scholarly journals Impact of physical parameterizations and initial conditions on simulated atmospheric transport and CO<sub>2</sub> mole fractions in the US Midwest

2018 ◽  
Author(s):  
Liza I. Díaz-Isaac ◽  
Thomas Lauvaux ◽  
Kenneth J. Davis
Keyword(s):  
Wind Speed ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Atmospheric Transport ◽  
Atmospheric Co2 ◽  
Large Set ◽  
The Us ◽  
Physics Parameterizations ◽  
The Impact ◽  
Physical Parameterizations

Abstract. Atmospheric transport model errors are one of the main contributors to the uncertainty affecting CO2 inverse flux estimates. In this study, we determine the leading causes of transport errors over the US Upper Midwest with a large set of simulations generated with the Weather Research and Forecasting (WRF) mesoscale model. The various WRF simulations are performed using different meteorological driver datasets and physical parameterizations including planetary boundary layer (PBL) schemes, land surface models (LSMs), cumulus parameterizations and microphysics parameterizations. All the different model configurations were coupled to CO2 fluxes and lateral boundary conditions from the CarbonTracker inversion system to simulate atmospheric CO2 mole fractions. PBL height, wind speed, wind direction, and atmospheric CO2 mole fractions are compared to observations during a month of the summer of 2008, and statistical analyses were performed to evaluate the impact of both physics parameterizations and meteorological datasets on these variables. All of the physical parameterizations and the meteorological initial and boundary conditions contribute 3 to 4 ppm to the model-to-model variability in daytime PBL CO2 except for the microphysics parameterization which has a smaller contribution. PBL height varies across ensemble members by 300 to 400 m, and is this variability is controlled by the same physics parameterizations. Daily PBL CO2 mole fraction errors are correlated with errors in the PBL height. We show that specific model configurations systematically overestimate or underestimate the PBL height averaged across the region with biases closely correlated with the choice of LSM, PBL scheme, and CP. Domain average PBL wind speed is overestimated in nearly every model configuration. Both PBLH and PBL wind speed biases show coherent spatial variations across the Midwest, with PBLH overestimated averaged across configurations by 300–400 m in the west, and PBL winds overestimated by about 1 m/s on average in the east. We find model configurations with lower biases averaged across the domain, but no single configuration is optimal across the entire region and for all meteorological variables. We conclude that model ensembles that include multiple physics parameterizations and meteorological initial conditions are likely to be necessary to encompass the atmospheric conditions most important to the transport of CO2 in the PBL, but that construction of such an ensemble will be challenging due to ensemble biases that vary across the region.

scholarly journals Impact of physical parameterizations and initial conditions on simulated atmospheric transport and CO<sub>2</sub> mole fractions in the US Midwest

2018 ◽  
Vol 18 (20) ◽  
pp. 14813-14835 ◽  
Author(s):  
Liza I. Díaz-Isaac ◽  
Thomas Lauvaux ◽  
Kenneth J. Davis
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Boundary Conditions ◽  
Planetary Boundary Layer ◽  
Initial Conditions ◽  
Atmospheric Transport ◽  
Atmospheric Co2 ◽  
The Us ◽  
Physics Parameterizations ◽  
Physical Parameterizations

