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1
Nerger, Lars. „On Serial Observation Processing in Localized Ensemble Kalman Filters“. Monthly Weather Review 143, Nr. 5 (01.05.2015): 1554–67. http://dx.doi.org/10.1175/mwr-d-14-00182.1.
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Abstract Ensemble square root filters can either assimilate all observations that are available at a given time at once, or assimilate the observations in batches or one at a time. For large-scale models, the filters are typically applied with a localized analysis step. This study demonstrates that the interaction of serial observation processing and localization can destabilize the analysis process, and it examines under which conditions the instability becomes significant. The instability results from a repeated inconsistent update of the state error covariance matrix that is caused by the localization. The inconsistency is present in all ensemble Kalman filters, except for the classical ensemble Kalman filter with perturbed observations. With serial observation processing, its effect is small in cases when the assimilation changes the ensemble of model states only slightly. However, when the assimilation has a strong effect on the state estimates, the interaction of localization and serial observation processing can significantly deteriorate the filter performance. In realistic large-scale applications, when the assimilation changes the states only slightly and when the distribution of the observations is irregular and changing over time, the instability is likely not significant.
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Huang, Bo, Xuguang Wang und Craig H. Bishop. „The High-Rank Ensemble Transform Kalman Filter“. Monthly Weather Review 147, Nr. 8 (31.07.2019): 3025–43. http://dx.doi.org/10.1175/mwr-d-18-0210.1.
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Abstract The ensemble Kalman filter is typically implemented either by applying the localization on the background error covariance matrix (B-localization) or by inflating the observation error variances (R-localization). A mathematical demonstration suggests that for the same effective localization function, the background error covariance matrix from the B-localization method shows a higher rank than the R-localization method. The B-localization method is realized in the ensemble transform Kalman filter (ETKF) by extending the background ensemble perturbations through modulation (MP-localization). Specifically, the modulation functions are constructed from the leading eigenvalues and eigenvectors of the original B-localization matrix. Because of its higher rank than the classic R-localized ETKF, the B-/MP-localized ETKF is termed as the high-rank ETKF (HETKF). The performances of the HETKF and R-localized ETKF were compared through cycled data assimilation experiments using the Lorenz model II. The results show that the HETKF outperforms the R-localized ETKF especially for a small ensemble. The improved analysis in the HETKF is likely associated with the higher rank from the B-/MP-localization method, since its higher rank is expected to contribute more positively to alleviating the rank deficiency issue and thus improve the analysis for a small ensemble. The HETKF is less sensitive to the localization length scales and inflation factors. Furthermore, the experiments suggest that the above conclusion comparing the HETKF and R-localized ETKF does not depend on how the analyzed ensemble perturbations are subselected in the HETKF.
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Bergeron, Jean, Robert Leconte, Mélanie Trudel und Sepehr Farhoodi. „On the Choice of Metric to Calibrate Time-Invariant Ensemble Kalman Filter Hyper-Parameters for Discharge Data Assimilation and Its Impact on Discharge Forecast Modelling“. Hydrology 8, Nr. 1 (24.02.2021): 36. http://dx.doi.org/10.3390/hydrology8010036.
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An important step when using some data assimilation methods, such as the ensemble Kalman filter and its variants, is to calibrate its parameters. Also called hyper-parameters, these include the model and observation errors, which have previously been shown to have a strong impact on the performance of the data assimilation method. Many metrics can be used to calibrate these hyper-parameters but may not all yield the same optimal set of values. The current study investigated the importance of the choice of metric used during the hyper-parameter calibration phase and its impact on discharge forecasts. The types of metrics used each focused on discharge accuracy, ensemble spread or observation-minus-background statistics. The calibration was performed for the ensemble square root Kalman filter over two catchments in Canada using two different hydrologic models per catchment. Results show that the optimal set of hyper-parameters depended heavily on the choice of metric used during the calibration phase, where data assimilation was applied. These sets of hyper-parameters in turn produced different hydrologic forecasts. This influence was reduced as the forecast lead time increased, because of not applying data assimilation in the forecast mode, and accordingly, convergence of model state ensembles produced in the calibration phase. However, the influence could remain considerable for a few days up to multiple weeks depending on the catchment and the model. As such, a preliminary analysis would be recommended for future studies to better understand the impact that metrics can have within and outside the bounds of hyper-parameter calibration.
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Bishop, Craig H., Bo Huang und Xuguang Wang. „A Nonvariational Consistent Hybrid Ensemble Filter“. Monthly Weather Review 143, Nr. 12 (01.12.2015): 5073–90. http://dx.doi.org/10.1175/mwr-d-14-00391.1.
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Abstract A consistent hybrid ensemble filter (CHEF) for using hybrid forecast error covariance matrices that linearly combine aspects of both climatological and flow-dependent matrices within a nonvariational ensemble data assimilation scheme is described. The CHEF accommodates the ensemble data assimilation enhancements of (i) model space ensemble covariance localization for satellite data assimilation and (ii) Hodyss’s method for improving accuracy using ensemble skewness. Like the local ensemble transform Kalman filter (LETKF), the CHEF is computationally scalable because it updates local patches of the atmosphere independently of others. Like the sequential ensemble Kalman filter (EnKF), it serially assimilates batches of observations and uses perturbed observations to create ensembles of analyses. It differs from the deterministic (no perturbed observations) ensemble square root filter (ESRF) and the EnKF in that (i) its analysis correction is unaffected by the order in which observations are assimilated even when localization is required, (ii) it uses accurate high-rank solutions for the posterior error covariance matrix to serially assimilate observations, and (iii) it accommodates high-rank hybrid error covariance models. Experiments were performed to assess the effect on CHEF and ESRF analysis accuracy of these differences. In the case where both the CHEF and the ESRF used tuned localized ensemble covariances for the forecast error covariance model, the CHEF’s advantage over the ESRF increased with observational density. In the case where the CHEF used a hybrid error covariance model but the ESRF did not, the CHEF had a substantial advantage for all observational densities.
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Etherton, Brian J. „Preemptive Forecasts Using an Ensemble Kalman Filter“. Monthly Weather Review 135, Nr. 10 (01.10.2007): 3484–95. http://dx.doi.org/10.1175/mwr3480.1.
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Abstract An ensemble Kalman filter (EnKF) estimates the error statistics of a model forecast using an ensemble of model forecasts. One use of an EnKF is data assimilation, resulting in the creation of an increment to the first-guess field at the observation time. Another use of an EnKF is to propagate error statistics of a model forecast forward in time, such as is done for optimizing the location of adaptive observations. Combining these two uses of an ensemble Kalman filter, a “preemptive forecast” can be generated. In a preemptive forecast, the increment to the first-guess field is, using ensembles, propagated to some future time and added to the future control forecast, resulting in a new forecast. This new forecast requires no more time to produce than the time needed to run a data assimilation scheme, as no model integration is necessary. In an observing system simulation experiment (OSSE), a barotropic vorticity model was run to produce a 300-day “nature run.” The same model, run with a different vorticity forcing scheme, served as the forecast model. The model produced 24- and 48-h forecasts for each of the 300 days. The model was initialized every 24 h by assimilating observations of the nature run using a hybrid ensemble Kalman filter–three-dimensional variational data assimilation (3DVAR) scheme. In addition to the control forecast, a 64-member forecast ensemble was generated for each of the 300 days. Every 24 h, given a set of observations, the 64-member ensemble, and the control run, an EnKF was used to create 24-h preemptive forecasts. The preemptive forecasts were more accurate than the unmodified, original 48-h forecasts, though not quite as accurate as the 24-h forecast obtained from a new model integration initialized by assimilating the same observations as were used in the preemptive forecasts. The accuracy of the preemptive forecasts improved significantly when 1) the ensemble-based error statistics used by the EnKF were localized using a Schur product and 2) a model error term was included in the background error covariance matrices.
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Zhou, Haiyan, Liangping Li und J. Jaime Gómez-Hernández. „Characterizing Curvilinear Features Using the Localized Normal-Score Ensemble Kalman Filter“. Abstract and Applied Analysis 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/805707.
