Articles | Volume 27, issue 2
https://doi.org/10.5194/npg-27-307-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-27-307-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 May 2020
Research article |
| 27 May 2020
| 27 May 2020
Correcting for model changes in statistical postprocessing – an approach based on response theory
Institut Royal Météorologique de Belgique, Avenue Circulaire, 3, 1180 Brussels, Belgium
European Meteorological Network (EUMETNET), Avenue Circulaire, 3, 1180 Brussels, Belgium
Stéphane Vannitsem
Institut Royal Météorologique de Belgique, Avenue Circulaire, 3, 1180 Brussels, Belgium
European Meteorological Network (EUMETNET), Avenue Circulaire, 3, 1180 Brussels, Belgium
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Anupama K. Xavier, Jonathan Demaeyer, and Stéphane Vannitsem
Earth Syst. Dynam., 15, 893–912, https://doi.org/10.5194/esd-15-893-2024, https://doi.org/10.5194/esd-15-893-2024, 2024
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This research focuses on understanding different atmospheric patterns like blocking, zonal, and transition regimes and analyzing their predictability. We used an idealized land–atmosphere coupled model to simulate Earth's atmosphere. Then we identified these blocking, zonal, and transition regimes using Gaussian mixture clustering and studied their predictability using Lyapunov exponents.
Jonathan Demaeyer, Jonas Bhend, Sebastian Lerch, Cristina Primo, Bert Van Schaeybroeck, Aitor Atencia, Zied Ben Bouallègue, Jieyu Chen, Markus Dabernig, Gavin Evans, Jana Faganeli Pucer, Ben Hooper, Nina Horat, David Jobst, Janko Merše, Peter Mlakar, Annette Möller, Olivier Mestre, Maxime Taillardat, and Stéphane Vannitsem
Earth Syst. Sci. Data, 15, 2635–2653, https://doi.org/10.5194/essd-15-2635-2023, https://doi.org/10.5194/essd-15-2635-2023, 2023
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A benchmark dataset is proposed to compare different statistical postprocessing methods used in forecasting centers to properly calibrate ensemble weather forecasts. This dataset is based on ensemble forecasts covering a portion of central Europe and includes the corresponding observations. Examples on how to download and use the data are provided, a set of evaluation methods is proposed, and a first benchmark of several methods for the correction of 2 m temperature forecasts is performed.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 605–631, https://doi.org/10.5194/npg-25-605-2018, https://doi.org/10.5194/npg-25-605-2018, 2018
Short summary
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We investigate the modeling of the effects of the unresolved scales on the large scales of the coupled ocean–atmosphere model MAOOAM. Two different physically based stochastic methods are considered and compared, in various configurations of the model. Both methods show remarkable performances and are able to model fundamental changes in the model dynamics. Ways to improve the parameterizations' implementation are also proposed.
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
Short summary
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.
Lesley De Cruz, Jonathan Demaeyer, and Stéphane Vannitsem
Geosci. Model Dev., 9, 2793–2808, https://doi.org/10.5194/gmd-9-2793-2016, https://doi.org/10.5194/gmd-9-2793-2016, 2016
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Large-scale weather patterns such as the North Atlantic Oscillation, which dictates the harshness of European winters, vary over the course of years. By recreating it in a simple ocean-atmosphere model, we hope to understand what drives this slow, hard-to-predict variability. MAOOAM is such a model, in which the resolution and included physical processes can easily be modified. The modular system allowed us to show the robustness of the slow variability against changes in model resolution.
Martin Bonte and Stéphane Vannitsem
EGUsphere, https://doi.org/10.5194/egusphere-2024-3915, https://doi.org/10.5194/egusphere-2024-3915, 2024
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In recent years, there has been more and more floods due to intense precipitation, such as the July 2021 event in Belgium. Predicting precipitation is a difficult task, even for the next hours. This study focuses on a tool to assess whether a given situation is stable or not (i.e. is likely to stay as it is or could evolve in an unpredictable manner).
