We describe transient simulations for 1951–2000 using the simplest ocean representations, ocean A (observed SST) and ocean B (Q-flux ocean). The simulations are made for “five forcings” (GHGs, stratospheric aerosols, solar irradiance, O3, and stratospheric H2O) and for “six forcings,” which adds the direct forcings by three tropospheric aerosols (sulfates, BC, and OC), all as defined in section 2. We extend the ocean B “six forcing” runs to 2050 for two distinct alternative scenarios of future climate forcings. The “business as usual” (BAU) scenario has a 1%/year CO2 growth rate, which yields an added forcing of almost 3 W/m2 in 2000–2050. The “alternative scenario,” defined in section 2.1, has an added forcing of 1.1 W/m2 in 2000–2050.
 We focus on the global mean response, as our aim is to investigate the global efficacy of the forcings. Study of the geographical distribution of climate change requires interactive ocean dynamics and a realistic representation of the stratosphere. Our present simple models are a useful prelude to such dynamical studies, especially if the latter employ the same forcings and atmospheric physics. Furthermore, for a crucial issue such as global ocean heat storage, the specified empirical mixing rates in the Q-flux ocean may provide as realistic an estimate as is possible at this time and, in any case, a standard for comparison. Sokolov and Stone  have shown that heat uptake by the Q-flux ocean provides a good approximation to that by ocean general circulation models, providing that there is no change in the mode of deep circulation. This condition should be satisfied for timescales less than a century with the moderate forcings that we employ.
5.2. Ocean Heat Storage
 A climate forcing, by definition, causes a planetary energy imbalance. An extended planetary energy imbalance must show up as a change of ocean heat content, because of the negligible heat conductivity of the continents and the small heat capacity of other heat reservoirs such as the atmosphere. We inferred previously [F-C] that the Earth had attained a positive rate of heat storage of 0.5–1 W/m2 by the middle 1990s, and we argued that the best confirmation of this planetary disequilibrium would be measurements of ocean temperature adequate to define heat storage. Recent analysis of global ocean data [Levitus et al., 2000] permits comparison of observations with the transient energy imbalance in climate scenarios. Model results for ocean B refer only to the upper 1000 m of the ocean, as the Q-flux model in our present simulations only extended to that depth.
 Figure 15a shows the observed heat content in the upper 500 m (top graph) and the upper 3000 m (middle and bottom graphs) of the ocean. The heat content is defined as anomalies relative to the mean for the period having both model results and observational data (1951–1994 in Figure 15a (top and middle graphs) and 1979–1994 in Figure 15a (bottom graph)). As done by F-C, we use the units W year/m2 averaged over the entire Earth to allow ready comparison with global climate forcings (1 W year/m2 = 1.61 × 1022 Joules). Note that the Levitus et al.  data set has annual data through 1998 for the upper 500 m of the ocean. Because of sparse observations at greater depths, only a 5-year mean (through 1994) is provided for 500–3000 m, and no data are provided for greater depths. Thus in Figure 15a (middle) the heat content for years 1995–1998 includes annual heat gain at 0–500 m, but heat content at 500–3000 m is fixed at the mean value for 1992–1996.
Figure 15. (a) Ocean heat content anomaly in units of W year/m2 averaged over the entire surface of the Earth (1 W year/m2 = 1.61 × 1022 Joules). The anomalies are relative to the common periods of data and simulations: 1951–1994 in top and middle graphs and 1979–1994 in bottom graph. Observed data are annual at 0–500 m (top graph), and the combination of this with 5-year mean data for depths 500–3000 m is shown (middle and bottom graphs). The combined data are repeated in the bottom graph to allow comparison with the SI95 simulations of F-C, which employed the Q-flux ocean model (ocean B) as well as two dynamic ocean models. The Q-flux model extends only to a depth of 1000 m. (b) Ocean temperature change versus depth based on the linear trend. Observations are annual and extend through 1998 in the upper 500 m. Below 500 m the data are 5-year mean and extend through 1994, which is the reason for the discontinuity in the model results. Note the scale change that occurs at 500 m. The full period is shown in the top graph, and the period of more reliable data, since 1955, is shown in the bottom graph.
