Localization Radius Research Articles

Ensemble Kalman Filter for Assimilating Experimental Data into Large-Eddy Simulations of Turbulent Flows

Data assimilation techniques are investigated for integrating high-speed high-resolution experimental data into large-eddy simulations. To this end, an ensemble Kalman filter is employed to assimilate velocity measurements of a turbulent jet at a Reynolds number of 13,500 into simulations. The goal of the current work is to examine the behavior of the assimilation algorithm for state estimation of turbulent flows that are of relevance to engineering applications. This is accomplished by investigating the impact that localization, measurement uncertainties, assimilation frequency, data sparsity and ensemble size have on the estimated state vector. For the flow configuration and computational setup considered in this study an optimal value of the localization radius is identified, which minimizes the error between experimental data and state vector. The impact of experimental uncertainties on the state estimation is demonstrated to provide solution bounds on the assimilation algorithm. It is found that increasing the number of ensembles has a positive impact on the state estimation. In comparison, decreasing the assimilation frequency or reducing the experimental data available for assimilation is found to have a negative impact on the state estimation. These findings demonstrate the viability of assimilating measurements into numerical simulations to improve state estimates, to support parameter evaluations and to guide model assessments.

Simulation of hopping in disordered fractal arrays of graphene quantum dots

Diffusion regimes of charge carriers in artificial quasi-fractal graphene quantum dot (GQD) superlattices forming hexagonal and triangular carpet are investigated. Using the generalized Miller-Abrahams relations for hopping rates we perform Monte Carlo simulation of charge carrier hopping in artificial 2d disordered arrays of armchair GQDs. The variations of the anomalous advection-diffusion parameters as functions of localization radius, electric field intensity, levels of energetic and structural disorder are studied.

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample. This is the role played by covariance localization in the large-size applications of the ensemble Kalman filter. In this paper, it is suggested that covariance localization can also be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i)~that can be sampled at a very low cost (proportional to the size of the state vector, with a small integer coefficient),(ii)~that automatically accounts for a localized prior covariance, and (iii)~that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i)~the effectiveness of covariance localization, (ii)~the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii)~the possibility to deal with non-Gaussian (even discrete) prior marginal distributions, by including (stochastic) anamorphosis transformations, (iv)~the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (v)~the scalability of the algorithm as a function of the size of the problem. The evaluation of the computational complexity of the algorithm suggests that it could become numerically competitive with local ensemble Kalman filters, even in the absence of nonlocal constraints, especially if the localization radius is large. All codes necessary to reproduce the example application described in this paper are openly available from github.com/brankart/ensdam.

Lagrangian Data Assimilation of Surface Drifters in a Double-Gyre Ocean Model Using the Local Ensemble Transform Kalman Filter

Abstract The assimilation of position data from Lagrangian observing platforms is underdeveloped in operational applications because of two main challenges: 1) nonlinear growth of model and observation error in the Lagrangian trajectories, and 2) the high dimensionality of realistic models. In this study, we propose a localized Lagrangian data assimilation (LaDA) method that is based on the local ensemble transform Kalman filter (LETKF). The algorithm is tested with an “identical twin” approach in observing system simulation experiments (OSSEs) using a simple double-gyre configuration of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model. Results from the OSSEs show that with a proper choice of localization radius, the LaDA can outperform conventional assimilation of surface in situ temperature and salinity measurements. The improvements are seen not only in the surface state estimate, but also throughout the ocean column to 1000 m depth. The impacts of localization radius and model error in estimating accuracy of both fluid and drifter states are further investigated.

Structural properties and variable-range hopping conductivity of Cu2SnS3

In the present work, we investigated the elemental composition, structural and electrical properties of Cu2SnS3 (CTS) ternary semiconductor synthesized by the pyrolytic decomposition of the precursors in vacuum. The molar ratio of Sn/Cu in the precursor solution was varied from 0.2 to 0.6. The x-ray diffraction and Raman analyses confirmed that the synthesized samples mainly consist of tetragonal CTS phase with space group The dependence of the conductivity of CTS samples on temperature was investigated in the temperature range 10-300 K. A crossover between nearest-neighbor hopping and Mott variable-range hopping conduction mechanisms were observed at Analysis of the data yielded the values of the relative acceptor concentration with the critical concentration of the metal–insulator transition (MIT) cm−3, the localization radius with the Bohr radius the dielectric permittivity far from the MIT κ0 = 10.7, the mean acceptor energy meV and the mean density of the localized states meV−1cm−3.

