Aerosols from anthropogenic and natural sources have been recognized as having an important impact on the climate system. However, the small size of aerosol particles (ranging from 0.01 to more than 10 μm in diameter) and their influence on solar and terrestrial radiation makes them difficult to represent within the coarse resolution of general circulation models (GCMs) such that small-scale processes, for example, sulfate formation and conversion, need parameterizing. It is the parameterization of emissions, conversion, and deposition and the radiative effects of aerosol particles that causes uncertainty in their representation within GCMs. The aim of this study was to perturb aspects of a sulfur cycle scheme used within a GCM to represent the climatological impacts of sulfate aerosol derived from natural and anthropogenic sulfur sources. It was found that perturbing volcanic SO2 emissions and the scavenging rate of SO2 by precipitation had the largest influence on the sulfate burden. When these parameters were perturbed the sulfate burden ranged from 0.73 to 1.17 TgS for 2050 sulfur emissions (A2 Special Report on Emissions Scenarios (SRES)), comparable with the range in sulfate burden across all the Intergovernmental Panel on Climate Change SRESs. Thus, the results here suggest that the range in sulfate burden due to model uncertainty is comparable with scenario uncertainty. Despite the large range in sulfate burden there was little influence on the climate sensitivity, which had a range of less than 0.5 K across the ensemble. We hypothesize that this small effect was partly associated with high sulfate loadings in the control phase of the experiment.
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 Recently, studies have been undertaken that perturb aspects of general circulation models (GCMs) to try to estimate the range of uncertainty associated with unresolved processes [Murphy et al., 2004; Stainforth et al., 2005]. Such studies have targeted the model representation of clouds and precipitation; generally considered to be the most uncertain areas within the atmospheric component of GCMs. These studies used the Hadley Centre Atmospheric Model coupled to a thermodynamic slab ocean model and were used to perform sensitivity tests. The models were initialized with preindustrial levels of CO2 and no aerosol; from this, atmospheric concentrations of CO2 were instantaneously doubled to estimate the range in climate sensitivity (equilibrium surface air temperature response to a doubling of atmospheric CO2) associated with the imposed physics perturbations. The climate sensitivity ranged from under 2 K to more than 11 K across the studies and indicated that the physics perturbations (and therefore the uncertainty in the model physics) were able to greatly alter the final equilibrium climate state within the GCMs. Neither study included the effects of aerosol, which also present a large source of uncertainty in GCMs.
 Sulfate aerosol is a useful surrogate for other aerosol species (which cannot be represented in this study) that induce a surface cooling, and has been widely used in GCM studies [Rotstayn et al., 2000; Williams et al., 2001; Kristjánsson et al., 2005]. Sulfates are also derived from both anthropogenic and natural emissions and so provides a means to estimate the uncertainty in the current and future climate state from nonanthropogenic sources.
 The total loading of sulfate in the atmosphere at any given time is known as the sulfate burden. The estimation of the current anthropogenic contribution to the sulfate burden within model studies varies from 1.19 m−2 [Takemura et al., 2005] to 5.5 m−2 [Ghan et al., 2001] with a mean value across several models of approximately 2.5 m−2 (average of the values of Forster et al. [2007, Table 2.4]). Each of the models given by Forster et al.  used the same emissions; the range in sulfate burden therefore being associated with the different parameterization schemes adopted to model the emissions, conversion and deposition of sulfur species within the atmosphere.
 The sulfate aerosol residing in the atmosphere is able to influence the climate through the direct and indirect radiative effects. The direct effect is the ability of aerosol to scatter or absorb radiation, in the case of tropospheric sulfate aerosol (as in this study) only the scattering of solar radiation will be considered. The indirect radiative effect is the ability of aerosol to influence the radiative properties of clouds and is split into two effects (first and second indirect effects). The first indirect effect is responsible for modulating cloud albedo whereas the second indirect effect is responsible for changing the cloud lifetime by influencing precipitation efficiency (see Haywood and Boucher  for more detail). In the case of sulfate aerosol, both the direct and indirect radiative effects act to cool the climate system.
 The different representations of the sulfur cycle across models leads to a range of values for the direct radiative effect, which has been published by Forster et al. . The mean value and uncertainty range in the direct radiative forcing (defined by Forster et al.  to be the change in net irradiance at the top of the atmosphere as a global mean once stratospheric temperatures have adjusted to the forcing agent) for sulfate aerosol is given as −0.4 ± 0.2 Wm−2 [Forster et al., 2007], which suggests the direct effect of this aerosol species alone is still uncertain by a factor of a 50%. The causes of the uncertainty are associated with aerosol optical properties, the effects of relative humidity (hygroscopic growth [see Haywood et al., 1997; Haywood and Ramaswamy, 1998]), emissions of precursor gases, cloud cover and burden, which are all represented differently in different models (see Boucher et al.  for an intercomparison).
 Accompanying the uncertainty in the direct radiative effect is the much larger uncertainty associated with the indirect radiative effect. Recent reviews by Lohmann and Feichter  have estimated the range in the first indirect radiative effect to be −0.5 to −1.9 Wm−2 and the second indirect radiative effect to be −0.3 to −1.4 Wm−2. Forster et al.  suggested that the range in the first indirect radiative effect is skewed toward more negative values and estimated the range to be −0.3 to −1.8 Wm−2 with a median value of −0.7 Wm−2. The sources of these uncertainties stem from the representation of clouds, precipitation, aerosol burden, cloud microphysics and radiative transfer as well as the effects of aerosol on ice cloud and snowfall [Lohmann, 2004] within GCMs.
 The studies given so far have provided estimates of the sulfate burden as well as the direct and indirect radiative effects for present-day conditions relative to preindustrial, and show a large spread in forcing and loading. However, they do not consider the uncertainty associated with future anthropogenic sulfur emissions and subsequent sulfate loadings. Pham et al.  use six scenarios (A1B, A1F1, A1T, A2, B1 and B2 taken from the Special Report on Emissions Scenarios (SRES) from the Intergovernmental Panel on Climate Change (IPCC)) to look at the range in the future sulfate burden. Pham et al.  suggest that (using the Laboratoire de Météorologie Dynamique (LMD) GCM only) the future anthropogenic sulfate loading may vary from 0.33 to 0.83 TgS, with a possibly even larger range if other models had been considered in the study.