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 It is possible that the observed heat storage in the Levitus et al.  analysis is an underestimate of the true value. In cases where no observations were available the procedure was to assign climatological values. Also no analysis is incorporated below 3000 m, where in at least some locations significant anomalies do occur [Bindoff and Church, 1992]. However, the vertical profile of the global ocean temperature trend (Figure 15b) suggests that the ocean beneath 3000 m would not contribute much to the full ocean value.
 The depth profile of ocean temperature change in Figure 15b is based on the linear trend for two alternative periods, which differ in their beginning date (1951 or 1955). The year 1951 corresponds to the beginning date of our climate model runs. However, the ocean heat content record since 1955 is considered to be more reliable because of a substantial expansion of the data sources that occurred in conjunction with global observing programs initiated in the mid 1950s.
 We discuss here possible relations between climate forcings and changes in the ocean heat content. We order the discussion according to timescale, from the brief perturbations (volcanoes) to the trend for the full period.
 We mark in Figure 15a, with the symbol V + 2, the dates (2 years after large volcanoes) at which minima in the ocean heat content would be expected to occur because of large volcanic eruptions. By the third year after the eruption the aerosol forcing is small and tends to be overshadowed by trends in other forcings such as greenhouse gases. The observed ocean heat content shows evidence of cooling after all three large eruptions (Agung, El Chichon, and Pinatubo) since 1950, although the date of the minimum differs from that predicted by −1 year for El Chichon and +1 year for Pinatubo. It is unlikely that there are other short-term competing climate forcings comparable in magnitude to the volcanic aerosol forcings, so the discrepancies in timing are probably an indication of the level of “dynamic” variability of ocean heat uptake and/or the level of measurement uncertainty. By dynamic variability we refer to internal climate system mechanisms rather than global radiative forcings; these could involve, for example, fluctuations in heat transport by the ocean or atmospheric fluctuations including changes of cloud cover. The dynamic variability and measurement uncertainty issues may be related; for example, we have not subsampled the model with the time-varying coverage of the Levitus data, which may account for some of the higher frequency variability in the observations.
 The magnitude of the observed negative heat storage anomalies after the volcanoes is reasonably similar to the expected values. The climate simulations for both ocean A and ocean B yield decreases of 1–2 W years/m2 in ocean heat content (ocean heat content is calculated in ocean A by integrating over time the heat flux at the ocean surface; see section 5.1.1). We discussed in section 4.1, in connection with Table 4, reasons that the ocean heat loss is less than would be estimated from instantaneous or even adjusted stratospheric aerosol forcing. In addition, the ocean heat uptake after a volcano is the net effect of the (negative) volcanic aerosol forcing and the (positive) portion of the greenhouse gas forcing that the climate system has not yet responded to. This disequilibrium greenhouse gas forcing was rather large by the time of the Pinatubo eruption. (The planetary radiation imbalance probably was small at the time of El Chichon because of the 1976–1981 jump of global temperature, regardless of the (presumably dynamical, in part) cause of that jump.) Our prior modeling (Plate 5 of F-C, which included two dynamical ocean models) and our current results for oceans A and B (Figures 12 and 13) together suggest that the planetary radiative imbalance at the time of the Pinatubo eruption was 0.75 ± 0.25 W/m2. This imbalance would reduce the 2-year (negative) heat storage after Pinatubo by 1–2 W year/m2. Indeed, the fact that the ocean did not cool as much after Pinatubo as would have been expected if it were the only forcing, we suggest, could be because of an existing positive planetary energy imbalance at the time of the Pinatubo eruption.
