Articles | Volume 25, issue 3
Nonlin. Processes Geophys., 25, 713–729, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article 19 Sep 2018
Research article | 19 Sep 2018
Nonlinear effects in 4D-Var
Massimo Bonavita et al.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphereFast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximationA methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspectiveA method for predicting the uncompleted climate transition processStatistical postprocessing of ensemble forecasts for severe weather at Deutscher WetterdienstTraining a convolutional neural network to conserve mass in data assimilationAn Early Warning Sign of Critical Transition in The Antarctic Ice Sheet – A New Data Driven Tool for Spatiotemporal Tipping PointData-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory networkFrom research to applications – examples of operational ensemble post-processing in France using machine learningCorrecting for model changes in statistical postprocessing – an approach based on response theoryBrief communication: Residence time of energy in the atmosphereBehavior of the iterative ensemble-based variational method in nonlinear problemsSimulating model uncertainty of subgrid-scale processes by sampling model errors at convective scalesData-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertaintySeasonal statistical–dynamical prediction of the North Atlantic Oscillation by probabilistic post-processing and its evaluationApplication of a local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systemsOrder of operation for multi-stage post-processing of ensemble wind forecast trajectoriesGeneralization properties of feed-forward neural networks trained on Lorenz systemsRevising the stochastic iterative ensemble smootherJoint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy dataNon-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate atmospheric general circulation modelFluctuations of finite-time Lyapunov exponents in an intermediate-complexity atmospheric model: a multivariate and large-deviation perspectiveData assimilation using adaptive, non-conservative, moving mesh modelsData assimilation as a learning tool to infer ordinary differential equation representations of dynamical modelsA Bayesian approach to multivariate adaptive localization in ensemble-based data assimilation with time-dependent extensionsExploring the sensitivity of Northern Hemisphere atmospheric circulation to different surface temperature forcing using a statistical–dynamical atmospheric modelReview article: Comparison of local particle filters and new implementationsData assimilation of radar reflectivity volumes in a LETKF schemeApplication of ensemble transform data assimilation methods for parameter estimation in reservoir modelingA novel approach for solving CNOPs and its application in identifying sensitive regions of tropical cyclone adaptive observationsChaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model errorEnsemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear caseEnsemble variational assimilation as a probabilistic estimator – Part 2: The fully non-linear caseOSSE for a sustainable marine observing network in the Sea of MarmaraParametric covariance dynamics for the nonlinear diffusive Burgers equationSensitivity analysis with respect to observations in variational data assimilation for parameter estimationExploring the Lyapunov instability properties of high-dimensional atmospheric and climate modelsFeature-based data assimilation in geophysicsQuasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smootherAccelerating assimilation development for new observing systems using EFSOOptimal transport for variational data assimilationThe Onsager–Machlup functional for data assimilationImpact of an observational time window on coupled data assimilation: simulation with a simple climate modelRemote sensing of ocean surface currents: a review of what is being observed and what is being assimilatedNon-Gaussian data assimilation of satellite-based leaf area index observations with an individual-based dynamic global vegetation modelData assimilation for moving mesh methods with an application to ice sheet modellingRegularization destriping of remote sensing imageryControllability, not chaos, key criterion for ocean state estimationAn estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filterFormulation of scale transformation in a stochastic data assimilation frameworkInsights on the role of accurate state estimation in coupled model parameter estimation by a conceptual climate model study
Sangeetika Ruchi, Svetlana Dubinkina, and Jana de Wiljes
Nonlin. Processes Geophys., 28, 23–41,Short summary
To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data are sparse and the model can be non-linear. We propose a novel approach to address these challenges.
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, and Matthieu Plu
Nonlin. Processes Geophys., 28, 1–22,Short summary
Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Pengcheng Yan, Guolin Feng, Wei Hou, and Ping Yang
Nonlin. Processes Geophys., 27, 489–500,Short summary
A system transiting from one stable state to another has to experience a period. Can we predict the end moment (state) if the process has not been completed? This paper presents a method to solve this problem. This method is based on the quantitative relationship among the parameters, which is used to describe the transition process of the abrupt change. By using the historical data, we extract some parameters for predicting the uncompleted climate transition process.
