Observation Error Covariance Research Articles

Optimal Interpolation of Precipitable Water Using Low Earth Orbit and Numerical Weather Prediction Data

The National Meteorological Satellite Center/Korean Meteorological Administration (NMSC/KMA) receives data directly from low Earth orbit (LEO) satellites (including NOAA-18,19; MetOp-A,B; and Suomi-NPP), and generates Level 2 products (e.g., temperature and humidity profile) in near real time. Total precipitable water (TPW) and layer precipitable water (LPW) are also generated using the retrieved humidity profiles. Today, forecasters need meteorologically-significant data fields composited from all available data sources, not multiple maps of observations from individual sources. Hence, TPW and LPW are reproduced using the optimal interpolation (OI) method with numerical weather prediction (NWP) data, in order to generate composite precipitable water (PW) products. In the OI procedure, PW data retrieved from the LEO satellites serve as observation data, while PW data from NWP serve as background data. Error covariances are estimated using a new approach, which considers correlations between observation errors to describe the characteristics of the errors better. Both background and observation error covariance matrices may have non-zero off-diagonal components. The composite PW products are validated using radiosonde data. The validation results for optimally-interpolated LPW (OI LPW) are much better than those for optimally-interpolated TPW (OI TPW). Generally, the OI LPW validation results are better than those for observation and background data; OI LPW data are ~5–10% more accurate than background data. Optimally-interpolated PW (OI PW) fields are applied to the correction of NWP forecast fields and the prediction of severe weather.

Bio‐Optical Data Assimilation With Observational Error Covariance Derived From an Ensemble of Satellite Images

AbstractAn ensemble‐based approach to specify observational error covariance in the data assimilation of satellite bio‐optical properties is proposed. The observational error covariance is derived from statistical properties of the generated ensemble of satellite MODIS‐Aqua chlorophyll (Chl) images. The proposed observational error covariance is used in the Optimal Interpolation scheme for the assimilation of MODIS‐Aqua Chl observations. The forecast error covariance is specified in the subspace of the multivariate (bio‐optical, physical) empirical orthogonal functions (EOFs) estimated from a month‐long model run. The assimilation of surface MODIS‐Aqua Chl improved surface and subsurface model Chl predictions. Comparisons with surface and subsurface water samples demonstrate that data assimilation run with the proposed observational error covariance has higher RMSE than the data assimilation run with “optimistic” assumption about observational errors (10% of the ensemble mean), but has smaller or comparable RMSE than data assimilation run with an assumption that observational errors equal to 35% of the ensemble mean (the target error for satellite data product for chlorophyll). Also, with the assimilation of the MODIS‐Aqua Chl data, the RMSE between observed and model‐predicted fractions of diatoms to the total phytoplankton is reduced by a factor of two in comparison to the nonassimilative run.

The conditioning of least‐squares problems in variational data assimilation

SummaryIn variational data assimilation a least‐squares objective function is minimised to obtain the most likely state of a dynamical system. This objective function combines observation and prior (or background) data weighted by their respective error statistics. In numerical weather prediction, data assimilation is used to estimate the current atmospheric state, which then serves as an initial condition for a forecast. New developments in the treatment of observation uncertainties have recently been shown to cause convergence problems for this least‐squares minimisation. This is important for operational numerical weather prediction centres due to the time constraints of producing regular forecasts. The condition number of the Hessian of the objective function can be used as a proxy to investigate the speed of convergence of the least‐squares minimisation. In this paper we develop novel theoretical bounds on the condition number of the Hessian. These new bounds depend on the minimum eigenvalue of the observation error covariance matrix and the ratio of background error variance to observation error variance. Numerical tests in a linear setting show that the location of observation measurements has an important effect on the condition number of the Hessian. We identify that the conditioning of the problem is related to the complex interactions between observation error covariance and background error covariance matrices. Increased understanding of the role of each constituent matrix in the conditioning of the Hessian will prove useful for informing the choice of correlated observation error covariance matrix and observation location, particularly for practical applications.

