Articles | Volume 24, issue 4
Nonlin. Processes Geophys., 24, 681–694, 2017
https://doi.org/10.5194/npg-24-681-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 24, 681–694, 2017
https://doi.org/10.5194/npg-24-681-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article 17 Nov 2017
Research article | 17 Nov 2017
Impact of an observational time window on coupled data assimilation: simulation with a simple climate model
Yuxin Zhao et al.
Related authors
A. A. Yuxin Zhao, B. B. Xiong Deng, and C. C. Shuo Yang
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2015-76, https://doi.org/10.5194/npg-2015-76, 2016
Preprint withdrawn
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An optimal time window centred at the assimilation time to collect measured data for an assimilation cycle, can improve the CDA analysis skill. We study the impact of optimal OTWs on the quality of parameter optimization and climate prediction in a simple coupled model. Results show that the optimal OTWs of valid atmosphere or ocean observations exist for the parameter being estimated and incorporating the parameter optimization will enhance the predictability both of the atmosphere and ocean.
Zhao Liu, Shaoqing Zhang, Yang Shen, Yuping Guan, and Xiong Deng
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2021-5, https://doi.org/10.5194/npg-2021-5, 2021
Revised manuscript under review for NPG
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A general methodology is introduced to capture regime transitions of the Atlantic meridional overturning circulation (AMOC). The assimilation models with different parameters simulate different paths for AMOC to switch between equilibrium states. Constraining model parameters with observations can significantly mitigate the model deviations, thus capturing AMOC regime transitions. This simple model study serves as a guideline for improving coupled general circulation models.
Shaoqing Zhang, Haohuan Fu, Lixin Wu, Yuxuan Li, Hong Wang, Yunhui Zeng, Xiaohui Duan, Wubing Wan, Li Wang, Yuan Zhuang, Hongsong Meng, Kai Xu, Ping Xu, Lin Gan, Zhao Liu, Sihai Wu, Yuhu Chen, Haining Yu, Shupeng Shi, Lanning Wang, Shiming Xu, Wei Xue, Weiguo Liu, Qiang Guo, Jie Zhang, Guanghui Zhu, Yang Tu, Jim Edwards, Allison Baker, Jianlin Yong, Man Yuan, Yangyang Yu, Qiuying Zhang, Zedong Liu, Mingkui Li, Dongning Jia, Guangwen Yang, Zhiqiang Wei, Jingshan Pan, Ping Chang, Gokhan Danabasoglu, Stephen Yeager, Nan Rosenbloom, and Ying Guo
Geosci. Model Dev., 13, 4809–4829, https://doi.org/10.5194/gmd-13-4809-2020, https://doi.org/10.5194/gmd-13-4809-2020, 2020
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Science advancement and societal needs require Earth system modelling with higher resolutions that demand tremendous computing power. We successfully scale the 10 km ocean and 25 km atmosphere high-resolution Earth system model to a new leading-edge heterogeneous supercomputer using state-of-the-art optimizing methods, promising the solution of high spatial resolution and time-varying frequency. Corresponding technical breakthroughs are of significance in modelling and HPC design communities.
Fortunat Joos, Renato Spahni, Benjamin D. Stocker, Sebastian Lienert, Jurek Müller, Hubertus Fischer, Jochen Schmitt, I. Colin Prentice, Bette Otto-Bliesner, and Zhengyu Liu
Biogeosciences, 17, 3511–3543, https://doi.org/10.5194/bg-17-3511-2020, https://doi.org/10.5194/bg-17-3511-2020, 2020
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Results of the first globally resolved simulations of terrestrial carbon and nitrogen (N) cycling and N2O emissions over the past 21 000 years are compared with reconstructed N2O emissions. Modelled and reconstructed emissions increased strongly during past abrupt warming events. This evidence appears consistent with a dynamic response of biological N fixation to increasing N demand by ecosystems, thereby reducing N limitation of plant productivity and supporting a land sink for atmospheric CO2.