 In an attempt to quantify some of the uncertainties associated with modeling aerosols (as highlighted above), a selection of experiments following the perturbed physics methods outlined by Murphy et al.  and Stainforth et al.  could be applied to an aerosol scheme within a GCM. For this project, a large ensemble of models were run using distributed computing within the public (and business) domain through climateprediction.net. Distributed computing is the ability to “tap in” to unused CPU (central processing unit) time and disk storage to run (for example) a general circulation model. Each downloaded model was given a specific set of perturbations to the physics and initial conditions such that all models were independent from each other.
 Using this enhanced computer power, the aim of this work is to quantify the response of the climate system to perturbations to a fully interactive sulfur cycle scheme within a GCM for present-day and future sulfur emissions. In quantifying the uncertainty associated with present and future sulfate aerosol effects, a selection of boundary condition, perturbed physics and initial condition perturbation experiments were run to explore the range in model responses to these perturbations. Section 2 will provide a background to the model used as well as a description of the interactive sulfur cycle. Section 3 will look at the experimental design including some more background on ensemble modeling and data retrieval issues. Section 4 looks at the statistical methods used to evaluate the performance of the large data set retrieved. Sections 5 and 6 will look at the range and response of the sulfate burden and surface air temperature to each of the perturbations given in section 3 with concluding remarks and a discussion in section 7.
2. Model Setup
2.1. Hadley Centre Model
 The atmospheric component of the model used in this study was the Hadley Centre Atmospheric Model version 3 (HadAM3) GCM. HadAM3 is a hydrostatic grid point model and for these experiments the horizontal resolution was 2.5° latitude by 3.75° longitude. There are 19 vertical levels that use a hybrid σ-p coordinate system where the hybrid system uses σ coordinates at the surface (σ is the pressure at a given level divided by the surface pressure), which changes to a purely pressure coordinate system at the top level (allows levels to follow orography). Model time steps are 30 min in duration (48 time steps per day) with 30 days in each month and 360 days in a model year. The parameterized schemes used in HadAM3 are radiation, clouds, boundary layer processes, convection, precipitation (convective and large scale), gravity wave drag, advection, diffusion and the sulfur cycle. For more detail on the schemes used in the Hadley Centre climate model see Gregory et al. , Johns et al. , Stratton  and Pope et al. .
 The ocean model used in this study is the Hadley Centre slab ocean model (coupled to HadAM3 to give HadSM3) and is a simple thermodynamic mixed layer ocean model [see Williams et al., 1999]. The simple slab ocean allows atmospheric boundary condition perturbations (such as doubling CO2) to change the distribution of sea surface temperatures (SST), however there is no dynamical response within the ocean. The lack of ocean dynamics allows the model to rapidly reach equilibrium within a few years and is less computationally expensive than a fully dynamical ocean model but there is no information on the time-dependent climate response as in climate change experiments (see Intergovernmental Panel on Climate Change (IPCC)  for more details). The ocean model also includes a representation of sea ice such that the sea ice albedo feedback mechanism [see Curry et al., 1995] can be represented. Because of the simple thermodynamic properties of the slab ocean, heat fluxes (anomalous heat convergences) from the surrounding ocean need to be calculated at each grid point to provide a realistic SST distribution. These heat fluxes are calculated in the calibration phase of the model where the model SST are held fixed at climatological values and the anomalous heat convergences are the heat flux required to maintain a realistic SST distribution (as there is no representation of ocean dynamics). The heat convergence field derived in the calibration phase is then applied to each of the subsequent model runs where SST are allowed to vary.
2.2. Sulfur Cycle
 HadSM3 has the capability to be coupled to a fully interactive sulfur cycle scheme which parameterizes the processes of sulfate aerosol formation from sulfur dioxide (SO2) and dimethyl sulfide (DMS) [see Woodage et al., 1999, 2003]. The interactive sulfur cycle gives a better representation of the climatic effects of sulfate aerosol than using a climatological sulfate distribution (which causes an overestimation in the indirect effect [see Jones et al., 2001]) or changing the surface albedo specification. The model has three sources of sulfur.
 1. Anthropogenic SO2 emissions (surface and high-level “chimney stack” emissions), which are taken from the Global Emissions Inventory Activity (http://www.geiacenter.org) 1B inventory and amounts to 67 Tg(S) a−1, representative of the emissions in the mid 1980s. Also available are 2050 anthropogenic SO2 emissions following the IPCC A2 SRES (surface and high-level chimney stack emissions), amounting to 105 Tg(S) a−1. Supplied by M. Collins (Met Office, Exeter, United Kingdom, personal communication, 2004).
 3. DMS emissions (emitted at the surface and highest over the ocean to represent phytoplankton emission), and amount to 40 Tg(S) a−1 from combining the DMS estimates study by Kettle et al.  and the parameterization of gaseous fluxes from Wanninkhof .
 Vertical and horizontal advection of SO2 are handled by the model's tracer advection scheme and mixing occurs at all levels (see Woodage et al.  for more details on the sulfur cycle scheme setup).
 In order to produce sulfate aerosol, both DMS and SO2 need to be oxidized. There are two methods of oxidizing SO2, through dry or aqueous phase oxidation whereas DMS undergoes dry oxidation only in the model. The dry oxidation is undertaken by reaction with the hydroxyl radical (OH) and aqueous oxidation by reaction with hydrogen peroxide (H2O2) with the values provided as monthly mean fields taken from STOCHEM simulations [see Collins et al., 1997]. There are three sulfate modes used in the model, these are Aitken mode particles (median radius, rAit = 0.024 μm), accumulation mode particles (median radius, racc = 0.095 μm) and dissolved sulfate (in cloud or precipitation drops). Removal of sulfur occurs through wet or dry deposition and is accounted for on all model levels. For a full discussion on the dry and wet deposition schemes refer to Jones et al.  and Woodage et al.  for more detail.
