Articles | Volume 26, issue 3
https://doi.org/10.5194/npg-26-227-2019
© Author(s) 2019. 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-26-227-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Aug 2019
Research article |
| 14 Aug 2019
| 14 Aug 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, USA
Nils Weitzel
Institut für Umweltphysik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Institut für Geowissenschaften und Meteorologie, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany
Adam H. Monahan
School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
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Jean-Philippe Baudouin, Nils Weitzel, Maximilian May, Lukas Jonkers, Andrew M. Dolman, and Kira Rehfeld
EGUsphere, https://doi.org/10.5194/egusphere-2024-1387, https://doi.org/10.5194/egusphere-2024-1387, 2024
This preprint is open for discussion and under review for Climate of the Past (CP).
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We explore past global temperatures, critical for climate change comprehension. We devise a method to test temperature reconstruction using climate simulations. Uncertainties, mainly from past temperature measurement methods and age determination, impact reconstructions over time. While more data enhances accuracy for long-term trends, high quality data are more important for short-term precision. Our study lays the groundwork for better reconstructions and suggests avenues for improvement.
Elisa Ziegler, Nils Weitzel, Jean-Philippe Baudouin, Marie-Luise Kapsch, Uwe Mikolajewicz, Lauren Gregoire, Ruza Ivanovic, Paul J. Valdes, Christian Wirths, and Kira Rehfeld
EGUsphere, https://doi.org/10.5194/egusphere-2024-1396, https://doi.org/10.5194/egusphere-2024-1396, 2024
This preprint is open for discussion and under review for Climate of the Past (CP).
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During the Last Deglaciation global surface temperature rose by about 4–7 degrees over several millennia. We show that changes of year-to-year up to century-to-century fluctuations of temperature and precipitation during the Deglaciation were mostly larger than during either the preceding or succeeding more stable periods in fifteen climate model simulations. The analysis demonstrates how ice sheets, meltwater and volcanism influence simulated variability to inform future simulation protocols.
Nils Weitzel, Heather Andres, Jean-Philippe Baudouin, Marie-Luise Kapsch, Uwe Mikolajewicz, Lukas Jonkers, Oliver Bothe, Elisa Ziegler, Thomas Kleinen, André Paul, and Kira Rehfeld
Clim. Past, 20, 865–890, https://doi.org/10.5194/cp-20-865-2024, https://doi.org/10.5194/cp-20-865-2024, 2024
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The ability of climate models to faithfully reproduce past warming episodes is a valuable test considering potentially large future warming. We develop a new method to compare simulations of the last deglaciation with temperature reconstructions. We find that reconstructions differ more between regions than simulations, potentially due to deficiencies in the simulation design, models, or reconstructions. Our work is a promising step towards benchmarking simulations of past climate transitions.
Ruth A. R. Digby, Nathan P. Gillett, Adam H. Monahan, Knut von Salzen, Antonis Gkikas, Qianqian Song, and Zhibo Zhang
Atmos. Chem. Phys., 24, 2077–2097, https://doi.org/10.5194/acp-24-2077-2024, https://doi.org/10.5194/acp-24-2077-2024, 2024
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The COVID-19 lockdowns reduced aerosol emissions. We ask whether these reductions affected regional aerosol optical depth (AOD) and compare the observed changes to predictions from Earth system models. Only India has an observed AOD reduction outside of typical variability. Models overestimate the response in some regions, but when key biases have been addressed, the agreement is improved. Our results suggest that current models can realistically predict the effects of future emission changes.
Manuel Chevalier, Anne Dallmeyer, Nils Weitzel, Chenzhi Li, Jean-Philippe Baudouin, Ulrike Herzschuh, Xianyong Cao, and Andreas Hense
Clim. Past, 19, 1043–1060, https://doi.org/10.5194/cp-19-1043-2023, https://doi.org/10.5194/cp-19-1043-2023, 2023
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Data–data and data–model vegetation comparisons are commonly based on comparing single vegetation estimates. While this approach generates good results on average, reducing pollen assemblages to single single plant functional type (PFT) or biome estimates can oversimplify the vegetation signal. We propose using a multivariate metric, the Earth mover's distance (EMD), to include more details about the vegetation structure when performing such comparisons.
