concentrations. Using a minimal set of physical hypotheses on the patterns of errors, we compute a guess of the error statistics that is optimal in regard to objective statistical criteria for the specific inversion system. With this very general approach applied to a real-data case, we recover sources of errors in the observations and in the prior state of the system that are consistent with expert knowledge while inferred from objective criteria and with affordable computation costs. By not assuming any specific error patterns, our results depict the variability and the inter-dependency of errors induced by complex factors such as the misrepresentation of the observations in the transport model or the inability of the model to reproduce well the situations of steep gradients of concentrations. Situations with probable significant biases (e.g., during the night when vertical mixing is ill-represented by the transport model) can also be diagnosed by our methods in order to point at necessary improvement in a model. By additionally analysing the sensitivity of the inversion to each observation, guidelines to enhance data selection in regional inversions are also proposed. We applied our method to a recent significant accidental methane release from an offshore platform in the North Sea and found methane fluxes of the same magnitude than what was officially declared.

scholarly journals Towards better error statistics for atmospheric inversions of methane surface fluxes

2013 ◽  
Vol 13 (2) ◽  
pp. 3735-3782
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
S. Conil ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Transport Model ◽  
Real Data ◽  
Surface Fluxes ◽  
Mass Composition ◽  
Error Statistics ◽  
The North ◽  
Error Covariance ◽  
Data Framework ◽  
General Statistical

Abstract. In this study, we adapt general statistical methods to compute the optimal error covariance matrices in a regional inversion system inferring methane surface emissions from atmospheric concentrations. We optimally estimate the error statistics with a minimal set of physical hypotheses on the patterns of errors. With this very general approach applied within a real-data framework, we recover sources of errors in the observations and in the prior state of the system that are consistent with expert knowledge. By not assuming any specific error patterns, our results show the variability and the inter-dependency of errors induced by complex factors such as the mis-representation of the observations in the transport model or the inability of the model to reproduce well the situations of steep gradients of air mass composition in the atmosphere. By analyzing the sensitivity of the inversion to each observation, ways to improve data selection in regional inversions are also proposed. We applied our method to a recent significant accidental methane release from an offshore platform in the North Sea.

scholarly journals On the parallelization of atmospheric inversions of CO<sub>2</sub> surface fluxes within a variational framework

2013 ◽  
Vol 6 (3) ◽  
pp. 783-790 ◽  
Author(s):  
F. Chevallier
Keyword(s):  
Transport Model ◽  
Spatial Scales ◽  
Computational Cost ◽  
Surface Fluxes ◽  
Atmospheric Measurements ◽  
Transport Modelling ◽  
Time Space ◽  
Variational Minimization ◽  
Analytical Approaches ◽  
Atmospheric Inversions

Abstract. The variational formulation of Bayes' theorem allows inferring CO2 sources and sinks from atmospheric concentrations at much higher time–space resolution than the ensemble or analytical approaches. However, it usually exhibits limited scalable parallelism. This limitation hinders global atmospheric inversions operated on decadal time scales and regional ones with kilometric spatial scales because of the computational cost of the underlying transport model that has to be run at each iteration of the variational minimization. Here, we introduce a physical parallelization (PP) of variational atmospheric inversions. In the PP, the inversion still manages a single physically and statistically consistent window, but the transport model is run in parallel overlapping sub-segments in order to massively reduce the computation wall-clock time of the inversion. For global inversions, a simplification of transport modelling is described to connect the output of all segments. We demonstrate the performance of the approach on a global inversion for CO2 with a 32 yr inversion window (1979–2010) with atmospheric measurements from 81 sites of the NOAA global cooperative air sampling network. In this case, we show that the duration of the inversion is reduced by a seven-fold factor (from months to days), while still processing the three decades consistently and with improved numerical stability.

scholarly journals Observation Error Statistics for Doppler Radar Radial Wind Superobservations Assimilated into the DWD COSMO-KENDA System

2019 ◽  
Vol 147 (9) ◽  
pp. 3351-3364 ◽  
Author(s):  
J. A. Waller ◽  
E. Bauernschubert ◽  
S. L. Dance ◽  
N. K. Nichols ◽  
R. Potthast ◽  
...  
Keyword(s):  
Doppler Radar ◽  
Weather Prediction ◽  
Processing System ◽  
Separation Distance ◽  
Observation Error ◽  
Error Statistics ◽  
Observation Operator ◽  
Uncertainty Estimates ◽  
Standard Deviations ◽  
The Impact