Nonlin. Processes Geophys., 27, 473–487,Short summary
Forecasts of ensemble systems are statistically aligned to synoptic observations at DWD in order to provide support for warning decision management. Motivation and design consequences for extreme and rare meteorological events are presented. Especially for probabilities of severe wind gusts global logistic parameterisations are developed that generate robust statistical forecasts for extreme events, while local characteristics are preserved.
Yvonne Ruckstuhl, Tijana Janjić, and Stephan Rasp
Nonlin. Processes Geophys. Discuss.,
Revised manuscript accepted for NPGShort summary
The assimilation of observations using standard algorithms can lead to violation of physical laws such as mass conservation, which has been shown to have detrimental impact on the system's forecast. We use a neural network (NN) to correct for this mass violation, using training data generated from expensive algorithms that can constrain such physical properties. We found in idealized setup that the NN can match the performance of these expensive algorithms, at neglectable computational costs.
Abd AlRahman AlMomani and Erik Bollt
Nonlin. Processes Geophys. Discuss.,
Revised manuscript accepted for NPGShort summary
In this paper, we introduce a new tool for data-driven discovery of early warning signs of critical transitions in ice shelves, from remote sensing data. Our approach adopts principles of directed spectral clustering methodology considering an asymmetric affinity matrix and the associated directed graph Laplacian. We applied our approach generally to reprocess the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.
Ashesh Chattopadhyay, Pedram Hassanzadeh, and Devika Subramanian
Nonlin. Processes Geophys., 27, 373–389,Short summary
The performance of three machine-learning methods for data-driven modeling of a multiscale chaotic Lorenz 96 system is examined. One of the methods is found to be able to predict the future evolution of the chaotic system well from just knowing the past observations of the large-scale component of the multiscale state vector. Potential applications to data-driven and data-assisted surrogate modeling of complex dynamical systems such as weather and climate are discussed.
Maxime Taillardat and Olivier Mestre
Nonlin. Processes Geophys., 27, 329–347,Short summary
Statistical post-processing of ensemble forecasts is now a well-known procedure in order to correct biased and misdispersed ensemble weather predictions. But practical application in European national weather services is in its infancy. Different applications of ensemble post-processing using machine learning at an industrial scale are presented. Forecast quality and value are improved compared to the raw ensemble, but several facilities have to be made to adjust to operational constraints.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 27, 307–327,Short summary
Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.
Carlos Osácar, Manuel Membrado, and Amalio Fernández-Pacheco
Nonlin. Processes Geophys., 27, 235–237,Short summary
We deduce that after a global thermal perturbation, the Earth's atmosphere would need about a couple of months to come back to equilibrium.
Nonlin. Processes Geophys. Discuss.,
Revised manuscript accepted for NPGShort summary
The ensemble-based variational method is a method to solve nonlinear data assimilation problem by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to closely analyze its behavior, and clarified the conditions for monotonic convergence in nonlinear context.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207,Short summary
A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.
Valentin Resseguier, Wei Pan, and Baylor Fox-Kemper
Nonlin. Processes Geophys., 27, 209–234,Short summary
Geophysical flows span a broader range of temporal and spatial scales than can be resolved numerically. One way to alleviate the ensuing numerical errors is to combine simulations with measurements, taking account of the accuracies of these two sources of information. Here we quantify the distribution of numerical simulation errors without relying on high-resolution numerical simulations. Specifically, small-scale random vortices are added to simulations while conserving energy or circulation.
Nonlin. Processes Geophys., 27, 121–131,Short summary
Seasonal prediction of the of the North Atlantic Oscillation (NAO) has been improved in recent years by improving dynamical models and ensemble predictions. One step therein was the so-called sub-sampling, which combines statistical and dynamical predictions. This study generalises this approach and makes it much more accessible. Furthermore, it presents a new verification approach for such predictions.