Carsten Abraham, Amber M. Holdsworth, and Adam H. Monahan
Nonlin. Processes Geophys., 26, 401–427, https://doi.org/10.5194/npg-26-401-2019, https://doi.org/10.5194/npg-26-401-2019, 2019
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Atmospheric stably stratified boundary layers display transitions between regimes of sustained and intermittent turbulence. These transitions are not well represented in numerical weather prediction and climate models. A prototype explicitly stochastic turbulence parameterization simulating regime dynamics is presented and tested in an idealized model. Results demonstrate that the approach can improve the regime representation in models.
Nils Weitzel, Andreas Hense, and Christian Ohlwein
Clim. Past, 15, 1275–1301, https://doi.org/10.5194/cp-15-1275-2019, https://doi.org/10.5194/cp-15-1275-2019, 2019
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A new method for probabilistic spatial reconstructions of past climate states is presented, which combines pollen data with a multi-model ensemble of climate simulations in a Bayesian framework. The approach is applied to reconstruct summer and winter temperature in Europe during the mid-Holocene. Our reconstructions account for multiple sources of uncertainty and are well suited for quantitative statistical analyses of the climate under different forcing conditions.
Hakase Hayashida, James R. Christian, Amber M. Holdsworth, Xianmin Hu, Adam H. Monahan, Eric Mortenson, Paul G. Myers, Olivier G. J. Riche, Tessa Sou, and Nadja S. Steiner
Geosci. Model Dev., 12, 1965–1990, https://doi.org/10.5194/gmd-12-1965-2019, https://doi.org/10.5194/gmd-12-1965-2019, 2019
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Ice algae, the primary producer in sea ice, play a fundamental role in shaping marine ecosystems and biogeochemical cycling of key elements in polar regions. In this study, we developed a process-based numerical model component representing sea-ice biogeochemistry for a sea ice–ocean coupled general circulation model. The model developed can be used to simulate the projected changes in sea-ice ecosystems and biogeochemistry in response to on-going rapid decline of the Arctic.
Gerald M. Lohmann and Adam H. Monahan
Atmos. Meas. Tech., 11, 3131–3144, https://doi.org/10.5194/amt-11-3131-2018, https://doi.org/10.5194/amt-11-3131-2018, 2018
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Using high-resolution surface irradiance data with original temporal resolutions between 0.01 s and 1 s from six different locations in the Northern Hemisphere, we characterize the changes in representation of temporal variability resulting from time averaging. Our results indicate that a temporal averaging time scale of around 1 s marks a transition in representing single-point irradiance variability, such that longer averages result in substantial underestimates of variability.
Adam H. Monahan
Nonlin. Processes Geophys., 25, 335–353, https://doi.org/10.5194/npg-25-335-2018, https://doi.org/10.5194/npg-25-335-2018, 2018
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Bivariate probability density functions (pdfs) of wind speed characterize the relationship between speeds at two different locations or times. This study develops such pdfs of wind speed from distributions of the components, following a well-established approach for univariate distributions. The ability of these models to characterize example observed datasets is assessed. The mathematical complexity of these models suggests further extensions of this line of reasoning may not be practical.
Hakase Hayashida, Nadja Steiner, Adam Monahan, Virginie Galindo, Martine Lizotte, and Maurice Levasseur
Biogeosciences, 14, 3129–3155, https://doi.org/10.5194/bg-14-3129-2017, https://doi.org/10.5194/bg-14-3129-2017, 2017
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In remote regions, cloud conditions may be strongly influenced by oceanic source of dimethylsulfide (DMS) produced by plankton and bacteria. In the Arctic, sea ice provides an additional source of these aerosols. The results of this study highlight the importance of taking into account both the sea-ice sulfur cycle and ecosystem in the flux estimates of oceanic DMS near the ice margins and identify key uncertainties in processes and rates that would be better constrained by new observations.
Jan-Erik Tesdal, James R. Christian, Adam H. Monahan, and Knut von Salzen
Atmos. Chem. Phys., 16, 10847–10864, https://doi.org/10.5194/acp-16-10847-2016, https://doi.org/10.5194/acp-16-10847-2016, 2016
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A global atmosphere model with explicit representation of aerosol processes is used to assess uncertainties in the climate impact of ocean DMS efflux and the role of spatial and temporal variability of the DMS flux in the effect on climate. The radiative effect of sulfate is nearly linearly related to global total DMS flux. Removing the spatial or temporal variability of DMS flux changes the global radiation budget, but the effect is of second-order importance relative to the global mean flux.