AbstractCurrently in operational numerical weather prediction (NWP) the density of high-resolution observations, such as Doppler radar radial winds (DRWs), is severely reduced in part to avoid violating the assumption of uncorrelated observation errors. To improve the quantity of observations used and the impact that they have on the forecast requires an accurate specification of the observation uncertainties. Observation uncertainties can be estimated using a simple diagnostic that utilizes the statistical averages of observation-minus-background and observation-minus-analysis residuals. We are the first to use a modified form of the diagnostic to estimate spatial correlations for observations used in an operational ensemble data assimilation system. The uncertainties for DRW superobservations assimilated into the Deutscher Wetterdienst convection-permitting NWP model are estimated and compared to previous uncertainty estimates for DRWs. The new results show that most diagnosed standard deviations are smaller than those used in the assimilation, hence, it may be feasible to assimilate DRWs using reduced error standard deviations. However, some of the estimated standard deviations are considerably larger than those used in the assimilation; these large errors highlight areas where the observation processing system may be improved. The error correlation length scales are larger than the observation separation distance and influenced by both the superobbing procedure and observation operator. This is supported by comparing these results to our previous study using Met Office data. Our results suggest that DRW error correlations may be reduced by improving the superobbing procedure and observation operator; however, any remaining correlations should be accounted for in the assimilation.

scholarly journals Natural streamflow simulation for two largest river basins in Poland: a baseline for identification of flow alterations

2016 ◽  
Vol 373 ◽  
pp. 101-107 ◽  
Author(s):  
Mikołaj Piniewski
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Spatial Scales ◽  
Swat Model ◽  
Rate Of Change ◽  
Low Flow ◽  
Large Set ◽  
Dam Reservoirs ◽  
Natural Flow ◽  
The Impact

Abstract. The objective of this study was to apply a previously developed large-scale and high-resolution SWAT model of the Vistula and the Odra basins, calibrated with the focus of natural flow simulation, in order to assess the impact of three different dam reservoirs on streamflow using the Indicators of Hydrologic Alteration (IHA). A tailored spatial calibration approach was designed, in which calibration was focused on a large set of relatively small non-nested sub-catchments with semi-natural flow regime. These were classified into calibration clusters based on the flow statistics similarity. After performing calibration and validation that gave overall positive results, the calibrated parameter values were transferred to the remaining part of the basins using an approach based on hydrological similarity of donor and target catchments. The calibrated model was applied in three case studies with the purpose of assessing the effect of dam reservoirs (Włocławek, Siemianówka and Czorsztyn Reservoirs) on streamflow alteration. Both the assessment based on gauged streamflow (Before-After design) and the one based on simulated natural streamflow showed large alterations in selected flow statistics related to magnitude, duration, high and low flow pulses and rate of change. Some benefits of using a large-scale and high-resolution hydrological model for the assessment of streamflow alteration include: (1) providing an alternative or complementary approach to the classical Before-After designs, (2) isolating the climate variability effect from the dam (or any other source of alteration) effect, (3) providing a practical tool that can be applied at a range of spatial scales over large area such as a country, in a uniform way. Thus, presented approach can be applied for designing more natural flow regimes, which is crucial for river and floodplain ecosystem restoration in the context of the European Union's policy on environmental flows.

scholarly journals On the parallelization of atmospheric inversions of CO<sub>2</sub> surface fluxes within a variational framework

2013 ◽  
Vol 6 (1) ◽  
pp. 37-57 ◽  
Author(s):  
F. Chevallier
Keyword(s):  
Transport Model ◽  
Spatial Scales ◽  
Computational Cost ◽  
Surface Fluxes ◽  
Atmospheric Measurements ◽  
Transport Modelling ◽  
Sources And Sinks ◽  
Variational Framework ◽  
Variational Minimization ◽  
Atmospheric Inversions

Abstract. The variational formulation of Bayes' theorem allows inferring CO2 sources and sinks from atmospheric concentrations at much higher space-time resolution than the ensemble approach or the analytical one. However, it usually exhibits limited scalable parallelism. This limitation hinders global atmospheric inversions operated on decadal time scales and regional ones with kilometric spatial scales, because of the computational cost of the underlying transport model that has to be run at each iteration of the variational minimization. Here, we introduce a Physical Parallelisation (PP) of variational atmospheric inversions. In the PP, the inversion still manages a single physically and statistically consistent window, but the transport model is run in parallel overlapping sub-segments in order to massively reduce the computation wall clock time of the inversion. For global inversions, a simplification of transport modelling is described to connect the output of all segments. We demonstrate the performance of the approach on a global inversion for CO2 with a 32-yr inversion window (1979–2010) with atmospheric measurements from 81 sites of the NOAA global cooperative air sampling network. In this case, we show that the duration of the inversion is reduced by a seven-fold factor (from months to days) while still processing the three decades consistently and with improved numerical stability.