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The localized normal-score ensemble Kalman filter is shown to work for the characterization of non-multi-Gaussian distributed hydraulic conductivities by assimilating state observation data. The influence of type of flow regime, number of observation piezometers, and the prior model structure are evaluated in a synthetic aquifer. Steady-state observation data are not sufficient to identify the conductivity channels. Transient-state data are necessary for a good characterization of the hydraulic conductivity curvilinear patterns. Such characterization is very good with a dense network of observation data, and it deteriorates as the number of observation piezometers decreases. It is also remarkable that, even when the prior model structure is wrong, the localized normal-score ensemble Kalman filter can produce acceptable results for a sufficiently dense observation network.
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Potthast, Roland, Anne Walter und Andreas Rhodin. „A Localized Adaptive Particle Filter within an Operational NWP Framework“. Monthly Weather Review 147, Nr. 1 (Januar 2019): 345–62. http://dx.doi.org/10.1175/mwr-d-18-0028.1.
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Particle filters are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naïve application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimension of many practical assimilation problems (known as the curse of dimensionality). The goal of this work is to develop a localized adaptive particle filter (LAPF), which follows closely the idea of the classical MCMC or bootstrap-type particle filter, but overcomes the problems of collapse and divergence based on localization in the spirit of the local ensemble transform Kalman filter (LETKF) and adaptivity with an adaptive Gaussian resampling or rejuvenation scheme in ensemble space. The particle filter has been implemented in the data assimilation system for the global forecast model ICON at Deutscher Wetterdienst (DWD). We carry out simulations over a period of 1 month with a global horizontal resolution of 52 km and 90 layers. With four variables analyzed per grid point, this leads to 6.6 × 106 degrees of freedom. The LAPF can be run stably and shows a reasonable performance. We compare its scores to the operational setup of the ICON LETKF.
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Delijani, Ebrahim Biniaz, Mahmoud Reza Pishvaie und Ramin Bozorgmehry Boozarjomehry. „Subsurface characterization with localized ensemble Kalman filter employing adaptive thresholding“. Advances in Water Resources 69 (Juli 2014): 181–96. http://dx.doi.org/10.1016/j.advwatres.2014.04.011.
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Chen, Yan, Weimin Zhang und Mengbin Zhu. „A localized weighted ensemble Kalman filter for high‐dimensional systems“. Quarterly Journal of the Royal Meteorological Society 146, Nr. 726 (15.12.2019): 438–53. http://dx.doi.org/10.1002/qj.3685.
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Auligné, Thomas, Benjamin Ménétrier, Andrew C. Lorenc und Mark Buehner. „Ensemble–Variational Integrated Localized Data Assimilation“. Monthly Weather Review 144, Nr. 10 (Oktober 2016): 3677–96. http://dx.doi.org/10.1175/mwr-d-15-0252.1.
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Hybrid variational–ensemble data assimilation (hybrid DA) is widely used in research and operational systems, and it is considered the current state of the art for the initialization of numerical weather prediction models. However, hybrid DA requires a separate ensemble DA to estimate the uncertainty in the deterministic variational DA, which can be suboptimal both technically and scientifically. A new framework called the ensemble–variational integrated localized (EVIL) data assimilation addresses this inconvenience by updating the ensemble analyses using information from the variational deterministic system. The goal of EVIL is to encompass and generalize existing ensemble Kalman filter methods in a variational framework. Particular attention is devoted to the affordability and efficiency of the algorithm in preparation for operational applications.
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Poterjoy, Jonathan. „A Localized Particle Filter for High-Dimensional Nonlinear Systems“. Monthly Weather Review 144, Nr. 1 (22.12.2015): 59–76. http://dx.doi.org/10.1175/mwr-d-15-0163.1.
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Abstract This paper presents a new data assimilation approach based on the particle filter (PF) that has potential for nonlinear/non-Gaussian applications in geoscience. Particle filters provide a Monte Carlo approximation of a system’s probability density, while making no assumptions regarding the underlying error distribution. The proposed method is similar to the PF in that particles—also referred to as ensemble members—are weighted based on the likelihood of observations in order to approximate posterior probabilities of the system state. The new approach, denoted the local PF, extends the particle weights into vector quantities to reduce the influence of distant observations on the weight calculations via a localization function. While the number of particles required for standard PFs scales exponentially with the dimension of the system, the local PF provides accurate results using relatively few particles. In sensitivity experiments performed with a 40-variable dynamical system, the local PF requires only five particles to prevent filter divergence for both dense and sparse observation networks. Comparisons of the local PF and ensemble Kalman filters (EnKFs) reveal advantages of the new method in situations resembling geophysical data assimilation applications. In particular, the new filter demonstrates substantial benefits over EnKFs when observation networks consist of densely spaced measurements that relate nonlinearly to the model state—analogous to remotely sensed data used frequently in weather analyses.
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Poterjoy, Jonathan, und Jeffrey L. Anderson. „Efficient Assimilation of Simulated Observations in a High-Dimensional Geophysical System Using a Localized Particle Filter“. Monthly Weather Review 144, Nr. 5 (Mai 2016): 2007–20. http://dx.doi.org/10.1175/mwr-d-15-0322.1.
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This study presents the first application of a localized particle filter (PF) for data assimilation in a high-dimensional geophysical model. Particle filters form Monte Carlo approximations of model probability densities conditioned on observations, while making no assumptions about the underlying error distribution. Unlike standard PFs, the local PF uses a localization function to reduce the influence of distant observations on state variables, which significantly decreases the number of particles required to maintain the filter’s stability. Because the local PF operates effectively using small numbers of particles, it provides a possible alternative to Gaussian filters, such as ensemble Kalman filters, for large geophysical models. In the current study, the local PF is compared with stochastic and deterministic ensemble Kalman filters using a simplified atmospheric general circulation model. The local PF is found to provide stable filtering results over yearlong data assimilation experiments using only 25 particles. The local PF also outperforms the Gaussian filters when observation networks include measurements that have non-Gaussian errors or relate nonlinearly to the model state, like remotely sensed data used frequently in atmospheric analyses. Results from this study encourage further testing of the local PF on more complex geophysical systems, such as weather prediction models.
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Sommer, Matthias, und Martin Weissmann. „Observation impact in a convective-scale localized ensemble transform Kalman filter“. Quarterly Journal of the Royal Meteorological Society 140, Nr. 685 (27.03.2014): 2672–79. http://dx.doi.org/10.1002/qj.2343.
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Ruchi, Sangeetika, und Svetlana Dubinkina. „Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling“. Nonlinear Processes in Geophysics 25, Nr. 4 (06.11.2018): 731–46. http://dx.doi.org/10.5194/npg-25-731-2018.
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Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimations in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ ensemble transform particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). The large number of uncertain parameters is of particular interest for subsurface reservoir modeling as it allows us to parameterize permeability on the grid. We prove that the updated parameters obtained by ETPF lie within the range of an initial ensemble, which is not the case for ETKF. We examine the performance of ETPF and ETKF in a twin experiment setup, where observations of pressure are synthetically created based on the known values of parameters. For a small number of uncertain parameters (one and five) ETPF performs comparably to ETKF in terms of the mean estimation. For a large number of uncertain parameters (2500) ETKF is robust with respect to the initial ensemble, while ETPF is sensitive due to sampling error. Moreover, for the high-dimensional test problem ETPF gives an increase in the root mean square error after data assimilation is performed. This is resolved by applying distance-based localization, which however deteriorates a posterior estimation of the leading mode by largely increasing the variance due to a combination of less varying localized weights, not keeping the imposed bounds on the modes via the Karhunen–Loeve expansion, and the main variability explained by the leading mode. A possible remedy is instead of applying localization to use only leading modes that are well estimated by ETPF, which demands knowledge of which mode to truncate.
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Bellsky, Thomas, Jesse Berwald und Lewis Mitchell. „Nonglobal Parameter Estimation Using Local Ensemble Kalman Filtering“. Monthly Weather Review 142, Nr. 6 (28.05.2014): 2150–64. http://dx.doi.org/10.1175/mwr-d-13-00200.1.
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Abstract The authors study parameter estimation for nonglobal parameters in a low-dimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global parameters, they present a methodology whereby spatially varying parameters can be estimated using observations only within a localized region of space. Taking a low-dimensional nonlinear chaotic conceptual model for atmospheric dynamics as a numerical test bed, the authors show that this parameter estimation methodology accurately estimates parameters that vary in both space and time, as well as parameters representing physics absent from the model.