Jiangyu Li and Shaoqing Zhang
Geosci. Model Dev., 13, 1035–1054, https://doi.org/10.5194/gmd-13-1035-2020, https://doi.org/10.5194/gmd-13-1035-2020, 2020
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Two assimilation systems developed using two nearly independent wave models are used to study the influences of various error sources including mode bias on wave data assimilation; a statistical method is explored to make full use of the merits of individual assimilation systems for bias correction, thus improving wave analysis greatly. This study opens a door to further our understanding of physical processes in waves and associated air–sea interactions for improving wave modeling.
Mingchen Ma, Yang Gao, Yuhang Wang, Shaoqing Zhang, L. Ruby Leung, Cheng Liu, Shuxiao Wang, Bin Zhao, Xing Chang, Hang Su, Tianqi Zhang, Lifang Sheng, Xiaohong Yao, and Huiwang Gao
Atmos. Chem. Phys., 19, 12195–12207, https://doi.org/10.5194/acp-19-12195-2019, https://doi.org/10.5194/acp-19-12195-2019, 2019
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Ozone pollution has become severe in China, and extremely high ozone episodes occurred in summer 2017 over the North China Plain. While meteorology impacts are clear, we find that enhanced biogenic emissions, previously ignored by the community, driven by high vapor pressure deficit, land cover change and urban landscape contribute substantially to ozone formation. This study has significant implications for ozone pollution control with more frequent heat waves and urbanization growth in future.
Sifan Gu and Zhengyu Liu
Geosci. Model Dev., 10, 4723–4742, https://doi.org/10.5194/gmd-10-4723-2017, https://doi.org/10.5194/gmd-10-4723-2017, 2017
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Both biotic 231Pa and 230Th and abiotic 231Pa and 230Th have been implemented in the ocean model of CESM. Under present-day climate forcing, our model is able to simulate water column 231Pa and 230Th activity and the sediment 231Pa-to-230Th activity ratio in good agreement with observations. In HOSING experiments, the biotic and abiotic sediment 231Pa-to-230Th activity ratios behave similarly over large areas of low productivity, but can differ substantially in some regions of high productivity.
Sifan Gu, Zhengyu Liu, Alexandra Jahn, Johannes Rempfer, Jiaxu Zhang, and Fortunat Joos
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-40, https://doi.org/10.5194/gmd-2017-40, 2017
Revised manuscript not accepted
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This paper is the documentation of the implementation of neodymium (Nd) isotopes in the ocean model of CESM. Our model can simulate both Nd concentration and Nd isotope ratio in good agreement with observations. Our Nd-enabled ocean model makes it possible for direct model-data comparison in paleoceanographic studies, which can help to resolve some uncertainties and controversies in our understanding of past ocean evolution. Therefore, our model provides a useful tool for paleoclimate studies.
Xiaolin Yu, Shaoqing Zhang, Xiaopei Lin, and Mingkui Li
Nonlin. Processes Geophys., 24, 125–139, https://doi.org/10.5194/npg-24-125-2017, https://doi.org/10.5194/npg-24-125-2017, 2017
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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.
Zhengyao Lu, Zhengyu Liu, Guangshan Chen, and Jian Guan
Clim. Past Discuss., https://doi.org/10.5194/cp-2016-128, https://doi.org/10.5194/cp-2016-128, 2017
Revised manuscript not accepted
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We use complex climate model simulations to study how the intensity of El Niño-Southern Oscillation (ENSO) changed for the last 300 thousand years. We consider external climatic forcings like orbital variations, greenhouse gases and ice-sheets. We find that orbital forcing dominates slow ENSO evolution by modulating the change of the coupled ocean-atmosphere instability, while the effects of GHGs and ice-sheet forcing tend to compensate each other.
