1. Introduction
A mechanism for explaining low-frequency SST variability is that the ocean is forced stochastically by fluxes representing weather noise (Hasselmann 1976). Weather noise is the part of the atmospheric variability that is not the response to the boundary or external forcing. In Hasselmann’s one-point slab ocean linear model, which is closely related to the theory of Brownian motion (Einstein 1905), the weather noise forcing is taken to be random noise independent of the climate state and therefore to have a white (frequency independent) power spectrum. In the absence of the weather noise forcing there is no SST variability. The heat capacity of the ocean acts as an integrator, leading to reddening of the power spectrum of the SST response, with low frequencies in the forcing enhanced relative to high frequencies. Damping toward the mean climate causes the response to flatten near zero frequency. The model thus provides a simple explanation for the red shape of the spectrum of observed SST variability. In this case, variability at all frequencies is present in the stochastic forcing, and the low frequency response is selectively amplified. This mechanism explains important characteristics of SST with a minimal set of assumptions relative to other explanations. Hasselmann’s model suggests the null hypothesis: that all surface temperature climate variability is the response to weather noise forcing.
A second mechanism is that there is internal surface temperature variability intrinsic to the coupled atmosphere–ocean system, even in the absence of weather noise forcing. An example of intrinsic coupled variability is the chaotic (El Niño–Southern Oscillation) ENSO-like variability simulated in the model of Zebiak and Cane (1987), a model with a noise-free slave atmosphere. A third mechanism is that surface temperature variability is produced by changes in external forcing (e.g., variability in the incoming solar flux). Variability produced by internal coupled variability or external forcing (e.g., diurnal and seasonal cycles) violates the null hypothesis. Elements of the weather noise, internal coupled, and external forcing mechanisms might all be required to explain reality (e.g., Flügel and Chang 1996), and the weather noise and internal coupled variability mechanisms may not be independent from each other or from the external forcing.
When Hasselmann’s theory is applied to understanding the behavior of coupled atmosphere–ocean models, it is instructive to explicitly include the feedback between the atmosphere and the SST variability forced by the noise. This was done by Barsugli and Battisti (1998, hereafter BB98) using an extension of Hasselmann’s model that includes a coupled linear thermodynamic atmosphere (Schopf 1985). The BB98 model will be used in later sections of this paper. The air–sea coupling in BB98 is proportional to the air–sea temperature difference. The atmospheric temperature is forced by specified “noise,” leading to a heat flux that causes a SST response. The atmospheric temperature adjusts in response to the new SST, and so on. The total atmospheric evolution consists of a response to the noise plus the response to the SST, while the ocean responds to the noise (indirectly through the atmosphere) and to the feedback from the atmospheric response to the SST. The result of this (stable) coupled feedback is reduced damping of the low-frequency SST anomalies and hence increased persistence of SST anomalies. The BB98 extension of Hasselmann’s theory can be used to aid in the interpretation of observations and results from more complex coupled models (Kirtman et al. 2005).
The BB98 model provides a framework for interpretation of uncoupled GCM experiments in which the atmosphere responds to a specified evolution of SST (Bretherton and Battisti 2000). An SST solution of the BB98 coupled model (representing the observed evolution) is produced by forcing the model with a specific realization of the noise. This will be referred to as the “control” case. Next, an ensemble of atmospheric simulations is made with each member forced by this SST, but by a different realization of the noise. The SST forced ensemble corresponds to the situation of forcing an ensemble of AGCM simulations with the same specified observed SST evolution (e.g., Lau 1985; Gates 1992; and many others). The different instances of the specified noise conceptually represent the different chaotic weather evolution of the atmosphere resulting from starting from different initial conditions. The result of forcing a member of the atmospheric ensemble with this SST is the response to the stochastic weather noise (different for each member) plus the response forced by the specified SST (the same for each member). The ensemble mean of a large number of such realizations using different specifications of the noise gives the forced response since the ensemble mean response to the noise is zero in this linear model. In the Bretherton and Battisti example, the SST forced response is only about 40% of the total atmospheric variability of the control case and is coherent with the control evolution. The result commonly found in SST forced atmospheric ensembles, that the ensemble mean response to the SST resembles the observed evolution but explains only on the order of half of the observed amplitude, is then consistent with the SST being forced by the atmospheric noise. The part of the atmospheric variability not explained as the response to the SST is the atmospheric response to the stochastic forcing. The SST forced response of the atmosphere is then more correctly interpreted as the feedback of the atmosphere to the noise-forced SST variability. It is important to note that there is only one noise evolution that is consistent with the SST evolution, the one specified for the control simulation.
