1. Introduction
Since the first climate simulation with the coupled atmosphere–ocean general circulation model (AOGCM) performed during the 1960s (Manabe and Bryan 1969), AOGCMs have undergone rapid development and significant improvement has been made. Now many features of the climate system are better reproduced in the latest AOGCMs and their credibility in climate simulation and future projection has been demonstrated (Meehl et al. 2007). However, a range of uncertainties that could arise from various sources is still affecting the level of confidence in modeling transient climate response in AOGCMs. Owing to the importance for climate policy making, it is urgent to evaluate, quantify, and eventually reduce these uncertainties. The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (Randall et al. 2007) has emphasized the need to better understand these uncertainties and called for systematic and quantitative evaluations.
A major source of uncertainty is the misrepresentation of physical processes in the model formulation. A notable misrepresentation in AOGCMs is the wide use of an unphysical virtual salt flux (VSF) to represent the freshwater flux (FWF) at the ocean surface. The VSF assumption was introduced as a result of the classical rigid-lid approximation, which suppressed fast external gravity waves in the ocean to allow longer time steps but led to a fixed volume of a model ocean (Bryan 1969). Under the rigid-lid approximation, the dilution and salinification effects of rainfall and evaporation have to be parameterized by a salt extraction or input, and the global hydrological cycle is felt by the oceanic model as a spurious salt cycle.
So far, whether the unphysical VSF formulation produces satisfactory results in climate studies has not been systematically investigated. The use of the VSF method could cause two model deficiencies: 1) the VSF model cannot simulate the change in sea surface height (SSH) induced by the mass fluxes associated with precipitation, evaporation, runoff, and sea/land ice melting and 2) the use of a reference salinity in calculating the equivalent virtual salt flux can distort the real freshwater flux over the ocean regions with low salinity, especially in the high-resolution climate models (see section 2 for details). As a consequence, the VSF model excludes the Goldsbrough–Stommel circulation induced by large-scale precipitation and evaporation (Huang and Schmitt 1993). In addition, it has been shown that due to the second deficiency, the seawater near river mouths is considerably fresher (up to 14 psu) in a VSF model than in a comparable FWF model (Griffies et al. 2005). The sharp gradient created by the extremely low values of salinity in the former model triggers numerical instability shortly after the start of the model integration.
Here we examine whether the deficiencies of the VSF formulation could induce large uncertainties in modeling the climate system and projecting its future evolution. The density structure of the oceans, which has a great impact on the global-scale ocean circulation, is sensitive to the surface freshwater forcing. In addition, it is projected that the earth’s hydrological cycle will be enhanced in the future (e.g., Manabe and Wetherald 1975), with some recent work indicating that this enhancement may be occurring in the present-day climate (Wu et al. 2005; Stocker and Raible 2005). In a warmer climate, more water vapor is evaporated from the low latitudes and transported to the high latitudes by the atmosphere, increasing the freshwater flux to the ocean regions of deep and intermediate water formation, which is sensitive to the salinity of the sinking water. Thus, an accurate representation of the freshwater flux in the model is particularly critical to climate projections.
The rigid-lid approximation is being gradually replaced by the free-surface method in the formulation of the latest climate models (e.g., Delworth et al. 2006; Johns et al. 2006). But the tracer budget still assumes a constant ocean volume and the VSF formulation is still being used as the standard oceanic boundary condition in some ocean climate models (e.g., Gordon et al. 2000; Smith and Gent 2004; Levermann et al. 2005; Sun and Bleck 2006; Stammer 2008). Furthermore, many previous climate modeling studies were based on VSF models. A systematic evaluation of the impact of the VSF formulation on climate simulation and projection is therefore urgently necessary.