Stéphane Vannitsem, X. San Liang, and Carlos A. Pires
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Anupama K. Xavier, Jonathan Demaeyer, and Stéphane Vannitsem
Earth Syst. Dynam., 15, 893–912, https://doi.org/10.5194/esd-15-893-2024, https://doi.org/10.5194/esd-15-893-2024, 2024
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David Docquier, Giorgia Di Capua, Reik V. Donner, Carlos A. L. Pires, Amélie Simon, and Stéphane Vannitsem
Nonlin. Processes Geophys., 31, 115–136, https://doi.org/10.5194/npg-31-115-2024, https://doi.org/10.5194/npg-31-115-2024, 2024
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Identifying causes of specific processes is crucial in order to better understand our climate system. Traditionally, correlation analyses have been used to identify cause–effect relationships in climate studies. However, correlation does not imply causation, which justifies the need to use causal methods. We compare two independent causal methods and show that these are superior to classical correlation analyses. We also find some interesting differences between the two methods.
Michel Journée, Edouard Goudenhoofdt, Stéphane Vannitsem, and Laurent Delobbe
Hydrol. Earth Syst. Sci., 27, 3169–3189, https://doi.org/10.5194/hess-27-3169-2023, https://doi.org/10.5194/hess-27-3169-2023, 2023
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The exceptional flood of July 2021 in central Europe impacted Belgium severely. This study aims to characterize rainfall amounts in Belgium from 13 to 16 July 2021 based on observational data (i.e., rain gauge data and a radar-based rainfall product). The spatial and temporal distributions of rainfall during the event aredescribed. In order to document such a record-breaking event as much as possible, the rainfall data are shared with the scientific community on Zenodo for further studies.
Jonathan Demaeyer, Jonas Bhend, Sebastian Lerch, Cristina Primo, Bert Van Schaeybroeck, Aitor Atencia, Zied Ben Bouallègue, Jieyu Chen, Markus Dabernig, Gavin Evans, Jana Faganeli Pucer, Ben Hooper, Nina Horat, David Jobst, Janko Merše, Peter Mlakar, Annette Möller, Olivier Mestre, Maxime Taillardat, and Stéphane Vannitsem
Earth Syst. Sci. Data, 15, 2635–2653, https://doi.org/10.5194/essd-15-2635-2023, https://doi.org/10.5194/essd-15-2635-2023, 2023
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A benchmark dataset is proposed to compare different statistical postprocessing methods used in forecasting centers to properly calibrate ensemble weather forecasts. This dataset is based on ensemble forecasts covering a portion of central Europe and includes the corresponding observations. Examples on how to download and use the data are provided, a set of evaluation methods is proposed, and a first benchmark of several methods for the correction of 2 m temperature forecasts is performed.
David Docquier, Stéphane Vannitsem, and Alessio Bellucci
Earth Syst. Dynam., 14, 577–591, https://doi.org/10.5194/esd-14-577-2023, https://doi.org/10.5194/esd-14-577-2023, 2023
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The climate system is strongly regulated by interactions between the ocean and atmosphere. However, many uncertainties remain in the understanding of these interactions. Our analysis uses a relatively novel approach to quantify causal links between the ocean surface and lower atmosphere based on satellite observations. We find that both the ocean and atmosphere influence each other but with varying intensity depending on the region, demonstrating the power of causal methods.
Stéphane Vannitsem
Nonlin. Processes Geophys., 30, 1–12, https://doi.org/10.5194/npg-30-1-2023, https://doi.org/10.5194/npg-30-1-2023, 2023
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The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of information theory. These tools allow the predictability of the succession of weather patterns and the irreversible nature of the dynamics to be clarified. It is shown that the predictability is increasing in the observations, while the opposite trend is found in model projections. The irreversibility displays an overall increase in time in both the observations and the model runs.
David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul
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Understanding whether variations in ocean heat content are driven by air-sea heat fluxes or by ocean dynamics is of crucial importance to enhance climate projections. We use a relatively novel causal method to quantify interactions between ocean heat budget terms based on climate models. We find that low-resolution models overestimate the influence of ocean dynamics in the upper ocean, and that changes in ocean heat content are dominated by air-sea fluxes at high resolution.
