scholarly journals Influence of CO<sub>2</sub> observations on the optimized CO<sub>2</sub> flux in an ensemble Kalman filter

2014 ◽  
Vol 14 (24) ◽  
pp. 13515-13530 ◽  
Author(s):  
J. Kim ◽  
H. M. Kim ◽  
C.-H. Cho
Keyword(s):  
Kalman Filter ◽  
North America ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Co2 Flux ◽  
Experimental Period ◽  
Diagonal Element ◽  
Cumulative Impact ◽  
Influence Matrix ◽  
The Tropics

Abstract. In this study, the effect of CO2 observations on an analysis of surface CO2 flux was calculated using an influence matrix in the CarbonTracker, which is an inverse modeling system for estimating surface CO2 flux based on an ensemble Kalman filter. The influence matrix represents a sensitivity of the analysis to observations. The experimental period was from January 2000 to December 2009. The diagonal element of the influence matrix (i.e., analysis sensitivity) is globally 4.8% on average, which implies that the analysis extracts 4.8% of the information from the observations and 95.2% from the background each assimilation cycle. Because the surface CO2 flux in each week is optimized by 5 weeks of observations, the cumulative impact over 5 weeks is 19.1%, much greater than 4.8%. The analysis sensitivity is inversely proportional to the number of observations used in the assimilation, which is distinctly apparent in continuous observation categories with a sufficient number of observations. The time series of the globally averaged analysis sensitivities shows seasonal variations, with greater sensitivities in summer and lower sensitivities in winter, which is attributed to the surface CO2 flux uncertainty. The time-averaged analysis sensitivities in the Northern Hemisphere are greater than those in the tropics and the Southern Hemisphere. The trace of the influence matrix (i.e., information content) is a measure of the total information extracted from the observations. The information content indicates an imbalance between the observation coverage in North America and that in other regions. Approximately half of the total observational information is provided by continuous observations, mainly from North America, which indicates that continuous observations are the most informative and that comprehensive coverage of additional observations in other regions is necessary to estimate the surface CO2 flux in these areas as accurately as in North America.

scholarly journals Influence of CO<sub>2</sub> observations on the optimized CO<sub>2</sub> flux in an ensemble Kalman filter

2014 ◽  
Vol 14 (9) ◽  
pp. 13561-13602
Author(s):  
J. Kim ◽  
H. M. Kim ◽  
C.-H. Cho
Keyword(s):  
Kalman Filter ◽  
North America ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Co2 Flux ◽  
Experimental Period ◽  
Cumulative Impact ◽  
Influence Matrix ◽  
Analysis Scheme ◽  
The Impact

Abstract. Various data assimilation schemes have been applied in studies on atmospheric CO2 inversion. An influence matrix based on the linear statistical analysis scheme can diagnose the impact of individual observations on a particular analysis. In this study, to estimate the effect of CO2 observations on an analysis of surface CO2 flux, both the analysis sensitivity and the information content were calculated using the influence matrix in the CarbonTracker, which is an inverse modeling system for estimating surface CO2 flux based on an ensemble Kalman filter. The experimental period was from January 2000 to December 2009. The global average self-sensitivity is 4.8%, which implies that the analysis extracts 4.8% of the information from the observations and 95.2% from the background each assimilation cycle. Because the surface CO2 flux in each week is optimized by five weeks of observations, the cumulative impact over five weeks would be greater than 4.8%. The analysis sensitivity is inversely proportional to the number of observations used in the assimilation, which is distinctly apparent in continuous observation categories with a sufficient number of observations. The time series of the globally averaged analysis sensitivities shows seasonal variations, with greater sensitivities in summer and lower sensitivities in winter, which is attributed to the surface CO2 flux uncertainty. The time-averaged analysis sensitivities in the Northern Hemisphere are greater than those in the Tropics and the Southern Hemisphere. The information content indicates an imbalance between the observation coverage in North America and that in other regions. Approximately half of the total observational information is provided by continuous observations, mainly from North America, which indicates that continuous observations are the most informative and that comprehensive coverage of additional observations in other regions is necessary to estimate the surface CO2 flux in these areas as accurately as in North America. In addition, the uncertainty of the surface CO2 flux in Asia, where observations are sparse, is reduced by assimilating five weeks of observations as opposed to one week of observations in North America, which indicates that a longer assimilation window with a lag is necessary to optimize the surface CO2 flux in Asia.