Xinyu Wen, Zhengyu Liu, Zhongxiao Chen, Esther Brady, David Noone, Qingzhao Zhu, and Jian Guan
Clim. Past, 12, 2077–2085, https://doi.org/10.5194/cp-12-2077-2016, https://doi.org/10.5194/cp-12-2077-2016, 2016
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In this paper, we challenge the usefulness of temperature effect and amount effect, the basic assumptions in past climate reconstruction using a stable water isotope proxy, in East Asia on multiple timescales. By modeling several time slices in the past 22 000 years using an isotope-enabled general circulation model, we suggest great caution when interpreting δ18O records in this area as indicators of surface temperature and/or local monsoonal precipitation, especially on a millennial timescale.
A. A. Yuxin Zhao, B. B. Xiong Deng, and C. C. Shuo Yang
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2015-76, https://doi.org/10.5194/npg-2015-76, 2016
Preprint withdrawn
Short summary
Short summary
An optimal time window centred at the assimilation time to collect measured data for an assimilation cycle, can improve the CDA analysis skill. We study the impact of optimal OTWs on the quality of parameter optimization and climate prediction in a simple coupled model. Results show that the optimal OTWs of valid atmosphere or ocean observations exist for the parameter being estimated and incorporating the parameter optimization will enhance the predictability both of the atmosphere and ocean.
A. Jahn, K. Lindsay, X. Giraud, N. Gruber, B. L. Otto-Bliesner, Z. Liu, and E. C. Brady
Geosci. Model Dev., 8, 2419–2434, https://doi.org/10.5194/gmd-8-2419-2015, https://doi.org/10.5194/gmd-8-2419-2015, 2015
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Carbon isotopes have been added to the ocean model of the Community Earth System Model version 1 (CESM1). This paper describes the details of how the abiotic 14C tracer and the biotic 13C and 14C tracers were added to the existing ocean model of the CESM. In addition, it shows the first results of the new model features compared to observational data for the 1990s.
P. X. Wang, B. Wang, H. Cheng, J. Fasullo, Z. T. Guo, T. Kiefer, and Z. Y. Liu
Clim. Past, 10, 2007–2052, https://doi.org/10.5194/cp-10-2007-2014, https://doi.org/10.5194/cp-10-2007-2014, 2014
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All regional monsoons belong to a cohesive global monsoon circulation system, albeit thateach regional subsystem has its own indigenous features. A comprehensive review of global monsoon variability reveals that regional monsoons can vary coherently across a range of timescales, from interannual up to orbital and tectonic. Study of monsoon variability from both global and regional perspectives is imperative and advantageous for integrated understanding of the modern and paleo-monsoon dynamics.
J. M. Marson, I. Wainer, M. M. Mata, and Z. Liu
Clim. Past, 10, 1723–1734, https://doi.org/10.5194/cp-10-1723-2014, https://doi.org/10.5194/cp-10-1723-2014, 2014
G.-S. Chen, Z. Liu, and J. E. Kutzbach
Clim. Past, 10, 1269–1275, https://doi.org/10.5194/cp-10-1269-2014, https://doi.org/10.5194/cp-10-1269-2014, 2014
G.-J. Han, X.-F. Zhang, S. Zhang, X.-R. Wu, and Z. Liu
Nonlin. Processes Geophys., 21, 357–366, https://doi.org/10.5194/npg-21-357-2014, https://doi.org/10.5194/npg-21-357-2014, 2014
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Ensemble Riemannian data assimilation over the Wasserstein space
Improving the Potential Accuracy and Usability of EURO-CORDEX Estimates of Future Rainfall Climate using Mean Squared Error Model Averaging
An early warning sign of critical transition in the Antarctic ice sheet – a data-driven tool for a spatiotemporal tipping point
Training a convolutional neural network to conserve mass in data assimilation
Behavior of the iterative ensemble-based variational method in nonlinear problems
Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation
A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective
A method for predicting the uncompleted climate transition process
Statistical postprocessing of ensemble forecasts for severe weather at Deutscher Wetterdienst
Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network
From research to applications – examples of operational ensemble post-processing in France using machine learning
Correcting for model changes in statistical postprocessing – an approach based on response theory
Brief communication: Residence time of energy in the atmosphere
Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales
Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty
Seasonal statistical–dynamical prediction of the North Atlantic Oscillation by probabilistic post-processing and its evaluation
Application of a local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems
Order of operation for multi-stage post-processing of ensemble wind forecast trajectories
Generalization properties of feed-forward neural networks trained on Lorenz systems
Revising the stochastic iterative ensemble smoother