Courtney Quinn, Terence J. O'Kane, and Vassili Kitsios
Nonlin. Processes Geophys., 27, 51–74,Short summary
This study presents a novel method for reduced-rank data assimilation of multiscale highly nonlinear systems. Time-varying dynamical properties are used to determine the rank and projection of the system onto a reduced subspace. The variable reduced-rank method is shown to succeed over other fixed-rank methods. This work provides implications for performing strongly coupled data assimilation with a limited number of ensemble members on high-dimensional coupled climate models.
Nonlin. Processes Geophys., 27, 35–49,Short summary
We present a new way to adaptively improve weather forecasts by incorporating last-minute observation information. The recently measured error, together with a statistical model, gives us an indication of the expected future error of wind speed forecasts, which are then adjusted accordingly. This new technique can be especially beneficial for customers in the wind energy industry, where it is important to have reliable short-term forecasts, as well as providers of extreme weather warnings.
Sebastian Scher and Gabriele Messori
Nonlin. Processes Geophys., 26, 381–399,Short summary
Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – it is
trained– and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate- and weather-related applications.
Patrick Nima Raanes, Andreas Størksen Stordal, and Geir Evensen
Nonlin. Processes Geophys., 26, 325–338,Short summary
A popular variational ensemble smoother for data assimilation and history matching is simplified. An exact relationship between ensemble linearizations (linear regression) and adjoints (analytic derivatives) is established.
Fei Lu, Nils Weitzel, and Adam H. Monahan
Nonlin. Processes Geophys., 26, 227–250,Short summary
ll-posedness of the inverse problem and sparse noisy data are two major challenges in the modeling of high-dimensional spatiotemporal processes. We present a Bayesian inference method with a strongly regularized posterior to overcome these challenges, enabling joint state-parameter estimation and quantifying uncertainty in the estimation. We demonstrate the method on a physically motivated nonlinear stochastic partial differential equation arising from paleoclimate construction.
Keiichi Kondo and Takemasa Miyoshi
Nonlin. Processes Geophys., 26, 211–225,Short summary
This study investigates non-Gaussian statistics of the data from a 10240-member ensemble Kalman filter. The large ensemble size can resolve the detailed structures of the probability density functions (PDFs) and indicates that the non-Gaussian PDF is caused by multimodality and outliers. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions and storm track regions where highly nonlinear processes appear frequently.
Nonlin. Processes Geophys., 26, 195–209,Short summary
The stability properties as characterized by finite-time Lyapunov exponents are investigated in an intermediate-complexity atmospheric model. Firstly, the dominant patterns of collective excitation are identified by an empirical orthogonal function analysis of the fluctuation field of all of the finite-time Lyapunov exponents. Secondly, a large-deviation principle is established for all of the Lyapunov exponents and the large-deviation rate functions are estimated.
Ali Aydoğdu, Alberto Carrassi, Colin T. Guider, Chris K. R. T Jones, and Pierre Rampal
Nonlin. Processes Geophys., 26, 175–193,Short summary
Computational models involving adaptive meshes can both evolve dynamically and be remeshed. Remeshing means that the state vector dimension changes in time and across ensemble members, making the ensemble Kalman filter (EnKF) unsuitable for assimilation of observational data. We develop a modification in which analysis is performed on a fixed uniform grid onto which the ensemble is mapped, with resolution relating to the remeshing criteria. The approach is successfully tested on two 1-D models.
Marc Bocquet, Julien Brajard, Alberto Carrassi, and Laurent Bertino
Nonlin. Processes Geophys., 26, 143–162,Short summary
This paper describes an innovative way to use data assimilation to infer the dynamics of a physical system from its observation only. The method can operate with noisy and partial observation of the physical system. It acts as a deep learning technique specialised to dynamical models without the need for machine learning tools. The method is successfully tested on chaotic dynamical systems: the Lorenz-63, Lorenz-96, and Kuramoto–Sivashinski models and a two-scale Lorenz model.
Andrey A. Popov and Adrian Sandu
Nonlin. Processes Geophys., 26, 109–122,Short summary
This work has to do with a small part of existing algorithms that are used in applications such as predicting the weather. We provide empirical evidence that our new technique works well on small but representative models. This might lead to creation of a better weather forecast and potentially save lives as in the case of hurricane prediction.
