Articles | Volume 30, issue 3
https://doi.org/10.5194/npg-30-289-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-30-289-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
NPG Letters
| 
21 Jul 2023
NPG Letters |
| 21 Jul 2023
| 21 Jul 2023
Using orthogonal vectors to improve the ensemble space of the ensemble Kalman filter and its effect on data assimilation and forecasting
Yung-Yun Cheng
Center for Weather Climate and Disaster Research, National Taiwan
University, Taipei, Taiwan
Shu-Chih Yang
CORRESPONDING AUTHOR
Department of Atmospheric Sciences, National Central University,
Taoyuan, Taiwan
GPS Science and Application Research Center, National Central
University, Taoyuan, Taiwan
RIKEN Center for Computational Science, Kobe, Japan
Zhe-Hui Lin
Department of Atmospheric Sciences, National Central University,
Taoyuan, Taiwan
Yung-An Lee
Department of Atmospheric Sciences, National Central University,
Taoyuan, Taiwan
Related authors
No articles found.
Gia Huan Pham, Shu-Chih Yang, Chih-Chien Chang, Shu-Ya Chen, and Cheng Yung Huang
Atmos. Meas. Tech., 17, 3605–3623, https://doi.org/10.5194/amt-17-3605-2024, https://doi.org/10.5194/amt-17-3605-2024, 2024
Short summary
Short summary
This research examines the characteristics of low-level GNSS radio occultation (RO) refractivity bias over ocean and land and its dependency on the RO retrieval uncertainty, atmospheric temperature, and moisture. We propose methods for estimating the region-dependent refractivity bias. Our methods can be applied to calibrate the refractivity bias under different atmospheric conditions and thus improve the applications of the GNSS RO data in the deep troposphere.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Prognostic assumed-probability-density-function (distribution density function) approach: further generalization and demonstrations
Bridging classical data assimilation and optimal transport: the 3D-Var case
Improving ensemble data assimilation through Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC)
Evolution of small-scale turbulence at large Richardson numbers
Inferring flow energy, space and time scales: freely-drifting vs fixed point observations
How far can the statistical error estimation problem be closed by collocated data?
Review article: Towards strongly coupled ensemble data assimilation with additional improvements from machine learning
Toward a multivariate formulation of the parametric Kalman filter assimilation: application to a simplified chemical transport model
Data-driven reconstruction of partially observed dynamical systems
Extending ensemble Kalman filter algorithms to assimilate observations with an unknown time offset
Applying prior correlations for ensemble-based spatial localization
A stochastic covariance shrinkage approach to particle rejuvenation in the ensemble transform particle filter
Ensemble Riemannian data assimilation: towards large-scale dynamical systems
Inferring the instability of a dynamical system from the skill of data assimilation exercises
Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system
Improving the potential accuracy and usability of EURO-CORDEX estimates of future rainfall climate using frequentist model averaging
Ensemble Riemannian data assimilation over the Wasserstein space
An early warning sign of critical transition in the Antarctic ice sheet – a data-driven tool for a spatiotemporal tipping point
Behavior of the iterative ensemble-based variational method in nonlinear problems
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
Correcting for model changes in statistical postprocessing – an approach based on response theory
Brief communication: Residence time of energy in the atmosphere
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
Jun-Ichi Yano
Nonlin. Processes Geophys., 31, 359–380, https://doi.org/10.5194/npg-31-359-2024, https://doi.org/10.5194/npg-31-359-2024, 2024
Short summary
Short summary
A methodology for directly predicting the time evolution of the assumed parameters for the distribution densities based on the Liouville equation, as proposed earlier, is extended to multidimensional cases and to cases in which the systems are constrained by integrals over a part of the variable range. The extended methodology is tested against a convective energy-cycle system as well as the Lorenz strange attractor.
Marc Bocquet, Pierre J. Vanderbecken, Alban Farchi, Joffrey Dumont Le Brazidec, and Yelva Roustan
Nonlin. Processes Geophys., 31, 335–357, https://doi.org/10.5194/npg-31-335-2024, https://doi.org/10.5194/npg-31-335-2024, 2024
Short summary
Short summary
A novel approach, optimal transport data assimilation (OTDA), is introduced to merge DA and OT concepts. By leveraging OT's displacement interpolation in space, it minimises mislocation errors within DA applied to physical fields, such as water vapour, hydrometeors, and chemical species. Its richness and flexibility are showcased through one- and two-dimensional illustrations.
Man-Yau Chan
Nonlin. Processes Geophys., 31, 287–302, https://doi.org/10.5194/npg-31-287-2024, https://doi.org/10.5194/npg-31-287-2024, 2024
Short summary
Short summary
Forecasts have uncertainties. It is thus essential to reduce these uncertainties. Such reduction requires uncertainty quantification, which often means running costly models multiple times. The cost limits the number of model runs and thus the quantification’s accuracy. This study proposes a technique that utilizes users’ knowledge of forecast uncertainties to improve uncertainty quantification. Tests show that this technique improves uncertainty reduction.
