arXiv subjects

Henk A. Dijkstra

Publications and source records attributed to Henk A. Dijkstra.

At least 37 records · Page 2Linked to original sources

arXiv2024

Quantification of salt transports due to exchange flow and tidal flow in estuaries

To understand mechanisms of salt intrusion in estuaries, we develop a semi-analytical model, that explicitly accounts for salt transport by both exchange flow and tidal flow. This model, after calibration, successfully hindcasts hydrodynamics and salinity dynamics in three estuaries that have strongly different characteristics. We find, from analyzing the model results for these three estuaries, that salt transport processes by exchange flow and tidal flow interact through the subtidal stratification. Transport by exchange flow creates stratification, thereby generating a phase shift of tidal salinity with respect to the tidal flow, which is important for the magnitude of the tidal salt transport. Conversely, the strength of tidal currents determines the vertical mixing that breaks down stratification. A new analytical formulation is presented for the component of the salt transport driven by the depth-averaged tidal flow. This salt transport is larger than the component associated with the vertical shear of the tidal current. Finally, a method that yields analytical equations that quantify the importance of different contributions to the salt transport using only primary information is developed using approximate solutions for the subtidal stratification. This method performs well for the estuaries considered.

physics.ao-ph↗

arXiv2024

Substantial Risk of 21st Century AMOC Tipping even under Moderate Climate Change

The Atlantic Meridional Overturning Circulation (AMOC) is a key component of the climate system and considered to be a tipping element. There is still a large uncertainty on the critical global warming level at which the AMOC will start to collapse. Here we analyse targeted climate model simulations, together with observations, reanalysis products and a suite of state-of-the-art climate model results to reassess this critical global warming level. We find a critical threshold of +3C global mean surface temperature increase compared to pre-industrial with a lower bound of +2.2C (10%-Cl). Such global mean surface temperature anomalies are expected to be reached after 2050. This means that the AMOC is more likely than not (> 50%) to tip within the 21st century under a middle-of-the-road climate change scenario and very likely (> 90%) to tip under a high emissions scenario. The AMOC collapse induced cooling is shown to be offset by the regional warming over Northwestern Europe during the 21st century, but will still induce severe impacts on society.

physics.ao-ph↗

arXiv2024

Estimation of AMOC transition probabilities using a machine learning based rare-event algorithm

The Atlantic Meridional Overturning Circulation (AMOC) is an important component of the global climate, known to be a tipping element, as it could collapse under global warming. The main objective of this study is to compute the probability that the AMOC collapses within a specified time window, using a rare-event algorithm called Trajectory-Adaptive Multilevel Splitting (TAMS). However, the efficiency and accuracy of TAMS depend on the choice of the score function. Although the definition of the optimal score function, called ``committor function" is known, it is impossible in general to compute it a priori. Here, we combine TAMS with a Next-Generation Reservoir Computing technique that estimates the committor function from the data generated by the rare-event algorithm. We test this technique in a stochastic box model of the AMOC for which two types of transition exist, the so-called F(ast)-transitions and S(low)-transitions. Results for the F-transtions compare favorably with those in the literature where a physically-informed score function was used. We show that coupling a rare-event algorithm with machine learning allows for a correct estimation of transition probabilities, transition times, and even transition paths for a wide range of model parameters. We then extend these results to the more difficult problem of S-transitions in the same model. In both cases of F-transitions and S-transitions, we also show how the Next-Generation Reservoir Computing technique can be interpreted to retrieve an analytical estimate of the committor function.

physics.ao-ph↗

arXiv2024

Resilience of the Atlantic Meridional Overturning Circulation

We address the issue of resilience of the Atlantic Meridional Overturning Circulation (AMOC) given the many indications that this dynamical system is in a multi-stable regime. A novel approach to resilience based on rare event techniques is presented which leads to a measure capturing `resistance to change` and `ability to return' aspects in a probabilistic way. The application of this measure to a conceptual model demonstrates its suitability for assessing AMOC resilience but also shows its potential use in many other non-autonomous dynamical systems. This framework is then extended to compute the probability that the AMOC undergoes a transition conditioned on an external forcing. Such conditional probability can be estimated by exploiting the information available when computing the resilience of this system. This allows us to provide a probabilistic view on safe operating spaces by defining a conditional safe operating space as a subset of the parameter space of the (possibly transient) imposed forcing.

