ocean model uncertainty in climate prediction

Ocean Model Uncertainty in Climate Prediction

Laure Zanna

Atmospheric, Oceanic and Planetary Physics,University of Oxford, OX1 3PUE-mail: [email protected]

1 Introduction

Numerical simulations are showing that land warming over the past fifty years occurred largely in re-sponse to an overall warming of the oceans rather than as a direct response to increasing greenhousegases concentration over land (Compo and Sardeshmukh, 2009). Hydrodynamic-radiative teleconnec-tions led to moistening and warming of the air over land and increase of the downward longwave radia-tion at the surface. Needless to say that the oceans may themselves have warmed from a combination ofnatural and anthropogenic influences but this mere fact addresses the crucial role of the ocean dynamicsand thermodynamics in future climate projections.

The ocean is effectively forced at the surface by momentum, heat, and freshwater fluxes, on a wide rangeof temporal and spatial scales, while energy dissipation occurs at molecular scales in short and abruptbursts. The relationship between the large scale circulation and small scale mixing is a consequence ofthe nonlinear turbulent nature of the ocean, with energy exchanged among all scales. Numerical climatemodels are based on such well-established physical principles. They have demonstrated to properlyreproduce many observed features of the climate therefore enhancing the confidence in model estimatesof climate projections.

Despite recent improvements in climate modelling, small and fast unresolved physical processes stillintroduce large model errors. Model error in climate models can be either be systematic or random andmanifest itself in different ways such as a lack of internal variability, underestimates of the frequency ofstorms or errors in mean temperature. Systematic errors are associated with the model framework andthe parametrization choices, while random errors are associated with unrepresented statistical fluctua-tions in sub-grid physical processes (e.g. convection or mixing).

2 Model errors in ocean components

Figure 1 shows the typical error of zonally averaged annual mean ocean temperature, between climatemodels from the Intergovernmental Panel on Climate Change (IPCC) and observations, which reachesseveral degrees in certain regions of the ocean (Solomon et al., 2007).

A poor representation of the thermodynamical and dynamical ocean properties lead to a poor represen-tation of the mean state of the climate (e.g., Fig. 1) and its variability. For example, let us considerthe Atlantic meridional overturning circulation (MOC) at 30N (defined as the zonally averaged stream-function), often used to describe the overall circulation and the transport of heat and salt from low tohigh-latitudes. The spread between the different IPCC models in their the mean value of the MOC andvariability is quite large (Fig. 1) and often outside of the observational estimates available for the 20thcentury. The spread in the mean state and variability is translated in an even larger spread in the fu-ture estimates of the MOC during the 21st century. The poor representation of oceanic processes hasobvious implications and consequences. It decreases the reliability of current and future estimates of

ECMWF Workshop on Model Uncertainty, 20-24 June 2011 101

ZANNA, L.: OCEAN MODEL UNCERTAINTY IN CLIMATE PREDICTION

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Figure 10.15. Evolution of the Atlantic meridional overturning circulation (MOC) at 30°N in simulations with the suite of comprehensive coupled climate models (see Table 8.1 for model details) from 1850 to 2100 using 20th Century Climate in Coupled Models (20C3M) simulations for 1850 to 1999 and the SRES A1B emissions scenario for 1999 to 2100. Some of the models continue the integration to year 2200 with the forcing held constant at the values of year 2100. Observationally based estimates of late-20th century MOC are shown as vertical bars on the left. Three simulations show a steady or rapid slow down of the MOC that is unrelated to the forcing; a few others have late-20th century simulated values that are inconsistent with observational estimates. Of the model simulations consistent with the late-20th century observational estimates, no simulation shows an increase in the MOC during the 21st century; reductions range from indistinguishable within the simulated natural variability to over 50% relative to the 1960 to 1990 mean; and none of the models projects an abrupt transition to an off state of the MOC. Adapted from Schmittner et al. (2005) with additions.

Figure 1: Left: Root-mean-square model error of annual mean temperature climatology over the period 1957-1990, zonally averaged over all ocean basins (in ◦ C). The typical error, based on all available IPCC modelsimulations, is plotted as function of depth and latitude. Right: Evolution of the Atlantic meridional overturningcirculation (MOC) at 30N using a suite of coupled climate models under the the SRES A1B emissions scenariofor 1999 to 2100. Some of the models continue the integration to year 2200 with the forcing held constant at thevalues of year 2100. Observationally based estimates of late-20th century MOC are shown as vertical bars on theleft (Solomon et al., 2007).

natural- and human-induced climate change given that any analysis is affected by the large model errors.Information can undoubtedly be inferred from the output of the different models - though multi-modelcomparison but these inference can be limited. Another path to provide useful estimates and spreadin projections can be obtained from perturbed parameter ensembles (e.g., Tett et al., 1999) howeverstructural uncertainties are not properly account for. Either with multi-model ensembles or perturbed-parameters ensembles, it is extremely difficult to properly account for all model errors and understandcauses of errors and associated mechanisms.