Abstract. Atmospheric transport model errors are one of the main contributors to the uncertainty affecting CO2 inverse flux estimates. In this study, we determine the leading causes of transport errors over the US upper Midwest with a large set of simulations generated with the Weather Research and Forecasting (WRF) mesoscale model. The various WRF simulations are performed using different meteorological driver datasets and physical parameterizations including planetary boundary layer (PBL) schemes, land surface models (LSMs), cumulus parameterizations and microphysics parameterizations. All the different model configurations were coupled to CO2 fluxes and lateral boundary conditions from the CarbonTracker inversion system to simulate atmospheric CO2 mole fractions. PBL height, wind speed, wind direction, and atmospheric CO2 mole fractions are compared to observations during a month in the summer of 2008, and statistical analyses were performed to evaluate the impact of both physics parameterizations and meteorological datasets on these variables. All of the physical parameterizations and the meteorological initial and boundary conditions contribute 3 to 4 ppm to the model-to-model variability in daytime PBL CO2 except for the microphysics parameterization which has a smaller contribution. PBL height varies across ensemble members by 300 to 400 m, and this variability is controlled by the same physics parameterizations. Daily PBL CO2 mole fraction errors are correlated with errors in the PBL height. We show that specific model configurations systematically overestimate or underestimate the PBL height averaged across the region with biases closely correlated with the choice of LSM, PBL scheme, and cumulus parameterization (CP). Domain average PBL wind speed is overestimated in nearly every model configuration. Both planetary boundary layer height (PBLH) and PBL wind speed biases show coherent spatial variations across the Midwest, with PBLH overestimated averaged across configurations by 300–400 m in the west, and PBL winds overestimated by about 1 m s−1 on average in the east. We find model configurations with lower biases averaged across the domain, but no single configuration is optimal across the entire region and for all meteorological variables. We conclude that model ensembles that include multiple physics parameterizations and meteorological initial conditions are likely to be necessary to encompass the atmospheric conditions most important to the transport of CO2 in the PBL, but that construction of such an ensemble will be challenging due to ensemble biases that vary across the region.

scholarly journals An Analytic Vortex Initialization Technique for Idealized Tropical Cyclone Studies in AGCMs

2011 ◽  
Vol 139 (2) ◽  
pp. 689-710 ◽  
Author(s):  
Kevin A. Reed ◽  
Christiane Jablonowski
Keyword(s):  
Wind Speed ◽  
Tropical Cyclone ◽  
General Circulation ◽  
Initial Conditions ◽  
Maximum Wind ◽  
Wind Speeds ◽  
Warm Core ◽  
The Impact ◽  
Physical Parameterizations ◽  
Vortex Initialization

Abstract The paper discusses the design of idealized tropical cyclone experiments in atmospheric general circulation models (AGCMs). The evolution of an initially weak, warm-core vortex is investigated over a 10-day period with varying initial conditions that include variations of the maximum wind speed and radius of maximum wind. The initialization of the vortex is built upon prescribed 3D moisture, pressure, temperature, and velocity fields that are embedded into tropical environmental conditions. The initial fields are in exact hydrostatic and gradient-wind balance in an axisymmetric form. The formulation is then generalized to provide analytic initial conditions for an approximately balanced vortex in AGCMs with height-based vertical coordinates. An extension for global models with pressure-based vertical coordinates is presented. The analytic initialization technique can easily be implemented on any AGCM computational grid. The characteristics of the idealized tropical cyclone experiments are illustrated in high-resolution model simulations with the Community Atmosphere Model version 3.1 (CAM 3.1) developed at the National Center for Atmospheric Research. The finite-volume dynamical core in CAM 3.1 with 26 vertical levels is used, and utilizes an aquaplanet configuration with constant sea surface temperatures of 29°C. The impact of varying initial conditions and horizontal resolutions on the evolution of the tropical cyclone–like vortex is investigated. Identical physical parameterizations with a constant parameter set are used at all horizontal resolutions. The sensitivity studies reveal that the initial wind speed and radius of maximum wind need to lie above a threshold to support the intensification of the analytic initial vortex at horizontal grid spacings of 0.5° and 0.25° (or 55 and 28 km in the equatorial regions). The thresholds lie between 15 and 20 m s−1 with a radius of maximum wind of about 200–250 km. In addition, a convergence study with the grid spacings 1.0°, 0.5°, 0.25°, and 0.125° (or 111, 55, 28, and 14 km) shows that the cyclone gets more intense and compact with increasing horizontal resolution. The 0.5°, 0.25°, and 0.125° simulations exhibit many tropical cyclone–like characteristics such as a warm-core, low-level wind maxima, a slanted eyewall-like vertical structure and a relatively calm eye. The 0.125° simulation even starts to resolve spiral rainbands and reaches maximum wind speeds of about 72–83 m s−1 at low levels. These wind speeds are equivalent to a category-5 tropical cyclone on the Saffir–Simpson hurricane scale. It is suggested that the vortex initialization technique can be used as an idealized tool to study the impact of varying resolutions, physical parameterizations, and numerical schemes on the simulation and representation of tropical cyclone–like vortices in global atmospheric models.

scholarly journals Estimating the Uncertainty in a Regional Climate Model Related to Initial and Lateral Boundary Conditions