Gerald M. Lohmann, Adam H. Monahan, and Detlev Heinemann
Atmos. Chem. Phys., 16, 6365–6379, https://doi.org/10.5194/acp-16-6365-2016, https://doi.org/10.5194/acp-16-6365-2016, 2016
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Increasing numbers of photovoltaic (PV) power systems call for the characterization of irradiance variability with very high spatiotemporal resolution. We use 1 Hz irradiance data recorded by as many as 99 pyranometers and show mixed sky conditions to differ substantially from clear and overcast skies. For example, the probabilities of strong fluctuations and their respective spatial autocorrelation structures are appreciably distinct under mixed conditions.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Shunji Kotsuki, Fumitoshi Kawasaki, and Masanao Ohashi
Nonlin. Processes Geophys., 31, 237–245, https://doi.org/10.5194/npg-31-237-2024, https://doi.org/10.5194/npg-31-237-2024, 2024
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In Earth science, data assimilation plays an important role in integrating real-world observations with numerical simulations for improving subsequent predictions. To overcome the time-consuming computations of conventional data assimilation methods, this paper proposes using quantum annealing machines. Using the D-Wave quantum annealer, the proposed method found solutions with comparable accuracy to conventional approaches and significantly reduced computational time.
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
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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.
Fumitoshi Kawasaki and Shunji Kotsuki
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-4, https://doi.org/10.5194/npg-2024-4, 2024
Revised manuscript accepted for NPG
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Recently, scientists have been looking into ways to control the weather to lead to a desirable direction for mitigating weather-induced disasters caused by torrential rainfall and typhoons. This study proposed using model predictive control, known as an advanced control method, to control a chaotic system. Through numerical experiments using a low-dimensional chaotic system, we demonstrated that the system can be controlled successfully with shorter forecasts compared to previous studies.
Marc Bocquet, Pierre J. Vanderbecken, Alban Farchi, Joffrey Dumont Le Brazidec, and Yelva Roustan
EGUsphere, https://doi.org/10.5194/egusphere-2023-2755, https://doi.org/10.5194/egusphere-2023-2755, 2023
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A novel approach, the Optimal Transport Data Assimilation, is introduced to merge data assimilation and optimal transport concepts. By leveraging optimal transport's displacement interpolation in space, it minimises mislocation errors within data assimilation applied to physical fields, such as water vapour, hydrometeors, chemical species, etc. Its richness and flexibility are showcased through one- and two-dimensional illustrations.
Pierre Le Bras, Florian Sévellec, Pierre Tandeo, Juan Ruiz, and Pierre Ailliot
EGUsphere, https://doi.org/10.5194/egusphere-2023-2649, https://doi.org/10.5194/egusphere-2023-2649, 2023
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The goal of this paper is to weight several dynamic models in order to improve the representativeness of a system. It is illustrated using a set of versions of an idealized model describing the Atlantic Meridional Overturning Circulation. The low-cost method is based on data-driven forecasts. It enables model performance to be evaluated on their dynamics. Taking into account both model performance and codependency, the derived weights outperform benchmarks in reconstructing a model distribution.
Man-Yau Chan
EGUsphere, https://doi.org/10.5194/egusphere-2023-2699, https://doi.org/10.5194/egusphere-2023-2699, 2023
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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.
Loris Foresti, Bernat Puigdomènech Treserras, Daniele Nerini, Aitor Atencia, Marco Gabella, Ioannis Vasileios Sideris, Urs Germann, and Isztar Zawadzki
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2023-24, https://doi.org/10.5194/npg-2023-24, 2023
Revised manuscript accepted for NPG
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We compared two ways to define the phase space of low-dimensional attractors describing the evolution of radar precipitation fields. The first defines the phase space by the domain-scale statistics of precipitation fields, such as their mean, spatial and temporal correlations. The second uses principal component analysis to account for the spatial distribution of precipitation. To represent different climates, radar archives over the United States and the Swiss Alpine region were used.