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Zhen, Yicun, und Fuqing Zhang. „A Probabilistic Approach to Adaptive Covariance Localization for Serial Ensemble Square Root Filters“. Monthly Weather Review 142, Nr. 12 (01.12.2014): 4499–518. http://dx.doi.org/10.1175/mwr-d-13-00390.1.
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Abstract This study proposes a variational approach to adaptively determine the optimum radius of influence for ensemble covariance localization when uncorrelated observations are assimilated sequentially. The covariance localization is commonly used by various ensemble Kalman filters to limit the impact of covariance sampling errors when the ensemble size is small relative to the dimension of the state. The probabilistic approach is based on the premise of finding an optimum localization radius that minimizes the distance between the Kalman update using the localized sampling covariance versus using the true covariance, when the sequential ensemble Kalman square root filter method is used. The authors first examine the effectiveness of the proposed method for the cases when the true covariance is known or can be approximated by a sufficiently large ensemble size. Not surprisingly, it is found that the smaller the true covariance distance or the smaller the ensemble, the smaller the localization radius that is needed. The authors further generalize the method to the more usual scenario that the true covariance is unknown but can be represented or estimated probabilistically based on the ensemble sampling covariance. The mathematical formula for this probabilistic and adaptive approach with the use of the Jeffreys prior is derived. Promising results and limitations of this new method are discussed through experiments using the Lorenz-96 system.
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Pang, Mijie, Jianbing Jin, Arjo Segers, Huiya Jiang, Li Fang, Hai Xiang Lin und Hong Liao. „Dust storm forecasting through coupling LOTOS-EUROS with localized ensemble Kalman filter“. Atmospheric Environment 306 (August 2023): 119831. http://dx.doi.org/10.1016/j.atmosenv.2023.119831.
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Li, L., H. Zhou, H. J. Hendricks Franssen und J. J. Gómez-Hernández. „Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter“. Hydrology and Earth System Sciences Discussions 8, Nr. 4 (12.07.2011): 6749–88. http://dx.doi.org/10.5194/hessd-8-6749-2011.
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Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can identify correctly the channels when a large number of conditioning piezometers are used even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.
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Xia, Chuan-An, Bill X. Hu, Juxiu Tong und Alberto Guadagnini. „Data Assimilation in Density-Dependent Subsurface Flows via Localized Iterative Ensemble Kalman Filter“. Water Resources Research 54, Nr. 9 (September 2018): 6259–81. http://dx.doi.org/10.1029/2017wr022369.
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Chen, Yan, Weimin Zhang und Pinqiang Wang. „An application of the localized weighted ensemble Kalman filter for ocean data assimilation“. Quarterly Journal of the Royal Meteorological Society 146, Nr. 732 (04.07.2020): 3029–47. http://dx.doi.org/10.1002/qj.3824.
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Li, L., H. Zhou, H. J. Hendricks Franssen und J. J. Gómez-Hernández. „Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter“. Hydrology and Earth System Sciences 16, Nr. 2 (27.02.2012): 573–90. http://dx.doi.org/10.5194/hess-16-573-2012.
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Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. This is a clear example of an aquifer that cannot be characterized by a multiGaussian distribution. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can characterize the non-multiGaussian underlying hydraulic distribution even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.
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Nerini, Daniele, Loris Foresti, Daniel Leuenberger, Sylvain Robert und Urs Germann. „A Reduced-Space Ensemble Kalman Filter Approach for Flow-Dependent Integration of Radar Extrapolation Nowcasts and NWP Precipitation Ensembles“. Monthly Weather Review 147, Nr. 3 (01.03.2019): 987–1006. http://dx.doi.org/10.1175/mwr-d-18-0258.1.
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Abstract A Bayesian precipitation nowcasting system based on the ensemble Kalman filter is formulated. Starting from the last available radar observations, the prediction step of the filter consists of a stochastic radar extrapolation technique, while the correction step updates the radar extrapolation nowcast using information from the most recent forecast by the numerical weather prediction model (NWP). The result is a flow-dependent and seamless blending scheme that is based on the spread of the nowcast and NWP ensembles, used as the definition of the forecast error. To simplify the matrix operations, the Bayesian update is performed in the subspace spanned by the principal components, hence the term reduced space. Synthetic data experiments demonstrated that the Bayesian nowcast correctly captures the flow dependency in both the NWP forecast and the radar extrapolation skills. Four experiments with real precipitation data and a relatively small ensemble size (21 members) represented a first test under realistic conditions, such as stratiform wintertime precipitation and localized summertime convection. The skill was quantified in terms of fractions skill score at 32-km scale and 2.0 mm h−1 intensity. The results indicate that the system is able to produce blended forecasts that are at least as skillful as the nowcast-only or the NWP-only forecasts at any lead time.
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Yoon, Young-noh, Edward Ott und Istvan Szunyogh. „On the Propagation of Information and the Use of Localization in Ensemble Kalman Filtering“. Journal of the Atmospheric Sciences 67, Nr. 12 (01.12.2010): 3823–34. http://dx.doi.org/10.1175/2010jas3452.1.
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Abstract Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averaging over states from free evolution of the model. Propagation of the effects of observations made in one region on forecasts in other regions is studied. The error covariance matrices from the analyses with localization and without localization are compared. From this study, major characteristics of the localization process and information propagation are extracted and summarized.
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Zhou, Yongbo, Yubao Liu und Wei Han. „Demonstrating the Potential Impacts of Assimilating FY-4A Visible Radiances on Forecasts of Cloud and Precipitation with a Localized Particle Filter“. Monthly Weather Review 151, Nr. 5 (Mai 2023): 1167–88. http://dx.doi.org/10.1175/mwr-d-22-0133.1.
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Abstract The Advanced Geostationary Radiation Imager (AGRI) on board the Fengyun-4A (FY-4A) satellite provides visible radiances that contain critical information on clouds and precipitation. In this study, the impact of assimilating FY-4A/AGRI all-sky visible radiances on the simulation of a convective system was evaluated with an observing system simulation experiment (OSSE) using a localized particle filter (PF). The localized PF was implemented into the Data Assimilation Research Testbed (DART) coupled with the Weather Research and Forecasting (WRF) Model. The results of a 2-day data assimilation (DA) experiment generated encouraging outcome at a synoptic scale. Assimilating FY-4A/AGRI visible radiances with the localized PF significantly improved the analysis and forecast of cloud water path (CWP), cloud coverage, rain rate, and rainfall areas. In addition, some positive impacts were produced on the temperature and water vapor mixing ratio in the vicinity of cloudy regions. Sensitivity studies indicated that the best results were achieved by the localized PF configured with a localization distance that is equivalent to the model grid spacing (20 km) and with an adequately short cycling interval (30 min). However, the localized PF could not improve cloud vertical structures and cloud phases due to a lack of related information in the visible radiances. Moreover, the localized PF was compared with the ensemble adjustment Kalman filter (EAKF) and it was indicated that the localized PF outperformed EAKF even when the number of ensemble members was doubled for the latter, indicating a great potential of the localized PF in assimilating visible radiances.
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Poterjoy, Jonathan, und Fuqing Zhang. „Systematic Comparison of Four-Dimensional Data Assimilation Methods With and Without the Tangent Linear Model Using Hybrid Background Error Covariance: E4DVar versus 4DEnVar“. Monthly Weather Review 143, Nr. 5 (01.05.2015): 1601–21. http://dx.doi.org/10.1175/mwr-d-14-00224.1.
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Abstract Two ensemble formulations of the four-dimensional variational (4DVar) data assimilation technique are examined for a low-dimensional dynamical system. The first method, denoted E4DVar, uses tangent linear and adjoint model operators to minimize a cost function in the same manner as the traditional 4DVar data assimilation system. The second method, denoted 4DEnVar, uses an ensemble of nonlinear model trajectories to replace the function of linearized models in 4DVar, thus improving the parallelization of the data assimilation. Background errors for each algorithm are represented using a hybrid error covariance, which includes climatological errors as well as ensemble-estimated errors from an ensemble Kalman filter (EnKF). Numerical experiments performed over a range of scenarios suggest that both methods provide similar analysis accuracy for dense observation networks, and in perfect model experiments with large ensembles. Nevertheless, E4DVar has clear benefits over 4DEnVar when substantial covariance localization is required to treat sampling error. The greatest advantage of the tangent-linear approach is that it implicitly propagates a localized, full-rank ensemble covariance in time, thus avoiding the need to localize a time-dependent ensemble covariance. The tangent linear and adjoint model operators also provide a means of evolving flow-dependent information from the climate-based error component, which is found to be beneficial for treating model error. Challenges that need to be overcome before adopting a pure ensemble framework are illustrated through experiments estimating time covariances with four-dimensional ensembles and comparing results with those estimated with a tangent linear model.
