Sensitivity of global warming to the pattern of tropical ocean warming

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Abstract The current generations of climate models are in substantial disagreement as to the projected patterns of sea surface temperatures (SSTs) in the ...

Climate Dynamics (2006) 27: 483–492 DOI 10.1007/s00382-006-0143-7

Joseph J. Barsugli Æ Sang-Ik Shin Prashant D. Sardeshmukh

Sensitivity of global warming to the pattern of tropical ocean warming

Received: 27 September 2005 / Accepted: 20 March 2006 / Published online: 22 April 2006  Springer-Verlag 2006

Abstract The current generations of climate models are in substantial disagreement as to the projected patterns of sea surface temperatures (SSTs) in the Tropics over the next several decades. We show that the spatial patterns of tropical ocean temperature trends have a strong influence on global mean temperature and precipitation and on global mean radiative forcing. We identify the SST patterns with the greatest influence on the global mean climate and find very different, and often opposing, sensitivities to SST changes in the tropical Indian and West Pacific Oceans. Our work stresses the need to reduce climate model biases in these sensitive regions, as they not only affect the regional climates of the nearby densely populated continents, but also have a disproportionately large effect on the global climate.

1 Introduction The current generation of climate models that couple atmospheric and oceanic general circulation models predict substantially different patterns of sea surface temperatures (SSTs) in the Tropics when run in anthropogenic climate change scenarios (Figs. 1a, b, 2). This is not surprising in light of the biases of such models in simulating the present day tropical mean climate and variability (see e.g. Covey et al. 2003 for the biases in the previous generation of coupled models). Clearly, not all of the predicted SST patterns can be correct. How much uncertainty might this error in the Tropics introduce into predictions of global mean temperature and precipitation, the basic metrics of climate? J. J. Barsugli (&) Æ S.-I. Shin Æ P. D. Sardeshmukh CIRES Climate Diagnostics Center and NOAA Earth System Research Laboratory, 325 Broadway, R/PSD1, Boulder, CO 80305-3328, USA E-mail: [email protected] Tel.: +1-303-4976042 Fax: +1-303-4976449

Are some regions of the Tropical oceans more important than others in this regard and therefore need to be modeled more accurately? To address such questions, an understanding of the global climate impact of the full range of possible tropical SST patterns is needed. We are interested in the potential impact of Tropical SST trends because the heat content of the upper Tropical ocean, as manifested in the SST, is an important driver of the global climate. Tropical SSTs will change in response to climate forcing, and will in turn force changes in other components of the climate system, primarily through their influence on the strength and location of tropical precipitation. The response to the anomalous atmospheric heat sources and sinks associated with the precipitation changes will be communicated dynamically throughout the Tropics and the rest of the globe through altered Hadley and Walker circulations and planetary Rossby waves. The broad global impacts of historical tropical SST changes are now well established, and account for the reliable simulations of global climate variations over the past halfcentury by atmosphere models (typically incorporating a land surface model) run with prescribed variations of tropical SSTs (e.g. Lau and Nath 1994; Saravanan 1998; Alexander et al. 2002; Hurrell et al. 2005). Recognition of their importance is also largely responsible for the progress in seasonal forecasting (Goddard et al. 2001; Compo and Sardeshmukh 2004). Specifying Tropical (Pacific) SSTs is also the basis for the so-called ‘‘pacemaker’’ runs currently being organized for the climate of the 20th century project (Kinter et al. 2005). Climate sensitivity can therefore be usefully probed through the sensitivity of atmosphere models to prescribed tropical SST changes. To develop a comprehensive understanding of this sensitivity, one would ideally wish to assess it for as wide a range of SST patterns as possible. Previous investigations, however, have been very restrictive in this regard. Some studies (e.g. Cess et al. 1996; Colman and McAvaney 1997) have usefully linked the differences in climate sensitivity among climate models to the differences in their internal

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Fig. 1 Tropical SST changes in climate model projections and observations. a Mean trend of 13 coupled climate model projections of Tropical SST (years 2000–2049 minus years 1950– 1999) using the SRES A2 emissions scenario submitted as part of the IPCC Fourth Assessment Report. All model simulations available to us were used. b Uncertainty (standard deviation) of 13 model-projected trends. c Observed 50-year linear trend of annual mean SSTs showing large warming in the Indian/West Pacific warm pool and the Eastern Tropical Pacific Oceans.