In the present study, we investigate this impact in detail by comparing the climate simulations with two versions of the Geophysical Fluid Dynamics Laboratory Climate Model version 2.1 (GFDL CM2.1): a FWF version and a VSF version. With these two model versions, we carried out two groups of model integrations. In the first group, a multicentury control run and two perturbation runs [0.1 and 1.0 Sv (Sv ≡ 106 m3 s−1) “water-hosing” runs] with the FWF version were carried out. The runs in the second group are the same except that the VSF version was used instead. In the unforced control runs, the climate system evolves under internal FWF/VSF forcing. In the forced water-hosing runs, external FWF/VSF forcings are imposed in the high-latitude North Atlantic. These runs are typically designed to study the dynamics of the Atlantic meridional overturning circulation (AMOC) and associated climate changes (Stouffer et al. 2006a; Yin and Stouffer 2007). Because the AMOC is highly sensitive to the freshwater flux, any bias in representing the flux could impact the simulation of the AMOC and its responses. In this study, we perform a comprehensive comparison to identify similarities and differences between the two groups. Given the two major deficiencies of the VSF formulation related to ocean salinity and mass, we pay special attention to the simulations of salinity and sea level, as well as the AMOC and climate variability. The paper is organized as follows: section 2 describes the coupled model and elucidates the virtual salt flux formulation; section 3 shows the comparison, followed by a discussion and conclusion.
2. Model description and virtual salt flux formulation
a. Model and experimental design
The GFDL CM2.1 used in the present study is a state-of-the-art AOGCM. It is characterized by its relatively fine resolution, up-to-date numerical schemes and realistic simulation of many features of the mean climate state and climate variability. The details of the model formulation and performance can be found in Delworth et al. (2006), Gnanadesikan et al. (2006), Wittenberg et al. (2006), Stouffer et al. (2006b), and Griffies et al. (2005). Here we give a brief description of the model, focusing on the freshwater coupling at the ocean surface and the virtual salt flux formulation. The horizontal resolution of the atmospheric model and land model is 2° latitude by 2.5° longitude. The atmospheric model has 24 vertical levels with the top at about 3 hPa. One can see GFDL Global Atmospheric Model Development Team (2004) for more details on the atmospheric model. The oceanic model is based on the GFDL Modular Ocean Model version 4 (MOM4) codes (Griffies et al. 2003). The horizontal resolution is 1°, with an enhanced latitudinal resolution in the tropics (⅓° at the equator). There are 50 vertical levels with 22 levels in the top 220 m. MOM4 has a free surface so that the dynamic sea level is accurately represented (Griffies et al. 2001). The detailed physical parameterization can be found in Griffies et al. (2003). A dynamical–thermodynamical sea ice model with the elastic–viscous–plastic technique for calculating ice internal stresses is used to predict sea ice (Winton 2000).
The component models are coupled together by a coupler that calculates and passes fluxes at the component model interfaces. At the ocean surface, either a freshwater flux (the standard model boundary condition) or a virtual salt flux can be used to represent the water exchange with the ocean, including precipitation, evaporation, runoff, and sea ice change (P − E + R + I). In the FWF version, the freshwater flux changes the salinity of the top grid cells of the oceanic model by changing their volumes. To avoid the creation of a strong halocline near river mouths, which could cause numerical problems, the predicted river runoff is discharged into a thick layer (upper 40 m) at the river mouths in the model. Six inland seas (Hudson Bay, Black Sea, Mediterranean Sea, Red Sea, Baltic Sea, and the Persian Gulf) are connected to the World Ocean by mixing processes at the corresponding passages. In the VSF version, the freshwater flux is converted into an equivalent virtual salt flux using a reference salinity of 35 psu (see section 2b for details). Because numerical instability can easily be triggered by a large localized freshwater flux in this model version (Griffies et al. 2005), the discharges of five major rivers are spread over wide areas (Fig. 1). This spread can cause different simulations of sea surface salinity (SSS) near river mouths between the two model versions (shown later).