It is necessary to estimate the properties of the weather noise forcing in order to evaluate its role in surface climate variability. One technique that has been used for this purpose is to construct statistical models of the atmospheric response to SST by simultaneous regressions of the atmospheric fluxes against the SST. For example, Kleeman and Moore (1997) use this approach to estimate the stochastic component of the surface wind stress as a residual. Similar procedures are applied by Blanke et al. (1997) and Kirtman and Schopf (1998) among others. As pointed out by Frankignoul (1999), this procedure can confuse the noise that is forcing the SST with the atmospheric response, due to the ocean’s finite heat capacity. In particular, if the SST variability is forced thermodynamically by noise, the regression approach will produce a heat flux that would tend to amplify the SST anomalies, while the feedback (the correct forced response) must damp the SST anomalies. This confusion of forcing and response can produce totally misleading conclusions, for example, about predictability of the SST anomalies. Similar considerations apply to time filtering of data and identifying stochastic noise with shorter time scales. To separate the atmospheric response component from the noise, the time-lagged correlations must also be considered (Frankignoul et al. 1998; Navarra and Tribbia 2005).
The purpose of this article is to show that the ideas in BB98 and Bretherton and Battisti (2000) suggest a dynamically consistent method 1) to separate weather noise forcing from the atmospheric response to SST and 2) to test the null hypothesis in a special coupled model framework. This method uses a generalization of the “interactive ensemble” coupling strategy (Kirtman and Shukla 2002). In the interactive ensemble an ensemble of AGCMs is forced by the same SST. Each AGCM is started with different initial conditions so that the weather noise can be viewed as random noise uncorrelated between members. These conditions are as in the standard SST forced ensemble. However, the SST, rather than being specified, is predicted from an OGCM forced by the ensemble mean of the AGCM surface fluxes (heat, momentum, and freshwater). In the limit of an infinite number of AGCMs in the ensemble, the surface fluxes provided to the ocean are noise free and are exactly the model’s atmospheric feedback/response to the time-evolving SST. Just as in simpler models, noise forcing can then be specified externally in the interactive ensemble surface fluxes, and the noise-forced SST evolution will be controlled to some extent and independent of the atmospheric initial conditions. This contrasts with the CGCM (one atmosphere coupled to one ocean) in which the addition of a specified noise of reasonable amplitude to the surface fluxes would not be expected a priori to produce reproducible effects in independent CGCM realizations.
Section 2 demonstrates the method in the context of the BB98 model, showing that it is a natural extension of previous work mentioned above. A single realization of the model’s response to a specified stochastic forcing provides the control surface temperature evolution and total surface heat flux, as in Bretherton and Battisti. The ensemble mean surface heat flux from an ensemble of atmospheric models forced by the control surface temperature evolution defines the feedback atmospheric surface heat flux. Removing this feedback heat flux from the total defines the noise surface heat flux. The interactive ensemble version of the coupled model is then forced by this surface heat flux noise, and it is shown that the control surface temperature evolution is recovered. The procedure is illustrated in section 3 using the simple model with surface fluxes and surface temperature data from atmospheric reanalyses.
Section 4 presents results from the application of the procedure to a coupled GCM in a “perfect model/perfect data” experiment analogous to the case of the simple model described in section 2. In this example, a 50-yr CGCM integration provides the control simulation data; an ensemble of AGCMs is forced by the control SST evolution to find the atmospheric feedback surface fluxes, in this case heat, momentum, and salinity fluxes); the feedbacks are subtracted from the control surface fluxes to define the weather noise surface fluxes; and the interactive ensemble version of the CGCM is forced by the weather noise surface fluxes. The results are summarized in section 5.
2. Interactive ensemble in the context of the simple model
As there is now no explicit forcing of the atmosphere by noise, the atmospheric solution is the forced response of the atmosphere to the ocean temperature. However, if the noise forcing of the atmosphere is eliminated, the original interactive ensemble version of the simple model will not produce any variability. To produce SST variability in the interactive ensemble, forcing applied to the ocean, representing specified fluxes, is included.
The necessary assumption concerning the noise forcing for this demonstration to be valid is that the ensemble mean of the different noise realizations Nj is zero (for an infinite ensemble). Otherwise, there is no requirement concerning the spectral distribution of the forcing in time, although it might be useful to consider stochastic forcing for conceptual purposes.
There is nothing in the simple model or the reconstruction of surface temperature variability using the interactive ensemble version that precludes their application to surface types other than ocean. The same models, although with different specifications of the heat capacity parameter β, can be applied to other surface types such as land or sea ice. In the case of land or sea ice, the values of β will usually be much less than for ocean.
