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NASA NTRSDate not supplied

GEOS Constituent Data Assimilation Beyond Aura MLS: Assimilating NASA SAGE III/ISS Profiles of Stratospheric Water Vapor and Ozone

Ozone and water vapor in the lower stratosphere are important trace gases for atmospheric chemistry and radiative budget. The Stratospheric Aerosol and Gas Experiment (SAGE) missions have been crucial in monitoring the stratospheric ozone loss and the subsequent recovery as well as the trends in water vapor linked to surface temperature trends. The SAGE III instrument aboard the International Space Station (ISS) continues the SAGE mission record, with high vertical resolution profiles of ozone and water vapor available since mid 2017. The NASA GEOS Earth system model has the new capability to assimilate multi-constituents from ground and space-based instruments using the GEOS Constituent Data Assimilation System (CoDAS). The recently released MERRA-2 Stratospheric Composition Reanalysis with Aura MLS (M2-SCREAM) assimilates version 4.2 MLS ozone, water vapor and other chemically-reactive species with the NASA GEOS model coupled to a stratospheric-only chemistry mechanism and transport constrained to the MERRA-2 reanalysis. While the number of solar occultation observations a day from SAGE III/ISS is about 1% of the total number of profiles observed globally by MLS, the chemical timescales of ozone and water vapor in the lower stratosphere are long enough that the SAGE III/ISS data may provide a useful constraint on the assimilated product. Using the same GEOS CoDAS configuration as M2-SCREAM, we will present a series of experiments to investigate if ozone and water vapor trends are consistent with the assimilation of SAGE observations with and without Aura retrievals, and to determine if the assimilation of SAGE observations produces a steady product for trend analysis, especially as the end of the Aura mission nears. In our experiments, assimilating only SAGE III/ISS water vapor profiles results in water vapor fields more consistent with experiments that assimilate MLS v5; however, in the polar regions SAGE III/ISS observations are not available and the values are unconstrained. We are encouraged by the positive benefit assimilating the less frequent SAGE III/ISS observations has on stratospheric composition. Sensitivity experiments such as these will allow us to assess the added value of SAGE data for continued monitoring of the stratospheric composition for climate and ozone recovery assessments.

SAGE↗
NASA NTRSDate not supplied

GEOS Constituent Data Assimilation Beyond Aura MLS: Assimilating NASA SAGE III/ISS Profiles of Stratospheric Water Vapor

Ozone and water vapor in the lower stratosphere are important trace gases for atmospheric chemistry and radiative budget. The Stratospheric Aerosol and Gas Experiment (SAGE) missions have been crucial in monitoring the stratospheric ozone loss and the subsequent recovery as well as the trends in water vapor linked to surface temperature trends. The SAGE III instrument aboard the International Space Station (ISS) continues the SAGE mission record, with high vertical resolution profiles of ozone and water vapor available since mid 2017. The NASA GEOS Earth system model has the new capability to assimilate multi-constituents from ground and space-based instruments using the GEOS Constituent Data Assimilation System (CoDAS). The recently released MERRA-2 Stratospheric Composition Reanalysis with Aura MLS (M2-SCREAM) assimilates version 4.2 MLS ozone, water vapor and other chemically-reactive species with the NASA GEOS model coupled to a stratospheric-only chemistry mechanism and transport constrained to the MERRA-2 reanalysis. While the number of solar occultation observations a day from SAGE III/ISS is about 1% of the total number of profiles observed globally by MLS, the chemical timescales of ozone and water vapor in the lower stratosphere are long enough that the SAGE III/ISS data may provide a useful constraint on the assimilated product. Using the same GEOS CoDAS configuration as M2-SCREAM, we will present a series of experiments to investigate if water vapor trends are consistent with the assimilation of SAGE observations with and without Aura retrievals, and to determine if the assimilation of SAGE observations produces a steady product for trend analysis, especially as the end of the Aura mission nears. In our experiments, assimilating only SAGE III/ISS water vapor profiles results in water vapor fields more consistent with experiments that assimilate MLS v5; however, in the polar regions SAGE III/ISS observations are not available and the modelled values are unconstrained. We are encouraged by the positive benefit assimilating the less frequent SAGE III/ISS observations has on stratospheric composition. Sensitivity experiments such as these will allow us to assess the added value of SAGE data for continued monitoring of the stratospheric composition for climate and ozone recovery assessments.