scholarly journals Scale-Dependent Representation of the Information Content of Observations in the Global Ensemble Kalman Filter Data Assimilation

2016 ◽  
Vol 144 (8) ◽  
pp. 2927-2945
Author(s):  
Nedjeljka Žagar ◽  
Jeffrey Anderson ◽  
Nancy Collins ◽  
Timothy Hoar ◽  
Kevin Raeder ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Large Scale ◽  
Variance Reduction ◽  
Weather Prediction ◽  
Current Data ◽  
Model Framework ◽  
The Tropics

Abstract Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

scholarly journals Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

2013 ◽  
Vol 13 (23) ◽  
pp. 11643-11660 ◽  
Author(s):  
A. Chatterjee ◽  
A. M. Michalak
Keyword(s):  
Kalman Filter ◽  
Inverse Modeling ◽  
Ensemble Kalman Filter ◽  
Co2 Flux ◽  
Estimation Problem ◽  
Square Root ◽  
Flux Estimation ◽  
Source Sink ◽  
Operational Constraints ◽  
Square Root Filter

Abstract. Data assimilation (DA) approaches, including variational and the ensemble Kalman filter methods, provide a computationally efficient framework for solving the CO2 source–sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA approaches (an ensemble square root filter and a variational technique) using a batch inverse modeling setup as a benchmark, within the context of a simple one-dimensional advection–diffusion prototypical inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) on the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA approaches to keep the problem setup analogous to a typical real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints. Overall, the variational approach (contingent on the availability of an adjoint transport model) more reliably captures the large-scale source–sink patterns. Conversely, the ensemble square root filter provides more realistic uncertainty estimates. Selection of one approach over the other must therefore be guided by the carbon science questions being asked and the operational constraints under which the approaches are being applied.

scholarly journals Estimating surface CO<sub>2</sub> fluxes from space-borne CO<sub>2</sub> dry air mole fraction observations using an ensemble Kalman Filter

2009 ◽  
Vol 9 (8) ◽  
pp. 2619-2633 ◽  
Author(s):  
L. Feng ◽  
P. I. Palmer ◽  
H. Bösch ◽  
S. Dance
Keyword(s):  
Kalman Filter ◽  
Mole Fraction ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Co2 Flux ◽  
Surface Flux ◽  
Surface Fluxes ◽  
Co2 Fluxes ◽  
Dry Air ◽  
Geographical Regions

Abstract. We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

scholarly journals Ensemble Kalman Filter Data Assimilation for the Model for Prediction Across Scales (MPAS)

2017 ◽  
Vol 145 (11) ◽  
pp. 4673-4692 ◽  
Author(s):  
Soyoung Ha ◽  
Chris Snyder ◽  
William C. Skamarock ◽  
Jeffrey Anderson ◽  
Nancy Collins
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Skill Score ◽  
Uniform Mesh ◽  
Frequency Noise ◽  
Variable Resolution ◽  
Variable Mesh ◽  
Covariance Models ◽  
The Tropics

A global atmospheric analysis and forecast system is constructed based on the atmospheric component of the Model for Prediction Across Scales (MPAS-A) and the Data Assimilation Research Testbed (DART) ensemble Kalman filter. The system is constructed using the unstructured MPAS-A Voronoi (nominally hexagonal) mesh and thus facilitates multiscale analysis and forecasting without the need for developing new covariance models at different scales. Cycling experiments with the assimilation of real observations show that the global ensemble system is robust and reliable throughout a one-month period for both quasi-uniform and variable-resolution meshes. The variable-mesh assimilation system consistently provides higher-quality analyses than those from the coarse uniform mesh, in addition to the benefits of the higher-resolution forecasts, which leads to substantial improvements in 5-day forecasts. Using the fractions skill score, the spatial scale for skillful precipitation forecasts is evaluated over the high-resolution area of the variable-resolution mesh. Skill decreases more rapidly at smaller scales, but the variable mesh consistently outperforms the coarse uniform mesh in precipitation forecasts at all times and thresholds. Use of incremental analysis updates (IAU) greatly decreases high-frequency noise overall and improves the quality of EnKF analyses, particularly in the tropics. Important aspects of the system design related to the unstructured Voronoi mesh are also investigated, including algorithms for handling the C-grid staggered horizontal velocities.

scholarly journals Predictability and Genesis of Hurricane Karl (2010) Examined through the EnKF Assimilation of Field Observations Collected during PREDICT