Sonja Totz, Stefan Petri, Jascha Lehmann, Erik Peukert, and Dim Coumou
Nonlin. Processes Geophys., 26, 1–12,
Alban Farchi and Marc Bocquet
Nonlin. Processes Geophys., 25, 765–807,Short summary
Data assimilation looks for an optimal way to learn from observations of a dynamical system to improve the quality of its predictions. The goal is to filter out the noise (both observation and model noise) to retrieve the true signal. Among all possible methods, particle filters are promising; the method is fast and elegant, and it allows for a Bayesian analysis. In this review paper, we discuss implementation techniques for (local) particle filters in high-dimensional systems.
Thomas Gastaldo, Virginia Poli, Chiara Marsigli, Pier Paolo Alberoni, and Tiziana Paccagnella
Nonlin. Processes Geophys., 25, 747–764,Short summary
Accuracy of numerical weather prediction forecasts is strongly related to the quality of initial conditions employed. To improve them, it seems advantageous to use radar reflectivity observations because of their high spatial and temporal resolution. This is tested in a high-resolution model whose domain covers Italy. Results show that the employment of reflectivity observations improves precipitation forecast accuracy, but the positive impact is lost after a few hours of forecast.
Sangeetika Ruchi and Svetlana Dubinkina
Nonlin. Processes Geophys., 25, 731–746,Short summary
Accurate estimation of subsurface geological parameters is essential for the oil industry. This is done by combining observations with an estimation from a model. Ensemble Kalman filter is a widely used method for inverse modeling, while ensemble transform particle filtering is a recently developed method that has been applied to estimate only a small number of parameters and in fluids. We show that for a high-dimensional inverse problem it is superior to an ensemble Kalman filter.
Linlin Zhang, Bin Mu, Shijin Yuan, and Feifan Zhou
Nonlin. Processes Geophys., 25, 693–712,Short summary
We propose a novel approach to solve conditional nonlinear optimal perturbation for identifying sensitive areas for tropical cyclone adaptive observations. This method is free of adjoint models and overcomes two obstacles, not having adjoint models and having dimensions higher than the problem space. All experimental results prove that it is a meaningful and effective method for solving CNOP and provides a new way for such research. This work aims to solve CNOP and identify sensitive areas.
Colin Grudzien, Alberto Carrassi, and Marc Bocquet
Nonlin. Processes Geophys., 25, 633–648,Short summary
Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.
Mohamed Jardak and Olivier Talagrand
Nonlin. Processes Geophys., 25, 565–587,Short summary
Ensemble variational assimilation (EnsVAR) has been implemented on two small-dimension non-linear chaotic toy models, as well as on a linearized version of those models. In the linear case, EnsVAR is exactly Bayesian and produced highly reliable ensembles. In the non-linear case, EnsVAR, implemented on temporal windows on the order of magnitude of the predictability time of the systems, shows as good performance as in the exactly linear case. EnsVar is as good an estimator as EnKF and PF.
Mohamed Jardak and Olivier Talagrand
Nonlin. Processes Geophys., 25, 589–604,Short summary
EnsVAR is fundamentally successful in that, even in conditions where Bayesianity cannot be expected, it produces ensembles which possess a high degree of statistical reliability. In non-linear strong-constraint cases, EnsVAR has been successful here only through the use of quasi-static variational assimilation. In the weak-constraint case, without QSVA, EnsVAR provided new evidence as to the favourable effect.
Ali Aydoğdu, Timothy J. Hoar, Tomislava Vukicevic, Jeffrey L. Anderson, Nadia Pinardi, Alicia Karspeck, Jonathan Hendricks, Nancy Collins, Francesca Macchia, and Emin Özsoy
Nonlin. Processes Geophys., 25, 537–551,Short summary
This study presents, to our knowledge, the first data assimilation experiments in the Sea of Marmara. We propose a FerryBox network for monitoring the state of the sea and show that assimilation of the temperature and salinity improves the forecasts in the basin. The flow of the Bosphorus helps to propagate the error reduction. The study can be taken as a step towards a marine forecasting system in the Sea of Marmara that will help to improve the forecasts in the adjacent Black and Aegean seas.