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate atmospheric general circulation model
Fluctuations of finite-time Lyapunov exponents in an intermediate-complexity atmospheric model: a multivariate and large-deviation perspective
Data assimilation using adaptive, non-conservative, moving mesh models
Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models
A Bayesian approach to multivariate adaptive localization in ensemble-based data assimilation with time-dependent extensions
Exploring the sensitivity of Northern Hemisphere atmospheric circulation to different surface temperature forcing using a statistical–dynamical atmospheric model
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Data assimilation of radar reflectivity volumes in a LETKF scheme
Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling
Nonlinear effects in 4D-Var
A novel approach for solving CNOPs and its application in identifying sensitive regions of tropical cyclone adaptive observations
Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error
Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case
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OSSE for a sustainable marine observing network in the Sea of Marmara
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Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation
Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
Feature-based data assimilation in geophysics
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother
Accelerating assimilation development for new observing systems using EFSO
Optimal transport for variational data assimilation
The Onsager–Machlup functional for data assimilation
Remote sensing of ocean surface currents: a review of what is being observed and what is being assimilated
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Data assimilation for moving mesh methods with an application to ice sheet modelling
Regularization destriping of remote sensing imagery
Controllability, not chaos, key criterion for ocean state estimation
An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, https://doi.org/10.5194/npg-28-295-2021, 2021
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Data assimilation aims to improve hydrologic and weather forecasts by combining available information from Earth system models and observations. The classical approaches to data assimilation usually proceed with some preconceived assumptions about the shape of their probability distributions. As a result, when such assumptions are invalid, the forecast accuracy suffers. In the proposed methodology, we relax such assumptions and demonstrate improved performance.
Stephen Jewson, Giuliana Barbato, Paola Mercogliano, Jaroslav Mysiak, and Maximiliano Sassi
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2021-12, https://doi.org/10.5194/npg-2021-12, 2021
Revised manuscript accepted for NPG
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Climate model simulations are uncertain. In some cases this makes it difficult to know how to use them. Significance testing is often used to deal with this issue but has various shortcomings. We describe two alternative ways to manage uncertainty in climate model simulations that avoid these shortcomings. We test them on simulations of future rainfall over Europe and show they produce more accurate projections than either using unadjusted climate model output or statistical testing.
Abd AlRahman AlMomani and Erik Bollt
Nonlin. Processes Geophys., 28, 153–166, https://doi.org/10.5194/npg-28-153-2021, https://doi.org/10.5194/npg-28-153-2021, 2021
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This paper introduces a tool for data-driven discovery of early warning signs of critical transitions in ice shelves from remote sensing data. Our directed spectral clustering method considers an asymmetric affinity matrix along with the associated directed graph Laplacian. We applied our approach to reprocessing the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.
Yvonne Ruckstuhl, Tijana Janjić, and Stephan Rasp
Nonlin. Processes Geophys., 28, 111–119, https://doi.org/10.5194/npg-28-111-2021, https://doi.org/10.5194/npg-28-111-2021, 2021
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The assimilation of observations using standard algorithms can lead to a violation of physical laws (e.g. mass conservation), which is shown to have a detrimental impact on the system's forecast. We use a neural network (NN) to correct this mass violation, using training data generated from expensive algorithms that can constrain such physical properties. We found that, in an idealized set-up, the NN can match the performance of these expensive algorithms at negligible computational costs.
Shin'ya Nakano
Nonlin. Processes Geophys., 28, 93–109, https://doi.org/10.5194/npg-28-93-2021, https://doi.org/10.5194/npg-28-93-2021, 2021
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The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.