Lev Ostrovsky, Irina Soustova, Yuliya Troitskaya, and Daria Gladskikh
Nonlin. Processes Geophys., 31, 219–227, https://doi.org/10.5194/npg-31-219-2024, https://doi.org/10.5194/npg-31-219-2024, 2024
Short summary
Short summary
The nonstationary kinetic model of turbulence is used to describe the evolution and structure of the upper turbulent layer with the parameters taken from in situ observations. As an example, we use a set of data for three cruises made in different areas of the world ocean. With the given profiles of current shear and buoyancy frequency, the theory yields results that satisfactorily agree with the measurements of the turbulent dissipation rate.
Aurelien Luigi Serge Ponte, Lachlan Astfalck, Matthew Rayson, Andrew Zulberti, and Nicole Jones
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-10, https://doi.org/10.5194/npg-2024-10, 2024
Revised manuscript accepted for NPG
Short summary
Short summary
We propose a novel method for the estimation of ocean flow properties in terms of its energy, spatial and temporal scales. The method relies on flow observations that are either collected at a fixed location or along the flow as they would if inferred from the trajectory of freely-drifting platforms. The accuracy of the method is quantified in different experimental configurations. We demonstrate freely drifting platforms can, even in isolation, enable to capture flow properties is a first.
Annika Vogel and Richard Ménard
Nonlin. Processes Geophys., 30, 375–398, https://doi.org/10.5194/npg-30-375-2023, https://doi.org/10.5194/npg-30-375-2023, 2023
Short summary
Short summary
Accurate estimation of the error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This work provides a conceptual view of the statistical error estimation problem in light of the increasing number of available datasets. We found that the total number of required assumptions increases with the number of overlapping datasets, but the relative number of error statistics that can be estimated increases.
Eugenia Kalnay, Travis Sluka, Takuma Yoshida, Cheng Da, and Safa Mote
Nonlin. Processes Geophys., 30, 217–236, https://doi.org/10.5194/npg-30-217-2023, https://doi.org/10.5194/npg-30-217-2023, 2023
Short summary
Short summary
Strongly coupled data assimilation (SCDA) generates coherent integrated Earth system analyses by assimilating the full Earth observation set into all Earth components. We describe SCDA based on the ensemble Kalman filter with a hierarchy of coupled models, from a coupled Lorenz to the Climate Forecast System v2. SCDA with a sufficiently large ensemble can provide more accurate coupled analyses compared to weakly coupled DA. The correlation-cutoff method can compensate for a small ensemble size.
Antoine Perrot, Olivier Pannekoucke, and Vincent Guidard
Nonlin. Processes Geophys., 30, 139–166, https://doi.org/10.5194/npg-30-139-2023, https://doi.org/10.5194/npg-30-139-2023, 2023
Short summary
Short summary
This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test bed is introduced that shows the ability of our equations to reproduce the statistics estimated from an ensemble of forecasts. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.
Pierre Tandeo, Pierre Ailliot, and Florian Sévellec
Nonlin. Processes Geophys., 30, 129–137, https://doi.org/10.5194/npg-30-129-2023, https://doi.org/10.5194/npg-30-129-2023, 2023
Short summary
Short summary
The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system without knowing the model equations. It is illustrated using the three-dimensional Lorenz system, where only two components are observed. The proposed data-driven procedure is low-cost, is easy to implement, uses linear and Gaussian assumptions and requires only a small amount of data. It is based on an iterative linear Kalman smoother with a state augmentation.
Elia Gorokhovsky and Jeffrey L. Anderson
Nonlin. Processes Geophys., 30, 37–47, https://doi.org/10.5194/npg-30-37-2023, https://doi.org/10.5194/npg-30-37-2023, 2023
Short summary
Short summary
Older observations of the Earth system sometimes lack information about the time they were taken, posing problems for analyses of past climate. To begin to ameliorate this problem, we propose new methods of varying complexity, including methods to estimate the distribution of the offsets between true and reported observation times. The most successful method accounts for the nonlinearity in the system, but even the less expensive ones can improve data assimilation in the presence of time error.
Chu-Chun Chang and Eugenia Kalnay
Nonlin. Processes Geophys., 29, 317–327, https://doi.org/10.5194/npg-29-317-2022, https://doi.org/10.5194/npg-29-317-2022, 2022
Short summary
Short summary
This study introduces a new approach for enhancing the ensemble data assimilation (DA), a technique that combines observations and forecasts to improve numerical weather predictions. Our method uses the prescribed correlations to suppress spurious errors, improving the accuracy of DA. The experiments on the simplified atmosphere model show that our method has comparable performance to the traditional method but is superior in the early stage and is more computationally efficient.