2005 ◽  
Vol 18 (7) ◽  
pp. 917-933 ◽  
Author(s):  
Wanli Wu ◽  
Amanda H. Lynch ◽  
Aaron Rivers
Keyword(s):  
Boundary Conditions ◽  
Climate Model ◽  
Initial Conditions ◽  
Climate Modeling ◽  
Regional Climate ◽  
Regional Climate Modeling ◽  
Regional Model ◽  
Lateral Boundary ◽  
Lateral Boundary Conditions ◽  
The Impact

Abstract There is a growing demand for regional-scale climate predictions and assessments. Quantifying the impacts of uncertainty in initial conditions and lateral boundary forcing data on regional model simulations can potentially add value to the usefulness of regional climate modeling. Results from a regional model depend on the realism of the driving data from either global model outputs or global analyses; therefore, any biases in the driving data will be carried through to the regional model. This study used four popular global analyses and achieved 16 driving datasets by using different interpolation procedures. The spread of the 16 datasets represents a possible range of driving data based on analyses to the regional model. This spread is smaller than typically associated with global climate model realizations of the Arctic climate. Three groups of 16 realizations were conducted using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) in an Arctic domain, varying both initial and lateral boundary conditions, varying lateral boundary forcing only, and varying initial conditions only. The response of monthly mean atmospheric states to the variations in initial and lateral driving data was investigated. Uncertainty in the regional model is induced by the interaction between biases from different sources. Because of the nonlinearity of the problem, contributions from initial and lateral boundary conditions are not additive. For monthly mean atmospheric states, biases in lateral boundary conditions generally contribute more to the overall uncertainty than biases in the initial conditions. The impact of initial condition variations decreases with the simulation length while the impact of variations in lateral boundary forcing shows no clear trend. This suggests that the representativeness of the lateral boundary forcing plays a critical role in long-term regional climate modeling. The extent of impact of the driving data uncertainties on regional climate modeling is variable dependent. For some sensitive variables (e.g., precipitation, boundary layer height), even the interior of the model may be significantly affected.

scholarly journals Cloud-Resolving Ensemble Simulations of Mediterranean Heavy Precipitating Events: Uncertainty on Initial Conditions and Lateral Boundary Conditions

2011 ◽  
Vol 139 (2) ◽  
pp. 403-423 ◽  
Author(s):  
Benoît Vié ◽  
Olivier Nuissier ◽  
Véronique Ducrocq
Keyword(s):  
Boundary Conditions ◽  
Case Studies ◽  
Short Range ◽  
Initial Conditions ◽  
Ensemble Prediction ◽  
Lateral Boundary ◽  
Synoptic Scale ◽  
Lateral Boundary Conditions ◽  
Convective Scale ◽  
The Impact

Abstract This study assesses the impact of uncertainty on convective-scale initial conditions (ICs) and the uncertainty on lateral boundary conditions (LBCs) in cloud-resolving simulations with the Application of Research to Operations at Mesoscale (AROME) model. Special attention is paid to Mediterranean heavy precipitating events (HPEs). The goal is achieved by comparing high-resolution ensembles generated by different methods. First, an ensemble data assimilation technique has been used for assimilation of perturbed observations to generate different convective-scale ICs. Second, three ensembles used LBCs prescribed by the members of a global short-range ensemble prediction system (EPS). All ensembles obtained were then evaluated over 31- and/or 18-day periods, and on 2 specific case studies of HPEs. The ensembles are underdispersive, but both the probabilistic evaluation of their overall performance and the two case studies confirm that they can provide useful probabilistic information for the HPEs considered. The uncertainty on convective-scale ICs is shown to have an impact at short range (under 12 h), and it is strongly dependent on the synoptic-scale context. Specifically, given a marked circulation near the area of interest, the imposed LBCs rapidly overwhelm the initial differences, greatly reducing the spread of the ensemble. The uncertainty on LBCs shows an impact at longer range, as the spread in the coupling global ensemble increases, but it also depends on the synoptic-scale conditions and their predictability.