physics.ao-ph↗

arXiv2024

Probability Estimates of a 21st Century AMOC Collapse

There is increasing concern that the Atlantic Meridional Overturning Circulation (AMOC) may collapse this century with a disrupting societal impact on large parts of the world. Preliminary estimates of the probability of such an AMOC collapse have so far been based on conceptual models and statistical analyses of proxy data. Here, we provide observationally based estimates of such probabilities from reanalysis data. We first identify optimal observation regions of an AMOC collapse from a recent global climate model simulation. Salinity data near the southern boundary of the Atlantic turn out to be optimal to provide estimates of the time of the AMOC collapse in this model. Based on the reanalysis products, we next determine probability density functions of the AMOC collapse time. The collapse time is estimated between 2037-2064 (10-90% CI) with a mean of 2050 and the probability of an AMOC collapse before the year 2050 is estimated to be 59 +/- 17%.

physics.ao-ph↗

arXiv2024

A detailed analysis of the origin of deep-decoupling oscillations

The variability of the strength of the Atlantic Meridional Overturning Circulation is influenced substantially by the formation of deep water in the North Atlantic. In many ocean models, so-called deep-decoupling oscillations have been found, whose timescale depends on the characteristics of convective vertical mixing processes. Their precise origin and sensitivity to the representation of mixing have remained unclear so far. To study this problem, we revisit a conceptual Welander model for the evolution of temperature and salinity in two vertically stacked boxes for surface and deep water, which interact through diffusion and/or convective adjustment. The model is known to exhibit several types of deep-decoupling oscillations, with phases of weak diffusive mixing interspersed with strong convective mixing, when the switching between them is assumed to be instantaneous. We present a comprehensive study of oscillations in Welander's model with non-instantaneous switching between mixing phases, as described by a smooth switching function. A dynamical systems approach allows us to distinguish four types of oscillations, in terms of their phases of diffusive versus convective mixing, and to identify the regions in the relevant parameter plane where they exist. The characteristic deep-decoupling oscillations still exist for non-instantaneous switching, but they require switching that is considerably faster than needed for sustaining oscillatory behaviour. Furthermore, we demonstrate how a gradual freshwater influx can lead to transitions between different vertical mixing oscillations. Notably, the convective mixing phase becomes shorter and even disappears, resulting in long periods of much reduced deep water formation. The results are relevant for the interpretation of ocean-climate variability in models and (proxy) observations.

math.DS↗

arXiv2024

Warning Signs for Boundary Noise and their Application to an Ocean Boussinesq Model

In this paper, we construct and discuss early-warning signs of the approach of a parameter to a deterministic bifurcation on a stochastic partial differential equation (SPDE) model with Gaussian white-noise on the boundary. We specifically focus on the qualitative behaviour of the time-asymptotic autocovariance and autocorrelation of the solutions of the linearized system. We also discuss the reliability of the tools from an analytic perspective and through various examples. Among those, the application of the early-warning signs for an ocean Boussinesq model is explored through numerical simulations. The analytic results obtained expand on previous work and present valuable early-warning signs for various applications.

math.PR↗

arXiv2024

The Role of Sea-ice Processes on the Probability of AMOC Transitions

Recent simulations performed with the Community Earth System Model (CESM) have suggested a crucial role of sea-ice processes in AMOC hysteresis behaviour under varying surface freshwater forcing. Here, we further investigate this issue using additional CESM simulations and a novel conceptual ocean-sea-ice box model. The CESM simulations show that the presence of sea ice gives rise to the existence of statistical equilibrium states with a weak AMOC strength. This is confirmed in the conceptual model, which captures the same AMOC hysteresis behaviour as in the CESM simulation and where steady states are computed versus forcing parameters. In the conceptual model, transition probabilities between the different equilibrium states are determined using rare event techniques. The transition probabilities from a strong AMOC state to a weak AMOC state increase when considering sea-ice processes and indicate that sea ice promotes these transitions. On the other hand, sea ice strongly reduces the probabilities of the reverse transition from a weak AMOC state to a strong AMOC state and this implies that sea ice also limits AMOC recovery. The results here indicate that sea-ice processes play a dominant role in AMOC hysteresis width and influence transition probabilities between the different equilibrium states.