The FWF and VSF versions of CM2.1 have been integrated for a multicentury period without the need of any flux adjustment. The last 200 years of the long-term integrations are regarded as the control runs. In the water-hosing runs, external freshwater fluxes of 0.1 and 1.0 Sv are uniformly input into 50°∼70°N of the North Atlantic. A 0.1 Sv freshwater addition in the high-latitude North Atlantic resembles the magnitude of the projected freshwater flux anomaly in the northern North Atlantic under realistic future CO2 scenarios, while a 1.0 Sv freshwater addition mimics the magnitude of the past meltwater pulses from the paleoglaciers, which are thought to have caused abrupt climate changes (Alley et al. 2003). So, both perturbation runs have important climate implications. The perturbation freshwater fluxes are removed after 100 years and the model integrations continue for additional one or two centuries.
b. Virtual salt flux formulation
3. Results
a. Unforced runs
According to Eq. (3), the error induced by the VSF formulation in representing the FWF is proportional to both the magnitude of the net freshwater flux and the SSS deviation from 35 psu at a particular model grid. Generally, SSS is lower than the reference salinity in the regions poleward of 40° latitude where precipitation dominates evaporation, in the moist tropics where the ITCZ brings abundant convective rainfall, and near river mouths and sea ice margins (Fig. 2a). In reality, ocean salinity ranges from 0 to 40 psu, so the magnitude of the negative SSS deviations can be larger than 20 psu. Over the subtropical regions, SSS is typically higher than the reference salinity with a maximum deviation of up to +3 psu in the North Atlantic. The zonal average shows a pronounced anticorrelation between the SSS deviation and the net freshwater flux (Fig. 2b). This anticorrelation indicates that the VSF formulation tends to overestimate the dilution effect of the net freshwater input into the ocean and underestimate the salinification effect of the net freshwater loss in the oceanic model. Thus, the long-term mean SSS in the VSF version tends to be lower in most ocean areas compared to the FWF version, given that the net freshwater flux across the ocean surface does not differ much between the two versions. Because the SSS deviation increases with the increase in latitude, the error also increases, particularly in the Northern Hemisphere.
The global annual mean SSS is stable and fairly realistic in both versions of the model during the multicentury integrations (not shown). In most areas of the low and middle latitudes (40°S–40°N), the SSS difference between the FWF and VSF versions cannot be distinguished from the background variability (Fig. 4a). In some areas within 40°S–40°N, the SSS is slightly higher in the VSF version, in contrast to the expected results. This is because the tendency of the salinity at the ocean surface is governed not only by the surface water flux but also by other complex oceanic processes. Because of the nonlinearity of the ocean climate system, the bias induced by the VSF formulation can be reduced or even reversed by other processes such as salt advection and mixing. The dipole feature near river mouths results from the different treatment of river runoff in the two versions of the model (Fig. 1). In the marginal and semienclosed seas where the advection and mixing processes are greatly limited, the bias induced by the VSF formulation is more significant. For example, because of the high salinity in the Mediterranean Sea above 38 psu, the dilution effect of the freshwater discharge from the Nile is underestimated in the VSF version, leading to a higher SSS in the eastern Mediterranean. A statistically significant freshening occurs in the high-latitude regions of the VSF version, including most areas of the Arctic, northern North Pacific, and Southern Ocean. The magnitude is large in the inland or semienclosed seas such as the Hudson Bay, Black Sea, North Sea, and the Arctic mediterranean. The special geometry of these seas inhibits the salt exchange with the open oceans.
The sea surface temperature (SST) is slightly warmer in the VSF version (Fig. 4b). The maximum warming occurs in the northern North Pacific and along the route of the Gulf Stream and North Atlantic Current. The two versions of the model give different simulations of the Goldsbrough–Stommel circulation, which slightly impacts the path of the Gulf Stream and North Atlantic Current (not shown). Due to the strong El Niño and SST variability in the central and eastern equatorial Pacific in this model (Wittenberg et al. 2006; Timmermann et al. 2007), the mean SST difference between the two versions is statistically insignificant in this region. Also the difference in the SST variability is statistically insignificant in most ocean areas (Fig. 5). Although the difference in the eastern equatorial Pacific passes the significance test based on the 200-yr simulation, it becomes statistically insignificant during the last 100 years. The slight trend in the SST variability may be due to slow adjustment of the coupled atmosphere–ocean system or to data sampling. It has been shown that the ENSO statistics in the FWF version could change a fair amount from one century to another (Wittenberg 2009). In addition, the significant difference in Fig. 5 does not resemble a typical ENSO pattern (in contrast to the 1.0-Sv hosing case, Fig. 13), so the difference in the ENSO variability cannot be concluded as statistically significant between the control runs of the two versions.