3. Results from the simple model interactive ensemble
To illustrate the procedure, the application of the interactive ensemble to testing the null hypothesis is illustrated using the simple model derived in the previous section. Two reanalysis datasets of monthly mean surface heat flux and surface temperature are used to represent the observations: the National Centers for Environmental Prediction (NCEP) reanalysis for 1950–99 (Kalnay et al. 1996) and the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) for 1958–2000 (Uppala et al. 2004, 2005).
First, Te for each month for the reanalysis period is found by solving (4) with To specified as the monthly evolution of surface temperature anomalies from the respective reanalysis (means as a function of month over the reanalysis period removed). Here Te represents the forced atmospheric temperature, defined as the mean from an ensemble of atmospheric simulations forced by the observed surface skin temperature. A time step of 5 days is used, with the monthly forcing data interpolated to the appropriate time, and the month length taken as 30 days. The surface heat flux from the atmospheric feedback to the observed surface temperature is then evaluated using (8b). The atmospheric heat flux feedback is removed from the observed net surface flux anomalies (net solar plus net longwave minus sensible minus latent, monthly means removed) using (8c). The resulting flux time series F* is used to force the interactive ensemble, Eqs. (5) and (6). This procedure is carried out at each grid point, whether ocean, land, or sea ice. However, the different heat capacities of the active layer of land, sea ice, and ocean need to be taken into account. For simplicity, an energy balance approximation is made over land and sea ice, with the left-hand side of (6) set to zero, to approximate the small heat capacity of land or sea ice compared to that of the ocean or atmosphere.
Following this procedure, the interactive ensemble produces a time series of monthly mean surface temperature for January 1950 through December 1999 using the NCEP data and for January 1958 through December 2000 using the ECMWF data. The correlation of the interactive ensemble surface temperature with the analyzed surface temperature and the ratio of the SST anomaly (SSTA) variance produced by the simple model to the observed variance is shown in Fig. 1 for the NCEP data and in Fig. 2 for the ECMWF data. These results can be viewed as estimates of the importance of weather-noise heat flux forcing in producing the surface temperature variability observed in the latter half of the twentieth century. In regions where the correlations are close to one, the surface temperature variability is produced by weather-noise heat flux forcing and the null hypothesis is satisfied, while in regions where correlations are not high other processes are important. Regions where the variability is noise forced then include almost all land and sea ice and much of the extratropical North Pacific and North Atlantic. There is also a large region in the tropical eastern Pacific where correlations are high. Other regions, such as the equatorial oceans, do not have large correlations.
However, the inference that the regions of high correlation are noise forced and that those where correlations are not high are not noise forced is both model dependent and data dependent. To interpret the results of Figs. 1 and 2, the effects of the assumptions and inaccuracies of both the simple model and the reanalysis procedure must be taken into account and evaluated. Some of these are enumerated below:
The reanalysis surface heat fluxes are derived quantities (forecast or model generated) constrained by the assimilated data. As such, errors can be introduced by poor data coverage as well as biases and inadequate parameterizations in the reanalysis models.
The BB98 atmospheric model is far from perfect: its physical parameterizations are broad caricatures of the actual physical processes and it lacks dynamics. This affects both the estimate of the weather-noise surface fluxes and the interactive ensemble response to those fluxes. In estimating the noise, the forced response removed using the simple model is only the local thermodynamic feedback of the atmosphere to the observed surface temperature anomalies. The atmospheric model physical parameterizations are not realistic, and the local feedbacks therefore contain errors. The neglect of atmospheric dynamics means that the simple model does not correctly represent the scale dependence and propagation characteristics of the atmospheric response to the SST and the associated feedbacks. The feedbacks from surface temperature anomalies in other locations (both nearby and remote) are neglected and are therefore aliased as “noise” by our definition. To more correctly calculate the feedbacks, it is necessary to use an atmospheric model that includes dynamics, such as an atmospheric GCM. For example, ENSO teleconnections present in the reanalysis surface fluxes from the physical system are not included in the simple model and are then included erroneously as part of the local weather noise. Then the remotely forced part of the response (for an estimate see Lau and Nath 1996) is not correctly removed, and errors are introduced into the derived noise. Calculating the atmospheric feedbacks using a model with more realistic physical parameterizations and dynamics, and using these feedbacks to define the weather noise heat flux would produce a more realistic estimate of the noise than using the simple model. A more realistic atmospheric model would also improve the physical significance of the interactive ensemble diagnosis.
