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 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 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 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 The Impact of RDP Measures on the Diversification of Agriculture and Rural Development—Seeking Additional Livelihoods: The Case of Poland

Agriculture ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 253
Author(s):  
Mirosław Biczkowski ◽  
Aleksandra Jezierska-Thöle ◽  
Roman Rudnicki
Keyword(s):  
Rural Development ◽  
Rural Areas ◽  
Spatial Scales ◽  
Development Program ◽  
Spatial Diversity ◽  
Agricultural Activities ◽  
Synthetic Index ◽  
Two Measures ◽  
The Impact ◽  
The Eu

The paper’s main aim is to assess the measures implemented within the Rural Development Program (RDP) 2007–2013 in Poland. This programme is dedicated to the diversification of business activities in rural areas and rural livelihood and, thus, the improvement of the multifunctionality of rural areas. The analysis covered two measures from Axis 3, Improvement of the quality of life in rural areas and diversification of rural economy: M311, diversification into non-agricultural activities; and M312, Establishment and development of micro-enterprise. The study and the discussion are presented from a geographical perspective and, in a broader context, take into account several conditions (natural, urban, agricultural and historical) and the spatial diversity of the allocation of European Union (EU) funds. Models of a policy of multifunctional rural development, implemented after accession to the EU, are presented. The research’s spatial scope covers Poland’s territory on two spatial scales: the system of regions (16 NUTS2 units) and poviats (314 LAU level 1 units). The analysis covers all the projects implemented in Poland under the two measures of Axis 3 of the RDP 2007–2013. A set of conditions was prepared for all LAU1 units, forming the background for assessing the impact of the EU funds on the development of non-agricultural activities. To determine the relationship between the RDP measures and the selected groups of conditions, a synthetic index and a correlation index are used. They are also used to determine the mutual relations between the two analyzed activities in terms of the spatial scales used. Access to the EU funds (RDP) has considerably enlarged the opportunities for accelerating agricultural modernisation and restructuration towards multifunctional development, as well as the opportunities for implementing new development and work methods in the countryside in Poland. The attractiveness of the two studied RDP measures varied across regions. The beneficiaries’ activity depended on the local potential (resources), culture and tradition of the region, and size and potential of the farm. In the areas where agriculture is deeply rooted, beneficiaries were more willing to engage in ventures tapping into the resources available in their farms. Thus, they create additional livelihood of income and workplaces for household members. In turn, the beneficiaries from the areas where farms are smaller and economically weaker often undertake activities related to setting up a new business (outside farming).

On the benefit of the Canadian Small Lake Model to better represent the impact of small natural lakes on GEM-Hydro streamflow simulations.

2021 ◽  
Author(s):  
Etienne Gaborit ◽  
Murray MacKay ◽  
Camille Garnaud ◽  
Vincent Fortin
Keyword(s):  
Water Balance ◽  
Grid Point ◽  
Hydrologic Model ◽  
Surface Fluxes ◽  
Dew Point ◽  
Multiple Model ◽  
Small Lake ◽  
Surface Component ◽  
Lake Model ◽  
The Impact

&lt;p&gt;This study aims at assessing the impact of a new lake model on streamflow simulations performed with the GEM-Hydro hydrologic model developed at ECCC. GEM-Hydro is at the heart of the National Surface and River Prediction System (NSRPS) which ECCC uses to forecast river flows over most of Canada. The GEM-Hydro model mainly consists of the GEM-Surf component to represent surface processes, and of the Watroute model to represent river and lake routing, in order to perform streamflow simulations and forecasts. The surface component of GEM-Hydro can simulate 5 different types of surfaces.&amp;#160; Currently, the water tile consists of a very simple algorithm which, in terms of water balance, consists of producing runoff fluxes simply equal to precipitation minus evaporation. This runoff over water surfaces is then provided as input, along with runoff and drainage generated over other surface tiles, to the Watroute model. The Watroute version used in GEM-Hydro currently only represents major lakes (area greater than 100km&lt;sup&gt;2&lt;/sup&gt;) along the river networks, and does not represent the impact that small lakes can have on streamflow, which mainly consists in slowing down runoff before it reaches the main streams of the network.&lt;/p&gt;&lt;p&gt;Recently, the Canadian Small Lake Model (CSLM) was implemented in the surface component of GEM-Hydro to represent the energy and water balance over water tiles more accurately. So far, CSLM simulations have been shown promising in terms of evaporation, ice cover, absolute and dew point temperature simulations, compared with the former algorithm used over water. However, the impact of CSLM on the resulting streamflow simulations performed with GEM-Hydro has not been evaluated yet. This study aims first at evaluating the impact of CSLM on streamflow simulations, and secondly at testing different CSLM configurations as well as different coupling strategies with Watroute, with the objective of finding the best set up for the prediction of streamflow in Canada. For example, overland runoff generated by the land tile can be provided to the water tile of the same grid point in different ways, and the outflow computed at the outlet of the water tile can be computed with different parameters. Moreover, different outflow computations have to be taken into account depending on if the water tile of a grid point represents subgrid-scale lakes, or if on the contrary it belongs to a lake spanning over multiple model grid points.&lt;/p&gt;&lt;p&gt;To do so, different GEM-Hydro open-loop simulations have been performed on the Lake of the Woods watershed, located in Canada, with and without CSLM to represent water tiles. The CSLM configurations leading to the best results are presented here. CSLM simulations are also evaluated in terms of surface fluxes, to ensure that the main purpose of the model, which is to improve surface fluxes to ultimately improve atmospheric forecasts, is preserved, compared to the default configuration of the model. Ideas for further improving the coupling between the GEM-Hydro surface and routing components, in terms of lake processes, are also presented and will be tested in future work.&lt;/p&gt;

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