 The sulfate burden resulting from the emissions as described and the oxidation processes given in the previous paragraph are shown in Figure 1. The sulfate burden in Figure 1a is a result of present-day anthropogenic SO2 emissions as well as natural sulfur emissions (DMS and volcanic SO2) and shows high sulfate loadings in the Northern Hemisphere (NH). Figure 1b shows the sulfate burden for 2050 anthropogenic SO2 emissions with the same DMS and volcanic SO2 emissions as in Figure 1a. The highest sulfate burden in 2050 is still in the NH but has shifted toward the equator but there is also a stronger contribution in the Southern Hemisphere (SH) where emissions from Southern Africa and South America have increased. In both Figures 1a and 1b the sulfate in remote regions such as the Southern Ocean and Antarctica is derived from DMS (although DMS contributes to the burden, globally) and local maxima such as in the Mediterranean are from volcanic sources such as Mount Etna.
 The scheme used in this study is almost identical to the scheme used by Jones et al.  (except this study does not represent the second indirect effect) and has a comparable global distribution of sulfate burden with that study. Jones et al.  compare the model sulfate loading to other studies as well as the concentrations of sulfate from Europe and North America. The sulfur cycle scheme gives a good representation of sulfate concentrations in remote regions and slightly underpredicts in polluted regions, but generally gives a good estimate of sulfate loading [see Jones et al., 2001, Figure 2].
 All sulfate aerosol particles are assumed to be spherical and ammonium sulfate (and water) with refractive indices taken from Toon et al. . Sulfate scattering properties are calculated from Mie theory with the calculations performed off-line and stored as a look up table for the model. The table contains the scattering and absorption coefficients for both Aitken and accumulation mode aerosol as well as the variation in these properties associated with changes in relative humidity. The only particles able to influence the magnitude of the direct radiative effect are the Aitken and accumulation mode particles. Dissolved particles are stored in cloud droplets (in the model) and are not considered in the radiative transfer calculations for the direct radiative effect.
 The model also represents the first indirect radiative effect by using all of the available sulfate mass (Aitken, accumulation and dissolved) at each grid point to determine the Cloud Droplet Number Concentration (CDNC) from all available Cloud Condensation Nuclei (CCN). The CDNC is calculated from
where CDNC and CCN are given in m−3. The first indirect effect is then calculated from the cloud droplet effective radius, which is a function of CDNC, via the method described by Jones et al. . In these experiments the second indirect effect is not represented.
 The studies by Murphy et al.  and Stainforth et al.  attempted to determine the range of climate sensitivities (equilibrium temperature response to a doubling of atmospheric CO2) associated with uncertainties in model parameterizations. They identified that to gain understanding of the possible range of climate response to anthropogenic activity, a large ensemble of GCM simulations needed to be run, sampling the range of uncertainty arising from perturbing the model physics. However, the previous work by Murphy et al.  and Stainforth et al.  did not include a sulfur cycle scheme and so the model sensitivity to perturbing physics within such a scheme has not yet been tested.
3.1. Sulfur Cycle Physics and Initial Condition Perturbations
 There are many parameters used in the sulfur cycle that carry uncertainty in their definition. However, a consequence of the novel framework of this experiment using public computers was that any proposed changes to the model had to be tested thoroughly and in time for a single release to the general public. It was therefore possible only to perturb a subset of interesting parameters, each affecting different parts of the sulfur cycle. Because of concerns raised by Jones et al.  concerning the ozone oxidation scheme, no sulfur chemistry parameters were directly perturbed. Because of the implications for radiative transfer calculations, it was also decided not to perturb the size of the sulphate aerosol modes. Perturbations to four parameters were used in this experiment, which are given in Table 1. The function of each of the parameters is as follows.
Table 1. Sulfur Cycle Physics Perturbations Used in This Experimenta
Perturbations are from the original list suggested by D. Roberts (Met Office, Exeter, United Kingdom, personal communication, 2003).
The units for the parameters are CLOUDTAU, hours; NUM_STAR, m2 cm−3; and L0 and L1, s−1. VOLSCA is a scaling factor and has no units.
1.13 × 10−7
1.13 × 10−6
1.13 × 10−8
nonaqueous aerosol microphysics
6.5 × 10−5
1.95 × 10−4
2.17 × 10−5
2.96 × 10−5
8.87 × 10−5
9.85 × 10−6
1.0 (7.5 Tg(S) a−1)
2.0 (15 Tg(S) a−1)
3.0 (22.5 Tg(S) a−1)
 1. CLOUDTAU (CT) is the timescale for air to transit through a cloud. CT is used together with the timescale for SO2 to be oxidized in cloud (Tox = 15 min) to estimate the probability of a molecule being oxidized when passing through a cloud and is given by
The expected lifetime of an SO2 molecule is then a function of 1/p and the cloud cover fraction (f). The rate of aqueous oxidation (being the reciprocal of the SO2 lifetime) is thereby related to CT; as CT increases (decreases) the oxidation rate also increases (decreases). The initial value of CT is 3 h.
 2. NUM_STAR is the threshold aerosol concentration at and above which new particle formation is suppressed in favor of condensation onto accumulation mode aerosol particles. This parameter was chosen to influence the balance between new particles and condensation.
 3. L0 and L1 are the scavenging coefficients for the washout (below cloud scavenging) of SO2 by precipitation. The calculation of washout is given by Woodage et al.  as
where R is the rainfall rate (mm h−1), S is the SO2 concentration (ppbv) and S0 is the threshold concentration of SO2. The relationship is constrained by the equation L0 = L1S0−2/3 such that Λ is a continuous function. Therefore L0 and L1 must be increased or decreased by the same factor. Woodage et al.  use the studies by Levine and Schwartz  and Adamowicz  to determine average values of L0 and L1, respectively and perturbing them in this study allows us to explore range in L0 and L1 about the calculated average by Woodage et al. .
