Publications by Laure Zanna

Global reconstruction of historical ocean heat storage and transport

Proceedings of the National Academy of Sciences National Academy of Sciences 116 (2019) 1126-1131

L Zanna, S Khatiwala, JM Gregory, J Ison, P Heimbach

Most of the excess energy stored in the climate system due to anthropogenic greenhouse gas emissions has been taken up by the oceans, leading to thermal expansion and sea-level rise. The oceans thus have an important role in the Earth’s energy imbalance. Observational constraints on future anthropogenic warming critically depend on accurate estimates of past ocean heat content (OHC) change. We present a reconstruction of OHC since 1871, with global coverage of the full ocean depth. Our estimates combine timeseries of observed sea surface temperatures with much longer historical coverage than those in the ocean interior together with a representation (a Green’s function) of time-independent ocean transport processes. For 1955–2017, our estimates are comparable with direct estimates made by infilling the available 3D time-dependent ocean temperature observations. We find that the global ocean absorbed heat during this period at a rate of 0.30 ± 0.06 W/m2 in the upper 2,000 m and 0.028 ± 0.026 W/m2 below 2,000 m, with large decadal fluctuations. The total OHC change since 1871 is estimated at 436 ± 91 ×1021 J, with an increase during 1921–1946 (145 ± 62 ×1021 J) that is as large as during 1990–2015. By comparing with direct estimates, we also infer that, during 1955–2017, up to one-half of the Atlantic Ocean warming and thermosteric sea-level rise at low latitudes to midlatitudes emerged due to heat convergence from changes in ocean transport.

Uncertainty and scale interactions in ocean ensembles: from seasonal forecasts to multi-decadal climate predictions

Quarterly Journal of the Royal Meteorological Society Wiley 145 (2018) 160-175

L Zanna, JM Brankart, M Huber, S Leroux, T Penduff, PD Williams

The ocean plays an important role in the climate system on timescales of weeks to centuries. Despite improvements in ocean models, dynamical processes involving multi‐scale interactions remain poorly represented, leading to errors in forecasts. We present recent advances in understanding, quantifying and representing of physical and numerical sources of uncertainty in novel regional and global ocean ensembles at different horizontal resolutions. At coarse‐resolution, uncertainty in 21st‐century projections of the upper overturning cell in the Atlantic is mostly a result of buoyancy fluxes, while the uncertainty in projections of the bottom cell is driven equally by both wind and buoyancy flux uncertainty. In addition, freshwater and heat fluxes are the largest contributors to Atlantic Ocean Heat Content regional projections and to its uncertainty, mostly as a result of uncertain ocean circulation projections. At both coarse‐ and eddy‐permitting resolution, the unresolved stochastic temperature and salinity fluctuations can lead to significant changes in large‐scale density across the Gulf Stream front, therefore leading to major changes in large‐scale transport. These perturbations can have an impact on the ensemble spread on monthly time‐scales and subsequently interact non‐linearly with the dynamics of the flow generating chaotic variability on multi‐annual timescales. In the Gulf Stream region, the ratio of chaotic variability to atmospheric‐forced variability in meridional heat transport is larger than 50% on timescales shorter than 2 years; while between 40 and 48 ∘S the ratio exceeds 50% on on time scales up to 28 years. Based on these simulations, we show that air‐sea interaction and ocean sub‐grid eddies remain an important source of error for simulating and predicting ocean circulation, sea level, and heat uptake on a range of spatial and temporal scales. We discuss how further refinement of these ensembles can help us assess the relative importance of oceanic versus atmospheric uncertainty in weather and climate.