Quantum Phase Transition in Phosphate Glasses Containing Multiple Transition Metal Oxides

The evidence for a Mott–Hubbard type metal–insulator transition (MIT) is presented in the xP2O5− yV2O5− (100− x − y)WO3 glass system (PVW) at a critical concentration of tungsten (W) ions. Electrons contributed by the reduced vanadium (V) and tungsten (W) ions are self-trapped to form small polarons, and the hopping motion of such charge carriers is the universally accepted transport mechanism. Whereas both the V and W ions are present in multiple oxidation states in these glasses, charges at the V4+ (reduced) sites contribute only to electrical conduction. We demonstrate that, in PVW glasses, electrons at the reduced tungsten sites are too strongly localized to contribute to electrical conduction, but the oxidized state still contributes an available orbital for electrons to tunnel through. This secondary contribution of the tungsten ions greatly facilitates small polaron hopping (SPH) conductivity. With decreasing vanadium concentration [nV= V/(V + W), where V and W are the molar concentrations of V and W ions in this equation], as the inter-atomic distance between V ions increases, the resistivity remains invariant in the composition range 0.5 < nV < 1. However, a sharp increase in resistivity is observed at nV ∼ 0.5, when the tungsten localization radius collapses drastically. Such a transition is similar to the Mott–Hubbard type MIT observed in many crystalline systems. We have demonstrated that MIT in PVW glasses occurs at a critical V–V distance, drastically changing the transfer integral between V sites and forcing conduction to take place through the deeper and energetically disfavored tungsten orbitals.

Electrical conductivity, thermoelectrical properties, and EPR spectroscopy of copper chromite ceramic samples doped with magnesium

The results of a study of copper chromite ceramic samples doped with magnesium are presented. The samples were synthesized according to the solid-phase method using a special procedure for preparing the initial mixture, which ensures a uniform distribution of magnesium with its content from 0.2 to 6%. The substitution of chromium for magnesium in the crystal lattice is confirmed by Raman scattering of light and EPR spectra. As the magnesium content increases from 0 to 6 at.%, the resistivity of the synthesized samples decreases by more than 3 orders of magnitude at room temperature. High thermopower values were obtained, and it was shown that the main charge carriers are holes, and the predominant mechanism of hole transport in doped samples is hopping transfer over localized states, whose density decreases with an increase in energy near the Fermi energy. It is shown that the localization radius increases with an increase in magnesium content.

Study of transport and magnetic properties of electron-doped superconducting cuprates Eu1.85Ce0.15Cu1-yZnyO4+α-δ

Transport and magnetic properties of electron-doped superconducting cuprates Eu1.85Ce0.15Cu1-yZnyO4+α-δ (ECCZO) with y = 0, 0.01, 0.02 and 0.05 have been studied from electrical resistivity and magnetic susceptibility measurements, in order to elucidate the effect of partially Zn-substitution for Cu to its superconductivity and localization of electron in normal state. It has been found that the onset of the critical temperature (Tc) from electrical resistivity and magnetic susceptibility measurements was observed at 13 K for y = 0 and δ values of 0.095. With increasing Zn concentration, the onset of Tc disappeared, indicating the destruction of superconductivity properties by Zn. Moreover, 0.01 of Zn substitution for Cu decreased radius of localization of electron (r) in normal state at low temperatures that may related to the evident of stripe-pinning effects by Zn in electron-doped system of ECCZO. Analysis of magnetic susceptibility data in normal state found a Zn-induced local moments in electron-doped high-Tc superconducting cuprates of ECCZO as observed in hole-doped cuprates.