d Standard deviation of linearly de-trended annual mean SST, showing the dominance of variability associated with the El Nin˜o phenomenon. SST observations are from the HadISST (Rayner et al. 2003) data set. All SST data and model output were interpolated to a common ‘‘T42 Gaussian grid’’ (128 longitudes and 64 latitudes) and smoothed with a T21 spherical harmonic spatial filter before calculating the trend and standard deviation. Linear trends were determined by least squares fit at each grid point

climate feedbacks, through analysis of their responses to prescribed spatially uniform ± 2 K SST changes. Such studies, however, have avoided the issue of the sensitivity to SST patterns by design. A few studies have attempted to link climate sensitivity to SST patterns, though indirectly. For example, Yao and Del Genio 2002 and Colman and McAvaney 1997 have shown that the overall climate sensitivity itself may depend on model’s SST bias in the present–day climate. That is, the same atmosphere model may exhibit different climate sensitivity (as measured by the global mean temperature change in the presence of external forcing) for different mean SST states. Schneider et al. (1997) demonstrate the dependence of global climate sensitivity on the value of SSTs in the cold tongue region of the Eastern Equatorial Pacific. However, these studies did not attempt to generalize these results beyond a single case. Another possible approach to this problem is to analyze atmospheric model simulations of the climate of the last several decades in which the history of observed SSTs is prescribed. One can then deduce relationships between variations of SST and radiative climate forcings, and compare these relationships with similar ones estimated from observations (Soden 1997; Sun et al. 2003). However, the patterns of the projected SST trend

(Fig. 1a) as well as that of its uncertainty (Fig. 1b) differ from the observed SST trend and variability over the past half-century (Fig. 1c,d). In other words, the projected SST patterns extend beyond the limited set of SST patterns (e.g. Penland and Sardeshmukh 1995) observed in the recent past, and therefore observational and model-based estimates of historical climate sensitivity may give only limited information about future climate sensitivity. In this paper we develop a more complete picture of how potentially novel patterns of SST change might impact the global climate by simulating the response of the atmosphere to SST changes at an array of 43 locations throughout the Tropics (Fig. 3) The nearly-uniform coverage of the Tropics by these SST ‘‘patches’’ avoids the geographical bias of historical SST patterns discussed above. This method is an extension of that used by Barsugli and Sardeshmukh (2002) to the full seasonal cycle, to all the Tropical oceans, and to a model better suited to climate change applications. The responses to SST patches at these 43 locations are summarized in ‘‘climate sensitivity maps’’ (see Methods). We show climate sensitivity maps that depict how global mean temperature, precipitation, and top-of-the-atmosphere (TOA) radiative forcing depend on the location of Tropical SST changes. We then diagnose the origin of

J. Barsugli et al.: Sensitivity of global warming to the pattern of tropical ocean warming

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Fig. 2 The 13 coupled climate model projections of tropical SST change used to construct Fig. 1a, b. Using the nomenclature of the repository at PCMDI (Program for Model Intercomparison and Diagnosis, http://www-pcmdi.llnl.gov) the climate models are as follows: CCCMA CGCM3.1, CNRM CM3, CSIRO MK3.0, GFDL CM2.0, GFDL CM2.1, GISS MODEL E_R, IMNCM3.0,

IPSL CM4, MIROC3.2_medres, MPI_ECHAM5, NCAR CCSM3.0, NCAR PCM1, and UKMO HADCM3. The particular choices of models and of emissions scenario are only intended to be illustrative of the variety of SST patterns projected by state-of-theart coupled climate models. Therefore, we have not labeled the individual plots with the source model names

a dramatic East–West ‘‘dipole’’ in sensitivity seen in many of these maps. We also use these sensitivity maps to estimate the maximum possible global response to Tropics-wide SST changes of given root-mean-square (RMS) amplitude. We then discuss the implications of our sensitivity analysis not only for climate projections, but also for analysis of historical data.

