Journal of Advances in Modeling Earth Systems, May 1, 2021
The behavior of the Earth's climate system, from day-today changes in weather to longer-term vari... more The behavior of the Earth's climate system, from day-today changes in weather to longer-term variations in climate, arises as a result of the interactions of diverse processes within the coupled land-ocean-atmosphere-cryosphere system over a vast range of spatiotemporal scales (see, e.g., Ghil and Lucarini (2020) for a recent review). Developing an accurate understanding of the underlying processes, including their response to external forcing and the interactions between different components, is an important first step in the development of realistic numerical forecasting models. Inevitably, even with a good understanding of the main processes being simulated, any given model will still be limited in its ability to represent the climate system, for example, due to deficiencies in the parameterization of unresolved processes. These limitations manifest as systematic biases in the output of the model compared to observations. By comparing the representation of a particular component in the model with its observed counterpart, shortcomings in the model implementation can be identified for improvement, at least subject to the severe limitation that
Low-frequency variability in the south Indian Ocean is studied by analyzing 200 years of output f... more Low-frequency variability in the south Indian Ocean is studied by analyzing 200 years of output from a fully coupled climate model simulation. At time scales of 2-10 years, the variability is dominated by westwardpropagating features that form on the eastern side of the basin. Using feature tracking and clustering, the spatiotemporal characteristics and preferred pathways of the propagating features are identified and studied in detail. By comparison of the phase speed and vertical structure of the propagating anomalies identified by the feature tracking with linear theory, we conclude that these features are likely mode 1 or 2 baroclinic planetary waves. The effects of this low-frequency variability on the climate system is investigated. By analysis of the mixed-layer temperature budget, it is shown that at particular geographic locations, the propagating features can substantially modify the near-surface ocean and induce significant fluxes of heat into the atmosphere. In turn, these heat fluxes can drive a coherent atmospheric response, although this response does not appear to feed back onto the ocean. Finally, we discuss the implications for the interannual climate predictability.
... échelles. *Corresponding author's e-mail: [email protected] Pag... more ... échelles. *Corresponding author's e-mail: [email protected] Page 2. Sampling Errors in Estimation of the Small Scales of Monthly Mean Climate / 161 ... scientist. Kraichnan (1967) and Leith (1968) (see also Ditlevsen et al. ...
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction o... more A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure but unlike the EDQNM is guaranteed to be realizable in the presence of transient waves. Jack Herring's important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and quasi-Lagrangian statistical dynamical closure theories, and the statistical dynamics of interactions of turbulence with topography. The impact of Herring's work is described and placed in the context of related developments. Some of the further works that have built on Herring's foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence theory are put in perspective by comparing related developments in strong interaction quantum field theory.
Australian & New Zealand industrial and applied mathematics journal, Jul 27, 2005
The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simu... more The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simulation of the vorticity form of the 2-D Navier-Stokes equation with a non-Markovian statistical closure theory for inhomogeneous flow over mean topography. The quasi-diagonal direct interaction approximation closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized β-plane. The competing effects of nonlinear waves at the large scales and fully developed turbulence at the small scales is examined by comparing closure theory with ensemble averaged results from direct numerical simulation at resolution k = 48 for circularly truncated wavenumber space. This work builds
ABSTRACT We report on an ensemble predictability study of a barotropic vorticity model that displ... more ABSTRACT We report on an ensemble predictability study of a barotropic vorticity model that displays low-frequency zonal-dipolar regime transitions. Low-frequency regime transitions in the model is reminiscent of regime change phenomena in the weather and climate systems wherein extreme and abrupt qualitative changes occur, seemingly randomly, after long periods of apparent stability. Insofar as the transitions relate to the blocking transition of the extra-tropical winter atmosphere, a novel aspect of the model considered is the lack of any source of background gradient of potential-vorticity and the consequent absence of Rossby waves. Perturbations in our ensemble prediction system are embedded onto the system's chaotic attractor under the full nonlinear dynamics as bred vectors. We find that the evolved perturbations remain globally distinct and align to identify low-dimensional subspaces associated with regions of large forecast error. We further demonstrate that while regime transitions are initiated by higher order non-Gaussian processes, they are predictable.