 Verification of the negative planetary radiation imbalance that occurred after Pinatubo is provided by Earth Radiation Budget Experiment (ERBE) satellite measurements [Minnis et al., 1993] as illustrated in Figure 12 of Hansen et al. . The ERBE data yield a radiation balance anomaly of −2.1 W year/m2 in the two years after Pinatubo. The magnitude of our simulated ocean heat content anomaly (Figure 15) is reasonably consistent with, but somewhat larger than, the ERBE measured imbalance. The ERBE imbalance shifts back to positive in 1993, consistent with the climate model, but not with the observed ocean heat storage minimum in 1994. Finally, we note that both the ocean heat content anomaly and the ERBE data are inconsistent with a Pinatubo peak forcing as large as the −5 W/m2 suggested by Andronova et al. .
5.2.2. Decadal variations
 The observed ocean heat content (Figure 15a) has significant decadal variability. The warming from 1968 to 1977 and the cooling from 1977 to 1983, for example, are much larger than the year-to-year variability or the estimated uncertainty in observed year-to-year and decade-to-decade changes of heat content [Levitus et al., 2000].
 These heat content changes do not appear to be caused by climate forcings. The simulations with a diffusive ocean model employing all of the known forcings, with and without the uncertain tropospheric aerosols, cannot produce the sharp increase of heat content in the early 1970s or a realistic representation of the cooling in the early 1980s. It is difficult to concoct a plausible underestimated forcing that might account for the observed variation. For example, if one suggested that solar cycle effects were underestimated by neglect of an indirect forcing (such as a forced cloud cover change), one would be faced with the contradiction that the time of minimum heat content in the mid 1980s and maximum heat content in the mid 1970s both occurred at the same phase of the solar cycle.
 It is more likely that the fluctuations are dynamical. However, they do not come about simply as a consequence of changing SST patterns that then alter fluxes to the atmosphere. This is shown by the simulation with ocean A (green line in Figure 10a (middle graph)), which used observed (HadISST1) SSTs for the period 1951–1999. On the basis of the energy fluxes at the ocean surface in this run the ocean heat storage is similar to that for the Q-flux ocean model. The failure of observed SSTs to produce the observed change of ocean heat content is not surprising. As discussed in section 3.4 in cases such as the North Atlantic Oscillation, specified SST calculations do not capture correctly the heat exchange between ocean and atmosphere associated with vertical motions in the ocean, and indeed that model (ocean A) can yield the wrong sign for the heat flux anomaly [Bretherton and Battisti, 2000]. That might also happen at low latitudes. For example, the west Indian Ocean warmed substantially over the past half century. It is possible that in reality the ocean warming in that region was associated with increased heat flux into the ocean surface; however, in ocean A the increasingly positive SST anomalies in that region yield an increased heat flux out of the ocean.
 Exploration of the decadal variations in ocean heat content will require use of dynamical ocean models, which are outside the scope of our present paper. We note that in previous simulations [F-C] with dynamical ocean models for the period beginning in 1979 (see Figure 15a (bottom)), one model had a variation in heat content in the 1990s that was unrelated to the climate forcings. However, that fluctuation was associated with unrealistic deep water formation in the North Pacific Ocean. Recent coupled model simulations by two different groups [Levitus et al., 2001; Barnett et al., 2001] do not capture the specific observed decadal variations, but Barnett et al.  note that their model does produce decadal fluctuations of the magnitude and timescale of those observed.
5.2.3. Long-Term change
 The change in the ocean heat content over the past half century is in good agreement with the climate model driven by known climate forcings. The dominant forcing and the cause of the long-term increase in ocean heat content is the GHG forcing, as shown by Figure 2. The positive ocean heat storage, because it is so directly connected to the planetary energy balance, is probably the best confirmation of the sign of the net climate forcing that has been operating on the planet during the past half century.
