Eirik Myrvoll-Nilsen

Publications

Journal articles and my PhD thesis, newest first. 15 publications, 2018–2026.

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2026

Non-linear forcing increases uncertainty in detecting a destabilization of the Atlantic Meridional Overturning Circulation
Hummel, Clara and Cotronei, Alessandro and Myrvoll-Nilsen, Eirik and Aksamit, Nikolas and Rypdal, Martin
Frontiers in Climate, 8, pp. 1826661, 2026
Journal article DOI PDF
The Atlantic Meridional Overturning Circulation (AMOC) plays a critical role in regulating global climate patterns with its potential destabilization and collapse posing significant risks. In this study, we introduce two novel methods to assess AMOC stability, based on a Bayesian framework to estimate its sensitivity, and ensembles of parabolic approximations, respectively. They provide alternative indicators to detect early warning signals (EWSs) for a potential destabilization. By incorporating non-linear and physically motivated drivers, such as temperature and Greenland meltwater runoff, we obtain a more realistic representation of AMOC dynamics and address an important limitation of previous studies, which often rely on linear forcing assumptions. We detect significant EWS for a potential ongoing AMOC destabilization in our sensitivity-based indicator across many combinations of forcing scenarios and response models. However, it revealed large variations, dependent on the considered forcing scenario and methodological choices. While an AR(1) response to linear forcing, consistent with assumptions in previous EWS analyses of the AMOC, emerged as the “best” fit based on Bayes factor analysis, other evaluation criteria provided no clear support. Even though the second EWS indicator, obtained using parabolic approximations, revealed a recent significant peak under linear forcing, and appears to suggests that the AMOC might have passed a critical transition in the late 20th century assuming a temperature driver, we find no clear indication of a considerable destabilization in either case. Our findings highlight the sensitivity of AMOC stability assessments to assumptions about forcing scenarios, response models, and evaluation criteria, emphasizing the need for careful interpretation of EWSs for abrupt transitions in the Earth's climate. While our methods advance EWS analyses by incorporating non-linear forcing and alternative response functions to better represent AMOC dynamics, they also underscore the limitations of applying such tools to complex climate subsystems, represented by one-dimensional time series.
Evaluating Model Uncertainty in Critical Threshold Estimations from Time Series Data: Application to the Atlantic Meridional Overturning Circulation
Cotronei, Alessandro and Myrvoll-Nilsen, Eirik and Rypdal, Martin
Frontiers in Climate, 8, pp. 1761461, 2026
Journal article DOI PDF
Analysis of tipping points (rapid, large-scale, and potentially irreversible transitions in Earth system components) is crucial for assessing the resilience of the Earth's subsystems and anticipating risks associated with climate change. Predicting tipping points from time-series data requires accounting for variability, system-specific factors, and high-quality data, which are often limited. Existing approaches, while useful, depend on strong assumptions that may reduce predictive accuracy. In this study, we focus on the model used to approximate system behavior, and argue that modeling assumptions can significantly alter estimates of critical thresholds, and including assessments of whether a system will reach a critical transition at all. We show that, in the case of the Atlantic Meridional Overturning Circulation (AMOC), assuming different polynomial degrees in simple model approximations can lead to entirely different estimates of the critical threshold, or even that no threshold exists. This effect is particularly exacerbated by the interannual variability of the AMOC fingerprints used. These considerations highlight the need for more advanced techniques and increased robustness in model selection and underlying assumptions when interpreting estimates of critical transitions.
Bayesian identification of early warning signals for long-range dependent climatic time series
Sørbye, Sigrunn H. and Myrvoll-Nilsen, Eirik and Rue, Håvard
arXiv, 2026
Preprint DOI PDF
Preprint.
Extrapolation from historical data cannot reliably predict the time of a potential AMOC collapse
Morr, Andreas and Ben-Yami, Maya and Groenke, Brian and Schötz, Christof and Cotronei, Alessandro and Myrvoll-Nilsen, Eirik and Bathiany, Sebastian and Rypdal, Martin and Boers, Niklas
arXiv, 2026
Preprint DOI PDF
Ditlevsen and Ditlevsen (Nature Communications, 2023) propose a statistical framework to estimate the timing of a potential collapse of the Atlantic Meridional Overturning Circulation (AMOC) based on extrapolating information from observed sea-surface temperature (SST) variability. Here we examine the sensitivity of their results and argue that four types of uncertainty are insufficiently explored: structural uncertainty associated with the assumed low-order bifurcation model, statistical uncertainty in the model fit, uncertainty in the representativeness of SST-based fingerprints as proxies for the high-dimensional AMOC dynamics, and uncertainty in the underlying data arising from non-stationary observational coverage and dataset preprocessing. Using synthetic experiments and a systematic analysis of alternative fingerprints and observational products, we show that the estimated tipping times are highly sensitive to these uncertainties, and extend several millennia into the future when they are thoroughly propagated.

