scholarly journals An improved Kalman Smoother for atmospheric inversions

2005 ◽  
Vol 5 (10) ◽  
pp. 2691-2702 ◽  
Author(s):  
L. M. P. Bruhwiler ◽  
A. M. Michalak ◽  
W. Peters ◽  
D. F. Baker ◽  
P. Tans
Keyword(s):  
Atmospheric Carbon Dioxide ◽  
Transport Model ◽  
Spatial Scales ◽  
Sequential Estimation ◽  
Time Step ◽  
Carbon Dioxide Fluxes ◽  
Sources And Sinks ◽  
Minimal Error ◽  
Kalman Smoother ◽  
Background State

Abstract. We explore the use of a fixed-lag Kalman smoother for sequential estimation of atmospheric carbon dioxide fluxes. This technique takes advantage of the fact that most of the information about the spatial distribution of sources and sinks is observable within a few months to half of a year of emission. After this period, the spatial structure of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through the observations sequentially, using only the subset of observations and modeled transport fields that most strongly constrain the fluxes at a particular time step. Estimates of each set of fluxes are sequentially updated multiple times, using measurements taken at different times, and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO2 and transported forward in time, and the final flux uncertainties and covariances are taken into account when estimating the covariances of the fluxes still being estimated. The computational demands of this technique are greatly reduced in comparison to the standard Bayesian synthesis technique where all observations are used at once with transport fields spanning the entire period of the observations. It therefore becomes possible to solve larger inverse problems with more observations and for fluxes discretized at finer spatial scales. We also discuss the differences between running the inversion simultaneously with the transport model and running it entirely off-line with pre-calculated transport fields. We find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated.

scholarly journals An improved Kalman Smoother for atmospheric inversions

2005 ◽  
Vol 5 (2) ◽  
pp. 1891-1923 ◽  
Author(s):  
L. M. P. Bruhwiler ◽  
A. M. Michalak ◽  
W. Peters ◽  
D. F. Baker ◽  
P. Tans
Keyword(s):  
Atmospheric Carbon Dioxide ◽  
Transport Model ◽  
Spatial Scales ◽  
Sequential Estimation ◽  
Time Step ◽  
Carbon Dioxide Fluxes ◽  
Sources And Sinks ◽  
Minimal Error ◽  
Kalman Smoother ◽  
Background State

Abstract. We explore the use of a fixed-lag Kalman smoother for sequential estimation of atmospheric carbon dioxide fluxes. This technique takes advantage of the fact that most of the information about the spatial distribution of sources and sinks is observable within a 5 few months to half of a year of emission. After this period, the spatial structure of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through the observations sequentially, using only the subset of observations and modeled transport fields that most strongly constrain the fluxes at a particular time step. Estimates of each set of fluxes 10 are sequentially updated multiple times, using measurements taken at different times, and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO2 and transported forward in time, and the final flux uncertainties and covariances are taken into account when estimating the covariances of the fluxes still being estimated. The computational demands 15 of this technique are greatly reduced in comparison to the standard Bayesian synthesis technique where all observations are used at once with transport fields spanning the entire period of the observations. It therefore becomes possible to solve larger inverse problems with more observations and for fluxes discretized at finer spatial scales. We also discuss the differences between running the inversion simultaneously with the 20 transport model and running it entirely off-line with pre-calculated transport fields. We find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated.

scholarly journals Technical note: A geostatistical fixed-lag Kalman smoother for atmospheric inversions

2008 ◽  
Vol 8 (2) ◽  
pp. 7755-7779
Author(s):  
A. M. Michalak
Keyword(s):  
Carbon Dioxide ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Correlation ◽  
Technical Note ◽  
Surface Fluxes ◽  
Carbon Dioxide Fluxes ◽  
Kalman Smoother ◽  
Geostatistical Approach ◽  
Flux Estimation

Abstract. Inverse modeling methods are now commonly used for estimating surface fluxes of carbon dioxide, using atmospheric mass fraction measurements combined with a numerical atmospheric transport model. The geostatistical approach to flux estimation takes advantage of the spatial and/or temporal correlation in fluxes and does not require prior flux estimates. In this work, a geostatistical implementation of a fixed-lag Kalman smoother is developed to improve the computational efficiency of the inverse problem. This method makes it feasible to perform multi-year inversions, at fine resolutions, and with large amounts of data. The new method is applied to the recovery of global gridscale carbon dioxide fluxes for 1997 to 2001 using pseudodata representative of a subset of the NOAA-ESRL Cooperative Air Sampling Network.