Monetary policy shock and industrial production: industry-level evidence from the US

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nazneen Ahmad ◽  
Sandeep Kumar Rangaraju
Keyword(s):  
Monetary Policy ◽  
Vector Autoregression ◽  
The United States ◽  
Manufacturing Industries ◽  
Large Set ◽  
Structural Shocks ◽  
Content Type ◽  
The Us ◽  
Monetary Policy Shock ◽  
The Impact

PurposeThis paper investigates the impact of a monetary policy shock on the production of a sample of 312 industries in manufacturing, mining and utilities in the United States using a factor-augmented vector autoregression (FAVAR) model.Design/methodology/approachThe authors use a FAVAR model that builds on Bernanke et al. (2005) and Boivin et al. (2009). The main assumption in this model is that the dynamics of a large set of macro variables are captured by some observed and unobserved common factors. The unobserved factors are extracted from a large set of macroeconomic data. The key advantage of using this model is that it allows extracting the impulse responses of a wide range of macroeconomic variables to structural shocks in the federal funds rate.FindingsThe results indicate that industries exhibit differential responses to an unanticipated monetary policy tightening. In general, manufacturing industries appear to be more sensitive compared to mining, and utility industries and durable manufacturing industries are found to be more sensitive than those within nondurable and other manufacturing industries to a monetary policy shock. While all industries respond to the policy shock, most of the responses are reversed between 12 and 22 months.Research limitations/implicationsThe implication of our results is that monetary policy can be used to impact most US industries for four years and beyond. The existence of disparate responses across industries underscores the difficulty of implementing a monetary policy that will generate the same impact across industries. As the effects of the policy are distinct, policymakers may want to attend to the unique impacts and implement industry-specific policy.Practical implicationsThe study is important in the context of the current challenges in the US economy caused by the spread of coronavirus. For example, to tackle the current pandemic, the researchers are trying to come up with cures for COVID-19. A considerable response of the chemical industry that provides materials to pharmaceutical and medicine manufacturing to the monetary policy shock implies that an expansionary monetary policy may facilitate an invention and adequate supply of the cure later on. The same policy may not effectively stimulate production in apparel or leather product industries that are being hard hit by the pandemic.Originality/valueThe study contributes to the literature in broadly two aspects. First, to the best of our knowledge, this is the first paper that investigates the impact of a monetary policy shock on a sample of 312 industries in manufacturing, mining and utilities in the US. Second, to identify structural shocks and investigate the effects of monetary policy shocks on economic activity, the authors diverge from the literature's traditional approach, i.e. the vector autoregression (VAR) method and use a FAVAR method. The FAVAR provides a comprehensive description of the impact of a monetary policy innovation on different industries.

scholarly journals Generalization and application of the flux-conservative thermodynamic equations in the AROME model of the ALADIN system

2016 ◽  
Vol 9 (6) ◽  
pp. 2129-2142 ◽  
Author(s):  
Daan Degrauwe ◽  
Yann Seity ◽  
François Bouyssel ◽  
Piet Termonia
Keyword(s):  
Energy Budget ◽  
Moisture Transport ◽  
Climate Model ◽  
Heavy Precipitation ◽  
Cold Pool ◽  
Physics Parameterizations ◽  
Nwp Model ◽  
The Impact ◽  
Thermodynamic Equations ◽  
Physical Parameterizations

Abstract. General yet compact equations are presented to express the thermodynamic impact of physical parameterizations in a NWP or climate model. By expressing the equations in a flux-conservative formulation, the conservation of mass and energy by the physics parameterizations is a built-in feature of the system. Moreover, the centralization of all thermodynamic calculations guarantees a consistent thermodynamical treatment of the different processes. The generality of this physics–dynamics interface is illustrated by applying it in the AROME NWP model. The physics–dynamics interface of this model currently makes some approximations, which typically consist of neglecting some terms in the total energy budget, such as the transport of heat by falling precipitation, or the effect of diffusive moisture transport. Although these terms are usually quite small, omitting them from the energy budget breaks the constraint of energy conservation. The presented set of equations provides the opportunity to get rid of these approximations, in order to arrive at a consistent and energy-conservative model. A verification in an operational setting shows that the impact on monthly-averaged, domain-wide meteorological scores is quite neutral. However, under specific circumstances, the supposedly small terms may turn out not to be entirely negligible. A detailed study of a case with heavy precipitation shows that the heat transport by precipitation contributes to the formation of a region of relatively cold air near the surface, the so-called cold pool. Given the importance of this cold pool mechanism in the life cycle of convective events, it is advisable not to neglect phenomena that may enhance it.