Olivier Pannekoucke, Marc Bocquet, and Richard Ménard
Nonlin. Processes Geophys., 25, 481–495,Short summary
The forecast of weather prediction uncertainty is a real challenge and is crucial for risk management. However, uncertainty prediction is beyond the capacity of supercomputers, and improvements of the technology may not solve this issue. A new uncertainty prediction method is introduced which takes advantage of fluid equations to predict simple quantities which approximate real uncertainty but at a low numerical cost. A proof of concept is shown by an academic model derived from fluid dynamics.
Victor Shutyaev, Francois-Xavier Le Dimet, and Eugene Parmuzin
Nonlin. Processes Geophys., 25, 429–439,Short summary
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. The sensitivity of the response function to the observation data is studied. The results are relevant for monitoring and prediction of sea and ocean states.
Lesley De Cruz, Sebastian Schubert, Jonathan Demaeyer, Valerio Lucarini, and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 387–412,Short summary
The predictability of weather models is limited largely by the initial state error growth or decay rates. We have computed these rates for PUMA, a global model for the atmosphere, and MAOOAM, a more simplified, coupled model which includes the ocean. MAOOAM has processes at distinct timescales, whereas PUMA surprisingly does not. We propose a new programme to compute the natural directions along the flow that correspond to the growth or decay rates, to learn which components play a role.
Matthias Morzfeld, Jesse Adams, Spencer Lunderman, and Rafael Orozco
Nonlin. Processes Geophys., 25, 355–374,Short summary
Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by defining likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. This issue can be addressed by selecting features of the data, and defining likelihoods based on the features, rather than by the usual mismatch of model output and data.
Anthony Fillion, Marc Bocquet, and Serge Gratton
Nonlin. Processes Geophys., 25, 315–334,Short summary
This study generalizes a paper by Pires et al. (1996) to state-of-the-art data assimilation techniques, such as the iterative ensemble Kalman smoother (IEnKS). We show that the longer the time window over which observations are assimilated, the better the accuracy of the IEnKS. Beyond a critical time length that we estimate, we show that this accuracy finally degrades. We show that the use of the quasi-static minimizations but generalized to the IEnKS yields a significantly improved accuracy.
Guo-Yuan Lien, Daisuke Hotta, Eugenia Kalnay, Takemasa Miyoshi, and Tse-Chun Chen
Nonlin. Processes Geophys., 25, 129–143,Short summary
The ensemble forecast sensitivity to observation (EFSO) method can efficiently clarify under what conditions observations are beneficial or detrimental for assimilation. Based on EFSO, an offline assimilation method is proposed to accelerate the development of data selection strategies for new observing systems. The usefulness of this method is demonstrated with the assimilation of global satellite precipitation data.
Nelson Feyeux, Arthur Vidard, and Maëlle Nodet
Nonlin. Processes Geophys., 25, 55–66,Short summary
In geophysics, numerical models are generally initialized through so-called data assimilation methods. They require computation of a distance between model fields and physical observations. The most common choice is the Euclidian distance. However, due to its local nature it is not well suited for capturing position errors. This papers investigates theoretical aspects of the use of the optimal transport-based Wasserstein distance in this context and shows that it is able to capture such errors.
Nonlin. Processes Geophys., 24, 701–712,Short summary
The optimisation of simulation paths is sometimes misleading. We can find a path with the highest probability by the method of least squares. However, it is not necessarily the route where the paths are most concentrated. This paper clarifies how we can find the mode of a distribution of paths by optimisation.
Yuxin Zhao, Xiong Deng, Shaoqing Zhang, Zhengyu Liu, Chang Liu, Gabriel Vecchi, Guijun Han, and Xinrong Wu
Nonlin. Processes Geophys., 24, 681–694,Short summary
Here with a simple coupled model that simulates typical scale interactions in the climate system, we study the optimal OTWs for the coupled media so that climate signals can be most accurately recovered by CDA. Results show that an optimal OTW determined from the de-correlation timescale provides maximal observational information that best fits the characteristic variability of the coupled medium during the data blending process.