The BB98 ocean model does not include ocean dynamics. Therefore, heat fluxes due to oceanic motions are neglected. Notice, for example, the Gulf Stream region in Figs. 1a and 2a, where correlations are low. One explanation for those low correlations could be oceanic advection of the noise-forced SST anomalies away from the forcing region (Frankignoul and Reynolds 1983; Saravanan and McWilliams 1998). In fact, the locations of many of the major ocean surface currents, such as the Kuroshio and Antarctic Circumpolar Current (ACC), among others, show up as regions of low correlation in Figs. 1a and 2a. Therefore, the interpretation of some of the regions of low correlation as not being weather noise forced could change if a dynamical ocean model is used in the interactive ensemble diagnosis and if the definition of weather noise forcing is generalized to include the surface momentum and freshwater fluxes.
Throughout the tropical oceans, the correlations are small (NCEP) or predominantly negative (ERA-40). This is probably a consequence of the neglect of the heat flux divergences due to ocean dynamics (e.g., forced by surface wind stress). We might expect that the SST variability in this region is caused by the heat flux divergence due to motions in the oceans forced by the surface wind stress and that the atmospheric heat fluxes exist primarily to damp this variability (i.e., are forced by the SST). If this is the case, the low correlations are due to the neglect of ocean dynamics. In addition, a systematic underestimation of the SST forced atmospheric heat flux in the BB98 atmospheric model could lead to the negative correlations in low latitude, for example, if the noise-forced heat flux was small compared to the feedback heat flux.
The ocean heat storage is not correctly represented. A single constant value is used for the depth of the ocean mixed layer in the simple model, whereas the mixed layer depth in reality varies in space and time. The variance ratios in Figs. 1b and 2b are much larger than one in extensive regions. This could be due in part to choosing a mixed layer depth that is too shallow in these areas. The regions where the simple model overestimates the SST variance are also regions of generally reduced correlation. Errors in the mixed layer depth specification could lead to errors in the correlations, as the mixed layer depth affects the phase of the response relative to the forcing (Schneider 1997). The reanalysis fluxes seem to contain useful phase information about the future in extratropical regions where the variance ratio is not much larger than one, which could be evidence that the mixed layer depth and the reanalysis fluxes are reasonably accurate for these regions. Interpreted in the context of the simple model, the observed SST evolution in the high-correlation regions is the local response to the local heat flux weather noise forcing.
Over land and sea ice, the reanalysis surface temperature used is the skin temperature, which is a forecast quantity forced locally by the reanalysis surface heat fluxes. Additionally, the net heat flux over these regions should be close to zero averaged over a sufficient time, as the heat capacity is small. In this situation, the low-frequency forced response surface heat flux found from (4) and the noise flux found from (2) will be equal and opposite, and a surface energy balance heat budget will reproduce the reanalysis surface temperature. Therefore, the diagnosis over land and sea ice is expected to be degenerate: the land and sea ice surface temperatures estimated from energy balance using reanalysis surface fluxes will agree with the reanalysis surface temperatures, and correlations will be high. While this is the case everywhere over land and sea ice using the ERA-40 data, as shown in Fig. 2, there are some land regions with low correlations found using the NCEP data shown in Fig. 1, such as near the equator in the Amazon, Indonesia, and Africa. In the Amazon low-correlation region, examination of the total NCEP surface heat flux shows that the condition of zero net heat flux does not hold, so the argument given above fails. Large discontinuities in the flux in August–September 1984 (to relative negative anomalies) and in January–February 1994 (back to pre-1984 levels) can be seen, although the surface temperature behaves smoothly. The simple model diagnosis then highlights areas where there are potentially serious problems with the NCEP reanalysis.
- External forcing (due, e.g., to changes in atmospheric gaseous composition, particle distribution, and incoming solar flux) is not included in the diagnostic calculations. In the simple model, changes in atmospheric composition might be represented by specifying time-dependent coefficients in the longwave radiative parameterization coefficients. Changes in incoming solar flux or effects of volcanic eruptions might be represented by specifying the time/space history of the external forcing G(t) on the right-hand side of Eq. (3) and in the specified surface temperature atmospheric ensemble (4):
If external forcing is not included in the interactive ensemble but is included in the observations/control model [e.g., by having G≠0 in (9) but G = 0 in (10)], then the atmospheric model ensemble diagnosis will interpret the external forcing contribution to the surface fluxes as noise external forcing, and the interactive ensemble forced with this estimate of the noise will reproduce the surface temperature evolution. To correctly diagnose the role of external forcing, it must be included in both the observed/control surface fluxes and the diagnostic atmospheric model.