were those released with a later version of the NCAR model (CAM 2.0). At each of the 43 locations in Fig. 3, we specified an SST anomaly patch with a maximum of 2 K at the center tapering to zero with a cosine-squared profile in latitude and longitude. Contours of the SST anomaly for two example patches are also shown in Fig. 3. Over each patch the average SST anomaly was 0.667 K. The dimensions of the 1 K anomaly contour were 45· 22 (longitude · latitude) for the Indo-Pacific patches and 33· 22 for the Atlantic patches. Based on prior experience (Barsugli and Sardeshmukh 2002) the patches were designed to be large enough to generate a robust climate signal, yet small enough to provide unprecedented spatial resolution of the climate sensitivity. We performed a ‘‘warm patch’’ as well as a ‘‘cold patch’’ experiment for each location. In each case the SST anomaly patch was added to (or subtracted from) the globally specified long-term mean (1950–1999) seasonal cycle of the SST. An ensemble of simulations with different initial conditions was needed for each patch to separate the climate signal adequately from the noise.

2 Methods We used the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM) 3.10, with T42 spectral resolution in the horizontal (310 km), and 18 levels in the vertical.1 This model, which includes a land surface model (LSM 1.0), was run in the standard configuration for the present climate supplied in the model release except that the specified orography and the long-term mean seasonal cycle of SST and sea ice

1

The specific model version was ccm3.10.11.brnchT.366physics.7.

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Fig. 3 Array of SST patches used in this study. Plotted are centers of the 43 SST patches used to investigate climate sensitivity to potential Tropical SST changes. At each location, SST anomalies were added to or subtracted from the 1950 to 1999 monthly SST climatology and the resulting SSTs were used as the boundary condition in an ensemble of atmospheric GCM simulations. Example Indo-Pacific and Atlantic SST patches are contoured

For the 27 patches in the Indo-Pacific basin we generated 32 ensemble members (16 warm, 16 cold) for each patch, with each member run for 18 months. For the 16 Atlantic patches we generated 40 ensemble members (20 warm, 20 cold), with each member run for 25 months in order to increase the sample size by covering two complete summers. This enhances the signal-to-noise ratio for the smaller Atlantic patches. All runs began from October 1 initial conditions drawn from a 100-year control run with a prescribed 1950–1999 mean seasonal cycle of global SST. We combined the results of the 43 SST patches into ‘‘climate sensitivity maps’’ depicting how the sensitivity of any quantity of interest, such as global mean air temperature, varies with the location of the SST anomaly. A sensitivity map is simply a contour map of the responses to the patches, with the response scaled by the area-averaged magnitude of the SST anomaly in each patch. The contoured values show the response to a hypothetical 1 K SST warming over a 1-km2 area at each location. This sensitivity may be either positive or negative. To generate meaningful sensitivity maps several steps were necessary (see also Barsugli and Sardeshmukh 2002). First we computed the linear response to SST for each patch as the difference of the ensemble mean responses to the ‘‘warm patch’’ and ‘‘cold patch’’ forcings. These linear responses were then normalized by the size of the SST forcing, resulting in the following formula for sensitivity of a scalar variable Z to the k-th SST patch (whose SST anomaly is given by T ¢k): Sk ¼

hZ ik; warm hZ ik; cold P 0 ; 2 T k ðxj Þ dAj j

where the angle brackets denote the ensemble means over the warm and cold runs separately, and dAj is the area element associated with the j-th grid point. We plotted these sensitivity values at the geographic centers of the patches, and applied a spatial smoothing spline based on the signal-to-noise ratio (Gu 1989; see Appendix A) to ensure that only the statistically robust features were retained. Finally, these smoothed values were contoured to produce the sensitivity map.