Magnetotransport and conductivity mechanisms in Cu2ZnSnxGe1\u2212xS4 single crystals

Resistivity, ρ(T), and magnetoresistance (MR) are investigated in the Cu2ZnSnxGe1−xS4 single crystals, obtained by the chemical vapor transport method, between x = 0–0.70, in the temperature range of T ~ 50–300 K in pulsed magnetic field of B up to 20 T. The Mott variable-range hopping (VRH) conductivity is observed within broad temperature intervals, lying inside that of T ~ 80–180 K for different x. The nearest-neighbor hopping conductivity and the charge transfer, connected to activation of holes into the delocalized states of the acceptor band, are identified above and below the Mott VRH conduction domain, respectively. The microscopic electronic parameters, including width of the acceptor band, the localization radius and the density of the localized states at the Fermi level, as well as the acceptor concentration and the critical concentration of the metal-insulator transition, are obtained with the analysis of the ρ(T) and MR data. All the parameters above exhibit extremums near x = 0.13, which are attributable mainly to the transition from the stannite crystal structure at x = 0 to the kesterite-like structure near x = 0.13. The detailed analysis of the activation energy in the low-temperature interval permitted estimations of contributions from different crystal phases of the border compounds into the alloy structure at different compositions.

A flexible additive inflation scheme for treating model error in ensemble Kalman filters

Data assimilation algorithms require an accurate estimate of the uncertainty of the prior (background) field that cannot be adequately represented by the ensemble of numerical model simulations. Partially, this is due to the sampling error that arises from the use of a small number of ensemble members to represent the background‐error covariance. It is also partially a consequence of the fact that the geophysical model does not represent its own error. Several mechanisms have been introduced so far to alleviate the detrimental effects of misrepresented ensemble covariances, allowing for the successful implementation of ensemble data assimilation techniques for atmospheric dynamics. One of the established approaches is additive inflation, which consists of perturbing each ensemble member with a sample from a given distribution. This results in a fixed rank of the effective model‐error covariance matrix. In this article, a more flexible approach is introduced, where the model error samples are treated as additional synthetic ensemble members, which are used in the update step of data assimilation but are not forecast. This way, the rank of the model‐error covariance matrix can be chosen independently of the ensemble. The effect of this altered additive inflation method on the performance of the filter is analyzed here in an idealized experiment. It is shown that the additional synthetic ensemble members can make it feasible to achieve convergence in an otherwise divergent parameter setting of data assimilation. The use of this method also allows for a less stringent localization radius.

Data assimilation experiment of precipitable water vapor observed by a hyper-dense GNSS receiver network using a nested NHM-LETKF system

We studied the assimilation of high-resolution precipitable water vapor (PWV) data derived from a hyper-dense global navigation satellite system network around Uji city, Kyoto, Japan, which had a mean inter-station distance of about 1.7 km. We focused on a heavy rainfall event that occurred on August 13–14, 2012, around Uji city. We employed a local ensemble transform Kalman filter as the data assimilation method. The inhomogeneity of the observed PWV increased on a scale of less than 10 km in advance of the actual rainfall detected by the rain gauge. Zenith wet delay data observed by the Uji network showed that the characteristic length scale of water vapor distribution during the rainfall ranged from 1.9 to 3.5 km. It is suggested that the assimilation of PWV data with high horizontal resolution (a few km) improves the forecast accuracy. We conducted the assimilation experiment of high-resolution PWV data, using both small horizontal localization radii and a conventional horizontal localization radius. We repeated the sensitivity experiment, changing the mean horizontal spacing of the PWV data from 1.7 to 8.0 km. When the horizontal spacing of assimilated PWV data was decreased from 8.0 to 3.5 km, the accuracy of the simulated hourly rainfall amount worsened in the experiment that used the conventional localization radius for the assimilation of PWV. In contrast, the accuracy of hourly rainfall amounts improved when we applied small horizontal localization radii. In the experiment that used the small horizontal localization radii, the accuracy of the hourly rainfall amount was most improved when the horizontal resolution of the assimilated PWV data was 3.5 km. The optimum spatial resolution of PWV data was related to the characteristic length scale of water vapor variability.