 4. VOLSCA is a scaling factor for continually emitting volcanic sources such as Mount Etna (nonexplosive eruptions). This parameter was chosen in order to examine the effect of uncertainty in the natural sulfur cycle. From IPCC  the emissions of SO2 from these volcanic sources varies in the range 6.0–20 Tg S a−1, which is due to very few measurements across all potential global sources.
 A more detailed description of the parameters is given by Woodage et al. [1999, 2003], who document the processes modeled in the sulfur cycle scheme.
 The first 3 parameters are perturbed to a maximum, minimum and best guess value (as suggested by D. Roberts, personal communication, 2003), which was intended to promote the largest plausible range of model responses. The volcanic emissions are scaled to cover the range of IPCC  estimates of volcanic SO2 emissions. The parameters given in Table 1 were also perturbed in combination as well as individually to sample as much of parameter space as possible. The total number of perturbations to the sulfur cycle scheme itself was 81 including the unperturbed model. There were other perturbations suggested in the original list but they were not tested in this experiment. The initial conditions of each model are also changed at the start of the calibration run to provide independent repeats of each perturbed physics member (predictability of the first kind [see Collins and Allen, 2002; Palmer, 2000]). A selection of three of the initial condition perturbations were used in calculating the average over initial conditions and gives a total of 243 model simulations.
3.2. Boundary Condition Perturbations
 Following the studies of Murphy et al.  and Stainforth et al. , this study subjects each of the 243 simulations given in section 3.1 to model boundary condition perturbations. In doing the boundary condition perturbations we intend to identify how these strong forcing perturbations (given below) influence the climate system and how they interact with the physics perturbations (prediction of the second kind [see Collins and Allen, 2002]).
 Initially the calibration (CAL) and control runs (CON) for all 243 simulations are set up with CO2 concentrations of 346 ppm globally with both natural and anthropogenic sulfur emissions switched on. The sulfur emissions were inventory 1B from the Global Emissions Inventory Activity (GEIA), which is representative of the mid 1980s and so the value of 346 ppm was chosen as that was the (approximate) CO2 concentration observed in 1985.
 The boundary conditions are perturbed from the end of the calibration phase (again for each of the 243 simulations) as follows.
 1. For the doubled CO2 experiment (2X), the global concentration of CO2 was doubled to 692 ppm to give a global warming experiment.
 2. For 2050 anthropogenic SO2 emissions (2050S), the model was set up to run with the emissions projected for 2050 following the IPCC A2 SRES.
 3. For doubled CO2 and 2050 anthropogenic SO2 emissions (BOTH), 1 and 2 above were perturbed simultaneously. This experiment combines the aerosol-greenhouse gas (GHG) effect to see if there are any nonlinear interactions in the climate response to a combined sulfate and CO2 perturbation.
 In the case of this study, the ensemble of 243 experiments are each integrated through five phases of spin up and boundary condition perturbations (each phase is run for 15 years for each member) to give a an overall grand ensemble. The reference to a phase (either CAL, CON, 2X, 2050S and BOTH) will refer to a specific boundary condition forcing for a given set of simulations (either all simulations or a subset of them), which will be defined in the text.
3.3. Data Retrieval
 Not all of the model integrations performed on the clients' computers were reliable. The model was deemed to be a failure and was removed from the analysis if the following criteria were met.
 1. Simulations contained flaws in the data associated with “overclocking” (overworking the processor) or a loss of information due to the computer being switched off at a critical data output point.
 2. Significant drift in surface air temperature occurred during the control run with the models drifting toward colder temperatures. If the trend is more than 0.02 K a−1 the model was deemed unstable [see Stainforth et al., 2005].
 The combination of these factors resulted in the loss of 25% [see Knight et al., 2007] of all data returned to the climateprediction.net database and for the sulfur cycle experiment a similar loss of approximately 25% of runs occurred, subject to the criteria in this section.
4. Statistical Analysis and Diagnostics
 Large quantities of data were used in this study and this section describes some of the statistical tools used.
4.1. Model Internal Variability
 A calculation of the model internal variability is required to identify whether the physics perturbations are influencing the model climate by changing the spread in the data points. To estimate the variability, the annual mean of a given diagnostic is averaged over the last 10 years of the control run for each initial condition ensemble member and then the deviation from that average is calculated as
where xij represents the annual mean value of a given diagnostic (x) for year i (i = 1,2,.,10; last 10 years of the control run) and initial condition j (j = 1,2,3; see section 3.2), j is the annual mean value of the diagnostic averaged over the last 10 years of the integration for each initial condition and varj is the variability in variable x. As there are three initial condition members and the variability in the last 10 years of the control run is taken into account, there are thirty data points over which to measure varj. To get a measure of the variability, the standard deviation of varj is taken as
where n is the number of data points and Svar is the standard deviation of the internal variability.
4.2. Analysis of Variance
 Having considered all of the possible perturbations to the model described in the previous sections, a method of analyzing such a large quantity of data quickly and efficiently is needed. The diagnostics used in this study to quantify the climate response to sulfur cycle perturbations are the sulfate burden and the Surface Air Temperature (SAT, 1.5m above the surface).
 The data is fitted with an analysis of variance (ANOVA) model to identify the effects of the perturbations on the GCM climate system. The ANOVA model is an extension of the linear regression model, where the factors of the right hand side of the equation are indicators for the left hand side (see von Storch and Zwiers  for further details and examples). Taking an example, the annual global mean surface air temperature (T) is influenced by changing the amount of sulfate in the atmosphere (S). When sulfates increase, the surface air temperature reduces compared to a base climate or control run. ANOVA is then conducted so that the response variable T is represented as a function of the average over all data points (μ), the effect of changing sulfate concentrations (Si) and the generated model internal variability (eij) as given in equation (8).
The factor Si is calculated from
where μi is the average effect of each scenario (“i” for low or high sulfate).
 Perturbing the parameters in combination with each other may lead to interaction between parameters such that the value of the response variable cannot be explained by the linear sum of the effects of the two individual perturbations, which equation (8) can be extended to account for [see von Storch and Zwiers, 1999; Ferro, 2004].
