Irreducible Southern Ocean State Uncertainty due to 1 Global Ocean Initial Conditions

How do ocean initial conditions impact historical and future climate projections in Earth system models? To answer this question, we use the 50-member Canadian Earth System Model (CanESM2) large ensemble, in which individual ensemble members are initialized using a strategic combination of different oceanic initial states and different atmospheric perturbations. We show that global ocean heat content anomalies associated with the different ocean initial states persist from initialization at year 1950 through the end of the simulations at year 2100. We also find that these anomalies most readily impact surface climate over the Southern Ocean. Ocean initial conditions affect Southern Ocean surface climate because persistent deep ocean temperature anomalies upwell along sloping isopycnal surfaces that delineate neighboring branches of the Upper and Lower Cells of the Global Meridional Overturning Circulation. As a result, up to a quarter of the ensemble variance in Southern Ocean turbulent heat fluxes, heat uptake, and surface temperature trends can be traced to variance in the ocean initial state. Such a discernible impact of varying ocean initial conditions on ensemble variance over the Southern Ocean is evident throughout the full 150 simulation years of the ensemble, even though upper ocean temperature anomalies due to varying ocean initial conditions rapidly dissipate over the first two decades of model integration over much of the rest of the globe. 16

The Earth's climate system is variable over a range of time scales, from seconds to decades 37 to millennia (Peixoto and Oort 1992). This abundant internal variability presents challenges for 38 understanding the climate system's response to anthropogenic greenhouse gas emissions and other 39 forcing agents: what part of the observed (or modeled) change in climate is due to the forcing, 40 greenhouse gas or otherwise, and what part is due to the internal variability of the Earth system? 41 "Large ensembles" are an important tool for separating the forced response from internal vari-The importance of the ocean state for driving Earth system evolution is already well recognized

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Given this wealth of evidence that the ocean state impacts climate evolution, it is reasonable to 99 hypothesize that large ensembles initialized from many different ocean states may exhibit variabil-100 ity not found in those initialized from a single ocean state. Indeed, one prior study exploring the 101 matter suggests that initializing a large ensemble with a range of ocean initial conditions increases historically-forced large ensemble starting from several distinct ocean initial states displayed sig-105 nificantly greater variance in global and regional temperature trends, even a century after initialization, compared to one starting from only a single ocean initial state. More specifically, the phase 107 of the Atlantic Meridional Overturning Circulation from which an ensemble member was initial-108 ized influenced northern hemispheric temperature trends, particularly in those regions proximal to the Southern Ocean where such initial conditions continue to impact ensemble variance in surface 130 climate, up to 150 years following model initialization in 1950 ( §3c). In §4, we conclude by dis-131 cussing the implications of our findings for the design of large ensembles, and how climate system 132 predictability may be limited by our imperfect knowledge of prior ocean states.  Hemispheric extratropical circulation features (including SAM, jet position, and location of the 152 maximum westerly wind stress; see Thomas et al. 2015). CanESM2 also simulates both the mean state and variability of meridional ocean heat transport well, including its gyre and overturning 154 components (see Yang and Saenko 2012).

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As illustrated in Figure 1, ocean initial conditions for the 50-member CanESM2 large ensemble 156 are constructed by branching 5 runs from different points in an 1850s pre-industrial control exper-a. Decomposition of Ensemble Variance 175 We now describe the process by which we estimate how much variance in the whole ensemble 176 is attributable to ocean initial conditions, and how much is attributable to atmospheric micro-177 perturbations.

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The variance σ 2 X in a climatically-relevant quantity X (such as temperature, surface fluxes, ocean 179 heat content, or others) between all ensemble members over a given year is computed as where X(t) is the average of X across all ensemble members at year t, and n is the number of 181 ensemble members (equal to 50 in the CanESM2 large ensemble). While this can be a function of 182 time, we drop this time-dependent notation in the following description for the sake of clarity.