ENSO bimodality and extremes

Geophysical Research Letters American Geophysical Union 46 (2019) 4883-4893

RR Rodrigues, A Subramanian, L Zanna, J Berner

<p style="text-align:justify;"> Tropical sea surface temperature (SST) and winds vary on a wide range of timescales and have a substantial impact on weather and climate across the globe. Here we study the variability of SST and zonal wind during El Niño‐Southern Oscillation (ENSO) between 1982 and 2014. We focus on changes in extreme statistics using higher‐order moments of SST and zonal winds. We find that ENSO characteristics exhibit bimodal distributions and fat tails with extreme warm and cold temperatures in 1982–1999, but not during 2000–2014. The changes in the distributions coincide with changes in the intensity of ENSO events and the phase of the Interdecadal Pacific Oscillation. We also find that the strongest Easterly Wind Bursts occur during extreme El Niños and not during La Niñas. Maps of SST kurtosis can serve as a diagnostic for the thermocline feedback mechanism responsible for the differences in ENSO diversity between the two periods. </p>

Investigating the predictability of North Atlantic sea surface height

Climate Dynamics (2019)

R Fraser, M Palmer, C Roberts, C Wilson, D Copsey, L Zanna

© 2019, The Author(s). Interannual sea surface height (SSH) forecasts are subject to several sources of uncertainty. Methods relying on statistical forecasts have proven useful in assessing predictability and associated uncertainty due to both initial conditions and boundary conditions. In this study, the interannual predictability of SSH dynamics in the North Atlantic is investigated using the output from a 150 year long control simulation based on HadGEM3, a coupled climate model at eddy-permitting resolution. Linear inverse modeling (LIM) is used to create a statistical model for the evolution of monthly-mean SSH anomalies. The forecasts based on the LIM model demonstrate skill on interannanual timescales O(1–2 years). Forecast skill is found to be largest in both the subtropical and subpolar gyres, with decreased skill in the Gulf Stream extension region. The SSH initial conditions involving a tripolar anomaly off Cape Hatteras lead to a maximum growth in SSH about 20 months later. At this time, there is a meridional shift in the 0 m-SSH contour on the order of 0.5 ∘–1.5 ∘-latitude, coupled with a change in SSH along the US East Coast. To complement the LIM-based study, interannual SSH predictability is also quantified using the system’s average predictability time (APT). The APT analysis extracted large-scale SSH patterns which displayed predictability on timescales longer than 2 years. These patterns are responsible for changes in SSH on the order of 10 cm along the US East Coast, driven by variations in Ekman velocity. Our results shed light on the timescales of SSH predictability in the North Atlantic. In addition, the diagnosed optimal initial conditions and predictable patterns could improve interannual forecasts of the Gulf Stream’s characteristics and coastal SSH.

Applications of Deep Learning to Ocean Data Inference and Subgrid Parameterization

Journal of Advances in Modeling Earth Systems (2019)

T Bolton, L Zanna

©2019. The Authors. Oceanographic observations are limited by sampling rates, while ocean models are limited by finite resolution and high viscosity and diffusion coefficients. Therefore, both data from observations and ocean models lack information at small and fast scales. Methods are needed to either extract information, extrapolate, or upscale existing oceanographic data sets, to account for or represent unresolved physical processes. Here we use machine learning to leverage observations and model data by predicting unresolved turbulent processes and subsurface flow fields. As a proof of concept, we train convolutional neural networks on degraded data from a high-resolution quasi-geostrophic ocean model. We demonstrate that convolutional neural networks successfully replicate the spatiotemporal variability of the subgrid eddy momentum forcing, are capable of generalizing to a range of dynamical behaviors, and can be forced to respect global momentum conservation. The training data of our convolutional neural networks can be subsampled to 10–20% of the original size without a significant decrease in accuracy. We also show that the subsurface flow field can be predicted using only information at the surface (e.g., using only satellite altimetry data). Our results indicate that data-driven approaches can be exploited to predict both subgrid and large-scale processes, while respecting physical principles, even when data are limited to a particular region or external forcing. Our in-depth study presents evidence for the successful design of ocean eddy parameterizations for implementation in coarse-resolution climate models.