The Effect of Thinning and Superobservations in a Simple One-Dimensional Data Analysis with Mischaracterized Error

A one-dimensional (1D) analysis problem is defined and analyzed to explore the interaction of observation thinning or superobservation with observation errors that are correlated or systematic. The general formulation might be applied to a 1D analysis of radiance or radio occultation observations in order to develop a strategy for the use of such data in a full data assimilation system, but is applied here to a simple analysis problem with parameterized error covariances. Findings for the simple problem include the following. For a variational analysis method that includes an estimate of the full observation error covariances, the analysis is more sensitive to variations in the estimated background and observation error standard deviations than to variations in the corresponding correlation length scales. Furthermore, if everything else is fixed, the analysis error increases with decreasing true background error correlation length scale and with increasing true observation error correlation length scale. For a weighted least squares analysis method that assumes the observation errors are uncorrelated, best results are obtained for some degree of thinning and/or tuning of the weights. Without tuning, the best strategy is superobservation with a spacing approximately equal to the observation error correlation length scale.

Impacts on sea ice analyses from the assumption of uncorrelated ice thickness observation errors: Experiments using a 1D toy model

Sea ice prediction centres are moving toward the assimilation of ice thickness observations under the simplifying assumption that the observation errors are uncorrelated. The assumption of uncorrelated observation errors is attractive because the errors can be represented by a diagonal observation error covariance matrix, which is inexpensive to invert. In this paper a set of idealized experiments are carried out to investigate the impact of this assumption on sea ice analyses. A background error covariance matrix is generated using a 1D toy model for sea, i.e. forced with idealized models of the ocean and atmosphere. Analysis error covariance matrices are then calculated using this matrix for both correlated and uncorrelated observation error covariance matrices, . The results indicate when the true is correlated, using a diagonal approximation results in an analysis that is overconfident at the large scales, in that the analysis error standard deviation at the large scales is underestimated. It is also shown that for the largest observation error correlation length scale tested, 150 km, the analysis error standard deviation for ice thickness is reduced by 10.8% relative to the background error standard deviation when has the correct correlation length scale of 150 km, whereas when a diagonal approximation to is used in combination with an inflation factor, the reduction is to 6.3%.

Developing an A Priori Database for Passive Microwave Snow Water Retrievals Over Ocean

AbstractA physically optimized a priori database is developed for Global Precipitation Measurement Microwave Imager (GMI) snow water retrievals over ocean. The initial snow water content profiles are derived from CloudSat Cloud Profiling Radar (CPR) measurements. A radiative transfer model in which the single‐scattering properties of nonspherical snowflakes are based on the discrete dipole approximate results is employed to simulate brightness temperatures and their gradients. Snow water content profiles are then optimized through a one‐dimensional variational (1D‐Var) method. The standard deviations of the difference between observed and simulated brightness temperatures are in a similar magnitude to the observation errors defined for observation error covariance matrix after the 1D‐Var optimization, indicating that this variational method is successful. This optimized database is applied in a Bayesian retrieval snow water algorithm. The retrieval results indicated that the 1D‐Var approach has a positive impact on the GMI retrieved snow water content profiles by improving the physical consistency between snow water content profiles and observed brightness temperatures. Global distribution of snow water contents retrieved from the a priori database is compared with CloudSat CPR estimates. Results showed that the two estimates have a similar pattern of global distribution, and the difference of their global means is small. In addition, we investigate the impact of using physical parameters to subset the database on snow water retrievals. It is shown that using total precipitable water to subset the database with 1D‐Var optimization is beneficial for snow water retrievals.

EFSR: Ensemble Forecast Sensitivity to Observation Error Covariance

Data assimilation (DA) methods require an estimate of observation error covariance [Formula: see text] as an external parameter that typically is tuned in a subjective manner. To facilitate objective and systematic tuning of [Formula: see text] within the context of ensemble Kalman filtering, this paper introduces a method for estimating how forecast errors would be changed by increasing or decreasing each element of [Formula: see text], without a need for the adjoint of the model and the DA system, by combining the adjoint-based [Formula: see text]-sensitivity diagnostics presented by Daescu previously with the technique employed by Kalnay et al. to derive ensemble forecast sensitivity to observations (EFSO). The proposed method, termed EFSR, is shown to be able to detect and adaptively correct misspecified [Formula: see text] through a series of toy-model experiments using the Lorenz ’96 model. It is then applied to a quasi-operational global DA system of the National Centers for Environmental Prediction to provide guidance on how to tune the [Formula: see text]. A sensitivity experiment in which the prescribed observation error variances for four selected observation types were scaled by 0.9 or 1.1 following the EFSR guidance, however, resulted in forecast improvement that is not statistically significant. This can be explained by the smallness of the perturbation given to the [Formula: see text]. An iterative online approach to improve on this limitation is proposed. Nevertheless, the sensitivity experiment did show that the EFSO impacts from each observation type were increased by the EFSR-guided tuning of [Formula: see text].