External forcing is only partially represented in the ECMWF reanalysis (time history of certain well-mixed greenhouse gases specified) and not included in the NCEP reanalysis model. The simple model diagnosis using the reanalysis fluxes then can be misleading in that external forcing is not fully represented in the surface heat flux, although its effects are present in the surface temperature, and in that external forcing is not included in the diagnostic atmospheric model.
4. Application in a coupled GCM
The application of the method to more complex coupled models is a straightforward extension of the above concepts. The weather noise in the surface fluxes is determined relative to the surface forced atmospheric ensemble mean surface fluxes. This noise is used to force the ocean in the interactive ensemble. The linearity or nonlinearity of the atmospheric model is not important as long as the atmospheric ensemble response to the specified surface forcing is well behaved. In the perfect model/perfect data configuration of section 2, the weather-noise-forced interactive ensemble will reproduce the control surface temperature evolution, even using nonlinear atmosphere and ocean GCMs as long as 1) the ocean initial conditions are the same, 2) the ocean has no internal variability that is not directly forced by the atmosphere, and 3) the noise-forced interactive ensemble solution is stable (no intrinsic coupled variability). This is because the method will then reconstruct the forcing and solution to the equations governing the ocean (land or sea ice), consistent with the model’s atmospheric feedback.
The perfect model/perfect data experiment then serves as a test as to whether the model’s climate variability satisfies the null hypothesis. If the experiment with perfect ocean initial state reproduces the control variability (and in addition the interactive ensemble is sensitive to the noise forcing), then the null hypothesis is satisfied. If the null hypothesis is violated because of ocean internal variability, it can be redefined to include oceanic as well as atmospheric “weather noise.” Whether or not it is violated because of intrinsic coupled variability is important for understanding the dominant modes of the simulated low-frequency climate variability. The BB98 model satisfies the null hypothesis.
We describe here an approximation to the perfect model/perfect data experimental design in a coupled GCM setting. The control, a long simulation of the coupled GCM, produces the observational data. The weather-noise surface fluxes are determined with the aid of an AGCM ensemble forced by the control SST, and an interactive ensemble version of the CGCM is forced by these fluxes. The weather noise forcing includes momentum and freshwater fluxes, as well as heat fluxes. Land surface/sea ice surface conditions are not specified in the calculation of the atmospheric feedback, and no weather noise forcing is applied over land or sea ice in the interactive ensemble; so this is an incomplete application of the method.
This example is presented for several reasons. A few are listed below.
It illustrates the reconstruction method using nonlinear dynamical atmosphere and ocean models that are much more realistic than those used in BB98. Comparison of the reconstruction using the same input data into the GCM and simple model configurations illustrates the model dependence of the method and the effects of model error when the data errors are not of concern.
It is a basic step in quantifying the comparison of the model’s internal climate variability to the null hypothesis. Identification of the model’s own coupled internal variability will be important for understanding the results of application of the method to data from the real climate system.
It helps document the importance of known sources of error in the reconstruction procedure, such as that due to the use of AGCM ensembles of finite size. This information will be important in evaluating and understanding the results from application of the procedure using reanalysis data, where the issues of (unknown) errors in the models and the data will have to be addressed.
a. Models
The coupled GCM is the anomaly coupled version of the Center for Ocean–Land–Atmosphere Studies (COLA) CGCM described fully in Kirtman et al. (2002 and references therein). The AGCM (COLA version 2) uses a spectral sigma-coordinate dynamical core based on the National Center for Atmospheric Research Community Climate Model version 3 (NCAR CCM3: Kiehl et al. 1998) with T42 horizontal resolution and 18 levels in the vertical. It contains the usual suite of atmospheric physical parameterizations. The land model is a version of the Simple Biosphere (SiB) model (Xue et al. 1991). The ocean model is the Modular Ocean Model version 3 (Geophysical Fluid Dynamics Laboratory MOM3: Pacanowski and Griffies 1998) with 1.5° horizontal resolution (meridional resolution increasing to 0.5° near the equator) and 25 levels in the vertical. The domain of the active ocean is 74°S–65°N, and a monthly climatological sea ice distribution is specified.