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Yoshida, Takuma, und Eugenia Kalnay. „Correlation-Cutoff Method for Covariance Localization in Strongly Coupled Data Assimilation“. Monthly Weather Review 146, Nr. 9 (13.08.2018): 2881–89. http://dx.doi.org/10.1175/mwr-d-17-0365.1.
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Abstract Strongly coupled data assimilation (SCDA), where observations of one component of a coupled model are allowed to directly impact the analysis of other components, sometimes fails to improve the analysis accuracy with an ensemble Kalman filter (EnKF) as compared with weakly coupled data assimilation (WCDA). It is well known that an observation’s area of influence should be localized in EnKFs since the assimilation of distant observations often degrades the analysis because of spurious correlations. This study derives a method to estimate the reduction of the analysis error variance by using estimates of the cross covariances between the background errors of the state variables in an idealized situation. It is shown that the reduction of analysis error variance is proportional to the squared background error correlation between the analyzed and observed variables. From this, the authors propose an offline method to systematically select which observations should be assimilated into which model state variable by cutting off the assimilation of observations when the squared background error correlation between the observed and analyzed variables is small. The proposed method is tested with the local ensemble transform Kalman filter (LETKF) and a nine-variable coupled model, in which three Lorenz models with different time scales are coupled with each other. The covariance localization with the correlation-cutoff method achieves an analysis more accurate than either the full SCDA or the WCDA methods, especially with smaller ensemble sizes.
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Steward, Jeffrey L., Jose E. Roman, Alejandro Lamas Daviña und Altuǧ Aksoy. „Parallel Direct Solution of the Covariance-Localized Ensemble Square Root Kalman Filter Equations with Matrix Functions“. Monthly Weather Review 146, Nr. 9 (13.08.2018): 2819–36. http://dx.doi.org/10.1175/mwr-d-18-0022.1.
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Abstract Recently, the serial approach to solving the square root ensemble Kalman filter (ESRF) equations in the presence of covariance localization was found to depend on the order of observations. As shown previously, correctly updating the localized posterior covariance in serial requires additional effort and computational expense. A recent work by Steward et al. details an all-at-once direct method to solve the ESRF equations in parallel. This method uses the eigenvectors and eigenvalues of the forward observation covariance matrix to solve the difficult portion of the ESRF equations. The remaining assimilation is easily parallelized, and the analysis does not depend on the order of observations. While this allows for long localization lengths that would render local analysis methods inefficient, in theory, an eigenpair-based method scales as the cube number of observations, making it infeasible for large numbers of observations. In this work, we extend this method to use the theory of matrix functions to avoid eigenpair computations. The Arnoldi process is used to evaluate the covariance-localized ESRF equations on the reduced-order Krylov subspace basis. This method is shown to converge quickly and apparently regains a linear scaling with the number of observations. The method scales similarly to the widely used serial approach of Anderson and Collins in wall time but not in memory usage. To improve the memory usage issue, this method potentially can be used without an explicit matrix. In addition, hybrid ensemble and climatological covariances can be incorporated.
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Pérez Hortal, Andrés A., Isztar Zawadzki und M. K. Yau. „A Sequential Non-Gaussian Approach for Precipitation Data Assimilation“. Monthly Weather Review 149, Nr. 4 (April 2021): 1069–87. http://dx.doi.org/10.1175/mwr-d-20-0086.1.
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AbstractIn two recent studies, the authors presented a new data assimilation (DA) method for precipitation observations that does not require Gaussianity or linearity assumptions. The method, called localized ensemble mosaic assimilation (LEMA), initializes the new ensemble forecast by relaxing the background ensemble (prior) toward a single analysis composed of different column states taken from the ensemble members with the lowest error in the precipitation forecast. However, a limitation of the LEMA method is that relaxing the background ensemble toward that analysis severely reduces the spread of the ensemble, thus, limiting its usefulness for cycled DA applications. This study presents a new version of LEMA, called localized ensemble mosaic assimilation sequence (LEMAS), suitable for cycled DA operations. LEMAS constructs an ensemble of analysis mosaics using a small group of members closer to the observations instead of only the closest one. The new ensemble forecast is then initialized by recentering the prior ensemble around the mean of the analysis ensemble while scaling the original background perturbations to match the spread of the analysis mosaics. A series of ideal and real DA experiments are used to evaluate the potential of LEMAS for the assimilation of hourly accumulation observations. A comparison of LEMAS with the local ensemble transform Kalman filter (LETKF) using idealized experiments shows that LEMAS produces similar or slightly better forecast quality than the LETKF in temperature, water vapor, winds, and precipitation. Extending this comparison to real DA experiments assimilating Stage-IV precipitation observations shows that both methods produce precipitation forecasts of comparable quality.
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Zhao, Yuxin, Shuo Yang, Di Zhou, Xiong Deng und Mengbin Zhu. „The Improved Localized Equivalent-Weights Particle Filter with Statistical Observation in an Intermediate Coupled Model“. Journal of Marine Science and Engineering 9, Nr. 11 (20.10.2021): 1153. http://dx.doi.org/10.3390/jmse9111153.
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Data assimilation has been widely applied in atmospheric and oceanic forecasting systems and particle filters (PFs) have unique advantages in dealing with nonlinear data assimilation. They have been applied to many scientific fields, but their application in geoscientific systems is limited because of their inefficiency in standard settings systems. To address these issues, this paper further refines the statistical observation and localization scheme which used in the classic localized equivalent-weights particle filter with statistical observation (LEWPF-Sobs). The improved method retains the advantages of equivalent-weights particle filter (EWPF) and the localized particle filter (LPF), while further refinements incorporate the effect of time series on the reanalyzed data into the statistical observation calculations, in addition to incorporating the statistical observation proposal density into the localization scheme to further improve the assimilation accuracy under sparse observation conditions. In order to better simulate the geoscientific system, we choose an intermediate atmosphere-ocean-land coupled model (COAL-IC) as the experimental model and divide the experiment into two parts: standard observation and sparse observation, which are analyzed by the spatial distribution results and root mean square error (RMSE) histogram. In order to better analyze the characteristics of the improved method, this method was chosen to be analyzed in comparison with the localized weighted ensemble Kalman filter (LWEnKF), the LPF and classical LEWPF-Sobs. From the experimental results, it can be seen that the improved method is better than the LWEnKF and LPF methods for various observation conditions. The improved method reduces the RMSE by about 7% under standard observation conditions compared to the traditional method, while the advantage of the improved method is even more obvious under sparse observation conditions, where the RMSE is reduced by about 85% compared to the traditional method. In particular, this improved filter not only combine the advantage of the two algorithms, but also overcome the computing resources.
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Arroyo, Elkin, Deepak Devegowda, Akhil Datta-Gupta und Jonggeun Choe. „Streamline-Assisted Ensemble Kalman Filter for Rapid and Continuous Reservoir Model Updating“. SPE Reservoir Evaluation & Engineering 11, Nr. 06 (01.12.2008): 1046–60. http://dx.doi.org/10.2118/104255-pa.