physics.geo-ph↗

arXiv2023

Multistability and Intermediate Tipping of the Atlantic Ocean Circulation

Tipping points (TP) in climate sub-systems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other sub-systems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably prior to the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.

physics.ao-ph↗

arXiv2023

Asymmetry of AMOC Hysteresis in a State-of-the-Art Global Climate Model

We study hysteresis properties of the Atlantic Meridional Overturning Circulation (AMOC) under a slowly-varying North Atlantic (20$^{\circ}$N -- 50$^{\circ}$N) freshwater flux forcing in state-of-the-art Global Climate Model (GCM), the Community Earth System Model. Results are presented of a full hysteresis simulation ($4,400$ model years) and show that there is a hysteresis width of about $0.4$ Sv. This demonstrates that an AMOC collapse and recovery do not only occur in conceptual and idealised climate models, but also in a state-of-the-art GCM. The AMOC recovery is about a factor six faster than the AMOC collapse and this asymmetry is due to the major effect of the North Atlantic sea-ice distribution on the AMOC recovery. The results have implications for projections of possible future AMOC behaviour and for explaining relatively rapid climate transitions in the geological past.

physics.ao-ph↗

arXiv2023

The effect of model freshwater flux biases on the multi-stable regime of the AMOC

It is known that global climate models (GCMs) have substantial biases in the surface freshwater flux which forces the ocean component of these models. Using numerical bifurcation analyses on a global ocean model, we study here the effect of a specific freshwater flux bias on the multiple equilibrium regime of the Atlantic Meridional Overturning Circulation (AMOC). We find that a (positive) freshwater flux bias over the Indian Ocean shifts the multiple equilibrium regime to larger values of North Atlantic freshwater input but hardly affects the associated hysteresis width. The magnitude of this shift depends on the way the anomalous North Atlantic freshwater flux is compensated. We explain the changes in bifurcation diagrams using the freshwater balance over the Atlantic basin. The results suggest that state-of-the-art GCMs may have an AMOC multiple equilibrium regime, but that it is located in a parameter regime that is considered unrealistic and hence is not explored.

physics.ao-ph↗

arXiv2023

New Physics-Based Early Warning Signal shows AMOC is on Tipping Course

One of the most prominent climate tipping elements is the Atlantic Meridional Overturning Circulation (AMOC), which can potentially collapse due to the input of fresh water in the North Atlantic. Although AMOC collapses have been induced in state-of-the-art Global Climate Models (GCMs) by strong freshwater forcing, an AMOC tipping event has so far not been found. Here, we show results of the first AMOC tipping event in such a GCM, the Community Earth System Model, including the large climate impacts of the associated AMOC collapse. Using these results, we develop a new physics-based and observable early warning signal of AMOC tipping: the minimum of the AMOC induced freshwater transport at the southern boundary of the Atlantic. Available observational and reanalysis data indicate that the present-day AMOC is on route to tipping. The new early warning signal is a useful alternative to classical statistical ones which, when applied to our simulated AMOC tipping event, turn out to be sensitive to the analysed time interval before tipping.

physics.ao-ph↗

arXiv2023

Data-driven methods to estimate the committor function in conceptual ocean models

In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general, and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare events algorithms like TAMS (trajectory-adaptive multilevel sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called the committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (analog Markov chains, neural networks, reservoir computing, dynamical Galerkin approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analog Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

physics.ao-ph↗

arXiv2023

Bifurcation analysis of a North Atlantic Ocean box model with two deep-water formation sites