Away from the surface, the VSF version simulates a higher salinity in the upper 1000 m within 40°S–40°N (Fig. 6a). In the high latitudes, the maximum freshening occurs in the upper 200 m with a magnitude of about 0.2 psu. The salinity difference is small below 1000 m. This pattern in the salinity difference reflects that the global volume-averaged salinity is conserved in the two versions. In terms of the ocean temperature difference, a warming dominates in the upper 1000 m (Fig. 6b). Given the small difference in salinity and temperature, the density structure of the ocean interior, water mass distribution, and meridional overturning circulation (Fig. 7) are similar in the two model versions. The long-term mean strength of the AMOC in both versions is about 23.5 Sv with a standard deviation of about 1.0 Sv (Figs. 7b and 9b). The core of the AMOC streamfunction at 50°N is slightly stronger in the VSF version, but the mass exchange at 30°S and 0° is slightly weaker than in the FWF version. This may be due to the difference in the net southward mass transport between the two versions (shown later).
In addition to the direct impact on salinity, the VSF formulation influences the simulations of sea level and related ocean circulation. The SSH difference between the two versions is statistically significant almost everywhere (Fig. 4c). In the VSF version, SSH is higher in the low and middle latitudes, notably in the Atlantic, but lower in the high latitudes, notably in the Southern Ocean. This pattern is basically consistent with the effect of the mass flux associated with precipitation and evaporation. Similar to ocean salinity, the SSH difference is largest in the marginal and inland seas such as in the Mediterranean Sea and Hudson Bay.
The zonally and vertically integrated volume/mass transport across individual ocean basins is very different in the two versions (Fig. 8). The transports in the VSF version are constant, as shown by the straight lines, whereas they vary with latitude in the FWF version. The variable transport reflects the intrabasin pattern of precipitation and evaporation and the related mass gain/loss. Interestingly, the transport by the Bering Strait throughflow is almost identical in the two versions. So, the interbasin mass budget with a net evaporation in the Atlantic and a net precipitation in the Pacific is closed through the southern boundary. In the FWF version, the southward mass transport at 35°N of the Atlantic is the sum of the Bering Strait throughflow transport and the net precipitation and runoff in the Arctic and northern North Atlantic. The transports are 1.17 and 0.83 Sv in the FWF and VSF versions, respectively. The additional transport in the FWF version and the southward western boundary current associated with the Goldsbrough–Stommel circulation may slightly influence the path of the Gulf Stream and North Atlantic Current.
b. Forced runs
Due to the relatively small bias, both versions display similar features in the SSS responses. The maximum freshening of up to 2 psu occurs in the western part of the perturbation region around the Labrador Sea, whereas the surface freshening in the eastern perturbation region is small (Fig. 10a). In most ocean areas, the difference in the SSS response is statistically insignificant.
In the 1.0 Sv water-hosing case, however, the bias induced by the VSF formulation is much clearer. A 1.0 Sv freshwater input causes a considerable decrease in the mean SSS from 34.4 to about 25.0 psu in the perturbation region–a roughly 10 psu freshening (Figs. 9a and 10b). Given such a large deviation from the reference salinity, the freshwater perturbation can be exaggerated up to 40% in the VSF version. This implies that the actual freshwater input becomes progressively larger with the decrease of the SSS, and could eventually reach 1.4 Sv. The SSS in the perturbation region continues to decrease in the VSF version, whereas it almost levels off after 50 years in the FWF version (Fig. 9a). The difference in the SSS response is statistically significant almost everywhere in the perturbation region (Fig. 10b), with the VSF version showing an additional freshening of up to 2 psu. The additional freshening is concentrated in the upper 100 m within 40°–80°N, whereas the salinity in the intermediate layer is higher in the VSF version (Fig. 11a).