2014 ◽  
Vol 71 (4) ◽  
pp. 1260-1275 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Control Experiment ◽  
Initial Condition ◽  
Field Observations ◽  
Ensemble Forecasts ◽  
Thermodynamic Structure ◽  
Cloud Systems ◽  
The Tropics

Abstract The genesis of Hurricane Karl (2010) is explored using analyses and forecasts from a cycling ensemble Kalman filter (EnKF) that assimilates routinely collected observations as well as dropsonde measurements that were taken during the Pre-Depression Investigation of Cloud Systems in the Tropics (PREDICT) field campaign. A total of 127 dropsonde observations were collected from six PREDICT flight missions over a 5-day period before and during Karl’s genesis. EnKF analyses that take into account the PREDICT dropsondes provide a detailed four-dimensional overview of the evolving kinematic and thermodynamic structure within the pregenesis disturbance. In particular, the additional field observations are found to increase the low- and midlevel circulation and column moisture in the EnKF analyses and reduce the position error of the low-level vortex. Deterministic forecasts from these analyses show a 24-h improvement in predicting genesis over a control experiment that omits the dropsonde observations. In ensemble forecasts for this event, the more accurate analyses translate into a higher confidence in predicting the intensification of Karl; that is, data assimilation experiments also suggest that initial condition errors at the mesoscale pose large challenges for predicting genesis, thus highlighting the need for improved observation networks and more advanced data assimilation methods.

scholarly journals Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

2013 ◽  
Vol 13 (5) ◽  
pp. 12825-12865
Author(s):  
A. Chatterjee ◽  
A. M. Michalak
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Co2 Flux ◽  
Estimation Problem ◽  
Advantages And Disadvantages ◽  
Flux Estimation ◽  
Operational Constraints ◽  
The Impact

Abstract. Data assimilation (DA) approaches, such as the variational and the ensemble Kalman filter, provide a computationally efficient framework for solving the CO2 source-sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of alternative DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA methods (an ensemble square root filter and a variational technique) using a simple 1-dimensional advection-diffusion inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are specifically designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) in order to isolate the degradation in the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA methods to keep the problem setup analogous to a real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints imposed to make the DA algorithms practically feasible. The overall advantages/disadvantages of the two examined DA approaches are complementary and highlight that, specifically for CO2 applications, selection of one method over the other should be dictated by the carbon science questions being asked, and the inversion conditions under which the approaches are being applied.

Ensemble Kalman Filter for Out of Sequence Measurement Tracking

2012 ◽  
Vol 132 (10) ◽  
pp. 1617-1625
Author(s):  
Sirichai Pornsarayouth ◽  
Masaki Yamakita
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

scholarly journals Assimilation of D-InSAR snow depth data by an ensemble Kalman filter

2021 ◽  
Vol 14 (6) ◽  
Author(s):  
Jinming Yang ◽  
Chengzhi Li
Keyword(s):  
Remote Sensing ◽  
Kalman Filter ◽  
Water Resource ◽  
Ensemble Kalman Filter ◽  
Snow Depth ◽  
Resource Assessment ◽  
Measured Data ◽  
Hydrological Process ◽  
Depth Data ◽  
Water Resource Assessment

AbstractSnow depth mirrors regional climate change and is a vital parameter for medium- and long-term numerical climate prediction, numerical simulation of land-surface hydrological process, and water resource assessment. However, the quality of the available snow depth products retrieved from remote sensing is inevitably affected by cloud and mountain shadow, and the spatiotemporal resolution of the snow depth data cannot meet the need of hydrological research and decision-making assistance. Therefore, a method to enhance the accuracy of snow depth data is urgently required. In the present study, three kinds of snow depth data which included the D-InSAR data retrieved from the remote sensing images of Sentinel-1 synthetic aperture radar, the automatically measured data using ultrasonic snow depth detectors, and the manually measured data were assimilated based on ensemble Kalman filter. The assimilated snow depth data were spatiotemporally consecutive and integrated. Under the constraint of the measured data, the accuracy of the assimilated snow depth data was higher and met the need of subsequent research. The development of ultrasonic snow depth detector and the application of D-InSAR technology in snow depth inversion had greatly alleviated the insufficiency of snow depth data in types and quantity. At the same time, the assimilation of multi-source snow depth data by ensemble Kalman filter also provides high-precision data to support remote sensing hydrological research, water resource assessment, and snow disaster prevention and control program.

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