Sangeetika Ruchi, Svetlana Dubinkina, and Jana de Wiljes
Nonlin. Processes Geophys., 28, 23–41, https://doi.org/10.5194/npg-28-23-2021, https://doi.org/10.5194/npg-28-23-2021, 2021
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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, https://doi.org/10.5194/npg-28-1-2021, https://doi.org/10.5194/npg-28-1-2021, 2021
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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, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
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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.
Reinhold Hess
Nonlin. Processes Geophys., 27, 473–487, https://doi.org/10.5194/npg-27-473-2020, https://doi.org/10.5194/npg-27-473-2020, 2020
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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.
Ashesh Chattopadhyay, Pedram Hassanzadeh, and Devika Subramanian
Nonlin. Processes Geophys., 27, 373–389, https://doi.org/10.5194/npg-27-373-2020, https://doi.org/10.5194/npg-27-373-2020, 2020
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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, https://doi.org/10.5194/npg-27-329-2020, https://doi.org/10.5194/npg-27-329-2020, 2020
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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, https://doi.org/10.5194/npg-27-307-2020, https://doi.org/10.5194/npg-27-307-2020, 2020
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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, https://doi.org/10.5194/npg-27-235-2020, https://doi.org/10.5194/npg-27-235-2020, 2020
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We deduce that after a global thermal perturbation, the Earth's
atmosphere would need about a couple of months to come back to equilibrium.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207, https://doi.org/10.5194/npg-27-187-2020, https://doi.org/10.5194/npg-27-187-2020, 2020
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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, https://doi.org/10.5194/npg-27-209-2020, https://doi.org/10.5194/npg-27-209-2020, 2020
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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.
André Düsterhus
Nonlin. Processes Geophys., 27, 121–131, https://doi.org/10.5194/npg-27-121-2020, https://doi.org/10.5194/npg-27-121-2020, 2020
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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, https://doi.org/10.5194/npg-27-51-2020, https://doi.org/10.5194/npg-27-51-2020, 2020
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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.
Nina Schuhen
Nonlin. Processes Geophys., 27, 35–49, https://doi.org/10.5194/npg-27-35-2020, https://doi.org/10.5194/npg-27-35-2020, 2020
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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, https://doi.org/10.5194/npg-26-381-2019, https://doi.org/10.5194/npg-26-381-2019, 2019
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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, https://doi.org/10.5194/npg-26-325-2019, https://doi.org/10.5194/npg-26-325-2019, 2019
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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, https://doi.org/10.5194/npg-26-227-2019, https://doi.org/10.5194/npg-26-227-2019, 2019
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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, https://doi.org/10.5194/npg-26-211-2019, https://doi.org/10.5194/npg-26-211-2019, 2019
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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.
Frank Kwasniok
Nonlin. Processes Geophys., 26, 195–209, https://doi.org/10.5194/npg-26-195-2019, https://doi.org/10.5194/npg-26-195-2019, 2019
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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, https://doi.org/10.5194/npg-26-175-2019, https://doi.org/10.5194/npg-26-175-2019, 2019
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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, https://doi.org/10.5194/npg-26-143-2019, https://doi.org/10.5194/npg-26-143-2019, 2019
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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, https://doi.org/10.5194/npg-26-109-2019, https://doi.org/10.5194/npg-26-109-2019, 2019
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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, https://doi.org/10.5194/npg-26-1-2019, https://doi.org/10.5194/npg-26-1-2019, 2019
Alban Farchi and Marc Bocquet
Nonlin. Processes Geophys., 25, 765–807, https://doi.org/10.5194/npg-25-765-2018, https://doi.org/10.5194/npg-25-765-2018, 2018
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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, https://doi.org/10.5194/npg-25-747-2018, https://doi.org/10.5194/npg-25-747-2018, 2018
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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, https://doi.org/10.5194/npg-25-731-2018, https://doi.org/10.5194/npg-25-731-2018, 2018
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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.
Massimo Bonavita, Peter Lean, and Elias Holm
Nonlin. Processes Geophys., 25, 713–729, https://doi.org/10.5194/npg-25-713-2018, https://doi.org/10.5194/npg-25-713-2018, 2018
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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.