Our sensitivity analysis formally yields an approximate Green’s function of the linear component of the atmospheric response to tropical SST forcing (Branstator 1985; Barsugli and Sardesmukh 2002). Therefore, one can formally construct a linear estimate Zlinear of the response to an arbitrary tropical SST anomaly field T as the inner product of the sensitivity and the temperature anomaly, Z Zlinear ffi S  T ¼ SðxÞ T ðxÞ dA; P

where the domain of integration, P is that spanned by the SST patches in Fig. 3. As such the sensitivity patterns may be interpreted as linearly optimal SST forcing patterns (Newman and Sardeshmukh 1998). That is, of all the hypothetical SST change patterns with fixed RMS amplitude over the tropical oceans, the pattern identical to that of the sensitivity map will yield the largest response in the quantity of interest.2 This property is useful for estimating upper bounds on the uncertainty in projected global climate changes associated with uncertainties in projected tropical SST changes. To test the Green’s function approximation we created a linear reconstruction of the response ylinear to historical SST patterns over the last half-century as the weighted sums over the responses to the individual patches: X ylinear ¼ ak ðtÞðyk; warm  yk; cold Þ; k

where P ak ðtÞ ¼

j

T ðxj ; tÞ Tk ðxj Þ P : 4a Tk ðxj Þ j

The factor of a (1.25) accounts for the mean overlap of the patches. We then compared the reconstructed anomalies ylinear to the ensemble mean anomalies yfull from a 24-member ensemble of runs with the same GCM where the full pattern of historical SSTs from 1950–2002 was specified globally. (This data was obtained from http://iridl.ldeo.columbia.edu. Note that these runs used slightly different orography and sea–ice boundary conditions than our runs. Anomalies were defined relative to the long-term mean seasonal cycle). As in Barsugli and Sardeshmukh (2002), this reconstruction may be done for the entire state vector of the model. Here, we restricted ourselves to reconstructing the global mean 850 hPa temperature and global mean precipitation. Figure 4 shows the timeseries of ylinear and yfull for these two quantities in Northern Hemisphere Winter (December–February) and summer (June–August). The 2

The normalized optimal SST pattern (denoted ‘‘pattern I’’ in  1=2 R ; where AP is the area Table 1) is given by Topt ¼ S A1P S 2 dA P spanned by the patches.

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Fig. 4 The linear reconstruction of the global mean response to historical SST patterns as the weighted sum (using a = 1.0) of the response to the individual patches (black lines) compared to the

model’s response to the full SST fields (gray lines) for the period 1950–2001. a Winter lower tropospheric temperature, b Summer temperature, c Winter precipitation, and d Summer precipitation

high correlations between the time series, ranging from 0.7 to over 0.9, demonstrate that the weighted sum of the patch responses does a very good job of reproducing the GCM response to extensive SST anomalies on a yearby-year basis.

atmosphere more than compensates for this to produce a net global cooling. In contrast to the wintertime results, the lower tropospheric temperature in northern summer (Fig. 5b) shows no region of negative sensitivity. There is, however, a strong North–South gradient of sensitivity in the Indian and West Pacific Oceans and an additional region of strong positive sensitivity in the Caribbean. Because of such gradients of sensitivity, the global mean temperature will also be sensitive to the patterns of SST changes in summer, with SST changes south of the Equator having relatively little impact on the global mean temperature. Climate models generally predict that the global mean precipitation will increase as the global mean temperature increases, consistent with an intensified hydrologic cycle. However, the uncertainty in precipitation is much larger than in temperature (Cubasch 2001). Our sensitivity maps for precipitation show that the global mean precipitation is likely to depend sensitively on the pattern of the Tropical SST warming throughout the year, not just on the mean tropical SST. The sensitivity patterns for Northern winter (Fig. 5d) shows an East–West dipole between the Indian and Western Pacific Oceans. This dipole was also found in an earlier, simpler study with a different atmosphere model (Barsugli and Sardeshmukh 2002). The North–South gradient in Northern summertime precipitation sensitivity (Fig. 5e) is also broadly similar to the summertime temperature sensitivity (Fig. 5b), but there are significant regions of negative sensitivity not seen for global mean temperature.