Investigation of global atmospheric carbonyl sulphide between 2004 and 2018: an observational and modelling study

2020 ◽  
Author(s):  
Michael P. Cartwright ◽  
Jeremy J. Harrison ◽  
David P. Moore ◽  
John J. Remedios ◽  
Martyn P. Chipperfield ◽  
...  
Keyword(s):  
Atmospheric Chemistry ◽  
Atmospheric Carbon Dioxide ◽  
Transport Model ◽  
Carbonyl Sulfide ◽  
Global Scale ◽  
Chemical Transport Model ◽  
Sources And Sinks ◽  
Continental Scale ◽  
Retrieval Scheme ◽  
The Relationship

<p>The challenge in quantifying the sources and sinks of atmospheric carbon dioxide (CO<sub>2</sub>) is that the CO<sub>2</sub> taken up by plants during photosynthesis cannot be distinguished from the CO<sub>2</sub> released by plants and micro-organisms during respiration. It has been shown that carbonyl sulfide (OCS), the sulphur-containing analogue of CO<sub>2</sub>, can be used as a proxy for photosynthesis. The relationship between the vegetative flux of OCS and CO<sub>2</sub> has been quantified for various species of plants and ecosystems, the results of which have been used in observing the relationship on a continental scale. The aim of this project is to both quantify the location and magnitude of the sources and sinks of atmospheric OCS, and to use these data to infer photosynthetic uptake of CO<sub>2</sub> by vegetation on a global scale.</p><p>A tracer version of the 3-dimensional chemical transport model TOMCAT has been adapted to include eleven different sources and sinks of OCS, including direct and indirect oceanic emissions, vegetative uptake and stratospheric photolysis. The modelled OCS (TOMCAT-OCS) distribution between 2004 and 2018 has been co-located spatially and temporally to OCS profiles measured by the Atmospheric Chemistry Experiment (ACE-FTS) over the 5 – 30 km altitude, showing generally good agreement. Furthermore, surface TOMCAT-OCS has been compared to OCS measurements made at twelve NOAA-ESRL sites, across both hemispheres, showing that the model captures the seasonal cycle at the surface.</p><p>There have been several calls in recent years for a new satellite product of atmospheric OCS, which this project aims to satisfy. Work is ongoing to retrieve OCS total columns from measurements taken by the Infrared Atmospheric Sounding Interferometer (IASI) instruments on-board the MetOp satellites. The University of Leicester IASI Retrieval Scheme (ULIRS) has been adapted to retrieve OCS columns globally. Various case studies for different geographic regions and time periods will be presented and compared to other satellite observations.</p>

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.

scholarly journals Technical Note: Adapting a fixed-lag Kalman smoother to a geostatistical atmospheric inversion framework

2008 ◽  
Vol 8 (22) ◽  
pp. 6789-6799 ◽  
Author(s):  
A. M. Michalak
Keyword(s):  
Carbon Dioxide ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Correlation ◽  
Technical Note ◽  
Surface Fluxes ◽  
Computationally Efficient ◽  
Carbon Dioxide Fluxes ◽  
Kalman Smoother ◽  
Geostatistical Approach

Abstract. Inverse modeling methods are now commonly used for estimating surface fluxes of carbon dioxide, using atmospheric mass fraction measurements combined with a numerical atmospheric transport model. The geostatistical approach to flux estimation takes advantage of the spatial and/or temporal correlation in fluxes and does not require prior flux estimates. In this work, a previously-developed, computationally-efficient, fixed-lag Kalman smoother is adapted for application with a geostatistical approach to atmospheric inversions. This method makes it feasible to perform multi-year geostatistical inversions, at fine resolutions, and with large amounts of data. The new method is applied to the recovery of global gridscale carbon dioxide fluxes for 1997 to 2001 using pseudodata representative of a subset of the NOAA-ESRL Cooperative Air Sampling Network.

scholarly journals Evolution of the Distribution of Upper-Tropospheric Humidity over the Indian Ocean: Connection with Large-Scale Advection and Local Cloudiness