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Summary The use of the ensemble Kalman filter (EnKF) is a promising approach for data assimilation and assessment of uncertainties during reservoir characterization and performance forecasting. It provides a relatively straightforward approach to incorporating diverse data types, including production and/or time-lapse seismic data. Unlike traditional sensitivity-based history matching methods, the EnKF relies on a cross-covariance matrix computed from an ensemble of reservoir models to relate reservoir properties to production data. For practical field applications, we need to keep the ensemble size small for computational efficiency. However, this leads to poor approximations of the cross-covariance and, often, loss of geologic realism through parameter overshoots, in particular by introducing localized patches of low and high permeabilities. Because the EnKF estimates are "optimal" only for Gaussian variables and linear dynamics, these difficulties are compounded by the strong nonlinearity of the multiphase history matching problems and for non-Gaussian prior models. Specifically, the updated parameter distribution tends to become multi-Gaussian with loss of connectivities of extreme values, such as high permeability channels and low permeability barriers, which are of special significance during reservoir characterization. We propose a novel approach to overcome some of these limitations by conditioning the cross-covariance matrix using information gleaned from streamline trajectories. Our streamline-assisted EnKF is analogous to the conventional assisted history matching, whereby the streamline trajectories are used to identify gridblocks contributing to the production response of a specific well. We then use these gridblocks only to compute the cross-covariance matrix and eliminate the influence of unrelated or distant observations and spurious correlations. We show that the streamline-assisted EnKF is an efficient and robust approach for history matching and continuous reservoir model updating. We illustrate the power and utility of our approach using both synthetic and field applications. Introduction Proper characterization of the reservoir and the assessment of uncertainty are crucial aspects of any optimal reservoir development plan and management strategy. To achieve this goal, it is necessary to reconcile geological models to the dynamic response of the reservoir through history matching. The topic of history matching has been of great interest and an area of active research in the oil industry (Datta-Gupta and King 2007; Emanuel and Milliken 1998; Oliver et al. 2001). The past decade has seen some significant developments in assisted and automatic history matching of high-resolution reservoir models and associated uncertainty quantification. Many of these techniques involve computation of sensitivities that relate changes in production response at a well to a change in reservoir parameters. Techniques of automatic history matching that typically do not use parameter sensitivities or gradient of the misfit function are stochastic algorithms such as Markov Chain Monte Carlo (MCMC), simulated annealing and genetic algorithms (Ma et al. 2008; Sen et al. 2005). A relatively recent and promising addition to this class of techniques is the use of ensemble Kalman Filters (EnKF) for data assimilation (Gu and Oliver 2005, 2006; Naevdal et al. 2005; Gao et al. 2006; Skjervheim et al. 2007; Dong et al. 2006). It is a Monte-Carlo approach that works with an ensemble of reservoir models. Specifically, the method utilizes cross-covariances between measurements and model parameters computed directly from the ensemble members to sequentially update the reservoir models. A major advantage of the EnKF is that it can be readily linked to any existing reservoir simulator. The ability to assimilate diverse data types and the ease of implementation have resulted in considerable interest in the approach. Moreover, EnKF uses a sequential updating technique; that is, the reservoir data is assimilated as and when it becomes available. The EnKF can assimilate the latest production data without re-running the simulator from the initial conditions. These characteristics make it particularly well-suited for continuous model updating. The increased application of downhole monitors, intelligent well systems, and permanent sensors to continuously record pressure, well rates, and temperature has provided a further boost to the sequential model updating through EnKF. In spite of all its favorable properties, the current implementation of EnKF approach comes with its own share of challenges. A key requirement in history matching is that the final model should honor the available geological information and retain geologic realism. It has been shown that the EnKF works well when the prior distribution of parameters is Gaussian; however, the estimates are suboptimal for non-Gaussian distributions. Over a sequence of many updates, multimodal permeability distributions tend to transform to Gaussian distribution. During geologic model updating, this can lead to a loss of structure and connectivity of the extremes in the permeability field. This has serious implications in the fluid flow because of the influence of high-permeability channels and low-permeability barriers. Although there are some variants of the Kalman filter that work with non-Gaussian distributions, such as the Gaussian summation approximation, the implementation on an ensemble framework tend to be very expensive (Anderson and Moore 1979). In the past few years, we have seen several applications of the EnKF for field-scale history matching, including some recent papers that attempt to deal with some of the challenges pertaining to its use (Gu and Oliver 2005, 2006; Naevdal et al. 2005; Gao et al. 2006; Skjervheim et al. 2007; Dong et al. 2006). In particular, localized overshooting of permeabilities has been reported, resulting in loss of geologic continuity. This is aggravated by the strong non-linearity inherent in multiphase flow simulations. Another common difficulty experienced when using the EnKF is filter divergence. The effect of filter divergence is such that the distribution produced by the filter drifts away from the truth. Filter divergence normally occurs because the prior probability distribution becomes too narrow (loss of variance) and the observations have progressively less impact on the model updates. One common approach to deal with filter divergence is to add some (white) noise to the prior ensemble to "inflate" its distribution and enhance the impact of new observations. Other problems and limitations of the EnKF, particularly for nonlinear problems and non-Gaussian parameter distributions, can be partly controlled using a large ensemble. However, for practical field applications, the ensemble size needs to be kept relatively small for computational efficiency. This paper describes an approach to address many of the currently reported difficulties in the use of the EnKF applied to reservoir history matching. The unique feature of our proposed approach is that the final models that constitute the ensemble tend to retain the geological information that went into building them initially. Over a sequence of many updates, our approach tends to preserve the shape of the initial permeability distribution and consequently retains key geological features. Our approach greatly decreases the severity of the overshooting problem reported in earlier implementations of the EnKF. Moreover, it allows the use of smaller ensemble size, while providing results comparable or better than the standard EnKF. The paper is organized as follows. First, we briefly review the major steps of the EnKF and the additional streamline-based conditioning of the cross-covariance proposed here. We also illustrate these steps using a synthetic example. Next, we discuss the underlying mathematical formulation in detail. We then demonstrate the power and practical utility of the approach using the benchmark PUNQ-S3 synthetic example (Gu and Oliver 2005) and a field example. Finally, an analysis of the scalability and speed-up factor for the parallel implementation of our code is given.
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Shen, Meng, Yan Chen, Pinqiang Wang und Weimin Zhang. „Assimilating satellite SST/SSH and in-situ T/S profiles with the Localized Weighted Ensemble Kalman Filter“. Acta Oceanologica Sinica 41, Nr. 2 (Februar 2022): 26–40. http://dx.doi.org/10.1007/s13131-021-1903-2.
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Tong, Juxiu, Bill X. Hu und Jinzhong Yang. „Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field“. Stochastic Environmental Research and Risk Assessment 26, Nr. 3 (05.11.2011): 467–78. http://dx.doi.org/10.1007/s00477-011-0534-0.
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Bishop, Craig H., und Daniel Hodyss. „Adaptive Ensemble Covariance Localization in Ensemble 4D-VAR State Estimation“. Monthly Weather Review 139, Nr. 4 (01.04.2011): 1241–55. http://dx.doi.org/10.1175/2010mwr3403.1.
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Abstract An adaptive ensemble covariance localization technique, previously used in “local” forms of the ensemble Kalman filter, is extended to a global ensemble four-dimensional variational data assimilation (4D-VAR) scheme. The purely adaptive part of the localization matrix considered is given by the element-wise square of the correlation matrix of a smoothed ensemble of streamfunction perturbations. It is found that these purely adaptive localization functions have spurious far-field correlations as large as 0.1 with a 128-member ensemble. To attenuate the spurious features of the purely adaptive localization functions, the authors multiply the adaptive localization functions with very broadscale nonadaptive localization functions. Using the Navy’s operational ensemble forecasting system, it is shown that the covariance localization functions obtained by this approach adapt to spatially anisotropic aspects of the flow, move with the flow, and are free of far-field spurious correlations. The scheme is made computationally feasible by (i) a method for inexpensively generating the square root of an adaptively localized global four-dimensional error covariance model in terms of products or modulations of smoothed ensemble perturbations with themselves and with raw ensemble perturbations, and (ii) utilizing algorithms that speed ensemble covariance localization when localization functions are separable, variable-type independent, and/or large scale. In spite of the apparently useful characteristics of adaptive localization, single analysis/forecast experiments assimilating 583 200 observations over both 6- and 12-h data assimilation windows failed to identify any significant difference in the quality of the analyses and forecasts obtained using nonadaptive localization from that obtained using adaptive localization.
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Knopfmeier, Kent H., und David J. Stensrud. „Influence of Mesonet Observations on the Accuracy of Surface Analyses Generated by an Ensemble Kalman Filter“. Weather and Forecasting 28, Nr. 3 (01.06.2013): 815–41. http://dx.doi.org/10.1175/waf-d-12-00078.1.