We describe a propagator renormalized, non-Markovian closure for inhomogeneous turbulent flows wi... more We describe a propagator renormalized, non-Markovian closure for inhomogeneous turbulent flows with particular emphasis on the role of the bare vertex terms. We outline a regularization procedure as an approximation to a formal vertex renormalization and comment on numerical and analytic investigations to higher order corrections.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representatio... more The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representation of crossdomain covariances between various coupled subsystems with disparate spatio-temporal scales, where often one or more subsystems are unobserved. In this study, we explore strong CDA using ensemble Kalman filtering methods applied to a conceptual multiscale chaotic model consisting of three coupled Lorenz attractors. We introduce the use of the local attractor dimension (i.e. the Kaplan-Yorke dimension, dim KY) to prescribe the rank of the background covariance matrix which we construct using a variable number of weighted covariant Lyapunov vectors (CLVs). Specifically, we consider the ability to track the nonlinear trajectory of each of the subsystems with different variants of sparse observations, relying only on the cross-domain covariance to determine an accurate analysis for tracking the trajectory of the unobserved subdomain. We find that spanning the global unstable and neutral subspaces is not sufficient at times where the nonlinear dynamics and intermittent linear error growth along a stable direction combine. At such times a subset of the local stable subspace is also needed to be represented in the ensemble. In this regard the local dim KY provides an accurate estimate of the required rank. Additionally, we show that spanning the full space does not improve performance significantly relative to spanning only the subspace determined by the local dimension. Where weak coupling between subsystems leads to covariance collapse in one or more of the unobserved subsystems, we apply a novel modified Kalman gain where the background covariances are scaled by their Frobenius norm. This modified gain increases the magnitude of the innovations and the effective dimension of the unobserved domains relative to the strength of the coupling and timescale separation. We conclude with a discussion on the implications for higher-dimensional systems.
concentrations or 4 times preindustrial CO 2 levels reveal very similar SRW responses to the atmo... more concentrations or 4 times preindustrial CO 2 levels reveal very similar SRW responses to the atmospheric only simulations with anomalously wider SST warming. Our results suggest that in a warmer climate, the changes in the strength and width of the HC act in concert to significantly alter SRW sources and propagation characteristics.
The South Pacific decadal oscillation (SPDO) characterizes the Southern Hemisphere contribution t... more The South Pacific decadal oscillation (SPDO) characterizes the Southern Hemisphere contribution to the Pacific-wide interdecadal Pacific oscillation (IPO) and is analogous to the Pacific decadal oscillation (PDO) centered in the North Pacific. In this study, upper ocean variability and potential predictability of the SPDO is examined in HadISST data and an atmosphere-forced ocean general circulation model. The potential predictability of the IPO-related variability is investigated in terms of both the fractional contribution made by the decadal component in the South, tropical and North Pacific Oceans and in terms of a doubly integrated first-order autoregressive (AR1) model. Despite explaining a smaller fraction of the total variance, we find larger potential predictability of the SPDO relative to the PDO. We identify distinct local drivers in the western subtropical South Pacific, where nonlinear baroclinic Rossby wave-topographic interactions act to low-pass filter decadal variability. In particular, we show that the Kermadec Ridge in the southwest Pacific enhances the decadal signature more prominently than anywhere else in the Pacific basin. Applying the doubly integrated AR1 model, we demonstrate that variability associated with the Pacific-South American pattern is a critically important atmospheric driver of the SPDO via a reddening process analogous to the relationship between the Aleutian low and PDO in the North Pacific-albeit that the relationship in the South Pacific appears to be even stronger. Our results point to the largely unrecognized importance of South Pacific processes as a key source of decadal variability and predictability.
While the Northern Hemisphere sea-ice has uniformly declined over the past several decades, the o... more While the Northern Hemisphere sea-ice has uniformly declined over the past several decades, the observed sea-ice in the Southern Hemisphere has exhibited regions of increase and decrease. Here we use a comprehensive set of ocean-sea-ice simulations (1990-2007) to elucidate the drivers of the observed heterogeneous sea-ice trends. We show wind variability is an important determinant of the heterogeneous pattern of the variability and trends in Southern Hemisphere sea-ice. Only in the West Pacific region does Southern Annular Mode wind forcing contribute significantly to the trend in sea-ice duration. El Niño Southern Oscillation wind forcing contribution to the sea-ice duration trend is confined to the Atlantic and Pacific. In the Indian Ocean, weather is a significant driver of the sea-ice duration trend. Only in the East Pacific region is wind forcing alone insufficient to give rise to the observed sea-ice decline and must be augmented by warming to reproduce the observations.