Linlin Zhang, Bin Mu, Shijin Yuan, and Feifan Zhou
Nonlin. Processes Geophys., 25, 693–712, https://doi.org/10.5194/npg-25-693-2018, https://doi.org/10.5194/npg-25-693-2018, 2018
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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, https://doi.org/10.5194/npg-25-633-2018, https://doi.org/10.5194/npg-25-633-2018, 2018
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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, https://doi.org/10.5194/npg-25-565-2018, https://doi.org/10.5194/npg-25-565-2018, 2018
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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, https://doi.org/10.5194/npg-25-589-2018, https://doi.org/10.5194/npg-25-589-2018, 2018
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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, https://doi.org/10.5194/npg-25-537-2018, https://doi.org/10.5194/npg-25-537-2018, 2018
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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, https://doi.org/10.5194/npg-25-481-2018, https://doi.org/10.5194/npg-25-481-2018, 2018
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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, https://doi.org/10.5194/npg-25-429-2018, https://doi.org/10.5194/npg-25-429-2018, 2018
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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, https://doi.org/10.5194/npg-25-387-2018, https://doi.org/10.5194/npg-25-387-2018, 2018
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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, https://doi.org/10.5194/npg-25-355-2018, https://doi.org/10.5194/npg-25-355-2018, 2018
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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, https://doi.org/10.5194/npg-25-315-2018, https://doi.org/10.5194/npg-25-315-2018, 2018
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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, https://doi.org/10.5194/npg-25-129-2018, https://doi.org/10.5194/npg-25-129-2018, 2018
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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, https://doi.org/10.5194/npg-25-55-2018, https://doi.org/10.5194/npg-25-55-2018, 2018
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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.
Nozomi Sugiura
Nonlin. Processes Geophys., 24, 701–712, https://doi.org/10.5194/npg-24-701-2017, https://doi.org/10.5194/npg-24-701-2017, 2017
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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.
Jordi Isern-Fontanet, Joaquim Ballabrera-Poy, Antonio Turiel, and Emilio García-Ladona
Nonlin. Processes Geophys., 24, 613–643, https://doi.org/10.5194/npg-24-613-2017, https://doi.org/10.5194/npg-24-613-2017, 2017
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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, https://doi.org/10.5194/npg-24-553-2017, https://doi.org/10.5194/npg-24-553-2017, 2017
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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, https://doi.org/10.5194/npg-24-515-2017, https://doi.org/10.5194/npg-24-515-2017, 2017
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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, https://doi.org/10.5194/npg-24-367-2017, https://doi.org/10.5194/npg-24-367-2017, 2017
Geoffrey Gebbie and Tsung-Lin Hsieh
Nonlin. Processes Geophys., 24, 351–366, https://doi.org/10.5194/npg-24-351-2017, https://doi.org/10.5194/npg-24-351-2017, 2017
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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, https://doi.org/10.5194/npg-24-329-2017, https://doi.org/10.5194/npg-24-329-2017, 2017
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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.
Cited articles
Anderson, J. L.: An ensemble adjustment Kalman Filter for data assimilation, Mon. Weather Rev., 129, 2884–2903, https://doi.org/10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2, 2001.
Anderson, J. L.: A local least squares framework for ensemble filtering, Mon. Weather Rev., 131, 634–642, https://doi.org/10.1175/1520-0493(2003)131<0634:ALLSFF>2.0.CO;2, 2003.
Anderson, J. L.: An adaptive covariance inflation error correction algorithm for ensemble filters, Tellus A, 59, 210–224, https://doi.org/10.1111/j.1600-0870.2006.00216.x, 2007.
Anderson, J. L.: Spatially and temporally varying adaptive covariance inflation for ensemble filter, Tellus A, 61, 72–83, https://doi.org/10.1111/j.1600-0870.2008.00361.x, 2009.
Chen, D., Zebiak, S. E., Busalacchi, A. J., and Cane, M. A.: An improved procedure for EI Nino forecasting: implications for predictability, Science, 269, 1699–1702, 1995.