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The total variance between ensemble members over a given year can be approximated as the 184 sum of two variances: (1) the variance between micro-ensembles, due to the different ocean states 185 used to initialize each micro-ensemble, is denoted by σ 2 X,ocean ; and (2) the variance within micro-186 ensembles, due to application of different atmospheric micro-perturbations in each ensemble mem-187 ber, is denoted by σ 2 X,atmos . In other words, In equation (2) above, the error, ε, includes the nonlinear interaction term; ε generally constitutes 189 less than 5% of the total variance, which we drop for convenience. This approximation, inspired 190 by the decomposition of variance performed by Hawkins and Sutton (2009), makes sources of 191 ensemble variance simple to compute and easy to attribute, to first-order.

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The variance within micro-ensembles, σ 2 X,atmos is computed as the average of the variance within each micro-ensemble: where X k, j is the value of X in the j-th member of the k-th micro-ensemble, and X k is the mean 195 of X in micro-ensemble k. In the above equation, m is the number of ensemble members in each 196 micro-ensemble (equal to 10 for the CanESM2 large ensemble), and p is the number of micro-197 ensembles (5 for the CanESM2 large ensemble). The variance between micro-ensembles, σ 2 X,ocean ,

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is computed as the variance of the individual micro-ensemble means: where X is the mean of X in the entire ensemble (i.e. over all 50 members of the CanESM2 large 200 ensemble).

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Because individual ensemble members within each micro-ensemble all start with identical ocean 202 initial conditions at year 1950, the variance within micro-ensembles, σ 2 X,atmos , is attributable solely 203 to initial micro-perturbations (on the order of machine error) in the surface atmospheric temper-204 ature. Similarly, the variance between micro-ensembles, σ 2 X,ocean , arises from the different ocean 205 initial conditions in each micro-ensemble; by considering the variance of the micro-ensemble 206 means, the impact of varying atmospheric micro-perturbations is averaged out. The fraction of the 207 ensemble variance in X due to ocean initial conditions at time t can then be written as follows: We label χ OcnICs (t) as statistically distinct from zero using a bootstrapped 90%-confidence ap-209 proach as follows. For 100 realizations, we randomly assign each of the 50 ensemble mem-210 bers into 5 micro-ensembles of 10 members each, and recompute the variance between micro-211 ensembles ( σ 2 X,between ) and within micro-ensembles ( σ 2 X,within ). These randomly-resampled 212 micro-ensembles are synthetic, in that their members do not share the same ocean initial con-213 ditions as do members of the original micro-ensembles. Therefore, non-zero values of σ 2 X,between 214 are attributable solely to chance, not to ocean initial conditions. We repeat the above randomiza-215 tion a total of 100 times, to get 100 synthetic realizations of σ 2 X,between , to compare to the variance 216 between the real micro-ensembles, σ 2 X,ocean . We treat σ 2 X,ocean as statistically different from zero 217 if σ 2 X,ocean > σ 2 X,between at least 90% of the time, accepting a 10% possibility that the difference 218 could be due to chance. We use a 90% confidence level, rather than the more customary 95% level, 219 in order to avoid type II errors that are more likely to arise when comparing the variance of two  micro-ensembles arise from internal variability, deep ocean temperature differences are generated by drift in the pre-industrial control experiment (see §2). 235 We further note that there is little coherence between anomalies over different areas: individual 236 micro-ensembles are neither uniformly cooler than average globally nor uniformly warmer. For  We now compute the fraction the total variance in ocean potential temperature in the CanESM2 319 large ensemble that is attributable to ocean initial conditions, χ OcnICs = σ 2 θ , ocean /σ 2 θ (i.e. the 320 fraction of the total ensemble variance that is between micro-ensembles, as detailed in Decompo-  However, in the upper ocean between 60S and 70S, we find that approximately 50% of ensemble 351 variance is between micro-ensembles over all time periods (Fig 8a-d), and is therefore attributable 352 to differences in ocean initial conditions. Indeed, we note a 'plume'-like feature that emerges temperature anomalies, which are due to differences in ocean initial conditions between micro-364 ensembles. 365 We also note that only about half of the temperature variance in the Southern Ocean upwelling 366 branch of the overturning circulation is attributable to ocean initial conditions (particularly over  The primary mechanism by which converging ocean heat impacts the surface climate is through 390 changes in surface turbulent (sensible and latent heat) fluxes (Sutton and Mathieu 2002). This rela-391 tionship is apparent from the physics that governs evolution of the ocean mixed layer temperature, where ρ is the density of seawater, c w is its heat capacity, h ML is the mixed layer depth, v is the  Similarly, surface temperature trends over the Southern Ocean also exhibit significant variance 413 due to ocean initial conditions (Fig 9c, which shows χ OcnICs = σ 2 dT s /dt, ocean /σ 2 dT s /dt ; note area be- larly to the upper ocean heat content variance, and is also weaker in magnitude.