Estimating model error covariances using particle filters.

A method is presented for estimating the error covariance of the errors in the model equations in observation space. Estimating model errors in this systematic way opens up the possibility to use data assimilation for systematic model improvement at the level of the model equations, which would be a huge step forward. This model error covariance is perhaps the hardest covariance matrix to estimate. It represents how the missing physics and errors in parametrizations manifest themselves at the scales the model can resolve.A new element is that we use an efficient particle filter to avoid the need to estimate the error covariance of the state as well, which most other data assimilation methods do require. Starting from a reasonable first estimate, the method generates new estimates iteratively during the data assimilation run, and the method is shown to converge to the correct model error matrix. We also investigate the influence of the accuracy of the observation error covariance on the estimation of the model error covariance and show that, when the observation errors are known, the model error covariance can be estimated well, but, as expected and perhaps unavoidably, the diagonal elements are estimated too low when the observation errors are estimated too high, and vice versa.

Quantifying the inflation factors of observation error variance for COMS and MTSAT Atmospheric Motion Vectors considering spatial observation error correlation

In this study, the spatial error correlations in the Atmospheric Motion Vectors (AMVs) derived from the geostationary satellite imagery over East Asia are investigated. Good characterization of systematic errors in observations is essential in order to extract the maximum amount of information from the observations during the assimilation process. The spatial structure of AMV error correlations was identified based on datasets of AMVs collocated with sonde observations for July 2015. Results of AMVs from water vapour (WV; 6.7 µm) and infrared (IR; 10.8 µm) channels of the Korean geostationary Communication, Ocean and Meteorological Satellite (COMS) and the Multifunction Transport Satellite‐2 (MTSAT) are presented. For both channels, the length scales of the spatial error correlations in the MTSAT AMVs are longer than those of the COMS AMVs. For MTSAT (COMS) AMVs, a longer (shorter) length‐scale yields more (less) inflated observation error variance, and a larger (smaller) inflation factor for the diagonal form of the observation error covariance matrix is required to obtain the best quality of analysis.

Calibration of imperfect models to biased observations

The problem of assimilating biased and inaccurate observations into inadequate models of the physical systems from which the observations were taken is common in the petroleum and groundwater fields. When large amounts of data are assimilated without accounting for model error and observation bias, predictions tend to be both overconfident and incorrect. In this paper, we propose a workflow for calibration of imperfect models to biased observations that involves model construction, model calibration, model criticism and model improvement. Model criticism is based on computation of model diagnostics which provide an indication of the validity of assumptions. During the model improvement step, we advocate identification of additional physically motivated parameters based on examination of data mismatch after calibration and addition of bias correction terms. If model diagnostics indicates the presence of residual model error after parameters have been added, then we advocate estimation of a “total” observation error covariance matrix, whose purpose is to reduce weighting of observations that cannot be matched because of deficiency of the model. Although the target applications of this methodology are in the subsurface, we illustrate the approach with two simplified examples involving prediction of the future velocity of fall of a sphere from models calibrated to a short-time series of biased measurements with independent additive random noise. The models into which the data are assimilated contain model errors due to neglect of physical processes and neglect of uncertainty in parameters. In every case, the estimated total error covariance is larger than the true observation covariance implying that the observations need not be matched to the accuracy of the measuring instrument. Predictions are much improved when all model improvement steps were taken.

Variational assimilation of IASI SO<sub>2</sub> plume height and total column retrievals in the 2010 eruption of Eyjafjallajökull using the SILAM v5.3 chemistry transport model