Chen, D.: Coupled data assimilation for ENSO prediction, Adv. Geosci., 18, 45–62, 2010.
Collins, W. D., Blackman, M. L., Hack, J., Henderson, T. B., Kiehl, J. T., Large, W. G., and Mckenna, D. S.: The community climate system model version 3 (CCSM), J. Climate, 19, 2122–2143, https://doi.org/10.1175/JCLI3761.1, 2006.
Delworth, T. L., Broccoli, A. J., Rosati, A., et al.: GFDL's CM2 Global Coupled Climate Models, Part I: Formulation and simulation characteristics, J. Climate, 19, 643–674, https://doi.org/10.1175/JCLI3629.1, 2006.
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10143–10162, https://doi.org/10.1029/94JC00572, 1994.
Evensen, G.: Data assimilation: The Ensemble Kalman Filter, Springer, 187 pp., 2007.
Gnanadesikan, A.: A simple predictive model for the structure of the oceanic pycnocline, Science, 283, 2077–2079, 1999.
Hamill, T. M. and Snyder, C.: A hybrid ensemble Kalman filter-3D variational analysis scheme, Mon. Weather Rev., 128, 2905–2919, https://doi.org/10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2, 2000.
Han, G., Wu, X., Zhang, S., Liu, Z., and Li, W.: Error covariance estimation for coupled data assimilation using a Lorenz atmosphere and a simple pycnocline ocean model, J. Climate, 26, 10218–10231, https://doi.org/10.1175/JCLI-D-13-00236.1, 2013.
Han, G., Zhang, X., Zhang, S., Wu, X., and Liu, Z.: Mitigation of coupled model biases included by dynamical core misfitting through parameter optimization: simulation with a simple pycnocline prediction model, Nonlin. Processes Geophys., 21, 357–366, https://doi.org/10.5194/npg-21-357-2014, 2014.
Hunt, B. R., Kalnay, E., Kostelich, E. J., Ott, E., Patil, D. J., Sauer, T., Szunyogh, I., Yorke, J. A., and Zimin, A. V.: Four-dimensional ensemble Kalman filtering, Tellus A, 56, 273–277, https://doi.org/10.1111/j.1600-0870.2004.00066.x, 2004.
Houtekamer, P. L. and Mitchell, H. L.: Ensemble kalman filtering, Q. J. Roy. Meteor. Soc., 131, 3269–3289, https://doi.org/10.1256/qj.05.135, 2005.
Kalman, R.: A new approach to linear filtering and prediction problems, Trans. ASME. Ser. D. J. Basic Eng., 82, 35–45, https://doi.org/10.1115/1.3662552, 1960.
Kalman, R. and Bucy, R.: New results in linear filtering and prediction theory, Trans. ASME. Ser. D. J. Basic Eng. 83, 95–109, https://doi.org/10.1115/1.3658902, 1961.
Laroche, S., Gauthier, P., Tanguay, M., Pellerin, S., and Morneau, J.: Impact of the different components of 4DVAR on the global forecast system of the Meteorological Service of Canada, Mon. Weather Rev., 135, 2355–2364, https://doi.org/10.1175/MWR3408.1, 2007.
Li, H., Kalnay, E., and Miyoshi, T.: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter, Q. J. Roy. Meteor. Soc., 135, 523–533, https://doi.org/10.1002/qj.371, 2009.
Liu H., Lu, F., Liu, Z., Liu, Y., and Zhang, S.: Assimilating Atmosphere Reanalysis in Coupled Data Assimilation, J. Meteorol. Res., 30, 572–583, https://doi.org/10.1007/s13351-016-6014-1, 2016.
Lorenz, E. N.: Deterministic non-periodic flow, J. Atmos. Sci., 20, 130–141, 1963.
Lu, F., Liu, Z., Zhang, S., and Liu, Y.: Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part I: Simple Model Study, Mon. Weather Rev., 143, 3823–3837, https://doi.org/10.1175/MWR-D-14-00322.1, 2015.