The Impact of Climate Change on Storage-Yield Curves for Multi-Reservoir Systems

1999 ◽  
Vol 30 (2) ◽  
pp. 129-146 ◽  
Author(s):  
N. R. Nawaz ◽  
A. J. Adeloye ◽  
M. Montaseri
Keyword(s):  
Climate Change ◽  
Surface Fluxes ◽  
Runoff Coefficient ◽  
Impact Study ◽  
Yield Functions ◽  
Reservoir Systems ◽  
English System ◽  
Multiple Reservoir ◽  
The Impact ◽  
Impacts Of Climate Change

In this paper, we report on the results of an investigation into the impacts of climate change on the storage-yield relationships for two multiple-reservoir systems, one in England and the other in Iran. The impact study uses established protocol and obtains perturbed monthly inflow series using a simple runoff coefficient approach which accounts for non-evaporative losses in the catchment, and a number of recently published GCM-based scenarios. The multi-reservoir analysis is based on the sequent-peak algorithm which has been modified to analyse multiple reservoirs and to accommodate explicitly performance norms and reservoir surface fluxes, i.e. evaporation and rainfall. As a consequence, it was also possible to assess the effect of including reservoir surface fluxes on the storage-yield functions. The results showed that, under baseline conditions, consideration of net evaporation will require lower storages for the English system and higher storages for the Iranian system. However, with perturbed hydroclimatology different impacts were obtained depending on the systems' yield and reliability. Possible explanations are offered for the observed behaviours.

scholarly journals Scale dependence of galaxy biasing investigated by weak gravitational lensing: An assessment using semi-analytic galaxies and simulated lensing data

2018 ◽  
Vol 613 ◽  
pp. A15 ◽  
Author(s):  
Patrick Simon ◽  
Stefan Hilbert
Keyword(s):  
Gravitational Lensing ◽  
Spatial Scales ◽  
Scale Dependence ◽  
Reconstruction Technique ◽  
Weak Gravitational Lensing ◽  
Physical Scale ◽  
The Galaxy ◽  
Galaxy Bias ◽  
The Impact ◽  
Lens Galaxies

Galaxies are biased tracers of the matter density on cosmological scales. For future tests of galaxy models, we refine and assess a method to measure galaxy biasing as a function of physical scalekwith weak gravitational lensing. This method enables us to reconstruct the galaxy bias factorb(k) as well as the galaxy-matter correlationr(k) on spatial scales between 0.01hMpc−1≲k≲ 10hMpc−1for redshift-binned lens galaxies below redshiftz≲ 0.6. In the refinement, we account for an intrinsic alignment of source ellipticities, and we correct for the magnification bias of the lens galaxies, relevant for the galaxy-galaxy lensing signal, to improve the accuracy of the reconstructedr(k). For simulated data, the reconstructions achieve an accuracy of 3–7% (68% confidence level) over the abovek-range for a survey area and a typical depth of contemporary ground-based surveys. Realistically the accuracy is, however, probably reduced to about 10–15%, mainly by systematic uncertainties in the assumed intrinsic source alignment, the fiducial cosmology, and the redshift distributions of lens and source galaxies (in that order). Furthermore, our reconstruction technique employs physical templates forb(k) andr(k) that elucidate the impact of central galaxies and the halo-occupation statistics of satellite galaxies on the scale-dependence of galaxy bias, which we discuss in the paper. In a first demonstration, we apply this method to previous measurements in the Garching-Bonn Deep Survey and give a physical interpretation of the lens population.

scholarly journals Evaluating the Impact of Intensive Case Management for Severe Vocational Injuries on Work Incapacity and Costs

2021 ◽  
Author(s):  
Rolando Leiva ◽  
Lise Rochaix ◽  
Noémie Kiefer ◽  
Jean-Claude K. Dupont
Keyword(s):  
Treatment Group ◽  
Case Management ◽  
Sick Leave ◽  
Insurance Fund ◽  
Large Set ◽  
Intensive Case Management ◽  
Exact Matching ◽  
Case Management Program ◽  
The Impact ◽  
Permanent Work

AbstractPurpose This study investigates the impact of an intensive case management program on sick leave days, permanent work incapacity levels and treatment costs for severe vocational injuries set up by the French National Insurance Fund in five health insurance districts. Methods The method employed relies on a four-step matching procedure combining Coarsened Exact Matching and Propensity Score Matching, based on an original administrative dataset. Average Treatment effects on the Treated were estimated using a parametric model with a large set of covariates. Results After one-year follow-up, workers in the treatment group had higher sickness absence rates, with 22 extra days, and the program led to 2.7 (95% CI 2.3–3.1) times more diagnoses of permanent work incapacity in the treatment group. With an estimated yearly operational cost of 2,722 € per treated worker, the average total extra treatment cost was 4,569 € for treated workers, which corresponds to a cost increase of 29.2% for the insurance fund. Conclusions The higher costs found for the treatment group are mainly due to longer sick leave duration for the moderate severity group, implying higher cash transfers in the form of one-off indemnities. Even though workers in the treated group have more diagnoses of permanent work incapacity, the difference of severity between groups is small. Our results on longer sick leave duration are partly to be explained by interactions between the case managers and the occupational physicians that encouraged patients to stay longer off-work for better recovery, despite the higher costs that this represented for the insurance fund and the well-documented adverse side effects of longer periods off-work.

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