2025

Synchronization of Layer-Counted Paleoclimatic Proxy Archives Using a Bayesian Regression Modeling Framework
Myrvoll-Nilsen, Eirik and Riechers, Keno and Boers, Niklas
Bayesian Analysis, 1(1), pp. 1–20, 2025
Journal article DOI PDF
Layer-counted proxy records from paleoclimatic archives are subject to considerable dating uncertainties. These uncertainties originate from irregularities in the archive’s deposition process that result, in turn, in errors during the layer counting process. Dating uncertainties can be quantified by assuming a probabilistic model for the relationship between the depth of a sample in the proxy archive and the age of that sample. However, systematic biases in counting or depositional processes can cause the counted chronology to deviate substantially from the true age and possibly corrupt the age model. By synchronizing a given chronology with other, independently dated archives, one can constrain the dating uncertainties and correct potential biases. This can be done by matching the chronology to tie-points obtained by identifying characteristic events which were recorded simultaneously by different archives or with independent methods. However, updating the counted age–depth relationship under the consideration of tie-points is not straightforward and no generally accepted method is presently available for layer-counted archives. A key requirement for such a method is that it should include an appropriate uncertainty-sensitive interpolation between tie-points. Using a Gaussian model to represent a potential bias, we show how tie-points and their uncertainties can be incorporated into a previously suggested Bayesian modeling framework to reflect the general uncertainties of a counted chronology. Both the uncertainty inherent to the tie-points and the age-correlation between the data from different depths in the archive are consistently represented in this approach. We demonstrate the methodology in two applications: first, using synthetic data, and second, applying the methodology to data from the NGRIP ice core, an iconic paleoclimate proxy archive.
Assessing AMOC stability using a Bayesian nested time-dependent autoregressive model
Hallali, Luc and Myrvoll-Nilsen, Eirik and Franzke, Christian LE
Nonlinear Processes in Geophysics, 32(4), pp. 383–395, 2025
Journal article DOI PDF
The Atlantic Meridional Overturning Circulation (AMOC) is a major climate element subject to possible ongoing loss of stability. Recent studies have found evidence of a gradual weakening in circulation, including early warning signals (EWSs), such as increased fluctuations and correlation time of the system, which are both known to be indicators of a possible forthcoming tipping point. To assess these changes in statistical behavior, we propose a robust and general statistical model based on a second-order autoregressive process with time-dependent parameters. This allows for the statistical changes from increased external variability and destabilization to be accounted for separately. We estimate the time evolution of the correlation parameters using a hierarchical Bayesian modeling framework, which also yields uncertainty quantification through the posterior distribution. To assess possible changes in AMOC stability, we apply the model to an AMOC fingerprint proxy based on the subpolar gyre and the global mean temperature anomaly. We find statistically significant EWSs, which suggests that AMOC is indeed undergoing a loss of stability and is getting closer to a tipping point. The methodology developed in this study is made publicly available as an extension of the R-package INLA.ews.
Bayesian analysis of early warning signals using a time-dependent model
Myrvoll-Nilsen, Eirik and Hallali, Luc and Rypdal, Martin
Earth System Dynamics, 16(5), pp. 1539–1556, 2025
Journal article DOI PDF