2017 ◽  
Vol 56 (7) ◽  
pp. 2035-2052 ◽  
Author(s):  
Thomas Garot ◽  
Hélène Brogniez ◽  
Renaud Fallourd ◽  
Nicolas Viltard
Keyword(s):  
Indian Ocean ◽  
Large Scale ◽  
Transport Model ◽  
Intraseasonal Variability ◽  
Back Trajectory ◽  
Time Step ◽  
Air Masses ◽  
Upper Troposphere ◽  
Upper Tropospheric Humidity ◽  
The Indian Ocean

AbstractThe spatial and temporal distribution of upper-tropospheric humidity (UTH) observed by the Sounder for Atmospheric Profiling of Humidity in the Intertropics by Radiometry (SAPHIR)/Megha-Tropiques radiometer is analyzed over two subregions of the Indian Ocean during October–December over 2011–14. The properties of the distribution of UTH were studied with regard to the phase of the Madden–Julian oscillation (active or suppressed) and large-scale advection versus local production of moisture. To address these topics, first, a Lagrangian back-trajectory transport model was used to assess the role of the large-scale transport of air masses in the intraseasonal variability of UTH. Second, the temporal evolution of the distribution of UTH is analyzed using the computation of the higher moments of its probability distribution function (PDF) defined for each time step over the domain. The results highlight significant differences in the PDF of UTH depending on the phase of the MJO. The modeled trajectories ending in the considered domain originate from an area that strongly varies depending on the phases of the MJO: during the active phases, the air masses are spatially constrained within the tropical Indian Ocean domain, whereas a distinct upper-tropospheric (200–150 hPa) westerly flow guides the intraseasonal variability of UTH during the suppressed phases. Statistical relationships between the cloud fractions and the UTH PDF moments of are found to be very similar regardless of the convective activity. However, the occurrence of thin cirrus clouds is associated with a drying of the upper troposphere (enhanced during suppressed phases), whereas the occurrence of thick cirrus anvil clouds appears to be significantly related to a moistening of the upper troposphere.

scholarly journals Spatial and temporal resolution of carbon flux estimates for 1983–2002

2007 ◽  
Vol 4 (6) ◽  
pp. 4697-4756 ◽  
Author(s):  
L. M. P. Bruhwiler ◽  
A. M. Michalak ◽  
P. P. Tans
Keyword(s):  
North America ◽  
Temporal Resolution ◽  
Carbon Flux ◽  
Seasonal Cycle ◽  
Transport Model ◽  
Spatial Scales ◽  
Carbon Fluxes ◽  
Chemical Transport Model ◽  
Data Product ◽  
Zonal Average

Abstract. We discuss the spatial and temporal resolution of monthly carbon flux estimates for the period 1983–2002 using a fixed-lag Kalman Smoother technique with a global chemical transport model, and the GLOBALVIEW data product. The observational network has expanded substantially over this period, and we the improvement in the constraints provided flux estimates by observations for the 1990's in comparison to the 1980's. The estimated uncertainties also decrease as observational coverage expands. In this study, we use the Globalview data product for a network that changes every 5 y, rather than using a small number of continually-operating sites (fewer observational constraints) or a large number of sites, some of which may consist almost entirely of extrapolated data. We show that the discontinuities resulting from network changes reflect uncertainty due to a sparse and variable network. This uncertainty effectively limits the resolution of trends in carbon fluxes. The ability of the inversion to distinguish, or resolve, carbon fluxes at various spatial scales is examined using a diagnostic known as the resolution kernel. We find that the global partition between land and ocean fluxes is well-resolved even for the very sparse network of the 1980's, although prior information makes a significant contribution to the resolution. The ability to distinguish zonal average fluxes has improved significantly since the 1980's, especially for the tropics, where the zonal ocean and land biosphere fluxes can be distinguished. Care must be taken when interpreting zonal average fluxes, however, since the lack of air samples for some regions in a zone may result in a large influence from prior flux estimates for these regions. We show that many of the TransCom 3 source regions are distinguishable throughout the period over which estimates are produced. Examples are Boreal and Temperate North America. The resolution of fluxes from Europe and Australia has greatly improved since the 1990's. Other regions, notably Tropical South America and the Equatorial Atlantic remain practically unresolved. Comparisons of the average seasonal cycle of the estimated carbon fluxes with the seasonal cycle of the prior flux estimates reveals a large adjustment of the summertime uptake of carbon for Boreal Eurasia, and an earlier onset of springtime uptake for Temperate North America. In addition, significantly larger seasonal cycles are obtained for some ocean regions, such as the Northern Ocean, North Pacific, North Atlantic and Western Equatorial Pacific, regions that appear to be well-resolved by the inversion.