K Emma Knowland↗
NASA NTRS2017

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-­‐based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 – 2020, reach the maximum in 2023 – 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series).

Data Assimilation↗
DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2018

Preliminary Evaluation of Influence of Aerosols on the Simulation of Brightness Temperature in the NASA's Goddard Earth Observing System Atmospheric Data Assimilation System

This document reports on preliminary results obtained when studying the impact of aerosols on the calculation of brightness temperature (BT) for satellite infrared (IR) instruments that are currently assimilated in a 3DVAR configuration of Goddard Earth Observing System (GEOS)-atmospheric data assimilation system (ADAS). A set of fifteen aerosol species simulated by the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model is used to evaluate the influence of the aerosol fields on the Community Radiative Transfer Model (CRTM) calculations taking place in the observation operators of the Gridpoint Statistical Interpolation (GSI) analysis system of GEOSADAS. Results indicate that taking aerosols into account in the BT calculation improves the fit to observations over regions with significant amounts of dust. The cooling effect obtained with the aerosol-affected BT leads to a slight warming of the analyzed surface temperature (by about 0:5oK) in the tropical Atlantic ocean (off northwest Africa), whereas the effect on the air temperature aloft is negligible. In addition, this study identifies a few technical issues to be addressed in future work if aerosol-affected BT are to be implemented in reanalysis and operational settings. The computational cost of applying CRTM aerosol absorption and scattering options is too high to justify their use, given the size of the benefits obtained. Furthermore, the differentiation between clouds and aerosols in GSI cloud detection procedures needs satisfactory revision.

3DVAR↗
NASA NTRS1992

The impact of dynamic data assimilation on the numerical simulations of the QE II cyclone and an analysis of the jet streak influencing the precyclogenetic environment

A mesoscale numerical model is combined with a dynamic data assimilation via Newtonian relaxation, or 'nudging', to provide initial conditions for subsequent simulations of the QE II cyclone. Both the nudging technique and the inclusion of supplementary data are shown to have a large positive impact on the simulation of the QE II cyclone during the initial phase of rapid cyclone development. Within the initial development period (from 1200 to 1800 UTC 9 September 1978), the dynamic assimilation of operational and bogus data yields a coherent two-layer divergence pattern that is not well defined in the model run using only the operational data and static initialization. Diagnostic analysis based on the simulations show that the initial development of the QE II storm between 0000 UTC 9 September and 0000 UTC 10 September was embedded within an indirect circulation of an intense 300-hPa jet streak, was related to baroclinic processes extending throughout a deep portion of the troposphere, and was associated with a classic two-layer mass-divergence profile expected for an extratropical cyclone.

Manobianco, John↗
NASA NTRSDate not supplied

Tropospheric Ozone in the NASA GEOS Model: Effects of Satellite Data Assimilation and Improvements in Background NO x Chemistry