3 Results The sensitivity map for global mean lower tropospheric air temperature (at the 850 hPa pressure level, roughly 1.5 km above sea level) in the Northern winter (Fig. 5a) shows dramatically different sensitivity to Indian and West Pacific Ocean warming.3 That the sensitivity is generally larger to warming in this ‘‘warm pool’’ (the warmest part of the global ocean with mean temperatures in excess of 28C) than elsewhere in the Tropics is not a surprise, given the maximum in the local precipitation response in that area (Fig. 8). What is surprising is the large region of negative sensitivity in the Indian Ocean, where a warm SST anomaly leads to a global mean cooling of the lower troposphere. A warm SST anomaly in this region does indeed induce a local atmospheric warming as one might expect, but the remote cooling induced by the dynamical response in the 3 The sensitivities shown in Fig. 5 are the result of the global response to a local SST change. For comparison, the baseline temperature sensitivity, obtained by taking the global average of only the local prescribed sea surface warming or cooling for a single patch, is 1/Ae (about 2 · 109 km2 in the units of Fig. 5a) where Ae is the surface area of the Earth.

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Fig. 5 Sensitivity of global mean temperature and precipitation to tropical SST. The sensitivity [in units of 109 K (K km2)1=109 km2] of the global mean air temperature in the lower troposphere (850 hPa pressure level) to the location of SST changes, for a Northern winter (December–February mean), b Northern summer (June–August mean), and c the annual mean. Positive (negative) values mean that a warm SST anomaly acts to increase (decrease) global mean lower tropospheric temperature.

For each patch shown in Fig. 3, the difference in global mean temperature between the warm and cold SST anomaly simulations is scaled according to the size and amplitude of the SST patch, plotted at the geographical center of the patch, and then contoured. d–f Global mean precipitation sensitivity [109 mm day1 (K km2)1]. The maps have been lightly smoothed to retain only statistically robust details

The above sensitivity maps were determined from the linear component of the responses. How different would these maps be if we had used only the ‘‘warm’’ or ‘‘cold’’ patches? We find that the ‘‘cold’’ sensitivities are generally weaker than the ‘‘warm’’ sensitivities, but the patterns are similar. For Northern winter the pattern correlations between the ‘‘warm’’ and ‘‘cold’’ sensitivity maps are 0.87 for lower tropospheric temperature sensitivity and 0.86 for precipitation sensitivity. For Northern summer, the pattern correlations drop to 0.7 for temperature and 0.66 for precipitation. The largest qualitative differences are seen in the wintertime temperature sensitivity to Atlantic SSTs and in the summertime precipitation sensitivity to Central and Western Pacific SSTs. In both these cases the linear sensitivity is very small. The sensitivity maps for annual mean temperature and precipitation shown in Fig. 5c and f are also the optimal SST forcing patterns on an annual time scale. These will be used below, along with the annual mean TOA radiative forcing sensitivity (Fig. 6) to estimate bounds on the uncertainty in annual-mean climate variables due to uncertainty in SST patterns. It is important to remember that while these maps depict the sensitivity of the annual-mean response to long-term trends in SST, there would still be a seasonal cycle in the climate response. In other words, the sensitivity of the winter and summer responses discussed earlier is just as relevant as that of the annual mean response. Finally, we wish to explore the origin of the striking East–West dipole pattern of the wintertime temperature

and precipitation sensitivity. Sensitivity maps for Northern extratropical air temperature and precipitation (averaged North of 30N, Fig. 7) have a similarly strong dipole structure as the sensitivity of the global mean quantities. Tropical and Southern Hemisphere temperature and precipitation show much smaller values and different patterns of sensitivity than either the global or the Northern Hemisphere averages. Therefore, the dipole results primarily from atmospheric teleconnections from the Tropical SST forcing to the Northern Hemisphere. Further evidence supporting this mecha-

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Fig. 6 Sensitivity of annual mean top of the atmosphere (TOA) radiative forcing (net insolation minus outgoing long wave radiation). a Local sensitivity, i.e. the sensitivity of the TOA radiative forcing integrated only over the area of the SST patch. The sensitivity shows uniformly positive values throughout the tropics. That is, warm SST results locally in more net incoming radiation. b Global TOA radiative forcing sensitivity