Abstract. This study focuses on two new aspects of inverse modelling of volcanic emissions. First, we derive an observation operator for satellite retrievals of plume height, and second, we solve the inverse problem using an algorithm based on the 4D-Var data assimilation method. The approach is first tested in a twin experiment with simulated observations and further evaluated by assimilating IASI SO2 plume height and total column retrievals in a source term inversion for the 2010 eruption of Eyjafjallajökull. The inversion resulted in temporal and vertical reconstruction of the SO2 emissions during 1–20 May 2010 with formal vertical and temporal resolutions of 500 m and 12 h.The plume height observation operator is based on simultaneous assimilation of the plume height and total column retrievals. The plume height is taken to represent the vertical centre of mass, which is transformed into the first moment of mass (centre of mass times total mass). This makes the observation operator linear and simple to implement. The necessary modifications to the observation error covariance matrix are derived.Regularization by truncated iteration is investigated as a simple and efficient regularization method for the 4D-Var-based inversion. In the twin experiments, the truncated iteration was found to perform similarly to the commonly used Tikhonov regularization, which in turn is equivalent to a Gaussian a priori source term. However, the truncated iteration allows the level of regularization to be determined a posteriori without repeating the inversion.In the twin experiments, assimilating the plume height retrievals resulted in a 5–20 % improvement in root mean squared error but simultaneously introduced a 10–20 % low bias on the total emission depending on assumed emission profile. The results are consistent with those obtained with real data. For Eyjafjallajökull, comparisons with observations showed that assimilating the plume height retrievals reduced the overestimation of injection height during individual periods of 1–3 days, but for most of the simulated 20 days, the injection height was constrained by meteorological conditions, and assimilation of the plume height retrievals had only small impact. The a posteriori source term for Eyjafjallajökull consisted of 0.29 Tg (with total column and plume height retrievals) or 0.33 Tg (with total column retrievals only) erupted SO2 of which 95 % was injected below 11 or 12 km, respectively.

Accounting for Correlated Observation Error in a Dual-Formulation 4D Variational Data Assimilation System

Appropriate specification of the error statistics for both observational data and short-term forecasts is necessary to produce an optimal analysis. Observation error stems from instrument error, forward model error, and error of representation. All sources of observation error, particularly error of representation, can lead to nonzero correlations. While correlated forecast error has been accounted for since the early days of atmospheric data assimilation, observation error has typically been treated as uncorrelated until relatively recently. Thinning, averaging, and/or inflation of the assigned observation error variance have been employed to compensate for unaccounted error correlations, especially for high-resolution satellite data. In this study, the benefits of accounting for nonzero vertical (interchannel) correlation for both the Advanced Technology Microwave Satellite (ATMS) and Infrared Atmospheric Sounding Interferometer (IASI) in the NRL Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR) are assessed. The vertical observation error covariance matrix for the ATMS and IASI instruments was estimated using the Desroziers method. The results suggest lowering the assigned error variance and introducing strong correlations, especially in the moisture-sensitive channels. Strong positive impact on forecast skill (verified against both the ECMWF analyses and high-quality radiosonde data) is shown in both the ATMS and IASI instruments. Additionally, the convergence of the iterative solver in NAVDAS-AR can be improved by small modifications to the observation error covariance matrices, resulting in further reduction in RMS error.

Investigating the Use of Ensemble Variance to Predict Observation Error of Representation

AbstractData assimilation schemes combine observational data with a short-term model forecast to produce an analysis. However, many characteristics of the atmospheric states described by the observations and the model differ. Observations often measure a higher-resolution state than coarse-resolution model grids can describe. Hence, the observations may measure aspects of gradients or unresolved eddies that are poorly resolved by the filtered version of reality represented by the model. This inconsistency, known as observation representation error, must be accounted for in data assimilation schemes. In this paper the ability of the ensemble to predict the variance of the observation error of representation is explored, arguing that the portion of representation error being detected by the ensemble variance is that portion correlated to the smoothed features that the coarse-resolution forecast model is able to predict. This predictive relationship is explored using differences between model states and their spectrally truncated form, as well as commonly used statistical methods to estimate observation error variances. It is demonstrated that the ensemble variance is a useful predictor of the observation error variance of representation and that it could be used to account for flow dependence in the observation error covariance matrix.

An Extension of the Ensemble Kalman Filter for Estimating the Observation Error Covariance Matrix Based on the Variational Bayes’s Method

Abstract This paper presents an extension of the ensemble Kalman filter (EnKF) that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes’s (VB) method. In numerical experiments, this capability is examined for a time-variant observation error covariance matrix, and it is noteworthy that this method works well even when the true observation error covariance matrix is nondiagonal. In addition, two complementary studies are presented. First, the stability of a long-run assimilation is demonstrated when there are unmodeled disturbances. Second, a maximum-likelihood (ML) method is derived and demonstrated for optimizing the hyperparameters used in this method.