Tropospheric ozone is a major atmospheric oxidant, the primary source of the hydroxyl radical, and a greenhouse gas. In the troposphere, it is produced from the oxidation of carbon monoxide and volatile organic compounds in the presence of nitrogen oxides (NO x =NO+NO 2 ) or has its origins in the stratosphere. The tropospheric ozone burdens in global atmospheric chemistry models disagree by a factor of 1.5, indicating an incomplete understanding of ozone sources and sinks. Here we examine the tropospheric ozone simulation in NASA Global Modeling and Assimilation Office’s (GMAO’s) GEOS model with the GEOS-Chem chemistry mechanism (version 14.2), using observations from satellites, aircraft, ozonesondes, and surface sites. This modeling framework is used to produce GMAO’s GEOS Composition Forecasts (GEOS-CF), and it has been updated extensively with new emission inventories, improved model physics, satellite data assimilation capability, and an up-to-date chemical mechanism that includes tropospheric halogen chemistry and NOx recycling from particulate nitrate. Earlier versions of the model using GEOS-Chem version 12.0 showed an underestimate in tropospheric ozone in the northern hemisphere. We evaluate the ozone simulation in the updated model, focusing on the effects of assimilating satellite NO 2 data from the Ozone Monitoring Instrument (OMI), constraining stratospheric ozone to satellite data, and updates to the NOx chemistry. We will examine changes in the vertical profiles of tropospheric ozone over the US in support of the Tropospheric Emissions: Monitoring of Pollution (TEMPO), and discuss implications for the tropospheric ozone budget.

Viral Shah↗
DOE OSTI2022

Towards physics-inspired data-driven weather forecasting: integrating data assimilation with a deep spatial-transformer-based U-NET in a case study with ERA5

Abstract. There is growing interest in data-driven weather prediction (DDWP), e.g., using convolutional neural networks such as U-NET that are trained on data from models or reanalysis. Here, we propose three components, inspired by physics, to integrate with commonly used DDWP models in order to improve their forecast accuracy. These components are (1) a deep spatial transformer added to the latent space of U-NET to capture rotation and scaling transformation in the latent space for spatiotemporal data, (2) a data-assimilation (DA) algorithm to ingest noisy observations and improve the initial conditions for next forecasts, and (3) a multi-time-step algorithm, which combines forecasts from DDWP models with different time steps through DA, improving the accuracy of forecasts at short intervals. To show the benefit and feasibility of each component, we use geopotential height at 500 hPa (Z500) from ERA5 reanalysis and examine the short-term forecast accuracy of specific setups of the DDWP framework. Results show that the spatial-transformer-based U-NET (U-STN) clearly outperforms the U-NET, e.g., improving the forecast skill by 45 %. Using a sigma-point ensemble Kalman (SPEnKF) algorithm for DA and U-STN as the forward model, we show that stable, accurate DA cycles are achieved even with high observation noise. This DDWP+DA framework substantially benefits from large (O(1000)) ensembles that are inexpensively generated with the data-driven forward model in each DA cycle. The multi-time-step DDWP+DA framework also shows promise; for example, it reduces the average error by factors of 2–3. These results show the benefits and feasibility of these three components, which are flexible and can be used in a variety of DDWP setups. Furthermore, while here we focus on weather forecasting, the three components can be readily adopted for other parts of the Earth system, such as ocean and land, for which there is a rapid growth of data and need for forecast and assimilation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1995

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of the tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiements were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiements. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. With few exceptions the error estimated generated by the Kalman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter ouput and the actual observations were drawn from a population with statistics given by the Kalman filter estimaes. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Miller, Robert N.↗
DOE OSTI2022

An ensemble data assimilation modeling system for operational outdoor microalgae growth forecasting

Microalgae have received increasing attention as a potential feedstock for biofuel or biobased products. Forecasting the microalgae growth is beneficial for managers in planning pond operations and harvesting decisions. This study proposed a biomass forecasting system comprised of the Huesemann Algae Biomass Growth Model (BGM), the Modular Aquatic Simulation System in Two Dimensions (MASS2), ensemble data assimilation (DA), and numerical weather prediction Global Ensemble Forecast System (GEFS) ensemble meteorological forecasts. The novelty of this study is to seek the use of ensemble DA to improve both BGM and MASS2 model initial conditions with the assimilation of biomass and water temperature measurements and consequently improve short-term biomass forecasting skills. This study introduces the theory behind the proposed integrated biomass forecasting system, with an application undertaken in pseudo-real-time in three outdoor ponds cultured with Chlorella sorokiniana in Delhi, California, United States. Results from all three case studies demonstrate that the biomass forecasting system improved the short-term (i.e., 7-day) biomass forecasting skills by about 60% on average, comparing to forecasts without using the ensemble DA method. Given the satisfactory performances achieved in this study, it is probable that the integrated BGM-MASS2-DA forecasting system can be used operationally to inform managers in making pond operation and harvesting planning decisions.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2022