The atmosphere and ocean are coupled once daily using utilities supplied with MOM3. There were some problems in the COLA implementation of these utilities, particularly with regard to surface properties seen by the atmosphere in some grid boxes that contain mixed surface type (land/water, land/sea ice, water/sea ice, or land/water/sea ice). The atmosphere of the coupled GCM (single atmosphere or interactive ensemble version) sees a climatological surface temperature in these regions (B. Kirtman 2006, personal communication; Fig. 3).
b. Experimental procedure
The control simulation is a 50-yr segment from a multicentury “current climate” run conducted with external forcing held constant. The AGCM ensemble has 10 members and is forced by the 50-yr evolution of the monthly mean control simulation SST with land (temperature, soil moisture) and sea ice (temperature) unconstrained. The ensemble mean surface fluxes of heat, momentum, and moisture are subtracted from the control surface fluxes to define the weather noise. The interactive ensemble configuration (Kirtman and Shukla 2002) is a single OGCM forced by the ensemble-mean surface fluxes of six AGCMs. Each AGCM is coupled to its own land model, starts with different initial conditions, and is forced by the same OGCM SST. The ocean initial condition is the same as that of the ocean in the control simulation. The interactive ensemble OGCM is forced by the monthly mean weather-noise surface fluxes. The AGCMs used in the control, the AGCM ensemble, and the interactive ensemble are identical in numerics, parameterizations, and resolution.
Differences between the control simulation evolution and the interactive ensemble reconstruction can occur for two reasons: 1) error from various approximations made in applying the method and 2) intrinsic variability of the interactive ensemble not due to the weather noise forcing. Potential sources of error include the finite model ensemble sizes, the use of monthly mean rather than instantaneous forcing in calculating the atmospheric feedbacks to the control SST and the interactive ensemble response to the weather noise, and incomplete implementation of the procedure over land and sea ice. Differences due to intrinsic variability of the interactive ensemble cause the null hypothesis to be violated.
c. Results
The correlation of the monthly interactive ensemble and the control simulation surface temperature anomalies and the variance ratio are shown in Fig. 3. The regions of highest correlation in Fig. 3a are in the northern and southern subtropical oceans, in regions generally similar to the regions of high oceanic correlation in Figs. 1a and 2a. Errors are introduced into the definition of the noise by the finite size of the AGCM ensemble (10 members) and the interactive ensemble AGCM ensemble (6 members). If these errors are uncorrelated with the control solution and with each other, an estimate of the highest correlation expected from the interactive ensemble is 0.86 (≈
Over land and sea ice, the specified noise forcing is zero in this incomplete implementation of the procedure, and correlations in Fig. 3a are generally much lower than over the oceans. Significant correlations are found over most land areas equatorward of 30° latitude, with largest correlations near the equator. The results over land can be viewed as an estimate of the “predictability” of land surface temperature anomalies, given that the SST is known, and should be similar to, but probably smaller than, the correlations from the SST forced AGCM ensemble.
Correlations of the SST are relatively large in the eastern and central equatorial Pacific. These high correlations are a consequence of similar ENSO-like variability in the control and noise-forced interactive ensemble simulations, as shown by the Niño-3.4 (5°S–5°N, 190°–240°E) SSTA evolutions in Fig. 4. The largest difference between the control and globally noise-forced interactive ensemble indices occurs in the first month of the simulation, possibly indicating a cold start issue in the SST forced AGCM ensemble. After the first few months, the two simulations agree well (correlation 0.77 over the full period; both have variance 0.52 K2).
There is more than one potential explanation for the agreement in the Niño-3.4 variability. One possibility is that it is noise forced. Another suggested by an anonymous reviewer is that the coupled model has internal coupled equatorial Pacific variability that is insensitive to the weather noise (Zebiak 1989 describes this kind of behavior) and which would reproduce the control evolution given the same ocean initial conditions. The fact that the noise-forced interactive ensemble and control Niño-3.4 indices have a large difference in the first month of simulation, despite starting from identical ocean initial states, argues against this noise-independent interpretation since, once differences develop, solutions to a chaotic system will continue to diverge.
Results from another simulation that we have carried out are also relevant to this issue. The simulation, which will be called ATL, is the same as the globally noise-forced interactive ensemble simulation except that the noise forcing is restricted to the North Atlantic between 15° and 65°N. A comparison of ATL with the control simulation is shown in Fig. 5. The correlation between the control and ATL simulations is high only in the region where the noise forcing is applied. Additionally, the variance outside the forcing region is much reduced, except in some isolated regions that will be discussed below. This is strong evidence that the Niño-3.4 variability (as well as the surface temperature variability in most other regions) is weather noise forced in the control simulation. The ATL Niño-3.4 SSTA, shown in Fig. 4, is of substantially smaller amplitude than (variance 0.14 K2) and uncorrelated with the control Niño-3.4 SSTA (correlation 0.057).