 The following hypotheses are used (with the ANOVA) for conducting the Student t-test (and acquiring a value of statistical significance; the level of significance required is ≤0.05).
 1. For H0, physics and/or forcing perturbations have no effect on the climate system and all diagnostics will show a normally distributed population across all perturbations (indistinguishable from the unperturbed model).
 2. For H1, assuming the separate population variances are equal, the physics and/or forcing perturbations will give different mean effects on the climate diagnostics retrieved (distinguishable from the unperturbed model).
5. Sulfate Burden Results
5.1. Distribution of All Ensemble Members
 The first step in identifying the effect of the physics perturbations is to look at the spread of global mean sulfate burden across all 81 ensemble members for each boundary condition forcing, averaged over initial conditions. To show the spread in the data, box-and-whisker plots of global, annual mean sulfate burden for each of the phases listed above are shown in Figures 2a–2d. The median and interquartile range (IQR) are also given beneath each box-and-whisker plot in Figure 2 to give an indication of the central point and the spread.
 One important point in Figure 2 is the increase in sulfate burden for each of the subsequent forcing experiments after the control phase (compare median estimates in Figure 2). The stronger SO2 emissions in 2050S than in CON causes the higher burden observed in 2050S relative to CON but in 2X there is no increase in SO2 emissions relative to present day (or in BOTH relative to 2050S). To understand the processes causing the increased burden, another study (D. Ackerley et al., Changes in the global sulfate burden due to perturbations in global CO2 concentrations, submitted to Journal of Climate, 2008) looked into the seasonal and geographical distribution of cloud and precipitation changes associated with doubling CO2 concentrations. The results suggested that precipitation and cloud cover reduction over much of the NH continents in boreal summer combined with high oxidant concentrations and strong sulfur emissions caused an increase in sulfate residence time (as wet deposition is more efficient at removing sulfate than dry deposition [see Seinfeld and Pandis, 1998]).
 In all the phases shown in Figures 2a–2d, the area of the box appears to be roughly equal either side of the median, suggesting that the data is uniformly distributed. The relative sizes of the boxes and the whiskers also show features about the distribution of the data set. In CON (Figure 2a) the whiskers are comparable in length to the whole box indicating that the distribution has short tails with no outliers. The data for the other forcing experiments in Figures 2b–2d also show similar properties to CON.
 A measure of the model internal variability needs to be made to identify whether the physics perturbations are influencing the spread in sulfate burden seen in Figure 2. The unperturbed models do not have any sulfur cycle physics perturbations but do contain initial condition perturbations which act to provide independent repeats of the same model physics (see section 3.2). Taking the sulfate burden in the control phase for the unperturbed model and using equations (6) and (7) gives a model internal variability of 0.053 m−2, whereas the standard deviation of the global mean sulfate burden (averaged over the last 10 years of the control phase for each ensemble member) due to all physics perturbations is 0.58 m−2, a factor of ten higher than the internal variability. Therefore the sulfur cycle physics perturbations are changing the concentration of sulfate in the model considerably more than model internal variability. The next sections will identify which perturbations influence the sulfate burden and quantify the magnitude of those effects.
5.2. Identifying the Effects of all Perturbations on the Sulfate Burden
 We need to compare the large number of perturbations (243 ensemble members) from this experiment to establish their effects on changing the global, annual mean sulfate burden between different model integrations. To estimate this variability, an analysis of variance model is used and adapted from section 4 and is applied to all forcing perturbations (CON, 2X, 2050S and BOTH). The last 10 years of global annual mean sulfate burden for each of the three initial condition members are used and gives a total of thirty data points, which can be used in the ANOVA model in equation (10) (described in section 4.2, equation (8)).
 In equation (10), Yijklmno is the global annual mean sulfate burden for a CO2 forcing (Ci) or anthropogenic sulfur forcing (Sj) and physics perturbations to CLOUDTAU (CTk), NUM_STAR (NSTl), Scavenging Parameters (SCVm) as well as increasing volcanic emissions (VOLn). The forcing perturbations have two levels either 1xCO2 to 2xCO2 for C, or present-day sulfur to 2050 sulfur for S (i and j = 2). Each of the physics perturbations have three levels which are maximum, minimum and best guess values (k, l and m = 3). Volcanic emission perturbations also have three levels, which are 1X, 2X and 3X base emissions (n = 3, see Table 1 and section 3.1).
 In the model derived from equation (10), M is the overall effect averaged over the last 10 years for each run, forcings and physics perturbations. Ci (Sj) is the main effect, relative to M, of the double CO2 (2050S) forcing with CTk, NSTl, SCVm and VOLn the main effects of each physics perturbation, also relative to M. The interaction (nonlinear) effects between each of the factors described above are shown in brackets in equation (10) with a colon between the symbols and again, all forcings and physics perturbation combinations are considered in this too. The final term (Zijklmno) in equation (10) is the error term due to model internal variability.
Table 2 shows a summary of the results from the ANOVA for all of the individual parameter and boundary condition perturbations (Ci, Sj, CTk, NSTl, SCVm and VOLn) to show their impact on the sulfate burden. Also included is one interaction term (S:SCV), which describes (slightly) more of the variation in the data set than the residuals (model internal variability). The other plausible interaction terms do not.
Table 2. ANOVA Table for Identifying the Perturbations Having the Largest Effects on the Global Annual Mean Sulfate Burdena
Details on the perturbations can be found in the text. The residuals are the remaining effects due to model internal variability. SS is the sums of squares, percent is the percentage of the variation described, DF is the degrees of freedom, and p is used as a measure of statistical significance (if ≤0.05, the value is considered statistically significant).
 The response to changing anthropogenic SO2 emissions describes 53.3% of the variation in the data and is strongly statistically significant (p < 0.05). The second and third largest proportions of the explained variation comes from SCV and VOL, which are also highly statistically significant, see Table 2. The effect of doubling CO2 accounts for 5% of the variation in the sulfate burden and also shows strong statistical significance (the mechanism for this effect discussed in more detail in the work by Ackerley et al. (submitted manuscript, 2008)). It appears that some 98.0% of the variation in the sulfate burden from the ANOVA analysis comes from perturbing anthropogenic or volcanic SO2 emissions (boundary condition), the scavenging parameters (physics) or doubling CO2 (boundary condition).