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changes in temperature and precipitation in the Northern extratropics that are induced by the tropical SST patches. The sum of the values in three panels for each variable yields the global mean sensitivity map. Note that the contour interval used in the panels a, d (the Northern extratropical response) is twice that used in the others

nism is seen in the existence and location of the ‘‘nodal line’’ of zero sensitivity near 110E longitude, across which the sensitivity changes sign, which is consistent with Barsugli and Sardeshmukh (2002). The teleconnection mechanism is also supported by results from idealized studies of the sensitivity of the Northern Hemisphere atmospheric response to tropical deep convection through the interaction of the latter’s uppertropospheric outflow with the upper-tropospheric jet streams creating a planetary Rossby wave source (Sardeshmukh and Hoskins 1988; Ting and Sardeshmukh 1993; Newman and Sardeshmukh 1998). The reproducibility of this dipole sensitivity in other climate models will therefore likely depend on how well the models capture the jet streams and the Rossby wave sources associated with tropical precipitation (Ting and Sardeshmukh 1993).

everywhere in the Tropics: a warm SST anomaly tends to increase the local rainfall. Yet, as we have shown, the sensitivity of the global mean precipitation may be positive or negative. The same conclusion holds true for TOA radiative forcing (Fig. 6). The local sensitivity is positive everywhere in the Tropics (see also Sun et al. 2003). However, the global sensitivity strongly resembles the global precipitation sensitivity, which may be positive or negative. The influence of tropical SST patterns on the global mean climate highlighted here has implications for observational studies of climate sensitivity and climate feedbacks. Our concern lies mainly with studies that relate observed variations (typically on annual or interannual time-scales) in components of radiative forcing to observed variations of surface temperature, averaged either regionally or over the globe (e.g. Ramanathan and Collins 1991; Inamdar and Ramanathan 1998). Such

4 Discussion An important lesson to draw from our analysis is that one cannot infer global climate sensitivity from local climate sensitivities. The global climate impact of localized SST perturbations is such that the remote response can in some cases overwhelm the contribution of the local response to global averages (Hartmann and Michelsen 1993; Bony et al. 1997). For example, the sensitivity map of local annual mean precipitation (Fig. 8) is a relatively bland field of positive values

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Fig. 8 Local precipitation sensitivity. The annual mean precipitation response is integrated only over the area of the SST patch to determine the sensitivity. Units are the same as in Fig. 4d–f

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studies implicitly include the global effects of the observed patterns of tropical SST variability. Therefore, to use these empirical climate sensitivities to predict the future climate requires the assumption that future Tropical SST trends not differ too greatly from the historically observed patterns of variability used to derive the empirical sensitivities. However, as we have shown in Figs. 1 and 2, climate models suggest that the patterns of future SST trends are likely to differ from the patterns of past SST variability. To what extent climate sensitivities that are derived empirically from a limited set of observed SST patterns would be modified in a possibly very different future climate deserves further investigation. How much potential uncertainty in global climate projections do our sensitivity patterns imply? We can estimate its magnitude by using the optimality property of our sensitivity maps as described in the methods section. In Table 1 we estimate the response to three hypothetical patterns of SST change: (1) the optimal SST patterns—that is, the sensitivity maps themselves for each variable and season, (2) a uniform 1 K SST warming over the domain covered by the patches, and (3) the optimal SST patterns with their domain averages removed so that there is no change in the mean Tropical SST. All three patterns are normalized to have a RMS amplitude of 1 K over the domain covered by the patches. The hypothetical response is obtained by spatially integrating the product of the gridded sensitivity values and the hypothetical SST changes (see Methods). Not surprisingly, the optimal SST pattern results in a much larger response than the uniform warming, even though the domainaveraged SST of the optimal pattern is less than 1 K. The response to the pattern III shows that sizable changes in the global mean can occur even when the mean SST in the Tropics is unchanged. These potential uncertainties, were they to be realized, are large en-

Table 1 Global mean linear response to patterns of Tropical SST change

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I II III I II III I II III

0.14 0.07 0.12 0.14 0.07 0.12 0.12 0.08 0.09

4.69 2.33 4.07 6.06 1.51 5.87 3.53 1.90 2.98

1.05 0.61 0.85 0.65 0.50 0.42 0.75 0.60 0.45

Response to the SST patterns described in the text. I: Optimal tropical SST pattern, II: uniform tropical 1 K warming, III: optimal tropical SST pattern with mean removed. TOA net radiative forcing is the net incoming solar minus the outgoing long wave radiation at the top of the model’s atmosphere