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In Figure 10, we examine surface flux anomalies (from 55S to the pole) over four time periods in 419 each micro-ensemble, calculated as the difference between the micro-ensemble mean and the full 420 ensemble mean (i.e. F X, k (t) − F X (t)). We find systematic differences between turbulent fluxes, 421 both latent (F LH ; Fig 10a) and sensible (F SH ; Fig 10b), in micro-ensembles with colder-than-422 average deep ocean temperatures (micro-ensembles 1 and 2) compared to those with warmer- where R ↓ SW +LW is the net (downward, shortwave plus longwave) radiative flux at the surface. In

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In other words, persistent cool anomalies in the deep ocean tend to augment ocean heat uptake 449 with CO 2 forcing, while persistent warm anomalies in the deep ocean tend to suppress ocean heat 450 uptake.

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In CanESM2, the micro-ensemble mean ocean heat uptake anomaly scales approximately one-452 to-one with the initial micro-ensemble mean deep ocean temperature anomaly: For example, an initial mean deep ocean temperature anomaly of -0.1K, as in micro-ensemble 1, 454 gives rise to approximately a 0.1 W m −2 mean anomaly in ocean heat uptake in micro-ensemble 1 455 over the first 100 years of the experiment (i.e. from 1950 to 2000, and from 2000 to 2050; Fig 10). 456 We note that this scaling depends on the rate at which the ocean meridional overturning upwells 457 anomalies from the deep ocean, which varies substantially between global climate models (see,

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Though it is clear that Southern Ocean heat uptake is sensitive to differences in deep ocean 460 temperature between micro-ensembles, we note that the ensemble range (i.e. the total ensemble 461 spread, which is attributable to both atmospheric micro-perturbations and ocean initial condition

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In Figure 11, we examine the variance in Southern Ocean heat uptake (from 55S to the pole, 476 as in Fig 10c) between micro-ensembles (σ 2 OHU, ocean ; blue lines) and within micro-ensembles 477 (σ 2 OHU, atmos ; purple lines). The total variance in the ocean heat uptake appears to decrease slightly 478 over the first several decades, but thereafter remains relatively constant (Fig 11a, black line). This   537 Surprisingly, we do not find that deep ocean temperature anomalies impact the Northern Hemi-538 sphere oceans, particularly the Arctic, over such long time scales. We submit that this is because  We hypothesize that this difference may be due to the substantial multidecadal periodicity in the Year 2271 Year 2321 Year 2371 Year 2421 Year 2471 Micro-ensemble 1 Micro-ensemble 2 Micro-ensemble 3 Micro-ensemble 4 Micro-ensemble 5 Years into an 1850s Preindustrial Control Run          flux, and (c) 30-year surface temperature trends, attributable to variance between micro-ensembles (χ OcnICs = σ 2 X,ocean /σ 2 X ) over the full 150 years of the ensemble. Hatched areas indicate that the fraction of ensemble variance attributable to ocean initial conditions is not statistically distinct from zero at p < 0.1 at more than 25% of the grid cells at that latitude. Dashed horizontal pink lines at 40S and 70S delineate the Southern Ocean.