An initial dimension reduction forms an integral part of many analyses in climate science. Differ... more An initial dimension reduction forms an integral part of many analyses in climate science. Different methods yield low-dimensional representations that are based on differing aspects of the data. Depending on the features of the data that are relevant for a given study, certain methods may be more suitable than others, for instance yielding bases that can be more easily identified with physically meaningful modes. To illustrate the distinction between particular methods and identify circumstances in which a given method might be preferred, in this paper we present a set of case studies comparing the results obtained using the traditional approaches of EOF analysis and k-means clustering with the more recently introduced methods such as archetypal analysis and convex coding. For data such as global sea surface temperature anomalies, in which there is a clear, dominant mode of variability, all of the methods considered yield rather similar bases with which to represent the data, while differing in reconstruction accuracy for a given basis size. However, in the absence of such a clear scale separation, as in the case of daily geopotential height anomalies, the extracted bases differ much more significantly between the methods. We highlight the importance in such cases of carefully considering the relevant features of interest, and of choosing the method that best targets precisely those features so as to obtain more easily interpretable results.
EarthArXiv (California Digital Library), Aug 12, 2021
Singular vectors (SVs) have long been employed in the initialization of ensemble numerical weathe... more Singular vectors (SVs) have long been employed in the initialization of ensemble numerical weather prediction (NWP) in order to capture the structural organization and growth rates of those perturbations or "errors" associated with initial condition errors and instability processes of the large scale flow. Due to their (super) exponential growth rates and spatial scales, initial SVs are typically combined empirically with evolved SVs in order to generate forecast perturbations whose structures and growth rates are tuned for specified lead-times. Here we present a systematic approach to generating finite time or "mixed" SVs (MSVs) based on a method for the calculation of covariant Lyapunov vectors (CLVs) and appropriate choices of the matrix cocycle. We first derive a data-driven reduced order model to characterize persistent geopotential height anomalies over Europe and Western Asia (Eurasia) over the period 1979-present from the NCEPv1 reanalysis. We then characterize and compare the MSVs and SVs of each persistent state over Eurasia for particular leadtimes from a day to over a week. Finally, we compare the spatio-temporal properties of SVs and MSVs in an examination of the dynamics of the 2010 Russian heatwave. We show that MSVs provide a systematic approach to generate initial forecast perturbations projected onto relevant expanding directions in phase space for typical NWP forecast lead-times.
Journal of Advances in Modeling Earth Systems, May 1, 2021
The behavior of the Earth's climate system, from day-today changes in weather to longer-term vari... more The behavior of the Earth's climate system, from day-today changes in weather to longer-term variations in climate, arises as a result of the interactions of diverse processes within the coupled land-ocean-atmosphere-cryosphere system over a vast range of spatiotemporal scales (see, e.g., Ghil and Lucarini (2020) for a recent review). Developing an accurate understanding of the underlying processes, including their response to external forcing and the interactions between different components, is an important first step in the development of realistic numerical forecasting models. Inevitably, even with a good understanding of the main processes being simulated, any given model will still be limited in its ability to represent the climate system, for example, due to deficiencies in the parameterization of unresolved processes. These limitations manifest as systematic biases in the output of the model compared to observations. By comparing the representation of a particular component in the model with its observed counterpart, shortcomings in the model implementation can be identified for improvement, at least subject to the severe limitation that
Low-frequency variability in the south Indian Ocean is studied by analyzing 200 years of output f... more Low-frequency variability in the south Indian Ocean is studied by analyzing 200 years of output from a fully coupled climate model simulation. At time scales of 2-10 years, the variability is dominated by westwardpropagating features that form on the eastern side of the basin. Using feature tracking and clustering, the spatiotemporal characteristics and preferred pathways of the propagating features are identified and studied in detail. By comparison of the phase speed and vertical structure of the propagating anomalies identified by the feature tracking with linear theory, we conclude that these features are likely mode 1 or 2 baroclinic planetary waves. The effects of this low-frequency variability on the climate system is investigated. By analysis of the mixed-layer temperature budget, it is shown that at particular geographic locations, the propagating features can substantially modify the near-surface ocean and induce significant fluxes of heat into the atmosphere. In turn, these heat fluxes can drive a coherent atmospheric response, although this response does not appear to feed back onto the ocean. Finally, we discuss the implications for the interannual climate predictability.
... échelles. *Corresponding author's e-mail: [email protected] Pag... more ... échelles. *Corresponding author's e-mail: [email protected] Page 2. Sampling Errors in Estimation of the Small Scales of Monthly Mean Climate / 161 ... scientist. Kraichnan (1967) and Leith (1968) (see also Ditlevsen et al. ...
