Ocean surface temperature variability: Large model–data differences at decadal and longer periods

Significance

Determining magnitudes of sea surface temperature variability is important for attributing past and predicting future changes in climate, and generally requires the use of proxies to constrain multidecadal and longer timescales of variability. We report a multiproxy estimate of sea surface temperature variability that is consistent between proxy types and with instrumental estimates but strongly diverges from climate model simulations toward longer timescales. At millennial timescales, model−data discrepancies reach two orders of magnitude in the tropics, indicating substantial problems with models or proxies, or both, and highlighting a need to better determine the variability of sea surface temperatures.

Abstract

The variability of sea surface temperatures (SSTs) at multidecadal and longer timescales is poorly constrained, primarily because instrumental records are short and proxy records are noisy. Through applying a new noise filtering technique to a global network of late Holocene SST proxies, we estimate SST variability between annual and millennial timescales. Filtered estimates of SST variability obtained from coral, foraminifer, and alkenone records are shown to be consistent with one another and with instrumental records in the frequency bands at which they overlap. General circulation models, however, simulate SST variability that is systematically smaller than instrumental and proxy-based estimates. Discrepancies in variability are largest at low latitudes and increase with timescale, reaching two orders of magnitude for tropical variability at millennial timescales. This result implies major deficiencies in observational estimates or model simulations, or both, and has implications for the attribution of past variations and prediction of future change.

Variations in sea surface temperature (SSTs) have widespread implications for society and are the basis of most regional decadal prediction efforts (1). Magnitudes of variability in regional SSTs are inferred either using observations or simulations from general circulation models (GCMs). At synoptic and interannual timescales, there is overall agreement between observational and GCM estimates of SST variability (2–4). At decadal timescales, however, instrumental records generally show greater regional SST variability than found in the Coupled Model Intercomparison Project Phase 5 (CMIP5) ensemble of GCM simulations (4) and in earlier simulations (5–7). Discrepancies are greatest at low latitudes where model−data mismatches in variance reach a factor of 2 (Fig. 1).

Fig. 1.

Variance ratio of the observed and simulated sea surface temperature variance for multidecadal (20−50 y) timescales from ref. 4. Simulated variance is from the mean variance of all CMIP5 historical simulations. Observed variance is from HadSST3 (8) and is corrected for sampling and instrumental errors. Locations of the temperature proxies used in this study are marked as symbols.

Estimating regional SST variability at multidecadal and longer timescales presents a quandary. Discrepancies with instrumentally observed SST variability at decadal timescales calls into question the credibility of GCM estimates at longer timescales. At the same time, instrumental observations covering more than 100 y of SST variability are sparse. For example, whereas 68% of ocean grid boxes in the Climate Research Unit’s instrumental compilation of SSTs have a 30-y interval with an observational density of at least 100 observations per year, only 19% of grid boxes have such coverage over a 100-y interval (8). Furthermore, SST variability observed during the last century represents contributions from natural and anthropogenic sources that are difficult to disentangle and are not necessarily representative of any other interval (9).

One is inevitably led to using paleoclimate proxies to constrain multidecadal and longer-term variability. Numerous paleoclimate reconstructions document low-frequency SST variability (10–15), but the degree to which these reconstructions afford quantitative constraints of annual average SST variability is unclear because of issues including noise, sampling artifacts, and possible proxy-specific biases. In the following, we apply a recently introduced procedure for filtering out artifacts from proxy spectral estimates (16) to a global dataset of high-resolution proxies to estimate SST variability from interannual to millennial timescales.

We next systematically compare these observational estimates against results from long GCM simulations. Although foregoing studies have analyzed proxy−model agreement for global average temperature (17) and other climate indices (18), to our knowledge, this is the first proxy−model comparison of regional SST variability.

Proxy Data

Building on an existing compilation (19), we analyze 33 high-resolution proxy records of marine temperature sampled from marine sediment cores (Uk37 and planktonic Mg/Ca) and corals (Sr/Ca, δ¹⁸O, and growth rate) (Fig. 2). We use paleo observations extending back no more than 7,000 y because observations from earlier in the Holocene may be influenced by transient adjustments associated with the last deglaciation. Proxy results are compared against instrumental SSTs (8) and long GCM simulations (20–23) (SI Appendix, Tables S1 and S2). To facilitate intercomparison, all proxy records are recalibrated using a single temperature relationship for each proxy type (SI Appendix, Proxy Calibration). The importance of using a consistent calibration can be seen in that the spatial correlation between instrumental and coral-derived interannual temperature variance is 0.84, whereas it would only be 0.26 were individually published calibrations instead used (SI Appendix, Fig. S4).