Andrey A. Popov, Amit N. Subrahmanya, and Adrian Sandu
Nonlin. Processes Geophys., 29, 241–253, https://doi.org/10.5194/npg-29-241-2022, https://doi.org/10.5194/npg-29-241-2022, 2022
Short summary
Short summary
Numerical weather prediction requires the melding of both computational model and data obtained from sensors such as satellites. We focus on one algorithm to accomplish this. We aim to aid its use by additionally supplying it with data obtained from separate models that describe the average behavior of the computational model at any given time. We show that our approach outperforms the standard approaches to this problem.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter Jan van Leeuwen, Gilad Lerman, and Efi Foufoula-Georgiou
Nonlin. Processes Geophys., 29, 77–92, https://doi.org/10.5194/npg-29-77-2022, https://doi.org/10.5194/npg-29-77-2022, 2022
Short summary
Short summary
The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
Short summary
Short summary
Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Zofia Stanley, Ian Grooms, and William Kleiber
Nonlin. Processes Geophys., 28, 565–583, https://doi.org/10.5194/npg-28-565-2021, https://doi.org/10.5194/npg-28-565-2021, 2021
Short summary
Short summary
In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.
Stephen Jewson, Giuliana Barbato, Paola Mercogliano, Jaroslav Mysiak, and Maximiliano Sassi
Nonlin. Processes Geophys., 28, 329–346, https://doi.org/10.5194/npg-28-329-2021, https://doi.org/10.5194/npg-28-329-2021, 2021
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
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, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
Short summary
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.
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
Short summary
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.
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
Short summary
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, https://doi.org/10.5194/npg-27-235-2020, https://doi.org/10.5194/npg-27-235-2020, 2020
Short summary
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.
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
Short summary
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, https://doi.org/10.5194/npg-27-51-2020, https://doi.org/10.5194/npg-27-51-2020, 2020
Short summary
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.
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
Short summary
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.
Cited articles
Bocquet, M. and Carrassi, A.: Four-dimensional ensemble variational data
assimilation and the unstable subspace, Tellus A, 69, 1304504, https://doi.org/10.1080/16000870.2017.1304504, 2017.
Carrassi, A., Trevisan, A., Descamps, L., Talagrand, O., and Uboldi, F.: Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF, Nonlin. Processes Geophys., 15, 503–521, https://doi.org/10.5194/npg-15-503-2008, 2008.
Chang, S., Penny, G., and Yang, S.-C.: Hybrid Gain Data Assimilation using
Variational Corrections in the Subspace Orthogonal to the Ensemble, Mon.
Weather Rev., 148, 2331–2350, https://doi.org/10.1175/MWR-D-19-0128.1, 2020.
Enomoto, T., Yamane, S., and Ohfuchi, W.: Simple sensitivity using ensemble
forecasts, J. Meteorol. Soc. Jpn., 93, 199–213, https://doi.org/10.2151/jmsj.2015-011,
2015.
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.
Hunt, B. R., Kostelich, E. J., and Szunyogh, I.: Efficient data
assimilation for spatiotemporal chaos: A local ensemble Kalman filter,
Physica D, 230, 112–126, 2007.
Lorenz, E. N.: Predictablilty: A problem partly solved, Conference
Paper, Seminar on Predictability, ECMWF, 1–18, 1996.
Lorenz, E. N.: Predictability – A Problem partly solved, in: Predictability of Weather and Climate, edited by: Palmer, T. N.
and Hagedorn, R.,
Cambridge University Press, Cambridge, Chap. 3, 40–58, 2006.
Lorenz, E. N. and Emanuel, K. A.: Optimal sites for supplementary weather
observations: Simulation with a small model, J. Atmos.Sci., 55, 399–414,
1998.
Penny, S. G: The hybrid local ensemble transform Kalman filter, Mon. Weather
Rev., 142, 2139–2149, https://doi.org/10.1175/MWR-D-13-00131.1, 2014.
Toth, Z. and Kalnay, E.: Ensemble forecasting at NMC: The generation of
perturbations, B. Am. Meteorol. Soc., 74, 2317–2330, 1993.
van Kekem, D. L.: Dynamics of the Lorenz-96 model: Bifurcations, symmetries and waves, PhD thesis, University of Groningen, ISBN 978-94-034-0979-5, 2018.
Wang, X., Bishop, C. H., and Julier, S. J.: Which is better, an ensemble of
positive-negative pairs or a centered spherical simplex ensemble?, Mon.
Weather Rev., 132, 1590–1605, 2004.
Whitaker, J. S., Hamill, T. M., Wei, X., Song, Y., and Toth, Z.: Ensemble
data assimilation with the NCEP Global Forecast System, Mon. Weather Rev.,
136, 463–481, https://doi.org/10.1175/2007MWR2018.1, 2008.
Yang, S.-C., Kalnay, E., and Enomoto, T.: Ensemble singular vecotrs and their
use as additive inflation in ENKF, Tellus A, 67, 26536, https://doi.org/10.3402/tellusa.v67.26536, 2015.
yungyun: yungyun0721/orthogonal_vector_code: initial_code_release (v1.0), Zenodo [code and data set], https://doi.org/10.5281/zenodo.8116811, 2023.
Short summary
In the ensemble Kalman filter, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the accuracy of analysis and prediction. This study proposes a new algorithm to use cost-free pseudomembers to expand the ensemble space effectively and improve analysis accuracy during the analysis step, without increasing the ensemble size during forecasting.
In the ensemble Kalman filter, the ensemble space may not fully capture the forecast errors due...