Remote and local influences in forecasting Pacific SST: a linear inverse model and a multimodel ensemble study

Climate Dynamics (2018) 1-19

DF Dias, A Subramanian, L Zanna, AJ Miller

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature A suite of statistical linear inverse models (LIMs) are used to understand the remote and local SST variability that influences SST predictions over the North Pacific region. Observed monthly SST anomalies in the Pacific are used to construct different regional LIMs for seasonal to decadal predictions. The seasonal forecast skills of the LIMs are compared to that from three operational forecast systems in the North American Multi-Model Ensemble (NMME), revealing that the LIM has better skill in the Northeastern Pacific than NMME models. The LIM is also found to have comparable forecast skill for SST in the Tropical Pacific with NMME models. This skill, however, is highly dependent on the initialization month, with forecasts initialized during the summer having better skill than those initialized during the winter. The data are also bandpass filtered into seasonal, interannual and decadal time scales to identify the relationships between time scales using the structure of the propagator matrix. Moreover, we investigate the influence of the tropics and extra-tropics in the predictability of the SST over the region. The Extratropical North Pacific seems to be a source of predictability for the tropics on seasonal to interannual time scales, while the tropics enhance the forecast skill for the decadal component. These results indicate the importance of temporal scale interactions in improving the predictions on decadal timescales. Hence, we show that LIMs are not only useful as benchmarks for estimates of statistical skill, but also to isolate contributions to the forecast skills from different timescales, spatial scales or even model components.

Eddy-mixing entropy and its maximization in forced-dissipative geostrophic turbulence

Journal of Statistical Mechanics: Theory and Experiment IOP Publishing 2018 (2018) 073206

T David, L Zanna, D Marshall

An equilibrium, or maximum entropy, statistical mechanics theory can be derived for ideal, unforced and inviscid, geophysical flows. However, for all geophysical flows which occur in nature,forcing and dissipation play a major role. Here, a study of eddy-mixing entropy in a forced dissipative barotropic ocean model is presented. We heuristically investigate the temporal evolution of eddy-mixing entropy, as defined for the equilibrium theory, in a strongly forced and dissipative system. It is shown that the eddy-mixing entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability; formation of large scale structures; and steady state fluctuations. The fact that the eddy-mixing entropy behaves in a dynamically balanced way is not a priori clear and provides a novel means of quantifying turbulent disorder in geophysical flows. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance of entropy and statistical mechanics in the study of geostrophic turbulence.

Lagrangian ocean analysis: Fundamentals and practices

OCEAN MODELLING 121 (2018) 49-75

E van Sebille, SM Griffies, R Abernathey, TP Adams, P Berloff, A Biastoch, B Blanke, EP Chassignet, Y Cheng, CJ Cotter, E Deleersnijder, K Doos, HF Drake, S Drijfhout, SF Gary, AW Heemink, J Kjellsson, IM Koszalka, M Lange, C Lique, GA MacGilchrist, R Marsh, CGM Adame, R McAdam, F Nencioli, CB Paris, MD Piggott, JA Polton, S Ruehs, SHAM Shah, MD Thomas, J Wang, PJ Wolfram, L Zanna, JD Zika

The signature of oceanic processes in decadal extratropical SST anomalies

Geophysical Research Letters John Wiley & Sons 45 (2018) 7719-7730

C O'Reilly, L Zanna

The relationship between decadal SST and turbulent heat‐fluxes is assessed and used to identify where oceanic processes play an important role in extratropical decadal SST variability. In observational datasets and coupled climate model simulations from the CMIP5 archive, positive correlations between upward turbulent heat flux and SSTs indicate an active role of oceanic processes over regions in the North Atlantic, Northwest Pacific, Southern Pacific and Southern Atlantic. The contrasting nature of oceanic influence on decadal SST anomalies in the Northwest Pacific and North Atlantic is identified. Over the Northwest Pacific, SST anomalies are consistent with changes in the horizontal wind‐driven gyre circulation on timescales of between 3‐7 years, in both the observations and models. Over the North Atlantic, SST anomalies are also preceded by atmospheric circulation anomalies, though the response is stronger at longer timescales ‐ peaking at around 20‐years in the observations and at around 10‐years in the models.