In contrast, the salinity difference is small and statistically insignificant in the subtropical North Atlantic owing to a negative feedback (Figs. 10b and 11a). With the southward propagation of the freshwater cap, the SSS in the subtropical North Atlantic decreases below 35 psu. This leads to an exaggeration of the net evaporation in the VSF version, counteracting the additional freshening to the north. In addition, there is a remarkable subsurface warming in the Nordic seas after the shutdown of the AMOC (Fig. 11b). It results from the blocking of the heat release from the ocean interior to the atmosphere by the freshwater cap and could have an impact on the dynamical behavior of the AMOC (Mignot et al. 2007). The warming is stronger in the VSF version.
In response to the hosing, the AMOC behaves similarly in the two versions (Fig. 9b). In the 0.1 Sv case, the AMOC in both versions weakens by 7 Sv or 30% relative to the control by the end of the hosing period. This weakening is mainly attributable to the cessation of the deep convection in the Labrador Sea. The AMOC recovers to the strength in the control within 50 years after the termination of the hosing. The AMOC shuts down rapidly in response to 1.0 Sv hosing, but starts to reintensify after 150 years. This suggests that the AMOC has a single stable state under the present-day climate condition in both versions. Even though the freshwater perturbation in the VSF version is effectively much larger than 1.0 Sv, the AMOC cannot be shifted into a stable “off” state (Yin and Stouffer 2007). In contrast, the AMOC recovers more quickly in the VSF version.
The global mean sea level rise (SLR) induced by the external freshwater input is distinctly different between the two model versions (Fig. 9c). In the FWF version, 0.1 Sv and 1.0 Sv freshwater additions, respectively, cause 0.88- and 8.80-m global SLR over the 100-yr period. In contrast, global sea level changes little in the VSF version. It should be noted that, in the rigid-lid models, the global mean sea level must remain exactly the same by definition. Although global sea level is not simulated directly in VSF models, it can be diagnosed on the basis of the net freshwater flux at the ocean surface. The FWF and VSF versions give analogous simulations about the change in the regional dynamic sea level (i.e., the deviation from the global mean) in individual basins (Fig. 9d), with some difference identified only in the detailed geographical pattern (Figs. 10c and 10d). In the 0.1 Sv hosing case, a dynamic SLR of about 0.3 m occurs in the Labrador Sea and extends to the northeast coast of North America (Fig. 10c; Yin et al. 2009). In the 1.0 Sv hosing case, the dynamic SLR is much larger and faster in the Arctic and North Atlantic owing to the shutdown of the AMOC (Fig. 10d). The maximum dynamic SLR above 1.2 m occurs in the Labrador Sea and the Greenland–Iceland–Norwegian Seas. Meanwhile, the dynamic sea level falls in other oceans, particularly in the North Pacific and Southern Ocean. This interbasin seesaw pattern of the dynamic sea level change is captured similarly by both versions (Fig. 9d). The regional sea level is far from equilibrium after 100 years because the steric adjustment associated with slow modification of water mass properties in the ocean interior might take 1000 years or more to complete (Knutti and Stocker 2000; Stouffer 2004).
In response to the slowdown of the AMOC and a cooling in the northern North Atlantic, sea ice extends during boreal winter in the 0.1 Sv case, especially in the Labrador Sea (Fig. 12a). A shutdown of the AMOC in the 1.0 Sv case significantly pushes forward the sea ice boundary, especially in the northeastern North Atlantic. So sea ice covers most areas north of 45°N during boreal winter, notably, the coast of western Europe (Fig. 12b). The responses of sea ice extent are quite similar in the two versions with some difference found only in sea ice thickness.