Fig. 2.

Raw proxy data (black) plotted against the corresponding model simulations sampled at the proxy locations (cyan). Both simulations and proxies are detrended, and the simulations are temporally averaged to the same resolution as the proxies. To provide continuous temporal overlap with the proxy records, interannual resolution records (A) are compared against a comprehensively forced simulation (20), whereas centennial resolution records (B and C) are compared against a GCM simulation forced only by orbital variations (21). Differences in variability between model simulations are small relative to model−data discrepancies.

The spectra of each proxy record in our collection is estimated using a multitaper procedure. Results indicate that centennial and millennial variations are substantially larger than those found at decadal timescales (Fig. 3A), as has been previously noted (10, 11, 14, 24), but the magnitude and shape of the spectral estimates between different proxy types is incommensurate. At overlapping frequencies, the Mg/Ca records average 2.1 times more variance than the Uk37 records and proportionately more high- than low-frequency variability. Mg/Ca estimates also show an order of magnitude more variability than indicated by coral records where their resolved frequencies overlap, near 1/200 y⁻¹. These discrepancies must be resolved if proxies are to provide a plausible estimate of temperature variability or afford a credible test of GCM simulations of SST variability (25).

Fig. 3.

Spectral estimates from proxy and instrumental SSTs. (A) Raw proxy spectral estimates. (B) Proxy spectral estimates after correction for measurement noise, bioturbational smoothing, and aliasing. (C) Same as B but showing the Cariaco Mg/Ca based SST spectra instead of corals. The Cariaco Mg/Ca record is not included in A and B. Insets show high-resolution proxy spectra and HadSST3 instrumental spectra estimated using the time interval in which they overlap. All other spectra are calculated over their full duration for years before 1950. The 95% confidence intervals are indicated by shading, and account for uncertainties in the Uk37 and Mg/Ca correction process where appropriate.

One possibility is that regional differences in temperature variability account for the discrepancies between proxies. Nearby Mg/Ca and Uk37 records are, however, in no better agreement. Furthermore, the core site locations associated with Mg/Ca measurements do not show any greater variability than the Uk37 sites in either instrumental records or GCM simulations (16). Discrepancies between coral and Mg/Ca or alkenone estimates are similarly unresolved by spatial variability. Instead, it appears that differences in variability between proxy types arise from differential noise influences.

Noise sources can be grouped into three categories involving errors associated with measurement noise, mixing of sediments by biological activity that leads to smoothing of measured signals, called bioturbation (26), and aliasing of high-frequency variability associated with irregular or infrequent sampling (27, 28). Other sources of uncertainty are also present, but we will show that the above well-recognized noise sources are sufficient to resolve interproxy discrepancies. Our approach is to design a filter for each proxy record to remove the noise effects (or amplify variability where it has been suppressed by bioturbation) depending on proxy type, sediment accumulation rates, and local SST variability. See Materials and Methods and ref. 16. for details.

There are four indications that the proxy correction technique gives accurate results. First, the technique recovers true SST variability in expectation when applied to synthetic records. Second, the inferred noise values correspond with independently derived error estimates available for four of the Mg/Ca records (16). Third, the corrected proxy spectral estimates for corals, Mg/Ca, and Uk37 are consistent among themselves in terms of magnitude and relative proportions of variability (Fig. 3 B and C). Greater reduction in Mg/Ca proxy variance (−53%) relative to that of Uk37 (−25%) and corals (−12%) results from the small numbers of individual samples combined together for each Mg/Ca estimate and the larger aliasing correction that is consequently required. Fourth and finally, records having a frequency resolution that overlaps with the instrumental record—corals and the high-resolution Mg/Ca record from the Cariaco Basin (10)—are consistent to within uncertainties with spectral estimates from local instrumental SST records (Fig. 3 B and C, Insets).