An Agenda for Land Data Assimilation Priorities: Realizing the Promise of Terrestrial Water, Energy, and Vegetation Observations From Space

The task of quantifying spatial and temporal variations in terrestrial water, energy, and vegetation conditions is challenging due to the significant complexity and heterogeneity of these conditions, all of which are impacted by climate change and anthropogenic activities. To address this challenge, Earth Observations (EOs) of the land and their utilization within data assimilation (DA) systems are vital. Satellite EOs are particularly relevant, as they offer quasi-global coverage, are non-intrusive, and provide uniformity, rapid measurements, and continuity. The past three decades have seen unprecedented growth in the number and variety of land remote sensing technologies launched by space agencies and commercial companies around the world. There have also been significant developments in land modeling and DA systems to provide tools that can exploit these measurements. Despite these advances, several important gaps remain in current land DA research and applications. This paper discusses these gaps, particularly in the context of using DA to improve model states for short-term numerical weather and sub-seasonal to seasonal predictions. We outline an agenda for land DA priorities so that the next generation of land DA systems will be better poised to take advantage of the significant current and anticipated shifts and advancements in remote sensing, modeling, computational technologies, and hardware resources.

land surface↗
NASA NTRS1994

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Todling, Ricardo↗
NASA NTRS2014

The Major Stratospheric Sudden Warming of January 2013: Analyses and Forecasts in the GEOS-5 Data Assimilation System

We examine the major stratosphere sudden warming (SSW) that occurred on 6 January 2013, using output from the NASA Global Modeling and Assimilation Office (GMAO) GEOS-5 (Goddard Earth Observing System) near-real-time data assimilation system (DAS). Results show that the major SSW of January 2013 falls into the vortex splitting type of SSW, with the initial planetary wave breaking occurring near 10 hPa. The vertical flux of wave activity at the tropopause responsible for the SSW occurred mainly in the Pacific Hemisphere, including the a pulse associated with the preconditioning of the polar vortex by wave 1 identified on 23 December 2012. While most of the vertical wave activity flux was in the Pacific Hemisphere, a rapidly developing tropospheric weather system over the North Atlantic on 28 December is shown to have produced a strong transient upward wave activity flux into the lower stratosphere coinciding with the peak of the SSW event. In addition, the GEOS-5 5-day forecasts accurately predicted the major SSW of January 2013 as well as the upper tropospheric disturbances responsible for the warming. The overall success of the 5-day forecasts provides motivation to produce regular 10-day forecasts with GEOS-5, to better support studies of stratosphere-troposphere interaction.

SSW↗
NASA NTRS2023

Towards an Indian Land Data Assimilation System (ILDAS): A Coupled Hydrologic-Hydraulic System for Water Balance Assessments