The response of the ENSO variability in the 1.0 Sv hosing experiment appears to be the most striking difference between the FWF and VSF versions. The shutdown of the AMOC leads to a great enhancement (30%) of the tropical Pacific SST variability in the FWF version, but a slight reduction in the VSF version (Figs. 13 and 14). The mean of the Niño-3 index shows that a general cooling (0.6°–0.7°C) occurs in both versions (Fig. 14). For the FWF version, the standard deviation of the Niño-3 index increases dramatically from 0.98°C in the control to 1.28°C in the 1.0 Sv hosing run, while the skewness reduces from 0.87 to 0.45. These changes indicate that the enhancement of the ENSO variability results from an intensification of cold (La Niña) events. For the VSF version, the ENSO variability is almost the same as in the control.
The explanation of this considerable difference between the FWF and VSF versions is related to the problem of the free-surface geopotential vertical coordinate ocean model under a heavy hosing. Given that the top layer thickness (10 m) in the FWF version can increase in response to the freshwater input, adding of 1.0-Sv freshwater flux over 100 years almost doubles the layer thickness to about 19 m by the end of the hosing (Fig. 15). The top layer thickness determines the minimum mixed layer depth. Because of the eastward thermocline tilt at the equatorial Pacific, the mean thermocline is very close to the ocean surface in the eastern part (∼20 m depth for the 20°C isotherm). As a consequence, the cold water from below can more easily touch the base of a thicker top layer in the FWF hosing run, thereby triggering cold events and substantially enhancing the SST variability (Fig. 15).
To confirm the mechanism, we performed an additional 1.0 Sv hosing experiment with the FWF version. In this case, the perturbation freshwater input in the northern North Atlantic is compensated by a global uniform freshwater extraction to prevent the increase in the top layer thickness. It is found that the enhancement of the ENSO variability is greatly inhibited in the new experiment (Fig. 14c). The result suggests that the enhancement of the ENSO variability in the FWF version is likely a model artifact.
In terms of the atmosphere, the dramatic responses to the shutdown of the AMOC have been demonstrated (Manabe and Stouffer 1988; Vellinga and Wood 2002; Zhang and Delworth 2005). In the FWF version, the annual mean surface air temperature decreases considerably over the northern North Atlantic and surrounding regions in the 1.0 Sv hosing experiment, with the magnitude up to 15°C (Fig. 16a). In the VSF version, the magnitude of the cooling is smaller over the northern North Atlantic but larger over the northern North Pacific. In terms of precipitation, the decrease in the northern North Atlantic and the southward shift of the ITCZ are pronounced in both versions (Fig. 16b) with the difference statistically insignificant over most areas. In addition, the 1.0 Sv hosing stimulates long waves in the Northern Hemisphere, as shown by the 500-hPa geopotential height anomaly (Fig. 16c). The long-wave pattern is captured similarly in the VSF version.
4. Discussion and conclusions
Early development of ocean and climate models was largely constrained by limited computer power and limited knowledge of the climate system. Unphysical assumptions in the model formulation, such as the virtual salt flux assumption in the oceanic component, simplified some issues and made the early simulations of the coupled atmosphere–ocean system possible. However, the VSF method has the potential to cause systematic errors, damaging the fidelity of model simulations and future projections. In the present study, we quantitatively evaluate the errors induced by the VSF formulation using a state-of-the-art climate model. We configured two versions of the GFDL CM2.1, which are exactly the same except for the representation of the freshwater flux at the ocean surface. The models ran under both internally generated and externally imposed freshwater forcing. The results from the virtual salt flux and real freshwater flux versions are compared in detail.