 The other main effects CTk (CLOUDTAU) and NSTl (NUM_STAR) however, despite having little influence on the annual global mean sulfate (see % column in Table 2) are both considered to have a statistically significant effect (p < 0.05), which is due to >29000 data points being used in the analysis (see Moore and McCabe  for a derivation of the ANOVA hypothesis test). However, CLOUDTAU and NUM_STAR influence the sulfate burden less than the residuals (despite the variation being statistically significant).
 The only interaction term accounting for slightly more variation in the sulfate burden than natural variability (higher SS in Table 2) is the interaction between the scavenging parameters and 2050 anthropogenic SO2 emissions. In Figure 3a the dashed line (CON) and the solid line (2050S) diverge from each other, which suggests that the transition from present day to 2050 anthropogenic SO2 emissions causes a proportionally larger response when perturbed with the scavenging parameter. For comparison, the effect of increasing anthropogenic SO2 emissions with volcanic SO2 emissions is shown in Figure 3b and the lines are parallel to each other which indicates there is no (or very little) interaction between volcanic and anthropogenic SO2 emissions for the sulfate burden.
 The rest of the terms in equation (10) that are not discussed here account for less than 0.6% of the variation in the sulfate burden individually and when effects are added together they account for only 0.8% of the variation and so were not given in Table 2.
 Taking this analysis further, Table 3 shows the results from running the ANOVA model on CON for the physics perturbations only (removes the large effect of perturbing the boundary conditions). The scavenging parameters and volcanic emissions scaling together account for more than 97% of the variation in the sulfate burden. However, very little of the variation is described by CLOUDTAU and NUM_STAR (see Table 3) suggesting that these perturbations have almost no effect on the range in sulfate burden and will not be considered in the rest of this analysis. The two interaction terms in Table 3 (the other interaction terms are not shown as they are at least an order of magnitude smaller than the residual) describe more of the variability in CON alone than across all perturbations (including boundary condition forcings as with the analysis in Table 2) but they describe less variation than the residual term and so can be considered unimportant.
Table 3. ANOVA Table for Identifying the Perturbations Having the Largest Effects on the Global Annual Mean Sulfate Burden in CONa
 The ANOVA test has shown that the physics perturbations all have a statistically significant effect on the sulfate burden. The strongest contributor to the variation in the sulfate burden is increasing anthropogenic SO2 emissions which causes the largest increase in sulfate burden (particularly when combined with doubled CO2 concentrations). This section will focus on the effects of the individual physics perturbations on the annual global mean sulfate burden in the CON and 2050S phases to quantify how much they influence the spread in sulfate burden.
 Box-and-whisker plots of the annual mean sulfate burden averaged over the last 10 years of each perturbed physics and initial conditions integration are shown in Figure 4, with the sulfate burden in the default model plotted in Figure 4a. Box-and-whisker plots representing the sulfate burden from CON are unshaded and those for 2050S are shaded. Figure 4 shows only perturbations having a large effect individually on the sulfate burden for CON and 2050S.
5.2.2. Control Phase
 Perturbing the scavenging parameter to a maximum (minimum) acts to strongly reduce (increase) the global annual mean sulfate burden relative to the default model (compare Figures 4b and 4c to Figure 4a). The median change relative to the default model for CON is a decrease (increase) in global annual mean sulfate burden by 0.52 (0.45) m−2, which is a change of approximately 13% (see Table 4).
Table 4. Global Annual Mean Sulfate Burden in Each of the Runs Containing Perturbations to the Scavenging Parameters and/or the Volcanic Emissions to Show Which Parameters Have the Largest Influence on the Sulfate Burden Across the Ensemblea
L0 and L1 Value
CON Sulfate Burden m−2)
2050S Sulfate Burden m−2)
The conventions in the first and second columns are that M implies maximum value, m implies minimum value, and D implies default (unperturbed) value. The 2X and 3X in the VOLSCA column signify 2 and 3 times volcanic emissions.
 The perturbations applied to the volcanic emissions act only to increase the sulfate burden relative to the default model (see Figures 4d and 4e and Table 4) since volcanic emissions were either doubled or trebled. Doubling volcanic emissions caused the global annual mean sulfate burden to increase by 0.41 m−2, which is similar to the increase caused by reduced scavenging. The comparable influence of minimum scavenging and doubled volcanic emissions in CON can be seen by comparing the unshaded boxes in Figures 4c and 4d.
 Trebling volcanic emissions increases the median global annual mean sulfate burden by 0.83 m−2 and suggests that volcanic emissions contribute approximately 0.4 m−2 to the global annual mean sulfate burden in HadSM3.
5.2.3. 2050 SO2 Emissions Phase
 Again (as in CON) the parameters having the largest influence on the spread in global mean sulfate burden are the scavenging parameters and volcanic emissions but there are some differences from those identified with CON. As with CON, setting scavenging to a maximum caused the sulfate burden to decrease by 0.72 m−2 (14%) relative to the default model (shaded box-and-whisker plot, Figure 4b). However, when comparing the shaded box-and-whisker plots in Figures 4c and 4e, setting scavenging to a minimum causes the sulfate burden to increase by 0.7 m−2 (approximately 14%) relative to the default model, which is comparable with the effect of trebling volcanic emissions (see Table 4).
 In the future sulfate emissions scenario (2050S), doubling volcanic emissions has a smaller effect on the sulfate burden than setting the scavenging parameters to a minimum (unlike in CON). This change in the efficiency of the scavenging perturbation between CON and 2050S is a result of the interaction effect noted from Figure 3a, whereas the effect of perturbing volcanic emissions remains approximately the same (0.4 and 0.8 m−2 increases for doubled and trebled volcanic emissions, respectively) despite changing anthropogenic emissions (see Figure 3b).