Model Simulations

Numerous long GCM simulations exist that can be evaluated against our proxy results (SI Appendix, Table S2). We focus on a five-member ensemble of simulations from the ECHAM5/MPIOM Earth system model that extends over the last 1,200 y and includes forcing associated with variations in solar output, Earth’s orbital configuration, atmospheric greenhouse gas concentrations, volcanic aerosols, and land use changes (20). We also analyze longer simulations from the same model with no forcing (20) or only using orbital forcing (21). All ECHAM5/MPIOM simulations produce similar local SST variability (Fig. 4) and have essentially constant spectral energy at frequencies below 1/50 y⁻¹.

Fig. 4.

SST spectral estimates from ECHAM5/MPIOM and the CMIP5/PMIP3 collection of simulations. The ECHAM5/MPIOM spectral estimates are from simulations that are unforced, forced only by changes in Earth’s orbital configuration, and forced using orbital, solar, volcanic, greenhouse gas, and land-used changes. The range of spectral estimates from the fully forced CMIP5/PMIP3 past1000 simulations are also shown. In all cases, spectral energy is nearly constant at frequencies below 1/50 y⁻¹.

In addition to ECHAM/MPIOM, we also analyze the 15 long-term historical simulations from across the 8 models contained in the CMIP5/Paleoclimate Modelling Intercomparison Project Phase III (PMIP3) last millenium ensemble (22, 23) (SI Appendix, Figs. S2 and S3). The ECHAM5/MPIOM simulations produce SST variability in the upper range of the CMIP5/PMIP3 simulations across all timescales. It follows that model−data differences discussed with respect to ECHAM5/MPIOM, hereafter simply referred to as the model, also hold more generally.

Results

Proxy spectral estimates (Fig. 3) show substantially greater variability than found in model simulations (Fig. 4), with the discrepancy increasing from interannual to millennial timescales (Fig. 5). There is also a clear meridional structure in the model−data mismatch that persists across timescales (Fig. 5). The tropically amplified pattern of model−data mismatch found at decadal timescales using instrumental records (Fig. 1) is also found at longer timescales (Fig. 5), but with proxy estimates showing systematically greater variability. At low latitudes (30°S−30°N), the proxy estimates average 45 times greater variance than is associated with model SST variability [95% confidence interval (c.i.) of 22–92] at multicentennial timescales (Fig. 5D), and this discrepancy grows to more than a factor of 100 (c.i. 118–1,470) at millennial timescales (Fig. 5E). Although averages can be sensitive to outliers, similar order-of-magnitude discrepancies are found when medians are instead used, giving ratios of 23 (c.i. 8–41) and 120 (c.i. 15–290) at multicentennial and millennial timescales, respectively.

Fig. 5.

Latitudinal dependence of the model−data mismatch at different timescales. Shown is the variance ratio between observed and GCM simulated sea surface temperature, where simulations are sampled at the data positions and observational estimates are corrected for sampling and measurement errors. Proxy comparisons (dots) are relative to different versions of the ECHAM5/MPIOM model results: at timescales less than 1,000 y (A−D), comparisons are from the fully forced results, whereas comparisons at millennial timescales (E) are for the orbital-only results. Ratios derived from the orbital-only simulation are also shown as small stars in D and demonstrate that results are consistent using either model version. Variance ratios from instrumental observations (HADSST3) at the proxy positions (cyan square) are shown in A and B. Error bars show 67% confidence intervals, comparable to a SE, and include uncertainties associated with the correction process (see Materials and Methods).

Discrepancies between model and data SST spectral estimates are smaller at midlatitudes to high latitudes (>30°N or S). At decadal timescales (Fig. 1), the models have slightly greater variance than the instrumental observations. At multicentennial timescales (Fig. 5D), proxy estimates average 10 (c.i. 6–18) times greater variance, and at millennial timescales, 49 (c.i. 34–151) times greater variance (Fig. 5E). Medians give 6 times (c.i. 3–8) and 35 times (c.i. 13–50) the variance at multicentennial and millennial timescales, respectively. Essentially the same results are obtained from either instrumental or coral records at high frequencies, from either Mg/Ca or Uk37 records at low frequencies, and using any of the CMIP5/PMIP3 simulations (SI Appendix, Figs. S2 and S3), indicating that the present results are robust and generalizable.