We found that, although the VSF formulation could theoretically generate systematic and significant bias, the VSF-induced error in the coupled general circulation models is generally small or statistically insignificant in the unforced control run. Relatively large biases are found only in the high latitudes, the marginal and inland seas, and the regions near river mouths. These biases do not influence the large-scale density structure of the ocean and the AMOC very much. The Goldsbrough–Stommel circulation slows down the subtropical gyre in the FWF version, especially in the North Atlantic. It is also found that the difference in the SST variability simulated by the two versions is statistically insignificant in most ocean regions.
In response to a small (0.1 Sv) external freshwater forcing, the VSF version gives a simulation very close to the FWF version in many aspects. The salinity difference is not statistically significant in most ocean areas. This is because salt advection and mixing in the open ocean play an important role in counteracting the salinity bias. In the 1.0 Sv hosing run, the VSF model shows some significant biases in salinity in the perturbation region. A notable difference in the hosing runs is that the global mean sea level gradually rises in the FWF version, while it remains basically unchanged in the VSF version. However, the regional dynamic sea level change is analogous. Both versions similarly captured the interbasin seesaw pattern of the dynamic sea level change in response to a shutdown of the AMOC. It is worthy of mention that, although many aspects have been improved in simulating sea level, the latest climate models still have some limitations in representing various sources of sea level rise. For example, the effect of gravity on regional sea level rise is being incorporated in the GFDL CM2.1 (Mitrovica et al. 2009). The new model would be more suitable for the studies on the land ice melting and regional sea level rise.
In the FWF version, the simulated enhancement of the ENSO variability in response to a large external hosing reflects a deficiency of using the FWF in the geopotential coordinate ocean model. The ENSO enhancement can be attributable to the overexpansion of the top model layer, which facilitates the upwelling of the cold thermocline water to the surface. It is greatly inhibited once the hosing is compensated and the top model layer thickness remains unchanged. However, a great ENSO enhancement in some other VSF model, which is not caused by the overexpansion of the top layer, results from the Atlantic–Pacific teleconnection through the atmosphere (Dong and Sutton 2007). We noticed that some ENSO characteristics differ between the control runs of the present VSF model and the one used by Dong and Sutton, providing some explanation of the differing results. As such, we conclude that there is still large uncertainty in modeling the Atlantic–Pacific teleconnection. The latest quasi-horizontal rescaled height and pressure coordinate models could be ideal tools to study this issue further.
In summary, the present study validates the VSF model when it is used to study the present-day climate and project near-term climate evolution. However, when a large external forcing is imposed, both the VSF formulation and the use of the FWF in the geopotential coordinate model could have some deficiencies. Therefore, one should remain cautious when applying these models for the studies under large external forcing. In addition to the uncertainty evaluation, the present study also provides a comprehensive description of the climate response in the water-hosing experiments, focusing on the ocean responses. Robust features in the climate response can be identified by comparing results from the two model versions, therefore providing information for both past and future climate changes.
Acknowledgments
We thank A. Adcroft, A. Weaver, R. Zhang, and anonymous reviewers for comments and suggestions. We also thank many others at GFDL for model and computer support.