There is a region of enhanced SST variability in the western equatorial Pacific in ATL in Fig. 5b. This is evidence of the equatorial Pacific internal coupled variability identified in the unforced interactive ensemble by Kirtman and Shukla (2002) and Kirtman et al. (2006). The region of this internal coupled variability corresponds to a region of relatively low correlation in Fig. 3a. A western Pacific index of SST defined as the average over 5°S–5°N, 160°E–180° has correlation 0.61 between the control and global noise-forced simulations. That is, the agreement between the noise-forced interactive ensemble and the control is reduced in the region where there is self-sustained internal coupled variability. On the other hand, the western Pacific index is uncorrelated between ATL and either the control or global noise-forced simulations. Therefore, the SST variability in this area is influenced by both the noise forcing and the internal coupled variability.
In contrast to the results shown in Figs. 1b and 2b, the ratio of the surface temperature variance of the interactive ensemble to the control simulations (Fig. 3a) is close to one for most of the ice-free ocean. The variance ratio is on the order of 0.5 for land equatorward of 30° latitude and small for land and sea ice poleward of 30° latitude. The regions of higher variance over land correspond to regions of higher correlation. Looking in more detail over the oceans, the ratio is somewhat greater than one in extensive regions, which could be due to the reduction in ocean stirring from using monthly mean rather than instantaneous weather noise forcing. This issue could be addressed in interactive ensemble CGCMs by “informing” the ocean about the mean strength of the instantaneous weather noise stirring of the atmospheric ensemble members.
d. Model dependence
To illustrate the effects of model error on the procedure, the calculations in section 3 using the simple model are repeated using the net surface heat flux and SST from the CGCM control simulation. As before, the atmosphere and ocean models lack dynamics and have “error” relative to the GCMs, which are perfect in the sense of being consistent with the data. Also, there is now no problem of input data error. Results are shown in Fig. 6. Compared to Figs. 1a and 2a, the correlations in Fig. 6a are generally higher. This increase could be due to the reduced error in the input data. The regions of high and low correlations over open ocean generally coincide in Figs. 1a, 2a, and 6a: high in the subtropics and midlatitudes in the eastern North Atlantic and North Pacific and in the southern subtropics, low in the western North Atlantic and North Pacific, very low in the equatorial Atlantic, with negative correlations in the equatorial Pacific, and low in the Southern Ocean. This agreement suggests that the CGCM simulation has realistic heat flux weather-noise characteristics, that the simple model responds realistically to this noise in some sense, and that the reanalysis surface heat fluxes contain useful information.
Figure 6c shows the change in the correlations from the simple model (Fig. 6a) to the CGCM (Fig. 3a). The changes, which are generally increases, come from using the consistent dynamical atmosphere and ocean models in place of the simplified ones. Although the role of atmospheric dynamics and mixed layer evolution remain to be diagnosed, most of these increases are consistent with the interpretation of being due to the inclusion of ocean dynamics, in particular western boundary currents in many locations, the ACC, and equatorial ocean dynamics in the Atlantic and Pacific.
e. Internal variability of the ocean
While the correlations in Fig. 3a are much more spatially uniform than those from the simple model, they still contain substantial spatial structure. Correlations over oceans are higher in the eastern subtropical and midlatitude North Atlantic and North Pacific than in surrounding regions: there is a tropical band of lower correlation and another band of lower correlation in the Southern Ocean. At least part of the explanation for this structure is the ocean model’s own internally generated weather noise. The effect of the ocean model’s internal variability on SST is estimated from a multidecade ocean-only simulation in which the OGCM surface fluxes were prescribed to be observed climatological wind stress and a parameterized damping heat flux (Wu et al. 2004). The OGCM’s internally generated SST variability is shown in Fig. 7. There is a general correspondence between the regions of larger internally generated SST variability in Fig. 7 and extratropical regions of lower correlations in Fig. 3. However, there is no tropical signal apparent in the ocean weather noise, consistent with the interpretation of the enhanced SST variance in the western equatorial Pacific in Fig. 5b as intrinsic coupled variability. This suggests that the weather noise in the null hypothesis should include variability intrinsic to the ocean and that a generalized interactive ensemble, with the SST determined by the ensemble mean of several OGCMs (Kirtman et al. 2006), could be used to help quantify the role of oceanic internal variability.
The role of atmospheric dynamics is not clear from Figs. 3a and 6a, nor is a mechanistic understanding of the role of the ocean dynamics in the various regions (e.g., advection of anomalous temperature by mean currents or mean temperature by anomalous currents, etc.). However, these roles can be isolated by suitably designed experiments. For example, atmospheric dynamics can be isolated by constructing an interactive ensemble consisting of AGCMs coupled to a slab mixed layer ocean, advection by variability in the currents can be reduced by setting the weather noise momentum flux to zero in the interactive ensemble CGCM, and so on. These types of simulations are underway and will be reported in due course.