Miyoshi, T.: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter, Mon. Weather Rev., 139, 1519–1535, https://doi.org/10.1175/2010MWR3570.1, 2011.
Pires, C., Vautard, R., and Talagrand, O.: On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus A, 48, 96–121, https://doi.org/10.1034/j.1600-0870.1996.00006.x, 1996.
Randall, D. A., Wood, R. A., Bony, S., Colman, R., Fichefet, T., Fyfe, J., Kattsov, V., Pitman, A., Shukla, J., Srinivasan, J., Stouffer, R. J., Sumi, A., and Taylor, K. E.: Climate models and their evaluation, Climate Change 2007: The physical Science Basis, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge University Press, 589–662, 2007.
Saha, S., Moorthi, S., Pan, H.-L., et al.: The NCEP Climate Forecast System Reanalysis, B. Am. Meteor. Soc., 91, 1015–1057, https://doi.org/10.1175/2010BAMS3001.1, 2010.
Singleton, T.: Data Assimilation experiments with a simple coupled ocean-atmosphere model, PhD thesis, University of Maryland, Collage Park, 116 pp., 2011.
Sugiura, N., Awaji, T., Masuda, S., Mochizuki, T., Toyoda, T., Miyama, T., Igarashi, H., and Ishikawa, Y.: Development of a four-dimensional variation coupled data assimilation system for enhanced analysis and prediction of seasonal to interannual climate variations, J. Geophys. Res., 113, C10017, https://doi.org/10.1029/2008JC004741, 2008.
Whitaker, J. S. and Hamill, T. M.: Ensemble data assimilation without perturbed observations, Mon. Weather Rev., 130, 1913–1924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2, 2002.
Yang, X., Rosati, A., Zhang, S., Delworth, T. L., Gudgel, R. G., Zhang, R., Vecchi, G., Anderson, W., Chang, Y., DelSole, T., Dixon, K., Msadek, R., Stern, W. F., Wittenberg, A., and Zeng, F.: A predictable AMO-like pattern in GFDL's fully coupled ensemble initialization and decadal forecasting system, J. Climate, 26, 650–661, https://doi.org/10.1175/JCLI-D-12-00231.1, 2013.
Zhang, S. and Anderson, J. L.: Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model, Tellus A, 55, 126–147, https://doi.org/10.1034/j.1600-0870.2003.00010.x, 2003.
Zhang, S., Harrison, M. J., Rosati, A., and Wittenberg, A.: System design and evaluation of coupled ensemble data assimilation for global oceanic climate studies, Mon. Weather Rev., 135, 3541–3564, https://doi.org/10.1175/MWR3466.1, 2007.
Zhang, S.: Impact of observation-optimized model parameters on decadal predictions: simulation with a simple pycnocline prediction model, Geophys. Res. Lett., 38, L02702, https://doi.org/10.1029/2010GL046133, 2011a.
Zhang, S.: A study of impacts of coupled model initial shocks and state-parameter optimization on climate predictions using a simple pycnocline prediction model, J. Climate, 24, 6210–6226, https://doi.org/10.1175/JCLI-D-10-05003.1, 2011b.
Zhang, S., Liu, Z., Rosati, A., and Delworth, T.: A study of enhancive parameter correction with coupled data assimilation for climate estimation and prediction using a simple coupled model, Tellus A, 64, 1–20, https://doi.org/10.3402/tellusa.v64i0.10963, 2012.
Zhang, S., Winton, M., Rosati, A., Delworth, T., and Huang, B.: Impact of enthalpy-based ensemble filtering sea ice data assimilation on decadal predictions: simulation with a conceptual pycnocline prediction model, J. Climate, 26, 2368–2378, https://doi.org/10.1175/JCLI-D-11-00714.1, 2013.
Zhang, S., Chang, Y.-S., Yang, X., and Rosati, A.: Balanced and coherent climate estimation by combining data with a biased coupled model, J. Climate, 27, 1302–1314, https://doi.org/10.1175/JCLI-D-13-00260.1, 2014.
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.
Here with a simple coupled model that simulates typical scale interactions in the climate...