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Abstract The expansion of surface mesoscale networks (mesonets) across the United States provides a high-resolution observational dataset for meteorological analysis and prediction. To clarify the impact of mesonet data on the accuracy of surface analyses, 2-m temperature, 2-m dewpoint, and 10-m wind analyses for 2-week periods during the warm and cold seasons produced through an ensemble Kalman filter (EnKF) approach are compared to surface analyses created by the Real-Time Mesoscale Analysis (RTMA). Results show in general a similarity between the EnKF analyses and the RTMA, with the EnKF exhibiting a smoother appearance with less small-scale variability. Root-mean-square (RMS) innovations are generally lower for temperature and dewpoint from the RTMA, implying a closer fit to the observations. Kinetic energy spectra computed from the two analyses reveal that the EnKF analysis spectra match more closely to the spectra computed from observations and numerical models in earlier studies. Data-denial experiments using the EnKF completed for the first week of the warm and cold seasons, as well as for two periods characterized by high mesoscale variability within the experimental domain, show that mesonet data removal imparts only minimal degradation to the analyses. This is because of the localized background covariances computed for the four surface variables having spatial scales much larger than the average spacing of mesonet stations. Results show that removing 75% of the mesonet observations has only minimal influence on the analysis.
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Majumdar, S. J., S. D. Aberson, C. H. Bishop, R. Buizza, M. S. Peng und C. A. Reynolds. „A Comparison of Adaptive Observing Guidance for Atlantic Tropical Cyclones“. Monthly Weather Review 134, Nr. 9 (01.09.2006): 2354–72. http://dx.doi.org/10.1175/mwr3193.1.
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Abstract Airborne adaptive observations have been collected for more than two decades in the neighborhood of tropical cyclones, to attempt to improve short-range forecasts of cyclone track. However, only simple subjective strategies for adaptive observations have been used, and the utility of objective strategies to improve tropical cyclone forecasts remains unexplored. Two objective techniques that have been used extensively for midlatitude adaptive observing programs, and the current strategy based on the ensemble deep-layer mean (DLM) wind variance, are compared quantitatively using two metrics. The ensemble transform Kalman filter (ETKF) uses ensembles from NCEP and the ECMWF. Total-energy singular vectors (TESVs) are computed by the ECMWF and the Naval Research Laboratory, using their respective global models. Comparisons of 78 guidance products for 2-day forecasts during the 2004 Atlantic hurricane season are made, on both continental and localized scales relevant to synoptic surveillance missions. The ECMWF and NRL TESV guidance identifies similar large-scale target regions in 90% of the cases, but are less similar to each other in the local tropical cyclone environment (56% of the cases) with a more stringent criterion for similarity. For major hurricanes, all techniques usually indicate targets close to the storm center. For weaker tropical cyclones, the TESV guidance selects similar targets to those from the ETKF (DLM wind variance) in only 30% (20%) of the cases. ETKF guidance using the ECMWF ensemble is more like that provided by the NCEP ensemble (and DLM wind variance) for major hurricanes than for weaker tropical cyclones. Minor differences in these results occur when a different metric based on the ranking of fixed storm-relative regions is used.
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Mu, Longjiang, Xi Liang, Qinghua Yang, Jiping Liu und Fei Zheng. „Arctic Ice Ocean Prediction System: evaluating sea-ice forecasts during Xuelong's first trans-Arctic Passage in summer 2017“. Journal of Glaciology 65, Nr. 253 (23.08.2019): 813–21. http://dx.doi.org/10.1017/jog.2019.55.
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AbstractIn an effort to improve the reliability of Arctic sea-ice predictions, an ensemble-based Arctic Ice Ocean Prediction System (ArcIOPS) has been developed to meet operational demands. The system is based on a regional Arctic configuration of the Massachusetts Institute of Technology general circulation model. A localized error subspace transform ensemble Kalman filter is used to assimilate the weekly merged CryoSat-2 and Soil Moisture and Ocean Salinity sea-ice thickness data together with the daily Advanced Microwave Scanning Radiometer 2 (AMSR2) sea-ice concentration data. The weather forecasts from the Global Forecast System of the National Centers for Environmental Prediction drive the sea ice–ocean coupled model. The ensemble mean sea-ice forecasts were used to facilitate the Chinese National Arctic Research Expedition in summer 2017. The forecasted sea-ice concentration is evaluated against AMSR2 and Special Sensor Microwave Imager/Sounder sea-ice concentration data. The forecasted sea-ice thickness is compared to the in-situ observations and the Pan-Arctic Ice-Ocean Modeling and Assimilation System. These comparisons show the promising potential of ArcIOPS for operational Arctic sea-ice forecasts. Nevertheless, the forecast bias in the Beaufort Sea calls for a delicate parameter calibration and a better design of the assimilation system.
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Steiner, Michael, Luca Cantarello, Stephan Henne und Dominik Brunner. „Flow-dependent observation errors for greenhouse gas inversions in an ensemble Kalman smoother“. Atmospheric Chemistry and Physics 24, Nr. 21 (11.11.2024): 12447–63. http://dx.doi.org/10.5194/acp-24-12447-2024.
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Abstract. Atmospheric inverse modeling is the process of estimating emissions from atmospheric observations by minimizing a cost function, which includes a term describing the difference between simulated and observed concentrations. The minimization of this difference is typically limited by uncertainties in the atmospheric transport model rather than by uncertainties in the observations. In this study, we showcase how a temporally varying, flow-dependent atmospheric transport uncertainty can enhance the accuracy of emission estimation through idealized experiments using an ensemble Kalman smoother system. We use the estimation of European CH4 emissions from the in situ measurement network as an example, but we also demonstrate the additional benefits for trace gases with more localized sources, such as SF6. The uncertainty in flow-dependent transport is determined using meteorological ensemble simulations that are perturbed by physics and driven at the boundaries by an analysis ensemble from a global meteorology and a CH4 simulation. The impact of direct representation of temporally varying transport uncertainties in atmospheric inversions is then investigated in an observation system simulation experiment framework in various setups and for different flux signals. We show that the uncertainty in the transport model varies significantly in space and time and that it is generally highest during nighttime. We apply inversions using only afternoon observations, as is common practice, but also explore the option of assimilating hourly data irrespective of the hour of day using a filter based on transport uncertainty and taking into account the temporal covariances. Our findings indicate that incorporating flow-dependent uncertainties in inversion techniques leads to more accurate estimates of GHG emissions. Differences between estimated and true emissions could be reduced more effectively by 9 % to 82 %, with generally larger improvements for the SF6 inversion problem and for the more challenging setup with small flux signals.
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Sun, Luyu, und Stephen G. Penny. „Lagrangian Data Assimilation of Surface Drifters in a Double-Gyre Ocean Model Using the Local Ensemble Transform Kalman Filter“. Monthly Weather Review 147, Nr. 12 (18.11.2019): 4533–51. http://dx.doi.org/10.1175/mwr-d-18-0406.1.
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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.
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Khade, V. M., J. A. Hansen, J. S. Reid und D. L. Westphal. „Ensemble filter based estimation of spatially distributed parameters in a mesoscale dust model: experiments with simulated and real data“. Atmospheric Chemistry and Physics Discussions 12, Nr. 11 (05.11.2012): 28837–89. http://dx.doi.org/10.5194/acpd-12-28837-2012.
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Abstract. The Ensemble Adjustment Kalman Filter (EAKF) is used to estimate the erodibility fraction parameter field in a coupled meteorology and dust aerosol model (Coupled Ocean Atmosphere Mesoscale Prediction System-COAMPS) over the Sahara desert. Erodibility is often employed as the key parameter to map dust source. It is used along with surface winds (or surface wind stress) to calculate dust emissions. Using the Saharan desert as a test bed, a perfect model Observation System Simulation Experiments (OSSEs) with 40 ensemble members, and observations of aerosol optical depth (AOD), the EAKF is shown to recover correct values of erodibility at about 80% of the points in the domain. It is found that dust advected from upstream grid points acts as noise and complicates erodibility estimation. It is also found that the rate of convergence is significantly impacted by the structure of the initial distribution of erodibility estimates; isotropic initial distributions exhibit slow convergence while initial distributions with geographically localized structure converge more quickly. Experiments using observations of Deep Blue AOD retrievals from the MODIS satellite sensor result in erodibility estimates that are considerably lower than the values used operationally. Verification shows that the use of the tuned erodibility field results in better predictions of AOD over the Western Sahara and Arabia.
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Khade, V. M., J. A. Hansen, J. S. Reid und D. L. Westphal. „Ensemble filter based estimation of spatially distributed parameters in a mesoscale dust model: experiments with simulated and real data“. Atmospheric Chemistry and Physics 13, Nr. 6 (27.03.2013): 3481–500. http://dx.doi.org/10.5194/acp-13-3481-2013.