 Observed temporal change of ocean heat content also has the potential to yield a good, perhaps the best, quantitative measure of the net global climate forcing. However, the rate of heat uptake by the ocean depends upon climate sensitivity and ocean mixing, as well as upon the net climate forcing [Hansen et al., 1984, 1985]. If it were accepted that the mixing in ocean models is reasonably realistic, at least as it affects the global penetration of heat anomalies, and if it were accepted that climate sensitivity is about 3°C for doubled CO2, then the observed ocean heat storage provides an indication that the net climate forcing is positive and of approximately the magnitude that we have assumed. In particular, under these assumptions, we find, as illustrated in Figure 15, that better agreement is obtained with a net climate forcing that includes the climate forcing by aerosols (six forcings) rather than the case without this negative aerosol forcing.
 Alternatively, if we knew the net global climate forcing, the rate of heat storage would provide an empirical measure of climate sensitivity. It is only if climate sensitivity is high that there is substantial “unrealized warming” due to the slow increase of greenhouse gases as the dominant climate forcing. Indeed, the recent positive trend of ocean heat storage and the fact that the ocean heat content dropped only slightly after Pinatubo are consistent with high climate sensitivity. However, there is such a large uncertainty in the indirect aerosol forcing that the ocean heat storage does not provide a very helpful measure of climate sensitivity. Furthermore, all of these inferences are limited by poorly quantified but substantial uncertainty in the observed ocean heat storage, which potentially could be measured with high accuracy.
 Barnett et al.  and Levitus et al.  previously reported global climate model results for ocean heat storage, which they found to be reasonably consistent with the Levitus et al.  data. Barnett et al.  used the National Center for Atmospheric Research (NCAR) Parallel Climate Model (PCM) [Dai et al., 2001], which has a sensitivity of 2.1°C for doubled CO2, and forcing by greenhouse gases and sulfate aerosols, with a net forcing of 2 W/m2 in 2000 relative to 1850. Levitus et al.  used the Geophysical Fluid Dynamics Laboratory (GFDL) model [Delworth et al., 2001], which has a of sensitivity 3.7°C for doubled CO2, and a forcing similar to that of Barnett et al. . Barnett et al.  found an ocean heat storage of 12 × 1022 J in the period 1955–1995, while Levitus et al.  obtained 33 × 1022 J. The observed heat storage [Levitus et al., 2000] is about 18 × 1022 J (this is reduced to 13–14 × 1022 J if the data are first averaged over decades; Barnett et al.  only report their model result after such averaging). When Levitus et al.  added solar and volcanic aerosol forcings, the heat storage was reduced to 20 × 1022 J. The reduction in heat storage probably was due mainly to the volcanic aerosols. Their solar forcing was +0.18 W/m2 over the interval 1865–2000. Their volcanic aerosol forcing averaged −0.54 W/m2 over 1960–1999; it is based on the data of Andronova et al.  and is thus larger than that which we employ, as discussed in section 2.2. The dependence of the simulated heat storage on the model sensitivity and the climate forcing in these studies is consistent with the discussion above. Their results are also consistent with the heat storage in our model over the same interval, which was 18 × 1022 J for five forcings and 14 × 1022 J for six forcings; our results refer just to the upper 1000 m of the ocean, because our present Q-flux ocean extended only to that depth.
5.3. Atmospheric Temperature Profile
 Climate forcings have a strong effect on the atmospheric temperature profile, as illustrated explicitly in Figure 6 of F-C and by Ramaswamy et al. . We do not attempt a comprehensive study here, which would require more realistic representations of the stratosphere and ocean as well as better information on the vertical profile of absorbing aerosols. However, our present simulations cover a longer period than those of F-C. This allows us to compare modeled and observed temperature profiles for both the era of satellite data and the longer period with radiosonde data.
 The satellite era begins in 1979 with the first MSU data, for which we use version d of Christy et al. . Radiosonde coverage was extensive by 1958, the International Geophysical Year, although the coverage is only considered to be reasonably global after 1964 [IPCC, 2001]. We use radiosonde data analysis of Parker et al. . The two radiosonde data sets, HadRT2.0 and HadRT2.1, differ in that the latter has been adjusted with the help of MSU data (version c) in an attempt to correct for bad radiosonde records. We illustrate both data sets, thus providing one indication of data uncertainty.