Jordi Isern-Fontanet, Joaquim Ballabrera-Poy, Antonio Turiel, and Emilio García-Ladona
Nonlin. Processes Geophys., 24, 613–643,Short summary
Ocean currents play a key role in Earth’s climate – they are of major importance for navigation and human activities at sea and impact almost all processes that take place in the ocean. Nevertheless, their observation and forecasting are still difficult. Here, we review the main techniques used to derive surface currents from satellite measurements and the existing approaches to assimilate this information into ocean models.
Hazuki Arakida, Takemasa Miyoshi, Takeshi Ise, Shin-ichiro Shima, and Shunji Kotsuki
Nonlin. Processes Geophys., 24, 553–567,Short summary
This is the first study assimilating the satellite-based leaf area index observations every 4 days into a numerical model simulating the growth and death of individual plants. The newly developed data assimilation system successfully reduced the uncertainties of the model parameters related to phenology and carbon dynamics. It also provides better estimates of the present vegetation structure which can be used as the initial states for the simulation of the future vegetation change.
Bertrand Bonan, Nancy K. Nichols, Michael J. Baines, and Dale Partridge
Nonlin. Processes Geophys., 24, 515–534,Short summary
We develop data assimilation techniques for numerical models using moving mesh methods. Moving meshes are valuable for explicitly tracking interfaces and boundaries in evolving systems. The application of the techniques is demonstrated on a one-dimensional model of an ice sheet. It is shown, using various types of observations, that the techniques predict the evolution of the edges of the ice sheet and its height accurately and efficiently.
Ranil Basnayake, Erik Bollt, Nicholas Tufillaro, Jie Sun, and Michelle Gierach
Nonlin. Processes Geophys., 24, 367–378,
Geoffrey Gebbie and Tsung-Lin Hsieh
Nonlin. Processes Geophys., 24, 351–366,Short summary
The best reconstructions of the past ocean state involve the statistical combination of numerical models and observations; however, the computationally efficient method that produces physically interpretable fields is thought to not be applicable to chaotic dynamical systems, such as ocean models with eddies. Here we use a model of the chaotic, forced pendulum to show that the most popular existing method is successful so long as there are enough uncertain boundary conditions through time.
Guocan Wu and Xiaogu Zheng
Nonlin. Processes Geophys., 24, 329–341,Short summary
The accuracy of the assimilation results crucially relies on the estimate accuracy of forecast error covariance matrix in data assimilation. Ensemble Kalman filter estimates the forecast error covariance matrix as the sampling covariance matrix of the ensemble forecast states, which need to be further inflated. The experiment results on the Lorenz-96 model show that the analysis error is reduced and the analysis sensitivity to observations is improved using the proposed inflation technique.
Feng Liu and Xin Li
Nonlin. Processes Geophys., 24, 279–291,Short summary
This is the first mathematical definitions of the spatial scale and its transformation based on Lebesgue measure. An Ito process-formed geophysical variable with respect to scale was also provided. The stochastic calculus for data assimilation discovered the new expressions of error caused by spatial scale transformation. The results improve the ability to understand the spatial scale transformation and related uncertainties in Earth observation, modelling and data assimilation.
Xiaolin Yu, Shaoqing Zhang, Xiaopei Lin, and Mingkui Li
Nonlin. Processes Geophys., 24, 125–139,Short summary
Parameter estimation (PE) with a global coupled data assimilation (CDA) system can improve the runs, but the improvement remains in a limited range. We have to come back to simple models to sort out the sources of noises. Incomplete observations and the chaotic nature of the atmosphere have much stronger influences on the PE through the state estimation (SE) process. Here, we propose the guidelines of how to enhance the signal-to-noise ratio under partial SE status.
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This paper deals with the effects of nonlinearity in a state-of-the-art atmospheric global data assimilation system. It is shown that these effects have become increasingly important over the years due to increased model resolution and use of nonlinear observations. The ability to deal with nonlinearities has thus become a crucial asset of data assimilation algorithms. At ECMWF this is done in a perturbative fashion. Advantages and limitations of this technique are discussed.
This paper deals with the effects of nonlinearity in a state-of-the-art atmospheric global data...