An Efficient Way to Account for Observation Error Correlations in the Assimilation of Data from the Future SWOT High-Resolution Altimeter Mission

AbstractMost data assimilation algorithms require the inverse of the covariance matrix of the observation errors. In practical applications, the cost of computing this inverse matrix with spatially correlated observation errors is prohibitive. Common practices are therefore to subsample or combine the observations so that the errors of the assimilated observations can be considered uncorrelated. As a consequence, a large fraction of the available observational information is not used in practical applications. In this study, a method is developed to account for the correlations of the errors that will be present in the wide-swath sea surface height measurements, for example, the Surface Water and Ocean Topography (SWOT) mission. It basically consists of the transformation of the observation vector so that the inverse of the corresponding covariance matrix can be replaced by a diagonal matrix, thus allowing to genuinely take into account errors that are spatially correlated in physical space. Numerical experiments of ensemble Kalman filter analysis of SWOT-like observations are conducted with three different observation error covariance matrices. Results suggest that the proposed method provides an effective way to account for error correlations in the assimilation of the future SWOT data. The transformation of the observation vector proposed herein yields both a significant reduction of the root-mean-square errors and a good consistency between the filter analysis error statistics and the true error statistics.

C-GLORSv5: an improved multipurpose global ocean eddy-permitting physical reanalysis

Abstract. Global ocean reanalyses combine in situ and satellite ocean observations with a general circulation ocean model to estimate the time-evolving state of the ocean, and they represent a valuable tool for a variety of applications, ranging from climate monitoring and process studies to downstream applications, initialization of long-range forecasts and regional studies. The purpose of this paper is to document the recent upgrade of C-GLORS (version 5), the latest ocean reanalysis produced at the Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC) that covers the meteorological satellite era (1980–present) and it is being updated in delayed time mode. The reanalysis is run at eddy-permitting resolution (1∕4° horizontal resolution and 50 vertical levels) and consists of a three-dimensional variational data assimilation system, a surface nudging and a bias correction scheme. With respect to the previous version (v4), C-GLORSv5 contains a number of improvements. In particular, background- and observation-error covariances have been retuned, allowing a flow-dependent inflation in the globally averaged background-error variance. An additional constraint on the Arctic sea-ice thickness was introduced, leading to a realistic ice volume evolution. Finally, the bias correction scheme and the initialization strategy were retuned. Results document that the new reanalysis outperforms the previous version in many aspects, especially in representing the variability of global heat content and associated steric sea level in the last decade, the top 80 m ocean temperature biases and root mean square errors, and the Atlantic Ocean meridional overturning circulation; slight worsening in the high-latitude salinity and deep ocean temperature emerge though, providing the motivation for further tuning of the reanalysis system. The dataset is available in NetCDF format at doi:10.1594/PANGAEA.857995.

Estimating observation error covariance matrix of seismic data from a perspective of image denoising

Estimating observation error covariance matrix properly is a key step towards successful seismic history matching. Typically, observation errors of seismic data are spatially correlated; therefore, the observation error covariance matrix is non-diagonal. Estimating such a non-diagonal covariance matrix is the focus of the current study. We decompose the estimation into two steps: (1) estimate observation errors and (2) construct covariance matrix based on the estimated observation errors. Our focus is on step (1), whereas at step (2) we use a procedure similar to that in Aanonsen et al. 2003. In Aanonsen et al. 2003, step (1) is carried out using a local moving average algorithm. By treating seismic data as an image, this algorithm can be interpreted as a discrete convolution between an image and a rectangular window function. Following the perspective of image processing, we consider three types of image denoising methods, namely, local moving average with different window functions (as an extension of the method in Aanonsen et al. 2003), non-local means denoising and wavelet denoising. The performance of these three algorithms is compared using both synthetic and field seismic data. It is found that, in our investigated cases, the wavelet denoising method leads to the best performance in most of the time.