 We present two views of the temperature profile. Figure 16 compares line graphs of observed and modeled temperature profiles for the global mean and for northern latitudes, low latitudes, and southern latitudes. We define low latitudes as 40N-40S, which is the latitude range at which the tropopause extends to about the 100 hPa level. Figure 17, the zonal mean temperature change versus latitude, provides a more pictorial view of the nature of the zonal temperature change.
Figure 16. Change of annual-mean temperature profile for 1958–1998 and 1979–1998 based on linear trends. Model results are for oceans A and B, with five and six forcings. Surface observations are the land-ocean data of Hansen et al. , with SSTs of Reynolds and Smith  for ocean areas. The bars on the MSU satellite data [Christy et al., 2000] are twice the standard statistical error adjusted for autocorrelation [Santer et al., 2000]. Radiosonde profiles become unreliable above about the 100-hPa level. Twice the ensemble standard deviation is shown at three pressure levels for ocean B with six forcings.
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Figure 17. Change of zonal-mean annual-mean temperature for 1958–1998 and 1979–1998 based on linear trends. Radiosonde data in the top row are for versions 2.0 and 2.1 of the HadRT analysis [Parker et al., 1997]. Model results are for oceans A and B, with five and six forcings. Note that ocean A with five forcings employs the ozone O3A data set, while the others use O3B (the latter has greater ozone depletion in the South Pole region).
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 Qualitatively, there is reasonable agreement between the simulated and observed temperature changes, particularly for the longer time period. However, Figure 16 reveals that the model warms more than observed in the upper troposphere, and the model cools less than observed in the stratosphere. The discrepancies occur primarily in the latter period, 1979–1998, the period with more complete observations of climate forcings. Agreement is best at southern latitudes. The simulated upper tropospheric warming is especially excessive at low latitudes. Simulated stratospheric cooling is too little at northern latitudes and low latitudes. The discrepancies are significant based on the standard deviation among the ensemble members, as illustrated at three pressure levels in Figure 16.
 Among the climate forcings, ozone, stratospheric water vapor, and aerosols probably are the best candidates for contributing to the discrepancies in simulated temperature profiles. Ozone should be considered first because it changed dramatically during 1979–1998, yet it was poorly measured in the lower stratosphere and troposphere. Indeed, much closer agreement with the observed change in temperature profile would have been obtained if we had employed the ozone change that was used by F-C. The ozone change of F-C had large ozone depletion near the 100 hPa level at all latitudes, including the tropics, based on the then available analysis of SAGE observations. The SPARC ozone trend assessment [WMO, 1998] excluded SAGE data below the 20-km level because of its uncertainties, but they did not replace it with any other estimate. As a result our current estimate for ozone change, as discussed in section 2.4, has a maximum ozone depletion rate near the tropical tropopause of only about 2% per decade. However, recent analyses of SAGE II data for October 1984 to April 2000 (J. Zawodny, private communication, 2000) yield an ozone depletion of more than 5% per decade with maximum depletion near 20 km altitude. This is less depletion than assumed by F-C, but it is substantial. Furthermore, the SAGE II period of data, beginning in late 1984, misses the period of rapid depletion of column-integrated ozone that occurred in 1980–1985 (Figure 6). Although column-integrated ozone amount does not show much depletion at low latitudes (Figure 6), this could be a result of increases in tropospheric ozone as suggested in the recent SAGE II analyses of J. Zawodny (private communication, 2000). Therefore it seems possible that the ozone depletion rate in the tropopause region for the full period 1979–1998 was larger than that in our current scenario. As shown in Figure 6 of F-C, ozone depletion near the tropopause could cause significant cooling in the upper troposphere and lower stratosphere.