 The efficiency of the scavenging parameter is the only physics perturbation (in this experiment) influenced by the amount of sulfate contained in the atmosphere (and therefore emissions), which would be an important consideration in transient climate change experiments where sulfur emissions are changing over time unlike in these experiments where the forcing is changed almost instantaneously (the sulfur cycle requires approximately three months to spin up).
5.3. Range in Sulfate Burden
Section 5 has so far identified the important single perturbations in governing the magnitude and range of the global mean sulfate burden as well as the important interaction effects between perturbations. In this section an estimate of the total range in sulfate burden associated with the physics perturbations is discussed.
 Since the scavenging parameters and volcanic emissions scaling had the largest influence on the range in sulfate burden for CON and 2050S, the global mean sulfate loading for perturbing these parameters individually and in combination can be seen in Table 4. Increased scavenging causes the largest decrease in sulfate burden and the combination of reduced scavenging and trebling volcanic emissions caused the largest increase in the sulfate burden, with the rest of the perturbations falling between these two extremes.
 From the values given in Table 4 (and accounting for model internal variability), the range in sulfate burden associated with the uncertainty in these perturbations in CON is 3.08–5.11 m−2 (0.52–0.87 Tg S). The unperturbed model has a global annual mean sulfate burden of 3.65 m−2, which is lower than the ensemble mean in CON and is due to the volcanic emissions scaling being set to one in the unperturbed model.
 The range in sulfate burden associated with increased anthropogenic SO2 emissions up to 2050S (including model internal variability) is 4.32–6.89 m−2 (0.73–1.17 Tg S) with the increase in spread associated with the nonlinear interaction between increased SO2 emissions and the scavenging parameters. The range in sulfate burden given in this paper (0.44 Tg S) for 2050 SO2 emissions following the IPCC A2 SRES is comparable with the range across six SRESs (A1B, A1F1, A1T, A2, B1 and B2) given by Pham et al.  who estimate a range of 0.5 Tg S by 2050. The upper and lower bounds given by Pham et al.  are 0.33–0.83 Tg S, which is smaller than the lower limit in this study as they only consider anthropogenic sulfate whereas this study uses the total sulfate burden as we include a perturbation to natural volcanic emissions. However, the range in sulfate burden due to perturbing the parameters given in Table 1 is comparable with the range across SRESs and suggests that the uncertainty on future sulfate concentrations is even larger than suggested in this study or by Pham et al. .
6. Surface Air Temperature Results
6.1. Distribution of All Ensemble Members
 Having investigated the response of atmospheric sulfate to each of the physics perturbations another variable of climate response, in this case surface air temperature at 1.5m (SAT) is considered. As sulfate aerosol induces a cooling (see section 1), the SAT may be influenced by the large spread in sulfate burden given in section 5.3. Box-and-whisker plots of the global annual mean surface air temperature averaged over initial conditions for all physics perturbations are shown in Figure 5.
 From Figure 5a, median SAT for CON is 13.66°C with an IQR of 0.21°C. The median values (IQR) for 2X, 2050S and BOTH are 16.94°C (0.30°C), 13.41°C (0.23°C) and 16.69°C (0.28°C), respectively (from Figures 5b–5d). The spread in SAT for each phase is relatively small (in comparison to the large spread in the burden) and suggests that the physics perturbations are having little effect on the variability of SAT.
 Using equations (6) and (7) the standard deviation in the model SAT internal variability is 0.052°C and the standard deviation in the global annual mean SAT is 0.063°C, which implies that the sulfur physics perturbations may enhance the model SAT variability slightly but the majority of the variability in the ensemble SAT comes from model internal variability.
 Comparing the range of temperature responses in this study and those of Stainforth et al. [2005, Figure 2a] shows that the range in temperature response associated with perturbing sulfur cycle physics is smaller than observed by Stainforth et al. . The histograms of SAT response in this study for all ensemble members is given in Figure 6. The range in the SAT response in 2X (Figure 6) is much smaller than that by Stainforth et al.  and does not show the same tendency for high values. The median SAT response, relative to CON, is slightly lower in 2X compared to the work by Stainforth et al.  but the difference is very small (3.3°C and 3.4°C, respectively). Also included in Figure 6 is the frequency distribution of all ensemble members for 2050S (Figure 6b) and BOTH (Figure 6c), neither of which show a large spread (as already identified above). However, BOTH is centered on a lower SAT than 2X (compare Figures 6c and 6a) because of the presence of increased anthropogenic sulfate relative to CON and 2X.
6.2. ANOVA on SAT
Figure 7a shows the plumes of SAT evolution for every year of each forcing phase for all ensemble members and Figure 7b shows a similar plot to 7a with SAT averaged over initial conditions. Unlike the sulfate burden, the SAT response to each forcing does not reach equilibrium within the first 1–2 years of the integration and so taking an average over the last 10 years of the data set would include the trend in SAT response as well as the response itself. The exceptions to this are the control phase and 2050S where the model is in equilibrium over most of the run (except for the first 3–4 years of 2050S).
 To incorporate all the forcing and physics perturbations and keeping the sample sizes equal, the last 3 years of each phase are considered for each initial condition member so that there are nine values available for each physics perturbation to go into the ANOVA model. The last 3 years are used as there is very little temperature trend in the doubled CO2 phases (2X and BOTH) after the first 12 years of the integration and absolutely no SAT trend in CON and 2050S. The assumption is that for all forcing phases, the trend in SAT for each of the phases is negligible compared to the overall temperature response induced by the forcing. The ANOVA model used is given in equation (10), which is the same as the one used for the sulfate burden, except SAT is now used.
 The two “scenario” factors considered here are with and without doubling CO2 (Ci) and with and without 2050 anthropogenic SO2 emissions (Sj), which both have two levels. The other factors are the main effects of the physics perturbations individually, which have the same symbols as those described in equation (10). The only interaction effect considered here is the interaction between doubling CO2 and 2050 anthropogenic SO2 emissions (as in BOTH) to see if there are any nonlinear effects of doing both perturbations together on SAT.