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction o... more A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure but unlike the EDQNM is guaranteed to be realizable in the presence of transient waves. Jack Herring's important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and quasi-Lagrangian statistical dynamical closure theories, and the statistical dynamics of interactions of turbulence with topography. The impact of Herring's work is described and placed in the context of related developments. Some of the further works that have built on Herring's foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence theory are put in perspective by comparing related developments in strong interaction quantum field theory.
Australian & New Zealand industrial and applied mathematics journal, Jul 27, 2005
The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simu... more The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simulation of the vorticity form of the 2-D Navier-Stokes equation with a non-Markovian statistical closure theory for inhomogeneous flow over mean topography. The quasi-diagonal direct interaction approximation closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized β-plane. The competing effects of nonlinear waves at the large scales and fully developed turbulence at the small scales is examined by comparing closure theory with ensemble averaged results from direct numerical simulation at resolution k = 48 for circularly truncated wavenumber space. This work builds
ABSTRACT We report on an ensemble predictability study of a barotropic vorticity model that displ... more ABSTRACT We report on an ensemble predictability study of a barotropic vorticity model that displays low-frequency zonal-dipolar regime transitions. Low-frequency regime transitions in the model is reminiscent of regime change phenomena in the weather and climate systems wherein extreme and abrupt qualitative changes occur, seemingly randomly, after long periods of apparent stability. Insofar as the transitions relate to the blocking transition of the extra-tropical winter atmosphere, a novel aspect of the model considered is the lack of any source of background gradient of potential-vorticity and the consequent absence of Rossby waves. Perturbations in our ensemble prediction system are embedded onto the system's chaotic attractor under the full nonlinear dynamics as bred vectors. We find that the evolved perturbations remain globally distinct and align to identify low-dimensional subspaces associated with regions of large forecast error. We further demonstrate that while regime transitions are initiated by higher order non-Gaussian processes, they are predictable.
We describe a propagator renormalized, non-Markovian closure for inhomogeneous turbulent flows wi... more We describe a propagator renormalized, non-Markovian closure for inhomogeneous turbulent flows with particular emphasis on the role of the bare vertex terms. We outline a regularization procedure as an approximation to a formal vertex renormalization and comment on numerical and analytic investigations to higher order corrections.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representatio... more The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representation of crossdomain covariances between various coupled subsystems with disparate spatio-temporal scales, where often one or more subsystems are unobserved. In this study, we explore strong CDA using ensemble Kalman filtering methods applied to a conceptual multiscale chaotic model consisting of three coupled Lorenz attractors. We introduce the use of the local attractor dimension (i.e. the Kaplan-Yorke dimension, dim KY) to prescribe the rank of the background covariance matrix which we construct using a variable number of weighted covariant Lyapunov vectors (CLVs). Specifically, we consider the ability to track the nonlinear trajectory of each of the subsystems with different variants of sparse observations, relying only on the cross-domain covariance to determine an accurate analysis for tracking the trajectory of the unobserved subdomain. We find that spanning the global unstable and neutral subspaces is not sufficient at times where the nonlinear dynamics and intermittent linear error growth along a stable direction combine. At such times a subset of the local stable subspace is also needed to be represented in the ensemble. In this regard the local dim KY provides an accurate estimate of the required rank. Additionally, we show that spanning the full space does not improve performance significantly relative to spanning only the subspace determined by the local dimension. Where weak coupling between subsystems leads to covariance collapse in one or more of the unobserved subsystems, we apply a novel modified Kalman gain where the background covariances are scaled by their Frobenius norm. This modified gain increases the magnitude of the innovations and the effective dimension of the unobserved domains relative to the strength of the coupling and timescale separation. We conclude with a discussion on the implications for higher-dimensional systems.
concentrations or 4 times preindustrial CO 2 levels reveal very similar SRW responses to the atmo... more concentrations or 4 times preindustrial CO 2 levels reveal very similar SRW responses to the atmospheric only simulations with anomalously wider SST warming. Our results suggest that in a warmer climate, the changes in the strength and width of the HC act in concert to significantly alter SRW sources and propagation characteristics.