Thomas Muschinski, Georg J. Mayr, Achim Zeileis, and Thorsten Simon
Nonlin. Processes Geophys., 30, 503–514, https://doi.org/10.5194/npg-30-503-2023, https://doi.org/10.5194/npg-30-503-2023, 2023
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Statistical post-processing is necessary to generate probabilistic forecasts from physical numerical weather prediction models. To allow for more flexibility, there has been a shift in post-processing away from traditional parametric regression models towards modern machine learning methods. By fusing these two approaches, we developed model output statistics random forests, a new post-processing method that is highly flexible but at the same time also very robust and easy to interpret.
Kenta Kurosawa, Shunji Kotsuki, and Takemasa Miyoshi
Nonlin. Processes Geophys., 30, 457–479, https://doi.org/10.5194/npg-30-457-2023, https://doi.org/10.5194/npg-30-457-2023, 2023
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This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.
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
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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.
Yung-Yun Cheng, Shu-Chih Yang, Zhe-Hui Lin, and Yung-An Lee
Nonlin. Processes Geophys., 30, 289–297, https://doi.org/10.5194/npg-30-289-2023, https://doi.org/10.5194/npg-30-289-2023, 2023
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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.
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
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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.
Mao Ouyang, Keita Tokuda, and Shunji Kotsuki
Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, https://doi.org/10.5194/npg-30-183-2023, 2023
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This research found that weather control would change the chaotic behavior of an atmospheric model. We proposed to introduce chaos theory in the weather control. Experimental results demonstrated that the proposed approach reduced the manipulations, including the control times and magnitudes, which throw light on the weather control in a real atmospheric model.
Qiwen Sun, Takemasa Miyoshi, and Serge Richard
Nonlin. Processes Geophys., 30, 117–128, https://doi.org/10.5194/npg-30-117-2023, https://doi.org/10.5194/npg-30-117-2023, 2023
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This paper is a follow-up of a work by Miyoshi and Sun which was published in NPG Letters in 2022. The control simulation experiment is applied to the Lorenz-96 model for avoiding extreme events. The results show that extreme events of this partially and imperfectly observed chaotic system can be avoided by applying pre-designed small perturbations. These investigations may be extended to more realistic numerical weather prediction models.
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
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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
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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.
Clara Deser and Adam S. Phillips
Nonlin. Processes Geophys., 30, 63–84, https://doi.org/10.5194/npg-30-63-2023, https://doi.org/10.5194/npg-30-63-2023, 2023
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Past and future climate change at regional scales is a result of both human influences and natural (internal) variability. Here, we provide an overview of recent advances in climate modeling and physical understanding that has led to new insights into their respective roles, illustrated with original results for the European climate. Our findings highlight the confounding role of internal variability in attribution, climate model evaluation, and accuracy of future projections.
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.
Tobias Necker, David Hinger, Philipp Johannes Griewank, Takemasa Miyoshi, and Martin Weissmann
Nonlin. Processes Geophys., 30, 13–29, https://doi.org/10.5194/npg-30-13-2023, https://doi.org/10.5194/npg-30-13-2023, 2023
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This study investigates vertical localization based on a convection-permitting 1000-member ensemble simulation. We derive an empirical optimal localization (EOL) that minimizes sampling error in 40-member sub-sample correlations assuming 1000-member correlations as truth. The results will provide guidance for localization in convective-scale ensemble data assimilation systems.
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.
Dikraa Khedhaouiria, Stéphane Bélair, Vincent Fortin, Guy Roy, and Franck Lespinas
Nonlin. Processes Geophys., 29, 329–344, https://doi.org/10.5194/npg-29-329-2022, https://doi.org/10.5194/npg-29-329-2022, 2022
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This study introduces a well-known use of hybrid methods in data assimilation (DA) algorithms that has not yet been explored for precipitation analyses. Our approach combined an ensemble-based DA approach with an existing deterministically based DA. Both DA scheme families have desirable aspects that can be leveraged if combined. The DA hybrid method showed better precipitation analyses in regions with a low rate of assimilated surface observations, which is typically the case in winter.
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.
Takemasa Miyoshi and Qiwen Sun
Nonlin. Processes Geophys., 29, 133–139, https://doi.org/10.5194/npg-29-133-2022, https://doi.org/10.5194/npg-29-133-2022, 2022
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The weather is chaotic and hard to predict, but the chaos implies an effective control where a small control signal grows rapidly to make a big difference. This study proposes a control simulation experiment where we apply a small signal to control
naturein a computational simulation. Idealized experiments with a low-order chaotic system show successful results by small control signals of only 3 % of the observation error. This is the first step toward realistic weather simulations.