Consistent assimilation of multiple data streams in a carbon cycle data assimilation system

Abstract. Data assimilation methods provide a rigorous statistical framework for constraining parametric uncertainty in land surface models (LSMs), which in turn helps to improve their predictive capability and to identify areas in which the representation of physical processes is inadequate. The increase in the number of available datasets in recent years allows us to address different aspects of the model at a variety of spatial and temporal scales. However, combining data streams in a DA system is not a trivial task. In this study we highlight some of the challenges surrounding multiple data stream assimilation for the carbon cycle component of LSMs. We give particular consideration to the assumptions associated with the type of inversion algorithm that are typically used when optimising global LSMs – namely, Gaussian error distributions and linearity in the model dynamics. We explore the effect of biases and inconsistencies between the observations and the model (resulting in non-Gaussian error distributions), and we examine the difference between a simultaneous assimilation (in which all data streams are included in one optimisation) and a step-wise approach (in which each data stream is assimilated sequentially) in the presence of non-linear model dynamics. In addition, we perform a preliminary investigation into the impact of correlated errors between two data streams for two cases, both when the correlated observation errors are included in the prior observation error covariance matrix, and when the correlated errors are ignored. We demonstrate these challenges by assimilating synthetic observations into two simple models: the first a simplified version of the carbon cycle processes represented in many LSMs and the second a non-linear toy model. Finally, we provide some perspectives and advice to other land surface modellers wishing to use multiple data streams to constrain their model parameters.

3D assimilation of Hiroshima Bay acoustic tomography data into a Princeton Ocean Circulation Model

A baroclinic data assimilation, based on the ensemble Kalman filter (EnKF) method, with coastal acoustic tomography (CAT) data is first applied to Princeton Ocean Model (POM) to elucidate a 3D structure of coastal upwelling which occurred in Hiroshima Bay due to a northerly wind from a typhoon. The CAT experiment with four acoustic stations was performed from Sept. 11 to Sept. 25, 2013, in the northern part of Hiroshima Bay, Japan. Reciprocal data were acquired at three stations and along three transmission lines with a triangular array and travel time were identified every 10 min for the first and second arrival rays which travel at different depth ranges. As for the EnKF method, the Kalman gain was determined to minimize the observed and simulated travel time differences and summations. The model error covariance was given by adding pseudorandom noises (zero mean value and one variance) with an appropriate multiplication factor to the POM result. The observation error covariance was estimated from the variation of observed travel times. A 3D structure of coastal upwelling which was difficult to be simulated by the POM was reconstructed by data assimilation and compared with the CTD result.

EnKF and 4D-Var data assimilation with chemical transport model BASCOE (version 05.06)

Abstract. We compare two optimized chemical data assimilation systems, one based on the ensemble Kalman filter (EnKF) and the other based on four-dimensional variational (4D-Var) data assimilation, using a comprehensive stratospheric chemistry transport model (CTM). This work is an extension of the Belgian Assimilation System for Chemical ObsErvations (BASCOE), initially designed to work with a 4D-Var data assimilation. A strict comparison of both methods in the case of chemical tracer transport was done in a previous study and indicated that both methods provide essentially similar results. In the present work, we assimilate observations of ozone, HCl, HNO3, H2O and N2O from EOS Aura-MLS data into the BASCOE CTM with a full description of stratospheric chemistry. Two new issues related to the use of the full chemistry model with EnKF are taken into account. One issue is a large number of error variance parameters that need to be optimized. We estimate an observation error variance parameter as a function of pressure level for each observed species using the Desroziers method. For comparison purposes, we apply the same estimate procedure in the 4D-Var data assimilation, where both scale factors of the background and observation error covariance matrices are estimated using the Desroziers method. However, in EnKF the background error covariance is modelled using the full chemistry model and a model error term which is tuned using an adjustable parameter. We found that it is adequate to have the same value of this parameter based on the chemical tracer formulation that is applied for all observed species. This is an indication that the main source of model error in chemical transport model is due to the transport. The second issue in EnKF with comprehensive atmospheric chemistry models is the noise in the cross-covariance between species that occurs when species are weakly chemically related at the same location. These errors need to be filtered out in addition to a localization based on distance. The performance of two data assimilation methods was assessed through an 8-month long assimilation of limb sounding observations from EOS Aura MLS. This paper discusses the differences in results and their relation to stratospheric chemical processes. Generally speaking, EnKF and 4D-Var provide results of comparable quality but differ substantially in the presence of model error or observation biases. If the erroneous chemical modelling is associated with moderately fast chemical processes, but whose lifetimes are longer than the model time step, then EnKF performs better, while 4D-Var develops spurious increments in the chemically related species. If, however, the observation biases are significant, then 4D-Var is more robust and is able to reject erroneous observations while EnKF does not.