The South Pacific decadal oscillation (SPDO) characterizes the Southern Hemisphere contribution t... more The South Pacific decadal oscillation (SPDO) characterizes the Southern Hemisphere contribution to the Pacific-wide interdecadal Pacific oscillation (IPO) and is analogous to the Pacific decadal oscillation (PDO) centered in the North Pacific. In this study, upper ocean variability and potential predictability of the SPDO is examined in HadISST data and an atmosphere-forced ocean general circulation model. The potential predictability of the IPO-related variability is investigated in terms of both the fractional contribution made by the decadal component in the South, tropical and North Pacific Oceans and in terms of a doubly integrated first-order autoregressive (AR1) model. Despite explaining a smaller fraction of the total variance, we find larger potential predictability of the SPDO relative to the PDO. We identify distinct local drivers in the western subtropical South Pacific, where nonlinear baroclinic Rossby wave-topographic interactions act to low-pass filter decadal variability. In particular, we show that the Kermadec Ridge in the southwest Pacific enhances the decadal signature more prominently than anywhere else in the Pacific basin. Applying the doubly integrated AR1 model, we demonstrate that variability associated with the Pacific-South American pattern is a critically important atmospheric driver of the SPDO via a reddening process analogous to the relationship between the Aleutian low and PDO in the North Pacific-albeit that the relationship in the South Pacific appears to be even stronger. Our results point to the largely unrecognized importance of South Pacific processes as a key source of decadal variability and predictability.
While the Northern Hemisphere sea-ice has uniformly declined over the past several decades, the o... more While the Northern Hemisphere sea-ice has uniformly declined over the past several decades, the observed sea-ice in the Southern Hemisphere has exhibited regions of increase and decrease. Here we use a comprehensive set of ocean-sea-ice simulations (1990-2007) to elucidate the drivers of the observed heterogeneous sea-ice trends. We show wind variability is an important determinant of the heterogeneous pattern of the variability and trends in Southern Hemisphere sea-ice. Only in the West Pacific region does Southern Annular Mode wind forcing contribute significantly to the trend in sea-ice duration. El Niño Southern Oscillation wind forcing contribution to the sea-ice duration trend is confined to the Atlantic and Pacific. In the Indian Ocean, weather is a significant driver of the sea-ice duration trend. Only in the East Pacific region is wind forcing alone insufficient to give rise to the observed sea-ice decline and must be augmented by warming to reproduce the observations.
An initial dimension reduction forms an integral part of many analyses in climate science. Differ... more An initial dimension reduction forms an integral part of many analyses in climate science. Different methods yield low-dimensional representations that are based on differing aspects of the data. Depending on the features of the data that are relevant for a given study, certain methods may be more suitable than others, for instance yielding bases that can be more easily identified with physically meaningful modes. To illustrate the distinction between particular methods and identify circumstances in which a given method might be preferred, in this paper we present a set of case studies comparing the results obtained using the traditional approaches of EOF analysis and k-means clustering with the more recently introduced methods such as archetypal analysis and convex coding. For data such as global sea surface temperature anomalies, in which there is a clear, dominant mode of variability, all of the methods considered yield rather similar bases with which to represent the data, while differing in reconstruction accuracy for a given basis size. However, in the absence of such a clear scale separation, as in the case of daily geopotential height anomalies, the extracted bases differ much more significantly between the methods. We highlight the importance in such cases of carefully considering the relevant features of interest, and of choosing the method that best targets precisely those features so as to obtain more easily interpretable results.
EarthArXiv (California Digital Library), Aug 12, 2021
Singular vectors (SVs) have long been employed in the initialization of ensemble numerical weathe... more Singular vectors (SVs) have long been employed in the initialization of ensemble numerical weather prediction (NWP) in order to capture the structural organization and growth rates of those perturbations or "errors" associated with initial condition errors and instability processes of the large scale flow. Due to their (super) exponential growth rates and spatial scales, initial SVs are typically combined empirically with evolved SVs in order to generate forecast perturbations whose structures and growth rates are tuned for specified lead-times. Here we present a systematic approach to generating finite time or "mixed" SVs (MSVs) based on a method for the calculation of covariant Lyapunov vectors (CLVs) and appropriate choices of the matrix cocycle. We first derive a data-driven reduced order model to characterize persistent geopotential height anomalies over Europe and Western Asia (Eurasia) over the period 1979-present from the NCEPv1 reanalysis. We then characterize and compare the MSVs and SVs of each persistent state over Eurasia for particular leadtimes from a day to over a week. Finally, we compare the spatio-temporal properties of SVs and MSVs in an examination of the dynamics of the 2010 Russian heatwave. We show that MSVs provide a systematic approach to generate initial forecast perturbations projected onto relevant expanding directions in phase space for typical NWP forecast lead-times.
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Papers by Terence O'kane