A tipping point is defined by the IPCC as a critical threshold beyond which a system reorganizes, often abruptly and/or irreversibly. Tipping points can be crossed solely by internal variation in the system or by approaching a bifurcation point where the current state loses stability, which forces the system to move to another stable state. It can be shown that before a bifurcation point is reached there are observable changes in the statistical properties of the state variable. These are known as early warning signals and include increased fluctuation and autocorrelation time. It is currently debated whether or not Dansgaard–Oeschger (DO) events, which are abrupt warmings of the North Atlantic region which occurred during the last glacial period, are preceded by early warning signals. To express the changes in statistical behavior we propose a model based on the well-known first-order autoregressive (AR) process, with modifications to the autocorrelation parameter such that it depends linearly on time. In order to estimate the time evolution of the autocorrelation parameter we adopt a hierarchical Bayesian modeling framework, from which Bayesian analysis can be performed using the methodology of integrated nested Laplace approximations. We then apply the model to segments of the oxygen isotope ratios from the Northern Greenland Ice Core Project record corresponding to 17 DO events. Statistically significant early warning signals are detected for a number of DO events, which suggests that such events could indeed exhibit signs of ongoing destabilization and may have been caused by approaching a bifurcation point. The methodology developed to perform the given early warning analyses can be applied more generally and is publicly available as the R package INLA.ews.
Quantifying uncertainty in foraminifera classification: How deep learning methods compare to human experts
Martinsen, Iver and Sørensen, Steffen Aagaard and Ortega, Samuel and Godtliebsen, Fred and Tejedor, Miguel and Myrvoll-Nilsen, Eirik
Artificial Intelligence in Geosciences, pp. 100145, 2025
Journal article DOI PDF
Foraminifera are shell-bearing microorganisms that are commonly found in marine deposits on the seabed. They are important indicators in many analyses, are used in climate change research, monitoring marine environments, evolutionary studies, and are also frequently used in the oil and gas industry. Although some research has focused on automating the classification of foraminifera images, few have addressed the uncertainty in these classifications. Although foraminifera classification is not a safety-critical task, estimating uncertainty is crucial to avoid misclassifications that could overlook rare and ecologically significant species that are informative indicators of the environment in which they lived. Uncertainty estimation in deep learning has gained significant attention and many methods have been developed. However, evaluating the performance of these methods in practical settings remains a challenge. To create a benchmark for uncertainty estimation in the classification of foraminifera, we administered a multiple choice questionnaire containing classification tasks to four senior geologists. By analyzing their responses, we generated human-derived uncertainty estimates for a test set of 260 images of foraminifera and sediment grains. These uncertainty estimates served as a baseline for comparison when training neural networks in classification. We then trained multiple deep neural networks using a range of uncertainty quantification methods to classify and state the uncertainty about the classifications. The results of the deep learning uncertainty quantification methods were then analyzed and compared with the human benchmark, to see how the methods performed individually and how the methods aligned with humans. Our results show that human-level performance can be achieved with deep learning and that test-time data augmentation and ensembling can help improve both uncertainty estimation and classification performance. Our results also show that human uncertainty estimates are helpful indicators for detecting classification errors and that deep learning-based uncertainty estimates can improve calibration and classification accuracy.