scholarly journals The role of boundary and initial conditions for dynamical seasonal predictability

2003 ◽  
Vol 10 (3) ◽  
pp. 211-232 ◽  
Author(s):  
T. J. Reichler ◽  
J. O. Roads
Keyword(s):  
Boundary Conditions ◽  
Time Scales ◽  
General Circulation ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Circulation Model ◽  
Forecast Skill ◽  
Initial State ◽  
Tropical Forcing ◽  
The Impact

Abstract. The importance of initial state and boundary forcing for atmospheric predictability is explored on global to regional spatial scales and on daily to seasonal time scales. A general circulation model is used to conduct predictability experiments with different combinations of initial and boundary conditions. The experiments are verified under perfect model assumptions as well as against observational data. From initial conditions alone, there is significant instantaneous forecast skill out to 2 months. Different initial conditions show different predictability using the same kind of boundary forcing. Even on seasonal time scales, using observed atmospheric initial conditions leads to a substantial increase in overall skill, especially during periods with weak tropical forcing. The impact of boundary forcing on predictability is detectable after 10 days and leads to measurable instantaneous forecast skill at very long lead times. Over the Northern Hemisphere, it takes roughly 4 weeks for boundary conditions to reach the same effect on predictability as initial conditions. During events with strong tropical forcing, these time scales are somewhat shorter. Over the Southern Hemisphere, there is a strongly enhanced influence of initial conditions during summer. We conclude that the long term memory of initial conditions is important for seasonal forecasting.

scholarly journals Calibration of a multi-physics ensemble for greenhouse gas atmospheric transport model uncertainty estimation

2018 ◽  
Author(s):  
Liza I. Díaz-Isaac ◽  
Thomas Lauvaux ◽  
Marc Bocquet ◽  
Kenneth J. Davis
Keyword(s):  
Boundary Conditions ◽  
Land Surface ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Wrf Model ◽  
Meteorological Variables ◽  
Multiple Model ◽  
Optimal Ensemble ◽  
Physics Ensemble ◽  
The Impact

Abstract. Atmospheric inversions have been used to assess biosphere-atmosphere CO2 surface exchanges at various scales, but variability among inverse flux estimates remains significant, especially at continental scales. Atmospheric transport errors are one of the main contributors to this variability. To characterize transport errors and their spatio-temporal structures, we present an objective method to generate a calibrated ensemble adjusted with meteorological measurements collected across a region, here the US upper Midwest in midsummer. Using multiple model configurations of the Weather Research and Forecasting (WRF) model, we show that a reduced number of simulations (less than 10 members) reproduces the transport error characteristics of a 45-member ensemble while minimizing the size of the ensemble. The large ensemble of 45-members was constructed using different physics parameterization (i.e., land surface models (LSMs), planetary boundary layer (PBL) schemes, cumulus parameterizations and microphysics parameterizations) and meteorological initial/boundary conditions. All the different models were coupled to CO2 fluxes and lateral boundary conditions from CarbonTracker to simulate CO2 mole fractions. Meteorological variables critical to inverse flux estimates, PBL wind speed, PBL wind direction and PBL height, are used to calibrate our ensemble over the region. Two calibration techniques (i.e., simulated annealing and a genetic algorithm) are used for the selection of the optimal ensemble using the flatness of the rank histograms as the main criterion. We also choose model configurations that minimize the systematic errors (i.e. monthly biases) in the ensemble. We evaluate the impact of transport errors on atmospheric CO2 mole fraction to represent up to 40 % of the model-data mismatch (fraction of the total variance). We conclude that a carefully-chosen subset of the physics ensemble can represent the errors in the full ensemble, and that transport ensembles calibrated with relevant meteorological variables provide a promising path forward for improving the treatment of transport errors in atmospheric inverse flux estimates.

scholarly journals Sensitivity Analysis of Hurricane Arthur (2014) Storm Surge Forecasts to WRF Physics Parameterizations and Model Configurations