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Abstract. The ensemble adjustment Kalman filter (EAKF) is used to estimate the erodibility fraction parameter field in a coupled meteorology and dust aerosol model (Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS)) over the Sahara desert. Erodibility is often employed as the key parameter to map dust source. It is used along with surface winds (or surface wind stress) to calculate dust emissions. Using the Saharan desert as a test bed, a perfect model Observation System Simulation Experiments (OSSEs) with 40 ensemble members, and observations of aerosol optical depth (AOD), the EAKF is shown to recover correct values of erodibility at about 80% of the points in the domain. It is found that dust advected from upstream grid points acts as noise and complicates erodibility estimation. It is also found that the rate of convergence is significantly impacted by the structure of the initial distribution of erodibility estimates; isotropic initial distributions exhibit slow convergence, while initial distributions with geographically localized structure converge more quickly. Experiments using observations of Deep Blue AOD retrievals from the MODIS satellite sensor result in erodibility estimates that are considerably lower than the values used operationally. Verification shows that the use of the tuned erodibility field results in better predictions of AOD over the west Sahara and the Arabian Peninsula.
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Yu, Y., J. Koller, V. K. Jordanova, S. G. Zaharia und H. C. Godinez. „Radiation belt data assimilation of a moderate storm event using a magnetic field configuration from the physics-based RAM-SCB model“. Annales Geophysicae 32, Nr. 5 (06.05.2014): 473–83. http://dx.doi.org/10.5194/angeo-32-473-2014.
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Abstract. Data assimilation using Kalman filters provides an effective way of understanding both spatial and temporal variations in the outer electron radiation belt. Data assimilation is the combination of in situ observations and physical models, using appropriate error statistics to approximate the uncertainties in both the data and the model. The global magnetic field configuration is one essential element in determining the adiabatic invariants for the phase space density (PSD) data used for the radiation belt data assimilation. The lack of a suitable global magnetic field model with high accuracy is still a long-lasting problem. This paper employs a physics-based magnetic field configuration for the first time in a radiation belt data assimilation study for a moderate storm event on 19 December 2002. The magnetic field used in our study is the magnetically self-consistent inner magnetosphere model RAM-SCB, developed at Los Alamos National Laboratory (LANL). Furthermore, we apply a cubic spline interpolation method in converting the differential flux measurements within the energy spectrum, to obtain a more accurate PSD input for the data assimilation than the commonly used linear interpolation approach. Finally, the assimilation is done using an ensemble Kalman filter (EnKF), with a localized adaptive inflation (LAI) technique to appropriately account for model errors in the assimilation and improve the performance of the Kalman filter. The assimilative results are compared with results from another assimilation experiment using the Tsyganenko 2001S (T01S) magnetic field model, to examine the dependence on a magnetic field model. Results indicate that the data assimilations using different magnetic field models capture similar features in the radiation belt dynamics, including the temporal evolution of the electron PSD during a storm and the location of the PSD peak. The assimilated solution predicts the energy differential flux to a relatively good degree when compared with independent LANL-GEO in situ observations. A closer examination suggests that for the chosen storm event, the assimilation using the RAM-SCB predicts a better flux at most energy levels during storm recovery phase but is slightly worse in the storm main phase than the assimilation using the T01S model.
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Chen, Zhiqiang, Jiping Liu, Mirong Song, Qinghua Yang und Shiming Xu. „Impacts of Assimilating Satellite Sea Ice Concentration and Thickness on Arctic Sea Ice Prediction in the NCEP Climate Forecast System“. Journal of Climate 30, Nr. 21 (November 2017): 8429–46. http://dx.doi.org/10.1175/jcli-d-17-0093.1.
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Here sea ice concentration derived from the Special Sensor Microwave Imager/Sounder and thickness derived from the Soil Moisture and Ocean Salinity and CryoSat-2 satellites are assimilated in the National Centers for Environmental Prediction Climate Forecast System using a localized error subspace transform ensemble Kalman filter (LESTKF). Three ensemble-based hindcasts are conducted to examine impacts of the assimilation on Arctic sea ice prediction, including CTL (without any assimilation), LESTKF-1 (with initial sea ice assimilation only), and LESTKF-E5 (with every 5-day sea ice assimilation). Assessment with the assimilated satellite products and independent sea ice thickness datasets shows that assimilating sea ice concentration and thickness leads to improved Arctic sea ice prediction. LESTKF-1 improves sea ice forecast initially. The initial improvement gradually diminishes after ~3-week integration for sea ice extent but remains quite steady through the integration for sea ice thickness. Large biases in both the ice extent and thickness in CTL are remarkably reduced through the hindcast in LESTKF-E5. Additional numerical experiments suggest that the hindcast with sea ice thickness assimilation dramatically reduces systematic bias in the predicted ice thickness compared with sea ice concentration assimilation only or without any assimilation, which also benefits the prediction of sea ice extent and concentration due to their covariability. Hence, the corrected state of sea ice thickness would aid in the forecast procedure. Increasing the number of ensemble members or extending the integration period to generate estimates of initial model states and uncertainties seems to have small impacts on sea ice prediction relative to LESTKF-E5.
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Pendergrass, Drew C., Daniel J. Jacob, Hannah Nesser, Daniel J. Varon, Melissa Sulprizio, Kazuyuki Miyazaki und Kevin W. Bowman. „CHEEREIO 1.0: a versatile and user-friendly ensemble-based chemical data assimilation and emissions inversion platform for the GEOS-Chem chemical transport model“. Geoscientific Model Development 16, Nr. 16 (24.08.2023): 4793–810. http://dx.doi.org/10.5194/gmd-16-4793-2023.
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Abstract. We present a versatile, powerful, and user-friendly chemical data assimilation toolkit for simultaneously optimizing emissions and concentrations of chemical species based on atmospheric observations from satellites or suborbital platforms. The CHemistry and Emissions REanalysis Interface with Observations (CHEEREIO) exploits the GEOS-Chem chemical transport model and a localized ensemble transform Kalman filter algorithm (LETKF) to determine the Bayesian optimal (posterior) emissions and/or concentrations of a set of species based on observations and prior information using an easy-to-modify configuration file with minimal changes to the GEOS-Chem or LETKF code base. The LETKF algorithm readily allows for nonlinear chemistry and produces flow-dependent posterior error covariances from the ensemble simulation spread. The object-oriented Python-based design of CHEEREIO allows users to easily add new observation operators such as for satellites. CHEEREIO takes advantage of the Harmonized Emissions Component (HEMCO) modular structure of input data management in GEOS-Chem to update emissions from the assimilation process independently from the GEOS-Chem code. It can seamlessly support GEOS-Chem version updates and is adaptable to other chemical transport models with similar modular input data structure. A post-processing suite combines ensemble output into consolidated NetCDF files and supports a wide variety of diagnostic data and visualizations. We demonstrate CHEEREIO's capabilities with an out-of-the-box application, assimilating global methane emissions and concentrations at weekly temporal resolution and 2∘ × 2.5∘ spatial resolution for 2019 using TROPOspheric Monitoring Instrument (TROPOMI) satellite observations. CHEEREIO achieves a 50-fold improvement in computational performance compared to the equivalent analytical inversion of TROPOMI observations.
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Aydoğdu, Ali, Alberto Carrassi, Colin T. Guider, Chris K. R. T. Jones und Pierre Rampal. „Data assimilation using adaptive, non-conservative, moving mesh models“. Nonlinear Processes in Geophysics 26, Nr. 3 (24.07.2019): 175–93. http://dx.doi.org/10.5194/npg-26-175-2019.
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Abstract. Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing.
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Kotsuki, Shunji, Kenta Kurosawa, Shigenori Otsuka, Koji Terasaki und Takemasa Miyoshi. „Global Precipitation Forecasts by Merging Extrapolation-Based Nowcast and Numerical Weather Prediction with Locally Optimized Weights“. Weather and Forecasting 34, Nr. 3 (01.06.2019): 701–14. http://dx.doi.org/10.1175/waf-d-18-0164.1.