Seasonal to annual ocean forecasting skill and the role of model and observational uncertainty

Quarterly Journal of the Royal Meteorological Society Wiley 144 (2018) 1947-1964

S Juricke, D Macleod, A Weisheimer, L Zanna, T Palmer

Accurate forecasts of the ocean state and the estimation of forecast uncertainties are crucial when it comes to providing skilful seasonal predictions. In this study we analyse the predictive skill and reliability of the ocean component in a seasonal forecasting system. Furthermore, we assess the effects of accounting for model and observational uncertainties. Ensemble forcasts are carried out with an updated version of the ECMWF seasonal forecasting model System 4, with a forecast length of ten months, initialized every May between 1981 and 2010. We find that, for essential quantities such as sea surface temperature and upper ocean 300 m heat content, the ocean forecasts are generally underdispersive and skilful beyond the first month mainly in the Tropics and parts of the North Atlantic. The reference reanalysis used for the forecast evaluation considerably affects diagnostics of forecast skill and reliability, throughout the entire ten‐month forecasts but mostly during the first three months. Accounting for parametrization uncertainty by implementing stochastic parametrization perturbations has a positive impact on both reliability (from month 3 onwards) as well as forecast skill (from month 8 onwards). Skill improvements extend also to atmospheric variables such as 2 m temperature, mostly in the extratropical Pacific but also over the midlatitudes of the Americas. Hence, while model uncertainty impacts the skill of seasonal forecasts, observational uncertainty impacts our assessment of that skill. Future ocean model development should therefore aim not only to reduce model errors but to simultaneously assess and estimate uncertainties.

The impact of tropical precipitation on summertime Euro-Atlantic circulation via a circumglobal wave-train

Journal of Climate American Meteorological Society 31 (2018) 6481-6504

C O'Reilly, T Woollings, L Zanna, A Weisheimer

The influence of tropical precipitation variability on summertime seasonal circulation anomalies in the Euro-Atlantic sector is investigated. The dominant mode of the maximum covariance analysis (MCA) between the Euro-Atlantic circulation and tropical precipitation reveals a cyclonic anomaly over the extratropical North Atlantic, contributing to anomalously wet conditions over western Europe and dry conditions over eastern Europe and Scandinavia (in the positive phase). The related mode of tropical precipitation variability is associated with tropical Pacific SST anomalies and is closely linked to the El Niño/Southern Oscillation (ENSO). The second MCA mode consists of weaker tropical precipitation anomalies but a stronger extratropical signal which reflects internal atmospheric variability. The teleconnection mechanism is tested in barotropic model simulations, which indicate that the observed link between the dominant mode of tropical precipitation and the Euro-Atlantic circulation anomalies is largely consistent with linear Rossby wave dynamics. The barotropic model response consists of a circumglobal wave-train in the extratropics that is primarily forced by divergence anomalies in the eastern tropical Pacific. Both the eastward and westward group propagation of the Rossby waves are found to be important in determining the circulation response over the Euro-Atlantic sector. The mechanism was also analysed in an operational seasonal forecasting system, ECMWF’s System 4. Whilst System 4 is well able to reproduce and skillfully forecast the tropical precipitation, the extratropical circulation response is absent over the Euro-Atlantic region, which is likely related to biases in the Asian jetstream.

Southern Ocean carbon-wind stress feedback

Climate Dynamics (2018) 1-15

B Bronselaer, L Zanna, DR Munday, J Lowe

© 2017 The Author(s) The Southern Ocean is the largest sink of anthropogenic carbon in the present-day climate. Here, Southern Ocean (Formula presented.) and its dependence on wind forcing are investigated using an equilibrium mixed layer carbon budget. This budget is used to derive an expression for Southern Ocean (Formula presented.) sensitivity to wind stress. Southern Ocean (Formula presented.) is found to vary as the square root of area-mean wind stress, arising from the dominance of vertical mixing over other processes such as lateral Ekman transport. The expression for p\hbox {CO}_{2} is validated using idealised coarse-resolution ocean numerical experiments. Additionally, we show that increased (decreased) stratification through surface warming reduces (increases) the sensitivity of the Southern Ocean (Formula presented.) to wind stress. The scaling is then used to estimate the wind-stress induced changes of atmospheric (Formula presented.) in CMIP5 models using only a handful of parameters. The scaling is further used to model the anthropogenic carbon sink, showing a long-term reversal of the Southern Ocean sink for large wind stress strength.