3 Singular Vectors in ocean models for climate predictions

Similarly to numerical weather prediction (NWP) and El Nino/Southern Oscillation (ENSO) prediction,the decadal prediction community is interested in making forecasts of different quantities such as re-gional sea surface temperatures, surface air temperatures or the strength of the MOC. In addition toproviding forecasts, it is necessary to provide reliable uncertainty estimates and even more important tounderstand the deficiencies of our observational system and various models. Singular vectors have beenextremely useful in the NWP community to sample errors in initial conditions and have been provenquite informative in interannual and decadal predictions as well.

Estimates of singular vectors in the GFDL coupled atmosphere-ocean general circulation model CM2.1(Delworth et al., 2006) used in the IPCC can inform us on the predictability of the MOC for example.Using the GFDL CM2.1 (Fig. 2), the growth of temperature, salinity and MOC anomalies are studiedin details in Tziperman et al. (2008). A few steps are required to approximate the singular vectors ofa coupled climate model, especially if the tangent linear and adjoint models are not available as it isthe case for GFDL CM2.1. First, a reduced space based on empirical orthogonal functions (EOFs)of temperature and salinity anomaly fields in the North Atlantic from the output of the control run ofGFDL CM2.1 is constructed. Second, under the assumption that the dynamics of this reduced space islinear, the propagator of the system is evaluated and the singular vectors of domain integrated energy andMOC are computed. The singular vectors can growth significantly over a period of 5 to 10 yr (Fig. 2),providing an estimate of the predictability time of the North Atlantic ocean circulation in this model.Obviously, the results are merely an upper bound on the predictability in this GCM. The methodologypresented may be used to produce initial perturbations to the ocean state that may result in a stricterestimate of ocean predictability than the common procedure of initializing with an identical ocean stateand a perturbed atmosphere. Moreover, the spatial structure of the leading singular vectors in this model,shown in Fig. 3, indicates a large sensitivity to anomalies at high latitudes especially at the boundary

102 ECMWF Workshop on Model Uncertainty, 20-24 June 2011


Maximum MOC Amplifica/on Curves

Figure 2: Left: Sea surface temperature: model (GFDL CM2.1) minus observations; Right: Maximum amplifi-cation curves. See Tziperman et al. (2008) for further details.

between the subtropical and subpolar gyres and in the subpolar gyre.

While the computation of the singular vectors in a complex climate model can be useful to estimateinitial uncertainties in the model, the analysis remains extremely difficult. Therefore it might be rec-ommended to turn to idealized models to further investigate error growth in ocean models for decadalpredictions.

Figure 3: Leading SV of temperature (left), salinity (middle) and density (right).

The limits of predictability of the MOC and upper ocean temperatures due to errors in ocean initialconditions and model parametrizations are investigated in an idealized configuration of the ocean MITgeneral circulation model (MITgcm; Marshall et al., 1997a,b) shown in Fig. 4. The optimal three-dimensional spatial structures of temperature and salinity perturbations, defined as the leading singularvectors and generating the maximum amplification of MOC and upper ocean temperature anomalies,are evaluated using tangent linear and adjoint models.



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A large amplification of MOC anomalies, mostly due to the interference of stable nonnormal modes,is initiated by the optimal perturbations. The largest amplification of MOC anomalies, found to beexcited by high-latitude deep density perturbations in the northern part of the basin especially at theboundary between the two gyres and in the subpolar gyre, is achieved after about 7.5 years (Fig. 5) .The anomalies grow as a result of a conversion of mean available potential energy into potential andkinetic energy of the perturbations, reminiscent of baroclinic instability. The time scale of growth ofMOC anomalies can be understood by examining the time evolution of deep zonal density gradients,which are related to the MOC via the thermal wind relation. The velocity of propagation of the densityanomalies, found to depend on the horizontal component of the mean flow velocity and the mean densitygradient, determines the growth time scale of the MOC anomalies and therefore provides an upper boundon the MOC predictability time (Zanna et al., 2011a).

If the singular vectors are constrained to the upper ocean, the maximum growth is found at about 18.5years. This timescale of 18.5 years is longer than the 7.5 years obtained when the perturbations areallowed over the entire ocean depth. This result implies that the predictability timescales of 10 to 20years obtained when only atmospheric perturbations are used to initialize ensemble experiments (e.g.,Griffies and Bryan, 1997; Pohlmann et al., 2004) may be overestimates. In addition to the difference ingrowth timescales, the MOC anomaly appears to be less sensitive to upper ocean perturbations than todeeper ones. We find here that a density perturbation of 0.02 kg/m3 in the upper ocean leads to an MOCanomaly of 1.7 Sv compared to 2.4 Sv when the anomalies are mostly located in the deep ocean (Zannaet al., 2011b).

The results suggest that the non-normal linearized ocean dynamics can give rise to enhanced MOCvariability if, for instance, overflows, eddies, and/or deep convection can excite high-latitude densityanomalies in the ocean interior with a structure resembling that of the singular vectors found. Thefindings also indicate that errors in ocean initial conditions or in model parameterizations or processes,particularly at depth, may significantly reduce the Atlantic ocean circulation and climate predictabilitytime to less than a decade.