The tipping of the Atlantic Meridional Overturning Circulation (AMOC) to a 'shutdown' state due to changes in the freshwater forcing of the ocean is of particular interest and concern due to its widespread ramifications, including a dramatic climatic shift for much of Europe. A clear understanding of how such a shutdown would unfold requires analyses of models from across the complexity spectrum. For example, detailed simulations of sophisticated Earth System Models have identified scenarios in which deep-water formation first ceases in the Labrador Sea before ceasing in the Nordic Seas, en route to a complete circulation shutdown. Here, we study a simple ocean box model with two polar boxes designed to represent deep-water formation at these two distinct sites. A bifurcation analysis reveals how, depending on the differences of freshwater and thermal forcing between the two polar boxes, transitions to 'partial shutdown' states are possible. Our results shed light on the nature of the tipping of AMOC and clarify dynamical features observed in more sophisticated models.

physics.ao-ph↗

arXiv2021

Partial tipping in a spatially heterogeneous world

Many climate subsystems are thought to be susceptible to tipping - and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization of the full (sub)system. Here, we explore tipping in conceptual, but spatially extended and spatially heterogenous models. These are extensions of conceptual models taken from all sorts of climate system components on multiple spatial scales. By analysis of the bifurcation structure of such systems, special stable equilibrium states are revealed: coexistence states with part of the spatial domain in one state, and part in another, with a spatial interface between these regions. These coexistence states critically depend on the size and the spatial heterogeneity of the (sub)system. In particular, in these systems a tipping point might lead to a partial tipping of the full (sub)system, in which only part of the spatial domain undergoes reorganization, limiting the impact of these events on the system's functioning.

nlin.PS↗

arXiv2021

Projections of the Transient State-Dependency of Climate Feedbacks

When the climate system is forced, e.g. by emission of greenhouse gases, it responds on multiple time scales. As temperatures rise, feedback processes might intensify or weaken. Current methods to analyze feedback strength, however, do not take such state dependency into account; they only consider changes in (global mean) temperature and assume all feedbacks are linearly related to that. This makes (transient) changes in feedback strengths almost intangible and generally leads to underestimation of future warming. Here, we present a multivariate (and spatially explicit) framework that facilitates dissection of climate feedbacks over time scales. Using this framework, information on the composition of projected (transient) future climates and feedback strengths can be obtained. Moreover, it can be used to make projections for many emission scenarios through linear response theory. The new framework is illustrated using the Community Earth System Model version 2 (CESM2).

physics.ao-ph↗

arXiv2021

Convection under internal waves in a mountain lake

Turbulent mixing processes in deep alpine Lake Garda (I) have not extensively been observed. Knowledge about drivers of turbulent fluxes are important for insights in the transport of matter, nutrients and pollutants, in the lake and in natural water bodies in general. In this paper, the occurrence of internal wave induced turbulent convection is addressed as opposed to the more common shear-induced turbulence in a density stratified environment. Observations are analyzed from a dedicated yearlong mooring holding 100 high-resolution temperature sensors at 1.5 m intervals under a single current meter in the deeper half of the 344 m deep lake-center. Episodically, the weakly density stratified waters in the lower 50 m above the lake floor show spectral slope and coherence evidence of short-term (15 to 30 minutes) convective motions under internal waves that are supported by the stronger stratified waters above. The near-homogeneous conditions are not attributable to frictional Ekman dynamics, but to large-scale internal wave crests.

physics.ao-ph↗

arXiv2021

Eddy memory as an explanation of intra-seasonal periodic behavior in baroclinic eddies

The baroclinic annular mode (BAM) is a leading-order mode of the eddy-kinetic energy in the Southern Hemisphere exhibiting. oscillatory behavior at intra-seasonal time scales. The oscillation mechanism has been linked to transient eddy-mean flow interactions that remain poorly understood. Here we demonstrate that the finite memory effect in eddy-heat flux dependence on the large-scale flow can explain the origin of the BAM's oscillatory behavior. We represent the eddy memory effect by a delayed integral kernel that leads to a generalized Langevin equation for the planetary-scale heat equation. Using a mathematical framework for the interactions between planetary and synoptic-scale motions, we derive a reduced dynamical model of the BAM - a stochastically-forced oscillator with a period proportional to the geometric mean between the eddy-memory time scale and the diffusive eddy equilibration timescale. Our model provides a formal justification for the previously proposed phenomenological model of the BAM and could be used to explicitly diagnose the memory kernel and improve our understanding of transient eddy-mean flow interactions in the atmosphere.

physics.ao-ph↗