5. Summary and discussion
A method has been described that can be used to diagnose and understand the mechanisms for low-frequency surface temperature variability. The method isolates the role of weather noise by forcing model simulations with observed/analyzed data. The method was illustrated using observed and synthetic data in a simple dynamics-free coupled model and synthetic data in a full coupled GCM. It was proved that a particular evolution of the surface temperature (the “observed” surface temperature) in a stochastically forced simple model is reproduced by a weather-noise-forced interactive ensemble version of the same model, when the weather noise forcing is defined to be the total surface heat flux minus the atmospheric heat flux feedback to the observed surface temperature (the surface temperature “forced” atmospheric response). The procedure, including the determination of the weather noise momentum and freshwater fluxes, was applied to an interactive ensemble configuration of a coupled GCM.
A null hypothesis for surface temperature variability is that it is forced by weather noise generated internally in the (atmosphere or ocean) component models so that there is consequently no intrinsic coupled variability. If this null hypothesis is satisfied, the method described here will reproduce the observed surface temperature variability, and it is straightforward to then design experiments to isolate the roles of various mechanisms and regional interactions. The null hypothesis appears to hold regionally over much of the World Ocean in the diagnosis of the SST variability in a coupled GCM, with the notable exception of the equatorial western Pacific.
The method was demonstrated in the simple model using data from atmospheric reanalyses. The usefulness of the method depends on the data being sufficiently accurate and the models being sufficiently realistic. A comparison with a similar diagnosis using CGCM-generated data and with the CGCM interactive ensemble indicates that the reanalysis fluxes may contain sufficient information and that the GCMs might be sufficiently realistic to be used together to give useful results concerning observed surface temperature variability.
In application to coupled GCMs, the complete determination of the weather noise surface fluxes and interactive ensemble diagnosis will require several extensions of procedures used in section 4. In particular, the atmospheric feedbacks to the surface evolution need to include the AGCM ensemble response to the evolution of the land surface and sea ice boundary conditions. Weather noise forcing in the interactive ensemble needs to be included over land and sea ice. Although the quantitative importance of these extensions on the determination of the weather noise over the oceans and the subsequent interactive ensemble SST reconstruction is not known, the land-induced feedbacks on the ocean could be expected to be comparable in magnitude to the ocean-induced feedbacks on land, which were shown in the CGCM example.
To directly apply the method to analyzed observations of the real climate system, for example, to address questions of attribution and detection of climate change, it has been illustrated using the simple model that external forcing should be consistently taken into account in both the analysis system model and the diagnostic models since the effect of the external forcing is already present in the observed surface temperature.
Acknowledgments
We thank Ben Kirtman for his assistance in performing the GCM experiments and Mike Fennessy for his help in processing the reanalysis data. Claude Frankignoul provided useful comments on an early draft. This research was supported by NSF Grant ATM-0342104.
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(a) Point correlation of monthly mean surface temperatures of the weather-noise-forced simple coupled model and the NCEP reanalysis for 1950–99. The weather noise is derived from the total surface fluxes of the NCEP reanalysis. Correlations in shaded regions are significantly different from zero with 95% confidence assuming 600 degrees of freedom. (b) Ratio of SST variance of simple model to observations.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
As in Fig. 1 but using data from the ERA-40 reanalysis for 1958–2000.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
(a) Point correlation of monthly mean surface temperature anomalies of weather-noise-forced interactive ensemble CGCM and the 50-yr control simulation. The weather noise is derived from the total surface fluxes of the control simulation using an SST forced AGCM ensemble. Surface temperature anomalies supplied to the atmosphere are identically zero in the white regions in the coupled GCM due to coupling issues. (b) Ratio of surface temperature variance of interactive ensemble to the control simulation.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
Control (black), global weather-noise-forced interactive ensemble (red), and North Atlantic weather-noise-forced interactive ensemble (purple) simulations of Niño-3.4 SSTA.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
(a) Point correlation and (b) surface temperature variance ratio, as in Fig. 3, but for weather noise forcing restricted to the North Atlantic between 15° and 65°N.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
(a) Correlation from simple model diagnosis, as in Fig. 1a, but with surface temperature and net surface heat flux data from the 50-yr CGCM control simulation. (b) Variance ratio from the simple model diagnosis, as in Fig. 1b. (c) Difference of correlations: CGCM diagnosis (Fig. 3a) minus simple model diagnosis (Fig. 5a).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
A measure of “weather noise” internal to the OGCM: standard deviation of monthly SST anomalies from 46 year of an OGCM-only simulation forced by climatological wind stress.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4026.1