The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model

Ocean Modelling 126 (2018) 56-62

SD Bachman, JA Anstey, L Zanna

© 2018 Elsevier Ltd A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier–Stokes-α model (LANS-α e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.

The impact of horizontal resolution on energy transfers in global ocean models

Fluids MDPI 2 (2017) 45

J Kjellsson, L Zanna

The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated. Here, we quantify the kinetic energy budget in a suite of realistic global ocean models, with varying horizontal resolution and horizontal viscosity. We show that eddy-permitting ocean models have weaker kinetic energy cascades than eddy-resolving models due to discrepancies in the effect of wind forcing, horizontal viscosity, potential to kinetic energy conversion, and nonlinear interactions on the kinetic energy (KE) budget. However, the change in eddy kinetic energy between the eddy-permitting and the eddy-resolving model is not enough to noticeably change the scale where the inverse cascade arrests or the Rhines scale. In addition, we show that the mechanism by which baroclinic flows organise into barotropic flows is weaker at lower resolution, resulting in a more baroclinic flow. Hence, the horizontal resolution impacts the vertical structure of the simulated flow. Our results suggest that the effect of mesoscale eddies can be parameterised by enhancing the potential to kinetic energy conversion, i.e., the horizontal pressure gradients, or enhancing the inverse cascade of kinetic energy.

A deformation-based parametrization of ocean mesoscale eddy reynolds stresses

Ocean Modelling Elsevier 112 (2017) 99-111

JA Anstey, L Zanna

Ocean mesoscale eddies strongly affect the strength and variability of large-scale ocean jets such as the Gulf Stream and Kuroshio Extension. Their spatial scales are too small to be fully resolved in many current climate models and hence their effects on the large-scale circulation need to be parametrized. Here we propose a parametrization of mesoscale eddy momentum fluxes based on large-scale flow deformation. The parametrization is argued to be suitable for use in eddy-permitting ocean general circulation models, and is motivated by an analogy between turbulence in Newtonian fluids (such as water) and laminar flow in non-Newtonian fluids. A primitive-equations model in an idealised double-gyre configuration at eddy-resolving horizontal resolution is used to diagnose the relationship between the proposed closure and the eddy fluxes resolved by the model. Favourable correlations suggest the closure could provide an appropriate deterministic parametrization of mesoscale eddies. The relationship between the closure and different representations of the Reynolds stress tensor is also described. The parametrized forcing possesses the key quasi-geostrophic turbulence properties of energy conservation and enstrophy dissipation, and allows for upgradient fluxes leading to the sharpening of vorticity gradients. The implementation of the closure for eddy-permitting ocean models requires only velocity derivatives and a single parameter that scales with model resolution.

The statistical nature of turbulent barotropic ocean jets

Ocean Modelling Elsevier 113 (2017) 34-49

TW David, D Marshall, L Zanna

Jets are an important element of the global ocean circulation. Since these jets are turbulent, it is important that they are characterized using a statistical framework. A high resolution barotropic channel ocean model is used to study jet statistics over a wide range of forcing and dissipation parameters. The first four moments of the potential vorticity distribution on contours of time-averaged streamfunction are considered: mean, standard deviation, skewness and kurtosis. A self-similar response to forcing is found in the mean and standard deviation for eastward barotropic jets which exhibit strong mixing barriers; this self-similarity is related to the global potential enstrophy of the flow. The skewness and kurtosis give a behaviour which is characteristic of mixing barriers, revealing a bi/trimodal statistical distribution of potential vorticity with homogenized potential vorticity on each side of the barrier. The mixing barrier can be described by a simple statistical model. This behaviour is shown to be lost in westward jets due to an asymmetry in the formation of zonal mixing barriers. Moreover, when the statistical analysis is performed on eastward jets in a streamfunction following frame of reference, the distribution becomes monomodal. In this way we can distinguish between the statistics due to wave-like meandering of the jet and the statistics due to the more diffusive eddies. The statistical signature of mixing barriers can be seen in more realistic representations of the Southern Ocean and is shown to be an useful diagnostic tool for identifying strong jets on isopycnal surfaces. The statistical consequences of the presence, and absence, of mixing barriers are likely to be valuable for the development of stochastic representations of eddies and their dynamics in ocean models.