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.
Juan Ruiz, Guo-Yuan Lien, Keiichi Kondo, Shigenori Otsuka, and Takemasa Miyoshi
Nonlin. Processes Geophys., 28, 615–626, https://doi.org/10.5194/npg-28-615-2021, https://doi.org/10.5194/npg-28-615-2021, 2021
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Effective use of observations with numerical weather prediction models, also known as data assimilation, is a key part of weather forecasting systems. For precise prediction at the scales of thunderstorms, fast nonlinear processes pose a grand challenge because most data assimilation systems are based on linear processes and normal distribution errors. We investigate how, every 30 s, weather radar observations can help reduce the effect of nonlinear processes and nonnormal distributions.
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.
Zhao Liu, Shaoqing Zhang, Yang Shen, Yuping Guan, and Xiong Deng
Nonlin. Processes Geophys., 28, 481–500, https://doi.org/10.5194/npg-28-481-2021, https://doi.org/10.5194/npg-28-481-2021, 2021
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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 the 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.
Guillaume Evin, Matthieu Lafaysse, Maxime Taillardat, and Michaël Zamo
Nonlin. Processes Geophys., 28, 467–480, https://doi.org/10.5194/npg-28-467-2021, https://doi.org/10.5194/npg-28-467-2021, 2021
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Forecasting the height of new snow is essential for avalanche hazard surveys, road and ski resort management, tourism attractiveness, etc. Météo-France operates a probabilistic forecasting system using a numerical weather prediction system and a snowpack model. It provides better forecasts than direct diagnostics but exhibits significant biases. Post-processing methods can be applied to provide automatic forecasting products from this system.
Davide Faranda, Mathieu Vrac, Pascal Yiou, Flavio Maria Emanuele Pons, Adnane Hamid, Giulia Carella, Cedric Ngoungue Langue, Soulivanh Thao, and Valerie Gautard
Nonlin. Processes Geophys., 28, 423–443, https://doi.org/10.5194/npg-28-423-2021, https://doi.org/10.5194/npg-28-423-2021, 2021
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Machine learning approaches are spreading rapidly in climate sciences. They are of great help in many practical situations where using the underlying equations is difficult because of the limitation in computational power. Here we use a systematic approach to investigate the limitations of the popular echo state network algorithms used to forecast the long-term behaviour of chaotic systems, such as the weather. Our results show that noise and intermittency greatly affect the performances.
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.
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.
Cited articles
Alberty, J., Carstensen, C., and Funken, S. A.: Remarks around 50 lines of
Matlab: short finite element implementation, Numer. Algorithms, 20, 117–137,
1999. a
Annan, J., Hargreaves, J., Edwards, N., and Marsh, R.: Parameter estimation in
an intermediate complexity Earth System Model using an ensemble Kalman
filter, Ocean Model., 8, 135–154, 2005. a
Apte, A., Hairer, M., Stuart, A., and Voss, J.: Sampling the Posterior: An
Approach to Non-Gaussian Data Assimilation, Physica D, 230, 50–64, 2007. a
Bakka, H., Rue, H., Fuglstad, G. A., Riebler, A., Bolin, D., Illian, J., . and Lindgren, F.: Spatial modeling with R‐INLA: A review, Wiley Interdisciplinary Reviews: Computational Statistics, 10, e1443, 2018. a
Branicki, M. and Majda, A. J.: Fundamental limitations of polynomial chaos for
uncertainty quantification in systems with intermittent instabilities, Commun.
Math. Sci., 11, 55–103, 2013. a
Cappé, O., Moulines, E., and Ryden, T.: Inference in Hidden Markov Models
(Springer Series in Statistics), Springer-Verlag, New York, NY, USA, 2005. a
Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data assimilation in
the geosciences: An overview of methods, issues, and perspectives, WIRES
Clim. Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018. a, b
Chekroun, M. D. and Kondrashov, D.: Data-adaptive harmonic spectra and
multilayer Stuart-Landau models, Chaos, 27, 093110, https://doi.org/10.1063/1.4989400, 2017. a
Chorin, A. J. and Tu, X.: Implicit sampling for particle filters, P. Natl.