In considering possible explanations for model−data discrepancies, we begin with the data. One possibility is that model grid boxes are unrepresentative of the scale of variability sampled by the proxies, but this seems unlikely because instrumental and proxy records agree with the models at interannual timescales (Figs. 3 and 5 A and B). Furthermore, the spatial coherence of temperature variability generally increases toward longer timescales (9) and discrepancies between point and grid box estimates would be expected to correspondingly diminish toward longer timescales, if gridding were at issue. Another issue is that proxy sites are disproportionately located in regions near the ocean margins—where higher sedimentation rates afford higher-resolution records. However, we find no systematic difference in model−data discrepancy between coastal and more interior sites, in agreement with other findings that coastal point observations and open ocean gridded SSTs have similar variability (29).

Another data issue is for foraminifera and alkenone-producing species to record specific seasons or dwell in subsurface regions having different temperature variability, but sampling the variability within single seasons and at different depth levels fails to resolve the model−data mismatch (SI Appendix, Fig. S6). Temporal changes in growth seasonality or depth habitat could lead to spurious proxy variability, and alkenone records may also be subject to time variable resuspension and transport (30). These processes are not identifiable in our results, however, in that estimates agree across the three different classes of proxies (Fig. 3), similar latitudinal model−data discrepancies are found when considering either the instrumental or proxy records (Fig. 5), and similar scaling is found in Mg/Ca records from distinct foram types (i.e., ruber and bulloides). Moreover, studies of foraminifera generally indicate that, in seeking homeostasis, there is a tendency toward muting, as opposed to increasing, the magnitude of recorded temperature variability (31). There are also sources of uncertainty associated with calibrating coral proxy records of sea surface temperature variability (32), but comparison between different coral-based SST proxy types and between coral and instrumental data suggests no systematic bias (SI Appendix, Reliability of Coral-Based Estimates of Marine Variability, and Figs. S4 and S5).

A final data issue is that we may have systematically underestimated noise contributions. An independent check of noise variance is available through analyzing the covariance of nearby records, and we find that these are consistent with the noise levels inferred from our proxy-correction approach (SI Appendix, Signal-to-Noise Estimates, and Fig. S1). Under the assumption that noise is uncorrelated between records, estimated signal-to-noise ratios are an order of magnitude too great for noise to explain the model−data mismatch. Although the net effect of the noise correction that we apply is to decrease proxy and instrumental variance, we find no evidence that proxy variance should be further reduced.

Discussion

The combined instrumental and proxy evidence indicates that models systematically underestimate regional temperature variability and that this mismatch increases toward longer timescales. This result is consistent with land surface temperatures reconstructed from tree rings, other terrestrial proxies, and documentary evidence also indicating greater regional variability than simulated by models at decadal and longer timescales (33–35). That the ECHAM5/MPIOM model simulation of the carbon cycle over the last millenium fails to reproduce the magnitude of preindustrial atmospheric CO₂ variability (20) may also result from too little natural variability. We also note that models generally fail to simulate the magnitude of climate variations indicated by more ancient paleoclimate records (36).

One possible reconciliation for model−data discrepancies in variability is for the models to have insufficient internal variability. For instance, ocean−atmosphere coupling may be too weak (37), or the energy cascade from the mesoscale to larger spatial scales (38) may be insufficient. These scenarios could also be related to models being too diffusive, as would be consistent with model−data discrepancies growing toward longer timescales and the fact that higher-resolution simulations in the CMIP5 ensemble tend to show greater regional variability (4).

Another means of model−data reconciliation is through greater natural external forcing. For example, regional SST variance is roughly doubled at multidecadal and centennial timescales in the GISS-E2-R ensemble of simulations (39) when using larger-magnitude volcanic forcing estimates (40) relative to smaller ones (41) (SI Appendix, Fig. S7). As another example, regional SST variability is twice as large at centennial and millennial timescales during early Holocene portions of the TraCE-21ka experiment (42) when ice melt contributes significant amounts of freshwater, compared with late Holocene variability when ice melt is set to zero (SI Appendix, Fig. S7). These results suggest that increased variability in freshwater fluxes, perhaps associated with shifts in rainfall, would also increase regional SST variability. A related set of possibilities involves underestimating the sensitivity to external forcing. We are not aware of transient simulations that produce variability as large as that indicated by the proxy record, including those that represent volcanic (39), freshwater (42), or solar forcing (43). Notably, however, ref. 43 demonstrates a similar pattern of response to solar variability in both proxy data and simulations, and that an equilibrium simulation of the Maunder Minimum (44) having a detailed representation of the stratosphere showed strong regional temperature responses to solar forcing, similar in magnitude to those reconstructed elsewhere from proxies. Together these examples illustrate that additional forcing and amplification mechanisms readily increase regional SST variability and may possibly resolve model–data discrepancies.