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Abstract Over the past few decades, precipitation forecasts by numerical weather prediction (NWP) models have been remarkably improved. Yet, precipitation nowcasting based on spatiotemporal extrapolation tends to provide a better precipitation forecast at shorter lead times with much less computation. Therefore, merging the precipitation forecasts from the NWP and extrapolation systems would be a viable approach to quantitative precipitation forecast (QPF). Although the optimal weights between the NWP and extrapolation systems are usually defined as a global constant, the weights would vary in space, particularly for global QPF. This study proposes a method to find the optimal weights at each location using the local threat score (LTS), a spatially localized version of the threat score. We test the locally optimal weighting with a global NWP system composed of the local ensemble transform Kalman filter and the Nonhydrostatic Icosahedral Atmospheric Model (NICAM-LETKF). For the extrapolation system, the RIKEN’s global precipitation nowcasting system called GSMaP_RNC is used. GSMaP_RNC extrapolates precipitation patterns from the Japan Aerospace Exploration Agency (JAXA)’s Global Satellite Mapping of Precipitation (GSMaP). The benefit of merging in global precipitation forecast lasts longer compared to regional precipitation forecast. The results show that the locally optimal weighting is beneficial.
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Li, Hongyi, Ting Yang, Lars Nerger, Dawei Zhang, Di Zhang, Guigang Tang, Haibo Wang et al. „NAQPMS-PDAF v2.0: a novel hybrid nonlinear data assimilation system for improved simulation of PM2.5 chemical components“. Geoscientific Model Development 17, Nr. 23 (29.11.2024): 8495–519. http://dx.doi.org/10.5194/gmd-17-8495-2024.
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Abstract. Identifying PM2.5 chemical components is crucial for formulating emission strategies, estimating radiative forcing, and assessing human health effects. However, accurately describing spatiotemporal variations in PM2.5 chemical components remains a challenge. In our earlier work, we developed an aerosol extinction coefficient data assimilation (DA) system (Nested Air Quality Prediction Model System with the Parallel Data Assimilation Framework (NAQPMS-PDAF) v1.0) that was suboptimal for chemical components. This paper introduces a novel hybrid nonlinear chemical DA system (NAQPMS-PDAF v2.0) to accurately interpret key chemical components (SO42-, NO3-, NH4+, OC, and EC). NAQPMS-PDAF v2.0 improves upon v1.0 by effectively handling and balancing stability and nonlinearity in chemical DA, which is achieved by incorporating the non-Gaussian distribution ensemble perturbation and hybrid localized Kalman–nonlinear ensemble transform filter with an adaptive forgetting factor for the first time. The dependence tests demonstrate that NAQPMS-PDAF v2.0 provides excellent DA results with a minimal ensemble size of 10, surpassing previous reports and v1.0. A 1-month DA experiment shows that the analysis field generated by NAQPMS-PDAF v2.0 is in good agreement with observations, especially in reducing the underestimation of NH4+ and NO3- and the overestimation of SO42-, OC, and EC. In particular, the Pearson correlation coefficient (CORR) values for NO3-, OC, and EC are above 0.96, and the R2 values are above 0.93. NAQPMS-PDAF v2.0 also demonstrates superior spatiotemporal interpretation, with most DA sites showing improvements of over 50 %–200 % in CORR and over 50 %–90 % in RMSE for the five chemical components. Compared to the poor performance in the global reanalysis dataset (CORR: 0.42–0.55, RMSE: 4.51–12.27 µg m−3) and NAQPMS-PDAF v1.0 (CORR: 0.35–0.98, RMSE: 2.46–15.50 µg m−3), NAQPMS-PDAF v2.0 has the highest CORR of 0.86–0.99 and the lowest RMSE of 0.14–3.18 µg m−3. The uncertainties in ensemble DA are also examined, further highlighting the potential of NAQPMS-PDAF v2.0 for advancing aerosol chemical component studies.
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Reynolds, C. A., M. S. Peng, S. J. Majumdar, S. D. Aberson, C. H. Bishop und R. Buizza. „Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones“. Monthly Weather Review 135, Nr. 12 (01.12.2007): 4006–29. http://dx.doi.org/10.1175/2007mwr2027.1.
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Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.
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Ruckstuhl, Y., und T. Janjić. „Combined State-Parameter Estimation with the LETKF for Convective-Scale Weather Forecasting“. Monthly Weather Review 148, Nr. 4 (31.03.2020): 1607–28. http://dx.doi.org/10.1175/mwr-d-19-0233.1.
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Abstract We investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two-dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to 6 h of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.
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Zhang, Yong-Fei, Cecilia M. Bitz, Jeffrey L. Anderson, Nancy Collins, Jonathan Hendricks, Timothy Hoar, Kevin Raeder und François Massonnet. „Insights on Sea Ice Data Assimilation from Perfect Model Observing System Simulation Experiments“. Journal of Climate 31, Nr. 15 (August 2018): 5911–26. http://dx.doi.org/10.1175/jcli-d-17-0904.1.
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Simulating Arctic sea ice conditions up to the present and predicting them several months in advance has high stakeholder value, yet remains challenging. Advanced data assimilation (DA) methods combine real observations with model forecasts to produce sea ice reanalyses and accurate initial conditions for sea ice prediction. This study introduces a sea ice DA framework for a sea ice model with a parameterization of the ice thickness distribution by resolving multiple thickness categories. Specifically, the Los Alamos Sea Ice Model, version 5 (CICE5), is integrated with the Data Assimilation Research Testbed (DART). A series of perfect model observing system simulation experiments (OSSEs) are designed to explore DA algorithms within the ensemble Kalman filter (EnKF) and the relative importance of different observation types. This study demonstrates that assimilating sea ice concentration (SIC) observations can effectively remove SIC errors, with the error of total Arctic sea ice area reduced by about 60% annually. When the impact of SIC observations is strongly localized in space, the error of total volume is also modestly improved. The largest simulation improvements are produced when sea ice thickness (SIT) and SIC are jointly assimilated, with the error of total volume decreased by more than 70% annually. Assimilating multiyear sea ice concentration (MYI) can reduce error in total volume by more than 50%. Assimilating MYI produces modest improvements in snow depth (errors are reduced by around 16%), while assimilating SIC and SIT has no obvious influence on snow depth. This study also suggests that different observation types may need different localization distances to optimize DA performance.
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Zhao, Fu, Xi Liang, Zhongxiang Tian, Ming Li, Na Liu und Chengyan Liu. „Southern Ocean Ice Prediction System version 1.0 (SOIPS v1.0): description of the system and evaluation of synoptic-scale sea ice forecasts“. Geoscientific Model Development 17, Nr. 17 (13.09.2024): 6867–86. http://dx.doi.org/10.5194/gmd-17-6867-2024.
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Abstract. An operational synoptic-scale sea ice forecasting system for the Southern Ocean, namely the Southern Ocean Ice Prediction System (SOIPS), has been developed to support ship navigation in the Antarctic sea ice zone. Practical application of the SOIPS forecasts had been implemented for the 38th Chinese National Antarctic Research Expedition for the first time. The SOIPS is configured on an Antarctic regional sea ice–ocean–ice shelf coupled model and an ensemble-based localized error subspace transform Kalman filter data assimilation model. Daily near-real-time satellite sea ice concentration observations are assimilated into the SOIPS to update sea ice concentration and thickness in the 12 ensemble members of the model state. By evaluating the SOIPS performance in forecasting sea ice metrics in a complete melt–freeze cycle from 1 October 2021 to 30 September 2022, this study shows that the SOIPS can provide reliable Antarctic sea ice forecasts. In comparison with non-assimilated EUMETSAT Ocean and Sea Ice Satellite Application Facility (OSI SAF) data, annual mean root mean square errors in the sea ice concentration forecasts at a lead time of up to 168 h are lower than 0.19, and the integrated ice edge errors in the sea ice forecasts in most freezing months at lead times of 24 and 72 h maintain around 0.5×106 km2 and below 1.0×106 km2, respectively. With respect to the scarce Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) observations, the mean absolute errors in the sea ice thickness forecasts at a lead time of 24 h are lower than 0.3 m, which is in the range of the ICESat-2 uncertainties. Specifically, the SOIPS has the ability to forecast sea ice drift, in both magnitude and direction. The derived sea ice convergence rate forecasts have great potential for supporting ship navigation on a fine local scale. The comparison between the persistence forecasts and the SOIPS forecasts with and without data assimilation further shows that both model physics and the data assimilation scheme play important roles in producing reliable sea ice forecasts in the Southern Ocean.