 Stratospheric water vapor probably contributes to the discrepancy between the observed and modeled temperature profile change. The positive trend of stratospheric water vapor in the model is less than the observed trend, as discussed in section 2.5. Water vapor change at the rate reported by Rosenlof et al.  would increase stratospheric cooling slightly, of the order of 0.1°C in 20 years [Oinas et al., 2001]. However, this can account for only a small fraction of the discrepancy.
 Tropospheric aerosols cool the surface but have only modest impact on the temperature profile in our present simulations. However, suspected inaccuracies in the aerosol vertical distribution and temporal change may cause the upper troposphere to warm relative to the near surface layers in the simulations. As discussed in section 2.6, the black carbon aerosols are mixed too high in the troposphere compared with limited available observations, with the amount of black carbon in the upper troposphere perhaps as much as a factor of 10 too large. The temporal issue arises because black carbon (and sulfates and organic carbon) aerosols are taken as proportional to fossil fuel use. However, T. Novakov (private communication, 2001) argues that the proportion of black carbon aerosols has decreased in recent decades in developed countries because of a decrease in inefficient coal burning in domestic and commercial sectors as well as improved efficiency of diesel engines, at least in the United States. Thus it is plausible that more realistic vertical and temporal distributions of black carbon would cause less warming of the troposphere relative to the surface. Quantitative analysis requires better knowledge of aerosol distributions and their temporal change. This topic is discussed further in section 6.
 In the period 1979–1998 the discrepancy between model and observations is primarily at low latitudes, and it is larger in ocean A than ocean B. This is most apparent in Figure 17, as the bulls-eye warming in the tropical upper troposphere. Excessive warming at this level did not occur in our previous simulations [F-C], because of greater ozone depletion near the tropopause, as discussed above. Ocean B has slightly less warming at the surface than ocean A at low latitudes during 1979–1998, and this difference increases in the middle to upper troposphere in the way temperature anomalies are observed to change with height in the tropics [Hurrell and Trenberth, 1998; Wentz and Schabel, 2000; Santer et al., 2001]. As shown in Table 5, the discrepancy between MSU lower tropospheric temperature change and the ocean B model results for six forcings is small, although the discrepancy is substantial for ocean A. The discrepancy with radiosonde temperature change for 1979–1998 is larger (Figure 17 and Table 5), but the radiosondes suffer from poor spatial sampling and temporal discontinuities [Gaffen et al., 2000], suggesting that in this case MSU may provide the more reliable result. However, there are also significant sources of potential error in the MSU temperature trends [Santer et al., 1999; Hurrell et al., 2000; Wentz et al., 2001].
 There are several possible interpretations of these results. Perhaps there is an error in the observed trend of low latitude SSTs, as only a small error (about 0.2°C over 2 decades) in the SST is required to explain the tropospheric temperature change. Such an error would be consistent with the smaller warming of tropical nighttime marine air temperature (NMAT) found by Christy et al.  for the period after 1979; that is, it would remove the difference between the NMAT and SST trends. Alternatively, the observed SST temperature trends may be accurate, and the difference between the NMAT and SST trends may be real, but the heat flux anomalies from the ocean to the troposphere may be inaccurately simulated. Given a positive SST anomaly, the model faithfully delivers a larger anomaly to the midtroposphere, but the model could be flawed in its simulated dynamical or thermodynamical energy fluxes or in the forcings that influence those fluxes.
 There are also real differences between the model and radiosonde observations for the longer period 1958–1998 at the tropical and northern latitudes, and on the global average, as summarized in Figure 16. We believe that these discrepancies are meaningful and probably related, at least in part, to inaccurate or incomplete representations of the three climate forcings' ozone, water vapor, and aerosols, as discussed above. Ozone depletion near the tropopause is probably understated in our scenario. We know that the measured stratospheric water vapor increase was larger than in our model. Suspected flaws in the BC aerosol scenario are in the sense to partially account for the discrepancies.