Variable-Range Hopping Conduction in the Kesterite and Wurtzstannite Cu2ZnGeS4 Single Crystals

Progress in the solar cell science and technology, based on quaternary compounds, recently has been focused on the materials with a partial or full cation substitution of Ge for Sn. In particular, this stimulated an interest to the Cu2ZnGeS4 (CZGeS) compound. However, for its effective utilization, deeper investigations of CZGeS transport properties are required. In the present manuscript, the resistivity, ρ(T), of the p-type CZGeS single crystals with the kesterite (KS) and wurtzstannite (WS) structures is investigated in the temperature range of ~50–300 K. The dependence of ρ(T) is described by the Mott type of the variable-range hopping (VRH) charge transfer mechanism within a broad temperature interval of ~60–150 K for the KS samples and of ~100–260 K for the WS samples. A quantitative analysis of the resistivity data in the VRH conduction regime permitted determination or estimation of a series of important microscopic parameters. These include the localization radius of acceptors, their concentration and density of the acceptor states, as well as positions of the mobility threshold and of the Fermi level in the acceptor band.

High-field magnetotransport in Cu2ZnGeS4 single crystals

The quaternary chalcogenides, attracting much attention in recent time as promising solar energy materials, permit an effective optimization of their composition by the Ge incorporation. In particular, this implies an interest to the Cu2ZnGeS4 compound, which utilization requires, however, a deeper understanding of its electronic properties in general. Here, we investigate magnetotransport of the p-type Cu2ZnGeS4 single crystals, including resistivity, ρ (T), magnetoresistance (MR) and Hall effect, in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping charge transfer has been established within a broad temperature interval of T between ∼100 and 200 K by investigations of ρ (T) in zero field. The positive and negative contributions to MR have been observed, attributing them to shrinkage of the impurity wave functions by the magnetic field and to the destructive interference of the hopping charge carriers, respectively. Observation of the negative Hall coefficient, RH (T), exhibiting the dependence close to that of ρ (T), gives a strong support to the Mott conduction mechanism in our p-type Cu2ZnGeS4 material. In addition, the conductivity, connected with thermal activation of holes on the mobility edge, Ec, has been identified both below and above the Mott conduction interval. Finally, the joint analysis of the ρ (T) and MR data has yielded a series of important microscopic parameters. These include such details of the hole spectrum in the acceptor band, as its semi-width, W, the density of localized states, g (μ), at the Fermi level, μ, the positions of μ and Ec, as well as values of the localization radius of holes, a, and of the acceptor concentration, NA.

Parameter and state estimation with ensemble Kalman filter based algorithms for convective‐scale applications

Representation of clouds in convection‐permitting models is sensitive to numerical weather prediction (NWP) model parameters that are often very crudely known (for example roughness length). Our goal is to allow for uncertainty in these parameters and estimate them from data using the ensemble Kalman filter (EnKF) approach. However, to deal with difficulties associated with convective‐scale applications, such as non‐Gaussianity and constraints on state and parameter values, modifications to classical EnKF are necessary. In this article, we evaluate and extend several recently developed EnKF‐based algorithms that either incorporate constraints such as mass conservation and positivity of precipitation explicitly or introduce higher order moments on the joint state and parameter estimation problem. We compare their results with the localized EnKF for a common idealized test case. The test case uses perfect model experiments with the one‐dimensional modified shallow‐water model, which was designed to mimic important properties of convection. We use a stochastic dynamical model for parameters, in order to prevent underdispersion in parameter space. To deal with localization for estimation of parameters, we introduce a method called global updating, which is a computationally cheap modification of spatial updating and was proven successful in this context. The sensitivity of the results to the number of ensemble members and localization, as well as observation coverage and frequency, is shown. Although all algorithms are capable of reducing the initial state and parameter errors, it is concluded that mass conservation is important when the localization radius is small and/or the observations are sparse. In addition, accounting for higher order moments in the joint space and parameter estimation problem is beneficial when the ensemble size is large enough or when applied to parameter estimation only.