Acad. Sci. USA, 106, 17249–17254, 2009. a
Chorin, A. J. and Lu, F.: Discrete approach to stochastic parametrization and
dimension reduction in nonlinear dynamics, P. Natl. Acad. Sci. USA, 112,
9804–9809, 2015. a
Chorin, A. J., Lu, F., Miller, R. M., Morzfeld, M., and Tu, X.: Sampling,
feasibility, and priors in data assimilation, Discrete Contin. Dyn. Syst. A,
36, 4227–4246, 2016. a
Cowles, M. K. and Carlin, B. P.: Markov chain Monte Carlo convergence
diagnostics: a comparative review, J. Am. Stat. Assoc., 91, 883–904, 1996. a
Cui, T., Marzouk, Y. M., and Willcox, K. E.: Data-driven model reduction for
the Bayesian solution of inverse problems, Int. J. Numer. Methods Fluids,
102, 966–990, 2015. a
Fang, M. and Li, X.: Paleoclimate Data Assimilation: Its Motivation,
Progress and Prospects, Sci. China Earth Sci., 59, 1817–1826,
https://doi.org/10.1007/s11430-015-5432-6, 2016. a
Farchi, A. and Bocquet, M.: Review article: Comparison of local particle filters and new implementations, Nonlin. Processes Geophys., 25, 765–807, https://doi.org/10.5194/npg-25-765-2018, 2018. a
Goosse, H., Crespin, E., de Montety, A., Mann, M. E., Renssen, H., and
Timmermann, A.: Reconstructing Surface Temperature Changes over the Past 600
Years Using Climate Model Simulations with Data Assimilation, J. Geophys.
Res., 115, https://doi.org/10.1029/2009JD012737, 2010. a
Guillot, D., Rajaratnam, B., and Emile-Geay, J.: Statistical Paleoclimate
Reconstructions via Markov Random Fields, Ann. Appl. Stat., 9, 324–352,
2015. a
Hairer, M., Stuart, A. M., and Voss, J.: Analysis of SPDEs Arising in Path
Sampling Part II: The Nonlinear Case, Ann. Appl.
Probab., 17, 1657–1706, https://doi.org/10.1214/07-AAP441, 2007. a
Haslett, J., Whiley, M., Bhattacharya, S., Salter-Townshend, M., Wilson, S. P.,
Allen, J., Huntley, B., and Mitchell, F.: Bayesian palaeoclimate
reconstruction, J. R. Stat. Soc. A, 169, 395–438, 2006. a
Jiang, S. W. and Harlim, J.: Parameter estimation with data-driven
nonparametric likelihood functions, arXiv preprint arXiv:1804.03272, 2018. a
Khouider, B., Majda, A. J., and Katsoulakis, M. A.: Coarse-grained stochastic
models for tropical convection and climate, P. Natl. Acad. Sci. USA,
100, 11941–11946, 2003. a
Lindgren, F. and Rue, H.: Bayesian Spatial Modelling with R-INLA, J. Stat.
Softw., 63, 1–25, 2015. a
Liu, J.: Monte Carlo Strategies in Scientific Computing, Springer, 2001. a
Llopis, F. P., Kantas, N., Beskos, A., and Jasra, A.: Particle Filtering
for Stochastic Navier–Stokes Signal Observed with Linear Additive
Noise, SIAM J. Sci. Comput., 40, A1544–A1565, 2018. a
Lu, F., Morzfeld, M., Tu, X., and Chorin, A. J.: Limitations of polynomial
chaos expansions in the Bayesian solution of inverse problems, J. Comput.