Of course, it is also possible to generate consistent magnitudes of variability for the wrong reasons. For example, consistent variability was found between a simulation and paleoclimate reconstruction of the El Niño Southern Oscillation, but where the simulation showed greater volcanic contributions than found in the reconstruction (18). More detailed study of forcing-response patterns seems important for identifying plausible mechanisms by which to reconcile model−proxy discrepancies. An obstacle, however, is that whereas age-model errors have little influence on the spectral estimation relied upon in this study (45), such age-model errors generally corrupt covariance estimates. Accurate analysis of forcing-response patterns using proxy data will likely require development of new statistical approaches that better account for timing errors.

Conclusions

Given the large number of parameterized contributions that combine to determine regional SST variability, it is not surprising that models do not reproduce magnitudes of variability out to arbitrarily long timescales. Similarly, the large number of possible influences upon the proxy record makes it difficult to rule out systematic biases in variance. Nonetheless, obtaining accurate estimates and simulations of regional SST variability is important in several respects. From a historical perspective, an accurate reconstruction of the magnitude of past changes is obviously preferable. There are also implications for attribution and prediction of changes. Testing whether changes in temperature are attributable to anthropogenic causes requires a null distribution representing natural variability that is typically obtained from control runs of a model (5). Insomuch as models underestimate natural SST variability, tests for anthropogenic effects will tend to be biased positive. Optimal detection techniques that seek to rotate the fingerprint of climate change so as to maximize signal-to-noise ratios in model simulations are likely even more susceptible to bias (46). Underestimation of internal variability can also be expected to lead to predicted ranges that are too narrow, possibly also because of the projection of anthropogenic forcing onto natural modes of variability (1).

Reconciliation of model−data mismatch in SST variability requires participation from the modeling, statistics, and paleoclimate communities. Continued study of the magnitude and sensitivity to forcing, model representation of SST variability, and the processes through which proxies record environmental change all appear important. It may also be relevant to seek a more complete representation of marine proxies within general circulation models, including the growth and life cycle of marine proxies (31) as well as the processes through which paleoclimate signals are recorded and preserved in sediments.

Materials and Methods

Dataset Selection and Sampling.

Only mid to late Holocene proxy records with a mean resolution of less than 100 y and a length of more than 4,000 y are included in the analysis. Coral records were chosen on the basis of being at least 200 y long and reported to mainly record SST. The Cariaco Mg/Ca record is the only annually resolved sediment record considered in this study. We limit our collection to records having relatively high resolution to facilitate skillful correction for the effects of measurement noise, bioturbation, and sampling (16). All time series are evenly interpolated before analysis. To minimize aliasing, data are first linearly interpolated to 10 times the target resolution, low-pass filtered using a finite response filter with a cutoff frequency of 1.2 divided by the target time step, and then resampled at the target resolution. Note that linear interpolation tends to reduce the variance near the Nyquist frequencies of a process that has been unevenly sampled (45), and we have therefore excluded variance estimates at the highest frequencies. The appropriate resolution for each proxy record is determined by sampling power-law processes according to the native resolution of a given proxy and empirically determining which frequencies are unbiased—usually those below about four times the mean sampling frequency (SI Appendix, Table S1).

Proxy Correction.