On the Selection of Localization Radius in Ensemble Filtering for Multiscale Quasigeostrophic Dynamics

Covariance localization remedies sampling errors due to limited ensemble size in ensemble data assimilation. Previous studies suggest that the optimal localization radius depends on ensemble size, observation density and accuracy, as well as the correlation length scale determined by model dynamics. A comprehensive localization theory for multiscale dynamical systems with varying observation density remains an active area of research. Using a two-layer quasigeostrophic (QG) model, this study systematically evaluates the sensitivity of the best Gaspari–Cohn localization radius to changes in model resolution, ensemble size, and observing networks. Numerical experiment results show that the best localization radius is smaller for smaller-scale components of a QG flow, indicating its scale dependency. The best localization radius is rather insensitive to changes in model resolution, as long as the key dynamical processes are reasonably well represented by the low-resolution model with inflation methods that account for representation errors. As ensemble size decreases, the best localization radius shifts to smaller values. However, for nonlocal correlations between an observation and state variables that peak at a certain distance, decreasing localization radii further within this distance does not reduce analysis errors. Increasing the density of an observing network has two effects that both reduce the best localization radius. First, the reduced observation error spectral variance further constrains prior ensembles at large scales. Less large-scale contribution results in a shorter overall correlation length, which favors a smaller localization radius. Second, a denser network provides more independent pieces of information, thus a smaller localization radius still allows the same number of observations to constrain each state variable.

Variable-range hopping conductivity in Lu-doped Bi2Te3

The Seebeck coefficient enhancement due to an increase of density-of-states effective mass of electron has been found in n-type Bi1.9Lu0.1Te3. This enhancement is assumed to be related to forming the narrow and non-parabolic impurity (Lu) band with local maximum of electronic density of states lying near the Fermi level. Minimum in the specific electrical resistivity, ρ, originated from change of conductivity mechanism was observed at temperature Tm ≈ 11 K. Above Tm, the ρ change is due to decrease of electron mobility via acoustic phonon scattering. Below Tm, the variable-range hopping conductivity takes place. The electron hops between the localized states of the impurity energy band occur via tunneling process. Using the temperature and magnetic field dependences of ρ, the localization radius of electron was estimated as ≈6 nm. Two parts in the magnetic field dependence of the electrical resistivity were found at temperature of 2 K. At weak magnetic fields, the ρ change is in agreement with the variable-range hopping conductivity mechanism. At high magnetic fields, the positive and almost linear transverse and longitudinal magnetoresistances were observed at low temperatures. Both variable-range hopping conductivity and positive linear magnetoresistance are characteristics of disordered and inhomogeneous semiconductors.

Development of a Hybrid En3DVar Data Assimilation System and Comparisons with 3DVar and EnKF for Radar Data Assimilation with Observing System Simulation Experiments

Abstract A hybrid ensemble–3DVar (En3DVar) system is developed and compared with 3DVar, EnKF, “deterministic forecast” EnKF (DfEnKF), and pure En3DVar for assimilating radar data through perfect-model observing system simulation experiments (OSSEs). DfEnKF uses a deterministic forecast as the background and is therefore parallel to pure En3DVar. Different results are found between DfEnKF and pure En3DVar: 1) the serial versus global nature and 2) the variational minimization versus direct filter updating nature of the two algorithms are identified as the main causes for the differences. For 3DVar (EnKF/DfEnKF and En3DVar), optimal decorrelation scales (localization radii) for static (ensemble) background error covariances are obtained and used in hybrid En3DVar. The sensitivity of hybrid En3DVar to covariance weights and ensemble size is examined. On average, when ensemble size is 20 or larger, a 5%–10% static covariance gives the best results, while for smaller ensembles, more static covariance is beneficial. Using an ensemble size of 40, EnKF and DfEnKF perform similarly, and both are better than pure and hybrid En3DVar overall. Using 5% static error covariance, hybrid En3DVar outperforms pure En3DVar for most state variables but underperforms for hydrometeor variables, and the improvement (degradation) is most notable for water vapor mixing ratio qυ (snow mixing ratio qs). Overall, EnKF/DfEnKF performs the best, 3DVar performs the worst, and static covariance only helps slightly via hybrid En3DVar.