The dynamical influence of the Atlantic Multidecadal Oscillation on continental climate

Journal of Climate American Meteorological Society 30 (2017) 7213-7230

CH O’Reilly, T Woollings, L Zanna

The Atlantic multidecadal oscillation (AMO) in sea surface temperature (SST) has been shown to influence the climate of the surrounding continents. However, it is unclear to what extent the observed impact of the AMO is related to the thermodynamical influence of the SST variability or the changes in large-scale atmospheric circulation. Here, an analog method is used to decompose the observed impact of the AMO into dynamical and residual components of surface air temperature (SAT) and precipitation over the adjacent continents. Over Europe the influence of the AMO is clearest during the summer, when the warm SAT anomalies are interpreted to be primarily thermodynamically driven by warm upstream SST anomalies but also amplified by the anomalous atmospheric circulation. The overall precipitation response to the AMO in summer is generally less significant than the SAT but is mostly dynamically driven. The decomposition is also applied to the North American summer and the Sahel rainy season. Both dynamical and residual influences on the anomalous precipitation over the Sahel are substantial, with the former dominating over the western Sahel region and the latter being largest over the eastern Sahel region. The results have potential implications for understanding the spread in AMO variability in coupled climate models and decadal prediction systems.

Scale-Aware Deterministic and Stochastic Parametrizations of Eddy-Mean Flow Interaction

Ocean Modelling Elsevier 111 (2017) 66-80

L Zanna, P Porta Mana, J Anstey, T David, T Bolton

The role of mesoscale eddies is crucial for the ocean circulation and its energy budget. The sub-grid scale eddy variability needs to be parametrized in ocean models, even at so-called eddy permitting resolutions. Porta Mana and Zanna (2014) propose an eddy parametrization based on a non-Newtonian stress which depends on the partially resolved scales and their variability. In the present study, we test two versions of the parametrization, one deterministic and one stochastic, at coarse and eddy-permitting resolutions in a double gyre quasi-geostrophic model. The parametrization leads to drastic improvements in the mean state and variability of the ocean state, namely in the jet rectification and the kinetic-energy spectra as a function of wavenumber and frequency for eddy permitting models. The parametrization also appears to have a stabilizing effect on the model, especially the stochastic version. The parametrization possesses attractive features for implementation in global models: very little computational cost, it is flow aware and uses the properties of the underlying flow. The deterministic coefficient is scale-aware, while the stochastic parameter is scale- and flow-aware with dependence on resolution, stratification and wind forcing.

A note on ‘Toward a stochastic parameterization of ocean mesoscale eddies’

Ocean Modelling Elsevier 113 (2017) 30-33

I Grooms, L Zanna

Porta Mana and Zanna (2014) recently proposed a subgrid-scale parameterization for eddy-permitting quasigeostrophic models. In this model the large-scale fluid is represented as a non-Newtonian viscoelastic medium, with a subgrid-stress closure that involves the Lagrangian derivative of large-scale quantities. This note derives this parameterization, including the nondimensional proportionality coefficient, using only two statistical assumptions: that the subgrid-scale term is locally homogeneous and decorrelates rapidly in space. The parameterization is then verified by comparing against eddy-resolving quasigeostrophic simulations, independently reproducing the results of Porta Mana and Zanna in a simpler model.

Stochastic Subgrid-Scale Ocean Mixing: Impacts on Low-Frequency Variability

JOURNAL OF CLIMATE 30 (2017) 4997-5019

S Juricke, TN Palmer, L Zanna