Mg/Ca records are subject to nonnegligible levels of errors from all three error categories (measurement noise, bioturbation, and aliasing of high-frequency variability associated with irregular or infrequent sampling), and we correct for these through an extension of the filtering approach of Kirchner (27). Measurement noise here includes instrumental error and vital effects associated with foraminifera that are related to biologically controlled influences on the calcification process. Our approach is to design synthetic temperature records whose spectra are consistent with those from the observations once the appropriate sources of noise have been applied. Synthetic Mg/Ca records are sampled according to seasonal growth times (31), bioturbated (26) (for unlaminated records), and subsampled according to the number of individuals combined into each actual proxy measurement. Each Mg/Ca subsample is then corrupted by independent realizations of normally distributed noise. Synthetic Uk37 records are similarly bioturbated and subjected to sampling noise, but the effects of aliasing are not included because Uk37 samples comprise millions of molecules from across many different years. A filter is estimated for each Mg/Ca or Uk37 record by taking the ratio of the spectra associated with the synthetic record before and after subjecting it to the various sources of error. Application of this filter to the actual record then yields our best estimate of the actual SST variability. See ref. 16 for a complete description, detailed evaluation, and application of this technique to centennially resolved Mg/Ca and Uk37 records.

Correcting the annually resolved coral, Cariaco (10), and instrumental records is simpler because bioturbation and aliasing can be ignored, and we simply subtract the noise contribution following the errors reported in the original publication (SI Appendix, Table S1). Except for the case of correcting for bioturbation, all adjustments lead to a decrease in the SST variance inferred from each indicator. The net result of applying our correction algorithms is to decrease the average variance associated with each proxy type as well as that of the instrumental record.

Spectral Estimation.

Spectra are estimated using Thomson’s multitaper method (47) with three windows. Time series are detrended before analysis, as it is standard for spectral estimation. The multitaper approach introduces a small bias at the lowest frequencies, and we omit the two lowest frequencies in Figs. 3 and 4. For visual display purposes, power spectra are smoothed using a Gaussian kernel with constant width in logarithmic frequency space (27) when using logarithmic axes. To avoid biased estimates at low- and high-frequency boundaries, the kernel is truncated on both sides to maintain its symmetry. Except for instrumental comparisons (Figs. 3 B and C, Insets, and Fig. 5 A and B), years after 1950 are not spectrally analyzed, to omit an interval that likely contains substantial nonstationarity.

The average power spectrum for each proxy type shown in Fig. 3 necessarily contains samples from regions with differing variability and that cover different frequency intervals. To avoid discontinuities across frequencies where the number of available estimates change, proxy spectra are scaled to an average value in the largest common frequency interval. Error bars in Fig. 3 account for this weighting. Note that ratio calculations (Fig. 5) neither require nor contain scaling. Mean regional SST spectral estimates (Fig. 4 and SI Appendix, Fig. S7) are derived by calculating the spectra for every ocean grid box between 50°S and 50°N and showing the area-weighted mean of all regional spectra. Confidence intervals for spectral estimates are obtained from Monte Carlo simulations, and they account for the effects associated with corrections to the proxy records, the weighting associated with combining different spectral estimates, the frequency-dependent smoothing kernel, and the normal uncertainties associated with a spectral estimate. Specifically, we simulate surrogate time series using the estimated β scaling relationship (16), then corrupt the records, correct them, and estimate the resulting spectra. The process is repeated one thousand times, and a χ² distribution is fit to the ensemble of results at each frequency using moment matching. Uncertainties in ratio estimates are estimated analogously except that they are approximated as following an F distribution. For purposes of averaging, individual proxy spectra are assumed to be independent. Likewise, each of the five ensemble members from the fully forced millennial GCM simulations are assumed independent.

Ratio of Proxy and GCM SST Variance.

Timescale-dependent variance ratios (Fig. 5) are derived by summing spectral energy estimates between respective frequencies. The confidence intervals for the mean and median ratios are derived by drawing realizations of ratios for every proxy from an F distribution, taking the mean or median, repeating this 100,000 times, and reporting the quantiles.

Comparison With Instrumental SST.

Instrumental SST variance estimates that are used for purposes of comparison come from the corrected HadSST3 variance spectra from ref. 16. Comparisons are made with respect to the grid box containing a given proxy record. We do not restrict the instrumental SST data to have at least 10 observations per year because this restriction would leave large data gaps in the instrumental records at the coral positions. For comparing the coral and Cariaco records against instrumental SSTs (Fig. 3 B and C, Insets), only overlapping years are analyzed for proxy and instrumental data. For the ratio between observed and model SST variability (Fig. 5), all years for which model results and each type of data overlap are included.