Phys., 282, 138–147, 2015. a
Lu, F., Tu, X., and Chorin, A. J.: Accounting for Model Error from Unresolved
Scales in Ensemble Kalman Filters by Stochastic Parameterization, Mon. Weather
Rev., 145, 3709–3723, 2017. a
Marzouk, Y. M. and Najm, H. N.: Dimensionality reduction and polynomial chaos
acceleration of Bayesian inference in inverse problems, J. Comput. Phys.,
228, 1862–1902, 2009. a
Maslowski, B. and Tudor, C. A.: Drift Parameter Estimation for
Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process,
B. Sci. Math., 137, 880–901, 2013. a
Morzfeld, M., Tu, X., Atkins, E., and Chorin, A. J.: A random map
implementation of implicit filters, J. Comput. Phys., 231, 2049–2066, 2012. a
O'Leary, D. P.: Near-Optimal Parameters for Tikhonov and Other
Regularization Methods, SIAM J. Sci. Comput., 23, 1161–1171, 2001. a
Parnell, A. C., Haslett, J., Sweeney, J., Doan, T. K., Allen, J. R., and
Huntley, B.: Joint palaeoclimate reconstruction from pollen data via forward
models and climate histories, Quaternary Sci. Rev., 151, 111–126,
2016. a
Penny, S. G. and Miyoshi, T.: A local particle filter for high-dimensional geophysical systems, Nonlin. Processes Geophys., 23, 391–405, https://doi.org/10.5194/npg-23-391-2016, 2016. a
Poterjoy, J.: A Localized Particle Filter for High-Dimensional
Nonlinear Systems, Mon. Weather Rev., 144, 59–76, 2016. a
Prakasa Rao, B. L. S.: Statistical Inference for Stochastic Partial
Differential Equations, in: Institute of Mathematical Statistics Lecture
Notes – Monograph Series, Institute of Mathematical
Statistics, Beachwood, OH, 47–70, 2001. a
Rypdal, K., Rypdal, M., and Fredriksen, H.-B.: Spatiotemporal Long-Range
Persistence in Earth's Temperature Field: Analysis of Stochastic-Diffusive
Energy Balance Models, J. Climate, 28, 8379–8395, 2015. a
Sigrist, F., Künsch, H. R., and Stahel, W. A.: Stochastic Partial
Differential Equation Based Modelling of Large Space-Time Data Sets, J. R.
Stat. Soc. B, 77, 3–33, 2015. a
Snyder, C. W.: Evolution of global temperature over the past two million years,
Nature, 538, 226–228, 2016. a
Steiger, N. J., Hakim, G. J., Steig, E. J., Battisti, D. S., and Roe, G. H.:
Assimilation of Time-Averaged Pseudoproxies for Climate
Reconstruction, J. Climate, 27, 426–441, 2014. a
Tingley, M. P. and Huybers, P.: A Bayesian Algorithm for Reconstructing
Climate Anomalies in Space and Time. Part I: Development
and Applications to Paleoclimate Reconstruction Problems, J. Climate,
23, 2759–2781, 2010. a
Tingley, M. P., Craigmile, P. F., Haran, M., Li, B., Mannshardt, E., and
Rajaratnam, B.: Piecing together the past: statistical insights into
paleoclimatic reconstructions, Quaternary Sci. Rev., 35, 1–22, 2012. a
Tolwinski-Ward, S. E., Evans, M. N., Hughes, M. K., and Anchukaitis, K. J.: An
efficient forward model of the climate controls on interannual variation in
tree-ring width, Clim. Dynam., 36, 2419–2439, 2011. a
Van der Vaart, A. W.: Asymptotic statistics, vol. 3, Cambridge university
press, 2000. a
Weaver, A. J., Eby, M., Wiebe, E. C., Bitz, C. M., Duffy, P. B., Ewen, T. L.,
Fanning, A. F., Holland, M. M., MacFadyen, A., Matthews, H. D., Meissner, K. J., Saenko, O., Schmittner, A., Wang, H., and Yoshimori, M.: The
UVic Earth System Climate Model: Model description, climatology, and
applications to past, present and future climates, Atmos. Ocean., 39,
361–428, 2001. a
Werner, J. P., Luterbacher, J., and Smerdon, J. E.: A Pseudoproxy Evaluation of
Bayesian Hierarchical Modeling and Canonical Correlation Analysis for Climate
Field Reconstructions over Europe, J. Climate, 26, 851–867, 2013. a
Whittle, P.: On stationary processes in the plane, Biometrika, 41, 434–449,
1954. a
Whittle, P.: Stochastic processes in several dimensions, B. Int. Statist.
Inst., 40, 974–994, 1963. a
Short summary
ll-posedness of the inverse problem and sparse noisy data are two major challenges in the modeling of high-dimensional spatiotemporal processes. We present a Bayesian inference method with a strongly regularized posterior to overcome these challenges, enabling joint state-parameter estimation and quantifying uncertainty in the estimation. We demonstrate the method on a physically motivated nonlinear stochastic partial differential equation arising from paleoclimate construction.
ll-posedness of the inverse problem and sparse noisy data are two major challenges in the...