2024

Comments on: Data integration via analysis of subspaces (DIVAS)
Godtliebsen, Fred and Myrvoll-Nilsen, Eirik and Holmström, Lasse
TEST, 33, pp. 683–685, 2024
Comment DOI PDF

2022

Comprehensive uncertainty estimation of the timing of Greenland warmings in the Greenland ice core records
Myrvoll-Nilsen, Eirik and Riechers, Keno and Rypdal, Martin Wibe and Boers, Niklas
Climate of the Past, 18, pp. 1275–1294, 2022
Journal article DOI PDF
Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial–interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The joint dating uncertainties for all depths can then be described by a multivariate Gaussian process from which the chronology (such as the GICC05) can be sampled. We show how the effect of a potential counting bias can be incorporated in our framework. Furthermore we present refined estimates of the occurrence times of Dansgaard–Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings.

2020

Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling
Myrvoll-Nilsen, Eirik and Sørbye, Sigrunn Holbek and Fredriksen, Hege-Beate and Rue, Håvard and Rypdal, Martin
Earth System Dynamics, 11(2), pp. 329–345, 2020
Journal article DOI PDF
Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from one-box and two-box energy balance models. The software developed to perform the given analyses is publicly available as the R package INLA.climate.
Efficient Bayesian analysis of long memory processes applied to climate
Myrvoll-Nilsen, Eirik
UiT The Arctic University of Norway, 2020
PhD thesis DOI PDF
Temperature fluctuations can be described by a persistent correlation structure known as long-range dependence (LRD). This is a phenomenon which implies that the autocorrelation function follows a power-law decay and that observations may still be significantly correlated even if the temporal or spatial distance between them is large. Moreover, temperature is known to be influenced by radiative forcing, or how much of the solar radiation is absorbed by the earth. This is affected by factors such as solar variation and emission of climate gases. The topic of this thesis is to develop efficient statistical methodology to obtain Bayesian inference for global and local climatic time series data. This is achieved using the general hierarchical modeling framework of latent Gaussian models. Bayesian analysis can be performed efficiently using the methodology of integrated nested Laplace approximation (INLA), utilising the sparse structure of the inverse covariance matrix of the latent Gaussian field. Obtaining inference for LRD processes using INLA is inefficient on account of their dense inverse covariance matrix. Paper I demonstrates how stationary Gaussian LRD processes with memory governed by a single-parameter can be approximated with great accuracy using a mixture of four first-order autoregressive processes. This approximation ensures that the LRD model retains conditional independence and that inference can be obtained in linear time and memory. Paper II details how this methodology can be used to design a Bayesian model for global mean surface temperature (GMST) that reflects climate dynamics by incorporating radiative forcing data. This model is available as the R-package INLA.climate and is used to estimate the transient climate response and to predict temperature response to future forcing scenarios. Paper III uses the GMST model to estimate equilibrium climate sensitivity, and paper IV applies the same methodology to gridded local time series.

2019

Warming trends and long-range dependent climate variability since year 1900: A Bayesian approach
Myrvoll-Nilsen, Eirik and Fredriksen, Hege-Beate and Sørbye, Sigrunn H and Rypdal, Martin
Frontiers in Earth Science, 7, pp. 214, 2019
Journal article DOI PDF
An approximate fractional Gaussian noise model with O(n)O(n) computational cost
Sørbye, Sigrunn Holbek and Myrvoll-Nilsen, Eirik and Rue, Håvard
Statistics and Computing, 29, pp. 821–833, 2019
Journal article DOI PDF
Fractional Gaussian noise (fGn) is a stationary time series model with long-memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length n using a likelihood-based approach is O(n2)O(n^2), exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to O(n3)O(n^3). This paper presents an approximate fGn model of O(n)O(n) computational cost, both with direct and indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive (AR) processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four AR components. Specifically, the given approximate fGn model is incorporated within the class of latent Gaussian models in which Bayesian inference is obtained using the methodology of integrated nested Laplace approximation. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

2018

Emergent scale invariance and climate sensitivity
Rypdal, Martin and Fredriksen, Hege-Beate and Myrvoll-Nilsen, Eirik and Rypdal, Kristoffer and Sørbye, Sigrunn H
Climate, 6(4), pp. 93, 2018
Journal article DOI PDF
Earth’s global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a bridge between the decadal- and centennial-scale fluctuations in the instrumental temperature record, and the millennial-scale equilibration following perturbations in the radiative balance. In particular, the emergent scale invariance makes it possible to infer equilibrium climate sensitivity (ECS) from the observed relation between radiative forcing and global temperature in the instrumental era. This is verified in ensembles of Earth system models (ESMs), where the inferred values of ECS correlate strongly to estimates from idealized model runs. For the range of forcing data explored in this paper, the method gives best estimates of ECS between 1.8 and 3.7 K, but statistical uncertainties in the best estimates themselves will provide a wider likely range of the ECS.