Nicolas Ghilain, Stéphane Vannitsem, Quentin Dalaiden, Hugues Goosse, Lesley De Cruz, and Wenguang Wei
Earth Syst. Sci. Data, 14, 1901–1916, https://doi.org/10.5194/essd-14-1901-2022, https://doi.org/10.5194/essd-14-1901-2022, 2022
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Modeling the climate at high resolution is crucial to represent the snowfall accumulation over the complex orography of the Antarctic coast. While ice cores provide a view constrained spatially but over centuries, climate models can give insight into its spatial distribution, either at high resolution over a short period or vice versa. We downscaled snowfall accumulation from climate model historical simulations (1850–present day) over Dronning Maud Land at 5.5 km using a statistical method.
Tommaso Alberti, Reik V. Donner, and Stéphane Vannitsem
Earth Syst. Dynam., 12, 837–855, https://doi.org/10.5194/esd-12-837-2021, https://doi.org/10.5194/esd-12-837-2021, 2021
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We provide a novel approach to diagnose the strength of the ocean–atmosphere coupling by using both a reduced order model and reanalysis data. Our findings suggest the ocean–atmosphere dynamics presents a rich variety of features, moving from a chaotic to a coherent coupled dynamics, mainly attributed to the atmosphere and only marginally to the ocean. Our observations suggest further investigations in characterizing the occurrence and spatial dependency of the ocean–atmosphere coupling.
Stephan Hemri, Sebastian Lerch, Maxime Taillardat, Stéphane Vannitsem, and Daniel S. Wilks
Nonlin. Processes Geophys., 27, 519–521, https://doi.org/10.5194/npg-27-519-2020, https://doi.org/10.5194/npg-27-519-2020, 2020
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.
Emmanuel Roulin and Stéphane Vannitsem
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2019-45, https://doi.org/10.5194/npg-2019-45, 2019
Preprint withdrawn
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We need seasonal predictions of temperature and precipitation to prepare hydrological outlooks. Since the skill is limited, statistical correction and combination of outputs from multiple models are necessary. We use the forecasts of past situations from the EUROSIP multi-model system for 6 case studies in Western Europe and the Mediterranean Region. We identify skill for spring temperature in most areas and winter precipitation in Sweden and Greece. Sample size for training appears crucial.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 605–631, https://doi.org/10.5194/npg-25-605-2018, https://doi.org/10.5194/npg-25-605-2018, 2018
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We investigate the modeling of the effects of the unresolved scales on the large scales of the coupled ocean–atmosphere model MAOOAM. Two different physically based stochastic methods are considered and compared, in various configurations of the model. Both methods show remarkable performances and are able to model fundamental changes in the model dynamics. Ways to improve the parameterizations' implementation are also proposed.
Stéphane Vannitsem and Pierre Ekelmans
Earth Syst. Dynam., 9, 1063–1083, https://doi.org/10.5194/esd-9-1063-2018, https://doi.org/10.5194/esd-9-1063-2018, 2018
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The El Niño–Southern Oscillation phenomenon is a slow dynamics present in the coupled ocean–atmosphere tropical Pacific system which has important teleconnections with the northern extratropics. These teleconnections are usually believed to be the source of an enhanced predictability in the northern extratropics at seasonal to decadal timescales. This question is challenged by investigating the causality between these regions using an advanced technique known as convergent cross mapping.
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.
Lesley De Cruz, Jonathan Demaeyer, and Stéphane Vannitsem
Geosci. Model Dev., 9, 2793–2808, https://doi.org/10.5194/gmd-9-2793-2016, https://doi.org/10.5194/gmd-9-2793-2016, 2016
Short summary
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Large-scale weather patterns such as the North Atlantic Oscillation, which dictates the harshness of European winters, vary over the course of years. By recreating it in a simple ocean-atmosphere model, we hope to understand what drives this slow, hard-to-predict variability. MAOOAM is such a model, in which the resolution and included physical processes can easily be modified. The modular system allowed us to show the robustness of the slow variability against changes in model resolution.
S. Vannitsem and L. De Cruz
Geosci. Model Dev., 7, 649–662, https://doi.org/10.5194/gmd-7-649-2014, https://doi.org/10.5194/gmd-7-649-2014, 2014
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Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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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
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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
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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
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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
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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
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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
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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
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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.
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.
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.
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.
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.
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.
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.
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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.
Postprocessing schemes used to correct weather forecasts are no longer efficient when the model...