4 Model resolution & the need for new parametrizations

Dynamical processes such as eddies, mixing and convection are crucial for climate as they impact thelarge-scale ocean circulation and uptake of tracers (temperature and carbon). Many of these processesare excited at the ocean surface (especially at high latitudes), at the interface between the oceanic reser-



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voir of heat, carbon and freshwater and the overlying atmosphere. To illustrate the energetic behaviourof the upper ocean, Fig. 6 shows the sea level height in a 1/10◦ horizontal resolution ocean model (Zhai,personal communication).

Ocean models used for climate studies and predictions typically have a horizontal resolution of abouthundred kms. Therefore mesoscale and sub-mesoscale variability (eddies, turbulent mixing, internalwaves and convection) are sub-grid scale and must be parameterized. As previously mentioned, the ma-jor source of model error is due to the imperfect or missing parameterizations of unresolved processes.

Figure 6: Sea surface elevation from an eddy-resolving model with 1/10 degree horizontal resolution.

Mesoscale eddies in the ocean interior are quasi-adiabatic and therefore their effect should be repre-sented as an eddy-induced velocity, which is the core of the Gent-McWilliams parametrization (Gentand McWilliams, 1990, GM). GM is now the standard parametrization in coupled climate models for in-terior ocean eddies. However upper ocean eddies have rather different dynamical properties, mesoscaleeddies (50 km scale) generated through baroclinic instability of the full water column and submesoscaleeddies (1 km scale) generated through ageostrophic baroclinic instabilities within the boundary layer.Currently parametrizations of upper ocean eddies are lacking in coupled climate models used in climatepredictions, though a few recent attempts have been made recently in idealized models. Fox-Kemper



et al. (2008) show that errors in upper ocean heat transport at high latitudes in the Southern Ocean canbe dramatically reduced by introducing the parametrized effects of the mesoscale eddies. Furthermore,the mixed layer depth can be improved by including the effect of submesoscale eddies, which involvesslumping fronts restratifying the boundary layer. Dynamical effects from upper ocean eddies have asubstantial impact on boundary layer and therefore on sea-surface temperatures, mixed layer depth, heatuptake which are key quantities for climate variability on timescales from days to decades and beyond.

5 Conclusions and Future directions

While the effects of anthropogenically-forced climate change are expected to continue, future regionalchanges on timescales of a few years to decades ahead will also be strongly influenced by natural climatefluctuations. Understanding and modelling these variations remains a challenge and unresolved oceanprocesses in climate models can be the cause of large model uncertainties in the predictions. Despitea few recent improvements described in the previous sections, parametrizations of unresolved oceanprocesses remain of utmost interest and difficulty. The development of unconventional (e.g. stochastic)parametrizations should therefore be addressed.

Given that the fast and small-scale processes set the properties of the mean climate and participatein exciting variability, it should be interesting to explore how the different parametrizations of oceanmixed-layer and convection affect the mean state and variability in climate models. Several interestingregions could be explored, especially the Atlantic and the Southern oceans due to the important roleof the overturning circulation and its potential role in climate with interannual to decadal variationsmodulating the global mean temperature.

Studies using low-order idealized climate models have shown the benefits of stochastic noise on therepresentation of the climate. Stochastic forcing can excite variability on all timescales (Perez et al.,2005; Saravanan and Mcwilliams, 1997; Alley et al., 2001; Zanna and Tziperman, 2008). For example,the addition of surface atmospheric stochastic noise can explain and reproduce the irregularity of ENSOand its amplitude, which purely deterministic models are incapable of.

Incorporating stochastic physics and parametrizations in ocean models could potentially improve therepresentation of the climate system in numerical models and provide reliable climate change projectionsand accurate estimates of uncertainties associated with the projections due to model errors. Stochasticparameterizations have the potential to reduce model error, they can change the mean and variance of aprobability distribution function.

A few studies have investigated the potential of the ocean mesoscale eddy field to be properly repre-sented by a stochastic process in idealized ocean models (Berloff, 2005) however this area is still largelyunder studied. Over the past year, many physical oceanographers have slowly built upon the knowledgedeveloped by the atmospheric community regarding stochastic parametrizations. Several groups arenow conducting research in developing stochastic parametrizations of ocean processes and introducingstochastic physics in the ocean component of coupled models for predictions.

Bridging the gap between observations, theory and modeling is crucial. Ocean observations are becom-ing more dense (both in space and time). Proper analysis of this data is needed but more importantlylinking the newly available data to theory, in search for new parametrizations and also to test, validateand constrain our models. For example, ocean heat content, ARGO and altimetry could be used toreduced model uncertainties to increasing CO2, especially on regional scales. Moreover, regional andglobal statistical models based on observations could be used as benchmarks for IPCC models, bothto test that the models capture the correct properties but also demonstrate the appropriate skill (Zanna,2011).



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References

Alley, R., Anandakrishnan, S., and Jung, P. (2001). Stochastic resonance in the north atlantic. Paleo-ceanography, 16(2):190–198.

Berloff, P. S. (2005). Random-forcing model of the mesoscale oceanic eddies. J. Fluid Mech., 529:71–95.

Compo, G. and Sardeshmukh, P. (2009). Oceanic influences on recent continental warming. Clim. Dyn.,32(2-3):333–342.

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