ough to be of concern for climate projections into the middle of this century, as their values are a significant fraction of the mean climate signals for most emissions scenarios over this period. The sensitivity to errors and uncertainties in the patterns of tropical SSTs shown here should be seen as modifying—either increasing or decreasing—the climate change projected by fully coupled atmosphere-ocean climate models with prescribed changing greenhouse gases and other external climate forcings. Because our results for Northern winter are consistent with earlier modeling studies of dynamical teleconnections from the Tropics to the extratropics, we have the most confidence in these results. We are somewhat less confident in the details of our sensitivity maps for the Northern summer season for two reasons—the fixed SST patch framework may poorly capture the coupled response of the Indian monsoon, and the summertime precipitation climatology of this particular atmospheric model is poor in the Caribbean area. In addition it should be noted that the sensitivity maps, and therefore the optimal patterns and global uncertainty estimates, are derived from the linear component of the response. Nevertheless, the reconstruction presented in the Methods section and the similarity between warm and cold sensitivity discussed in the Results section demonstrate the usefulness of the linear approximation. Our computed equilibrated responses may differ from those in a fully coupled framework. One could, of course, think of repeating our entire analysis with fully coupled climate models, but given their tropical SST biases, their sensitivity estimates would also be suspect. The large amplitude SST anomalies we used are virtually guaranteed to trigger precipitation. Therefore, the sensitivity to small amplitude SST anomalies in climatologically dry areas may be overestimated by our method. Regardless of whether or not our sensitivity results are confirmed in quantitative detail by other studies, our principal conclusion—that SST patterns matter—is consistent with previous work and is physically reasonable. The fact that a 4 W m2 global radiative forcing– comparable to the direct radiative effect of doubling atmospheric carbon dioxide—can come about by a 1 K rearrangement of tropical SSTs without changing the tropical mean SST should clearly be of concern to climate modelers. Our analysis has identified two particularly sensitive areas–the Tropical Indian and West Pacific Oceans, with often opposing climate sensitivity. The varied factors determining the ocean temperatures and precipitation in these areas—atmospheric aerosols, ocean dynamics, nearby land use changes, etc.—will therefore have a particularly large effect on the global climate. In light of the differences among climate model projections, our work stresses the need for more accurate prediction of SST trends in these sensitive areas, and not just the overall amplitude of the Tropical Ocean warming, in order to reduce the uncertainty in global climate forecasts.

J. Barsugli et al.: Sensitivity of global warming to the pattern of tropical ocean warming Fig. 9 Unsmoothed values of the sensitivity of lower tropospheric temperature (850 hPa pressure level) and precipitation corresponding to the smoothed values contoured in Fig. 4. The numerical values of the sensitivity are shown in text at the center of each patch (red = positive, blue = negative). Units are as in Fig. 4

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Acknowledgments This work was supported in part by a grant from NOAA’s Office of Global Programs, but does not reflect the official position of NOAA or of the US Government. We thank Jeffrey Yin for help with accessing the IPCC model output and Gil Compo for his assistance. We also appreciate the insightful comments of the two anonymous reviewers.

5 Appendix A: smoothing of the sensitivity maps A thin-plate spatial smoothing spline based on the signal-to-noise ratio (Gu 1989) was applied to the climate sensitivites to ensure that only statistically robust features were retained in the sensitivity map. The smoothing parameter used in the spline calculation was based on an a-priori estimate of the expected variance of the ensemble mean responses. This procedure fits a smooth surface to the sampled data so that the vari-

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ance of the residuals is consistent with the expected variance at the sampling locations. In this manner, variations among nearby data points that could have arisen merely by chance are smoothed out, and the effective sample size at these points is increased. For global sensitivity, the expected variance was taken to be the variance from the 100-year climatological SST control run divided by the sample size (the ensemble size times the number of seasons). Because the variance of precipitation over a patch will likely depend strongly on the total precipitation signal for that patch, the expected variance for the local sensitivities were calculated separately for each patch from the intraensemble variance. In practice the smoothing results in only small changes to the sensitivity maps shown in this paper. For example, Fig. 9 shows the actual values of the sensitivities used in constructing Fig. 4 before smoothing and contouring.

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