A Systematic Comparison of Particle Filter and EnKF in Assimilating Time‐Averaged Observations

AbstractThe particle filter (PF) and the ensemble Kalman filter (EnKF) are two promising and popularly adopted types of ensemble‐based data assimilation methods for paleoclimate reconstruction. However, no systematic comparison between them has been attempted. We compare these two uncertainty based methods in pseudoproxy experiments where synthetic seasonal mean sea surface temperature observations are assimilated. Their skills are evaluated with regards to local, hemispherically averaged and globally averaged analysis error, and their ability to capture large‐scale modes of variability. It is found that the EAKF (Ensemble Adjustment Kalman filter, a variant of EnKF) performs better than the PF with only one third of the ensemble size, despite PF's theoretical superiority in allowing for non‐Gaussian statistics and nonlinear dynamics. The success of the EAKF is attributed to the facts that (1) Gaussian assumption is somewhat appropriate for this application; (2) The EAKF is less sensitive to sampling errors than the PF due to the different methodological natures. Sixteen members are enough to estimate accurate covariance for the EAKF, but 48 (even 96) members still underrepresent the state space of high‐dimensional system for the PF. Our study highlights the importance of a large localization radius in the application of the EnKF to paleoclimate reconstruction due to the sparse proxy network and suggests that additional techniques, such as localization or clustered particle filter, are needed to improve the PF for paleoclimate reconstruction, in addition to the simple importance resampling currently adopted by most research.

High-field hopping magnetotransport in kesterites

Transport properties of the kesterite-like single crystals of Cu2ZnSnS4, Cu2ZnSnxGe1−xSe4 and Cu2ZnGeS4 are investigated in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping (VRH) conduction is established by investigations of the resistivity, ρ (T), in all the materials mentioned above within broad temperature intervals of ΔTv4 ∼ 50–150 K, 50–250 K and 100–200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below Tv2 ∼ 3–4 K, the nearest-neighbour hopping (NNH) charge transfer between T ∼ 250–320 K and the conductivity by activation of holes on the mobility threshold at temperatures outside ΔTv4, respectively, are observed in these materials. In Cu2ZnSnS4, magnetoresistance (MR) contains only a positive contribution, connected mainly to a shrinkage of impurity wave functions by the magnetic field. At the same time, a negative contribution to MR, attributable to interference effects in VRH, is observed in Cu2ZnSnxGe1−xSe4 and, especially, in Cu2ZnGeS4. The joint analysis of the MR and ρ (T) data has yielded important electronic parameters of the materials. This includes widths of the acceptor band W and of the Coulomb gap Δ, the NNH activation energy En, the localization radius a, the acceptor concentration NA and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu2ZnSnS4 with decreasing T is observed, whereas in Cu2ZnSnxGe1−xSe4 all the parameter W, En, g (μ), a and NA are non-monotonic functions of x. Finally, in Cu2ZnGeS4 the Hall coefficient RH (T) is negative (despite of the p-type conduction), exhibiting the dependence close to that of ρ (T) in the Mott VRH interval.

Accounting for CO2 variability over East Asia with a regional joint inversion system and its preliminary evaluation

A regional surface carbon dioxide (CO2) flux inversion system, the Tan-Tracker-Region, was developed by incorporating an assimilation scheme into the Community Multiscale Air Quality (CMAQ) regional chemical transport model to resolve fine-scale CO2 variability over East Asia. The proper orthogonal decomposition-based ensemble four-dimensional variational data assimilation approach (POD-4DVar) is the core algorithm for the joint assimilation framework, and simultaneous assimilations of CO2 concentrations and surface CO2 fluxes are applied to help reduce the uncertainty in initial CO2 concentrations. A persistence dynamical model was developed to describe the evolution of the surface CO2 fluxes and help avoid the “signal-to-noise” problem; thus, CO2 fluxes could be estimated as a whole at the model grid scale, with better use of observation information. The performance of the regional inversion system was evaluated through a group of single-observation-based observing system simulation experiments (OSSEs). The results of the experiments suggest that a reliable performance of Tan-Tracker-Region is dependent on certain assimilation parameter choices, for example, an optimized window length of approximately 3 h, an ensemble size of approximately 100, and a covariance localization radius of approximately 320 km. This is probably due to the strong diurnal variation and spatial heterogeneity in the fine-scale CMAQ simulation, which could affect the performance of the regional inversion system. In addition, because all observations can be artificially obtained in OSSEs, the performance of Tan-Tracker-Region was further evaluated through different densities of the artificial observation network in different CO2 flux situations. The results indicate that more observation sites would be useful to systematically improve the estimation of CO2 concentration and flux in large areas over the model domain. The work presented here forms a foundation for future research in which a thorough estimation of CO2 flux variability over East Asia could be performed with the regional inversion system.