 The results of the analysis of variance model are shown in Table 5. The forcing perturbations 2X (C) and 2050S (S) describe 99.41% of the variability in the SAT and when combined with the model internal variability (residual) describes 99.97% of the variability whereas the total combined effect of each of the individual physics perturbations on SAT is very small. The effect of doubling CO2 is by far the dominant effect on SAT which again suggests that the effect of increasing CO2 above present-day levels is much stronger than the effect of increased sulfate concentrations. Table 5 contains the perturbations describing the largest amount of SAT variation as well as the results for each of the individual physics perturbations and the C:S interaction term (p = 0.36 suggesting no nonlinear SAT interaction between CO2 and anthropogenic sulfate forcings and that the combined response is additive).
Table 5. ANOVA Table for Identifying the Perturbations Having the Largest Effects on the Global Annual Mean Surface Air Temperaturea
The perturbations are explained in the text. The interaction term C:S indicates whether the CO2 and SO2 effects interact with each other (possible nonlinear interaction). The residuals are the remaining effects due to model internal variability. The column headers are identical to those in Table 2.
 Despite the physics perturbations having a very small impact on SAT variation, the effects are all strongly statistically significant. However, the relatively insensitive response suggests that when HadSM3 is perturbed from the present-day scenario, the sulfur physics perturbations used here have little impact on SAT (or climate sensitivity). The cause of the small response is due to the nonlinear relationship in equation (1) where the high initial sulfate concentrations in CON do not allow a large increase in CDNC when SO2 emissions are increased in 2050S, which induces a weak change in the first indirect radiative effect and therefore a small temperature response.
7. Conclusions and Discussion
 This study has identified aspects of the sulfur cycle scheme in HadSM3 that cause uncertainty in the climate response to sulfate and/or GHG forcing, which are important considerations when making future projections of climate change influenced by anthropogenic activity. Parameter perturbation experiments such as this one have been performed in other studies [Murphy et al., 2004; Stainforth et al., 2005] but such a study had not been performed on the representation of the atmospheric sulfur cycle until now. Another important consideration is that this experiment was run with one model (HadSM3) and one scenario (IPCC, A2 SRES) and provides scope for undertaking a multimodel and multiscenario ensemble to quantify the full range of uncertainty within sulfate aerosol modeling in GCMs.
 From this study, the most important parameters in governing the sulfate burden range were the effects of below cloud scavenging of SO2 by precipitation and the magnitude of volcanic SO2 emissions. Neither the parameterization for the amount of time air remains within a cloud or the threshold concentration of accumulation mode aerosol to suppress new particle formation had a large effect on the sulfate burden. This suggests the sulfur cycle scheme in HadSM3 is sensitive to parameters that affect emissions and deposition being perturbed and not sensitive to perturbations of parameters affecting the chemical processes leading to sulfate formation. However, since this study only tests a small subset of the parameters used in the chemical processes leading to sulfate formation, we cannot comment as to whether perturbing other parameters will have a larger effect.
 Perturbing the volcanic emissions caused the sulfate burden to increase by 0.4 and 0.8 m−2 when doubled and trebled, respectively and suggests that sulfur from volcanoes contributes 0.4 m−2 to the global mean sulfate burden in the unperturbed model. The increases in sulfate burden from changing volcanic SO2 emissions were also unaffected by changing the anthropogenic emissions. However, the scavenging parameters influence on the sulfate burden did depend on the magnitude of the anthropogenic SO2 emissions and caused the sulfate burden to increase or decrease by 13% (14%), relative to the unperturbed model, in CON (2050S). This dependency may be important in transient climate change simulations where the sulfur emissions vary in time throughout the run.
 The range in sulfate burden in the present-day (control) run was 3.08–5.11 m−2 (0.52–0.87 Tg S), which suggests that even with anthropogenic emissions held fixed there could be a large range in the sulfate burden because of the parameterized processes. When the anthropogenic SO2 emissions were increased to those expected for 2050 following the IPCC A2 SRES the sulfate burden ranged from 4.32 to 6.89 m−2 (0.73–1.17 Tg S). The difference between the low– and high–sulfate burden case in the control phase was smaller (0.35 Tg S) than in 2050S (0.44 Tg S), which is associated with the dependency of the scavenging parameters on the total sulfate load. Importantly, the results here suggest that the range in sulfate burden due to model uncertainty is comparable with scenario uncertainty as discussed by Pham et al.  and may be enhanced further when including changes in CO2 concentrations (see Ackerley et al., submitted manuscript, 2008).
 Despite the large spread in sulfate burden, there was very little spread in the surface air (1.5m) temperature response. The cause of the observed small response is due to the combination of high sulfate aerosol concentrations in the control phase and the nonlinear representation of the CDNC-CCN relation given in equation (1). An increase in sulfate burden and hence CCN concentrations in the 2050S phase does not lead to a large increase in CDNC concentrations compared to the control phase where CCN concentrations are also high. The small indirect radiative effect therefore was unable to cause a large surface air temperature response. To induce a larger temperature response and range it would be worth perturbing the climate model from preindustrial conditions where the initial levels of sulfate (CCN) are low enough to allow a large indirect radiative effect to develop, which may then be sensitive to the parameter perturbations.
 This work was funded by the Natural Environmental Research Council e-science grant NER/S/G/2003/1193 and was enabled through working with the climateprediction.net team with particular thanks to Tolu Aina, Carl Christensen, Nick Faull, Steven Pascoe, Jamie Kettleborough, David Stainforth, and the principal investigator Myles Allen. Special thanks also go to Ben Booth and Mat Collins for discussions on the sulfur cycle scheme within the Met Office and for providing the sulfur emissions data for 2050 (IPCC A2 SRES). Special thanks also go to David Stephenson and Chris Ferro for their statistical advice and insight into using R for producing the ANOVA model. We are also very grateful for the supercomputing resources supplied by the Rutherford Appleton Laboratory (RAL) and the support from Alan Iwi, also at RAL. Finally, we would like to thank all the participants who dedicated computer time to running the climateprediction.net sulfur cycle experiment.