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The spread of the discharges of five major rivers (shading) in the VSF version of the CM2.1.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
The net freshwater flux at the ocean surface (mm day−1, shading) and the SSS deviation from 35 psu (contours) in the FWF version of the CM2.1 (200-yr mean): (a) the geographical distribution and (b) the zonal mean.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Error induced by the VSF formulation in equilibrium and transient runs. (a) The relative error induced by the VSF formulation as a function of local salinity. (b) Time evolution of the salinity of a top model cell (10-m thickness) in response to external freshwater input (1 and 10 mm day−1). Physically, the positive values in (a) imply an overestimate of the freshwater flux, whereas the negative values imply an underestimate. The original salinity in (b) is set to 35 psu. The salt exchange with the surrounding cells is ignored in this simple case.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Differences of the 200-yr mean climate states in the VSF and FWF versions (VSF minus FWF): (a) SSS (psu), (b) SST (°C), (c) SSH (cm), and (d) the barotropic streamfunction (Sv). Shading indicates the regions where the difference is statistically significant at 95% confidence level through the t test. Contours show the long-term mean state in the FWF version. The global mean value is subtracted in (c). Notice that (d) shows FWF minus VSF to illustrate the Goldsbrough–Stommel circulation.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Difference of interannual and longer time scale variability of SST (°C) in the control runs. Contours show the standard deviation of SST in the FWF version (200 yr). Shading indicates that the difference between the FWF and VSF versions (VSF minus FWF) is statistically significant at 95% confidence level through the F test.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Difference of the zonally averaged ocean (a) salinity (psu) and (b) temperature (°C) in the control runs. Shading shows the 200-yr mean difference (VSF minus FWF); contours show the long-term mean in the FWF version.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Streamfunction of the meridional overturning circulation (Sv): (a) global and (b) Atlantic Ocean. The long-term mean circulation in the FWF version is shaded and the difference between the VSF and FWF versions is shown by contours.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
The zonally and vertically integrated northward volume transport in different ocean basins.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Climate evolution in the control and water-hosing experiments. (a) The SSS in the perturbation region, (b) the AMOC index, (c) the global mean sea level, and (d) the dynamic sea level change in different ocean basins in the 1.0 Sv hosing run. The AMOC index is defined as the maximum overturning streamfunction at 45°N in the Atlantic. The global mean SLR induced by the freshwater input in the FWF version is removed in (d) to facilitate the comparison.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Anomalies of SSS (psu) and SSH (cm) in the water-hosing experiments (years 81–100). (a),(b) SSS; (c),(d) SSH; (a),(c) 0.1 Sv hosing; (b),(d) 1.0 Sv hosing. Contours show the anomalies relative to the long-term control in the FWF version. Shading shows statistically significant difference (at 95% confidence level through the t test) in the responses between the FWF and VSF versions (VSF minus FWF). Contour intervals are 0.4, 1.0, 5.0, and 20.0 in (a),(b),(c), and (d), respectively.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Anomalies of the zonally averaged (a) salinity (psu) and (b) temperature (°C) in the Atlantic Ocean in the 1.0 Sv water-hosing experiment (years 81–100). Contours show the anomalies relative to the control in the FWF version; shading shows the difference between the FWF and VSF versions (VSF minus FWF).
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Sea ice extent in March (sea ice concentration greater than 15%) in the control and water-hosing experiments: (a) 0.1 Sv case and (b) 1.0 Sv case. Blue shows the long-term control and red shows years 81–100 in the hosing experiment. Solid (dashed) lines indicate the FWF (VSF) version.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Different responses of the SST variability in the 1.0 Sv water-hosing experiment. Contours show the standard deviation of SST (°C) in the FWF hosing run (the first 100 years). Shading indicates the difference between the FWF and VSF versions (VSF minus FWF) is statistically significant at 95% confidence level through the F test.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Time evolution of Niño-3 index in the control runs and the 1.0 Sv water-hosing experiments. (a) FWF version and (b) VSF version; (c) statistics of Niño-3 index based on 100-year results. In (c), 001, 101, and 201 denote the periods of years 001–100, 101–200, and 201–300, respectively. FWFc denotes the water-hosing experiment with a global compensation. The Niño-3 index is defined as the mean SST in 5°S–5°N, 90°–150°W.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Thermal structure along the equator and impact of the overexpansion of the top layer. Shading is the long-term mean temperature in the control run of the FWF version. The blue straight line schematically illustrates the base of the top layer in the control, while the black straight line indicates the base of the top layer by the end of the 1.0 Sv hosing experiment.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
Atmospheric responses to the 1.0 Sv water-hosing experiments (years 81–100): (a) surface air temperature (°C), (b) precipitation (mm day−1), and (c) 500-hPa geopotential height (m). Contours show the results of the FWF version; shading shows that the difference between the VSF and FWF versions is statistically significant at 95% confidence level through the t test.
Citation: Journal of Climate 23, 1; 10.1175/2009JCLI3084.1