Effective management of water resources requires reliable estimates of land surface states and fluxes, including water balance components. But most land surface models run in uncoupled mode and do not produce river discharge at catchment scales to be useful for water resources management applications. Such integrated systems are also rare over India where hydrometeorological extremes have wreaked havoc on the economy and people. So, an Indian Land Data Assimilation System (ILDAS) with a coupled land surface and a hydrodynamic model has been developed and driven by multiple meteorological forcings (0.1°, daily) to estimate land surface states, channel discharge, and floodplain inundation. ILDAS benefits from an integrated framework as well as the largest suite of observation records collected over India and has been used to produce a reanalysis product for 1981–2021 using four forcing datasets, namely, Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS), ECMWF’s ERA-5, and Indian Meteorological Department (IMD) gridded precipitation. We assessed the uncertainty and bias in these precipitation datasets and validated all major components of the terrestrial water balance, i.e., surface runoff, soil moisture, terrestrial water storage anomalies, evapotranspiration, and streamflow, against a combination of satellite and in situ observation datasets. Our assessment shows that ILDAS can represent the hydrological processes reasonably well over the Indian landmass with IMD precipitation showing the best relative performance. Evaluation against ESA-CCI soil moisture shows that MERRA-2 based estimates outperform the others, whereas ERA-5 performs best in simulating evapotranspiration when evaluated against MODIS ET. Evaluations against observed records show that CHIRPS-based estimates have the highest performance in reconstructing surface runoff and streamflow. Once operational, this system will be useful for supporting transboundary water management decision making in the region.

Indian Land Data Assimilation System (ILDAS)↗
DOE OSTI2022

Toward data assimilation of ship-induced aerosol–cloud interactions

Satellite imagery can detect temporary cloud trails or ship tracks formed from aerosols emitted from large ships traversing our oceans, a phenomenon that global climate models cannot directly reproduce. Ship tracks are observable examples of marine cloud brightening, a potential solar climate intervention that shows promise in helping combat climate change. In this paper, we demonstrate a simulation-based approach in learning the behavior of ship tracks based upon a novel stochastic emulation mechanism. Our method uses wind fields to determine the movement of aerosol–cloud tracks and uses a stochastic partial differential equation (SPDE) to model their persistence behavior. This SPDE incorporates both a drift and diffusion term which describes the movement of aerosol particles via wind and their diffusivity through the atmosphere, respectively. We first present our proposed approach with examples using simulated wind fields and ship paths. We then successfully demonstrate our tool by applying the approximate Bayesian computation method-sequential Monte Carlo for data assimilation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2017

Similarity Assessment of Land Surface Model Outputs in the North American Land Data Assimilation System

Multimodel ensembles are often used to produce ensemble mean estimates that tend to have increased simulation skill over any individual model output. If multimodel outputs are too similar, an individual LSM would add little additional information to the multimodel ensemble, whereas if the models are too dissimilar, it may be indicative of systematic errors in their formulations or configurations. The article presents a formal similarity assessment of the North American Land Data Assimilation System (NLDAS) multimodel ensemble outputs to assess their utility to the ensemble, using a confirmatory factor analysis. Outputs from four NLDAS Phase 2 models currently running in operations at NOAA/NCEP and four new/ upgraded models that are under consideration for the next phase of NLDAS are employed in this study. The results show that the runoff estimates from the LSMs were most dissimilar whereas the models showed greater similarity for root zone soil moisture, snow water equivalent, and terrestrial water storage. Generally, the NLDAS operational models showed weaker association with the common factor of the ensemble and the newer versions of the LSMs showed stronger association with the common factor, with the model similarity increasing at longer time scales. Trade-offs between the similarity metrics and accuracy measures indicated that the NLDAS operational models demonstrate a larger span in the similarity-accuracy space compared to the new LSMs. The results of the article indicate that simultaneous consideration of model similarity and accuracy at the relevant time scales is necessary in the development of multimodel ensemble.

land surface models↗
NASA NTRS1994

Technical report series on global modeling and data assimilation. Volume 1: Documentation of the Goddard Earth Observing System (GEOS) General Circulation Model, version 1

This technical report documents Version 1 of the Goddard Earth Observing System (GEOS) General Circulation Model (GCM). The GEOS-1 GCM is being used by NASA's Data Assimilation Office (DAO) to produce multiyear data sets for climate research. This report provides a documentation of the model components used in the GEOS-1 GCM, a complete description of model diagnostics available, and a User's Guide to facilitate GEOS-1 GCM experiments.

Suarez, Max J.↗
DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