2017 ◽  
Vol 32 (5) ◽  
pp. 1745-1764 ◽  
Author(s):  
Fan Zhang ◽  
Ming Li ◽  
Andrew C. Ross ◽  
Serena Blyth Lee ◽  
Da-Lin Zhang
Keyword(s):  
Wind Speed ◽  
Boundary Conditions ◽  
Storm Surge ◽  
Cloud Microphysics ◽  
Sensitivity Analyses ◽  
Storm Intensity ◽  
Closure Scheme ◽  
Local Closure ◽  
Physics Parameterizations ◽  
Initial And Boundary Conditions

Abstract Through a case study of Hurricane Arthur (2014), the Weather Research and Forecasting (WRF) Model and the Finite Volume Coastal Ocean Model (FVCOM) are used to investigate the sensitivity of storm surge forecasts to physics parameterizations and configurations of the initial and boundary conditions in WRF. The turbulence closure scheme in the planetary boundary layer affects the prediction of the storm intensity: the local closure scheme produces lower equivalent potential temperature than the nonlocal closure schemes, leading to significant reductions in the maximum surface wind speed and surge heights. On the other hand, higher-class cloud microphysics schemes overpredict the wind speed, resulting in large overpredictions of storm surge at some coastal locations. Without cumulus parameterization in the outermost domain, both the wind speed and storm surge are grossly underpredicted as a result of large precipitation decreases in the storm center. None of the choices for the WRF physics parameterization schemes significantly affect the prediction of Arthur’s track. Sea surface temperature affects the latent heat release from the ocean surface and thus storm intensity and storm surge predictions. The large-scale atmospheric circulation models provide the initial and boundary conditions for WRF, and influence both the track and intensity predictions, thereby changing the spatial distribution of storm surge along the coastline. These sensitivity analyses underline the need to use an ensemble modeling approach to improve the storm surge forecasts.

scholarly journals Calibration of a multi-physics ensemble for estimating the uncertainty of a greenhouse gas atmospheric transport model

2019 ◽  
Vol 19 (8) ◽  
pp. 5695-5718 ◽  
Author(s):  
Liza I. Díaz-Isaac ◽  
Thomas Lauvaux ◽  
Marc Bocquet ◽  
Kenneth J. Davis
Keyword(s):  
Boundary Conditions ◽  
Land Surface ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Optimization Techniques ◽  
Meteorological Variables ◽  
Multiple Model ◽  
Optimal Ensemble ◽  
Physics Ensemble ◽  
The Impact

Abstract. Atmospheric inversions have been used to assess biosphere–atmosphere CO2 surface exchanges at various scales, but variability among inverse flux estimates remains significant, especially at continental scales. Atmospheric transport errors are one of the main contributors to this variability. To characterize transport errors and their spatiotemporal structures, we present an objective method to generate a calibrated ensemble adjusted with meteorological measurements collected across a region, here the upper US Midwest in midsummer. Using multiple model configurations of the Weather Research and Forecasting (WRF) model, we show that a reduced number of simulations (less than 10 members) reproduces the transport error characteristics of a 45-member ensemble while minimizing the size of the ensemble. The large ensemble of 45 members was constructed using different physics parameterization (i.e., land surface models (LSMs), planetary boundary layer (PBL) schemes, cumulus parameterizations and microphysics parameterizations) and meteorological initial/boundary conditions. All the different models were coupled to CO2 fluxes and lateral boundary conditions from CarbonTracker to simulate CO2 mole fractions. Observed meteorological variables critical to inverse flux estimates, PBL wind speed, PBL wind direction and PBL height are used to calibrate our ensemble over the region. Two optimization techniques (i.e., simulated annealing and a genetic algorithm) are used for the selection of the optimal ensemble using the flatness of the rank histograms as the main criterion. We also choose model configurations that minimize the systematic errors (i.e., monthly biases) in the ensemble. We evaluate the impact of transport errors on atmospheric CO2 mole fraction to represent up to 40 % of the model–data mismatch (fraction of the total variance). We conclude that a carefully chosen subset of the physics ensemble can represent the uncertainties in the full ensemble, and that transport ensembles calibrated with relevant meteorological variables provide a promising path forward for improving the treatment of transport uncertainties in atmospheric inverse flux estimates.

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