scholarly journals Comparison of generalized non-data-driven lake and reservoir routing models for global-scale hydrologic forecasting of reservoir outflow at diurnal time steps

2020 ◽  
Vol 24 (5) ◽  
pp. 2711-2729 ◽  
Author(s):  
Joseph L. Gutenson ◽  
Ahmad A. Tavakoly ◽  
Mark D. Wahl ◽  
Michael L. Follum
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Model Performance ◽  
Global Scale ◽  
Army Corps ◽  
Time Step ◽  
Large Spatial Scale ◽  
Reservoir Routing ◽  
Routing Methods ◽  
Improved Model

Abstract. Large-scale hydrologic forecasts should account for attenuation through lakes and reservoirs when flow regulation is present. Globally generalized methods for approximating outflow are required but must contend with operational complexity and a dearth of information on dam characteristics at global spatial scales. There is currently no consensus on the best approach for approximating reservoir release rates in large spatial scale hydrologic forecasting, particularly at diurnal time steps. This research compares two parsimonious reservoir routing methods at daily steps: Döll et al. (2003) and Hanasaki et al. (2006). These reservoir routing methods have been previously implemented in large-scale hydrologic modeling applications and have been typically evaluated seasonally. These routing methods are compared across 60 reservoirs operated by the U.S. Army Corps of Engineers. The authors vary empirical coefficients for both reservoir routing methods as part of a sensitivity analysis. The method proposed by Döll et al. (2003) outperformed that presented by Hanasaki et al. (2006) at a daily time step and improved model skill over most run-of-the-river conditions. The temporal resolution of the model influences model performances. The optimal model coefficients varied across the reservoirs in this study and model performance fluctuates between wet years and dry years, and for different configurations such as dams in series. Overall, the method proposed by Döll et al. (2003) could enhance large-scale hydrologic forecasting, but can be subject to instability under certain conditions.

scholarly journals The importance of transport model uncertainties for the estimation of CO<sub>2</sub> sources and sinks using satellite measurements

2010 ◽  
Vol 10 (20) ◽  
pp. 9981-9992 ◽  
Author(s):  
S. Houweling ◽  
I. Aben ◽  
F.-M. Breon ◽  
F. Chevallier ◽  
N. Deutscher ◽  
...  
Keyword(s):  
Transport Model ◽  
Atmospheric Transport ◽  
A Priori ◽  
Model Errors ◽  
Tracer Transport ◽  
Satellite Measurements ◽  
Transport Models ◽  
Sources And Sinks ◽  
The Impact ◽  
Ppm Level

Abstract. This study presents a synthetic model intercomparison to investigate the importance of transport model errors for estimating the sources and sinks of CO2 using satellite measurements. The experiments were designed for testing the potential performance of the proposed CO2 lidar A-SCOPE, but also apply to other space borne missions that monitor total column CO2. The participating transport models IFS, LMDZ, TM3, and TM5 were run in forward and inverse mode using common a priori CO2 fluxes and initial concentrations. Forward simulations of column averaged CO2 (xCO2) mixing ratios vary between the models by σ=0.5 ppm over the continents and σ=0.27 ppm over the oceans. Despite the fact that the models agree on average on the sub-ppm level, these modest differences nevertheless lead to significant discrepancies in the inverted fluxes of 0.1 PgC/yr per 106 km2 over land and 0.03 PgC/yr per 106 km2 over the ocean. These transport model induced flux uncertainties exceed the target requirement that was formulated for the A-SCOPE mission of 0.02 PgC/yr per 106 km2, and could also limit the overall performance of other CO2 missions such as GOSAT. A variable, but overall encouraging agreement is found in comparison with FTS measurements at Park Falls, Darwin, Spitsbergen, and Bremen, although systematic differences are found exceeding the 0.5 ppm level. Because of this, our estimate of the impact of transport model uncerainty is likely to be conservative. It is concluded that to make use of the remote sensing technique for quantifying the sources and sinks of CO2 not only requires highly accurate satellite instruments, but also puts stringent requirements on the performance of atmospheric transport models. Improving the accuracy of these models should receive high priority, which calls for a closer collaboration between experts in atmospheric dynamics and tracer transport.

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